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[ "\nInterference phenomena are a well-known and crucial aspect of\n quantum mechanics,\n famously exemplified by the two-slit experiment. There are many\nsituations, however, in which interference effects are artificially or\nspontaneously suppressed. The theory of decoherence is\nprecisely the study of such situations. It is is relevant (or is\nclaimed to be relevant) to a variety of questions ranging from the\nmeasurement problem to the arrow of time, and in particular to the\nquestion of whether and how the ‘classical world’ may\nemerge from quantum mechanics. (See also the entry on\n philosophical issues in quantum theory.)", "\nIn\n Section 1\n we discuss the concept of suppression of interference and give a\nsimplified survey of the theory, emphasising features that will be\nrelevant later. In fact, the term decoherence refers to two largely\noverlapping areas of research. The characteristic feature of the first\n(often called ‘environmental’ or ‘dynamical’\ndecoherence) is the study of concrete models of (spontaneous)\ninteractions between a system and its environment that lead to\nsuppression of interference effects. The second (the theory of\n‘decoherent histories’ or ‘consistent\nhistories’) is an abstract and more general formalism capturing\nessential features of decoherence. The two are obviously closely\nrelated, and will be reviewed in turn.\n Section 2\n then criticises the claim that decoherence solves the measurement\nproblem of quantum mechanics, and discusses the exacerbation of the\nproblem through the inclusion of environmental interactions. It is\nthus important to consider not decoherence by itself, but the\ninterplay between decoherence and the various approaches to the\nfoundations of quantum mechanics that provide possible solutions to\nthe measurement problem and related puzzles.\n Section 3\n deals with the role of decoherence in relation to a number of such\napproaches, including mainstream foundational approaches such as\nEverett, Bohm and GRW, traditional approaches such as those by von\nNeumann, Heisenberg and Bohr, and a few more. Finally, in\n Section 4\n we describe the overall picture of the emergent structures that\nresult from this use of decoherence, as well as a few more speculative\n applications.[1]", "\nSuppression of interference has featured in many papers since the\nbeginning of quantum mechanics, such as Mott’s (1929) analysis\nof \\(\\alpha\\)-particle tracks. The modern foundation of decoherence as a\nsubject in its own right was laid by H.-D. Zeh in the early 1970s (Zeh\n1970, 1973). Equally influential were the papers by W. Zurek from the\nearly 1980s (Zurek 1981, 1982). Some of these earlier examples of\ndecoherence (e.g., suppression of interference between left-handed and\nright-handed states of a molecule) are mathematically more accessible\nthan more recent ones. A concise and readable introduction to the\ntheory is provided by Zurek in Physics Today (1991). This\narticle was followed by publication of several letters with\nZurek’s replies (1993), which highlight controversial issues.\nMore recent surveys are given in Zeh (2003a), Zurek (2003), and in the\nbooks by Giulini et al. (1996, second edition Joos et\nal. 2003), and by Schlosshauer (2007)." ]

[ { "content_title": "1. Theory of Decoherence", "sub_toc": [ "1.1 Environmental decoherence", "1.2 Decoherent histories", "1.3 Comparison" ] }, { "content_title": "2. Decoherence and the Measurement Problem", "sub_toc": [ "2.1 Solving the measurement problem?", "2.2 Widening the measurement problem" ] }, { "content_title": "3. The Role(s) of Decoherence in Different Approaches to Quantum Mechanics", "sub_toc": [ "3.1 Everett theories", "3.2 Pilot-wave theories", "3.3 Spontaneous collapse theories", "3.4 Orthodox approaches", "3.5 Other approaches" ] }, { "content_title": "4. Scope of Decoherence", "sub_toc": [ "4.1 The world according to decoherence", "4.2 Further applications" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThe two-slit experiment is a paradigm example of an\ninterference experiment. One repeatedly sends electrons or\nother particles through a screen with two narrow slits, the electrons\nimpinge upon a second screen, and we ask for the probability\ndistribution of detections over the surface of the screen. One might\nnaively try to calculate them by summing over the probabilities of\ndetection at the slits multiplied by the probabilities for detection\nat the screen conditional on detection at the slits. But these are the\ncorrect probabilities for a different experiment, with\ndetections at the slits, whether or not we believe that measurements\nare related to a ‘true’ collapse of the wave function\n(i.e. that only one of the components survives the\nmeasurement and proceeds to hit the\n screen[2]).\n If there are no such detections, in general there is an additional\nso-called interference term in the correct expression for the\nprobability, and this term depends on both the wave\ncomponents that pass through the\n slits.[3]\n ", "\nThere are, however, situations in which this interference term does\nnot appear or is negligible, and the naive formula applies. This is\nthe case if some other systems interact with the electron between the\nslits and the screen, leading to enough\n entanglement\n with the components of the wave going through the two slits. Then,\nthe probabilities of detection at the screen are as if we had\nperformed a detection at the slits.", "\nIt is not difficult to see why this must be so. If Alice and Bob share\na pair of systems that are entangled, then the probabilities for the\nresults of any measurements Bob might make do not depend on\nwhether or not Alice also makes any measurements (this is the quantum\nmechanical no-signalling theorem). In exactly the same way, the\npattern of detections at the screen cannot distinguish mere\nentanglement with some other systems from the actual use of those\nsystems for detection at the slits.", "\nSo, for example, there could be sufficiently many stray particles that\nscatter off the\n electron.[4]\n The phase relation between the two components of the wave function,\nwhich is responsible for interference, is now well-defined only at the\nlevel of the larger system composed of electron and stray particles,\nand can produce interference only in a suitable experiment including\nthe larger system. Such a phenomenon of suppression of interference is\nwhat is called decoherence." ], "section_title": "1. Theory of Decoherence", "subsections": [ { "content": [ "\n‘Environmental’ decoherence is decoherence that arises\nthrough suitable interaction of a system with its environment. The\nstudy of environmental decoherence consists to a large extent in the\nconstruction and investigation of concrete models of such\ninteractions. We have already mentioned taking an environment of\nrelatively light particles that scatter off a relatively heavy\nparticle. Such a model can be used to study e.g. chiral molecules. Or\none can take an atom in interaction with the electromagnetic field, or\na harmonic oscillator in a thermal bath of oscillators, and many more.\nVarious features of interest typically arise in such models: some are\nin common to most models, others are highly model-dependent.", "\nOne feature of these environmental interactions is that they suppress\ninterference between states from some preferred set\n(‘eigenstates of the decohering variable’). This can be a\ndiscrete set of states, e.g. the upper and lower component of the wave\nfunction in our simple example of the two-slit experiment, or left-\nand right-handed states in models of chiral molecules; when an atom\ninteracts with the electromagnetic field, the preferred states will be\nthe stationary states (which are the states we observe in\nspectroscopy). Or it could be some continuous set, e.g. the\n‘coherent states’ of a harmonic oscillator (in which case\nthe terminology of ‘eigenstates’ or\n‘eigenbasis’ of a preferred observable is not quite\naccurate). The intuitive picture is one in which the environment\nmonitors the system of interest by spontanesouly and continuously\n‘measuring’ some quantity characterised by the set of\npreferred states (i.e. the environment interacts with the system in\nsuch a way that it could in principle be used as a measuring\napparatus).", "\nSuch a ‘measurement-like’ interaction intuitively does not\ndisturb the eigenstates of the monitored observable. Thus these\npreferred states can in fact be characterised in terms of their\nrobustness or stability with respect to the interaction with the\nenvironment. The system gets entangled with the environment, but the\nstates between which interference is suppressed are the ones that\nwould themselves get least entangled with the environment\nunder this interaction. In this connection, one also says that\ndecoherence induces ‘effective superselection rules’,\nmeaning the following. A strict superselection rule applies when there\nare some observables – in technical terminology they are called\nclassical – that commute with all observables (for a review, see\nWightman 1995). Intuitively, these observables are infinitely robust,\nsince no possible interaction can disturb them (at least as long as\nthe interaction Hamiltonian is considered to be an observable). By an\neffective superselection rule one means, analogously, that\ncertain observables (e.g. chirality) will not be disturbed by the\ninteractions that actually take place.", "\nIn many models of decoherence, the preferred states are robust in an\neven stronger sense, because information about them is stored in a\nredundant way in the environment (say, because a Schrödinger cat\nhas interacted with so many stray particles: photons, air molecules,\ndust). This information can later be acquired by an observer without\nfurther disturbing the system (we observe – however that may be\ninterpreted – whether the cat is alive or dead by intercepting\non our retina a small fraction of the light that has interacted with\nthe cat). ", "\nWhat states are preferred will depend on the details of the\ninteraction, but in many cases, interactions are characterised by\npotentials that are functions of position, so preferred states are\noften related to position. For the chiral molecule, the left- and\nright-handed states are indeed characterised by different spatial\nconfigurations of the atoms in the molecule. For the harmonic\noscillator, one should think of the environment\n‘measuring’ approximate eigenstates of position, or rather\napproximate joint eigenstates of position and momentum, so-called\ncoherent states (since information about the time of flight is also\nrecorded in the environment). ", "\nThe resulting localisation can be on a very short length scale, i.e.\nthe characteristic length above which coherence is dispersed\n(‘coherence length’) can be very short. A speck of dust of\nradius \\(a = 10^{-5}\\)cm floating in the air will have\ninterference suppressed between spatially localised components with a\nwidth of \\(10^{-13}\\)cm. Even more strikingly, the time scales for\nthis process are often minute. This coherence length is reached after\na microsecond of exposure to air, and suppression of interference on a\nlength scale of \\(10^{-12}\\)cm is achieved already after a\n nanosecond.[5]\n ", "\nWithin the environmental decoherence literature, models tend to be\nformulated in terms of master equations for the evolution of the\ndensity operator describing the system. As a consequence of\ndecoherence this very quickly becomes (at least approximately)\ndiagonal in the basis of preferred states (whether discrete or\ncontinuous). Thus, the master equation for the density operator for\nthe system is essentially equivalent to an evolution equation for the\nprobability distribution over the preferred states. In models\nwhere coherent states are preferred, one can then compare this to the\nLiouville evolution of probability distributions over classical phase\nspace, and in fact one obtains extremely good quantitative agreement.\n", "\nThese features are not claimed to obtain in all cases of interaction\nwith some environment. It is a matter of detailed physical\ninvestigation to assess which systems exhibit which features, and how\ngeneral the lessons are that we might learn from studying specific\nmodels. One should thus beware of common overgeneralisations. For\ninstance, decoherence does not affect only and all\n‘macroscopic systems’. It is true that middle-sized\nobjects, say, on the Earth’s surface will be very effectively\ndecohered by the air in the atmosphere, and this is an excellent\nexample of decoherence at work. On the other hand, there are also very\ngood examples of decoherence-like interactions affecting microscopic\nsystems, such as in the interaction of \\(\\alpha\\)-particles with the gas\nin a bubble chamber. (Note, however, that this also relies on the\n\\(\\alpha\\)-particles being emitted in states that are superpositions of\nstrongly outward directed wavepackets.) Further, there are arguably\nmacroscopic systems for which interference effects are not suppressed.\nFor instance, it has been shown to be possible to sufficiently shield\nSQUIDS (a type of superconducting devices) from decoherence for the\npurpose of observing superpositions of different macroscopic currents\n– contrary to what one had expected (see e.g. Leggett 1984, and\nesp. 2002, Section 5.4). Anglin, Paz and Zurek (1997) examine some\nless well-behaved models of environmental decoherence and provide a\nuseful corrective as to its scope." ], "subsection_title": "1.1 Environmental decoherence" }, { "content": [ "\nAs mentioned above, when interference is suppressed in a two-slit\nexperiment, the naive probability formula applies, and we can\ncalculate the detection probabilities at the screen by adding\nprobabilities for what are formally the ‘trajectories’\nfollowed by individual electrons. The decoherent histories or\nconsistent histories formalism (originating with Griffiths 1984;\nOmnès 1988, 1989; and Gell-Mann and Hartle 1990) takes this as\nthe defining feature of decoherence. (See also the entry on the\n consistent histories approach to quantum mechanics.\n There are some differences between the various authors, but we shall\ngloss them\n over.[6])", "\nIn a nutshell, the formalism is as follows. Take a sequence of times\n\\(t_1 ,\\ldots ,t_n\\), and take\northogonal families of (Heisenberg-picture) projections at those\n times,[7]\n with", "\nOne defines histories as time-ordered sequences of projections\nat the given times, choosing one projection from each family,\nrespectively. Such histories form a so-called alternative and\nexhaustive set of histories.", "\nTake a state \\(\\varrho\\). We wish to define probabilities for the set of\nhistories. If one takes the usual probability formula based on\nrepeated application of the Born rule, one obtains", "\nWe shall take (2) as defining ‘candidate probabilities’.\nIn general these probabilities exhibit interference, in the sense that\nsumming over them is not equivalent to omitting the intermediate\nprojections in (2) (‘coarse-graining’ the histories). In\nthe special cases in which the interference terms vanish for any pair\nof distinct histories, we say that the set of histories satisfies the\nconsistency or (weak) decoherence condition. It is easy\nto see that this condition takes the form", "\nfor any pair of distinct histories (the real part of the ‘decoherence\nfunctional’ vanishes).", "\nIf this is satisfied, we can view (2) as defining the distribution\nfunctions for a stochastic process with the histories as trajectories.\nDecoherence in the sense of this abstract formalism is thus defined\nsimply by the condition that the quantum probabilities for later\nevents can be calculated as if the state had collapsed at the\nintermediate times. Qualitatively one recovers classical behaviour, in\nthe sense that the histories are assigned quantum probabilities that\nnevertheless satisfy the classical formula of total probability. ", "\nA stronger form of the decoherence condition, namely the vanishing of\nboth the real and imaginary part of the decoherence functional, can be\nused to prove theorems on the existence of (later) ‘permanent\nrecords’ of (earlier) events in a history, which is a\ngeneralisation of the idea of ‘environmental\n monitoring’.[8]\n For instance, if the state \\(\\varrho\\) is a pure state \\(\\lvert \\psi \\rangle\\langle\\psi\\rvert\\)\nthis (strong) decoherence condition is equivalent, for all \\(n\\),\nto the orthogonality of the vectors", "\nand this in turn is equivalent to the existence of a set of orthogonal\nprojections\n\\(R_{\\alpha_1 \\ldots\\alpha_i}(t_i)\\)\n(for any \\(t_i \\le t_n\\))\nthat extend consistently the given set of histories and are perfectly\ncorrelated with the histories of the original set (Gell-Mann and\nHartle 1990). Note, however, that these ‘generalised\nrecords’ need not be stored in separate degrees of freedom, such\nas an environment or measuring\n apparatus.[9]", "\nVarious authors have taken the theory of decoherent histories as\nproviding an interpretation of quantum mechanics. For instance,\nGell-Mann and Hartle sometimes talk of decoherent histories as a\nneo-Everettian approach, while Omnès appears to think of\nhistories along neo-Copenhagen lines (perhaps as an experimental\ncontext creating a ‘quantum phenomenon’ that can stretch\nback into the\n past).[10]\n Griffiths (2002) has probably developed the most detailed of these\ninterpretational approaches (also addressing various earlier\ncriticisms, e.g. by Dowker and Kent (1995, 1996)). In itself, however,\nthe formalism is interpretationally neutral and has the particular\nmerit of bringing out that when interference is suppressed, one can\nreidentify different components of the state over time, making this\nformalism especially appropriate for discussing temporal evolution at\nthe level of the non-interfering components." ], "subsection_title": "1.2 Decoherent histories" }, { "content": [ "\nWork on environmental decoherence and that on decoherent histories tend to\nbe unfortunately rather separate. In comparing the two, we shall need\nto look both at cases that can be described by both formalisms (and\nask whether or not the two descriptions are equivalent), and at cases\nwhere only the more abstract formalism of decoherent histories\napplies.", "\nWith regard to the latter, there are of course cases in which the\ndecoherence functional vanishes just by numerical coincidence. But\nthere are also systematic cases of vanishing of interference\neven without environmental monitoring, namely in the presence of\n‘conservation-induced’ decoherence (see e.g. Halliwell\n2010). As an example, take an isolated system (say, with discrete\nenergy levels), and consider histories composed of projections onto\nits energy states at arbitrary times. Because energy is conserved, in\nthe energy basis each individual component is following the\nSchrödinger equation without interfering with the other\ncomponents, and the corresponding histories decohere. While some\nauthors in the decoherent histories literature take\nconservation-induced decoherence to be a significant novelty of the\ntheory, it should be noted that it lacks the robustness of\nenvironment-induced decoherence, since it lacks a mechanism that\nactively suppresses interference.", "\nWith regard to the former case, environmental decoherence can be\neasily described also in terms of decoherent histories. One needs to\ntake times that are separated by intervals larger than the decoherence\ntime scale, and projections onto the preferred states. Then the\nenvironmental monitoring ensures that the resulting histories\ndecohere. (In case of a continuous set of preferred states, one might\nneed to generalise the histories formalism slightly, using\n‘effects’ rather than projections; see e.g. Kent 1998.) In\nthis sense, environmental decoherence can be seen as a special case of\ndecoherent histories, but the descriptions given by the two formalisms\nare somewhat different. While decoherent histories define\nmulti-time distributions over the preferred states (at discrete\ntimes), models of environmental decoherence essentially describe\nsingle-time distributions over the preferred states. While they\nhave the advantage of being well-defined at all times, these\nsingle-time distributions do not explicitly describe any temporal\nevolution at the level of the individual components. ", "\nIn a number of models of environmental decoherence, however, it is\nobvious what the dynamical behaviour should be even at the level of\nindividual components. Specifically, in models where the preferred\nstates are coherent states, comparison of the master equation for the\nreduced state of the system with the evolution of a classical\nLiouville distribution suggests that the trajectories of individual\ncomponents in fact approximate surprisingly well the corresponding\nNewtonian trajectories. Intuitively, one can explain this by noting\nthat the preferred states (which are wave packets that are narrow in\nposition and remain so because they are also narrow in momentum) are\nthe states that tend to get least entangled with the environment.\nTherefore they will tend to follow the Schrödinger equation more\nor less undisturbed. But, as a matter of fact, narrow wave packets\nfollow approximately Newtonian trajectories, at least if the external\npotentials in which they move are uniform enough across the width of\nthe packets (results of this kind are known as ‘Ehrenfest\ntheorems’). Thus, the resulting trajectories will be close to\nNewtonian ones (on the relevant\n scales).[11]", "\nThis picture cannot be exact, because as soon as a localised\nwave packet has spread enough, it will be decohered into new more\nlocalised packets, so that intuitively one will get some kind of\n‘fanning out’ of trajectories. In fact, such deviations\nfrom Newtonian behaviour are due both to the tendency of the\nindividual components to spread and to the localising effect of the\ninteraction with the environment, which further enhances the\ncollective spreading of the components (because a narrowing in\nposition corresponds to a widening in momentum). See Rosaler (2016)\nfor a very nice treatment (that uses an ‘open systems’\nversion of Ehrenfest). A vivid example are the observed trajectories\nof \\(\\alpha\\)-particles in a cloud chamber, which are indeed extremely\nclose to Newtonian ones, except for additional tiny\n ‘kinks’.[12]", "\nIn other models, e.g. when the electromagnetic field privileges the\nstationary states of an atom, there is no such comparison with\nclassical equations, and the lack of multi-time distributions becomes\na limitation of the model. Such limitations might be overcome by\ncombining models of environmental decoherence with more\nphenomenological models of ‘continuous measurement’ (as\ndone in a different example by Bhattacharya, Habib and Jacobs 2000).\nAs shown by Brun (2002), the dynamics of stationary states (quantum\njumps!) can be obtained from first principles in the decoherent\nhistories formalism. " ], "subsection_title": "1.3 Comparison" } ] }, { "main_content": [ "\nOne often hears the claim that decoherence solves the measurement\nproblem of quantum mechanics (see the entry on\n philosophical issues in quantum theory).\n Physicists who work on decoherence generally know better, but it is\nimportant to see why even in the presence of decoherence phenomena,\nthe measurement problem remains or in fact gets even worse.", "\nThe measurement problem is really a complex of problems, revolving\naround the question of whether one can apply quantum mechanics itself\nto the description of quantum measurements. One can just deny this, if\none takes quantum mechanics to be a phenomenological theory. But if\nquantum mechanics is not the fundamental theory that explains the\nphenomenology of quantum measurements, the question arises how we can\nexplain what ‘measurements’ and ‘results’ are.\nThis is the measurement problem in the wide sense of the term.", "\nIf instead we assume that quantum mechanics is itself applicable to\nthe description of measurements, then the question becomes one of how\none should model a measurement within quantum theory, specifically as\nsome appropriate interaction between a ‘system’ and an\n‘apparatus’, and of whether by so doing one can\nderive from the unitary evolution for the total system of\nsystem and apparatus the three phenomenological aspects of quantum\nmeasurements: that measurements have results, that these results\nobtain with some characteristic probabilities, and that depending on\nthe result of a measurement the state of the system is generally\ntransformed in a characteristic way (for this subdivision of the\nproblem, see Maudlin 1995). This derivation, however, appears to be\nimpossible.", "\nIndeed, as pointed out already by von Neumann (1932, Section VI.3),\none cannot reproduce the correct probabilities by assuming that they\narise because we are ignorant of the exact state of a macroscopic\napparatus. But whatever the exact initial state of the apparatus, if\nthe system (say, an electron) is described by a superposition of two\ngiven states, say, spin in \\(x\\)-direction equal \\(+\\frac{1}{2}\\) and spin in\n\\(x\\)-direction equal \\(-\\frac{1}{2}\\), and we let it interact\nwith a measuring apparatus that couples to these states, the final\nquantum state of the composite will be a sum of two components, one in\nwhich the apparatus has coupled to (has registered) \\(x\\)-spin \\(= +\\frac{1}{2}\\), and one in which the apparatus has coupled to (has registered)\n\\(x\\)-spin \\(= -\\frac{1}{2}\\).[13]\n This is the measurement problem in the narrow sense of the term. " ], "section_title": "2. Decoherence and the Measurement Problem", "subsections": [ { "content": [ "\nThe fact that interference is typically very well suppressed between\nlocalised states of macroscopic objects suggests that it is at least\nrelevant to why macroscopic objects in fact appear to us to be in\nlocalised states. In the special case of measuring apparatuses, it\nwould then be relevant to why we never observe an apparatus pointing,\nsay, to two different results. Does modelling measurements\nincluding the decoherence interactions with the environment\nallow one to derive that measurements always have results? This is\nsomewhat part of the ‘folklore’ of decoherence, but as\npointed out by many physicists and philosophers alike (e.g. Pearle\n1997; Bub 1997, Chapter 8; Adler 2003; Zeh 2003a, pp. 14–15), it\nis not the case: while decoherence does explain why we do\nnot observe superpositions of measurement results, it does\nnot explain why we do observe measurement results in the\nfirst place.", "\nIndeed, what happens if we include decoherence in the description?\nDecoherence tells us, among other things, that plenty of interactions\nare taking place all the time in which differently localised states of\nthe apparatus registering, say, different \\(x\\)-spin values of an\nelectron couple to different states of the environment. But now, by\nthe same arguments as above, the composite of electron,\napparatus and environment will be a superposition of (i) a state\ncorresponding to the environment coupling to the apparatus coupling in\nturn to the value \\(+\\frac{1}{2}\\) for the spin, and of (ii) a state corresponding\nto the environment coupling to the apparatus coupling in turn to the\nvalue \\(-\\frac{1}{2}\\) for the spin. We are thus left with the following choice,\nwhether or not we include decoherence: either the composite\nsystem is not described by such a superposition, because the\nSchrödinger equation actually breaks down and needs to be\nmodified, or it is described by such a superposition, but then we need\nto either to supplement quantum mechanics with appropriate hidden\nvariables, or to give an appropriate interpretation of the\nsuperposition.", "\nTherefore, decoherence as such does not provide a solution to the\nmeasurement problem, at least not unless it is combined with an\nappropriate foundational approach to the theory – whether this\nbe one that attempts to solve the measurement problem, such as\nBohm, Everett or GRW; or one that attempts to dissolve it, such\nas various versions of the Copenhagen interpretation. (See also\nWallace 2012b.)" ], "subsection_title": "2.1 Solving the measurement problem?" }, { "content": [ "\nDecoherence is clearly neither a dynamical evolution contradicting the\nSchrödinger equation, nor a new supplementation or interpretation\nof the theory. As we shall discuss, however, it both reveals important\ndynamical effects within the Schrödinger evolution, and\nmay be suggestive of possible interpretational moves. As such\nit has much to offer to the philosophy of quantum mechanics. At first,\nhowever, it seems that discussion of environmental interactions should\nactually exacerbate the existing problems. Intuitively, if the\nenvironment is carrying out lots of spontaneous measurements even\nwithout our intervention, then the measurement problem ought to apply\nmore widely, also to these spontaneously occurring\nmeasurements.", "\nIndeed, while it is well-known that localised states of macroscopic\nobjects spread very slowly with time under the free Schrödinger\nevolution (i.e., if there are no interactions), the situation turns\nout to be different if they are in interaction with the environment.\nAlthough the different components that couple to the environment will\nbe individually incredibly localised, collectively they can have a\nspread that is many orders of magnitude larger. That is, the state of\nthe object and the environment could be a superposition of zillions of\nvery well localised terms, each with slightly different positions, and\nthat are collectively spread over a macroscopic distance,\neven in the case of everyday\n objects.[14]\n Given that everyday macroscopic objects are particularly subject to\ndecoherence interactions, this raises the question of whether quantum\nmechanics can account for the appearance of the everyday world even\napart from the measurement problem.", "\nThere is thus an even wider problem, which we can call the problem of\nthe classical regime of quantum mechanics, and quite analogous\nto the measurement problem. Can quantum mechanics be applied to the\ndescription of classical systems? We can deny it (as orthodox\napproaches do), but then what are classical systems in the first\nplace? And if we apply quantum mechanics also to the systems that seem\nto populate our everyday world, can we derive from quantum\nmechanics the behaviour that is characteristic of such\n‘classical’ systems? But such a derivation appears\nimpossible. To put it crudely: if everything is in interaction with\neverything else, everything is generically entangled with everything\nelse, and that is a worse problem than measuring apparatuses being\nentangled with measured systems." ], "subsection_title": "2.2 Widening the measurement problem" } ] }, { "main_content": [ "\nDespite the fact that decoherence interactions extend the measurement\nproblem to the wider problem of the classical regime, decoherence\nis relevant to the solution of both problems because at the\nlevel of components of the wave function the quantum description\nof decoherence phenomena (tantalisingly!) includes both measurement\nresults and other quantum phenomena (such as quantum jumps) as well as\nclassical behaviour. This suggests that to a large extent decoherence\nprovides an interpretation-neutral strategy for tackling the\nmeasurement problem and the problem of the classical regime (a thesis\ndeveloped in greater detail by Rosaler 2016), and that the solution to\nthese problems lies in combining decoherence with the main\nfoundational approaches to quantum mechanics. ", "\nThere are a wide range of approaches to the foundations of quantum\nmechanics, however (see also the entry on\n philosophical issues in quantum theory).\n In some cases, one just needs to point out how an approach fits into\nthe overall picture suggested by decoherence, other approaches are in\nfact less able to exploit the results of decoherence. (The term\n‘approach’ here is more appropriate than the term\n‘interpretation’, because several of these are in fact\nmodifications of or additions to the theory.) We\nshall thus discuss in turn a number of approaches and how they relate\nto decoherence. These will be: the three most widespread approaches in\nthe philosophy of physics (Everett, Bohm and GRW), followed by the\nmore ‘orthodox’ approaches of von Neumann, Heisenberg and\nBohr, and a few others.", "\nWe shall start with the Everett theory (or many-worlds interpretation)\nin some of its main variants. This is in fact most closely related to\ndecoherence, since the latter can be used to naturally identify stable\n(if branching) structures within the universal wave function that can\ninstantiate the multiplicity of worlds or measurement records or\nconscious experiences characteristic of Everettian views. Another\napproach that arguably makes crucial use of decoherence is pilot-wave\ntheory (or de Broglie–Bohm theory, or Bohmian mechanics), where\nparticle positions (or other suitable ‘beables’) are\nguided in their temporal evolution by the universal wave function. The\nbranching structure of the latter will clearly have an effect on the\ncharacter of the evolution of the variables it guides. Instead,\nspontaneous collapse theories intuitively have less to do with\ndecoherence because they seek to suppress unwanted superpositions.\nStill, they are also arguably able to make use of decoherence,\nperhaps with some qualifications.", "\nMore traditional approaches to quantum mechanics that somehow\nprivilege the notion of measurement or observation also may have\nless-than-obvious connections with decoherence and in fact fit less\nwell with it, but we shall look at von Neumann’s,\nHeisenberg’s and Bohr’s views. Finally, we shall briefly\nmention other approaches and remark on their various relations to\ndecoherence. These will be Nelson’s stochastic mechanics, modal\ninterpretations, and QBism. " ], "section_title": "3. The Role(s) of Decoherence in Different Approaches to Quantum Mechanics", "subsections": [ { "content": [ "\nThe Everett theory (see the entries on\n Everett’s relative-state interpretation\n and on the\n many-worlds interpretation)\n was originally developed in 1957, before the theory of decoherence\n(Everett 1957). As we shall see, in recent years decoherence has\nbecome a defining notion of the theory, but it arguably fits rather\nwell also with Everett’s original formulation.", "\nThe central technical notion in Everett’s own formulation of the\ntheory is a relative state: e.g. the electron is in a state of\nspin up relative to the corresponding read-out state of the apparatus\nand in a state of spin down relative to the other read-out state. But Everett is interested in the emergence of\nstable structures in the universal wavefunction in terms of\nrelative states. His paradigm example is that of a hydrogen atom: put\na proton and an electron in a box, both spread out over the entire\nvolume. After a while, the proton and electron will have relaxed. The\nposition of the proton will still be spread out over the entire box,\nbut relative to each position state of the proton, the electron wil\nnow be in the usual ground state of the hydrogen atom. According to\nEverett, this is what we mean by a stable atom forming. Everett\nthinks of classical systems (a cannonball!) along the same lines, and\nuses these arguments as justifying the assumption that classical\nsystems exist, in particular ones that are complex enough to store\n(and perhaps act upon) records of measurement-like interactions they\nhave had with their environments. Everett’s aim is to recover\nthe usual predictions of quantum mechanics for the memory registers of\nsuch\n‘servomechanisms’.[15][16]\n", "\nIt should be clear that the theory of decoherence is an ideal\ntechnical tool if (like Everett) one wishes to identify stable\nstructures within the universal wave function. And, indeed, some of\nthe main workers in the field such as Zeh (2000) and (perhaps more\nguardedly) Zurek (1998) and Gell-Mann and Hartle (e.g. 1990) suggest\nthat decoherence is most naturally understood in terms of Everett-like\n interpretations.[17]\n This role of decoherence has been emphasised most prominently by\nSaunders (e.g. 1993) and by Wallace (e.g. 2003), and is in fact\nresponsible for the extraordinary renaissance of the Everett theory\nwithin the philosophy of physics since the\n mid-1990s.[18]", "\nUntil then, Everett was thought to be suffering from a problem of the\n‘preferred\n basis’:[19]\n it was thought that without putting in by hand what should count as\n‘worlds’, there were too many possible ways of defining\nsuch worlds, or too many ways of defining relative states. But looking\nfor potentially relevant structures that are already present in the\nwave function allows one to identify worlds (or other relevant\nstructures) without having to postulate the existence of some\npreferred states (whether or not they form an orthonormal basis). ", "\nA justification for this identification can be variously\ngiven by suggesting that a ‘world’ should be a\ntemporally extended structure and thus reidentification over\ntime will be a necessary condition for defining worlds; or similarly\nby suggesting that in order for observers to have evolved\nthere must be stable records of past events (Saunders 1993,\nand the unpublished Gell-Mann and Hartle 1994 – see the\n Other Internet Resources\n section below); or that observers must be able to access robust\nstates, preferably through the existence of redundant information\nin the environment (Zurek’s ‘existential\ninterpretation’,\n 1998).[20]\n But the most comprehensive justification of the use of decoherence in\nterms of how Everett can be understood using structures in the\nuniversal wave function has been given by Wallace, starting with his\n(2003) and given its final form in his book (2012a). Wallace places\nhis discussion in the wider context of an approach to emergence based\non Dennett’s notion of ‘real patterns’. Higher-level\ntheories are functionally instantiated by lower-level (more\nfundamental) ones if there exist relatively simple mappings from\nsolutions of the lower-level theory over a certain domain to solutions\nof the higher-level theory. Higher-level structures are thus reduced\nto patterns at the more fundamental level, which are real in the\n(quasi-)Dennettian sense that they are objectively useful in terms of\nboth predicting and explaining phenomena at the higher level. At the\nsame time they are emergent, because they could be multiply realised,\nand because finding the relevant mapping may be possible only in a\ntop-down perspective. Everettian worlds are such real patterns,\nbecause decoherence ensures their dynamical independence of each\nother. ", "\nAlternatively to some global notion of a world, one can look at the\ncomponents of the (mixed) state of a (local) system, either from the\npoint of view that the different components defined by decoherence\nwill separately affect (different components of the state of) another\nsystem, or from the point of view that they will separately underlie\nthe conscious experience (if any) of the system. The former sits well\nwith the relational interpretation of Everett as put forward in the\n1990s by Saunders (e.g. 1993), possibly with Zurek’s (1998)\nviews, and arguably with Everett’s (1957) original notion of\nrelative\n state.[21]\n The latter leads directly to the idea of ‘many-minds’ in\nthe sense used by Zeh (2000; also 2003a, p. 24). As Zeh puts it, \nthe ‘psycho-physical parallelism’ invoked by von Neumann \n(cf. below Section 3.4.1) is to be understood as the\nrequirement of supervenience of the mental on the physical: only one\nmental state is experienced, so there should be only one corresponding\ncomponent in the physical state. In a decohering no-collapse universe\none can instead introduce a new psycho-physical parallelism,\nin which individual minds supervene on each non-interfering component\nin the physical state. (This is different from the many-minds\ninterpretation of Albert and Loewer (1988), where the mental\ndoes not supervene on the physical, because individual minds\nhave trans-temporal identity of their\nown.[22]) Zeh\nindeed suggests that, given decoherence, this is the most natural\ninterpretation of quantum\n mechanics.[23]\n" ], "subsection_title": "3.1 Everett theories" }, { "content": [ "\n‘Hidden variables’ approaches seek to explain quantum\nphenomena as equilibrium statistical effects arising from a\ndeeper-level theory, rather strongly in analogy with attempts at\nunderstanding thermodynamics in terms of statistical mechanics (see\nthe entry on\n philosophy of statistical mechanics).\n Of these, the most developed are the so-called pilot-wave theories,\nin particular the theory by de Broglie and Bohm (see also the entry on\n Bohmian mechanics).\n Pilot-wave theories are no-collapse formulations of quantum mechanics\nthat assign to the wave function the role of determining the evolution\nof (‘piloting’, ‘guiding’) the variables\ncharacterising the system, say particle configurations, as in de\nBroglie’s (1928) and Bohm’s (1952) theory, or fermion\nnumber density, as in Bell’s (1987, Chapter 19)\n‘beable’ quantum field theory, or again field\nconfigurations, as in various proposals for pilot-wave quantum field\ntheories (for a recent survey, see Struyve 2011).", "\nDe Broglie’s idea was to modify classical Hamiltonian mechanics\nin such a way as to make it analogous to classical wave optics, by\nsubstituting for Hamilton and Jacobi’s action function the phase\n\\(S\\) of a physical wave. Such a ‘wave mechanics’ of\ncourse yields non-classical motions, but in order to understand how de\nBroglie’s dynamics relates to typical quantum phenomena, we must\ninclude Bohm’s (1952, Part II) analysis of the appearance of\ncollapse. In the case of measurements, Bohm argued that the wave\nfunction evolves into a superposition of components that are and\nremain separated in the total configuration space of measured system\nand apparatus, so that the total configuration is\n‘trapped’ inside a single component of the wave\nfunction, which will guide its further evolution, as if the wave had\ncollapsed (‘effective’ wave function). This analysis\nallows one to recover the apparent collapse upon measurement (and the\nquantum probabilities are further recovered via statistical\nconsiderations). ", "\nIt is natural to extend this analysis from the case of measurements\ninduced by an apparatus to that of ‘spontaneous\nmeasurements’ as performed by the environment in the theory of\ndecoherence, thus applying the same strategy to recover both quantum\nand classical phenomena. The resulting picture is one in which de\nBroglie–Bohm theory, in cases of decoherence, describes the\nmotion of particles that are trapped inside one of the extremely well\nlocalised components selected by the decoherence interaction. Thus, de\nBroglie–Bohm trajectories will partake of the classical motions\non the level defined by decoherence (the width of the components).\nThis use of decoherence would arguably resolve the puzzles discussed,\ne.g., by Holland (1996) with regard to the possibility of a\n‘classical limit’ of de Broglie’s theory. One\nbaffling problem, for instance, is that trajectories with different\ninitial conditions cannot cross in de Broglie–Bohm theory,\nbecause the wave guides the particles by way of a first-order\nequation, while, as is well known, Newton’s equations are\nsecond-order and possible trajectories in Newton’s theory do\ncross. Now, however, the non-interfering components produced by\ndecoherence can indeed cross, and so will the trajectories of\nparticles trapped inside them.", "\nIf the main instances of decoherence are indeed coextensive with\ninstances of separation in configuration, de Broglie–Bohm theory\ncan thus use the results of decoherence relating to the\nformation of classical structures, while providing an interpretation\nof quantum mechanics that explains why these structures are indeed\nobservationally\n relevant.[24]\n This picture is natural, but not self-evident. De Broglie–Bohm\ntheory and decoherence contemplate two a priori distinct\nmechanisms connected to apparent collapse: respectively, separation of\ncomponents in configuration space and suppression of interference.\nWhile the former obviously implies the latter, it is equally obvious\nthat decoherence need not imply separation in configuration space. One\ncan expect, however, that decoherence interactions of the form of\napproximate position measurements will.", "\nA discussion of the role of decoherence in pilot-wave theory in the\nform suggested above has been given by Rosaler (2015, 2016). An\ninformal discussion is given in Bohm and Hiley (1993, Chapter 8),\npartial results are given by Appleby\n (1999),[25]\n and some simulations have been realised by Sanz and co-workers (e.g.\nSanz and Borondo\n 2009).[26]\n Relevant results have also been derived by Toroš, Donadi and\nBassi (2016) who show quantitative correspondence with a spontaneous\ncollapse model (see also Romano 2016). A rather different approach is\ninstead suggested by Allori (2001; see also Allori and Zanghì\n 2009).[27]", "\nWhile, as argued above, it appears plausible that decoherence might be\ninstrumental in recovering the classicality of pilot-wave trajectories\nin the case of the non-relativistic particle theory, it is less clear\nwhether this strategy might work equally well in the case of field\ntheory. Doubts to this effect have been raised, e.g., by Saunders\n(1999) and by Wallace (2008, 2012b). Essentially, these authors doubt\nwhether the configuration-space variables, or some coarse-grainings\nthereof, are, indeed, decohering\n variables.[28]" ], "subsection_title": "3.2 Pilot-wave theories" }, { "content": [ "\nSpontaneous collapse theories\n seek to modify the Schrödinger equation, so that superpositions\nof different ‘everyday’ states do not arise or are very\nunstable. The best known such theory is the so-called GRW theory\n(Ghirardi Rimini and Weber 1986), in which a material particle\nspontaneously undergoes localisation in the sense that at\nrandom times it experiences a collapse of the form used to describe\napproximate position\n measurements.[29]\n In the original model, the collapse occurs independently for each\nparticle (a large number of particles thus ‘triggering’\ncollapse much more frequently); in later models the frequency for each\nparticle is weighted by its mass, and the overall frequency for\ncollapse is thus tied to mass\n density.[30]", "\nCan decoherence be put to use in GRW? Such approaches may have\nintuitively little to do with decoherence since they seek to suppress\nprecisely those superpositions that are created by decoherence.\nNevertheless their relation to decoherence is interesting (and, as we\nshall see in the next section, interestingly different from the role\nthat decoherence at least implicitly plays in von Neumann’s\ncollapse postulate).", "\nQualitatively at least, since spontaneous collapse produces\nlocalisation, the effect appears formally similar as in some of the\nmodels of decoherence. But we have ‘true’ collapse instead\nof suppression of interference, and spontaneous collapse occurs\nwithout there being any interaction between the system and\nanything else. In cases in which the decoherence interaction indeed\nalso takes the form of approximate position measurements, the relation\nbetweeen spontaneous collapse and decoherence presumably boils down to\na quantitative comparison. If collapse happens faster than\ndecoherence, then the superposition of components relevant to\ndecoherence will not have time to arise, and insofar as the collapse\ntheory is successful in recovering classical phenomena, decoherence\nplays no role in this recovery. Instead, if decoherence takes place\nfaster than collapse, then the collapse mechanism can find\n‘ready-made’ structures onto which to truly collapse the\nwave function. ", "\nNot much explicit work has been done on modelling decoherence in the\nsetting of spontaneous collapse theories, however. Simple comparison\nof the relevant rates in models of decoherence and in spontaneous\ncollapse theories suggests that decoherence is generally faster (Tegmark\n1993, esp. Table 2). The more detailed model by Toroš, Donadi and\nBassi (2016, esp. Section V) indicates that the effect of the collapse\nis amplified through the presence of the environment, i.e. the\ncollapse rate is increased. The situation may be more complex when the\ndecoherence interaction does not approximately privilege position\n(e.g. when instead it selects for currents in a SQUID), because\ncollapse and decoherence might actually ‘pull’ in\ndifferent\n directions.[31]", "\nA further aspect of the relation between decoherence and spontaneous\ncollapse theories relates to the experimental testability of\nspontaneous collapse theories. Indeed, if we assume that collapse is a\nreal physical process, decoherence will make it extremely difficult in\npractice to detect empirically when and where exactly spontaneous\ncollapse takes place: on the one hand, decoherence makes it look as if\ncollapse has taken place already, while on the other it makes it\ndifficult to perform interference experiments to check whether\ncollapse has not yet taken place. (See the nice discussion of this\nissue in Chapter 5 of Albert (1992)).", "\nEven worse, what might be interpreted as evidence for collapse could\nbe reinterpreted as ‘mere’ suppression of interference\nwithin an Everett or pilot-wave approach, and only those cases in\nwhich the collapse theory predicts collapse but the system is shielded\nfrom decoherence (or perhaps in which the two pull in different\ndirections) could be used to test collapse theories\nexperimentally.", "\nOne particularly bad scenario for experimental testability is related\nto the speculation (in the context of the ‘mass density’\nversion) that the cause of spontaneous collapse may be connected with\ngravitation. Tegmark (1993, Table 2) quotes some admittedly uncertain\nestimates for the suppression of interference due to a putative\nquantum gravity, but they are quantitatively very close to the rate of\ndestruction of interference due to the GRW collapse (at least outside\nof the microscopic domain). Similar conclusions are arrived at in the\nmore detailed work by Kay (1998). If there is indeed such a\nquantitative similarity between these possible effects, then it would\nbecome extremely difficult to distinguish between the two. In the\npresence of gravitation, any positive effect could be interpreted as\nsupport for either collapse or decoherence. And in those cases in\nwhich the system is effectively shielded from decoherence (say, if the\nexperiment is performed in free fall), then if the collapse mechanism\nis indeed triggered by gravitational effects, no collapse should be\nexpected\n either.[32]" ], "subsection_title": "3.3 Spontaneous collapse theories" }, { "content": [ "\nIn the final Chapter VI of his book (von Neumann 1932), von Neumann\nprovided a systematic discussion of quantum mechanics with collapse\nupon measurement (described by what he calls an intervention of type\n\\(\\mathbf{1})\\), as distinct from the Schrödinger equation\n(intervention of type \\(\\mathbf{2})\\), and traditionally associated with a\nrole for conscious observation. (The two types of interventions are\nintroduced already in Section V.1, but von Neumann postpones their\nconceptual discussion to the final chapter.)", "\nIn actual fact, von Neumann starts his discussion by pointing out that\nmeasurements are different from other physical processes both\nphenomenologically and by presupposing conscious observation. But he\ninsists on preserving what he calls ‘psycho-physical\nparallelism’, requiring that the process of observation be\ndescribable also in purely physical terms. He thus requires that a\nboundary be drawn between the ‘observed’ and the\n‘observer’, but also crucially that this boundary be\nmovable arbitrarily far towards the observer end. (Note that\nvon Neumann stops short of at least explicitly attributing to\nconsciousness a causal role in collapsing the quantum state.)", "\nVon Neumann thus needs to show that the final predictions for what we\nconsciously observe are insensitive to how far along such a\n‘measurement chain’ one chooses to continue applying\nintervention \\(\\mathbf{2}\\), thus ensuring that every step in the process of\nobservation can be described purely in physical terms. In von\nNeumann’s example of a measurement of temperature, we need not\napply intervention \\(\\mathbf{1}\\) to the system itself, but may apply it to\nthe thermometer, or to the retina in the eye, or to the optic nerve,\nor anywhere else within the physical realm between the system and the\n‘abstract ego’ of the observer. By the same token,\nhowever, we can (much more practically!) apply it also directly to the\nmeasured system. ", "\nAs a preliminary, von Neumann discusses the relation between states of\nsystems and subsystems, in particular the notion of partial trace and\nthe biorthogonal decomposition theorem (i.e. the theorem stating that\nan entangled quantum state can always be written in terms of perfect\ncorrelations between two special bases for the subsystems). He also\nshows (as mentioned above) that the usual statistics of measurements\ncannot be recovered by assuming that the ‘observer’ is\ninitially in a mixed state. He then proves that it is always possible\nto define an interaction Hamiltonian that will correlate perfectly the\neigenstates of any given observable of an ‘observed’\nsystem with the eigenstates of some other suitable observable of an\n‘observer’, leaving as an exercise for the reader to show\nthat predictions are independent of where one places the boundary\nbetween the two.", "\nWhat the reader is supposed to do is to imagine a series of such\ninteractions, between the system and the thermometer, between the\nthermometer and the light, between the light and the retina, etc., and\nrely on the absence of interference at each step to argue that,\neven if we describe a number of systems using intervention \\(\\mathbf{2}\\),\nthey behave for the purpose of the application of intervention\n\\(\\mathbf{1}\\) as if they had collapsed already. In this sense, even\nthough he is quite clearly not thinking in terms of mechanisms for\nsuppressing interference, he is relying on decoherence. A fuller\ntreatment (e.g. a detailed model of how the thermometer interacts with\nlight, and some of the light is then sampled by the eye) would\nresemble more closely an analysis in terms of environmental\ndecoherence. ", "\nSimilar considerations may be made about Heisenberg’s views on\nquantum mechanics, even though Heisenberg’s conceptual framework\nis arguably rather different from von Neumann’s.", "\nFor Heisenberg, the application of quantum mechanics requires a\n‘cut’ between the system to be described quantum\nmechanically, and what is to be considered external to the system and\nis to be treated classically. Indeed, if one were to apply quantum\nmechanics to the entire universe, one would have a perfectly closed\nsystem in which nothing would ever happen. But Heisenberg places\nspecial emphasis on the idea that any special system must be\ndescribable using quantum mechanics (indeed, that such a system is in\nprinciple always able to display interference effects if placed under\nthe appropriate\n conditions[33]).\n Self-consistency of the theory then requires the arbitrary\nmovability of the cut away from the system. (The most detailed\npresentation of these ideas is in Heisenberg’s draft reply to\nthe\n Einstein–Podolsky–Rosen argument\n – see Crull and Bacciagaluppi (2011) in the\n Other Internet Resources.)", "\nIf one thinks about some of the examples that Heisenberg considers to\nbe measurements, it is even clearer than in von Neumann’s case\nthat the movability of the Heisenberg cut in fact requires\ndecoherence. In particular, his discussion of \\(\\alpha\\)-particle tracks\ninvolves successive measurements whenever the \\(\\alpha\\)-particle\nionises an atom in a cloud chamber. If we require that the Heisenberg\ncut be movable to the level of the entire cloud chamber, we shift\ndirectly to a Mott-type analysis of the \\(\\alpha\\)-particle tracks.", "\nOne further aspect that is characteristic for Heisenberg and that\nprima facie does not fit with the theory of decoherence, is\nthat Heisenberg does not take quantum states as fundamental.\nFor him, Schrödinger’s notion of a ‘state’ was\njust a mathematical artifact that is convenient for calculating\ntransition probabilities between values of (measured) observables.\nThis can also be seen as underpinning the movability of the cut: there\nis no matter of fact about when the collapse takes place, and all that\nmatters physically are the transition probabilities between values of\nobservables. This view is still compatible with decoherence, however,\nas long as one sees the role of the quantum state there as again just\na convenient tool for calculating transition probabilities (say, in a\ndecoherent histories\n framework).[34]", "\nBohr shared with von Neumann and with Heisenberg the idea that that\nquantum mechanics is in principle applicable to any physical system\n(as shown e.g. by his willingness in the course of his debates with\nEinstein to apply the uncertainty relations to parts of the\nexperimental apparatus when not used as an apparatus), while\ndenying that it is meaningful to apply it to the entire universe. What\nis central to Bohr’s views, however, is not so much the\nmovability of the cut within a given experimental arrangement, but the\nfact that different experimental arrangements will generally select\ncomplementary aspects of the description of a physical system,\ncorresponding to different equally necessary classical pictures that\nhowever cannot be combined. In this sense, for Bohr classical concepts\nare conceptually prior to quantum mechanics. In a terminology\nreminiscent of Kant, the quantum state is not an anschaulich\n(‘intuitive’) representation of a quantum object, but only\na symbolic representation, a shorthand for the quantum\nphenomena that are constituted by applying the various complementary\nclassical pictures. (See also the entry on the\n Copenhagen interpretation.)", "\nThus, if we understand the theory of decoherence as pointing to how\nclassical concepts might in fact emerge from quantum mechanics, we see\na tension with Bohr’s basic position. According to decoherence,\neven though classical concepts are autonomous in the sense of being\nemergent, they are not fundamentally prior to quantum\nmechanics. In another sense, however, decoherence does support\nBohr’s point of view, because we can see decoherence (in\nparticular environmental decoherence) as suggesting that there are no\nquantum phenomena without classical records: it is the\nsuppression of interference that creates the conditions for restoring\nthe objectivity that gets lost through what Bohr sees as the loss of\nindependent reality attaching to both the system and the measuring\n apparatus.[35]\n ", "\nBoth of these aspects can be seen in the reception of Everett’s\nideas by Bohr and his circle. While Everett saw his own theory as\ndirectly opposed to von Neumann’s approach, he believed that he\ncould provide a justification for Bohr’s idea of\ncomplementarity. Bohr, however, rejected the attempt to apply the\nnotion of quantum state to a description of the whole universe. (The\nrejection of Everett’s ideas in Copenhagen in fact rather\ntragically contributed to Everett leaving physics in favour of\nmilitary operations\n research.[36])\n " ], "subsection_title": "3.4 Orthodox approaches" }, { "content": [ "\nNelson’s (1966, 1985) stochastic mechanics is a proposal to\nrecover the wave function and the Schrödinger equation as\neffective elements in the description of a fundamental diffusion\nprocess in configuration space. Insofar as the proposal is\n successful,[37]\n it shares many features with de Broglie–Bohm theory. Indeed,\nthe current velocity for the particles in Nelson’s theory turns\nout to be equal to the de Broglie–Bohm velocity, and the\nparticle distribution in Nelson’s theory is equal to that in de\nBroglie–Bohm theory (in equilibrium).", "\nIt follows that many results from pilot-wave theories can be imported\ninto Nelson’s stochastic mechanics, including those based on\ndecoherence. In particular, the strategies used in pilot-wave\ntheories to recover the appearance of collapse and the emergence of a\nclassical regime can be applied also to the case of stochastic\nmechanics, even though so far very little has been done along these\nlines. Doing so will arguably also resolve some conceptual puzzles\nspecific to Nelson’s theory, such as the problem of two-time\ncorrelations raised in Nelson\n (2006).[38]\n ", "\nThe first ‘modal interpretation’ of quantum mechanics was\nproposed by Van Fraassen (1973, 1991), and was strictly an\ninterpretation of the theory (while other later versions came more to\nresemble pilot-wave theories; see the entry on\n modal interpretations).\n Van Fraassen’s basic intuition was that the quantum state of a\nsystem should be understood as describing a collection of\npossibilities, represented by components in the (mixed) quantum state.\nHis proposal considers only decompositions at single instants, and is\nagnostic about re-identification over time. Thus, it can directly\nexploit only the fact that decoherence produces descriptions in terms\nof classical-like states, which will count as possibilities in Van\nFraassen’s sense. This ensures ‘empirical adequacy’\nof the quantum description (crucial in Van Fraassen’s\n constructive empiricism).\n The dynamical aspects of decoherence can be exploited indirectly, in\nthat single-time components will exhibit records of the past,\nwhich ensure adequacy with respect to observations, but about whose\nveridicity Van Fraassen remains agnostic.", "\nA different strand of modal interpretations is loosely associated with\nthe (distinct) views of Kochen (1985), Healey (1989) and Dieks (see\ne.g. Dieks and Vermaas 1998). We focus on the last of these to fix\nideas. Van Fraassen’s possible decompositions are restricted to\none singled out by a mathematical criterion (related to the\nbiorthogonal decomposition theorem mentioned above in\n Section 3.4.1),\n and a dynamical picture is explicitly sought (and was later\ndeveloped). In the case of an ideal (non-approximate) quantum\nmeasurement, this special decomposition coincides with that defined by\nthe eigenstates of the measured observable and the corresponding\npointer states, and the interpretation thus appears to solve the\nmeasurement problem (for this case at least). In\nDieks’s original intentions, the approach was meant to provide\nan attractive interpretation of quantum mechanics also in the case of\ndecoherence interactions, since at least in simple models of\ndecoherence the same kind of decomposition singles out more or less\nalso those states between which interference is suppressed (with a\nproviso about very degenerate states).", "\nInterestingly, this approach fails when applied to other models of\ndecoherence, e.g., that in Joos and Zeh (1985, Section III.2). Indeed,\nit appears that in more general models of decoherence the components\nsingled out by this version of the modal interpretation are given by\ndelocalised states, and are unrelated to the localised\ncomponents naturally privileged by decoherence (Donald 1998;\nBacciagaluppi 2000). Thus the relation with decoherence has been the\ntouchstone for these versions of the modal interpretation. Note that\nVan Fraassen’s original interpretation is untouched by this\nproblem, and so are possibly some more recent modal or modal-like\ninterpretations by Spekkens and Sipe (2001), Bene and Dieks (2002),\nand Berkovitz and Hemmo (2006).", "\nThe general idea of modal interpretations, more or less in the spirit\nof Van Fraassen, can be applied more widely. For one thing, it is\ncognate to some of the views expressed in the decoherent histories\nliterature. Decoherent histories could be seen as alternative possible\nhistories of the world, one of which is in fact actualised. A\ndiscussion in these terms has been outlined by Hemmo (1996). Such\nviews are also possibly quite close to Everett’s own views, who\n(maybe surprisingly for the modern reader) was not a realist but an\nempiricist. A discussion of Everett with parallels to Van Fraassen is\ngiven by Barrett (2015). One final view that has some similarities\nwith Van Fraassen’s and should be equally able to exploit the\nresults of decoherence is Rovelli’s\n relational quantum mechanics\n (see also Van Fraassen 2010).", "\nQBism (originally short for ‘quantum Bayesianism’) is a\nview of quantum mechanics developed by Chris Fuchs and co-workers,\nwhich has made current the idea that subjective probabilities à\nla de Finetti can be used also in quantum mechanics (see the entry on\n quantum Bayesian and pragmatist views of quantum theory).\n The position is more radical than this, however, in that it does not\nonly claim that the quantum probabilities as defined by the quantum\nstate should be interpreted subjectively, but that the quantum state\nitself is merely an expression of an agent’s degrees of\n belief.[39]", "\nThe role of decoherence in QBism is rather downplayed. E.g. Fuchs and\nSchack (2012, Section 7) see it in light of the reflection principle\n(concerning an agent’s beliefs about their future beliefs).\nSpecifically, in the context of a von Neumann measurement chain, an\nagent can use the state of the system as decohered by some later\nelements of the chain as an expression of their beliefs about what\ntheir beliefs will be after the previous elements of the measurement\nchain have been completed. (And of course, the results of decoherence\ncan be taken into account if an agent is considering making\nmeasurements on a system that is in interaction with some\nenvironment.)" ], "subsection_title": "3.5 Other approaches" } ] }, { "main_content": [ "\nWe have seen in the last section that not all approaches to quantum\nmechanics can make full use of decoherence. In those approaches that\ncan, however, decoherence is instrumental in yielding a wealth of\nstructures that emerge from the unitary Schrödinger (or\nHeisenberg) dynamics. How far can this programme of\ndecoherence (Zeh 2003a, p. 9) be successfully developed? " ], "section_title": "4. Scope of Decoherence", "subsections": [ { "content": [ "\nWhat seems very clear is that decoherence is crucial for the emergence\nof much of the macroscopic world around us, from the motions in the\nsolar system (cf. the discussion of the motion of Saturn’s moon\nHyperion – for an assessment of which see Schlosshauer (2008))\nand down to the working of enzymes (which relies on their molecular\nshapes). The detailed picture of the world that emerges from\ndecoherence, however, is full of subtleties.", "\nFor one thing, while the more ‘macroscopic’ a system, the\nmore pervasive the effects of decoherence and the more complex the\nstructures that emerge through it, this is only a rule of thumb. Not\nall molecules are chiral (bound ammonia groups tend to be\nin superpositions for instance), and there is no clear-cut criterion\nfor when a system should count as macroscopic. Indeed, even apart from\nexamples like superconducting systems, there might be surprising cases\nin which not all interference effects have been suppressed by\ndecoherence even at the macroscopic level. A famous proposal by\nHameroff and Penrose (1996) links the phenomenon of consciousness with\nthe possibility of quantum superpositions within microtubules (and\ntheir subsequent active suppression via collapse); other authors\ninterpret the mathematically quantum-like effects described within\n‘quantum cognition’ as actual quantum effects (for both, see the\nentry on\n quantum approaches to consciousness).\n At present, most macroscopic quantum effects remain speculative at\nbest, but plausible cases for the continuing relevance of quantum\nsuperpositions at the macroscopic level can be found in quantum\nbiology, notably the studies of possible quantum effects in the\nnavigational system of migrating birds (Cai, Guerreschi and Briegel\n2010).", "\nCloser to home, while the classical world is recognised as having been\nall the time a dynamical pattern emerging from quantum mechanics, it\nturns out to be less classical than we might have expected. One\ninteresting example is the description of classically chaotic systems.\nA straightforward application of the techniques allowing one to derive\nNewtonian trajectories at the level of components has been employed by\nZurek and Paz (1994) to derive chaotic trajectories in\nquantum mechanics. The problem with the quantum description of chaotic\nbehaviour is that prima facie it should be impossible. Chaos\nis characterised roughly as extreme sensitivity in the behaviour of a\nsystem on its initial conditions, in the sense that the distance\nbetween the trajectories arising from different initial conditions\nincreases exponentially in time (see the entry on\n chaos).\n Since the Schrödinger evolution is unitary, it\npreserves all scalar products and all distances between quantum state\nvectors. Thus, it would seem, close initial conditions lead to\ntrajectories that are uniformly close throughout all of time, and no\nchaotic behaviour is possible (‘problem of quantum\nchaos’). The crucial point that enables Zurek and Paz’s\nanalysis is that the relevant trajectories defined by decoherence are\nat the level of components of the state of the system.\nUnitarity is preserved because the vectors in the environment, to\nwhich these different components are coupled, are and remain\northogonal: how the components themselves more specifically evolve is\nimmaterial. Explicit modelling yields a picture of quantum chaos in\nwhich different trajectories branch (a feature absent from classical\nchaos, which is deterministic) and then indeed diverge exponentially.\n(As with the crossing of trajectories in de Broglie–Bohm theory\nin\n Section 3.2,\n one has behaviour at the level of components that is qualitatively\ndifferent from the behaviour derived for wave functions of an isolated\nsystem.) The qualitative picture is the same as we mentioned above in\n Section 1.3,\n of classical trajectories that are kicked slightly off course\n(trajectories with slight kinks). In the case of classically chaotic\nsystems, however, this has a dramatic effect. This means that systems\nlike the weather turn out to be ‘branching’ all the time\ndue to decoherence interactions, so that what we usually think of as\nclassical unpredictability is in fact quantum indeterminism! (For an\nexcellent discussion, see Wallace 2012a, Chapters 3 and 10.) ", "\nAnd as we have also mentioned, quantum phenomena themselves\nare a feature of the world that emerges through decoherence (Zeh\n2003a, p. 33; see also Bacciagaluppi 2002, Section 6.2): not only the\nstability of the outcomes of laboratory measurements, and thus\n‘quantum phenomena’ in the specific sense of Bohr, but\nalso quantum jumps or the appearance of \\(\\alpha\\)-particle trajectories\nare a direct consequence of decoherence. The classical world yielded\nby decoherence is thus one (or one of many!) punctuated by quantum\nphenomena." ], "subsection_title": "4.1 The world according to decoherence" } ] } ]

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[ "\nQuantum theory is fundamental to contemporary\n physics.[1]\n It is natural to view a fundamental physical theory as describing or\nrepresenting the physical world. But many physicists and some\nphilosophers have questioned or rejected this view of quantum theory.\nThey have viewed the theory as concerned with our observation and\ndescription of, knowledge or beliefs about, or interactions with the\nworld. Views of this kind have been expressed since the 1920s when\nquantum theory emerged in close to its present form. This entry is\nconcerned with more recent developments of this tradition by\nphysicists and philosophers, much of it described as quantum-Bayesian\nor pragmatist. This entry discusses the form of quantum-Bayesianism\nknown as QBism in section 1, addressing common objections in section\n2. After section 3 briefly notes pragmatist influences on QBism\nsection 4 sketches a variety of self-described pragmatist approaches\nto quantum theory, while section 5 mentions some related views." ]

[ { "content_title": "1. QBism", "sub_toc": [ "1.1 History", "1.2 Probability", "1.3 Measurement", "1.4 Nonlocality", "1.5 Decoherence", "1.6 Generalizations of QBism" ] }, { "content_title": "2. Objections and Replies", "sub_toc": [ "2.1 Solipsist?", "2.2 Instrumentalist?", "2.3 Is QBist Quantum Theory Explanatory?", "2.4 Is the Born Rule a New Bayesian Norm?", "2.5 Is QBism too Subjective?", "2.6 Should a QBist believe that an agent prepares a physically real state?", "2.7 Other Objections and Replies" ] }, { "content_title": "3. QBism and Pragmatism", "sub_toc": [] }, { "content_title": "4. Pragmatist Views", "sub_toc": [ "4.1 Stapp", "4.2 Bächtold", "4.3 Healey" ] }, { "content_title": "5. Related Views", "sub_toc": [ "5.1 Friederich", "5.2 Brukner and Zeilinger" ] }, { "content_title": "6. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nBecause the term ‘Bayesianism’ may be understood in many\ndifferent ways, a variety of views of quantum theory could be\nconsidered Quantum-Bayesian. QBism is a form of Quantum Bayesianism\nthat may be traced back to a point of view on states and probabilities\nin quantum theory adopted by C.M. Caves, C.A. Fuchs, and R. Schack\n(2002). In its more recent incarnation (Fuchs, Mermin, & Schack\n2014) its proponents have adopted the name QBism for reasons discussed\nin\n §1.1.\n In deference to its contemporary proponents, this shorter name is\nused. Fuchs, Mermin, and Schack 2014, and DeBrota and Stacey (2019,\n Other Internet Resources)\n provide elementary introductions to QBism; Fuchs and Schack 2015, and\nFuchs and Stacey 2019 give more detailed summaries of the view; von\nBaeyer 2016 is a popular book-length introduction", "\nQBists maintain that rather than (either directly or indirectly)\nrepresenting a physical system, a quantum state represents the\nepistemic state of the one who assigns it concerning that\nagent’s possible future experiences. It does this by specifying\nthe agent’s coherent degree of belief (credence) in each of a\nvariety of alternative experiences that may result from a specific act\nthe agent may perform. To get an idea of the kinds of experience and\nact the QBist has in mind it is helpful to think of the possible\noutcomes of a quantum measurement on a physical system. But QBists\nhave proposed the extension of the view to encompass every\nexperience that may result from any action (Fuchs, Mermin,\nand Schack 2014; Mermin 2017).", "\nAs quantum theory is usually presented, the Born Rule provides an\nalgorithm for generating probabilities for alternative outcomes of a\nmeasurement of one or more observables on a quantum system. These\nprobabilities have traditionally been regarded as objective, in line\nwith the idea that the theory is irreducibly indeterministic.", "\nBy contrast, QBists hold a subjective Bayesian or personalist view of\nquantum probabilities (see entry on\n interpretations of probability).\n Taking a quantum state merely to provide input to the Born Rule\nspecifying these probabilities, they regard quantum state assignments\nas equally subjective. The quantum state assigned by an agent then\nprovides a convenient representation of an important part of his or\nher own overall state of belief. So quantum theory as a whole is\n“a users’ manual that any agent can pick up and use to\nhelp make wiser decisions in this world of inherent uncertainty”\n(Fuchs 2010, 8,\n Other Internet Resources).", "\nQBists argue that from this point of view quantum theory faces no\nconceptual problems associated with measurement or non-locality. While\nQBism has implications for the nature of physical science, from this\npoint of view quantum theory has few if any direct\nimplications for the nature of physical reality." ], "section_title": "1. QBism", "subsections": [ { "content": [ "\nContemporary QBists (Mermin 2014: 422; Fuchs 2011) have sought\nprecedents among such authorities as Erwin Schrödinger, Niels\nBohr, Wolfgang Pauli, J.A. Wheeler, and William James. But what came\nto be known as quantum-Bayesianism and later QBism began as a\ncollaboration between Caves, Fuchs, and Schack at the turn of the\n21st century (Caves, Fuchs, and Schack 2002a,b), although\nCaves no longer considers himself a QBist. N. David Mermin (2014,\n2019) became a convert more recently and has proposed extending the\nQBist vision of science to resolve at least one long-standing\nconceptual issue raised by classical physics. Stacey (2019,\n Other Internet Resources)\n tracks changes from the Quantum-Bayesianism of 2002 to the QBism of\n2019.", "\nIn conformity with standard terminology, on which the word\n“Bayesian” does not carry a commitment to denying\nobjective probability, proponents of QBism no longer take the\n“B” to refer simply to Bayesianism. Insisting that\nprobability has no physical existence even in a quantum world, they\nfollow Bruno de Finetti in identifying probability with coherent\ndegree of belief or credence. But according to Fuchs (2016,\n Other Internet Resources)\n “B” should not be taken to abbreviate\n“Brunism” since de Finetti would not have accepted all of\nQBism’s metaphysics: so “QBism” is now best\nunderstood simply as a stand-alone proper name for the view of quantum\ntheory described in what follows." ], "subsection_title": "1.1 History" }, { "content": [ "\nApplied to radioactive decay, the Born Rule of quantum theory is taken\nsuccessfully to predict such things as the half-life of the first\nexcited state of the hydrogen atom—that the probability that an\natom of hydrogen in this state will be found to have decayed to the\nground state after \\(1.1 \\times 10^{-9}\\) seconds (i.e., just over a\nbillionth of a second) is ½. This prediction has been\nexperimentally confirmed by measuring how the frequency with which\nphotons are emitted by a large number of hydrogen atoms in the decay\nof this excited state decreases over time. Most physicists regard this\nand other probabilities predicted by quantum theory as objective\nphysical features of the world, typically identifying the probability\nof decay with the relative frequency of decay as measured in such an\nexperiment.", "\nBut there are strong reasons not to equate probability with any actual\nrelative frequency (see entry\n interpretations of probability,\n §3.4). Many philosophers, including Karl Popper (1967) and David\nLewis (1986), have taken Born probabilities instead to exemplify a\ndistinctive kind of objective property (propensity or chance,\nrespectively) that may be ascribed to actual or possible individual\nevents. Lewis took quantum indeterminism to be the last hold-out of\nobjective chance.", "\nBy contrast, QBists adopt a subjectivist or personalist interpretation\nof probability, in quantum theory as elsewhere (see entry on\n interpretations of probability,\n §3.3). This makes the Born Rule of quantum theory not a law of\nnature but an empirically motivated norm of rationality a wise agent\nshould follow in addition to those whose violation would render the\nagent’s degrees of belief incoherent. As usually formulated, the\nBorn Rule specifies probabilities for various possible measurement\noutcomes given a quantum state: But QBists also adopt a subjectivist\nor personalist interpretation of quantum states.", "\nThe Schrödinger equation specifying the time development of a\nsystem’s quantum state \\(\\psi\\)", "\nis often thought of as the basic dynamical law of quantum mechanics,\nwhere \\(H\\) (called the Hamiltonian operator) is said to represent the\nsystem’s energy. Instead QBists take this equation as providing\na synchronic constraint on an agent’s credences concerning the\nagent‘s experiences at different times, and not a diachronic\nconstraint on the system’s properties at those times. QBists\nalso consider the Hamiltonian (along with all other observables)\nwithin the purview of each individual agent rather than objectively\ndetermined by the system’s properties. It follows that equally\nrational agents who assign the same quantum state to a system at a\ntime \\(t_1\\) may consistently assign it different states at a time\n\\(t_2\\) because they apply the constraint supplied by the\nSchrödinger equation in different ways.", "\nIn its usual formulation the Born Rule does not look like a normative\nconstraint on credences. QBists prefer to reformulate it purely as a\nrelation among (subjective) probabilities without reference to a\nquantum state. In the form of Equation \\((\\ref{ex2})\\) it relates\nprobabilities \\(q\\) of actual measurement outcomes \\(j\\) to\nprobabilities of outcomes of a hypothetical fiducial\nmeasurement of a special kind called a\n SIC.[2]", "\nThis equation is not just a revision of the law of total probability\nit resembles, i.e.,", "\nbecause \\(p(i)\\), \\(r(j\\mathbin{|}i)\\) in \\((\\ref{ex2})\\) refer to a\nhypothetical measurement, not the actual measurement.", "\nIn more detail, suppose an agent has degrees of belief \\(p(i)\\) that\nthe outcome of a SIC on a system would be the \\(i\\)th, and\ndegree of belief \\(r(j\\mathbin{|}i)\\) in the \\(j\\)th\noutcome of an actual measurement \\(M\\) conditional on the\n\\(i\\)th outcome for the hypothetical SIC on that system.\nThen QBists take Equation \\((\\ref{ex2})\\), stating a condition on the\nagent’s degree of belief \\(q(j)\\) that the outcome of \\(M\\) will\nbe the \\(j\\)th, as their preferred formulation of the Born\nRule. In this expression \\(d\\) stands for the dimension of the\nsystem’s Hilbert space (assumed to be a positive integer).", "\nTheir idea is that when the fiducial measurement is a SIC,\n\\(r(j\\mathbin{|}i)\\)) encodes the agent’s belief about the type\nof measurement \\(M\\), while \\(p(i)\\) encodes his or her quantum state\nfor the system on which this measurement is performed. They maintain\nthat the Born Rule in this form is an empirically motivated addition\nto probability theory—a normative requirement of quantum\nBayesian coherence (Fuchs and Schack 2013; DeBrota, Fuchs, Pienaar,\nand Stacey, 2021) that supplements the usual coherence conditions on\ndegrees of belief required to avoid a Dutch book (a set of bets an\nagent is guaranteed to lose, come what may).", "\nIt is common (at least in physical applications) to identify\nprobability 1 with objective certainty, at least for finite\nprobability spaces. Einstein, Podolsky, and Rosen (1935, EPR) made\nthis identification in the following sufficient condition for reality\nwith which they premised their famous argument for the incompleteness\nof quantum mechanical description of physical reality:", "\n\n\nIf, without in any way disturbing a system, we can predict with\ncertainty (i.e., with probability equal to unity) the value of a\nphysical quantity, then there exists an element of physical reality\ncorresponding to this physical quantity. (EPR: 777)\n", "\nQBists (Caves, Fuchs, and Schack 2007) reject this identification and\nrefute EPR’s argument that quantum description is incomplete by\ndenying this premise. Eschewing all objective physical probabilities,\nthey rather identify probability 1 with an agent’s subjective\ncertainty—full belief in a statement or event that an equally\nwell informed rational agent may believe to a lesser degree, or not at\nall." ], "subsection_title": "1.2 Probability" }, { "content": [ "\nThose who believe that a quantum state completely describes the system\nto which it is assigned and that this state always evolves linearly\n(e.g., according to the Schrödinger equation) face the notorious\nquantum measurement problem: Application of quantum theory to the\ninteraction between a quantum system and a quantum measuring device\nwould almost always leave these in a state that describes the\nmeasurement as having no outcome, contrary to the direct experience of\ncountless experimentalists (see entry on\n philosophical issues in quantum theory,\n §4).", "\nSome have followed Dirac (1930) and von Neumann (1932) in assuming\nthat a measurement is a physical process in which a quantum state\nalmost never evolves linearly but rather changes discontinuously and\nstochastically into one of a variety of possible states, each of which\nmay describe its outcome. But attempts to state precisely when such a\nprocess occurs and to verify its occurrence experimentally have been\nunsuccessful, and many understand quantum theory as excluding its\noccurrence.", "\nQBists avoid this problem by denying that a quantum state (even\nincompletely) describes the system to which it assigned. Any user of\nquantum theory assigns his or her personal quantum state on the basis\nof available information, subject only to the normative constraints of\nquantum-Bayesian coherence. This state assignment need conform neither\nto “the way that system really is”, nor to the state\nassignments of other users. Quantum mechanics is a single user theory,\nand any coincidence among states assigned by different users is just\nthat—coincidence. An agent may reassign a state on the basis of\nnewly acquired information, perhaps described as observation of the\noutcome of a measurement. When this happens, the new state is often\nnot continuous with the old state. This represents no physical\ndiscontinuity associated with measurement, but merely reflects the\nagent’s updated epistemic state in the light of experience.", "\nNevertheless, in certain circumstances different users may be expected\nto come to assign similar or even identical quantum states by updating\ntheir prior credences to take account of common (though never\nidentical) experiences, some of which each may describe as experiences\nof the outcomes of quantum measurements on systems. Because QBists\ntake the quantum state to have the role of representing an\nagent’s epistemic state they may avail themselves of personalist\nBayesian arguments purporting to show the convergence of priors on\nupdating in the light of common information. Also, just as de Finetti\nshowed that a subjectivist agent’s credences may evolve as if\nrefining estimates of an unknown objective probability, QBists (Caves,\nFuchs, and Schack 2002b) have shown that the credences of a user of\nquantum theory may evolve as if refining his or her assignment of an\nunknown objective quantum state.", "\nJ.S. Bell (2004) argued forcefully that the word\n“measurement” has no place in a formulation of quantum\nmechanics with any pretension to physical precision. QBists frequently\nuse this word in formulating their view, but unlike Bohr and his\nCopenhagen followers they do not think of a measurement as a purely\nphysical process, but as describing an agent’s action on the\nworld that results in a specific experience of it. They view quantum\ntheory not as offering descriptions of the world involving the\nimprecise physical term “measurement”, but as an\nintellectual tool for helping its users interact with the world to\npredict, control, and understand their experiences of it. Fuchs (2010,\n Other Internet Resources)\n and Mermin (2017) are quite explicit and unapologetic that a\nthoroughgoing QBist presentation of quantum theory would speak of\nagents, their actions and their experiences—all primitive terms\nthey take neither to require nor to admit of precise physical\nspecification." ], "subsection_title": "1.3 Measurement" }, { "content": [ "\nBell’s arguments (2004) have convinced some physicists and many\nphilosophers that certain patterns of correlation among spatially\nseparated events correctly predicted by quantum theory manifest\nnon-local influences between some of these events (see entry on\n action at a distance in quantum mechanics).\n QBists use their view of measurement-as-experience to reject any such\nnon-local influences.", "\nFor a QBist, what science rests on are not objective reports of\nlocalized physical events but the individual agent’s\nexperiences. Being present at a single location, at no time does an\nindividual agent experience spatially separated\n events.[3]\n Correlations taken to manifest non-local influences supposedly\nconcern events in different places—say where Alice is and where\nBob is. But Alice can only experience events where she is, not at\nBob’s distant location. When she hears Bob’s report of\nwhat he experienced at a distant location, this is an experience she\nhas where she is, not where Bob reports having had his\nexperience. So quantum theory is answerable to patterns of correlation\nnot among spatially separated physical events, but among Alice’s\n(as also among Bob’s) spatially coincident experiences. QBists\nargue that Alice, Bob, and any other agent can use quantum theory\nsuccessfully to account for her or his experiences with no appeal to\nany physical states (hidden or otherwise) or non-local physical\ninfluences." ], "subsection_title": "1.4 Nonlocality" }, { "content": [ "\nClassical mechanics is generally taken to be reducible to quantum\nmechanics, at least approximately in some appropriate limit. For\nexample, Newton’s second law of motion is sometimes said to be\nderivable from the Schrödinger equation in the limit of large\nmass. But to retrieve classical dynamics it is generally thought\nnecessary to supplement any such derivation with an account of why\nordinary macroscopic objects do not exhibit the interference behavior\ncharacteristic of quantum superpositions.", "\nQuantum models of environmental decoherence are commonly thought to\nprovide such an account (see entry on\n the role of decoherence in quantum mechanics).\n These typically involve the Schrödinger equation, this time\napplied to a system in interaction with its quantum environment. The\napplication can show how interactions entangle the quantum states of\nsystem and environment in a way that selects a “pointer\nbasis” in which the system’s reduced (mixed) state remains\nvery nearly diagonal indefinitely. Somehow a particular element of\nthis basis is supposed to be identifiable as the system’s\nphysical state, evolving in a way that approximates classical\ndynamics.", "\nIf the Schrödinger equation were a dynamical law governing the\nevolution of a physical quantum state this would provide a physical\nfoundation on which to base a reduction of classical dynamics to\nquantum dynamics that appealed to quantum decoherence. But QBists\ndeny that the Schrödinger equation is a dynamical law\ngoverning the evolution of an objective quantum state. For them it\nmerely provides a constraint on an agent’s current epistemic\nstate. Fuchs (2010,\n Other Internet Resources)\n concluded that decoherence has no role to play in the misguided\nprogram attempting to reduce classical to quantum dynamics.", "\nInstead, QBists Fuchs and Schack (2012) have viewed decoherence as a\ncondition on an agent’s present assignment of a quantum state to\na system following one contemplated measurement, when making decisions\nregarding the possible outcomes of a second measurement. As such, it\nfunctions as a normative synchronic coherence condition that may be\nseen as a consequence of van Fraassen’s (1984) Reflection\nPrinciple. Instead of taking decoherence to select possible outcomes\nof a physical measurement process, QBists take these to be just\nwhatever experiences may follow the agent’s action on the\nworld." ], "subsection_title": "1.5 Decoherence" }, { "content": [ "\nMermin (2014, 2019) has proposed extending QBism’s view of the\nrole experience in science to what he calls CBism (Classical Bohrism).\nAccording to Carnap, Einstein was seriously worried about the problem\nof the Now:", "\n\n\nthat the experience of the Now means something special for man,\nsomething essentially different from the past and the future, but that\nthis important difference does not and cannot occur within physics.\n(Carnap 1963: 37–38)\n", "\nAccording to Mermin, Einstein had nothing to worry about because there\n\\(is\\) a place in physics for the present moment. He takes the present\nmoment as something that is immediately experienced by each of us, and\nso (from a CBist perspective) just the sort of thing that physics is\nultimately about. By contrast, he says", "\n\n\nspace-time is an abstraction that I construct to organize such\nexperiences. (Mermin 2014: 422–3)\n", "\nAccording to Mermin, a common Now is an inference for each person from\nhis or her immediate experience: But that it is as fundamental a\nfeature of two perceiving subjects that when two people are together\nat an event, if the event is Now for one of them, then it is Now for\nboth.", "\nUnlike QBism, CBism is not a subjective or personalist view of states\nand probabilities in physics. But both QBism and CBism depend on a\ngeneral view of science as an individual quest to organize one’s\npast experiences and to anticipate one’s future experiences.\nThis is a view that has antecedents even in views expressed by\nphysicists generally thought of as realists, such as Einstein (1949:\n673–4) and Bell, whom Mermin (2019: 8) quotes as follows:", "\n\n\nI think we invent concepts, like “particle” or\n“Professor Peierls”, to make the immediate sense of data\nmore intelligible. (J.S. Bell, letter to R.E. Peierls,\n24-February-1983)\n" ], "subsection_title": "1.6 Generalizations of QBism" } ] }, { "main_content": [], "section_title": "2. Objections and Replies", "subsections": [ { "content": [ "\nA common reaction among those first hearing about QBism is to dismiss\nit as a form of solipsism. Mermin (2017) replies as follows:", "\n\n\nFacile charges of solipsism miss the point. My experience of you leads\nme to hypothesize that you are a being very much like myself, with\nyour own private experience. This is as firm a belief as any I have. I\ncould not function without it. If asked to assign this hypothesis a\nprobability I would choose 1.0.\nAlthough I have no direct personal access to your own experience, an\nimportant component of my private experience is the impact on me of\nyour efforts to communicate, in speech or writing, your verbal\nrepresentations of your own experience. Science is a collaborative\nhuman effort to find, through our individual actions on the world and\nour verbal communications with each other, a model for what is common\nto all of our privately constructed external worlds. Conversations,\nconferences, research papers, and books are an essential part of the\nscientific process. (84–85)\n", "\nIn his critical assessment of quantum Bayesianism, Timpson (2008)\noffers a more detailed defense against the charge of solipsism.", "\nBut even if one accepts the existence of other people and their\nexperiences, adopting QBism does seem severely to restrict one’s\napplication of quantum theory to anticipations of one’s own\nexperiences, with no implications for those of anyone else." ], "subsection_title": "2.1 Solipsist?" }, { "content": [ "\nBy portraying it as a tool for helping a user get by in an uncertain\nworld, QBism has been characterized as merely a form of\ninstrumentalism about quantum theory. But this is no reason to reject\nthe view absent arguments against such instrumentalism.", "\nInstrumentalism is usually contrasted with realism as a view of\nscience (see entry on\n scientific realism).\n The contrast is often taken to depend on opposing views of the\ncontent, aims, and epistemic reach of scientific theories. Crudely,\nthe realist takes theoretical statements to be either true or false of\nthe world, science to aim at theories that truly describe the world,\nand theories of mature science to have given us increasingly reliable\nand accurate knowledge even of things we can’t observe: While\nthe instrumentalist takes theoretical statements to be neither true\nnor false of the world, science to aim only at theories that\naccommodate and predict our observations, and theories even in mature\nscience to have given us increasingly reliable and accurate\npredictions only of things we can observe.", "\nQBism offers a more nuanced view, both of quantum theory as a theory\nand of science in general. Fuchs (2017a) adopted the slogan\n“participatory realism” for the view of science he takes\nto emerge from QBism (if not also a variety of more or less related\nviews of quantum theory). For QBism a quantum state assignment is true\nor false relative to the epistemic state of the agent assigning it,\ninsofar as it corresponds to that agent’s partial beliefs\nconcerning his or her future experiences (beliefs the agent should\nhave adopted in accordance with the Born Rule). But what makes this\nquantum state assignment true or false is not the physical world\nindependent of the agent.", "\nThe QBist does not take quantum theory truly to describe the world:\nbut (s)he does take that to be the aim of science—an\naim to which quantum theory contributes only indirectly. For\nexample, the Born Rule in the form of Equation \\((\\ref{ex2})\\).", "\n\n\nis less agent-specific than any probability assignments themselves.\nIt’s a rule that any agent should pick up and use…. it\nlives at the level of the impersonal. And because of that, the Born\nRule correlates with something that one might want to call real.\n(Fuchs 2017: 119)\n", "\nFuchs thinks one thing quantum theory has taught us about the world is\nthat it is much richer than we may have thought: as agents using\nquantum theory to make wise decisions we are not just placing bets on\nan unknown but timelessly existing future but actively\ncreating that future reality: “reality is more than any\nthird-person perspective can capture”. That is the sense in\nwhich he takes QBism to support a strong participatory realism, about\nthe world in and on which we act and about how science should describe\nit.", "\nBy contrast, Mermin 2019 draws related but possibly less radical\nconclusions about science that (perhaps contrary to his intentions)\nsome might interpret as a kind of instrumentalism or even\nphenomenalism:", "\n\n\n…science in general, and quantum mechanics in particular, is a\ntool that each of us uses to organize and make sense of\nour own private experience. p.2\n\n\nThe fact is that my science has a subject (me) as well as an object\n(my world). Your science has a subject (you) as well as an object\n(your world). ... While each of us constructs a different world, the\nworld of science is our joint construction of the vast body of\nphenomena that we try to infer, through language, to be common to our\nown individual worlds. Science arises out of our use of language to\nindicate to each other our individual experiences out of which we each\nconstruct our own individual worlds. p.5\n" ], "subsection_title": "2.2 Instrumentalist?" }, { "content": [ "\nRealists often appeal to scientific explanation when arguing against\ninstrumentalists. Quantum theory is generally acknowledged to provide\nus with a wide variety of successful explanations of phenomena we\ncan’t explain without it. Timpson (followed by Brown 2019)\nobjects that QBists cannot account for its explanatory success.", "\n\n\n… think of the question of why some solids conduct and some\ninsulate; why yet others are in between, while they all contain\nelectrons, sometimes in quite similar densities…. Ultimately we\nare not interested in agents’ expectation that matter structured\nlike sodium would conduct; we are interested in why it in fact\ndoes so. (Timpson 2008: 600)\n", "\nQBists face two problems here. In their view a user of quantum theory\ncan’t appeal to a description of objective, physical quantum\nstates in explaining the phenomena; and quantum theory’s Born\nrule outputs subjective probabilities for each user independently that\nbear not on what is objectively likely to happen but only on what\n(s)he should expect to experience, given her prior beliefs and\nexperiences.", "\nFuchs and Schack (2015) reply that explanations offered by quantum\ntheory have a similar character to explanations offered by probability\ntheory and give examples. This does not address the first problem. But\nQBists could rationalize biting that bullet by pointing to\nlong-standing problems of measurement and non-locality faced by\ninterpretations that take quantum states to be physically real that\ndon’t arise in their view. To respond to the second problem they\ncould try to develop a subjectivist view of scientific explanation as\nultimately a matter of making an economical and effective unity out of\nall an agent’s beliefs and expectations." ], "subsection_title": "2.3 Is QBist Quantum Theory Explanatory?" }, { "content": [ "\nBacciagaluppi (2014) has raised an objection against the claim that\nthe Born rule as formulated in Equation \\((\\ref{ex2})\\) states an\nempirically motivated normative addition to Bayesian coherence\nconditions. His basic objection is that QBism assumes the probability\n\\(q(j)\\) of an actual measurement outcome (as also the probability\n\\(p(j)\\) of a hypothetical measurement outcome) is independent of the\nprocedure by which this measurement is performed. That this is so\nfollows from the usual formulation of the Born Rule relating Born\nprobabilities of measurement outcomes to quantum state assignments.\nBut QBism cannot justify the procedure-independence of \\(q(j)\\) and\n\\(p(j)\\) in this way because it considers the Born Rule in the form of\nEquation \\((\\ref{ex2})\\) to be primitive, and so incapable of\nempirical support from the relation between quantum states and\noutcomes of laboratory procedures.", "\nThere are also technical problems with Equation \\((\\ref{ex2})\\), which\nassumes the existence of SICs in the relevant Hilbert space. But\ninfinite as well as finite-dimensional Hilbert spaces are used in\nquantum theory, and SICs have not (yet) been shown to exist in every\nfinite\n dimension.[4]\n Informationally-complete (but not necessarily symmetric) POVMs do\nexist in all finite dimensional spaces. Fuchs and Schack (2015) give a\nschematic alternative to Equation \\((\\ref{ex2})\\) that does not\nrequire symmetry of an informationally-complete POVM representing a\nhypothetical fiducial measurement." ], "subsection_title": "2.4 Is the Born Rule a New Bayesian Norm?" }, { "content": [ "\nThe QBist approach to quantum theory is often criticized as too\nsubjective in its treatment of quantum states, measurement outcomes,\nand probabilities.", "\nMany people assume a wave-function or state vector represents a\nphysical quantum state. On this assumption a quantum state is\nontic—a fundamental element of reality obeying the quantum\ndynamics that underlies classical dynamical laws. Bacciagaluppi (2014)\nurges QBists to accept this approach to dynamics even while\nmaintaining a subjectivist or pragmatist interpretation of\nprobability. But doing so would undercut the QBist account of\ndiscontinuous change of quantum state on measurement as simply\ncorresponding to epistemic updating.", "\nMost people take it for granted that a competently performed quantum\nmeasurement procedure has a unique, objective outcome. QBists deny\nthis, assimilating a measurement outcome to an agent’s personal\nexperience—including her experience of another agent’s\nverbal report of his outcome. QBists take a measurement outcome to be\npersonal to the agent whose action elicited it. This tenet is key both\nto QBist denial that quantum phenomena involve any nonlocal influence\n(Fuchs, Mermin and Schack 2014) and to the QBist (DeBrota, Fuchs and\nSchack 2020) resolution of the paradox of Wigner’s friend (see\nthe entry on\n Everett’s relative-state formulation of quantum mechanics).\n But their notions of experience and agency are broad enough to\nencompass personal experiences of agents other than individual,\nconscious humans.", "\nBy rejecting the objective authority of observation reports QBists\nchallenge what many have considered a presupposition of the scientific\nmethod. This rejection also threatens to undercut the standard\npersonalist argument (see entry on\n Bayesian epistemology,\n §6.2.F) that the opinions of agents with very different prior\ndegrees of belief will converge after they have accumulated sufficient\ncommon evidence.", "\nQBists consider a subjective view of quantum probability a core\ncommitment of the view, even when that probability is\n1 (Caves, Fuchs and Schack 2007). But Stairs (2011)\nand others have argued that QBist strategies for resolving conceptual\nproblems associated with non-locality may be co-opted by a qualified\nobjectivist about quantum probabilities.", "\nQBists identify probability 1 with an individual\nagent’s subjective certainty, in contrast to the objective\ncertainty EPR took to entail the existence of a physical quantity\nwhose value could be predicted with probability 1.\nStairs (2011) referred to developments of David Lewis’s (1986:\nAppendix C) best systems analysis as providing an alternative notion\nof objective probability in which this entailment fails (see entry on\n interpretations of probability,\n §3.6). So QBist subjectivism about probability is not necessary\nto block the EPR inference to an element of reality (or beable, to use\nBell’s term) grounding the objective certainty of Bob’s\ndistant measurement outcome on his component of a non-separable system\nfollowing Alice’s measurement on her component, thereby\nundercutting Bell’s proof that quantum theory is not locally\ncausal." ], "subsection_title": "2.5 Is QBism too Subjective?" }, { "content": [ "\nA QBist is convinced that an agent should take quantum mechanics as a\nguide for setting her subjective degrees of belief about the outcomes\nof future measurements. Myrvold (2020a,b) has used results of Pusey,\nBarrett and Rudolph (2012) and Barrett, Cavalcanti, Lal, and Maroney\n(2014) to argue that anyone with that conviction should also believe\nthat preparations with which she associates distinct pure quantum\nstates result in ontically distinct states of affairs, a conclusion\nthat QBists reject.", "\nHis argument depends on results proved within the ontological models\nframework of Harrigan and Spekkens (2010). Myrvold defends this\nframework as merely codifying a form of reasoning implicit in much of\nscience and daily life which there is no good reason to reject when\napplied in the quantum domain. One reasons that an action on a\nphysical system affects what one will experience later only via the\nphysical transmission of that action’s effect from the system to\nevents one later experiences. If so, then the action of preparing a\nsystem’s quantum state must affect some physical property of the\nsystem reflected in what the framework calls its ontic state.", "\nIn response, QBists insist that quantum states have no ontic hold on\nthe world and that the QBist notion of quantum indeterminism is a far\nmore radical variety than anything proposed in the quantum debate\nbefore because it says that nature does what it wants, without a\nmechanism underneath (Fuchs 2017b, p. 272; 2018, p. 19). The QBist\nSchack rejects Myrvold’s form of reasoning in the quantum domain\nas follows (Schack 2018).", "\n\n\nThere are no laws that determine objective probabilities for\nmeasurement outcomes. The world does not evolve according to a\nmechanism.\n" ], "subsection_title": "2.6 Should a QBist believe that an agent prepares a physically real state?" }, { "content": [ "\nOther objections to QBism may be found in Brown (2019) and Zwirn\n(forthcoming).", "\nAccording to Brown (2019, p. 75) “…a variant of\nBerkeleyan idealism suffuses QBism.” QBists insist on the\nexistence of a real world in which agents and their experiences are\nembedded, along with rocks, trees and everything else in the usual\nworld of common experience. But they deny that quantum mechanics\nitself describes this world, while hoping eventually to infer more\nabout it from our successful use of quantum mechanics to anticipate\neach of our experiences when acting on it. Brown objects to the\ncurrently ineffable character of the world for a QBist, contrasting\nthis unfavorably with the way a realist about a quantum state can use\nit to describe the physical world and explain how it gives rise to our\nexperiences by affecting our brains.", "\nBrown also objects to the QBists’ understanding of the\nSchrödinger equation, assuming they consider this to track\nchanges not in the physical state of a quantum system but in what an\nagent believes she is likely to experience were she to act on it. But\nQBists understand this equation as a normative constraint on an\nagent’s belief state at a single time, not as a constraint on\nhow that state evolves (see\n §1.2).", "\nBrown further questions QBist entitlement to divide up the external\nworld, either into subsystems or spatiotemporally, complaining that\n“That part of QBism which relates to ‘a theory of\nstimulation and response’ between the agent and the world is not\ngrounded in known physics.” (2019, p. 81)", "\nBarzegar (2020) has replied to Brown’s objections. His reply\nincludes a defense of a claim by Fuchs (2017, p. 118) that Brown\n(2019) sought to refute––the claim that QBism is pursuing\nEinstein’s (1949) program of “the real”.", "\nFollowing a largely sympathetic sketch of QBism, Zwirn (forthcoming,\n§10) highlights ways in which some of its key notions remain\nunclear. Regarding quantum mechanics as an extension of subjective\nprobability theory, QBists (DeBrota and Stacey (2019), see\n Other Internet Resources)\n reject the demand to provide a reductive definition of the notion of\nan agent. Zwirn presses this demand because in this context the agent\nis not merely a passive witness: “It is the interaction between\nan agent and the external world that creates a result. Without agent,\nthere is no result.”", "\nZwirn (forthcoming) also challenges QBists to clarify their key\nconcepts of world and experience: “QBism\nendorses the existence of an external world independent of any agent,\nbut it is not clear if the external world is unique and shared by all\nagents or if each agent has her own external world.”", "\nZwirn believes that his own view of Convivial Solipsism (Zwirn 2016,\n2020) improves on QBism because it provides clear answers to these\nchallenging questions. In his view an agent is something whose\nconscious experiences are produced by a common external physical\nworld, but organized into that agent’s personal external\nworld." ], "subsection_title": "2.7 Other Objections and Replies" } ] }, { "main_content": [ "\nMost QBists are physicists rather than philosophers. But Fuchs locates\nQBism in the tradition of classical American pragmatism (see entry on\n pragmatism).\n While quoting Peirce and referring to Dewey, Fuchs (2011; 2016, Other\nInternet Resources) acknowledges especially the influence of William\nJames’s ideas of pure experience and an open and pluralistic\nuniverse in which “new being comes in local spots and patches\nwhich add themselves or stay away at random, independently of the\nrest” (2016, 9, Other Internet Resources). Mermin’s CBist\nintroduction of the “Now” into physics and Fuchs’s\nchoice of title for his 2014 (Other Internet Resources) both show\naffinity with James’s reaction against what he called the\nblock-universe (see entry\n being and becoming in modern physics).\n Moreover, they both credit the influence on QBism of Niels Bohr. Bohr\nhimself never acknowledged pragmatist influences on his view of\nquantum theory. But in a late\n interview[5]\n he expressed enthusiasm for James’s conception of\nconsciousness, and he was almost certainly acquainted with some of\nJames’s ideas by the Danish philosopher Høffding, a\nfriend and admirer of James." ], "section_title": "3. QBism and Pragmatism", "subsections": [] }, { "main_content": [ "\nPragmatists agree with QBists that quantum theory should not be\nthought to offer a description or representation of physical reality:\nin particular, to ascribe a quantum state is not to describe physical\nreality. But they deny that this makes the theory in any way\nsubjective. It is objective not because it faithfully mirrors the\nphysical world, but because every individual’s use of the theory\nis subject to objective standards supported by the common knowledge\nand goals of the scientific community. So an individual’s\nassignment of a quantum state may be correct (or incorrect) even\nthough no quantum state is an element of physical reality; Born\nprobabilities are similarly objective; and measurement is a physical\nprocess with a unique objective outcome, albeit\nepistemically-characterized." ], "section_title": "4. Pragmatist Views", "subsections": [ { "content": [ "\nIn attempting to clarify the Copenhagen interpretation of quantum\ntheory, Stapp called it pragmatic and used James’s views on\ntruth and experience to provide an appropriate philosophical\nbackground for the Copenhagen interpretation “which is\nfundamentally a shift to a philosophic perspective resembling that of\nWilliam James” (1972: 1105).", "\nThe significance of this viewpoint for science is its negation of the\nidea that the aim of science is to construct a mental or mathematical\nimage of the world itself. According to the pragmatic view, the proper\ngoal of science is to augment and order our experience. (Stapp 1972:\n1104)", "\nHe follows Bohr (1958), Landau and Lifshitz (1977), and others in\ninsisting on the objective character of quantum measurements, taking\n“our experience” not as individual and subjective but as\nconstituted by physical events, on whose correct description in the\neveryday language of the laboratory we can (and must) all agree if\nphysical science is to continue its progress." ], "subsection_title": "4.1 Stapp" }, { "content": [ "\nBächtold (2008a,b) takes an approach to quantum theory he calls\npragmatist. Quoting C.S. Peirce’s pragmatic maxim, he offers\nwhat he calls pragmatic definitions of terms used by researchers in\nmicrophysics, including “preparation”,\n“measurement”, “observable”, and\n“microscopic system”. His “pragmatist”\napproach to interpreting a theory is to isolate the pragmatic\nfunctions to be fulfilled by successful research activity in\nmicrophysics, and then to show that quantum theory alone fulfills\nthese functions.", "\nWhile acknowledging that his interpretation has an instrumentalist\nflavor, in his 2008a he distinguishes it from the instrumentalism of\nPeres (1995) and others, who all (allegedly) claim some metaphysical\nideas but seek to remove the expression “microscopic\nsystem” from the vocabulary used by quantum physicists. By\ncontrast, his “pragmatic definition” of that expression\nlicenses this usage, taking “quantum system” to refer to a\nspecified set of preparations.", "\nBächtold (2008b: chapter 2) elaborates on his pragmatist\nconception of knowledge, appealing to a variety of philosophical\nprogenitors, including Peirce, James, Carnap, Wittgenstein, Putnam,\nand Kant. But his overall approach to quantum theory has strong\naffinities with operationalist approaches to the theory." ], "subsection_title": "4.2 Bächtold" }, { "content": [ "\nIn recent work, Healey (2012a,b, 2017a,b, 2020) has also taken what he\ncalls a pragmatist approach to quantum theory. He contrasts this with\ninterpretations that attempt to say what the world would (or could) be\nlike if quantum theory were true of it. On his approach quantum states\nare objective, though a true quantum state assignment does not\ndescribe or represent the condition or behavior of a physical system.\nBut quantum states are relational: Different agents may correctly and\nconsistently assign different quantum states to the same system in the\nsame circumstances—not because these represent their subjective\npersonal beliefs, but because each agent has access to different\nobjective information backing these (superficially conflicting) state\nassignments. Each such assignment may be said to correctly represent\nobjective probabilistic relations between its backing conditions and\nclaims about values of magnitudes.", "\nOn this approach, quantum theory is not about agents or their states\nof belief: and nor does it (directly) describe the physical world. It\nis a source of objectively good advice about how to describe\nthe world and what to believe about it as so described. This advice is\ntailored to meet the needs of physically situated, and hence\ninformationally-deprived, agents like us. It is good because the\nphysical world manifests regular statistical patterns the right Born\nprobabilities help a situated agent to predict and explain. But the\nadvice is available even with no agents in a position to benefit from\nit: there are quantum states and Born probabilities in possible worlds\nwith no agents.", "\nBorn probabilities are neither credences nor frequencies. They are\nobjective because they are authoritative. Setting credences equal to\nBorn probabilities derived from the correct quantum state for one in\nthat physical situation is a wise epistemic policy for any agent in a\nworld like ours. Born probabilities are equally objective even when\nthey differ more radically from Lewis’s (1986) chances because\nthey are based on more (physically) limited information.", "\nHealey’s approach is pragmatist in several respects. It\nprioritizes use over representation in its general approach to quantum\ntheory; its account of probability and causation is pragmatist, in\nquantum theory and elsewhere; and it rests on a theory of content that\nBrandom (2000) calls inferentialist pragmatism. While not endorsing\nany pragmatist identification of truth with “what works”,\nin its deflationary approach to truth and representation it follows\nthe contemporary pragmatist Huw Price (2003, 2011). Healey (2020)\nargues for a conception of realism according to which this pragmatist\napproach is realist rather than anti-realist.", "\nIndependently of similar suggestions by Bacciagaluppi (2014) and\nStairs (2011), Healey co-opts some QBist strategies for dissolving the\nmeasurement problem and removing worries about non-locality, while\nrejecting the accompanying subjectivism about quantum states, Born\nprobabilities, and measurement outcomes.", "\nWhile QBists take quantum state assignments to be subject only to the\ndemand that an agent’s degrees of belief be coherent and conform\nto Equation \\((\\ref{ex2})\\), Healey takes these to be answerable to\nthe statistics of objective events, including (but not restricted to)\noutcomes of quantum measurements. This makes the objective existence\nof quantum states independent of that of agents even though their main\nfunction is as a source of good advice to any agents there happen to\nbe. And it makes quantum states relative, not to the epistemic\nsituation of actual agents, but to the physical situation of actual\nand merely hypothetical agents.", "\nWhile QBists follow de Finetti in taking all probabilities to be\ncredences of actual agents, Healey’s pragmatist takes\nprobabilities to exist independently of the existence of agents but\nnot to be physical propensities or frequencies, nor even to supervene\non Lewis’s Humean mosaic (see entry on\n David Lewis\n §5). There are probabilities insofar as probability statements\nare objectively true, which they may be when sensitive to though not\ndetermined by physical facts.", "\nThere is no measurement problem since reassignment of quantum state on\nmeasurement is not a physical process but corresponds to\nrelativization of that state to a different physical situation from\nwhich additional information has become physically accessible to a\nhypothetical agent so situated.", "\nThere is no instantaneous action at a distance in a quantum world,\ndespite the probabilistic counterfactual dependencies between\nspace-like separated events such as (macroscopic) outcomes of\nmeasurements confirming violation of Bell inequalities. On a\npragmatist approach, these dependencies admit no conceptual\npossibility of intervention on one outcome that would alter (any\nrelevant probability of) the other. So there is no instantaneous\nnon-local influence, in conformity to Einstein’s principle of\nlocal action.", "\nOn Healey’s pragmatist approach, an application of the Born rule\ndirectly specifies probabilities for claims about the values of\nphysical magnitudes (dynamical variables of classical physics as well\nas new variables such as strangeness and color): it does not\nexplicitly specify probabilities for measurement outcomes. But the\nBorn rule is legitimately applied only to claims with sufficiently\nwell-defined content. The content of a claim about the value of a\nphysical magnitude on a system depends on how the system interacts\nwith its environment. Quantum theory may be used to model such\ninteraction. Only if a system’s quantum state is then stably\ndecohered in some basis (see entry on\n the role of decoherence in quantum mechanics)\n do claims about the value of the associated “pointer\nmagnitude” acquire a sufficiently well-defined content to\nlicense application of the Born rule to them. Because of this\nrestriction on its legitimate application, the Born rule may be\nconsistently applied to claims of this form (not just to claims about\nthe outcomes of measurements) without running afoul of no-go results\nsuch as that of Kochen and Specker (see entry on\n the Kochen-Specker theorem).", "\nWhat endows a claim (e.g., about the value of a magnitude) with\ncontent is the web of inferences in which it is located. Such a claim\nhas a well-defined content if many reliable inferences link it to\nother claims with well-defined content. It is the nature of a\nsystem’s interaction with its environment that determines which\ninferences to and from a magnitude claim about it are reliable.\nQuantum decoherence and inferentialist pragmatism work together here\nto make objective sense of the Born rule with no need to mention\nmeasurement: Though of course at some stage all actual measurements do\ninvolve interactions with an environment well modeled by quantum\ndecoherence.", "\nContra to Mermin’s view (see\n §1.6),\n concepts are not invented by each of us to make his or her experience\nmore intelligible. They acquire content from the social practice of\nlinguistic communication about a physical world that perception\nrepresents (to humans as well as organisms with no capacity for\nlanguage) as independently existing.", "Jansson (2020) challenges the claim of Healey’s\npragmatist approach to offer objective explanations of phenomena,\nwhile acknowledging the attractions of a position that seeks to occupy\nthe middle ground between explanation seeking realism and prediction\nfocused instrumentalism. She concludes (2020: 165) that", "\n\n\nMany explanations according to this approach to quantum theory seem to\nat least partially black-box crucial information about the physical\nground for the appropriate assignment of quantum states or\napplications of the Born rule. …neither quantum states nor the\nBorn rule can act as initial explanatory input. While this is a\nserious cost, it is not clear that a pragmatist approach to quantum\ntheory has to resist this conclusion.\n", "\nOne taking Healey’s pragmatist approach to quantum theory could\nreply as follows (see Healey 2020, §7.7). The primary target of\nan explanatory application of quantum theory is not a collection of\nevents but a probabilistic phenomenon they manifest. A probabilistic\nphenomenon is a probabilistic data model of a statistical regularity.\nOne explains the phenomenon by demonstrating how the probabilities of\nthe model are a consequence of the Born rule, as applied to events\nthat manifest the regularity. Since the explanandum is not\nitself a physical condition, it is inappropriate to demand a physical\nexplanans (such as a physically real quantum state). But the\ndemonstration is explanatory only if each event manifesting the\nregularity itself depended on whatever physical conditions obtained,\nincluding whatever conditions backed assignment of the quantum state\ninput to the Born rule. One can have good evidence for such backing\nconditions while unable to specify exactly what they are. The more\ncomplete the description of the physical conditions on which each\nevent manifesting the regularity depended, the better the explanation\nof the probabilistic phenomenon they manifest.", "\nLewis (2020) raises concerns about Healey’s application of\ninferentialist pragmatism to the content of claims in quantum theory\nand its applications. His first worry concerns the distinction between\nthe prescriptive content of quantum claims (about the quantum state,\nfor example) and descriptive non-quantum claims about magnitudes like\nposition and energy.", "\nBut, as he notes, a claim’s having a distinctive prescriptive\nfunction does not show that it has no representational content. A\npragmatist could reply that a quantum state represents something other\nthan an “element of physical reality” while functioning to\nprescribe credences about such elements: Healey (2017a) suggests that\na quantum state represents probabilistic relations between them.", "\nLewis’s second worry is that Healey’s position fails to\nadequately take into account the role of conditional or counterfactual\ninferences in conferring content both on quantum, and on non-quantum\nmagnitude, claims. Through its prescriptive role in applications of\nthe Born rule, Lewis maintains, a claim about a quantum state or a\nmagnitude implies many counterfactual probabilistic claims about\nmagnitudes. For an inferentialist then, quantum claims and magnitude\nclaims derive content from the corresponding inferences.", "\nOn Healey’s (2017, pp. 208–210) pragmatist approach, a\nclaim assigning a quantum state does derive much of its content from\ninferences involving counterfactuals. The inference is to a\ncounterfactual whose antecedent is (or supervenes on) a claim about\nmagnitudes, and whose consequent specifies a probability as great as\n1 for a different magnitude claim that is meaningful\nin these counterfactual circumstances. Healey could argue that the\nmagnitude claims Lewis considers do not derive content from his\ncorresponding counterfactuals, on the grounds that they do not\nmaterially imply those counterfactuals and so in quantum theory an\ninference from the claim to the counterfactual is not reliable.\nAccording to Healey’s inferentialist pragmatism, only reliable\nmaterial inferences confer content. Magnitude claims about the\ntrajectory of a molecule might be meaningful and true according to an\nalternative theory such as\n Bohmian mechanics.\n But in Healey’s pragmatist view (2012b, pp. 1547–8), even\nan imprecise claim about the location and velocity of a molecule is\ntrue only in a situation that can be modeled by decoherence of a kind\nthat would block the inference to the counterfactual.", "\nLewis’s final worry is that this application of inferentialist\npragmatism renders the content of a claim highly sensitive to the\nphysical environment of the system concerned. He correctly notes that,\non this pragmatist approach, quantum theory requires acknowledgement\nof radical changes to physical concepts that do not flow from other\napplications of pragmatism.", "\nOne taking Healey’s pragmatist approach might respond to this\nworry by noting that these conceptual changes are a straightforward\nconsequence of the application of inferentialist pragmatism to quantum\ntheory. For an inferentialist pragmatist, a material inference can\ncontribute to the content of a claim only if it is reliable, but in\nthe quantum domain physical inferences of a sort we all make in\neveryday life fail dramatically. The sensitivity of physical concepts\nto a system’s physical environment is arguably the natural\nresult of reconfiguring our physical concepts to restore the\nreliability of inferences involving them." ], "subsection_title": "4.3 Healey" } ] }, { "main_content": [ "\nThe view that a quantum state describes physical reality is sometimes\ncalled \\(\\psi\\)-ontic, by contrast with a \\(\\psi\\)-epistemic view that\nit represents an agent’s incomplete information about an\nunderlying physical state. When Harrigan and Spekkens (2010)\noriginally defined these terms they applied them only to what they\ncalled ontic models of quantum theory. But others have since used them\nmore broadly to classify alternative views of quantum states outside\nof the ontological models framework. QBists and pragmatists are not\nthe only ones to adopt a view that is neither \\(\\psi\\)-ontic nor\n\\(\\psi\\)-epistemic in these broader senses. Other views share the\npragmatist thought that quantum states aren’t a function of any\nagent’s actual epistemic state because quantum state assignments\nare required to conform to objective standards of correctness. This\nsection covers two such views." ], "section_title": "5. Related Views", "subsections": [ { "content": [ "\nFriederich (2011, 2015) favors what he calls a therapeutic approach to\ninterpreting quantum theory, taking his cue from the later philosophy\nof Ludwig Wittgenstein. This approach grounds the objectivity of\nquantum state assignments in the implicit constitutive rules governing\nthis practice. Those rules determine the state an agent has to assign\ndepending on her knowledge of the values of observables, perhaps\nobtained by consulting the outcome of their measurement on the system.\nFriederich agrees with Healey that differently situated agents may\ntherefore have to assign different states to the same system in the\nsame circumstances insofar as their situations permit some to consult\noutcomes inaccessible to others, and makes the point by saying a\nsystem is not \\(in\\) whichever quantum state it is assigned.", "\nFriederich treats quantum probabilities as rational quasi-Lewisian\nconstraints on credence and, together with his relational account of\nquantum states, this enables him to refute the claim that Bell’s\ntheorem demonstrates instantaneous action at a distance. He uses (what\nhe calls) his epistemic conception of quantum states to dissolve the\nmeasurement problem by denying that an entangled superposition of\nsystem and apparatus quantum states is incompatible with the\noccurrence of a definite, unique outcome. Like Healey, he appeals to\ndecoherence in picking out the particular observable(s) a suitable\ninteraction may be considered to measure.", "\nSo far Friederich’s therapeutic approach parallels\nHealey’s pragmatist approach (though there are significant\ndifferences of detail, especially as regards their treatments of\nprobability and causation). But Friederich rejects Healey’s\ninferentialist account of the content of claims about the values of\nphysical magnitudes, taking restrictions on legitimate applications of\nthe Born Rule to follow directly from the constitutive rules governing\nits use rather than from the need to apply it only to magnitude claims\nwith well-defined content. And Friederich seriously explores the\npossibility that a set of magnitude claims collectively assigning a\nprecise value to all dynamical variables may be not only\nmeaningful but true together. His idea is that the constitutive rules\ngoverning the Born Rule may forbid any attempt to apply the rule in a\nway that would imply the existence of a non-contextual probability\ndistribution over their possible values, thus avoiding conflict with\nno-go theorems like that of Kochen and Specker." ], "subsection_title": "5.1 Friederich" }, { "content": [ "\nBrukner and Zeilinger (2003), Zeilinger (2005) follow Schrödinger\n(1935) and many others in viewing a quantum state as a catalogue of\nour knowledge about a system. Their view is not \\(\\psi\\)-epistemic\nbecause it denies that the system has an ontic state about\nwhich we may learn by observing it. Instead, a system is characterized\nby its information content. An elementary system contains information\nsufficient to answer one question. For a spin ½ system, a\nquestion about spin component in any direction may be answered by a\nsuitable observation. But the answer cannot typically be understood as\nrevealing the pre-existing value of spin-component in that direction,\nand answering this question by observation randomizes the answer to\nany future question about spin-component in different directions. So\nthe catalog of knowledge takes the form of a probability distribution\nover possible answers to all meaningful question about a quantum\nsystem that contains only one entry with probability 1 that might be\nconsidered a property that would be revealed if observed.", "\nBrukner (2018) has recently used an extension of Wigner’s friend\nparadox (Wigner 1962) to argue that even the answers to such questions\ngiven by observation cannot be regarded as reflecting objective\nproperties of the devices supposedly recording them. If sound, such an\nargument provides a reason to modify this view of quantum states to\nmake it closer to that of QBists." ], "subsection_title": "5.2 Brukner and Zeilinger" } ] }, { "main_content": [ "\nA variety of QBist and pragmatist views of quantum theory have been\nproposed since quantum theory assumed close to its present form. In\nrecent years this has been an active area of research especially by\nphilosophically aware physicists working in quantum foundations.\nPhilosophers have tended to dismiss such approaches, objecting to\ntheir instrumentalism and/or anti-realism. But there is much to learn\nfrom responses to such objections and good philosophical\nreasons to take these views more seriously." ], "section_title": "6. Conclusion", "subsections": [] } ]

[ "Bacciagaluppi, Guido, 2014, “A Critic Looks at QBism”,\nin M.C. Galavotti, S. Hartmann, M. Weber, W. Gonzalez, D. Dieks, and\nT. Uebel (eds.), New Directions in the Philosophy of Science,\nSwitzerland: Springer International, pp. 403–415.", "Bächtold, Manuel, 2008a, “Interpreting Quantum\nMechanics According to a Pragmatist Approach”, Foundations\nof Physics, 38(9): 843–68.\ndoi:10.1007/s10701-008-9240-2", "–––, 2008b, L’Interprétation de\nla Mécanique Quantique: une approche pragmatiste, Paris:\nHermann.", "Barrett, Jonathan, Cavalcanti, Eric. G., Lal, Raymond, and\nMaroney, Owen J.E., 2014, “No \\(\\psi\\)-epistemic Model Can Fully\nExplain the Indistinguishability of Quantum States ”,\nPhysical Review Letters 112, 250403.", "Barzegar, Ali, 2020, “QBism Is Not So Simply\nDismissed”, Foundations of Physics, 50(7):\n693–707. doi:10.1007/s10701-020-00347-3", "Bell, John S., 2004, Speakable and Unspeakable in Quantum\nMechanics: Collected Papers on Quantum Philosophy, 2nd\nedition, Cambridge: Cambridge University Press.", "Bohr, Niels, 1958, The Philosophical Writings of Niels Bohr\nVolume II: Essays 1932–57 on Atomic Physics and Human\nKnowledge, Woodbridge, CT: Ox Bow Press, 1987.", "Brandom, Robert B., 2000, Articulating Reasons: An\nIntroduction to Inferentialism, Cambridge, MA: Harvard University\nPress.", "Brown, Harvey R., 2019, “The Reality of the Wavefunction:\nOld Arguments and New”, in Philosophers Look at Quantum\nMechanics, Alberto Cordero (ed.), Cham: Springer Nature, pp.\n63–86.", "Brukner, Časlav, 2018, “A No-Go Theorem for\nObserver-Independent Facts”, Entropy, 20(350):\n1–10.", "Brukner, Časlav and Anton Zeilinger, 2003, “Information\nand Fundamental Elements of the Structure of Quantum Theory”, in\nTime, Quantum and Information, Lutz Castell and Otfried\nIschebeck (eds.), Berlin: Springer, pp. 323–54.\ndoi:10.1007/978-3-662-10557-3_21", "Carnap, Rudolph, 1963, “Intellectual Biography”, in\nPaul Arthur Schilpp (ed.), The Philosophy of Rudolph Carnap,\nLa Salle, IL.: Open Court, pp. 3–84.", "Caves, Carlton M., Christopher A. Fuchs and Rüdiger Schack,\n2002a, “Quantum Probabilities as Bayesian Probabilities”,\nPhysical Review A, 65(022305): 1–6.\ndoi:10.1103/PhysRevA.65.022305", "–––, 2002b, “Unknown Quantum States: the\nQuantum de Finetti Representation”, Journal of Mathematical\nPhysics, 43(9): 4537–4559. doi:10.1063/1.1494475", "–––, 2007, “Subjective Probability and\nQuantum Certainty”, Studies in History and Philosophy of\nModern Physics, 38(2): 255–74.\ndoi:10.1016/j.shpsb.2006.10.007", "DeBrota, John B., Fuchs, Christopher A. and Schack, Rüdiger,\n2020, “Respecting One’s Fellow: QBism’s Analysis of\nWigner’s Friend”, Foundations of Physics, 50:\n1859–1874. doi.org/10.1007/s10701-020-00369-x", "DeBrota, John B., Fuchs, Christopher A., Pienaar, Jacques L. and\nStacey, Blake C., 2021, “Born’s Rule as a Quantum\nExtension of Bayesian Coherence”, Physical Review A,\n104(022207): 1–12. doi.org/10.1103/PhysRevA.104.022207", "Dirac, Paul A.M., 1930, The Principles of Quantum\nMechanics, Cambridge: Cambridge University Press.", "Einstein, Albert, 1949, “Remarks Concerning the Essays\nBrought Together in This Co-operative Volume”, in Albert\nEinstein: Philosopher-Scientist, La Salle, IL: Open Court, pp.\n665–688.", "Einstein, Albert, Boris Podolsky, & Nathan Rosen, 1935 [EPR],\n“Can Quantum-Mechanical Description of Physical Reality be\nConsidered Complete?” Physical Review, 47(10):\n777–80. doi:10.1103/PhysRev.47.777", "Friederich, Simon, 2011, “How to Spell Out the Epistemic\nConception of Quantum States”, Studies in History and\nPhilosophy of Modern Physics, 42(3): 149–157.\ndoi:10.1016/j.shpsb.2011.01.002", "–––, 2015, Interpreting Quantum Theory: a\nTherapeutic Approach, London: Palgrave MacMillan.\ndoi:10.1057/9781137447159", "Fuchs, Christopher A., 2011, Coming of Age With Quantum\nInformation: Notes on a Paulian Idea, Cambridge: Cambridge\nUniversity Press.", "–––, 2017a, “On Participatory\nRealism”, in I. Durham and D. Rickles (eds.), Information\nand Interaction. The Frontiers Collection, Cham: Springer, pp.\n113–134. doi:10.1007/978-3-319-43760-6_7", "–––, 2017b, “Notwithstanding Bohr, the\nReasons for QBism”, Mind and Matter, 15(2):\n245–300.", "Fuchs, Christopher A., N. David Mermin, and Rüdiger Schack,\n2014, “An Introduction to QBism with an Application to the\nLocality of Quantum Mechanics”, American Journal of\nPhysics, 82(8): 749–54. doi:10.1119/1.4874855", "Fuchs, Christopher A. & Rüdiger Schack, 2012,\n“Bayesian Conditioning, the Reflection Principle, and Quantum\nDecoherence” in Yemima Ben-Menahem and Meir Hemmo (eds.),\nProbability in Physics, Berlin: Springer, pp. 233–247.\ndoi:10.1007/978-3-642-21329-8_15", "–––, 2013, “Quantum-Bayesian\nCoherence”, Reviews of Modern Physics 85(4):\n1693–1715. doi:10.1103/RevModPhys.85.1693", "–––, 2015, “QBism and the Greeks: Why a\nQuantum State Does Not Represent An Element of Physical\nReality”, Physica Scripta, 90(1): 015104.\ndoi:10.1088/0031-8949/90/1/015104\n [Fuchs and Schack 2015 available online]", "Fuchs, Christopher A, & Stacey, Blake C., 2019, “QBism:\nQuantum Theory as a Hero’s Handbook”, in Foundations\nof Quantum Theory, E.M. Rasel, W.P. Schleich, and S. Wölk\n(eds.), Amsterdam, Oxford, Tokyo, Washington D.C.: IOS Press, pp.\n133–202.\n [Fuchs and Stacey 2019 available online]", "Harrigan, Nicholas & Robert W. Spekkens, 2010,\n“Einstein, Incompleteness and the Epistemic View of Quantum\nStates”, Foundations of Physics, 40(2):125–57.\ndoi:10.1007/s10701-009-9347-0", "Healey, Richard, 2012a, “Quantum Theory: A Pragmatist\nApproach”, British Journal for the Philosophy of\nScience, 63(4): 729–771. doi:10.1093/bjps/axr054", "–––, 2012b, “Quantum Decoherence in a\nPragmatist View: Dispelling Feynman’s Mystery”,\nFoundations of Physics, 42: 1534–1555,\ndoi:10.1007/s10701–012–9681–5", "–––, 2017a, “Quantum States as Objective\nInformational Bridges”, Foundations of Physics, 47(2):\n161–173. doi:10.1007/s10701–015–9949–7", "–––, 2017b, The Quantum Revolution in\nPhilosophy, Oxford: Oxford University Press.", "–––, 2020, “Pragmatist Quantum\nRealism”, in Scientific Realism and the Quantum, Steven\nFrench and Juha Saatsi (eds.), Oxford: Oxford University Press, pp.\n123–46.", "Jansson, Lina, 2020, “Can Pragmatism about Quantum Theory\nHandle Objectivity about Explanations?”, in Scientific\nRealism and the Quantum, Steven French and Juha Saatsi (eds.),\nOxford: Oxford University Press, pp. 147–67.", "Landau, L.D. & E.M. Lifshitz, 1977, Quantum\nMechanics, 3rd edition, Oxford: Pergamon Press.", "Lewis, David K., 1986, “A Subjectivist’s Guide to\nObjective Probability”, Philosophical Papers (Volume\nII), Oxford: Oxford University Press, pp. 83–132.\ndoi:10.1093/0195036468.003.0004", "Lewis, Peter J., 2020, “Quantum Mechanics and its\n(Dis)Contents”, in Scientific Realism and the Quantum,\nSteven French and Juha Saatsi (eds.), Oxford: Oxford University Press,\npp. 168–82.", "Mermin, N. David, 2014, “QBism Puts the Scientist Back into\nScience”, Nature, 507(7493): 421–3.\ndoi:10.1038/507421a", "–––, 2017, “Why QBism is Not the\nCopenhagen Interpretation and What John Bell Might Have Thought of\nIt”, in Bertlmann and Zeilinger 2017: 83–93.", "–––, 2019, “Making Better Sense of Quantum\nMechanics”, Reports on Progress in Physics, 82(012002):\n1–16.", "Myrvold, Wayne, 2020a, “On the Status of Quantum State\nRealism”, in Scientific Realism and the Quantum, Steven\nFrench and Juha Saatsi (eds.), Oxford: Oxford University Press, pp.\n229–51.", "–––, 2020b, “Subjectivists About Quantum\nProbabilities Should Be Realists About Quantum States”, in\nQuantum, Probability, Logic, Meir Hemmo and Orly Shenker\n(eds.), Springer Nature Switzerland, pp. 449–65.", "Peres, Asher, 1995, Quantum Theory: Concepts and Methods,\nDordrecht: Kluwer Academic.", "Popper, Karl R., 1967, “Quantum Mechanics Without the\nObserver”, in Mario Bunge (ed.), Quantum Theory and\nReality, New York: Springer, pp. 7–44.", "Price, Huw, 2003, “Truth as Convenient Friction”,\nThe Journal of Philosophy, 100(4): 167–190.", "–––, 2011, Naturalism without Mirrors,\nNew York and Oxford: Oxford University Press.", "Pusey, Matthew A., Barrett, Jonathan., and Rudolph, Terry, 2012,\n“On the Reality of the Quantum State”, Nature\nPhysics, 8: 475–78.", "Renes, Joseph M., Robin Blume-Kohout, Andrew James Scott, &\nCarlton M. Caves, 2004, “Symmetric Informationally Complete\nQuantum Measurements”, Journal of Mathematical Physics,\n45(6): 2171–80. doi:10.1063/1.1737053", "Stairs, Allen, 2011, “A Loose and Separate Certainty: Caves,\nFuchs and Schack on Quantum Probability One”, Studies in\nHistory and Philosophy of Modern Physics, 42(3):\n158–166.", "Stapp, Henry Pierce, 1972, “The Copenhagen\nInterpretation”, American Journal of Physics, 40(8):\n1098–1116. doi:10.1119/1.1986768", "Schrödinger, E., 1935, “Discussion of Probability\nRelations Between Separated Systems”, Mathematical\nProceedings of the Cambridge Philosophical Society, 31(4):\n555–63. doi:10.1017/S0305004100013554", "Timpson, Christopher Gordon, 2008, “Quantum Bayesianism: A\nStudy”, Studies in History and Philosophy of Modern\nPhysics, 39(3): 579–609.\ndoi:10.1016/j.shpsb.2008.03.006", "van Fraassen, C., 1984, “Belief and the Will”,\nJournal of Philosophy, 81(5): 235–56.\ndoi:10.2307/2026388", "von Baeyer, Hans Christian, 2016, QBism: the Future of Quantum\nPhysics. Cambridge, MA: Harvard University Press.", "von Neumann, John, 1932, Mathematische Grundlagen der\nQuantenmechanik, Berlin: Julius Springer. First English edition\nMathematical Foundations of Quantum Mechanics, Princeton:\nPrinceton University Press, 1955.", "Wigner, Eugene, 1962, “Remarks on the Mind-Body\nProblem”, in I.J. Good (ed.), The Scientist Speculates: An\nAnthology of Partly-Baked Ideas, London: Heinemann, pp.\n284–302.", "Zeilinger, Anton, 2005, “The Message of the Quantum”,\nNature, 438(7069): 743. doi:10.1038/438743a", "Zwirn, Herve, 2016, “The Measurement Problem: Decoherence\nand Convivial Solipsism”, Foundations of Physics,\n46(6): 635–667. doi:10.1007/s10701-016-9999-5", "–––, 2020, “Nonlocality versus Modified\nRealism”, Foundations of Physics, 50(1): 1–26.\ndoi:10.1007/s10701-019-00314-7", "–––, forthcoming “Is QBism a Possible\nSolution to the Conceptual Problems of QuantumMechanics?” in\nThe Oxford Handbook of the History of Quantum\nInterpretations, Olival Freire Jr, Guido Bacciagaluppi, Olivier\nDarrigol, Thiago Hartz, Christian Joas, Alexei Kojevnikov, and Osvaldo\nPessoa Jr. (eds.), Oxford: Oxford University Press." ]

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[ "\nIt is widely accepted that consciousness or, more generally, mental\nactivity is in some way correlated to the behavior of the material\nbrain. Since quantum theory is the most fundamental theory of matter\nthat is currently available, it is a legitimate question to ask\nwhether quantum theory can help us to understand consciousness.\nSeveral approaches answering this question affirmatively, proposed in\nrecent decades, will be surveyed. There are three basic types of\ncorresponding approaches: (1) consciousness is a manifestation of\nquantum processes in the brain, (2) quantum concepts are used to\nunderstand consciousness without referring to brain activity, and (3)\nmatter and consciousness are regarded as dual aspects of one\nunderlying reality. Major contemporary variants of these\nquantum-inspired approaches will be discussed. It will be pointed out\nthat they make different epistemological assumptions and use quantum\ntheory in different ways. For each of the approaches discussed, both\nproblematic and promising features will be highlighted." ]

[ { "content_title": "1. Introduction", "sub_toc": [] }, { "content_title": "2. Philosophical Background Assumptions", "sub_toc": [] }, { "content_title": "3. Quantum Brain", "sub_toc": [ "3.1 Neurophysiological Levels of Description", "3.2 Stapp: Quantum State Reductions and Conscious Acts", "3.3 Vitiello and Freeman: Quantum Field Theory of Brain States", "3.4 Beck and Eccles: Quantum Mechanics at the Synaptic Cleft", "3.5 Penrose and Hameroff: Quantum Gravity and Microtubuli" ] }, { "content_title": "4. Quantum Mind", "sub_toc": [ "4.1 Applying Quantum Concepts to Mental Systems", "4.2 Concrete Applications" ] }, { "content_title": "5. Mind and Matter as Dual Aspects", "sub_toc": [ "5.1 Compositional and Decompositional Approaches", "5.2 Mind-Matter Correlations", "5.3 Further Developments" ] }, { "content_title": "6. Conclusions", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThe problem of how mind and matter are related to each other has many\nfacets, and it can be approached from many different starting points.\nThe historically leading disciplines in this respect are philosophy\nand psychology, which were later joined by behavioral science,\ncognitive science and neuroscience. In addition, the physics of\ncomplex systems and quantum physics have played stimulating roles in\nthe discussion from their beginnings.", "\nAs regards the issue of complexity, this is evident: the brain is one\nof the most complex systems we know. The study of neural networks,\ntheir relation to the operation of single neurons and other important\ntopics do and will profit a lot from complex systems approaches. As\nregards quantum physics, there can be no reasonable doubt that quantum\nevents occur and are efficacious in the brain as elsewhere in the\nmaterial world—including biological\n systems.[1]\n But it is controversial whether these events are efficacious and\nrelevant for those aspects of brain activity that are correlated with\nmental activity.", "\nThe original motivation in the early 20th century for relating quantum\ntheory to consciousness was essentially philosophical. It is fairly\nplausible that conscious free decisions (“free will”) are\nproblematic in a perfectly deterministic\n world,[2]\n so quantum randomness might indeed open up novel possibilities for\nfree will. (On the other hand, randomness is problematic for\ngoal-directed volition!)", "\nQuantum theory introduced an element of randomness standing out\nagainst the previous deterministic worldview preceding it, in which\nrandomness expresses our ignorance of a more detailed description (as\nin statistical mechanics). In sharp contrast to such epistemic\nrandomness, quantum randomness in processes such as the spontaneous\nemission of light, radioactive decay, or other examples has been\nconsidered a fundamental feature of nature, independent of our\nignorance or knowledge. To be precise, this feature refers to\nindividual quantum events, whereas the behavior of\nensembles of such events is statistically\ndetermined. The indeterminism of individual quantum events is\nconstrained by statistical laws.", "\nOther features of quantum theory, which became attractive in\ndiscussing issues of consciousness, were the concepts of\ncomplementarity and entanglement. Pioneers of quantum physics such as\nPlanck, Bohr, Schrödinger, Pauli (and others) emphasized the\nvarious possible roles of quantum theory in reconsidering the old\nconflict between physical determinism and conscious free will. For\ninformative overviews with different focal points see e.g., Squires\n(1990), Kane (1996), Butterfield (1998), Suarez and Adams (2013). " ], "section_title": "1. Introduction", "subsections": [] }, { "main_content": [ "\nVariants of the dichotomy between mind and matter range from their\nfundamental distinction at a primordial level of description to the\nemergence of mind (consciousness) from the brain as an extremely\nsophisticated and highly developed material system. Informative\noverviews can be found in Popper and Eccles (1977), Chalmers (1996),\nand Pauen (2001).", "\nOne important aspect of all discussions about the relation between\nmind and matter is the distinction between descriptive and\nexplanatory approaches. For instance, correlation is\na descriptive term with empirical relevance, while causation\nis an explanatory term associated with theoretical attempts to\nunderstand correlations. Causation implies correlations between cause\nand effect, but this does not always apply the other way around:\ncorrelations between two systems can result from a common cause in\ntheir history rather than from a direct causal interaction.", "\nIn the fundamental sciences, one typically speaks of causal relations\nin terms of interactions. In physics, for instance, there are four\nfundamental kinds of interactions (electromagnetic, weak, strong,\ngravitational) which serve to explain the correlations that are\nobserved in physical systems. As regards the mind-matter problem, the\nsituation is more difficult. Far from a theoretical understanding in\nthis field, the existing body of knowledge essentially consists of\nempirical correlations between material and mental states. These\ncorrelations are descriptive, not explanatory; they are not causally\nconditioned. It is (for some purposes) interesting to know\nthat particular brain areas are activated during particular\nmental activities; but this does, of course, not explain why\nthey are. Thus, it would be premature to talk about mind-matter\ninteractions in the sense of causal relations. For the sake of\nterminological clarity, the neutral notion of relations between mind\nand matter will be used in this article.", "\nIn many discussions of material [ma] brain states and mental [me]\nstates of consciousness, the relations between them are conceived in a\ndirect way\n (A):", "\nThis illustrates a minimal framework to study reduction,\nsupervenience, or emergence relations (Kim 1998; Stephan 1999) which\ncan yield both monistic and dualistic pictures. For instance, there is\nthe influential stance of strong reduction, stating that all\nmental states and properties can be reduced to the material domain or\neven to physics\n (physicalism).[3]\n This point of view claims that it is both necessary and sufficient to\nexplore and understand the material domain, e.g., the brain, in order\nto understand the mental domain, e.g., consciousness. It leads to a\nmonistic picture, in which any need to discuss mental states is\neliminated right away or at least considered as epiphenomenal. While\nmind-brain correlations are still legitimate though causally\nirrelevant from an epiphenomenalist point of view, eliminative\nmaterialism renders even correlations irrelevant.", "\nMuch discussed counterarguments against the validity of such strong\nreductionist approaches are qualia arguments, which emphasize the\nimpossibility for physicalist accounts to properly incorporate the\nquality of the subjective experience of a mental state, the\n“what it is like to be” (Nagel 1974) in that state. This\nleads to an explanatory gap between third-person and first-person\naccounts for which Chalmers (1995) has coined the notion of the\n“hard problem of consciousness”. Another, less discussed\ncounterargument is that the physical domain itself is not causally\nclosed. Any solution of fundamental equations of motion (be it\nexperimentally, numerically, or analytically) requires to fix boundary\nconditions and initial conditions which are not given by the\nfundamental laws of nature (Primas 2002). This causal gap applies to\nclassical physics as well as quantum physics, where a basic\nindeterminacy due to collapse makes it even more challenging. A third\nclass of counterarguments refer to the difficulties to include notions\nof temporal present and nowness in a physical description (Franck\n2004, 2008; Primas 2017).", "\nHowever, relations between mental and material states can also be\nconceived in a non-reductive fashion, e.g. in terms of emergence\nrelations (Stephan 1999). Mental states and/or properties can be\nconsidered as emergent if the material brain is not necessary or not\nsufficient to explore and understand\n them.[4]\n This leads to a dualistic picture (less radical and more plausible\nthan Cartesian dualism) in which residua remain if one attempts to\nreduce the mental to the material. Within a dualistic scheme of\nthinking, it becomes almost inevitable to discuss the question of\ncausal influence between mental and material states. In particular,\nthe causal efficacy of mental states upon brain states\n(“downward causation”) has recently attracted growing\ninterest (Velmans, 2002; Ellis et al.\n 2011).[5]\n The most popular approaches along those lines as far as quantum\nbehavior of the brain is concerned will be discussed in\n Section 3,\n “Quantum Brain”. ", "\nIt has been an old idea by Bohr that central conceptual features of\nquantum theory, such as complementarity, are also of pivotal\nsignificance outside the domain of physics. In fact, Bohr became\nfamiliar with complementarity through the psychologist Edgar Rubin\nand, more indirectly, William James (Holton 1970) and immediately saw\nits potential for quantum physics. Although Bohr was also convinced of\nthe extraphysical relevance of complementarity, he never elaborated\nthis idea in concrete detail, and for a long time after him no one\nelse did so either. This situation has changed: there are now a number\nof research programs generalizing key notions of quantum theory in a\nway that makes them applicable beyond physics.", "\nOf particular interest for consciousness studies are approaches that\nhave been developed in order to pick up Bohr’s proposal with\nrespect to psychology and cognitive science. The first steps in this\ndirection were made by the group of Aerts in the early 1990s (Aerts\net al. 1993), using non-distributive propositional lattices\nto address quantum-like behavior in non-classical systems. Alternative\napproaches have been initiated by Khrennikov (1999), focusing on\nnon-classical probabilities, and Atmanspacher et al. (2002),\noutlining an algebraic framework with non-commuting operations. The\nrecent development of ideas within this framework of thinking is\naddressed in\n Section 4,\n “Quantum Mind”. Other lines of thinking are due to Primas\n(2007, 2017), addressing complementarity with partial Boolean\nalgebras, and Filk and von Müller (2008), indicating links\nbetween basic conceptual categories in quantum physics and\npsychology.", "\nAs an alternative to (A), it is possible to conceive mind-matter\nrelations indirectly\n (B),\n via a third category:", "\nThis third category, here denoted [mame], is often regarded as being\nneutral with respect to the distinction between [ma] and [me], i.e.,\npsychophysically neutral. In scenario (B), issues of reduction and\nemergence concern the relation between the unseparated\n“background reality” [mame] and the distinguished aspects\n[ma] and [me].", "\nSuch “dual aspect” frameworks of thinking have received\nincreasing attention in contempory discussion, and they have a long\ntradition reaching back as far as to Spinoza. In the early days of\npsychophysics, Fechner (1861) and Wundt (1911) advocated related\nviews. Whitehead, the modern pioneer of process philosophy, referred\nto mental and physical poles of “actual occasions”, which\nthemselves transcend their bipolar appearances (Whitehead 1978). Many\napproaches in the tradition of Feigl (1967) and Smart (1963), called\n“identity theories”, conceive mental and material states\nas essentially identical “central states”, yet considered\nfrom different perspectives. Other variants of this idea have been\nsuggested by Jung and Pauli (1955) [see also Meier (2001)], involving\nJung’s conception of a psychophysically neutral, archetypal\norder, or by Bohm and Hiley (Bohm 1990; Bohm and Hiley 1993; Hiley\n2001), referring to an implicate order which unfolds into the\ndifferent explicate domains of the mental and the material. They will\nbe discussed in more detail in\n Section 5,\n “Brain and Mind as Dual Aspects”. ", "\nVelmans (2002, 2009) has developed a similar approach, backed up with\nempirical material from psychology, and Strawson (2003) has proposed a\n“real materialism” which uses a closely related scheme.\nAnother proponent of dual-aspect thinking is Chalmers (1996), who\nconsiders the possibility that the underlying, psychophysically\nneutral level of description could be best characterized in terms of\ninformation.", "\nBefore proceeding further, it should be emphasized that many\npresent-day approaches prefer to distinguish between first-person and\nthird-person perspectives rather than mental and material states. This\nterminology serves to highlight the discrepancy between immediate\nconscious experiences (“qualia”) and their description, be\nit behavioral, neural, or biophysical. The notion of the “hard\nproblem” of consciousness research refers to bridging the gap\nbetween first-person experience and third-person accounts of it. In\nthe present contribution, mental conscious states are implicitly\nassumed to be related to first-person experience. This does not mean,\nhowever, that the problem of how to define consciousness precisely is\nconsidered as resolved. Ultimately, it will be (at least) as difficult\nto define a mental state in rigorous terms as it is to define a\nmaterial state." ], "section_title": "2. Philosophical Background Assumptions", "subsections": [] }, { "main_content": [ "\nIn this section, some popular approaches for applying quantum theory\nto brain states will be surveyed and compared, most of them\nspeculative, with varying degrees of elaboration and viability.\n Section 3.1\n addresses three different neurophysiological levels of description,\nto which particular quantum approaches refer. Subsequently, the\nindividual approaches themselves will be discussed —\n Section 3.2:\n Stapp,\n Section 3.3:\n Vitiello and Freeman,\n Section 3.4:\n Beck and Eccles,\n Section 3.5:\n Penrose and Hameroff. ", "\nIn the following, (some of) the better known and partly worked out\napproaches that use concepts of quantum theory for inquiries into the\nnature of consciousness will be presented and discussed. For this\npurpose, the philosophical distinctions A/B\n (Section 2)\n and the neurophysiological distinctions addressed in\n Section 3.1\n will serve as guidelines to classify the respective quantum\napproaches in a systematic way. However, some preliminary\nqualifications concerning different ways to use quantum theory are in\norder.", "\nThere are quite a number of accounts discussing quantum theory in\nrelation to consciousness that adopt basic ideas of quantum theory in\na purely metaphorical manner. Quantum theoretical terms such\nas entanglement, superposition, collapse, complementarity, and others\nare used without specific reference to how they are defined precisely\nand how they are applicable to specific situations. For instance,\nconscious acts are just postulated to be interpretable\nsomehow analogously to physical acts of measurement, or correlations\nin psychological systems are just postulated to be\ninterpretable somehow analogously to physical entanglement. Such\naccounts may provide fascinating science fiction, and they may even be\nimportant to inspire nuclei of ideas to be worked out in detail. But\nunless such detailed work leads beyond vague metaphors and analogies,\nthey do not yet represent scientific progress. Approaches falling into\nthis category will not be discussed in this contribution.", "\nA second category includes approaches that use the status quo\nof present-day quantum theory to describe neurophysiological and/or\nneuropsychological processes. Among these approaches, the one with the\nlongest history was initiated by von Neumann in the 1930s, later taken\nup by Wigner, and currently championed by Stapp. It can be roughly\ncharacterized as the proposal to consider intentional conscious acts\nas intrinsically correlated with physical state reductions. Another\nfairly early idea dating back to Ricciardi and Umezawa in the 1960s is\nto treat mental states, particularly memory states, in terms of vacuum\nstates of quantum fields. A prominent proponent of this approach at\npresent is Vitiello. Finally, there is the idea suggested by Beck and\nEccles in the 1990s, according to which quantum mechanical processes,\nrelevant for the description of exocytosis at the synaptic cleft, can\nbe influenced by mental intentions.", "\nThe third category refers to further developments or\ngeneralizations of present-day quantum theory. An obvious\ncandidate in this respect is the proposal by Penrose to relate\nelementary conscious acts to gravitation-induced reductions of quantum\nstates. Ultimately, this requires the framework of a future theory of\nquantum gravity which is far from having been developed. Together with\nPenrose, Hameroff has argued that microtubuli might be the right place\nto look for such state reductions. " ], "section_title": "3. Quantum Brain", "subsections": [ { "content": [ "\nA mental system can be in many different conscious, intentional,\nphenomenal mental states. In a hypothetical state space, a sequence of\nsuch states forms a trajectory representing what is often called the\nstream of consciousness. Since different subsets of the state space\nare typically associated with different stability properties, a mental\nstate can be assumed to be more or less stable, depending on its\nposition in the state space. Stable states are distinguished by a\nresidence time at that position longer than that of metastable or\nunstable states. If a mental state is stable with respect to\nperturbations, it “activates” a mental representation\nencoding a content that is consciously perceived.", "\nMoving from this purely psychological, or cognitive, description to\nits neurophysiological counterpart leads us to the question: What is\nthe neural correlate of a mental representation? According to standard\naccounts (cf. Noë and Thompson (2004) for discussion), mental\nrepresentations are correlated with the activity of neuronal\nassemblies, i.e., ensembles of several thousands of coupled neurons.\nThe neural correlate of a mental representation can be characterized\nby the fact that the connectivities, or couplings, among those neurons\nform an assembly confined with respect to its environment, to which\nconnectivities are weaker than within the assembly. The neural\ncorrelate of a mental representation is activated if the neurons\nforming the assembly operate more actively, e.g., produce higher\nfiring rates, than in their default mode.", "\nIn order to achieve a stable operation of an activated neuronal\nassembly, there must be a subtle balance between inhibitory and\nexcitatory connections among neurons (cf. Figure 1). If the transfer\nfunction of individual neurons is strictly monotonic, i.e., increasing\ninput leads to increasing output, assemblies are difficult to\nstabilize. For this reason, results establishing a non-monotonic\ntransfer function with a maximal output at intermediate input are of\nhigh significance for the modeling of neuronal assemblies (Kuhn et\nal. 2004). For instance, network models using lattices of coupled\nmaps with quadratic maximum (Kaneko and Tsuda 2000) are paradigmatic\nexamples of such behavior. These and other familiar models of neuronal\nassemblies (for an overview see Anderson and Rosenfeld 1988) are\nmostly formulated in a way not invoking well-defined elements\nof quantum theory. An explicit exception is the approach by Umezawa,\nVitiello and others (see\n Section 3.3).", "\nThe fact that neuronal assemblies are mostly described in terms of\nclassical behavior does not rule out that classically undescribable\nquantum effects may be significant if one focuses on individual\nconstituents of assemblies, i.e., single neurons or interfaces between\nthem. These interfaces, through which the signals between neurons\npropagate, are called synapses. There are electrical and chemical\nsynapses, depending on whether they transmit a signal electrically or\nchemically.", "\nAt electrical synapses, the current generated by the action potential\nat the presynaptic neuron flows directly into the postsynaptic cell,\nwhich is physically connected to the presynaptic terminal by a\nso-called gap junction. At chemical synapses, there is a cleft between\npre- and postsynaptic cell. In order to propagate a signal, a chemical\ntransmitter (glutamate) is released at the presynaptic terminal. This\nrelease process is called exocytosis. The transmitter diffuses across\nthe synaptic cleft and binds to receptors at the postsynaptic\nmembrane, thus opening an ion channel (Kandel et al. 2000,\npart III; see Fig. 2). Chemical transmission is slower than electric\ntransmission.", "\nA model developed by Beck and Eccles applies concrete quantum\nmechanical features to describe details of the process of exocytosis.\nTheir model proposes that quantum processes are relevant for\nexocytosis and, moreover, are tightly related to states of\nconsciousness. This will be discussed in more detail in\n Section 3.4.", "\nAt this point, another approach developed by Flohr (2000) should be\nmentioned, for which chemical synapses with a specific type of\nreceptors, so-called NMDA\n receptors,[6]\n are of paramount significance. Briefly, Flohr observes that the\nspecific plasticity of NMDA receptors is a necessary condition for the\nformation of extended stable neuronal assemblies correlated to\n(higher-order) mental representations which he identifies with\nconscious states. Moreover, he indicates a number of mechanisms caused\nby anaesthetic agents, which block NMDA receptors and consequently\nlead to a loss of consciousness. Flohr’s approach is\nphysicalistic and reductive, and it is entirely independent of any\nspecific quantum ideas.", "\nThe lowest neurophysiological level, at which quantum processes have\nbeen proposed as a correlate to consciousness, is the level at which\nthe interior of single neurons is considered: their cytoskeleton. It\nconsists of protein networks essentially made up of two kinds of\nstructures, neurofilaments and microtubuli (Fig. 3, left), which are\nessential for various transport processes within neurons (as well as\nother cells). Microtubuli are long polymers usually constructed of 13\nlongitudinal α and β-tubulin dimers arranged in a tubular\narray with an outside diameter of about 25 nm (Fig. 3, right). For\nmore details see Kandel et al. (2000), Chap. II.4.", "\nThe tubulins in microtubuli are the substrate which, in\nHameroff’s proposal, is used to embed Penrose’s\ntheoretical framework neurophysiologically. As will be discussed in\nmore detail in\n Section 3.5,\n tubulin states are assumed to depend on quantum events, so that\nquantum coherence among different tubulins is possible. Further, a\ncrucial thesis in the scenario of Penrose and Hameroff is that the\n(gravitation-induced) collapse of such coherent tubulin states\ncorresponds to elementary acts of consciousness." ], "subsection_title": "3.1 Neurophysiological Levels of Description" }, { "content": [ "\nThe act of measurement is a crucial aspect in the framework of quantum\ntheory, that has been the subject of controversy for more than eight\ndecades now. In his monograph on the mathematical foundations of\nquantum mechanics, von Neumann (1955, Chap. V.1) introduced, in an\nad hoc manner, the projection postulate as a mathematical\ntool for describing measurement in terms of a discontinuous,\nnon-causal, instantaneous (irreversible) act given by (1) the\ntransition of a quantum state to an eigenstate bj\nof the measured observable B (with a certain probability).\nThis transition is often called the collapse or\nreduction of the wavefunction, as opposed to (2) the\ncontinuous, unitary (reversible) evolution of a system according to\nthe Schrödinger equation.", "\nIn Chapter VI, von Neumann (1955) discussed the conceptual distinction\nbetween observed and observing system. In this context, he applied (1)\nand (2) to the general situation of a measured object system (I), a\nmeasuring instrument (II), and (the brain of) a human observer (III).\nHis conclusion was that it makes no difference for the result of\nmeasurements on (I) whether the boundary between observed and\nobserving system is posited between I and (II & III) or between (I\n& II) and III. As a consequence, it is inessential whether a\ndetector or the human brain is ultimately referred to as the\n “observer”.[7]", "\nBy contrast to von Neumann’s fairly cautious stance, London and\nBauer (1939) went further and proposed that it is indeed human\nconsciousness which completes the quantum measurement process\n(see Jammer (1974, Sec. 11.3 or Shimony (1963) for a detailed\naccount). In this way, they attributed a crucial role to consciousness\nin understanding quantum measurement in terms of an update of the\nobserver’s knowledge. In the 1960s, Wigner (1967) radicalized\nthis\n proposal,[8]\n by suggesting an impact of consciousness on the physical state of the\nmeasured system, not only an impact on observer knowledge. In order to\ndescribe measurement as a real dynamical process generating\nirreversible facts, Wigner called for some nonlinear modification of\n(2) to replace von Neumann’s projection\n (1).[9]", "\nSince the 1980s, Stapp has developed his own point of view on the\nbackground of von Neumann and Wigner. In particular, he tries to\nunderstand specific features of consciousness in relation to quantum\ntheory. Inspired by von Neumann, Stapp uses the freedom to place the\ninterface between observed and observing system and locates it in the\nobserver’s brain. He does not suggest any formal modifications\nto present-day quantum theory (in particular, he stays essentially\nwithin the “orthodox” Hilbert space representation), but\nadds major interpretational extensions, in particular with respect to\na detailed ontological framework.", "\nIn his earlier work, Stapp (1993) started with Heisenberg’s\ndistinction between the potential and the actual (Heisenberg 1958),\nthereby taking a decisive step beyond the operational Copenhagen\ninterpretation of quantum mechanics. While Heisenberg’s notion\nof the actual is related to a measured event in the sense of\nthe Copenhagen interpretation, his notion of the potential,\nof a tendency, relates to the situation before\nmeasurement, which expresses the idea of a reality independent of\n measurement.[10]", "\nImmediately after its actualization, each event holds the tendency for\nthe impending actualization of another, subsequent actual event.\nTherefore, events are by definition ambiguous. With respect to their\nactualized aspect, Stapp’s essential move is to “attach to\neach Heisenberg actual event an experiential aspect. The latter is\ncalled the feel of this event, and it can be considered to be\nthe aspect of the actual event that gives it its status as an\nintrinsic actuality” (Stapp 1993, p. 149). ", "\nWith respect to their tendency aspect, it is tempting to understand\nevents in terms of\n scheme (B)\n of\n Section 2.\n This is related to Whitehead’s ontology, in which mental and\nphysical poles of so-called “actual occasions” are\nconsidered as psychological and physical aspects of reality. The\npotential antecedents of actual occasions are psychophysically neutral\nand refer to a mode of existence at which mind and matter are\nunseparated. This is expressed, for instance, by Stapp’s notion\nof a “hybrid ontology” with “both idea-like and\nmatter-like qualities” (Stapp 1999, 159). Similarities with a\ndual-aspect approach (B) (cf.\n Section 5)\n are evident.", "\nIn an interview of 2006, Stapp (2006) specifies some ontological\nfeatures of his approach with respect to Whitehead’s process\nthinking, where actual occasions rather than matter or mind are\nfundamental elements of reality. They are conceived as based on a\nprocessual rather than a substantial ontology (see the entry on\n process philosophy).\n Stapp relates the fundamentally processual nature of actual occasions\nto both the physical act of state reduction and the correlated\npsychological intentional act.", "\nAnother significant aspect of his approach is the possibility that\n“conscious intentions of a human being can influence the\nactivities of his brain” (Stapp 1999, p. 153). Different from\nthe possibly misleading notion of a direct interaction, suggesting an\ninterpretation in terms of scheme (A) of\n Section 2,\n he describes this feature in a more subtle manner. The requirement\nthat the mental and material outcomes of an actual occasion must\nmatch, i.e. be correlated, acts as a constraint on the way in which\nthese outcomes are formed within the actual occasion (cf. Stapp 2006).\nThe notion of interaction is thus replaced by the notion of a\nconstraint set by mind-matter correlations (see also Stapp 2007).", "\nAt a level at which conscious mental states and material brain states\nare distinguished, each conscious experience, according to Stapp\n(1999, p. 153), has as its physical counterpart a quantum state\nreduction actualizing “the pattern of activity that is sometimes\ncalled the neural correlate of that conscious experience”. This\npattern of activity may encode an intention and, thus, represent a\n“template for action”. An intentional decision for an\naction, preceding the action itself, is then the key for anything like\nfree will in this picture.", "\nStapp argues that the mental effort, i.e. attention devoted to such\nintentional acts, can protract the lifetime of the neuronal assemblies\nthat represent the templates for action due to quantum Zeno-type\neffects. Concerning the neurophysiological implementation of this\nidea, intentional mental states are assumed to correspond to\nreductions of superposition states of neuronal assemblies. Additional\ncommentary concerning the concepts of attention and intention in\nrelation to James’ idea of a holistic stream of consciousness\n(James 1950 [1890]) was given by Stapp (1999).", "\nFor further progress, it will be mandatory to develop a coherent\nformal framework for this approach and elaborate on concrete details.\nFor instance, it is not yet worked out precisely how quantum\nsuperpositions and their collapses are supposed to occur in neural\ncorrelates of conscious events. Some indications are outlined by\nSchwartz et al. (2005). With these desiderata for future\nwork, the overall conception is conservative insofar as the physical\nformalism remains unchanged.", "\nThis is why Stapp insisted for years that his approach does not change\nwhat he calls “orthodox” quantum mechanics, which is\nessentially encoded in the statistical formulation by von Neumann\n(1955). From the point of view of standard present-day quantum\nphysics, however, it is certainly unorthodox to include the mental\nstate of observers in the theory. Although it is true that quantum\nmeasurement is not yet finally understood in terms of physical theory,\nintroducing mental states as the essential missing link is highly\nspeculative from a contemporary perspective.", "\nThis link is a radical conceptual move. In what Stapp now denotes as a\n“semi-orthodox” approach (Stapp 2015), he proposes that\nthe blind-chance kind of randomness of individual quantum events\n(“nature’s choices”) be reconceived as “not\nactually random but positively or negatively biased by the positive or\nnegative values in the minds of the observers that are actualized by\nits (nature’s) choices” (p. 187). This hypothesis leads\ninto mental influences on quantum physical processes which are widely\nunknown territory at present. " ], "subsection_title": "3.2 Stapp: Quantum State Reductions and Conscious Acts" }, { "content": [ "\nIn the 1960s, Ricciardi and Umezawa (1967) suggested to utilize the\nformalism of quantum field theory to describe brain states, with\nparticular emphasis on memory. The basic idea is to conceive of memory\nstates in terms of states of many-particle systems, as inequivalent\nrepresentations of vacuum states of quantum\n fields.[11]\n This proposal has gone through several refinements (e.g., Stuart\net al. 1978, 1979; Jibu and Yasue 1995). Major recent\nprogress has been achieved by including effects of dissipation, chaos,\nfractals and quantum noise (Vitiello 1995; Pessa and Vitiello 2003;\nVitiello 2012). For readable nontechnical accounts of the approach in\nits present form, embedded in quantum field theory as of today, see\nVitiello (2001, 2002).", "\nQuantum field theory (see the entry on\n quantum field theory)\n deals with systems with infinitely many degrees of freedom. For such\nsystems, the algebra of observables that results from imposing\ncanonical commutation relations admits of multiple Hilbert-space\nrepresentations that are not unitarily equivalent to each other. This\ndiffers from the case of standard quantum mechanics, which deals with\nsystems with finitely many degrees of freedom. For such systems, the\ncorresponding algebra of observables admits of unitarily equivalent\nHilbert-space representations.", "\nThe inequivalent representations of quantum field theory can be\ngenerated by spontaneous symmetry breaking (see the entry on\n symmetry and symmetry breaking),\n occurring when the ground state (or the vacuum state) of a system is\nnot invariant under the full group of transformations providing the\nconservation laws for the system. If symmetry breaks down, collective\nmodes are generated (so-called Nambu-Goldstone boson modes), which\npropagate over the system and introduce long-range correlations in\nit.", "\nThese correlations are responsible for the emergence of ordered\npatterns. Unlike in standard thermal systems, a large number of bosons\ncan be condensed in an ordered state in a highly stable fashion.\nRoughly speaking, this provides a quantum field theoretical derivation\nof ordered states in many-body systems described in terms of\nstatistical physics. In the proposal by Umezawa these dynamically\nordered states represent coherent activity in neuronal assemblies.", "\nThe activation of a neuronal assembly is necessary to make\nthe encoded content consciously accessible. This activation is\nconsidered to be initiated by external stimuli. Unless the assembly is\nactivated, its content remains unconscious, unaccessed memory.\nAccording to Umezawa, coherent neuronal assemblies correlated to such\nmemory states are regarded as vacuum states; their activation leads to\nexcited states and enables a conscious recollection of the content\nencoded in the vacuum (ground) state. The stability of such states and\nthe role of external stimuli have been investigated in detail by\nStuart et al. (1978, 1979).", "\nA decisive further step in developing the approach has been achieved\nby taking dissipation into account. Dissipation is possible\nwhen the interaction of a system with its environment is considered.\nVitiello (1995) describes how the system-environment interaction\ncauses a doubling of the collective modes of the system in its\nenvironment. This yields infinitely many differently coded vacuum\nstates, offering the possibility of many memory contents without\noverprinting. Moreover, dissipation leads to finite lifetimes of the\nvacuum states, thus representing temporally limited rather than\nunlimited memory (Alfinito and Vitiello 2000; Alfinito et al.\n2001). Finally, dissipation generates a genuine arrow of time for the\nsystem, and its interaction with the environment induces entanglement.\nPessa and Vitiello (2003) have addressed additional effects of chaos\nand quantum noise.", "\nUmezawa’s proposal addresses the brain as a many-particle system\nas a whole, where the “particles” are more or less\nneurons. In the language of\n Section 3.1,\n this refers to the level of neuronal assemblies, which correlate\ndirectly with mental activity. Another merit of the quantum\nfield theory approach is that it avoids the restrictions of standard\nquantum mechanics in a formally sound way. Conceptually speaking, many\nof the pioneering presentations of the proposal nevertheless confused\nmental and material states (and their properties). This has been\nclarified by Freeman and Vitiello (2008): the model “describes\nthe brain, not mental states.” ", "\nFor a corresponding description of brain states, Freeman and Vitiello\n2006, 2008, 2010) studied neurobiologically relevant observables such\nas electric and magnetic field amplitudes and neurotransmitter\nconcentration. They found evidence for non-equilibrium analogs of\nphase transitions (Vitiello 2015) and power-law distributions of\nspectral energy densities of electrocorticograms (Freeman and Vitiello\n2010, Freeman and Quian Quiroga 2013). All these observables are\nclassical, so that neurons, glia cells, “and other physiological\nunits are not quantum objects in the many-body model of\nbrain” (Freeman and Vitiello 2008). However, Vitiello (2012)\nalso points out that the emergence of (self-similar, fractal)\npower-law distributions in general is intimately related to\ndissipative quantum coherent states (see also recent developments of\nthe Penrose-Hameroff scenario,\n Section 3.5).", "\nThe overall conclusion is that the application of quantum field theory\ndescribes why and how classical behavior emerges at the level of brain\nactivity considered. The relevant brain states themselves are viewed\nas classical states. Similar to a classical thermodynamical\ndescription arising from quantum statistical mechanics, the idea is to\nidentify different regimes of stable behavior (phases, attractors) and\ntransitions between them. This way, quantum field theory provides\nformal elements from which a standard classical description of brain\nactivity can be inferred, and this is its main role in large parts of\nthe model. Only in their last joint paper, Freeman and Vitiello (2016)\nenvision a way in which the mental can be explicitly included. For a\nrecent review including technical background see Sabbadini and\nVitiello (2019). " ], "subsection_title": "3.3 Vitiello and Freeman: Quantum Field Theory of Brain States" }, { "content": [ "\nProbably the most concrete suggestion of how quantum mechanics in its\npresent-day appearance can play a role in brain processes is due to\nBeck and Eccles (1992), later refined by Beck (2001). It refers to\nparticular mechanisms of information transfer at the synaptic cleft.\nHowever, ways in which these quantum processes might be relevant for\nmental activity, and in which their interactions with mental states\nare conceived, remain unclarified to the present\n day.[12]\n ", "\nAs presented in\n Section 3.1,\n the information flow between neurons in chemical synapses is\ninitiated by the release of transmitters in the presynaptic terminal.\nThis process is called exocytosis, and it is triggered by an arriving\nnerve impulse with some small probability. In order to describe the\ntrigger mechanism in a statistical way, thermodynamics or quantum\nmechanics can be invoked. A look at the corresponding energy regimes\nshows (Beck and Eccles 1992) that quantum processes are\ndistinguishable from thermal processes for energies higher than\n10-2 eV (at room temperature). Assuming a typical length\nscale for biological microsites of the order of several nanometers, an\neffective mass below 10 electron masses is sufficient to ensure that\nquantum processes prevail over thermal processes.", "\nThe upper limit of the time scale of such processes in the quantum\nregime is of the order of 10-12 sec. This is significantly\nshorter than the time scale of cellular processes, which is\n10-9 sec and longer. The sensible difference between the\ntwo time scales makes it possible to treat the corresponding processes\nas decoupled from one another.", "\nThe detailed trigger mechanism proposed by Beck and Eccles (1992) is\nbased on the quantum concept of quasi-particles, reflecting the\nparticle aspect of a collective mode. Skipping the details of the\npicture, the proposed trigger mechanism refers to tunneling processes\nof two-state quasi-particles, resulting in state collapses. It yields\na probability of exocytosis in the range between 0 and 0.7, in\nagreement with empirical observations. Using a theoretical framework\ndeveloped earlier (Marcus 1956; Jortner 1976), the quantum trigger can\nbe concretely understood in terms of electron transfer between\nbiomolecules. However, the question remains how the trigger may be\nrelevant for conscious mental states. There are two aspects to this\nquestion.", "\nThe first one refers to Eccles’ intention to utilize quantum\nprocesses in the brain as an entry point for mental causation. The\nidea, as indicated in\n Section 1,\n is that the fundamentally indeterministic nature of individual\nquantum state collapses offers room for the influence of mental powers\non brain states. In the present picture, this is conceived in such a\nway that “mental intention (volition) becomes neurally effective\nby momentarily increasing the probability of\nexocytosis” (Beck and Eccles 1992, 11360). Further\njustification of this assumption is not given.", "\nThe second aspect refers to the problem that processes at\nsingle synapses cannot be simply correlated to mental\nactivity, whose neural correlates are coherent assemblies of neurons.\nMost plausibly, prima facie uncorrelated random processes at\nindividual synapses would result in a stochastic network of neurons\n(Hepp 1999). Although Beck (2001) has indicated possibilities (such as\nquantum stochastic resonance) for achieving ordered patterns at the\nlevel of assemblies from fundamentally random synaptic processes, this\nremains an unsolved problem.", "\nWith the exception of Eccles’ idea of mental causation, the\napproach by Beck and Eccles essentially focuses on brain states and\nbrain dynamics. In this respect, Beck (2001, 109f) states explicitly\nthat “science cannot, by its very nature, present any answer to\n[…] questions related to the mind”. Nevertheless, their\nbiophysical approach may open the door to controlled speculation about\nmind-matter relations.", "\nA more recent proposal targeting exocytosis processes at the synaptic\ncleft is due Fisher (2015, 2017). Similar to the quasi-particles by\nBeck and Eccles, Fisher refers to so-called Posner molecules, in\nparticular to calcium phosphate, Ca\\(_9\\)(PO\\(_4\\))\\(_6\\). The nuclear\nspins of phosphate ions serve as entangled qubits within the\nmolecules, which protect their coherent states against fast\ndecoherence (resulting in extreme decoherence times in the range of\nhours or even days). If the Posner molecules are transported into\npresynaptic glutamatergic neurons, they will stimulate further\nglutamate release and amplify postsynaptic activity. Due to nonlocal\nquantum correlations this activity may be enhanced over multiple\nneurons (which would respond to Hepp’s concern).", "\nThis is a sophisticated mechanism that calls for empirical tests. One\nof them would be to modify the phosphorus spin dynamics within the\nPosner molecules. For instance, replacing Ca by different Li isotopes\nwith different nuclear spins gives rise to different decoherence\ntimes, affecting postsynaptic activity. Corresponding evidence has\nbeen shown in animals (Sechzer et al. 1986, Krug et al. 2019). In\nfact, lithium is known to be efficacious in tempering manic phases in\npatients with bipolar disorder." ], "subsection_title": "3.4 Beck and Eccles: Quantum Mechanics at the Synaptic Cleft" }, { "content": [ "\nIn the scenario developed by Penrose and neurophysiologically\naugmented by Hameroff, quantum theory is claimed to be effective for\nconsciousness, but the way this happens is quite sophisticated. It is\nargued that elementary acts of consciousness are non-algorithmic,\ni.e., non-computable, and they are neurophysiologically realized as\ngravitation-induced reductions of coherent superposition states in\nmicrotubuli.", "\nUnlike the approaches discussed so far, which are essentially based on\n(different features of) status quo quantum theory, the\nphysical part of the scenario, proposed by Penrose, refers to future\ndevelopments of quantum theory for a proper understanding of the\nphysical process underlying quantum state reduction. The grander\npicture is that a full-blown theory of quantum gravity is required to\nultimately understand quantum measurement (see the entry on\n quantum gravity).", "\nThis is a far-reaching assumption. Penrose’s rationale for\ninvoking state reduction is not that the corresponding randomness\noffers room for mental causation to become efficacious (although this\nis not excluded). His conceptual starting point, at length developed\nin two books (Penrose 1989, 1994), is that elementary conscious acts\ncannot be described algorithmically, hence cannot be computed. His\nbackground in this respect has a lot to do with the nature of\ncreativity, mathematical insight, Gödel’s incompleteness\ntheorems, and the idea of a Platonic reality beyond mind and\nmatter.", "\nPenrose argues that a valid formulation of quantum state reduction\nreplacing von Neumann’s projection postulate must faithfully\ndescribe an objective physical process that he calls\nobjective reduction. As such a physical process remains\nempirically unconfirmed so far, Penrose proposes that effects not\ncurrently covered by quantum theory could play a role in state\nreduction. Ideal candidates for him are gravitational effects since\ngravitation is the only fundamental interaction which is not\nintegrated into quantum theory so far. Rather than modifying elements\nof the theory of gravitation (i.e., general relativity) to achieve\nsuch an integration, Penrose discusses the reverse: that novel\nfeatures have to be incorporated in quantum theory for this purpose.\nIn this way, he arrives at the proposal of gravitation-induced\nobjective state reduction.", "\nWhy is such a version of state reduction non-computable? Initially one\nmight think of objective state reduction in terms of a stochastic\nprocess, as most current proposals for such mechanisms indeed do (see\nthe entry on\n collapse theories).\n This would certainly be indeterministic, but probabilistic and\nstochastic processes can be standardly implemented on a computer,\nhence they are definitely computable. Penrose (1994, Secs 7.8 and\n7.10) sketches some ideas concerning genuinely non-computable, not\nonly random, features of quantum gravity. In order for them to become\nviable candidates for explaining the non-computability of\ngravitation-induced state reduction, a long way still has to be\ngone.", "\nWith respect to the neurophysiological implementation of\nPenrose’s proposal, his collaboration with Hameroff has been\ninstrumental. With his background as an anaesthesiologist, Hameroff\nsuggested to consider microtubules as an option for where reductions\nof quantum states can take place in an effective way, see e.g.,\nHameroff and Penrose (1996). The respective quantum states are assumed\nto be coherent superpositions of tubulin states, ultimately extending\nover many neurons. Their simultaneous gravitation-induced collapse is\ninterpreted as an individual elementary act of consciousness. The\nproposed mechanism by which such superpositions are established\nincludes a number of involved details that remain to be confirmed or\ndisproven.", "\nThe idea of focusing on microtubuli is partly motivated by the\nargument that special locations are required to ensure that quantum\nstates can live long enough to become reduced by gravitational\ninfluence rather than by interactions with the warm and wet\nenvironment within the brain. Speculative remarks about how the\nnon-computable aspects of the expected new physics mentioned above\ncould be significant in this\n scenario[13]\n are given in Penrose (1994, Sec. 7.7).", "\nInfluential criticism of the possibility that quantum states can in\nfact survive long enough in the thermal environment of the brain has\nbeen raised by Tegmark (2000). He estimates the decoherence time of\ntubulin superpositions due to interactions in the brain to be less\nthan 10-12 sec. Compared to typical time scales of\nmicrotubular processes of the order of milliseconds and more, he\nconcludes that the lifetime of tubulin superpositions is much too\nshort to be significant for neurophysiological processes in the\nmicrotubuli. In a response to this criticism, Hagan et al.\n(2002) showed that a corrected version of Tegmark’s model\nprovides decoherence times up to 10 to 100 μsec, and it has been\nargued that this can be extended up to the neurophysiologically\nrelevant range of 10 to 100 msec under particular assumptions of the\nscenario by Penrose and Hameroff.", "\nMore recently, a novel idea has entered this debate. Theoretical\nstudies of interacting spins have shown that entangled states can be\nmaintained in noisy open quantum systems at high temperature and far\nfrom thermal equilibrium. In these studies the effect of decoherence\nis counterbalanced by a simple “recoherence” mechanism\n(Hartmann et al. 2006, Li and Paraoanu 2009). This indicates\nthat, under particular circumstances, entanglement may persist even in\nhot and noisy environments such as the brain.", "\nHowever, decoherence is just one piece in the debate about the overall\npicture suggested by Penrose and Hameroff. From another perspective,\ntheir proposal of microtubules as quantum computing devices has\nrecently received support from work of Bandyopadhyay’s lab at\nJapan, showing evidence for vibrational resonances and conductivity\nfeatures in microtubules that should be expected if they are\nmacroscopic quantum systems (Sahu et al. 2013).\nBandyopadhyay’s results initiated considerable attention and\ncommentary (see Hameroff and Penrose 2014). In a well-informed\nin-depth analysis, Pitkänen (2014) raised concerns to the effect\nthat the reported results alone may not be sufficient to confirm the\napproach proposed by Hameroff and Penrose with all its\nramifications.", "\nIn a different vein, Craddock et al. (2015, 2017) discussed\nin detail how microtubular processes (rather than, or in addition to,\nsynaptic processes, see Flohr 2000) may be affected by anesthetics,\nand may also be responsible for neurodegenerative memory disorders. As\nthe correlation between anesthetics and consciousness seems obvious at\nthe phenomenological level, it is interesting to know the intricate\nmechanisms by which anesthetic drugs act on the cytoskeleton of\nneuronal\n cells,[14]\n and what role quantum mechanics plays in these mechanisms. Craddock\net al. (2015, 2017) point out a number of possible quantum\neffects (including the power-law behavior addressed by Vitiello, cf.\n Section 3.3)\n which can be investigated using presently available technologies.\nRecent empirical results about quantum interactions of anesthetics are\ndue to Li et al. (2018) and Burdick et al. (2019).\n", "\nFrom a philosophical perspective, the scenario of Penrose and Hameroff\nhas occasionally received outspoken rejection, see e.g., Grush and\nChurchland (1995) and the reply by Penrose and Hameroff (1995).\nIndeed, their approach collects several top level mysteries, among\nthem the relation between mind and matter itself, the ultimate\nunification of all physical interactions, the origin of mathematical\ntruth, and the understanding of brain dynamics across hierarchical\nlevels. Combining such deep and fascinating issues certainly needs\nfurther work to be substantiated, and should neither be too quickly\ncelebrated nor offhandedly dismissed. After more than two decades\nsince its inception one thing can be safely asserted: the approach has\nfruitfully inspired important innovative research on quantum effects\non consciousness, both theoretical and empirical. " ], "subsection_title": "3.5 Penrose and Hameroff: Quantum Gravity and Microtubuli" } ] }, { "main_content": [], "section_title": "4. Quantum Mind", "subsections": [ { "content": [ "\nToday there is accumulating evidence in the study of consciousness\nthat quantum concepts like complementarity, entanglement, dispersive\nstates, and non-Boolean logic play significant roles in mental\nprocesses. Corresponding quantum-inspired approaches address purely\nmental (psychological) phenomena using formal features also employed\nin quantum physics, but without involving the full-fledged framework\nof quantum mechanics or quantum field theory. The term “quantum\ncognition” has been coined to refer to this new area of\nresearch. Perhaps a more appropriate characterization would be\nnon-commutative structures in cognition. ", "\nOn the surface, this seems to imply that the brain activity correlated\nwith those mental processes is in fact governed by quantum physics.\nThe quantum brain approaches discussed in\n Section 3\n represent attempts that have been proposed along these lines. But is\nit necessarily true that quantum features in psychology imply quantum\nphysics in the brain? ", "\nA formal move to incorporate quantum behavior in mental systems,\nwithout referring to quantum brain activity, is based on a state space\ndescription of mental systems. If mental states are defined on the\nbasis of cells of a neural state space partition, then this partition\nneeds to be well tailored to lead to robustly defined states. Ad hoc\nchosen partitions will generally create incompatible descriptions\n(Atmanspacher and beim Graben 2007) and states may become entangled\n(beim Graben et al. 2013). ", "\nThis implies that quantum brain dynamics is not the only possible\nexplanation of quantum features in mental systems. Assuming that\nmental states arise from partitions of neural states in such a way\nthat statistical neural states are co-extensive with individual mental\nstates, the nature of mental processes depends strongly on the kind of\npartition chosen. If the partition is not properly constructed, it is\nlikely that mental states and observables show features that resemble\nquantum behavior although the correlated brain activity may be\nentirely classical: quantum mind without quantum brain.", "\nIntuitively, it is not difficult to understand why non-commuting\noperations or non-Boolean logic should be relevant, even inevitable,\nfor mental systems that have nothing to do with quantum physics.\nSimply speaking, the non-commutativity of operations means nothing\nelse than that the sequence, in which operations are applied, matters\nfor the final result. And non-Boolean logic refers to propositions\nthat may have unsharp truth values beyond yes or no, shades of\nplausibility or credibility as it were. Both versions obviously abound\nin psychology and cognitive science (and in everyday life).\nPylkkänen (2015) has even suggested to use this intuitive\naccessibility of mental quantum features for a better conceptual grasp\nof quantum physics. ", "\nThe particular strength of the idea of generalizing quantum theory\nbeyond quantum physics is that it provides a formal framework which\nboth yields a transparent well-defined link to conventional quantum\nphysics and has been used to describe a number of concrete\npsychological applications with surprisingly detailed theoretical and\nempirical results. Corresponding approaches fall under the third\ncategory mentioned in\n Section 3:\n further developments or generalizations of quantum theory.", "\nOne rationale for the focus on psychological phenomena is that their\ndetailed study is a necessary precondition for further questions as to\ntheir neural correlates. Therefore, the investigation of mental\nquantum features resists the temptation to reduce them (within\nscenario A) all-too quickly to neural activity. There are several\nkinds of psychological phenomena which have been addressed in the\nspirit of mental quantum features so far: (i) decision processes, (ii)\norder effects, (iii) bistable perception, (iv) learning, (v) semantic\nnetworks, (vi) quantum agency,and (vii) super-quantum entanglement\ncorrelations. These topics will be outlined in some more detail in the\nfollowing\n Section 4.2." ], "subsection_title": "4.1 Applying Quantum Concepts to Mental Systems" }, { "content": [ "\nAn early precursor of work on decision processes is due to Aerts and\nAerts (1994). However, the first detailed account appeared in a\ncomprehensive publication by Busemeyer et al. (2006). The key\nidea is to define probabilities for decision outcomes and decision\ntimes in terms of quantum probability amplitudes. Busemeyer et\nal. found agreement of a suitable Hilbert space model (and\ndisagreement of a classical alternative) with empirical data.\nMoreover, they were able to clarify the long-standing riddle of the\nso-called conjunction and disjunction effects (Tversky and Shafir\n1992) in decision making (Pothos and Busemeyer 2009). Another\napplication refers to the asymmetry of similarity judgments (Tversky\n1977), which can be adequately understood by quantum approaches (see\nAerts et al. 2011, Pothos et al. 2013).", "\nOrder effects in polls, surveys, and questionnaires, recognized for a\nlong time (Schwarz and Sudman 1992), are still insufficiently\nunderstood today. Their study as contextual quantum features (Aerts\nand Aerts 1994, Busemeyer et al. 2011) offers the potential\nto unveil a lot more about such effects than the well-known fact that\nresponses can drastically alter if questions are swapped. Atmanspacher\nand Römer (2012) proposed a complete classification of possible\norder effects (including uncertainty relations, and independent of\nHilbert space representations), and Wang et al. (2014)\ndiscovered a fundamental covariance condition (called the QQ equation)\nfor a wide class of order effects.", "\nAn important issue for quantum mind approaches is the complexity or\nparsimony of Hilbert space models as compared to classical (Bayesian,\nMarkov, etc.) models. Atmanspacher and Römer (2012) as well as\nBusemeyer and Wang (2018) addressed this issue for order effects, with\nthe result that quantum approaches generally require less free\nvariables than competing classical models and are, thus, more\nparsimonious and more stringent than those. Busemeyer and Wang (2017)\nstudied how measuring incompatible observables sequentially induces\nuncertainties on the second measurement outcome. ", "\nThe perception of a stimulus is bistable if the stimulus is ambiguous,\nsuch as the Necker cube. This bistable behavior has been modeled\nanalagous to the physical quantum Zeno effect. (Note that this differs\nfrom the quantum Zeno effect as used in\n Section 3.2.)\n The resulting Necker-Zeno model predicts a quantitative relation\nbetween basic psychophysical time scales in bistable perception that\nhas been confirmed experimentally (see Atmanspacher and Filk 2013 for\nreview).", "\nMoreover, Atmanspacher and Filk (2010) showed that the Necker-Zeno\nmodel violates temporal Bell inqualitities for particular\ndistinguished states in bistable\n perception.[15]\n This theoretical prediction is yet to be tested experimentally and\nwould be a litmus test for quantum behavior in mental systems. Such\nstates have been denoted as temporally nonlocal in the sense\nthat they are not sharply (pointwise) localized along the time axis\nbut appear to be stretched over an extended time interval (an extended\npresent). Within this interval, relations such as\n“earlier” or “later” are illegitimate\ndesignators and, accordingly, causal connections are ill-defined.", "\nAnother quite obvious arena for non-commutative behavior is learning\nbehavior. In theoretical studies, Atmanspacher and Filk (2006) showed\nthat in simple supervised learning tasks small recurrent networks not\nonly learn the prescribed input-output relation but also the sequence\nin which inputs have been presented. This entails that the recognition\nof inputs is impaired if the sequence of presentation is changed. In\nvery few exceptional cases, with special characteristics that remain\nto be explored, this impairment is avoided.", "\nThe difficult issue of meaning in natural languages is often explored\nin terms of semantic networks. Gabora and Aerts (2002) described the\nway in which concepts are evoked, used, and combined to generate\nmeaning depending on contexts. Their ideas about concept association\nin evolution were further developed by Gabora and Aerts (2009). A\nparticularly thrilling application is due to Bruza et al.\n(2015), who challenged a long-standing dogma in linguistics by\nproposing that the meaning of concept combinations (such as\n“apple chip”) is not uniquely separable into the meanings\nof the combined concepts (“apple” and “chip”).\nBruza et al. (2015) refer to meaning relations in terms of\nentanglement-style features in quantum representations of concepts and\nreported first empirical results in this direction. ", "\nA quantum approach for understanding issues related to agency,\nintention, and other controversial topics in the philosophy of mind\nhas been proposed by Briegel and Müller (2015), see also\nMüller and Briegel (2018). This proposal is based on work on\nquantum algorithms for reinforcement learning in neural networks\n(“projective simulation”, Paparo et al. 2012),\nwhich can be regarded as a variant of quantum machine learning (Wittek\n2014). The gist of the idea is how agents can develop agency as a kind\nof independence from their environment and the deterministic laws\ngoverning it (Briegel 2012). The behavior of the agent itself is\nsimulated as a non-deterministic quantum random walk in its memory\nspace.", "\nQuantum entanglement implies correlations exceeding standard classical\ncorrelations (by violating Bell-type inequalitites) but obeying the\nso-called Tsirelson bound. However, this bound does not exhaust the\nrange by which Bell-type correlations can be violated in principle.\nPopescu and Rohrlich (1994) found such correlations for particular\nquantum measurements, and the study of such super-quantum correlations\nhas become a vivid field of contemporary research, as the review by\nPopescu (2014) shows. ", "\nOne problem in assessing super-quantum correlations in mental systems\nis to delineate genuine (non-causal) quantum-type correlations from\n(causal) classical correlations that can be used for signaling.\nDzhafarov and Kujala (2013) derived a compact way to do so and\nsubtract classical context effects such as priming in mental systems\nso that true quantum correlations remain. See Cervantes and Dzhafarov\n(2018) for empirical applications, and Atmanspacher and Filk (2019)\nfor further subtleties. " ], "subsection_title": "4.2 Concrete Applications" } ] }, { "main_content": [], "section_title": "5. Mind and Matter as Dual Aspects", "subsections": [ { "content": [ "\nDual-aspect approaches consider mental and material domains of reality\nas aspects, or manifestations, of one underlying reality in which mind\nand matter are unseparated. In such a framework, the distinction\nbetween mind and matter results from the application of a basic tool\nfor achieving epistemic access to, i.e., gather knowledge about, both\nthe separated domains and the underlying\n reality.[16]\n Consequently, the status of the underlying, psychophysically neutral\ndomain is considered as ontic relative to the mind-matter\ndistinction.", "\nAs mentioned in\n Section 2,\n dual-aspect approaches have a long history, essentially starting with\nSpinoza as a most outspoken protagonist. Major directions in the 20th\ncentury have been described and compared to some detail by\nAtmanspacher (2014). An important distinction between two basic\nclasses of dual-aspect thinking is the way in which the\npsychophysically neutral domain is related to the mental and the\nphysical. For Russell and the neo-Russellians the\ncompositional arrangements of psychophysically neutral\nelements decide how they differ with respect to mental or physical\nproperties. As a consequence, the mental and the physical are\nreducible to the neutral domain. Chalmers’ (1996, Chap. 8) ideas\non “consciousness and information” fall into this class.\nTononi’s theoretical framework of “integrated information\ntheory” (see Oizumi et al. 2014, Tononi and Koch 2015)\ncan be seen as a concrete implementation of a number of features of\nChalmers’ proposal. No quantum structures are involved in this\nwork.", "\nThe other class of dual-aspect thinking is decompositional\nrather than compositional. Here the basic metaphysics of the\npsychophysically neutral domain is holistic, and the mental and the\nphysical (neither reducible to one another nor to the neutral) emerge\nby breaking the holistic symmetry or, in other words, by making\ndistinctions. This framework is guided by the analogy to quantum\nholism, and the predominant versions of this picture are quantum\ntheoretically inspired as, for instance, proposed by Pauli and Jung\n(Jung and Pauli 1955; Meier 2001) and by Bohm and Hiley (Bohm 1990;\nBohm and Hiley 1993; Hiley 2001). They are based on speculations that\nclearly exceed the scope of contemporary quantum theory. ", "\nIn Bohm’s and Hiley’s approach, the notions of implicate\nand explicate order mirror the distinction between ontic and epistemic\ndomains. Mental and physical states emerge by explication, or\nunfoldment, from an ultimately undivided and psychophysically neutral\nimplicate, enfolded order. This order is called holomovement\nbecause it is not static but rather dynamic, as in Whitehead’s\nprocess philosophy. De Gosson and Hiley (2013) give a good\nintroduction of how the holomovement can be addressed from a formal\n(algebraic) point of view. ", "\nAt the level of the implicate order, the term active\ninformation expresses that this level is capable of\n“informing” the epistemically distinguished, explicate\ndomains of mind and matter. It should be emphasized that the usual\nnotion of information is clearly an epistemic term. Nevertheless,\nthere are quite a number of dual-aspect approaches addressing\nsomething like information at the ontic, psychophysically neutral\n level.[17]\n Using an information-like concept in a non-epistemic manner appears\ninconsistent if the common (syntactic) significance of Shannon-type\ninformation is intended, which requires distinctions in order to\nconstruct partitions, providing alternatives in the set of given\nevents. Most information-based dual-aspect approaches do not\nsufficiently clarify their notion of information, so that\nmisunderstandings easily arise." ], "subsection_title": "5.1 Compositional and Decompositional Approaches" }, { "content": [ "\nWhile the proposal by Bohm and Hiley essentially sketches a conceptual\nframework without further concrete details, particularly concerning\nthe mental domain, the Pauli-Jung conjecture (Atmanspacher and Fuchs\n2014) concerning dual-aspect monism offers some more material to\ndiscuss. An intuitively appealing way to represent their approach\nconsiders the distinction between epistemic and ontic domains of\nmaterial reality due to quantum theory in parallel with the\ndistinction between epistemic and ontic mental domains.", "\nOn the physical side, the epistemic/ontic distinction refers to the\ndistinction between a “local realism” of empirical facts\nobtained from classical measuring instruments and a “holistic\nrealism” of entangled systems (Atmanspacher and Primas 2003).\nEssentially, these domains are connected by the process of\nmeasurement, thus far conceived as independent of conscious observers.\nThe corresponding picture on the mental side refers to a distinction\nbetween conscious and unconscious\n domains.[18]\n In Jung’s depth psychological conceptions, these two domains\nare connected by the emergence of conscious mental states from the\nunconscious, analogous to physical measurement.", "\nIn Jung’s depth psychology it is crucial that the unconscious\nhas a collective component, unseparated between individuals\nand populated by so-called archetypes. They are regarded as\nconstituting the psychophysically neutral level comprising both the\ncollective unconscious and the holistic reality of quantum theory. At\nthe same time they operate as “ordering factors”, being\nresponsible for the arrangement of their psychical and physical\nmanifestations in the epistemically distinguished domains of mind and\nmatter. More details of this picture can be found in Jung and Pauli\n(1955), Meier (2001), Atmanspacher and Primas (2009), Atmanspacher and\nFach (2013), and Atmanspacher and Fuchs (2014).", "\nThis scheme is clearly related to\n scenario (B)\n of\n Sec. 2,\n combining an epistemically dualistic with an ontically monistic\napproach. Correlations between the mental and the physical are\nconceived as non-causal, thus respecting the causal closure of the\nphysical against the mental. However, there is a causal\nrelationship (in the sense of formal rather than efficient causation)\nbetween the psychophysically neutral, monistic level and the\nepistemically distinguished mental and material domains. In\nPauli’s and Jung’s terms this kind of causation is\nexpressed by the ordering operation of archetypes in the collective\nunconscious.", "\nIn other words, this scenario offers the possibility that the mental\nand material manifestations may inherit mutual correlations due to the\nfact that they are jointly caused by the psychophysically neutral\nlevel. One might say that such correlations are remnants reflecting\nthe lost holism of the underlying reality. They are not the\nresult of any direct causal interaction between mental and\nmaterial domains. Thus, they are not suitable for an\nexplanation of direct efficient mental causation. Their\nexistence would require some psychophysically neutral activity\nentailing correlation effects that would be misinterpreted as mental\ncausation of physical events. Independently of quantum theory, a\nrelated move was suggested by Velmans (2002, 2009). But even without\nmental causation,\n scenario (B)\n is relevant to ubiquitous correlations between conscious mental\nstates and physical brain states." ], "subsection_title": "5.2 Mind-Matter Correlations" }, { "content": [ "\nIn the Pauli-Jung conjecture, these correlations are called\nsynchronistic and have been extended to psychosomatic\nrelations (Meier 1975). A comprehensive typology of mind-matter\ncorrelations following from Pauli’s and Jung’s dual-aspect\nmonism was proposed by Atmanspacher and Fach (2013). They found that a\nlarge body of empirical material concerning more than 2000 cases of\nso-called “exceptional experiences” can be classified\naccording to their deviation from the conventional reality model of a\nsubject and from the conventional relations between its components\n(see Atmanspacher and Fach 2019 for more details). Synchronistic\nevents in the sense of Pauli and Jung appear as a special case of such\nrelational deviations. ", "\nAn essential condition required for synchronistic correlations is that\nthey are meaningful for those who experience them. It is\ntempting to interpret the use of meaning as an attempt to introduce\nsemantic information as an alternative to syntactic information as\naddressed above. (Note the parallel to active information as in the\napproach by Bohm and Hiley.) Although this entails difficult problems\nconcerning a clear-cut definition and operationalization, something\nakin to meaning, both explicitly and implicitly, might be a relevant\ninformational currency for mind-matter relations within the framework\nof decompositional dual-aspect thinking (Atmanspacher 2014).", "\nPrimas (2003, 2009, 2017) proposed a dual-aspect approach where the\ndistinction of mental and material domains originates from the\ndistinction between two different modes of time: tensed (mental) time,\nincluding nowness, on the one hand and tenseless (physical) time,\nviewed as an external parameter, on the other (see the entries on\n time\n and on\n being and becoming in modern physics).\n Regarding these two concepts of time as implied by a symmetry\nbreaking of a timeless level of reality that is psychophysically\nneutral, Primas conceives the tensed time of the mental domain as\nquantum-correlated with the parameter time of physics via\n“time-entanglement”. This scenario has been formulated in\na Hilbert space framework with appropriate time operators (Primas\n2009, 2017), so it offers a formally elaborated dual-aspect quantum\nframework for basic aspects of the mind-matter problem. It shows some\nconvergemce with the idea of temporally nonlocal mental states as\naddresed in\n Section 4.2.", "\nAs indicated in\n Section 3.2,\n the approach by Stapp contains elements of dual-aspect thinking as\nwell, although this is not much emphasized by its author. The\ndual-aspect quantum approaches discussed in the present section tend\nto focus on the issue of a generalized mind-matter\n“entanglement” more than on state reduction. The primary\npurpose here is to understand correlations between mental and material\ndomains rather than direct causally efficacious interactions between\nthem.", "\nA final issue of dual-aspect approaches in general refers to the\nproblem of panpsychism or panexperientialism, respectively (see the\nreview by Skrbina 2003, and the entry on\n panpsychism).\n In the limit of a universal symmetry breaking at the\npsychophysically neutral level, every system has both a\nmental and a material aspect. In such a situation it is important to\nunderstand “mentality” much more generally than\n“consciousness”. Unconscious or proto-mental acts as\nopposed to conscious mental acts are notions sometimes used to\nunderline this difference. The special case of human consciousness\nwithin the mental domain might be regarded as special as its material\ncorrelate, the brain, within the material domain." ], "subsection_title": "5.3 Further Developments" } ] }, { "main_content": [ "\nThe historical motivation for exploring quantum theory in trying to\nunderstand consciousness derived from the realization that\ncollapse-type quantum events introduce an element of randomness, which\nis primary (ontic) rather than due to ignorance or missing information\n(epistemic). Approaches such as those of Stapp and of Beck and Eccles\nemphasize this (in different ways), insofar as the ontic randomness of\nquantum events is regarded to provide room for mental causation, i.e.,\nthe possibility that conscious mental acts can influence brain\nbehavior. The approach by Penrose and Hameroff also focuses on state\ncollapse, but with a significant move from mental causation to the\nnon-computability of (particular) conscious acts.", "\nAny discussion of state collapse or state reduction (e.g. by\nmeasurement) refers, at least implicitly, to superposition states\nsince those are the states that are reduced. Insofar as entangled\nsystems remain in a quantum superposition as long as no measurement\nhas occurred, entanglement is always co-addressed when state reduction\nis discussed. By contrast, some of the dual-aspect quantum approaches\nutilize the topic of entanglement differently, and independently of\nstate reduction in the first place. Inspired by and analogous to\nentanglement-induced nonlocal correlations in quantum physics,\nmind-matter entanglement is conceived as the hypothetical origin of\nmind-matter correlations. This exhibits the highly speculative picture\nof a fundamentally holistic, psychophysically neutral level of reality\nfrom which correlated mental and material domains emerge.", "\nEach of the examples discussed in this overview has both promising and\nproblematic aspects. The approach by Beck and Eccles is most detailed\nand concrete with respect to the application of standard quantum\nmechanics to the process of exocytosis. However, it does not solve the\nproblem of how the activity of single synapses enters the dynamics of\nneural assemblies, and it leaves the mental causation of quantum\nprocesses as a mere claim. Stapp’s approach suggests a radically\nexpanded ontological basis for both the mental domain and status-quo\nquantum theory as a theory of matter without essentially changing the\nformalism of quantum theory. Although related to inspiring\nphilosophical and some psychological background, it still lacks\nempirical confirmation. The proposal by Penrose and Hameroff exceeds\nthe domain of present-day quantum theory by far and is the most\nspeculative example among those discussed. It is not easy to see how\nthe picture as a whole can be formally worked out and put to empirical\ntest.", "\nThe approach initiated by Umezawa is embedded in the framework of\nquantum field theory, more broadly applicable and formally more\nsophisticated than standard quantum mechanics. It is used to describe\nthe emergence of classical activity in neuronal assemblies on the\nbasis of symmetry breakings in a quantum field theoretical framework.\nA clear conceptual distinction between brain states and mental states\nhas often been missing. Their relation to mental states is has\nrecently been indicated in the framework of a dual-aspect\napproach.", "\nThe dual-aspect approaches of Pauli and Jung and of Bohm and Hiley are\nconceptually more transparent and more promising. Although there is\nnow a huge body of empirically documented mind-matter correlations\nthat supports the Pauli-Jung conjecture, it lacks a detailed formal\nbasis so far. Hiley’s work offers an algebraic framework which\nmay lead to theoretical progress. A novel dual-aspect quantum proposal\nby Primas, based on the distinction between tensed mental time and\ntenseless physical time, marks a significant step forward,\nparticularly as concerns a consistent formal framework.", "\nMaybe the best prognosis for future success among the examples\ndescribed in this overview, at least on foreseeable time scales, goes\nto the investigation of mental quantum features without focusing on\nassociated brain activity to begin with. A number of corresponding\napproaches have been developed which include concrete models for\nconcrete situations and have lead to successful empirical tests and\nfurther predictions. On the other hand, a coherent theory behind\nindividual models and relating the different types of approaches is\nstill to be settled in detail. With respect to scientific practice, a\nparticularly promising aspect is the visible formation of a scientific\ncommunity with conferences, mutual collaborations, and some\nperspicuous attraction for young scientists to join the field. " ], "section_title": "6. Conclusions", "subsections": [] } ]

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[ "\nIn the May 15, 1935 issue of Physical Review Albert Einstein\nco-authored a paper with his two postdoctoral research associates at\nthe Institute for Advanced Study, Boris Podolsky and Nathan Rosen. The\narticle was entitled “Can Quantum Mechanical Description of\nPhysical Reality Be Considered Complete?” (Einstein et\nal. 1935). Generally referred to as “EPR”, this paper\nquickly became a centerpiece in debates over the interpretation of\nquantum theory, debates that continue today. Ranked by impact, EPR is\namong the top ten of all papers ever published in Physical\nReview journals. Due to its role in the development of quantum\ninformation theory, it is also near the top in their list of currently\n“hot“ papers. The paper features a striking case where two\nquantum systems interact in such a way as to link both their spatial\ncoordinates in a certain direction and also their linear momenta (in\nthe same direction), even when the systems are widely separated in\nspace. As a result of this “entanglement”, determining\neither position or momentum for one system would fix (respectively)\nthe position or the momentum of the other. EPR prove a general lemma\nconnecting such strict correlations between spatially separated\nsystems to the possession of definite values. On that basis they argue\nthat one cannot maintain both an intuitive condition of local action\nand the completeness of the quantum description by means of the wave\nfunction. This entry describes the lemma and argument of that 1935\npaper, considers several different versions and reactions, and\nexplores the ongoing significance of the issues raised." ]

[ { "content_title": "1. Can Quantum Mechanical Description of Physical Reality Be Considered Complete?", "sub_toc": [ "1.1 Setting and prehistory", "1.2 The argument in the text", "1.3 Einstein’s versions of the argument" ] }, { "content_title": "2. A popular form of the argument: Bohr’s response", "sub_toc": [] }, { "content_title": "3. Development of EPR", "sub_toc": [ "3.1 Spin and The Bohm version", "3.2 Bell and beyond" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Can Quantum Mechanical Description of Physical Reality Be Considered Complete?", "subsections": [ { "content": [ "\nBy 1935 conceptual understanding of the quantum theory was dominated\nby Niels Bohr’s ideas concerning complementarity. Those ideas centered\non observation and measurement in the quantum domain. According to\nBohr’s views at that time, observing a quantum object involves an\nuncontrollable physical interaction with a measuring device that\naffects both systems. The picture here is of a tiny object banging\ninto a big apparatus. The effect this produces on the measuring\ninstrument is what issues in the measurement “result”\nwhich, because it is uncontrollable, can only be predicted\nstatistically. The effect experienced by the quantum object limits\nwhat other quantities can be co-measured with precision. According to\ncomplementarity when we observe the position of an object, we affect\nits momentum uncontrollably. Thus we cannot determine both position\nand momentum precisely. A similar situation arises for the\nsimultaneous determination of energy and time. Thus complementarity\ninvolves a doctrine of uncontrollable physical interaction that,\naccording to Bohr, underwrites the Heisenberg uncertainty relations\nand is also the source of the statistical character of the quantum\ntheory. (See the entries on the\n Copenhagen Interpretation\n and the\n Uncertainty Principle.)", "\nInitially Einstein was enthusiastic about the quantum theory. By 1935,\nhowever, while recognizing the theory’s significant achievements, his\nenthusiasm had given way to disappointment. His reservations were\ntwofold. Firstly, he felt the theory had abdicated the historical task\nof natural science to provide knowledge of significant aspects of\nnature that are independent of observers or their observations.\nInstead the fundamental understanding of the quantum wave function\n(alternatively, the “state function”, “state\nvector”, or “psi-function”) was that it only treated\nthe outcomes of measurements (via probabilities given by the Born\nRule). The theory was simply silent about what, if anything, was\nlikely to be true in the absence of observation. That there could be\nlaws, even probabilistic laws, for finding things if one looks, but no\nlaws of any sort for how things are independently of whether one\nlooks, marked quantum theory as irrealist. Secondly, the quantum\ntheory was essentially statistical. The probabilities built into the\nstate function were fundamental and, unlike the situation in classical\nstatistical mechanics, they were not understood as arising from\nignorance of fine details. In this sense the theory was\nindeterministic. Thus Einstein began to probe how strongly the quantum\ntheory was tied to irrealism and indeterminism.", "\nHe wondered whether it was possible, at least in principle, to ascribe\ncertain properties to a quantum system in the absence of measurement.\nCan we suppose, for instance, that the decay of an atom occurs at a\ndefinite moment in time even though such a definite decay time is not\nimplied by the quantum state function? That is, Einstein began to ask\nwhether the formalism provides a description of quantum systems that\nis complete. Can all physically relevant truths about systems be\nderived from quantum states? One can raise a similar question about a\nlogical formalism: are all logical truths (or semantically valid\nformulas) derivable from the axioms. Completeness, in this sense, was\na central focus for the Göttingen school of mathematical logic\nassociated with David Hilbert. (See entry on\n Hilbert’s Program.)\n Werner Heisenberg, who had attended Hilbert’s lectures, picked up\nthose concerns with questions about the completeness of his own,\nmatrix approach to quantum mechanics. In response, Bohr (and others\nsympathetic to complementarity) made bold claims not just for the\ndescriptive adequacy of the quantum theory but also for its\n“finality”, claims that enshrined the features of\nirrealism and indeterminism that worried Einstein. (See Beller 1999,\nChapters 4 and 9, on the rhetoric of finality and Ryckman 2017,\nChapter 4, for the connection to Hilbert.) Thus complementarity became\nEinstein’s target for investigation. In particular, Einstein had\nreservations about the uncontrollable physical effects invoked by Bohr\nin the context of measurement interactions, and about their role in\nfixing the interpretation of the wave function. EPR’s focus on\ncompleteness was intended to support those reservations in a\nparticularly dramatic way. ", "\nMax Jammer (1974, pp. 166–181) locates the development of the\nEPR paper in Einstein’s reflections on a thought experiment he\nproposed during discussions at the 1930 Solvay conference. (For more\non EPR and Solvay 1930 see Howard, 1990 and Ryckman, 2017, pp.\n118–135.) The experiment imagines a box that contains a clock\nset to time precisely the release (in the box) of a photon with\ndeterminate energy. If this were feasible, it would appear to\nchallenge the unrestricted validity of the Heisenberg uncertainty\nrelation that sets a lower bound on the simultaneous uncertainty of\nenergy and time. (See the entry on the\n Uncertainty Principle\n and also Bohr 1949, who describes the discussions at the 1930\nconference.) The uncertainty relations, understood not just as a\nprohibition on what is co-measurable, but on what is simultaneously\nreal, were a central component in the irrealist interpretation of the\nwave function. Jammer (1974, p. 173) describes how Einstein’s thinking\nabout this experiment, and Bohr’s objections to it, evolved into a\ndifferent photon-in-a-box experiment, one that allows an observer to\ndetermine either the momentum or the position of the photon\nindirectly, while remaining outside, sitting on the box. Jammer\nassociates this with the distant determination of either momentum or\nposition that, we shall see, is at the heart of the EPR paper. Carsten\nHeld (1998) cites a related\n correspondence with Paul Ehrenfest\n from 1932 in which Einstein described an arrangement for the indirect\nmeasurement of a particle of mass m using correlations with a\nphoton established through Compton scattering. Einstein’s reflections\nhere foreshadow the argument of EPR, along with noting some of its\ndifficulties.", "\nThus without an experiment on m it is possible to predict\nfreely, at will, either the momentum or the position\nof m with, in principle, arbitrary precision. This is the\nreason why I feel compelled to ascribe objective reality to\nboth. I grant, however, that it is not logically necessary.\n(Held 1998, p. 90)\n", "\nWhatever their precursors, the ideas that found their way into EPR\nwere discussed in a series of meetings between Einstein and his two\nassistants, Podolsky and Rosen. Podolsky was commissioned to compose\nthe paper and he submitted it to Physical Review in March of\n1935, where it was sent for publication the day after it arrived.\nApparently Einstein never checked Podolsky’s draft before submission.\nHe was not pleased with the result. Upon seeing the published version,\nEinstein complained that it obscured his central concerns.", "\nFor reasons of language this [paper] was written by Podolsky after\nseveral discussions. Still, it did not come out as well as I had\noriginally wanted; rather, the essential thing was, so to speak,\nsmothered by formalism [Gelehrsamkeit]. (Letter from Einstein to Erwin\nSchrödinger, June 19, 1935. In Fine 1996, p. 35.)\n", "\nUnfortunately, without attending to Einstein’s reservations, EPR is\noften cited to evoke the authority of Einstein. Here we will\ndistinguish the argument Podolsky laid out in the text from lines of\nargument that Einstein himself published in articles from 1935 on. We\nwill also consider the argument presented in Bohr’s reply to EPR,\nwhich is possibly the best known version, although it differs from the\nothers in important ways." ], "subsection_title": "1.1 Setting and prehistory" }, { "content": [ "\nThe EPR text is concerned, in the first instance, with the logical\nconnections between two assertions. One asserts that quantum mechanics\nis incomplete. The other asserts that incompatible quantities (those\nwhose operators do not commute, like the x-coordinate of\nposition and linear momentum in direction x) cannot have\nsimultaneous “reality” (i.e., simultaneously real values).\nThe authors assert the disjunction of these as a first premise (later\nto be justified): one or another of these must hold. It follows that\nif quantum mechanics were complete (so that the first assertion\nfailed) then the second one would hold; i.e., incompatible quantities\ncannot have real values simultaneously. They take as a second premise\n(also to be justified) that if quantum mechanics were complete, then\nincompatible quantities (in particular coordinates of position and\nmomentum) could indeed have simultaneous, real values. They conclude\nthat quantum mechanics is incomplete. The conclusion certainly follows\nsince otherwise (if the theory were complete) one would have a\ncontradiction over simultaneous values. Nevertheless the argument is\nhighly abstract and formulaic and even at this point in its\ndevelopment one can readily appreciate Einstein’s disappointment.", "\nEPR now proceed to establish the two premises, beginning with a\ndiscussion of the idea of a complete theory. Here they offer only a\nnecessary condition; namely, that for a complete theory “every\nelement of the physical reality must have a counterpart in the\nphysical theory.” The term “element“ may remind one\nof Mach, for whom this was a central, technical term connected to\nsensations. (See the entry on\n Ernst Mach.)\n The use in EPR of elements of reality is also technical but\ndifferent. Although they do not define an “element of physical\nreality” explicitly (and, one might note, the language of\nelements is not part of Einstein’s usage elsewhere), that expression\nis used when referring to the values of physical quantities\n(positions, momenta, and so on) that are determined by an underlying\n“real physical state”. The picture is that quantum systems\nhave real states that assign values to certain quantities. Sometimes\nEPR describe this by saying the quantities in question have\n“definite values”, sometimes “there exists an\nelement of physical reality corresponding to the quantity”.\nSuppose we adapt the simpler terminology and call a quantity on a\nsystem definite if that quantity has a definite value; i.e.,\nif the real state of the system assigns a value (an “element of\nreality”) to the quantity. The relation that associates real\nstates with assignments of values to quantities is functional so that\nwithout a change in the real state there is no change among values\nassigned to quantities. In order to get at the issue of completeness,\na primary question for EPR is to determine when a quantity has a\ndefinite value. For that purpose they offer a minimal sufficient\ncondition (p. 777):", "\nIf, without in any way disturbing a system, we can predict with\ncertainty (i.e., with probability equal to unity) the value of a\nphysical quantity, then there exists an element of reality\ncorresponding to that quantity.\n", "\nThis sufficient condition for an “element of reality” is\noften referred to as the EPR\n Criterion of Reality.\n By way of illustration EPR point to those quantities for which the\nquantum state of the system is an eigenstate. It follows from the\nCriterion that at least these quantities have a definite value;\nnamely, the associated eigenvalue, since in an eigenstate the\ncorresponding eigenvalue has probability one, which we can determine\n(predict with certainty) without disturbing the system. In fact,\nmoving from eigenstate to eigenvalue to fix a definite value is the\nonly use of the Criterion in EPR.", "\nWith these terms in place it is easy to show that if, say, the values\nof position and momentum for a quantum system were definite (were\nelements of reality) then the description provided by the wave\nfunction of the system would be incomplete, since no wave function\ncontains counterparts for both elements. Technically, no state\nfunction—even an improper one, like a delta function—is a\nsimultaneous eigenstate for both position and momentum; indeed, joint\nprobabilities for position and momentum are not well-defined in any\nquantum state. Thus they establish the first premise: either quantum\ntheory is incomplete or there can be no simultaneously real\n(“definite”) values for incompatible quantities. They now\nneed to show that if quantum mechanics were complete, then\nincompatible quantities could have simultaneous real values, which is\nthe second premise. This, however, is not easily established. Indeed\nwhat EPR proceed to do is odd. Instead of assuming completeness and on\nthat basis deriving that incompatible quantities can have real values\nsimultaneously, they simply set out to derive the latter assertion\nwithout any completeness assumption at all. This\n“derivation” turns out to be the heart of the paper and\nits most controversial part. It attempts to show that in certain\ncircumstances a quantum system can have simultaneous values for\nincompatible quantities (once again, for position and momentum), where\nthese are definite values; that is, they are assigned by the real\nstate of the system, hence are “elements of reality”.", "\nThey proceed by sketching an iconic thought experiment whose\nvariations continue to be important and widely discussed. The\nexperiment concerns two quantum systems that are spatially distant\nfrom one another, perhaps quite far apart, but such that the total\nwave function for the pair links both the positions of the systems as\nwell as their linear momenta. In the EPR example the total linear\nmomentum is zero along the x-axis. Thus if the linear\nmomentum of one of the systems (we can call it Albert’s) along the\nx-axis were found to be p, the x-momentum\nof the other system (call it Niels’) would be found to be\n−p. At the same time their positions along x\nare also strictly correlated so that determining the position of one\nsystem on the x-axis allows us to infer the position of the\nother system along x. The paper constructs an explicit wave\nfunction for the combined (Albert+Niels) system that embodies these\nlinks even when the systems are widely separated in space. Although\ncommentators later raised questions about the legitimacy of this wave\nfunction, it does appear to guarantee the required correlations for\nspatially separated systems, at least for a moment (Jammer 1974, pp.\n225–38; see also Halvorson 2000). In any case, one can model the\nsame conceptual situation in other cases that are clearly well defined\nquantum mechanically (see\n Section 3.1).", "\nAt this point of the argument (p. 779) EPR make two critical\nassumptions, although they do not call special attention to them. (For\nthe significance of these assumptions in Einstein’s thinking see\nHoward 1985 and also section 5 of the entry on\n Einstein.)\n The first assumption (separability) is that at the time when\nthe systems are separated, maybe quite far apart, each has its own\nreality. In effect, they assume that each system maintains a separate\nidentity characterized by a real physical state, even though each\nsystem is also strictly correlated with the other in respect both to\nmomentum and position. They need this assumption to make sense of\nanother. The second assumption is that of locality. Given\nthat the systems are far apart, locality supposes that “no real\nchange can take place” in one system as a direct consequence of\na measurement made on the other system. They gloss this by saying\n“at the time of measurement the two systems no longer\ninteract.” Note that locality does not require that nothing at\nall about one system can be disturbed directly by a distant\nmeasurement on the other system. Locality only rules out that a\ndistant measurement may directly disturb or change what is counted as\n“real“ with respect to a system, a reality that\nseparability guarantees. On the basis of these two assumptions they\nconclude that each system can have definite values (“elements of\nreality”) for both position and momentum simultaneously. There\nis no straightforward argument for this in the text. Instead they use\nthese two assumptions to show how one could be led to assign position\nand momentum eigenstates to one system by making measurements on the\nother system, from which the simultaneous attribution of elements of\nreality is supposed to follow. Since this is the central and most\ncontroversial part of the paper, it pays to go slowly here in trying\nto reconstruct an argument on their behalf.", "\nHere is one attempt. (Dickson 2004 analyzes some of the modal\nprinciples involved and suggests one line of argument, which he\ncriticizes. Hooker 1972 is a comprehensive discussion that identifies\nseveral generically different ways to make the case.) Locality affirms\nthat the real state of a system is not affected by distant\nmeasurements. Since the real state determines which quantities are\ndefinite (i.e., have assigned values), the set of definite quantities\nis also not affected by distant measurements. So if by measuring a\ndistant partner we can determine that a certain quantity is definite,\nthen that quantity must have been definite all along. As we have seen,\nthe\n Criterion of Reality\n implies that a quantity is definite if the state of the system is an\neigenstate for that quantity. In the case of the strict correlations\nof EPR, measuring one system triggers a reduction of the joint state\nthat results in an eigenstate for the distant partner. Hence any\nquantity with that eigenstate is definite. For example, since\nmeasuring the momentum of Albert’s system results in a momentum\neigenstate for Niels’, the momentum of Niels’ system is definite.\nLikewise for the position of Niels’ system. Given separability, the\ncombination of locality and the Criterion establish a quite general\nlemma; namely, when quantities on separated systems have strictly\ncorrelated values, those quantities are definite. Thus the strict\ncorrelations between Niels’ system and Albert’s in the EPR situation\nguarantee that both position and momentum are definite; i. e., that\neach system has definite position and momentum simultaneously.", "\nEPR point out that position and momentum cannot be measured\nsimultaneously. So even if each can be shown to be definite in\ndistinct contexts of measurement, can both be definite at the same\ntime? The lemma answers “yes”. What drives the argument is\nlocality, which functions logically to decontextualize the reality of\nNiels’ system from goings on at Albert’s. Accordingly, measurements\nmade on Albert’s system are probative for features corresponding to\nthe real state of Niels’ system but not determinative of them. Thus\neven without measuring Albert’s system, features corresponding to the\nreal state of Niels’ system remain in place. Among those features are\na definite position and a definite momentum for Niels’ system along\nsome particular coordinate direction.", "\nIn the penultimate paragraph of EPR (p. 780) they address the problem\nof getting real values for incompatible quantities simultaneously.", "\nIndeed one would not arrive at our conclusion if one insisted that two\nor more physical quantities can be regarded as simultaneous elements\nof reality only when they can be simultaneously measured or predicted.\n… This makes the reality [on the second system] depend upon the\nprocess of measurement carried out on the first system, which does not\nin any way disturb the second system. No reasonable definition of\nreality could be expected to permit this.\n", "\nThe unreasonableness to which EPR allude in making “the reality\n[on the second system] depend upon the process of measurement carried\nout on the first system, which does not in any way disturb the second\nsystem” is just the unreasonableness that would be involved in\nrenouncing locality understood as above. For it is locality that\nenables one to overcome the incompatibility of position and momentum\nmeasurements of Albert’s system by requiring their joint consequences\nfor Niels’ system to be incorporated in a single, stable reality\nthere. If we recall\n Einstein’s acknowledgment to Ehrenfest\n that getting simultaneous position and momentum was “not\nlogically necessary”, we can see how EPR respond by making it\nbecome necessary once locality is assumed.", "\nHere, then, are the key features of EPR.", "\nThe EPR experiment with interacting systems accomplishes a form of\nindirect measurement. The direct measurement of Albert’s system\nyields information about Niels’ system; it tells us what we\nwould find if we were to measure there directly. But it does this\nat-a-distance, without any physical interaction taking place between\nthe two systems. Thus the thought experiment at the heart of EPR\nundercuts the picture of measurement as necessarily involving a tiny\nobject banging into a large measuring instrument. If we look back at\nEinstein’s reservations about complementarity, we can appreciate\nthat by focusing on an indirect, non-disturbing kind of measurement\nthe EPR argument targets Bohr’s program for explaining central\nconceptual features of the quantum theory. For that program relied on\nuncontrollable interaction with a measuring device as a necessary\nfeature of any measurement in the quantum domain. Nevertheless the\ncumbersome machinery employed in the EPR paper makes it difficult to\nsee what is central. It distracts from rather than focuses on the\nissues. That was Einstein’s complaint about Podolsky’s\ntext in his June 19, 1935 letter to Schrödinger.\nSchrödinger responded on July 13 reporting reactions to EPR that\nvindicate Einstein’s concerns. With reference to EPR he\nwrote:", "\nI am now having fun and taking your note to its source to provoke the\nmost diverse, clever people: London, Teller, Born, Pauli, Szilard,\nWeyl. The best response so far is from Pauli who at least admits that\nthe use of the word “state” [“Zustand”] for\nthe psi-function is quite disreputable. What I have so far seen by way\nof published reactions is less witty. … It is as if one person\nsaid, “It is bitter cold in Chicago”; and another\nanswered, “That is a fallacy, it is very hot in Florida.”\n(Fine 1996, p. 74)\n" ], "subsection_title": "1.2 The argument in the text" }, { "content": [ "\nIf the argument developed in EPR has its roots in the 1930 Solvay\nconference, Einstein’s own approach to issues at the heart of EPR has\na history that goes back to the 1927 Solvay conference. (Bacciagaluppi\nand Valentini 2009, pp. 198–202, would even trace it back to\n1909 and the localization of light quanta.) At that 1927 conference\nEinstein made a short presentation during the general discussion\nsession where he focused on problems of interpretation associated with\nthe collapse of the wave function. He imagines a situation where\nelectrons pass through a small hole and are dispersed uniformly in the\ndirection of a screen of photographic film shaped into a large\nhemisphere that surrounds the hole. On the supposition that quantum\ntheory offers a complete account of individual processes then, in the\ncase of localization, why does the whole wave front collapse to just\none single flash point? It is as though at the moment of collapse an\ninstantaneous signal were sent out from the point of collapse to all\nother possible collapse positions telling them not to flash. Thus\nEinstein maintains (Bacciagaluppi and Valentini 2009, p. 488),", "\nthe interpretation, according to which |ψ|² expresses the\nprobability that this particle is found at a given point,\nassumes an entirely peculiar mechanism of action at a distance, which\nprevents the wave continuously distributed in space from producing an\naction in two places on the screen.\n", "\nOne could see this as a tension between local action and the\ndescription afforded by the wave function, since the wave function\nalone does not specify a unique position on the screen for detecting\nthe particle. Einstein continues,", "\nIn my opinion, one can remove this objection only in the following\nway, that one does not describe the process solely by the\nSchrödinger wave, but that at the same time one localizes the\nparticle during propagation.\n", "\nIn fact Einstein himself had tried this very route in May of 1927\nwhere he proposed a way of “localizing the particle” by\nassociating spatial trajectories and velocities with particle\nsolutions to the Schrödinger equation. (See Belousek 1996 and\nHolland 2005; also Ryckman 2017.) Einstein abandoned the project and\nwithdrew the draft from publication, however, after finding that\ncertain intuitive independence conditions were in conflict with the\nproduct wave function used by quantum mechanics to treat the\ncomposition of independent systems. The problem here anticipates the\nmore general issues raised by EPR over separability and composite\nsystems. This proposal was Einstein’s one and only flirtation with the\nintroduction of hidden variables into the quantum theory. In the\nfollowing years he never embraced any proposal of that sort, although\nhe hoped for progress in physics to yield a more complete theory, and\none where the observer did not play a fundamental role. “We\nbelieve however that such a theory [“a complete description of\nthe physical reality”] is possible” (p. 780). Commentators\nhave often mistaken that remark as indicating Einstein’s predilection\nfor hidden variables. To the contrary, after 1927 Einstein regarded\nthe hidden variables project — the project of developing a more\ncomplete theory by starting with the existing quantum theory and\nadding things, like trajectories or real states — an improbable\nroute to that goal. (See, for example, Einstein 1953a.) To improve on\nthe quantum theory, he thought, would require starting afresh with\nquite different fundamental concepts. At Solvay he acknowledges Louis\nde Broglie’s pilot wave investigations as a possible direction to\npursue for a more complete account of individual processes. But then\nhe quickly turns to an alternative way of thinking, one that he\ncontinued to recommend as a better framework for progress, which is\nnot to regard the quantum theory as describing individuals and their\nprocesses at all and, instead, to regard the theory as describing only\nensembles of individuals. Einstein goes on to suggest difficulties for\nany scheme, like de Broglie’s and like quantum theory itself, that\nrequires representations in multi-dimensional configuration space.\nThese are difficulties that might move one further toward regarding\nquantum theory as not aspiring to a description of individual systems\nbut as more amenable to an ensemble (or collective) point of view, and\nhence not a good starting point for building a better, more complete\ntheory. His subsequent elaborations of EPR-like arguments are perhaps\nbest regarded as no-go arguments, showing that the existing\nquantum theory does not lend itself to a sensible realist\ninterpretation via hidden variables. If real states, taken as hidden\nvariables, are added into the existing theory, which is then tailored\nto explain individual events, the result is either an incomplete\ntheory or else a theory that does not respect locality. Hence, new\nconcepts are needed. With respect to EPR, perhaps the most important\nfeature of Einstein’s reflections at Solvay 1927 is his insight that a\nclash between completeness and locality already arises in considering\na single variable (there, position) and does not require an\nincompatible pair, as in EPR.", "\nFollowing the publication of EPR Einstein set about almost immediately\nto provide clear and focused versions of the argument. He began that\nprocess within few weeks of EPR, in the June 19 letter to\nSchrödinger, and continued it in an article published the\nfollowing year (Einstein 1936). He returned to this particular form of\nan incompleteness argument in two later publications (Einstein 1948\nand Schilpp 1949). Although these expositions differ in details they\nall employ composite systems as a way of implementing indirect\nmeasurements-at-a-distance. None of Einstein’s accounts contains the\n Criterion of Reality\n nor the tortured EPR argument over when values of a quantity can be\nregarded as “elements of reality”. The Criterion and these\n“elements” simply drop out. Nor does Einstein engage in\ncalculations, like those of Podolsky, to fix the total wave function\nfor the composite system explicitly. Unlike EPR, none of Einstein’s\narguments makes use of simultaneous values for complementary\nquantities like position and momentum. He does not challenge the\nuncertainty relations. Indeed with respect to assigning eigenstates\nfor a complementary pair he tells Schrödinger “ist mir\nwurst”—literally, it’s sausage to me; i.e., he couldn’t\ncare less. (Fine 1996, p. 38). These writings probe an incompatibility\nbetween affirming locality and separability, on the one hand, and\ncompleteness in the description of individual systems by means of\nstate functions, on the other. His argument is that we can have at\nmost one of these but never both. He frequently refers to this dilemma\nas a “paradox”.", "\nIn the letter to Schrödinger of June 19, Einstein points to a\nsimple argument for the dilemma which, like the argument from the 1927\nSolvay Conference, involves only the measurement of a single variable.\nConsider an interaction between the Albert and Niels systems that\nestablishes a strict correlation between their positions. (We need not\nworry about momentum, or any other quantity.) Consider the evolved\nwave function for the total (Albert+Niels) system when the two systems\nare far apart. Now assume a principle of locality-separability\n(Einstein calls it a Trennungsprinzip—separation\nprinciple): Whether a determinate physical situation holds for Niels’\nsystem (e.g., that a quantity has a particular value) does not depend\non what measurements (if any) are made locally on Albert’s system. If\nwe measure the position of Albert’s system, the strict correlation of\npositions implies that Niels’ system has a certain position. By\nlocality-separability it follows that Niels’ system must already have\nhad that position just before the measurement on Albert’s system. At\nthat time, however, Niels’ system alone does not have a state\nfunction. There is only a state function for the combined system and\nthat total state function does not single out an existing position for\nNiels’ system (i.e., it is not a product one of whose factors is an\neigenstate for the position of Niels’ system). Thus the description of\nNiels’ system afforded by the quantum state function is incomplete. A\ncomplete description would say (definitely yes) if a quantity of\nNiels’ system had a certain value. (Notice that this argument does not\neven depend on the reduction of the total state function for the\ncombined system.) In this formulation of the argument it is clear that\nlocality-separability conflicts with\n the eigenvalue-eigenstate link,\n which holds that a quantity of a system has a value if and only if\nthe state of the system is an eigenstate (or a proper mixture of\neigenstates) of that quantity with that value as eigenvalue. The\n“only if” part of the link would need to be weakened in\norder to interpret quantum state functions as complete descriptions.\n(See the entry on\n Modal Interpretations\n and see Gilton 2016 for a history of the eigenvalue-eigenstate\nlink.)", "\nThis argument rests on the ordinary and intuitive notion of\ncompleteness as not omitting relevant truths. Thus, in the argument,\nthe description given by the state function of a system is judged\nincomplete when it fails to attribute a position to the system in\ncircumstances where the system indeed has a position. Although this\nsimple argument concentrates on what Einstein saw as the essentials,\nstripping away most technical details and distractions, he frequently\nused another argument involving more than one quantity. (It is\nactually buried in the EPR paper, p. 779, and a version also occurs in\nthe June 19, 1935 letter to Schrödinger. Harrigan and Spekkens,\n2010 suggest reasons for preferring a many-variables argument.) This\nsecond argument focuses clearly on the interpretation of quantum state\nfunctions in terms of “real states” of a system, and not\non any issues about simultaneous values (real or not) for\ncomplementary quantities. It goes like this.", "\nSuppose, as in EPR, that the interaction between the two systems links\nposition and also linear momentum, and that the systems are far apart.\nAs before, we can measure either the position or the momentum of\nAlbert’s system and, in either case, we can infer (respectively) a\nposition or a momentum for Niels’ system. It follows from the\nreduction of the total state function that, depending on whether we\nmeasure the position or the momentum of Albert’s system, Niels’ system\nwill be left (respectively) either in a position eigenstate or in a\nmomentum eigenstate. Suppose too that separability holds, so that\nNiels’ system has some real physical state of affairs. If locality\nholds as well, then the measurement of Albert’s system does not\ndisturb the assumed “reality” for Niels’ system. However,\nthat reality appears to be represented by quite different state\nfunctions, depending on which measurement of Albert’s system one\nchooses to carry out. If we understand a “complete\ndescription” to rule out that one and the same physical state\ncan be described by state functions with distinct physical\nimplications, then we can conclude that the quantum mechanical\ndescription is incomplete. Here again we confront a dilemma between\nseparability-locality and completeness. Many years later Einstein put\nit this way (Schilpp 1949, p. 682);", "\n[T]he paradox forces us to relinquish one of the following two\nassertions:\n\n(1) the description by means of the psi-function is complete\n\n(2) the real states of spatially separate objects are independent of\neach other.\n", "\nIt appears that the central point of EPR was to argue that any\ninterpretation of quantum state functions that attributes real\nphysical states to systems faces these alternatives. It also appears\nthat Einstein’s different arguments make use of different notions of\ncompleteness. In the first argument completeness is an ordinary notion\nthat amounts to not leaving out any relevant details. In the second,\ncompleteness is a technical notion which has been dubbed\n“bijective completeness“ (Fine 1996 ): no more than one\nquantum state should correspond to a real state. These notions are\nconnected. If completeness fails in the bijective sense, and more than\none quantum state corresponds to some real state, we can argue that\nthe ordinary notion of completeness also fails. For distinct quantum\nstates will differ in the values they assign to certain quantities.\n(For example, the observable corresponding to the projector on a state\ntakes value 1 in one case but not in the other.) Hence each will omit\nsomething that the other affirms, so completeness in the ordinary\nsense will fail. Put differently, ordinary completeness implies\nbijective completeness. (The converse is not true. Even if the\ncorrespondence of quantum states to real states were one-to-one, the\ndescription afforded by a quantum state might still leave out some\nphysically relevant fact about its corresponding real state.) Thus a\ndilemma between locality and “completeness“ in Einstein’s\nversions of the argument still implicates ordinary completeness. For\nif locality holds, then his two-variable argument shows that bijective\ncompleteness fails, and then completeness in the ordinary sense fails\nas well.", "\nAs we have seen, in framing his own EPR-like arguments for the\nincompleteness of quantum theory, Einstein makes use of\n separability\n and\n locality,\n which are also tacitly assumed in the EPR paper. Using the language\nof “independent existence“ he presents these ideas clearly\nin an article that he sent to Max Born (Einstein 1948). ", "\nIt is … characteristic of … physical objects that they\nare thought of as arranged in a space-time continuum. An essential\naspect of this arrangement … is that they lay claim, at a\ncertain time, to an existence independent of one another, provided\nthese objects “are situated in different parts of space”.\n… The following idea characterizes the relative independence of\nobjects (A and B) far apart in space: external influence on A has no\ndirect influence on B. (Born, 1971, pp. 170–71)\n", "\nIn the course of his correspondence with Schrödinger, however,\nEinstein realized that assumptions about separability and locality\nwere not necessary in order to get the incompleteness conclusion that\nhe was after; i.e., to show that state functions may not provide a\ncomplete description of the real state of affairs with respect to a\nsystem. Separability supposes that there is a real state of affairs\nand locality supposes that one cannot influence it immediately by\nacting at a distance. What Einstein realized was that separability was\nalready part of the ordinary conception of a macroscopic object. This\nsuggested to him that if one looks at the local interaction of a\nmacro-system with a micro-system one could avoid having to assume\neither separability or locality in order to conclude that the quantum\ndescription of the whole was incomplete with respect to its\nmacroscopic part. ", "\nThis line of thought evolves and dominates over problems with\ncomposite systems and locality in his last published reflections on\nincompleteness. Instead he focuses on problems with the stability of\nmacro-descriptions in the transition to a classical level from the\nquantum. ", "\nthe objective describability of individual macro-systems (description\nof the “real-state”) can not be renounced without the\nphysical picture of the world, so to speak, decomposing into a fog.\n(Einstein 1953b, p. 40. See also Einstein 1953a.)\n", "\nIn the August 8, 1935 letter to Schrödinger Einstein says that he\nwill illustrate the problem by means of a “crude macroscopic\nexample”.", "\nThe system is a substance in chemically unstable equilibrium, perhaps\na charge of gunpowder that, by means of intrinsic forces, can\nspontaneously combust, and where the average life span of the whole\nsetup is a year. In principle this can quite easily be represented\nquantum-mechanically. In the beginning the psi-function characterizes\na reasonably well-defined macroscopic state. But, according to your\nequation [i.e., the Schrödinger equation], after the course of a\nyear this is no longer the case. Rather, the psi-function then\ndescribes a sort of blend of not-yet and already-exploded systems.\nThrough no art of interpretation can this psi-function be turned into\nan adequate description of a real state of affairs; in reality there\nis no intermediary between exploded and not-exploded. (Fine 1996, p.\n78)\n", "\nThe point is that after a year either the gunpowder will have\nexploded, or not. (This is the “real state” which in the\nEPR situation requires one to assume separability.) The state\nfunction, however, will have evolved into a complex superposition over\nthese two alternatives. Provided we maintain the eigenvalue-eigenstate\nlink, the quantum description by means of that state function will\nyield neither conclusion, and hence the quantum description is\nincomplete. For a contemporary response to this line of argument, one\nmight look to the program of decoherence. (See\n Decoherence.)\n That program points to interactions with the environment which may\nquickly reduce the likelihood of any interference between the\n“exploded” and the “not-exploded” branches of\nthe evolved psi-function. Then, breaking the eigenvalue-eigenstate\nlink, decoherence adopts a perspective according to which the (almost)\nnon-interfering branches of the psi-function allow that the gunpowder\nis indeed either exploded or not. Even so, decoherence fails to\nidentify which alternative is actually realized, leaving the quantum\ndescription still incomplete. Such decoherence-based interpretations\nof the psi-function are certainly “artful”, and their\nadequacy is still under debate (see Schlosshauer 2007, especially\nChapter 8).", "\nThe reader may recognize the similarity between Einstein’s\n exploding gunpowder example\n and Schrödinger’s cat (Schrödinger 1935a, p. 812). In the\ncase of the cat an unstable atom is hooked up to a lethal device that,\nafter an hour, is as likely to poison (and kill) the cat as not,\ndepending on whether the atom decays. After an hour the cat is either\nalive or dead, but the quantum state of the whole atom-poison-cat\nsystem at this time is a superposition involving the two possibilities\nand, just as in the case of the gunpowder, is not a complete\ndescription of the situation (life or death) of the cat. The\nsimilarity between the gunpowder and the cat is hardly accidental\nsince Schrödinger first produced the cat example in his reply of\nSeptember 19, 1935 to Einstein’s August 8 gunpowder letter. There\nSchrödinger says that he has himself constructed “an\nexample very similar to your exploding powder keg”, and proceeds\nto outline the cat (Fine 1996, pp. 82–83). Although the\n“cat paradox” is usually cited in connection with the\nproblem of quantum measurement (see the relevant section of the entry\non\n Philosophical Issues in Quantum Theory)\n and treated as a paradox separate from EPR, its origin is here as an\nargument for incompleteness that avoids the twin assumptions of\nseparability and locality. Schrödinger’s development of\n“entanglement”, the term he introduced for the\ncorrelations that result when quantum systems interact, also began in\nthis correspondence over EPR — along with a treatment of what he\ncalled quantum “steering” (Schrödinger 1935a, 1935b;\nsee\n Quantum Entanglement and Information)." ], "subsection_title": "1.3 Einstein’s versions of the argument" } ] }, { "main_content": [ "\nThe literature surrounding EPR contains yet another version of the\nargument, a popular version that—unlike any of\nEinstein’s—features the\n Criterion of Reality.\n Assume again an interaction between our two systems linking their\npositions and their linear momenta and suppose that the systems are\nfar apart. If we measure the position of Albert’s system, we can infer\nthat Niels’ system has a corresponding position. We can also predict\nit with certainty, given the result of the position measurement of\nAlbert’s system. Hence, in this version, the Criterion of Reality is\ntaken to imply that the position of Niels’ system constitutes an\nelement of reality. Similarly, if we measure the momentum of Albert’s\nsystem, we can conclude that the momentum of Niels’ system is an\nelement of reality. The argument now concludes that since we can\nchoose freely to measure either position or momentum, it\n“follows” that both must be elements of reality\nsimultaneously.", "\nOf course no such conclusion follows from our freedom of choice. It is\nnot sufficient to be able to choose at will which quantity to measure;\nfor the conclusion to follow from the Criterion alone one would need\nto be able to measure both quantities at once. This is precisely the\npoint that Einstein recognized in his\n 1932 letter to Ehrenfest\n and that EPR addresses by assuming locality and separability. What is\nstriking about this version is that these principles, central to the\noriginal EPR argument and to the dilemma at the heart of Einstein’s\nversions, are obscured here. Instead this version features the\nCriterion and those “elements of reality”. Perhaps the\ndifficulties presented by Podolsky’s text contribute to this reading.\nIn any case, in the physics literature this version is commonly taken\nto represent EPR and usually attributed to Einstein. This reading\ncertainly has a prominent source in terms of which one can understand\nits popularity among physicists; it is Niels Bohr himself.", "\nBy the time of the EPR paper many of the early interpretive battles\nover the quantum theory had been settled, at least to the satisfaction\nof working physicists. Bohr had emerged as the\n“philosopher” of the new theory and the community of\nquantum theorists, busy with the development and extension of the\ntheory, were content to follow Bohr’s leadership when it came to\nexplaining and defending its conceptual underpinnings (Beller 1999,\nChapter 13). Thus in 1935 the burden fell to Bohr to explain what was\nwrong with the EPR “paradox”. The major article that he\nwrote in discharging this burden (Bohr 1935a) became the canon for how\nto respond to EPR. Unfortunately, Bohr’s summary of EPR in that\narticle, which is the version just above, also became the canon for\nwhat EPR contained by way of argument.", "\nBohr’s response to EPR begins, as do many of his treatments of the\nconceptual issues raised by the quantum theory, with a discussion of\nlimitations on the simultaneous determination of position and\nmomentum. As usual, these are drawn from an analysis of the\npossibilities of measurement if one uses an apparatus consisting of a\ndiaphragm connected to a rigid frame. Bohr emphasizes that the\nquestion is to what extent can we trace the interaction between the\nparticle being measured and the measuring instrument. (See Beller\n1999, Chapter 7 for a detailed analysis and discussion of the\n“two voices” contained in Bohr’s account. See too\nBacciagaluppi 2015.) Following the summary of EPR, Bohr (1935a, p.\n700) then focuses on the Criterion of Reality which, he says,\n“contains an ambiguity as regards the meaning of the expression\n‘without in any way disturbing a system’.” Bohr\nagrees that in the indirect measurement of Niels’ system achieved when\none makes a measurement of Albert’s system “there is no question\nof a mechanical disturbance” of Niels’ system. Still, Bohr\nclaims that a measurement on Albert’s system does involve “an\ninfluence on the very conditions which define the possible types of\npredictions regarding the future behavior of [Niels’] system.”\nThe meaning of this claim is not at all clear. Indeed, in revisiting\nEPR fifteen years later, Bohr would comment, ", "\nRereading these passages, I am deeply aware of the inefficiency of\nexpression which must have made it very difficult to appreciate the\ntrend of the argumentation (Bohr 1949, p. 234).\n", "\nUnfortunately, Bohr takes no notice there of Einstein’s later versions\nof the argument and merely repeats his earlier response to EPR. In\nthat response, however inefficiently, Bohr appears to be directing\nattention to the fact that when we measure, for example, the position\nof Albert’s system conditions are in place for predicting the position\nof Niels’ system but not its momentum. The opposite would be true in\nmeasuring the momentum of Albert’s system. Thus his “possible\ntypes of predictions” concerning Niels’ system appear to\ncorrespond to which variable we measure on Albert’s system. Bohr\nproposes then to block the EPR Criterion by counting, say, the\nposition measurement of Albert’s system as an “influence”\non the distant system of Niels. If we assume it is an influence that\ndisturbs Niels’ system, then the Criterion could not be used, as in\nBohr’s version of the argument, in producing an element of reality for\nNiels’ system that challenges completeness.", "\nThere are two important things to notice about this response. The\nfirst is this. In conceding that Einstein’s indirect method for\ndetermining, say, the position of Niels’ system does not mechanically\ndisturb that system, Bohr departs from his original program of\ncomplementarity, which was to base the uncertainty relations and the\nstatistical character of quantum theory on uncontrollable physical\ninteractions, interactions that were supposed to arise inevitably\nbetween a measuring instrument and the system being measured. Instead\nBohr now distinguishes between a genuine physical interaction (his\n“mechanical disturbance”) and some other sort of\n“influence” on the conditions for specifying (or\n“defining”) sorts of predictions for the future behavior\nof a system. In emphasizing that there is no question of a robust\ninteraction in the EPR situation, Bohr retreats from his earlier,\nphysically grounded conception of complementarity.", "\nThe second important thing to notice is how Bohr’s response needs to\nbe implemented in order to block the argument of EPR and Einstein’s\nlater arguments that pose a dilemma between principles of locality and\ncompleteness. In these arguments the locality principle makes explicit\nreference to the reality of the unmeasured system: the reality\npertaining to Niels’ system does not depend on what measurements (if\nany) are made locally on Albert’s system. Hence Bohr’s suggestion that\nthose measurements influence conditions for specifying types of\npredictions would not affect the argument unless one includes those\nconditions as part of the reality of Niels’ system. This is exactly\nwhat Bohr goes on to say, “these conditions constitute an\ninherent element of the description of any phenomena to which the term\n‘physical reality’ can be properly attached” (Bohr\n1935a, p. 700). So Bohr’s picture is that these\n“influences”, operating directly across any spatial\ndistances, result in different physically real states of Niels’ system\ndepending on the type of measurement made on Albert’s. (Recall EPR\nwarning against just this move.) ", "\nThe quantum formalism for interacting systems describes how a\nmeasurement on Albert’s system reduces the composite state and\ndistributes quantum states and associated probabilities to the\ncomponent systems. Here Bohr redescribes that formal reduction using\nEPR’s language of influences and reality. He turns ordinary local\nmeasurements into “influences” that automatically change\nphysical reality elsewhere, and at any distance whatsoever. This\ngrounds the quantum formalism in a rather magical ontological\nframework, a move quite out of character for the usually pragmatic\nBohr. In his correspondence over EPR, Schrödinger compared ideas\nlike that to ritual magic. ", "\nThis assumption arises from the standpoint of the savage, who believes\nthat he can harm his enemy by piercing the enemy’s image with a\nneedle. (Letter to Edward Teller, June 14, 1935, quoted in\nBacciagaluppi 2015)\n", "\nIt is as though EPR’s talk of “reality” and its elements\nprovoked Bohr to adopt the position of Moliere’s doctor who, pressed\nto explain why opium is a sedative, invents an inherent dormative\nvirtue, “which causes the senses to become drowsy.”\nUsually Bohr sharply deflates any attempt like this to get behind the\nformalism, insisting that “the appropriate physical\ninterpretation of the symbolic quantum-mechanical formalism amounts\nonly to predictions, of determinate or statistical character”\n(Bohr 1949, p. 238).", "\nCould this portrait of nonlocal influences automatically shaping a\ndistant reality be a by-product of Bohr’s “inefficiency of\nexpression”? Despite Bohr’s seeming tolerance for a breakdown of\nlocality in his response here to EPR, in other places Bohr rejects\nnonlocality in the strongest terms. For example in discussing an\nelectron double slit experiment, which is Bohr’s favorite model for\nillustrating the novel conceptual features of quantum theory, and\nwriting only weeks before the publication of EPR, Bohr argues as\nfollows.", "\nIf we only imagine the possibility that without disturbing the\nphenomena we determine through which hole the electron passes, we\nwould truly find ourselves in irrational territory, for this would put\nus in a situation in which an electron, which might be said to pass\nthrough this hole, would be affected by the circumstance of whether\nthis [other] hole was open or closed; but … it is completely\nincomprehensible that in its later course [the electron] should let\nitself be influenced by this hole down there being open or shut. (Bohr\n1935b)\n", "\nIt is uncanny how closely Bohr’s language mirrors that of EPR. But\nhere Bohr defends locality and regards the very contemplation of\nnonlocality as “irrational” and “completely\nincomprehensible”. Since “the circumstance of whether this\n[other] hole was open or closed” does affect the possible types\nof predictions regarding the electron’s future behavior, if we expand\nthe concept of the electron’s “reality”, as he appears to\nsuggest for EPR, by including such information, we do\n“disturb” the electron around one hole by opening or\nclosing the other hole. That is, if we give to “disturb”\nand to “reality” the very same sense that Bohr appears to\ngive them when responding to EPR, then we are led to an\n“incomprehensible” nonlocality, and into the territory of\nthe irrational (like Schrödinger’s savage).", "\nThere is another way of trying to understand Bohr’s position.\nAccording to one common reading (see\n Copenhagen Interpretation),\n after EPR Bohr embraced a relational (or contextual) account of\nproperty attribution. On this account to speak of the position, say,\nof a system presupposes that one already has put in place an\nappropriate interaction involving an apparatus for measuring position\n(or at least an appropriate frame of reference for the measurement;\nDickson 2004). Thus “the position” of the system refers to\na relation between the system and the measuring device (or measurement\nframe). (See\n Relational Quantum Mechanics,\n where a similar idea is developed independently of measurements.) In\nthe EPR context this would seem to imply that before one is set up to\nmeasure the position of Albert’s system, talk of the position of\nNiels’ system is out of place; whereas after one measures the position\nof Albert’s system, talk of the position of Niels’ system is\nappropriate and, indeed, we can then say truly that Niels’ system\n“has” a position. Similar considerations govern momentum\nmeasurements. It follows, then, that local manipulations carried out\non Albert’s system, in a place we may assume to be far removed from\nNiels’ system, can directly affect what is meaningful to say about, as\nwell as factually true of, Niels’ system. Similarly, in the double\nslit arrangement, it would follow that what can be said meaningfully\nand said truly about the position of the electron around the top hole\nwould depend on the context of whether the bottom hole is open or\nshut. One might suggest that such relational actions-at-a-distance are\nharmless ones, perhaps merely “semantic”; like becoming\nthe “best” at a task when your only competitor—who\nmight be miles away—fails. Note, however, that in the case of\nordinary relational predicates it is not inappropriate (or\n“meaningless”) to talk about the situation in the absence\nof complete information about the relata. So you might be the best at\na task even if your competitor has not yet tried it, and you are\ndefinitely not an aunt (or uncle) until one of your siblings gives\nbirth. But should we say that an electron is nowhere at all until we\nare set up to measure its position, or would it be inappropriate\n(meaningless?) even to ask? ", "\nIf quantum predicates are relational, they are different from many\nordinary relations in that the conditions for the relata are taken as\ncriterial for the application of the term. In this regard one might\ncontrast the relativity of simultaneity with the proposed relativity\nof position. In relativistic physics specifying a world-line fixes a\nframe of reference for attributions of simultaneity to events\nregardless of whether any temporal measurements are being made or\ncontemplated. But in the quantum case, on this proposal, specifying a\nframe of reference for position (say, the laboratory frame) does not\nentitle one to attribute position to a system, unless that frame is\nassociated with actually preparing or completing a measurement of\nposition for that system. To be sure, analyzing predicates in terms of\noccurrent measurement or observation is familiar from neopositivist\napproaches to the language of science; for example, in Percy\nBridgman’s operational analysis of physical terms, where the actual\napplications of test-response pairs constitute criteria for any\nmeaningful use of a term (see\n Theory and Observation in Science ).\n Rudolph Carnap’s later introduction of reduction sentences (see the\nentry on the\n Vienna Circle)\n has a similar character. Still, this positivist reading entails just\nthe sort of nonlocality that Bohr seemed to abhor.", "\nIn the light of all this it is difficult to know whether a coherent\nresponse can be attributed to Bohr reliably that would derail EPR. (In\ndifferent ways, Dickson 2004 and Halvorson and Clifton 2004 make an\nattempt on Bohr’s behalf. These are examined in Whitaker 2004 and Fine\n2007. See also the essays in Faye and Folse 2017.) Bohr may well have\nbeen aware of the difficulty in framing the appropriate concepts\nclearly when, a few years after EPR, he wrote,", "\nThe unaccustomed features of the situation with which we are\nconfronted in quantum theory necessitate the greatest caution as\nregard all questions of terminology. Speaking, as it is often done of\ndisturbing a phenomenon by observation, or even of creating physical\nattributes to objects by measuring processes is liable to be\nconfusing, since all such sentences imply a departure from conventions\nof basic language which even though it can be practical for the sake\nof brevity, can never be unambiguous. (Bohr 1939, p. 320. Quoted in\nSection 3.2 of the entry on the\n Uncertainty Principle.)\n " ], "section_title": "2. A popular form of the argument: Bohr’s response", "subsections": [] }, { "main_content": [], "section_title": "3. Development of EPR", "subsections": [ { "content": [ "\nFor about fifteen years following its publication, the EPR paradox was\ndiscussed at the level of a thought experiment whenever the conceptual\ndifficulties of quantum theory became an issue. In 1951 David Bohm, a\nprotégé of Robert Oppenheimer and then an untenured\nAssistant Professor at Princeton University, published a textbook on\nthe quantum theory in which he took a close look at EPR in order to\ndevelop a response in the spirit of Bohr. Bohm showed how one could\nmirror the conceptual situation in the EPR thought experiment by\nlooking at the dissociation of a diatomic molecule whose total spin\nangular momentum is (and remains) zero; for instance, the dissociation\nof an excited hydrogen molecule into a pair of hydrogen atoms by means\nof a process that does not change an initially zero total angular\nmomentum (Bohm 1951, Sections 22.15–22.18). In the Bohm\nexperiment the atomic fragments separate after interaction, flying off\nin different directions freely to separate experimental wings.\nSubsequently, in each wing, measurements are made of spin components\n(which here take the place of position and momentum), whose measured\nvalues would be anti-correlated after dissociation. In the so-called\nsinglet state of the atomic pair, the state after dissociation, if one\natom’s spin is found to be positive with respect to the orientation of\nan axis perpendicular to its flight path, the other atom would be\nfound to have a negative spin with respect to a perpendicular axis\nwith the same orientation. Like the operators for position and\nmomentum, spin operators for different non-orthogonal orientations do\nnot commute. Moreover, in the experiment outlined by Bohm, the atomic\nfragments can move to wings far apart from one another and so become\nappropriate objects for assumptions that restrict the effects of\npurely local actions. Thus Bohm’s experiment mirrors the entangled\ncorrelations in EPR for spatially separated systems, allowing for\nsimilar arguments and conclusions involving locality, separability,\nand completeness. Indeed, a late note of Einstein’s, that may have\nbeen prompted by Bohm’s treatment, contains a very sketchy spin\nversion of the EPR argument – once again pitting completeness\nagainst locality (“A coupling of distant things is\nexcluded.” Sauer 2007, p. 882). Following Bohm (1951) a paper by\nBohm and Aharonov (1957) went on to outline the machinery for a\nplausible experiment in which entangled spin correlations could be\ntested. It has become customary to refer to experimental arrangements\ninvolving determinations of spin components for spatially separated\nsystems, and to a variety of similar set-ups (especially ones for\nmeasuring photon polarization), as “EPRB”\nexperiments—“B” for Bohm. Because of technical\ndifficulties in creating and monitoring the atomic fragments, however,\nthere seem to have been no immediate attempts to perform a Bohm\nversion of EPR." ], "subsection_title": "3.1 Spin and The Bohm version" } ] } ]

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W., Spekkens, 2010, “Einstein,\nincompleteness, and the epistemic view of quantum states”,\nFoundations of Physics, 40: 125–157.", "Held, C., 1998, Die Bohr-Einstein-Debatte: Quantenmechanik und\nPhysikalische Wirklichkeit, Paderborn: Schöningh.", "Holland, P., 2005, “What’s wrong with Einstein’s 1927\nhidden-variable interpretation of quantum mechanics?”,\nFoundations of Physics, 35: 177–196.", "Hooker, C. A., 1972, “The nature of quantum mechanical\nreality: Einstein versus Bohr”, in R. G. Colodny, ed.,\nParadigms and Paradoxes, Pittsburgh: University of Pittsburgh\nPress, pp. 67–302. ", "Howard, D., 1985, “Einstein on locality and\nseparability.” Studies in History and Philosophy of\nScience 16: 171–201.", "Howard, D., 1990, “‘Nicht Sein Kann Was Nicht Sein\nDarf’, or the Prehistory of EPR, 1909–1935”, in A. I.\nMiller (ed.), Sixty-Two Years of Uncertainty, New York:\nPlenum Press, pp. 61–111.", "Jammer, M., 1974, The Philosophy of Quantum Mechanics,\nNew York: Wiley.", "Larsson, J.-A., 2014, “Loopholes in Bell inequality tests of\nlocal realism”, Journal of Physics A, 47: 424003.", "Malley, J., 2004, “All Quantum observables in a\nhidden-variable model must commute simultaneously”, Physical\nReview A, 69 (022118): 1–3.", "Putz, G. and N. Gisin, 2016, “Measurement dependent\nlocality”, New Journal of Physics, 18: 05506.", "Ryckman, T., 2017, Einstein, New York and London:\nRoutledge.", "Sauer, T., 2007, “An Einstein manuscript on the EPR paradox\nfor spin observables”, Studies in History and Philosophy of\nModern Physics, 38: 879–887.", "Schilpp, P.A., (ed.), 1949, Albert Einstein:\nPhilosopher-Scientist, La Salle, IL: Open Court.", "Schlosshauer, M., 2007, Decoherence and the\nQuantum-to-Classical Transition, Heidelberg/Berlin:\nSpringer.", "Schrödinger, E., 1935a, “Die gegenwärtige\nSituation in der Quantenmechanik”, Naturwissenschaften,\n23: 807–812, 823–828, 844–849; English translation\nin Trimmer, 1980.", "–––, 1935b, “Discussion of probability\nrelations between separated systems”, Proceedings of the\nCambridge Philosophical Society, 31: 555–562.", "Trimmer, J. D., 1980, “The present situation in quantum\nmechanics: A translation of Schrödinger’s ‘cat\nparadox’ paper”, Proceedings of the American\nPhilosophical Society, 124: 323–338", "Weinstein, S. 2009, “Nonlocality without nonlocality”,\nFoundations of Physics, 39: 921–936.", "Whitaker, M. A. B., 2004, “The EPR Paper and Bohr’s\nresponse: A re-assessment”, Foundations of Physics, 34:\n1305–1340.", "Winsberg, E., and A. Fine, 2003, “Quantum life: Interaction,\nentanglement and separation”, Journal of Philosophy, C:\n80–97." ]

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[ "\n\nWhat are the metaphysical implications of quantum physics? One way of\napproaching this question is to consider the impact of the theory on\nour understanding of objects as individuals with well defined identity\nconditions. According to the ‘Received View’, which was\nelaborated as the quantum revolution was taking place, quantum theory\nimplies that the fundamental particles of physics cannot be regarded\nas individual objects in this sense. Such a view has motivated the\ndevelopment of non-standard formal systems which are appropriate for\nrepresenting non-individual objects. However, it has also been argued\nthat quantum physics is in fact compatible with a metaphysics of\nindividual objects, but that such objects are indistinguishable in a\nsense which leads to the violation of Leibniz’s famous Principle of\nthe Identity of Indiscernibles. This last claim has also been\ncontested opening up a further way of understanding the individuality of quantum entities. As a result, we are faced with a form of\nunderdetermination of the relevant metaphysics by the physics, in\nwhich we have, on the one hand, quantum objects-as-individuals and, on\nthe other, quantum objects-as-non-individuals. It has been argued that\nthis underdetermination of such fundamental metaphysical ‘packages’\nhas important implications for the realism-antirealism debate.\n" ]

[ { "content_title": "1. Introduction", "sub_toc": [] }, { "content_title": "2. Quantum Non-Individuality", "sub_toc": [] }, { "content_title": "3. Quantum Individuality", "sub_toc": [] }, { "content_title": "4. Quantum Physics and the Identity of Indiscernibles", "sub_toc": [] }, { "content_title": "5. Non-individuality and self-identity", "sub_toc": [] }, { "content_title": "6. Metaphysical Underdetermination", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nIt is typically held that chairs, trees, rocks, people and many of the\nso-called ‘everyday’ objects we encounter can be regarded\nas individuals. The issue, then, is how this individuality is to be\nunderstood, or what constitutes the ‘principle’ of\nindividuality. This is an issue which has a very long history in\nphilosophy. A number of approaches to it can be broadly delineated. ", "\n\nWe might begin by noting that a tree and rock, say, can be\ndistinguished in terms of their different properties. We might\nthen go further and insist that this also forms the basis for ascribing\nindividuality to them. Even two apparently very similar\nobjects, such as two coins of the same denomination or so-called\nidentical twins, will display some differences in their\nproperties – a scratch here, a scar there, and so on. On this\naccount such differences are sufficient to both distinguish and\nindividuate the objects. This undergirds the so-called\n‘bundle’ view of objects, according to which an object\nis nothing but a bundle of properties. In order to guarantee\nindividuation, no two objects can then be absolutely\nindistinguishable, or indiscernible, in the sense of\npossessing exactly the same set of properties. This last\nclaim has been expressed as the Principle of Identity of\nIndiscernibles and it ensures the individuality of the objects that\nfall under its scope; we shall return to it below.", "\n\nHowever, this approach has been criticised on the grounds (among\nothers) that we can surely conceive of two absolutely\nindistinguishable objects: thinking of Star Trek, we could imagine a\nreplicator device which precisely reproduces an object, such as a coin\nor even a person, giving two such objects exactly the same set of\nproperties. Not quite, one might respond, since these two objects do\nnot and indeed cannot exist at the same place at the same time; that\nis, they do not possess the same spatio-temporal properties. In terms\nof these properties, then, the objects can still be\ndistinguished and hence regarded as different individuals. Clearly,\nthen, this approach to the issue of individuality must be underpinned\nby the assumption that individual objects are\nimpenetrable.", "\n\nA more thorough-going criticism of this property based approach to\nindividuality insists that it conflates epistemological issues\nconcerning how we distinguish objects, with ontological issues\nconcerning the metaphysical basis of individuality. Thus, it is argued,\nto talk of distinguishability requires at least two objects but we can\nimagine a universe in which there exists only one. In such a situation,\nit is claimed, it would be inappropriate to say that the object is\ndistinguishable but not that it is an individual. Although we do not\nactually find ourselves in such situations, of course, still, it is\ninsisted, distinguishability and individuality should be kept\nconceptually distinct.", "\n\nIf this line of argument is accepted, then the principle of\nindividuality must be sought in something over and above the properties\nof an object. One candidate is the notion of substance, in which\nproperties are taken to inhere in some way. Locke famously described\nsubstance as a ‘something, we know not what’, since to\ndescribe it we would have to talk of its properties, but bare substance,\nby its very nature, has no properties itself.", "\n\nAlternatively, the individuality of an object has been expressed in\nterms of its ‘haecceity’ or ‘primitive\nthisness’ (Adams 1979). As the name suggests, this is taken to\nbe the primitive basis of individuality, which cannot be analysed\nfurther. However, it has also been identified with the notion of\nself-identity, understood as a relational property (Adams\nibid.) and expressed more formally as\n‘a=a’. Each individual is understood to\nbe identical to itself. This may seem like a form of the\nproperty-based approach we started with, but self-identity is a rather\npeculiar kind of property. As we’ll see, denying that quantum objects\nare self-identical may be one way of capturing the idea that they are\nnon-individuals. ", "\n\nThis is just a sketch of some of the various positions that have\nbeen adopted. There has been considerable debate over which of them\napplies to the everyday objects mentioned above. But at least it is\ngenerally agreed that such objects should be regarded as individuals to\nbegin with. What about the fundamental objects posited by current\nphysical theories, such as electrons, protons, neutrons etc.? Can these\nbe regarded as individuals? One response is that they cannot, since\nthey behave very differently in aggregates from ‘classical’\nindividuals." ], "section_title": "1. Introduction", "subsections": [] }, { "main_content": [ "\n\nThe argument for the above conclusion – that the fundamental\nobjects of physics cannot be regarded as individuals – can be\nsummed up as follows: First of all, both ‘classical’ and\n‘quantal’ objects of the same kind (e.g. electrons) can be\nregarded as indistinguishable in the sense of possessing the same\nintrinsic properties, such as rest mass, charge, spin etc. Consider now\nthe distribution of two such indistinguishable particles over two\nboxes, or two states in general: ", "\n\nIn classical physics, (3) is given a weight of twice that of (1) or\n(2), corresponding to the two ways the former can be achieved by\npermuting the particles. This gives us four combinations or complexions\nin total and hence we can conclude that the probability of finding one\nparticle in each state, for example, is 1/2. (Note that it is assumed\nthat none of the four combinations is regarded as privileged in any\nway, so each is just as likely to occur.) This is an example of the\nwell-known ‘Maxwell-Boltzmann’ statistics to which, it is\nclaimed, thermodynamics was reduced at the turn of the twentieth century. ", "\n\nIn quantum statistical mechanics, however, we have two\n‘standard’ forms: one for which there are three possible\narrangements in the above situation (both particles in one box, both\nparticles in the other, and one in each box), giving\n‘Bose-Einstein’ statistics; and one for which there is\nonly one arrangement (one particle in each box), giving\n‘Fermi-Dirac’ statistics (which underpins the Pauli\nExclusion Principle and all that entails). Setting aside the\ndifferences between these two kinds of quantum statistics, the\nimportant point for the present discussion is that in the quantum\ncase, a permutation of the particles is not regarded as giving rise to\na new arrangement. This result lies at the very heart of quantum\nphysics; putting things slightly more formally, it is expressed by the\nso-called ‘Indistinguishability Postulate’:", "If a particle permutation P is applied to any\nstate function for an assembly of particles, then there is no way of\ndistinguishing the resulting permuted state function from the original\nunpermuted one by means of any observation at any time.", "\n\n(The state function of quantum mechanics determines the probability of\nmeasurement results. Hence what the Indistinguishability Postulate\nexpresses is that a particle permutation does not lead to any\ndifference in the probabilities for measurement outcomes.) ", "\n\nThe argument then continues as follows: that a permutation of the\nparticles is counted as giving a different arrangement in classical\nstatistical mechanics implies that, although they are\nindistinguishable, such particles can be regarded as individuals\n(indeed, Boltzmann himself made this explicit in the first axiom of\nhis ‘Lectures on Mechanics’, couched in terms of the\nimpenetrability assumption noted above). Since this individuality\nresides in something over and above the intrinsic properties of the\nparticles in terms of which they can be regarded as indistinguishable,\nit has been called ‘Transcendental Individuality’ by Post\n(1963). This notion can be cashed out in various well-known ways, as\nindicated in the Introduction above: in terms of some kind of\nunderlying Lockean substance, for example, or in terms\nof primitive thisness. More generally, one might\napproach it in modal fashion, through the doctrine of haecceitism:\nthis asserts that two possible worlds may describe some individual in\nqualitatively the same way (that is, as possessing the same set of\nproperties), yet represent that individual differently by ascribing a\ndifferent haecceity or thisness in each world, or more generally, by\nascribing some non-qualitative aspect to the individual (Lewis 1986;\nHuggett 1999a).", "\n\nConversely, it is argued, if such permutations are not counted in\nquantum statistics, it follows that quantum objects cannot be\nregarded as individuals in any of these senses (Post 1963). In\nother words, they are very different from most everyday\nobjects in that they are ‘non-individuals’, in some\nsense.", "\n\nThis radical metaphysical conclusion can be traced back to the\nreflections of Born and Heisenberg themselves and was further\nelaborated in the very earliest discussions of the foundations of\nquantum physics. As Weyl put it in his classic text on group theory\nand quantum mechanics:", "… the possibility that one of the identical twins\nMike and Ike is in the quantum state E1 and the other in the quantum\nstate E2 does not include two differentiable cases which are permuted\non permuting Mike and Ike; it is impossible for either of these\nindividuals to retain his identity so that one of them will always be\nable to say ‘I’m Mike’ and the other ‘I’m Ike.’\nEven in principle one cannot demand an alibi of an electron! (Weyl\n1931)", "\n\nRecalling the discussion sketched in the Introduction, if we were to\ncreate a twin using some kind of Star trek replicator, say, then in the\nclassical domain such a twin could insist that ‘I’m here and\nshe’s there’ or, more generally, ‘I’m in this state and\nshe’s in that one’ and ‘swapping us over makes a\ndifference’. In the classical domain each (indistinguishable)\ntwin has a metaphysical ‘alibi’ grounded in their\nindividuality. Weyl’s point is that in quantum mechanics, they do not. " ], "section_title": "2. Quantum Non-Individuality", "subsections": [] }, { "main_content": [ "\n\nThis conclusion – that quantal objects are not individuals\n– is not the whole story, however. First of all, the contrast\nbetween classical and quantum physics with regard to individuality and\nnon-individuality is not as straightforward as it might seem. As\nalready indicated, the above account involving permutations of\nparticles in boxes appears to fit nicely with an understanding of\nindividuality in terms of Lockean substance or primitive thisness.\nHowever, one can give an alternative field-theoretic account in which\nparticles are represented as dichotomic ‘Yes/No’ fields:\nwith such a field, the field amplitude is simply ‘Yes’ at\nlocation x if the ‘particle’ is present at x\nand ‘No’ if it is not (Redhead 1983). On this account,\nindividuality is conferred via spatio-temporal location together with\nthe assumption of impenetrability mentioned in the Introduction. Thus\nthe above account of particle individuality in terms of either Lockean\nsubstance or primitive thisness is not necessary for classical\nstatistical mechanics. ", "\n\nThe particles-and-boxes picture above corresponds to the physicists’\nmultidimensional ‘phase space’, which describes which\nindividuals have which properties, whereas the field- theoretic\nrepresentation corresponds to ‘distribution space’, which\nsimply describes which properties are instantiated in what numbers.\nHuggett has pointed out that the former supports haecceitism, whereas\nthe latter does not and, furthermore, that the empirical evidence\nprovides no basis for choosing between these two spaces (Huggett 1999a).\nThus the claim that classical statistical mechanics is wedded to\nhaecceitism also becomes suspect.", "\n\nSecondly, the above argument from permutations can be considered from\na radically different perspective. In the classical case the\nsituations with one particle in each box are given a weight of\n‘2’ in the counting of possible arrangements. In the case\nof quantum statistics this situation is given a weight of\n‘1’. With this weighting, there are two possible\nstatistics, as we noted: Bose-Einstein, corresponding to a symmetric\nstate function for the assembly of particles and Fermi-Dirac,\ncorresponding to an anti-symmetric state function. Given the\nIndistinguishability Postulate, it can be shown that symmetric state\nfunctions will always remain symmetric and anti-symmetric always\nanti-symmetric. Thus, if the initial condition is imposed that the\nstate of the system is either symmetric or anti-symmetric, then only\none of the two possibilities – Bose-Einstein or Fermi-Dirac\n– is ever available to the system, and this explains why the\nweighting assigned to ‘one particle in each state’ is half\nthe classical value. This gives us an alternative way of understanding\nthe difference between classical and quantum statistics, not in terms\nof the lack of individuality of the objects, but rather in terms of\nwhich states are accessible to them (French 1989). In other words, the\nimplication of the different ‘counting’ in quantum\nstatistics can be understood as not that the objects are\nnon-individuals in some sense, but that there are different sets of\nstates available to them, compared to the classical case. On this\nview, the objects can still be regarded as individuals, with the issue remaining as to how that individuality is to be cashed out.", "\n\nBoth of these perspectives raise interesting and distinct metaphysical issues (for\na useful introduction see Castellani 1998b). Let us consider, first,\nthe objects-as-individuals ‘package’. How is the relevant\nnotion of individuality to be articulated? One option would be to take\none of the traditional lines and ground it some form of primitive thisness or\nLockean substance. However, this kind of metaphysics is anathema to\nmany of a naturalistic persuasion, not least because it lies beyond\nthe physical pale, as it were. Alternatively, one might take\nindividuality to be primitive but then assuage any naturalistic\ntendencies by tying it to the idea of ‘countability’\n– in the sense that we can always count how many quantum objects\nare in a given state – and take the latter to be both physically\nsignificant and capable of being ‘read off’ from the\ntheory (Dorato and Morganti 2013). Nevertheless, it may be felt that\nnaturalism is better satisfied by eschewing such primitivist moves and\ntaking the individuality of the objects to be reducible to their\ndiscernibility and ground the latter in their properties, as presented\nby the theory (a feeling that may be further supported by doubts as to\nthe physical plausibility of possible worlds containing only one\nobject, as mentioned above). Of course, for this to work, we need some\nassurance that no two objects are indiscernible (or indistinguishable)\nin the relevant sense. Traditionally this assurance has been provided\nby Leibniz’s famous Principle of the Identity of Indiscernibles, so\nlet us consider the status of this Principle in the context of modern\nphysics." ], "section_title": "3. Quantum Individuality", "subsections": [] }, { "main_content": [ "\n\nNow, of course, both quantum and classical objects of the same kind\n– such as electrons, say – are indistinguishable in the\nsense that they possess all intrinsic properties – charge, spin,\nrest mass etc. – in common. However, quantum objects are\nindistinguishable in a much stronger sense in that it is not just that\ntwo or more electrons possess the same intrinsic properties but that\n– on the standard understanding – no measurement\nwhatsoever could in principle determine which one is which. If the\nnon-intrinsic, state-dependent properties are identified with all the\nmonadic or relational properties which can be expressed in terms of\nphysical magnitudes standardly associated with self-adjoint operators\nthat can be defined for the objects, then it can be shown that two\nbosons or two fermions in a joint symmetric or anti-symmetric state\nrespectively have the same monadic properties and the same relational\nproperties one to another (French and Redhead 1988; see also\nButterfield 1993). This has immediate implications for the Principle\nof the Identity of Indiscernibles which, expressed crudely, insists\nthat two things which are indiscernible, must be, in fact,\nidentical. ", "\n\nSetting aside the historical issue of Leibniz’s own attitude towards\nhis Principle (see, for example, Rodriguez-Pereyra 2014),\nsupporters of it have tended to retreat from the claim that it is\nnecessary and have adopted the alternative view that it is at least contingently true (in the\nface of apparent counter-examples such as possible worlds containing\njust two indistinguishable spheres). There is the further issue as to\nhow the Principle should be characterised and, in particular, there is\nthe question of what properties are to be included within the scope of\nthose relevant to judgments of indiscernibility. Excluding the\nproperty of self-identity (which, again, we’ll come back to below),\nthree forms of the Principle can be broadly distinguished according to\nthe properties involved: the weakest form, PII(1), states that it is\nnot possible for two individuals to possess all properties and\nrelations in common; the next strongest, PII(2), excludes\nspatio-temporal properties from this description; and the strongest\nform, PII(3), includes only monadic, non-relational properties. Thus,\nfor example, PII(3) is the claim that no two individuals can possess\nall the same monadic properties (a strong claim indeed, although it is\none way of understanding Leibniz’s own view).", "\n\nIn fact, PII(2) and PII(3) are clearly violated in classical\nphysics, where distinct particles of the same kind are typically\nregarded as indistinguishable in the sense of possessing all intrinsic\nproperties in common and such properties are regarded as non-relational\nin general and non-spatio-temporal in particular. (Of course, Leibniz\nhimself would not have been perturbed by this result, since he took the\nPrinciple of Identity of Indiscernibles to ultimately apply only to\n‘monads’, which were the fundamental entities of his\nontology. Physical objects such as particles were regarded by him as\nmerely ‘well founded phenomena’.) However, PII(1) is not\nviolated classically, since classical statistical mechanics typically\nassumes that such particles are impenetrable, in precisely the sense\nthat their spatio-temporal trajectories cannot overlap. Hence they can\nbe individuated via their spatio-temporal properties, as indicated\nabove.", "\n\nThe situation appears to be very different in quantum mechanics,\nhowever. If the particles are taken to possess both their intrinsic\nand state-dependent properties in common, as suggested above, then\nthere is a sense in which even the weakest form of the Principle,\nPII(1), fails (Cortes 1976; Teller 1983; French and Redhead 1988; for\nan alternative view, see van Fraassen 1985 and 1991). On this\nunderstanding, the Principle of Identity of Indiscernibles is actually\nfalse. Hence it cannot be used to effectively guarantee individuation\nvia the state-dependent properties by analogy with the classical\ncase. If one wishes to maintain that quantum particles are\nindividuals, then their individuality will have to be taken as\nconferred by Lockean substance, primitive thisness or, in general,\nsome form of non-qualitative haecceistic difference.", "\n\nHowever, this conclusion has been challenged. First of all, it has been\nquestioned whether quantum particles can be said to possess the\nrelevant state-dependent properties in the sense that would be\ndamaging to PII (Massimi 2001; see also Mittelstaedt and Castellani 2000). However, this argument only applies to monadic,\nstate-dependent properties and so the above conclusion still holds for\nPII(2) and PII(3). In effect, what has been shown is that those\nversions of PII which allow relations to individuate are not the\nweakest forms of the Principle, but the only forms which are\napplicable.", "\n\nThis shift to relations as individuating elements has led to the development of a form\nof PII, based on Quine’s suggestions about discernibility, which\nallows objects to be ‘weakly’ discernible in relational\nterms (Saunders 2003a and 2006; for a useful overview see Bigaj\n2015a). Consider for example, two fermions in a spherically-symmetric\nsinglet state. The fermions are not only indistinguishable in the\nabove sense but also possess exactly the same set of spatio-temporal\nproperties and relations. However, each enters into the symmetric but\nirreflexive relation of ‘having opposite direction of each\ncomponent of spin to …’ on the basis of which they can be\nsaid to be ‘weakly discernible’ (for general discussions of different\nkinds of discernibility see Caulton and Butterfield 2012a; Bigaj 2014;\nKetland 2011; Ladyman, Linnebo and Pettigrew 2012). If we extend PII\nto incorporate such relations, the Principle can, it seems, be made\ncompatible with quantum physics and the individuality of the fermions\ncan be grounded in these irreflexive relations, without having to\nappeal to anything like primitive thisness. This result has also been\nextended to bosons (Muller and Saunders 2008; Muller and Seevinck\n2009), although some of the details are contentious, in particular\nwith regard to the interpretation of some of the mathematical features\nthat are appealed to in this account (see Bigaj 2015a and 2015b; Caulton 2013; Huggett and Norton 2014; Norton 2015). In addition to such technical issues, there is the\nfurther philosophical concern that the appeal to irreflexive relations\nin order to ground the individuality of the objects which bear such\nrelations involves a circularity: in order to appeal to such\nrelations, one has had to already individuate the particles which are\nso related and the numerical diversity of the particles has been\npresupposed by the relation which hence cannot account for it (see\nFrench and Krause 2006; Hawley 2006 and 2009). One response to this\nworry would be to question the underlying assumption that relata must\nhave the relevant ontological priority over relations and adopt some\nform of structuralist view of objects according to which the relata\nare eliminable in terms of relations (perhaps ‘emerging’, in some\nsense as ‘intersections’ of them) or, more mildly perhaps,\nargue that neither are accorded priority but come as a\n‘package’ as it were (for further discussion see French\n2014). It has been suggested, for example, that this whole discussion\nof weak discernibility reveals a category of entity that has received\nlittle attention so far, namely that of ‘relationals’: objects that\ncan be discerned by means of relations only (Muller 2011, 2015). I\nshall return to the structuralist perspective below (but for an alternative, ‘coherentist’ account, see Calosi and Morganti 2018). More generally,\nhowever, it has been argued that this whole debate is orthogonal to\nthat over the status of PII since what weak discernibility grounds is\nmerely numerical distinctness, rather than the robust sense of\ndiscernibility that PII was originally concerned with (Ladyman and\nBigaj 2010). The latter involves some sense of difference over and\nabove numerical distinctness but weakly discernible relations such as\n‘having opposite direction of each component of spin to\n…’ do not provide this. Hence, it is claimed, PII remains\nviolated by quantum mechanics (although see Friebe 2014 where the principle is defended in the context of a specific understanding of quantum entanglement). ", "\n\nThe above considerations are typically presented within the\n‘orthodox’ interpretation of quantum mechanics but there\nare a further set of responses which step outside of this. Thus van\nFraassen, for example (van Fraassen 1985 and 1991) has advocated a\nform of ‘modal’ interpretation, in the context of which\n(standard) PII can be retained. At the core of this approach lies a\ndistinction between two kinds of state: the ‘value’ state,\nwhich is specified by stating which observables have values and what\nthey are; and the ‘dynamic’ state, which is specified by\nstating how the system will develop both if isolated and if acted upon\nin some definite fashion. The evolution of the latter is\ndeterministic, in accordance with Schroedinger’s equation, but\nthe value state changes unpredictably, within the limits set by the\ndynamic state (for criticism see some of the papers in Dieks and\nVermaas 1998). Because the actual values of observables do not\nincrease predictive power if added to the relevant dynamic state\ndescription, they are deemed to be ‘empirically\nsuperfluous’. In the case of fermions, at least, distinct value\nstates can be assigned to each particle and PII saved.", " \n\nHowever concerns have been raised over the objectivity of such value\nstate attributions (Massimi op. cit., p. 318, fn. 11) and one might\nregard the associated ‘empirically superfluous’ properties\nas merely conceptual. This bears again on the important issue of what kinds\nof properties may be admitted to lie within the scope of the\nPrinciple. Clearly some would appear to be beyond the pale: saving PII\nby regarding the particle labels themselves as intrinsic properties is\nsurely unacceptable. Furthermore, bosons must be treated differently,\nsince they can have the same dynamic and value states. In this case,\nvan Fraassen suggests that each boson is individuated by its history,\nwhere this is again to be understood as ‘empirically\nsuperfluous’. Of course, it might seem odd that an approach\nwhich originally sought to avoid the grounding of the individuality of\nobjects in something like Lockean substance should find itself having\nto include empirically superfluous factors within the scope of\nPII.", "\n\nAnother ‘unorthodox’ approach incorporates the Bohmian\ninterpretation of quantum mechanics and in particular it has been\nsuggested that it might form the basis of an alternative conception of\nparticle individuality in terms of their spatio-temporal\ntrajectories. As is well known, attributing distinguishing\nspatio-temporal trajectories to quantum objects faces acute\ndifficulties under the orthodox interpretation of quantum\nmechanics. On the Bohm interpretation, however, they are allowed;\nindeed, the only observable admitted is that of position. What this\ninterpretation gives us is a dual ontology of point particles plus\n`pilot’ wave, where the role of the latter is to determine the\ninstantaneous velocities of the former through the so-called\n‘guidance equations’. These ‘complete’ the standard\nformulation of quantum mechanics so that, in addition to the quantum\nstate, whose development is determined by the Schrödinger equation,\nthere is also a set of single-particle trajectories, each of which is\ndetermined by the guidance equation, plus the initial positions of the\nparticles (for a review see Cushing et al. 1996). Such an\ninterpretation appears to provide a natural home for the metaphysical\npackage which takes quantum objects to be individuals (see, for\nexample, Brown et al. 1999) and, indeed, a form of PII(1) can\nnow be defended against the above conclusion.", "\n\nNevertheless, things are not quite as straightforward as they might\nseem: it has been argued that intrinsic properties cannot be\nconsidered as possessed solely by the objects but in some sense must\nbe assigned to the pilot wave as well (Brown et al.1994). Thus, again, there is an\nontological cost involved in retaining this view of objects as\nindividuals.", "\n\nWhat if one were to consider the evolution of the system concerned in\nthe multi-dimensional ‘configuration space’ in terms of which\nthe wave function must be described? Here the implications of\nconsidering particle permutations are encoded in the topology of such\na space by identifying points corresponding to such a permutation and\nthereby constructing what is known as the ‘reduced configuration\nspace’ formed by the action of the permutation group on the full\nconfiguration space. As in the case of ‘ordinary’ space-time,\nsome form of ‘impenetrability assumption’ must be adopted to\nensure that – in the case of those particles that are not bosons at\nleast – no two particles occupy the same point of this reduced\nspace.Here Bohmian\nmechanics offers some advantage: it turns out that the guidance equations\nensure the non-coincidence of the relevant particle trajectories\n(Brown et al. 1999). In effect ‘impenetrability’\nis built into the dynamics and thus the configuration space approach\nand de Broglie-Bohm interpretation fit nicely together.", "\n\nReturning to the core point, one can maintain that quantum objects are\nindividuals, even granted the implications of quantum statistics. And\none can either take that individuality to be ungrounded and\n‘primitive’ or ground it in some form of primitive thisness or, more\nplausibly for many, in the associated properties via an updated and\nextended form of PII (criticisms and concerns\nnotwithstanding). However, there is also the alternative, articulated\nduring the throes of the quantum revolution itself, as noted above,\nwhich is to take quantum objects to be non-individuals in some\nsense. Of course, if this alternative metaphysical ‘package’ is\nadopted then Leibniz’s Principle simply does not apply. But now the\nobvious question arises: what sense can we make of this notion of\n‘non-individuality’?" ], "section_title": "4. Quantum Physics and the Identity of Indiscernibles", "subsections": [] }, { "main_content": [ "\n\nLet us recall Weyl’s statement that one can’t ask alibis\nof electrons. Dalla Chiara and Toraldo di Francia refer to quantum\nphysics as ‘the land of anonymity’, in the sense that, on\nthis view, the objects cannot be uniquely labelled (1993 and 1995). They ask,\nthen, how can we talk about what happens in such a land? Their\nsuggestion is that quantum objects can be regarded as\n‘intensional-like entities’, where the intensions are\nrepresented by conjunctions of intrinsic properties. The extension of\nthe natural kind, ‘electron’, say, is then given by the\ncollection of indistinguishable elements, or a\n‘quaset’. The theory of such quasets then gives the possibility of a\nsemantics for quantum objects without alibis (ibid.).", "\n\nAlternatively, but relatedly, non-individuality can be understood in\nterms of the denial of self-identity. This suggestion can be found most\nprominently in the philosophical reflections of Born,\nSchrödinger, Hesse and Post (Born 1943; Schrödinger 1952;\nHesse 1963; Post 1963). It is immediately and clearly problematic,\nhowever: how can we have objects that are not identical to themselves? Such\nself-identity seems bound up with the very notion of objecthood in the\nsense that it is an essential part of what it is to be that object (thus it has been suggested that non-individuality might be better understood in terms of the loss of patio-temporal trajectories in quantum physics; see Arenhart, Bueno and Krause 2019). This\nintuition is summed up in the Quinean slogan, ‘no entity without\nidentity’ (Quine 1969), with all its attendant consequences\nregarding reference etc.", "\n\nHowever, Barcan Marcus has offered an alternative perspective,\ninsisting on ‘No identity without entity.’ (Marcus 1993)\nand arguing that although ‘… all terms may\n“refer” to objects… not all objects are things,\nwhere a thing is at least that about which it is appropriate to assert\nthe identity relation.’ (ibid., p. 25) Object-reference\nthen becomes a wider notion than thing-reference. Within such a\nframework, we can then begin to get a formal grip on the notion of\nobjects which are not self-identical through so-called\n‘Schrödinger logics’, introduced by da Costa (da\nCosta and Krause 1994) These are many-sorted logics in which the\nexpression x = y is not a well-formed formula in\ngeneral; it is where x and y are one sort of term, but\nnot for the other sort corresponding to quantum objects. A semantics\nfor such logics can be given in terms of ‘quasi-sets’ (da\nCosta and Krause 1997). The motivation behind such developments is the\nidea that collections of quantum objects cannot be considered as sets\nin the usual Cantorian sense of ‘… collections into a\nwhole of definite, distinct objects of our intuition or of our\nthought.’ (Cantor 1955, p. 85). Quasi-set theory incorporates\ntwo kinds of basic posits or ‘Urelemente’: m-atoms, whose\nintended interpretation are the quantal objects and M-atoms, which\nstand for the ‘everyday’ objects, and which fall within\nthe remit of classical set theory with Ur-elements. Quasi-sets are\nthen the collections obtained by applying the usual Zermelo-Fraenkel\nframework plus Ur-element ZFU-like axioms to a basic domain composed\nof m-atoms, M-atoms and aggregates of them (Krause 1992; for a\ncomparison of qua-set theory with quasi-set theory, see Dalla Chiara,\nGiuntini and Krause 1998).", "\n\nThese developments supply the beginnings of a categorial framework for\nquantum ‘non- individuality’ which, it is claimed, helps\nto articulate this notion and, bluntly, make it philosophically\nrespectable (extensive details are given in French and Krause 2006;\nsee also Arenhart 2012; Domenach and Holik 2007; Domenach, Holik and\nKrause, 2008; Krause 2010). Crucially, within\nthis formal framework, a sense of countability is retained in that\ncollections of quantum entities possess a (kind of) cardinality but\nnot an ordinality, so we can, in effect, say how many objects there\nare, even though we cannot place them in numerical order. Critical\ndiscussions of both these formal details and of the basis for\nattributing ‘non-individuality’ to quantum objects can be\nfound in Bueno et. al. 2011 and Sant’ Anna 2019. Much of this criticism has proceeded on\nthe basis of insisting that we do not need to adopt such an apparently\nradical approach. Thus advocates of ‘weak discernibility’, discussed\nabove, have argued that this notion yields an appropriately naturalist sense\nof individuality, suitable for quantum physics, whereas Dorato and\nMorganti (2013) insist, as already noted, that one can retain\ncountability, and individuality, as primitive notions and that this is\nto be preferred over any shift to non-individuality (for a response to\nthe latter and defence of the above formal framework, see Arenhart and\nKrause 2014). Jantzen on the other hand, has argued that identity and cardinality are tied together as a ‘matter of meaning’ rather than metaphysics and that, consequently, talk of entities without identity is either meaningless or, in fact, talk about something else altogether (Jantzen 2019). Likewise Bueno has insisted that identity is too fundamental to be given up so readily and suggests that we can infer\nthe non-individuality of quantum particles directly from their\nindistinguishability with identity itself understood as a ‘useful idealization’ that simplifies our conceptual framework and allows us to predict the behaviour of the relevant objects – in this case quantal entities (Bueno 2014; for responses see Arenhart 2017a and Krause and Arenhart 2019). ", "\nBoth the framework of quasi-set theory and the underlying metaphysics\nhave been extended into the foundations of Quantum Field Theory, where\nit has been argued, one has non-individual ‘quanta’\n(Teller 1995). A form of quasi-set theory may provide one way of\nformally capturing this notion (French and Krause 2006; for concerns about such a move see Sant’ Anna 2019). It has also\nbeen suggested that this offers a way of understanding the sense in\nwhich quantum objects may be regarded as vague (French and Krause\n2003), although it has been questioned whether vagueness is the\nappropriate notion here (Darby 2010) and also whether quasi-set theory\noffers the most perspicuous way of capturing this sense (Smith\n2008). Finally, for those who are leery of quasi-sets and their attendant formal apparatus, there is also the option of returning to Weyl’s original insight, which underpins the quote above, and appropriating his idea of an ‘aggregate’. If this is interpreted non-set-theoretically as an equivalence relation, where the relevant elements are understood as simply objects that have certain properties in common, one can continue to maintain that such objects do not have well-defined identity conditions (Bueno 2019). Indeed, there may be a variety of such frameworks, both formal and metaphysical, in terms of which non-individuality may be understood (Arenhart 2017b). " ], "section_title": "5. Non-individuality and self-identity", "subsections": [] }, { "main_content": [ "\n\nWe now appear to have an interesting situation. Quantum mechanics is\ncompatible with two distinct metaphysical ‘packages’, one\nin which the objects are regarded as individuals and one in which they\nare not. Thus, we have a form of ‘underdetermination’ of\nthe metaphysics by the physics (see van Fraassen 1985 and 1991; French\n1989; Huggett 1997). This has implications for the broader issue of\nrealism within the philosophy of science. If asked to spell out her\nbeliefs, the realist will point to currently accepted fundamental\nphysics, such as quantum mechanics, and insist that the world is, at\nleast approximately, however the physics says it is. Of course, there\nare the well-known problems of ontological change (giving rise to the\nso-called Pessimistic Meta-Induction) and Underdetermination of\nTheories by the Empirical data. However, this underdetermination of\nmetaphysical packages seems to pose an even more fundamental problem,\nas the physics involved is well entrenched and the difference in the\nmetaphysics seemingly as wide as it could be. These packages support\ndramatically different world-views: one in which quantum objects, such\nas electrons, quarks and so forth, are individuals and one in which\nthey are not. The realist must then face the question: which package\ncorresponds to the world? ", " One option would be to refuse to answer and insist that all the\nrealist is required to do is to state how the world is, according to\nour best theories; that is, to articulate her realism in terms of\nelectrons, quarks etc. and what physics tells us about them and no\nmore, metaphysically speaking. This might be called a\n‘shallow’ form of realism (Magnus 2012) and it raises the\nobvious worry that the content of such shallow realism amounts to no\nmore than a recitation of the relevant physical content of our best\ntheories, with no consideration of whether that content is concerned\nwith objects or not, and whether the former are individuals or\nnot. ", "\n\nAt the other extreme, one might be tempted to give up realism\naltogether and adopt an anti-realist stance. Thus the constructive\nempiricist, taking realism to be metaphysically informed, and hence\n‘deep’ rather than ‘shallow’, draws as the\nlesson from this underdetermination, ‘so much for\nmetaphysics’ and realism along with it. Since on this view, all\nthat theories can tell us is how the world could be, the\ndifferent metaphysical packages of objects-as-individuals and as\nnon-individuals simply amount to different ways of spelling that out\n(van Fraassen 1991). ", "\nIn between these extremes are various options for handling the\nunderdetermination, corresponding to different levels of ‘deep’\nrealism. Thus one might try to argue that the underdetermination can\nbe ‘broken’ in some way. One might, for\nexample, appeal to some metaphysical factor or other in support of one\npackage over the other, or shift to meta-metaphysical considerations\nin order to argue, for example, that individuality based on weak\ndiscernibility has certain advantages over rival accounts and also\nover non-individuality, with its attendant non-standard formal\nunderpinning. However Arenhart argues that weak discernibility generates further metaphysical underdetermination and hence cannot support a fully naturalistic understanding of quantum mechanics as some of its advocates have claimed (Arenhart 2017b). Alternatively, of course, one could argue the other way\nand insist that the non-individuality package avoids having to choose between different\nmetaphysical accounts of individuality, at least, and that the formal\nshift to quasi-set theory is not as dramatic as might be\nthought. Ultimately, however, its not at all clear what weight should\nbe given to the various factors involved or even if a coherent\nweighting scheme can be applied in the first place.", "\nInstead one might appeal to broadly methodological factors to break\nthe underdetermination. Thus it has been argued that the package of\nobjects-as-non-individuals meshes better with quantum field theory\n(QFT) where, it is claimed, talk of individuals is avoided from the\nword go (Post 1963; Redhead and Teller 1991 and 1992; Teller\n1995). The central argument for this claim focuses on the core\nunderstanding that objects may indeed be regarded as individuals in\nquantum physics but as such are subject to restrictions on the sets of\nstates they may occupy. The states that are inaccessible to the\nparticles of a particular kind, such as electrons say, can be taken as\ncorresponding to just so much ‘surplus structure’. In\nparticular, if the view of particles as individuals is adopted, then\nit is entirely mysterious as to why a particular sub-set of these\ninaccessible, surplus states, namely those that are non-symmetric, are\nnot actually realised. Applying the general methodological principle\nthat a theory which does not contain such surplus structure is to be\npreferred over one that does, Redhead and Teller conclude that we have\ngrounds for preferring the non-individuals package and the mystery of\nthe inaccessible states simply does not arise (Redhead and Teller 1991\nand 1992).", "\n\nThis line of argument has been criticised by Huggett on the grounds\nthat the apparent mystery is a mere fabrication: the inaccessible\nnon-symmetric states can be ruled out as simply not physically\npossible (Huggett 1995). The surplus structure, then, is a consequence\nof the representation chosen and has no further metaphysical\nsignificance. However, it has been insisted that a theory should also\ntell us why a particular state of affairs is not possible. So,\nconsider the possible state of affairs in which a cold cup of tea\nspontaneously starts to boil. Statistical mechanics can explain why we\nnever observe such a possibility, whereas the\nquantum-objects-as-individuals view cannot explain why we never\nobserve non-symmetric states and hence it is deficient in this regard\n(Teller 1998).", "\n\nUnfortunately, the analogy is problematic. Statistical mechanics does\nnot say that the above situation never occurs but only that the\nprobability of its occurrence is extremely low. The question then\nreduces to that of ‘why is this probability so low?’ The\nanswer to that is typically given in terms of the very low number of\nstates corresponding to the tea boiling compared to the vast number of\nstates for which it remains cold. Why, then, this disparity in the\nnumber of accessible states? Or, equivalently, why do we find\nourselves in situations in which entropy increases? One answer takes\nus back to the initial conditions of the Big Bang. A similar line can\nthen be taken in the case of quantum statistics. Why do we never\nobserve non-symmetric states? Because that is the way the universe is\nand we should not expect quantum mechanics alone to have to explain\nwhy certain initial conditions obtain and not others. Here we recall\nthat the symmetry of the Hamiltonian ensures that if a particle is in\na state of a particular symmetry (corresponding to Bose-Einstein\nstatistics, say, or Fermi-Dirac) to begin with, it will remain in\nstates of that symmetry. Hence, if non-symmetric states do not feature\nin the initial conditions which held at the beginning of the universe,\nthey will remain forever inaccessible to the particles. The issue then\nturns on different views of the significance of the above\n‘surplus structure’ (see Belousek 2000.)", "\n\nFurthermore, even if we accept the methodological principle of\n‘the less surplus structure the better’, it is not clear\nthat QFT understood in terms of non-individual ‘quanta’\noffers any significant advantage in this respect (although see da Costa and Holik 2015 for an account in these terms of states with undefined particle number, characteristic of QFT). Indeed, it has been\nargued that the formalism of QFT is also compatible with the alternative\npackage of objects as individuals. Van Fraassen has\npressed this claim (1991), drawing on de Muynck’s construction of\nstate spaces for QFT which involve labelled particles\n(1975). Butterfield, however, has argued that the existence of\nstates that are superpositions of particle number, within QFT,\nundermines the equivalence (1993). Nevertheless, Huggett insists, in\nthis case the undermining is empirical, rather than methodological\n(Huggett 1995). When the number is constant, it is the states for\narbitrary numbers of particles which are so much surplus structure and\nnow, if the methodological argument is applied, it is the individuals\npackage which is to be preferred.", "\nIt is also worth noting, perhaps, that some of this\n‘surplus’ structure corresponds to so-called\n‘paraparticle’ statistics, or forms of quantum statistics\nthat are neither bosonic nor fermionic. These were acknowledged as\npossible by Dirac as early as the 1930s but were only fully developed\ntheoretically from the late 1950s. For a brief period in the mid-1960s\nit was thought that quarks might be paraparticles, before the same\nstatistical behaviour came to be described in terms of the new\nintrinsic property of ‘colour’ leading to the development\nof quantum chromodynamics, which effectively pushed paraparticle\ntheory into the theoretical twilight (for a summary of the history see\nFrench and Krause 2006, Ch. 3; for a discussion of paraparticles in\nthe context of issues relating to particle indistinguishability, see\nCaulton and Butterfield 2012b). This suggests that paraparticle\nstatistics can always be re-described in conventional terms – a\nsuggestion that has been taken up by Baker et. al. in the context of\nalgebraic QFT, thereby eliminating this form of surplus structure at\nleast (Baker, Halvorson and Swanson 2015).", "\nThere remains considerable scope for further exploration of all these\nissues and concerns in the context of quantum field theory (see also\nAuyang 1995) and a collection of relevant historical and philosophical\nreflections can be found in Cao (1999).", "\nA further approach to this underdetermination is to reject both\npackages and seek a third way. Thus Morganti has argued that both of\nthe above metaphysical packages assume that everything qualitative\nabout an object must be encoded in terms of a property that it\npossesses (Morganti 2009). Dropping this assumption allows us to\nconsider quantum statistics as describing ‘inherent’\nproperties of the assembly as a whole. The (anti-)symmetry of the\nrelevant states is then accounted for in terms of the disposition of\nthe system to give rise to certain correlated outcomes upon\nmeasurement. This is presented as an extension of Teller’s\n‘relational holism’ (Teller 1989), and\nrelatedly, the notion of ‘inherence’ involves the denial\nof the supervenience of the properties of the whole on those of the\nparts. However, as just indicated, it comes with a cost: that of\nadmitting holistic dispositional properties and the metaphysics of\nthese in the quantum context requires further development, as does the\nsense in which such inherent properties ‘emerge’ when\nsystems interact. Earlier and along similar metaphysical lines, Lavine\nsuggested that quantum objects can be regarded as the smallest\npossible amounts of ‘stuff’ and, crucially, that a\nmulti-particle state represents a further amount of stuff such that it\ndoes not contain proper parts (1991; see also Jantzen 2019). Such a view, he claims, avoids\nthe metaphysically problematic aspects of both the individuals and\nnon-individuals packages. Of course, there are then the issues of the\nmetaphysics and logic of ‘stuff’, but it can be argued\nthat these are familiar and not peculiar to quantum mechanics. One\nsuch issue concerns the nature of ‘stuff’: is it our\nfamiliar primitive substance? Substance as a fundamental metaphysical\nprimitive faces well-known difficulties and it has been suggested that\nit should be dropped in favour of some form of ‘bundle\ntheory’, as mentioned at the very beginning of this article. If\nthe individual objects are understood to be bundles of\n‘tropes’, where a trope is an individual instance of a\nproperty or a relation, and if this notion is broadened to include\nindividuals whose existence depends on that of others which are not a\npart of them then, it is claimed, this notion may be flexible enough\nto accommodate quantum physics (Simons 1998; see also Morganti\n2013). Another issue concerns the manner in which ‘stuff’\ncombines: how do we go from the amounts of stuff represented by two\nindependent photons, to the amount represented by a joint two-photon\nstate? The analogies Lavine gives are well known: drops of water,\nmoney in the bank, bumps on a rope (Teller 1983; Hesse 1963). Of\ncourse, these may also be appropriated by the non-individual objects\nview but, more significantly, they are suggestive of a field-theoretic\napproach in which the ‘stuff’ in question is the quantum\nfield. ", "\n\nHere we return to issues concerning the metaphysics of quantum field\ntheory and it is worth pointing out that underdetermination may arise\nhere too. In classical physics we are faced with a choice between the\nview of the field as a kind of global substance or stuff and an\nalternative conception in terms of field quantities assigned to and\nhence as properties of, the points of space-time. In the case of\nquantum field theory, the field quantities are not well-defined at\nsuch points (because of difficulties in defining exact locational\nstates in quantum field theory) but are instead regarded as\n‘smeared’ over space-time regions (see Teller 1999). The\nunderdetermination remains, of course: between an understanding of the\ngiven quantum field in terms of some kind of global substance and the\nalternative conception in terms of the properties of\nspace-time regions. Taking the first option obviously\nrequires a metaphysically articulated form of substantivalism\napplicable to quantum field theory. Many commentators have preferred\nthe second option, but now, of course, attention must be paid to the\nmetaphysical status of the space-time regions over which the field\nproperties are taken to be instantiated. Typically, these will be\ntaken to be composed of points of space-time and conceiving of a field\nin terms of a set of properties meshes comfortably with the approach\nthat takes space-time to be a kind of substance or ‘stuff’\nitself. But this too faces well known difficulties in the context of\nmodern physics (see, for example, Earman 1989). In particular,\nspace-time substantivalism has been argued to have extremely\nunpalatable consequences (Earman and Norton 1987). Unfortunately, such\na properties-based account of fields is difficult to reconcile with\nthe alternative view of space-time as merely a system of relations\n(such as contiguity) between physical bodies: if the field quantities\nare properties of space-time regions and the latter are understood,\nultimately, to be reducible to relations between physical objects,\nwhere the latter are conceived of in field-theoretic terms, then a\ncircularity arises (see Rovelli 1999). One way forward would be to\ndraw on alternative accounts of the nature of spacetime. Thus Stachel\nhas suggested that we drop the sharp,\nmetaphysical distinction between things and\nrelations between things and adopt a broadly\n‘structuralist’ view of spacetime (Stachel 1999; see the\nessays in Rickles, French & Saatsi 2006). Suitably extended, such\na ‘structuralist’ approach might offer a way around the\nabove incompatibility by regarding both space-time and the quantum\nfield in structural terms, rather than in terms of substances,\nproperties or relations (see Auyang 1995; Cao 2003; French and Ladyman\n2003; Kantorovich 2003; Lyre 2004; Saunders 2003b).", "\nThis takes us to a further possible response to the above metaphysical\nunderdetermination which urges realism to retreat from a metaphysics\nof objects and develop an ontology of structure compatible with the\nphysics (Ladyman 1998 and 2014). An early attempt to do this in the\nquantum context can be seen in the work of Cassirer who noted the\nimplications of the new physics for the standard notion of individual\nobjects and concluded that quantum objects were describable only as\n‘“points of intersection” of certain\nrelations’ (1937, p. 180) Setting aside the neo-Kantian elements\nin Cassirer’s structuralism, this view of quantum entities has been\ndeveloped in the context of a form of ‘ontic’ structural realism\n(Ladyman and Ross 2007). Drawing on the views\nof both Weyl and Wigner, quantum objects are here understood as\nontologically constituted, group theoretically, in terms of sets of\ninvariants, such as rest mass, charge, spin, and so on (Castellani\n1998a). From this perspective, both the individuality and\nnon-individuality packages get off on the wrong feet, as it were, by\nassuming that the way the world is, according to physics, is a world\nof objects, which can either be regarded as individuals, whether\nprimitively or via weak discernibility, or as non-individuals, whether\nformally represented through quasi-set theory or not. \n\nHow, then, should we regard the ‘Indistinguishability Postulate’ with which we began this discussion of identity and individuality in the quantum context? Both the above packages rest upon a certain understanding of particle permutations, as encapsulated in that Postulate, namely that these are to be conceived in terms of swapping the particles between states, or boxes in our illustrative sketch. However, we can also think of the ‘Indistinguishability Postulate’ as expressing a fundamental symmetry constraint on quantum mechanics, to the effect that the relevant states should be invariant under particle permutations. An alternative way of regarding this ‘permutation invariance’ that aligns with a widely accepted view of symmetry principles in general is that it expresses a certain representational redundancy in the formalism. Thus, referring to our sketch above, the permuted arrangement of one particle in each box, which is counted in classical statistical mechanics but not in the quantum form, can be considered as ‘representationally redundant’ in this sense. This casts ‘permutation invariance’ as one of a number of such symmetry principles that have acquired a fundamental role in modern physics (Huggett 1999b; French and Rickles 2003). Not surprisingly perhaps, such a re-casting may also have metaphysical implications in that when applied to certain systems obeying Fermi-Dirac statistics – that is, systems of ‘material’ particles – the composition of such systems (in the sense that they may be regarded as composed or made up of sub-systems considered as ‘parts’) violates standard mereological principles (Caulton 2015; for some possible responses see Bigaj 2016). More generally it has been argued that ‘permutation invariance’ is incompatible with a particle ontology understood even in a metaphysically minimal sense (Jantzen 2011). Given the fundamental significance of the former, it has been suggested that the latter must then be jettisoned. A possible alternative is to adopt a form of space-time substantivalism and take property-bearing regions of space-time to provide the appropriate ontological basis (Jantzen 2011). However that runs into the sorts of problems touched on above.\n\nMore radically, perhaps, dropping the above ‘object-oriented’\nassumption would undercut the metaphysical underdetermination entirely and open up space for an alternative ontology in terms of which quantum entities are conceived of as nothing more than\nfeatures of ‘the structure of the world’ (see French and Ladyman 2003). This can then be articulated in terms of the relevant laws and symmetries with the properties of such putative entities understood as the determinate aspects of this structure (see French 2014; for further consideration of such an ontology in the context of ‘structural realism’, see Ladyman 2014)." ], "section_title": "6. Metaphysical Underdetermination", "subsections": [] } ]

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[ { "href": "../identity-indiscernible/", "text": "identity: of indiscernibles" }, { "href": "../identity-relative/", "text": "identity: relative" }, { "href": "../physics-holism/", "text": "physics: holism and nonseparability" }, { "href": "../qm/", "text": "quantum mechanics" }, { "href": "../structural-realism/", "text": "structural realism" } ]

[ "\nAn ongoing debate in the foundations of quantum physics concerns the\nrole of mathematical rigor. The contrasting views of von Neumann and\nDirac provide interesting and informative insights concerning two\nsides of this debate. Von Neumann’s contributions often\nemphasize mathematical rigor and Dirac’s contributions emphasize\npragmatic concerns. The discussion below begins with an assessment of\ntheir contributions to the foundations of quantum mechanics. Their\ncontributions to mathematical physics beyond quantum mechanics are\nthen considered, and the focus will be on the influence that these\ncontributions had on subsequent developments in quantum theorizing,\nparticularly with regards to quantum field theory and its foundations.\nThe entry\n quantum field theory\n provides an overview of a variety of approaches to developing a\nquantum theory of fields. The purpose of this article is to provide a\nmore detailed discussion of mathematically rigorous approaches to\nquantum field theory, as opposed to conventional approaches, such as\nLagrangian quantum field theory, which are generally portrayed as\nbeing more heuristic in character. The current debate concerning\nwhether Lagrangian quantum field theory or axiomatic quantum field\ntheory should serve as the basis for interpretive analysis is then\ndiscussed." ]

[ { "content_title": "1. Introduction", "sub_toc": [] }, { "content_title": "2. Von Neumann and the Foundations of Quantum Theory", "sub_toc": [ "2.1 The Separable Hilbert Space Formulation of Quantum Mechanics", "2.2 Rings of Operators, Quantum Logics, and Continuous Geometries" ] }, { "content_title": "3. Dirac and the Foundations of Quantum Theory", "sub_toc": [ "3.1 Dirac’s \\(\\delta\\) Function, Principles, and Bra-Ket Notation", "3.2 The Rigged Hilbert Space Formulation of Quantum Mechanics" ] }, { "content_title": "4 Mathematical Rigor: Two Paths", "sub_toc": [ "4.1 Algebraic Quantum Field Theory", "4.2 Wightman’s Axiomatic Quantum Field Theory" ] }, { "content_title": "5 Philosophical Issues", "sub_toc": [ "5.1 Pragmatics versus Axiomatics ", "5.2 Middle Grounds" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThere are two competing mathematical strategies that are used in\nconnection with physical theory; one emphasizes rigor and the other\npragmatics. The pragmatic approach often compromises mathematical\nrigor, but offers instead expediency of calculation and elegance of\nexpression. A case in point is the notion of an infinitesimal, a\nnon-zero quantity that is smaller than any finite quantity.\nInfinitesimals were used by Kepler, Galileo, Newton, Leibniz and many\nothers in developing and using their respective physical theories,\ndespite lacking a mathematically rigorous foundation, as Berkeley\nclearly showed in his famous 1734 treatise The Analyst\ncriticizing infinitesimals. Such criticisms did not prevent various\n18th Century mathematicians, scientists, and engineers such as Euler\nand Lagrange from using infinitesimals to get accurate answers from\ntheir calculations. Nevertheless, the pull towards rigor led to the\ndevelopment in the 19th century of the concept of a limit by Cauchy\nand others, which provided a rigorous mathematical framework that\neffectively replaced the theory of infinitesimals. A rigorous\nfoundation was eventually provided for infinitesimals by Robinson\nduring the second half of the 20th Century, but infinitesimals are\nrarely used in contemporary physics. For more on the history of\ninfinitesimals, see the entry on\n continuity and infinitesimals.", "\nThe competing mathematical strategies are manifest in a more recent\ndiscussion concerning the mathematical foundations of quantum\nmechanics. In the preface to von Neumann’s (1955) treatise on\nthat topic, he notes that Dirac provides a very elegant and powerful\nformal framework for quantum mechanics, but complains about the\ncentral role in that framework of an “improper function with\nself-contradictory properties,” which he also characterizes as a\n“mathematical fiction.” He is referring to the Dirac\n\\(\\delta\\) function, which has the following incompatible properties:\nit is defined over the real line, is zero everywhere except for one\npoint at which it is infinite, and yields unity when integrated over\nthe real line. Von Neumann promotes an alternative framework, which he\ncharacterizes as being “just as clear and unified, but without\nmathematical objections.” He emphasizes that his framework is\nnot merely a refinement of Dirac’s; rather, it is a radically\ndifferent framework that is based on Hilbert’s theory of\noperators.", "\nDirac is of course fully aware that the \\(\\delta\\) function is not a\nwell-defined expression. But he is not troubled by this for two\nreasons. First, as long as one follows the rules governing the\n\\(\\delta\\) function (such as using the \\(\\delta\\) function only under\nan integral sign, meaning in part not asking the value of a \\(\\delta\\)\nfunction at a given point), then no inconsistencies will arise.\nSecond, the \\(\\delta\\) function can be eliminated, meaning that it can\nbe replaced with a well-defined mathematical expression. However, the\ndrawback in that case is, according to Dirac, that the substitution\nleads to a more cumbersome expression that obscures the argument. In\nshort, when pragmatics and rigor lead to the same conclusion,\npragmatics trumps rigor due to the resulting simplicity, efficiency,\nand increase in understanding.", "\nAs in the case of the notion of an infinitesimal, the Dirac \\(\\delta\\)\nfunction was eventually given a mathematically rigorous foundation.\nThat was done within Schwartz’s theory of distributions, which\nwas later used in developing the notion of a rigged Hilbert space. The\ntheory of distributions was used to provide a mathematical framework\nfor quantum field theory (Wightman 1964). The rigged Hilbert space was\nused to do so for quantum mechanics (Böhm 1966) and then for\nquantum field theory (Bogoluliubov et al. 1975).", "\nThe complementary approaches, rigor and pragmatics, which are\nexhibited in the development of quantum mechanics, later came about in\na more striking way in connection with the development of quantum\nelectrodynamics (QED) and, more generally, quantum field theory (QFT).\nThe emphasis on rigor emerges in connection with two frameworks,\nalgebraic QFT and Wightman’s axiomatic QFT. Algebraic QFT has\nits roots in the work of von Neumann on operator algebras, which was\ndeveloped by him in an attempt to generalize the Hilbert space\nframework. Wightman’s axiomatic QFT has its roots in\nSchwartz’s theory of distributions, and it was later developed\nin the rigged Hilbert space framework. Roughly, the basic distinction\nbetween the two approaches is that the algebra of operators is the\nbasic mathematical concept in algebraic QFT, while operator-valued\ndistributions (the quantum analogues of field quantities) are\nfundamental in Wightman’s axiomatic QFT. It is worth noting that\nalgebraic QFT is generally formulated axiomatically, and that it is\njust as deserving of the name “axiomatic” QFT. However,\nthat term is often taken to refer specifically to the approach based\non operator-valued distributions. To avoid any possible confusion,\nthat approach is referred to here as “Wightman’s\naxiomatic” QFT. The emphasis on pragmatics arises most notably\nin Lagrangian QFT, which uses perturbation theory, path integrals, and\nrenormalization techniques. Although some elements of the theory were\neventually placed on a firmer mathematical foundation, there are still\nserious questions about its being a fully rigorous approach on a par\nwith algebraic and Wightman’s axiomatic QFT. Nevertheless, it\nhas been spectacularly successful in providing numerical results that\nare exceptionally accurate with respect to experimentally determined\nquantities, and in making possible expedient calculations that are\nunrivaled by other approaches.", "\nThe two approaches to QFT continue to develop in parallel. Fleming\n(2002, pp. 135–136) brings this into focus in his discussion of\ndifferences between Haag’s Local Quantum Physics (1996)\nand Weinberg’s Quantum Field Theory (1995);\nHaag’s book presents algebraic QFT, and Weinberg’s book\npresents Lagrangian QFT. While both books are ostensibly about the\nsame subject, Haag gives a precise formulation of QFT and its\nmathematical structure, but does not provide any techniques for\nconnecting with experimentally determined quantities, such as\nscattering cross sections. Weinberg gives a pragmatic formulation that\nengages with physical intuition and provides heuristics that are\nimportant for performing calculations; however, it is not as\nmathematically rigorous. Moreover, there are a number of important\ntopics that are examined in one book while not even mentioned in the\nother. For example, unitarily inequivalent representations are\ndiscussed by Haag, but not by Weinberg. By contrast, Weinberg\ndiscusses Feynman’s rules for path integrals, which are not\nmentioned at all by Haag. There is also the issue of demographics.\nMost particle and experimental physicists will read and study\nWeinberg’s book, but very few will read Haag’s book.\nBecause of these differences, Fleming (2002, p. 136) suggests that one\nmight question whether the two books are really about the same\nsubject. This gives rise to the question whether any formulation of\nQFT is worthy of philosophical attention to its foundations. In\nparticular, there is a debate between Wallace (2006, 2011) and Fraser\n(2009, 2011) over whether an interpretation of QFT should be based on\nthe standard textbook treatment of QFT or an axiomatic formulation of\nQFT." ], "section_title": "1. Introduction", "subsections": [] }, { "main_content": [ "\nIn the late 1920s, von Neumann developed the separable Hilbert space\nformulation of quantum mechanics, which later became the definitive\none (from the standpoint of mathematical rigor, at least). In the\nmid-1930s, he worked extensively on lattice theory (see the entry on\n quantum logic),\n rings of operators, and continuous geometries. Part of his expressed\nmotivation for developing these mathematical theories was to develop\nan appropriate framework for QFT and a better foundation for quantum\nmechanics. During this time, he noted two closely related structures,\nmodular lattices and finite type-II factors (a special type of ring of\noperators), that have what he regarded as desirable features for\nquantum theory. These observations led to his developing a more\ngeneral framework, continuous geometries, for quantum theory. Matters\ndid not work out as von Neumann had expected. He soon realized that\nsuch geometries must have a transition probability function, if they\nare to be used to describe quantum mechanical phenomena, and that the\nresulting structure is not a generalization at all beyond the operator\nrings that were already available. Moreover, it was determined much\nlater that the type-III factors are the most important type of ring of\noperators for quantum theory. In addition, a similar verdict was\ndelivered much later with regards to his expectations concerning\nlattice theory. The lattices that are appropriate for quantum theory\nare orthomodular – a lattice is orthomodular only if it is\nmodular, but the converse is false. Of the three mathematical\ntheories, it is the rings of operators that have proven to be the most\nimportant framework for quantum theory. It is possible to use a ring\nof operators to model key features of physical systems in a purely\nabstract, algebraic setting (this is discussed in section 4.1). A\nrelated issue concerns whether it is necessary to choose a\nrepresentation of the ring in a Hilbert space; see Haag and Kastler\n(1964), Ruetsche (2003), and Kronz and Lupher (2005) for further\ndiscussion of this issue. In any case, the separable Hilbert space\nremains a crucial framework for quantum theory. The simplest examples\nof separable Hilbert spaces are the finite dimensional ones, in which\ncase the algebra of operators is a type-I\\(_n\\) factor (n is a\npositive integer). The operators are n-by-n complex matrices, which\nare typically used to describe internal degrees of freedom such as\nspin. Readers wanting to familiarize themselves with these basic\nexamples should consult the entry on\n quantum mechanics." ], "section_title": "2. Von Neumann and the Foundations of Quantum Theory", "subsections": [ { "content": [ "\nMatrix mechanics and wave mechanics were formulated roughly around the\nsame time between 1925 and 1926. In July 1925, Heisenberg finished his\nseminal paper “On a Quantum Theoretical Interpretation of\nKinematical and Mechanical Relations”. Two months later, Born\nand Jordan finished their paper, “On Quantum Mechanics”,\nwhich is the first rigorous formulation of matrix mechanics. Two\nmonths after this, Born, Heisenberg, and Jordan finished “On\nQuantum Mechanics II”, which is an elaboration of the earlier\nBorn and Jordan paper; it was published in early 1926. These three\npapers are reprinted in van der Waerden (1967). Meanwhile,\nSchrödinger was working on what eventually became his four famous\npapers on wave mechanics. The first was received by Annalen der\nPhysik in January 1926, the second was received in February, and\nthen the third in May and the fourth in June. All four are reprinted\nin Schrödinger (1928).", "\nSchrödinger was the first to raise the question of the\nrelationship between matrix mechanics and wave mechanics in\nSchrödinger (1926), which was published in Annalen in\nspring 1926 between the publication of his second and third papers of\nthe famous four. This paper is also reprinted in Schrödinger\n(1928). It contains the germ of a mathematical equivalence proof, but\nit does not contain a rigorous proof of equivalency: the mathematical\nframework that Schrödinger associated with wave mechanics is a\nspace of continuous and normalizable functions, which is too small to\nestablish the appropriate relation with matrix mechanics. Shortly\nthereafter, Dirac and Jordan independently provided a unification of\nthe two frameworks. But their respective approaches required essential\nuse of \\(\\delta\\) functions, which were suspect from the standpoint of\nmathematical rigor. In 1927, von Neumann published three papers in\nGöttinger Nachrichten that placed quantum mechanics on a\nrigorous mathematical foundation and included a rigorous proof (i.e.,\nwithout the use of \\(\\delta\\) functions) of the equivalence of matrix\nand wave mechanics. These papers are reprinted in von\nNeumann(1961–1963, Volume I, Numbers 8–10). In the preface\nto his famous 1932 treatise on quantum mechanics (von Neumann 1955),\nwhich is an elegant summary of the separable Hilbert space formulation\nof quantum mechanics that he provided in the earlier papers, he\nacknowledges the simplicity and utility of Dirac’s formulation\nof quantum mechanics, but finds it ultimately unacceptable. He\nindicates that he cannot endure the use of what could then only be\nregarded as mathematical fictions. Examples of these fictions include\nDirac’s assumption that every self-adjoint operator can be put\nin diagonal form and his use of \\(\\delta\\) functions, which von\nNeumann characterizes as “improper functions with\nself-contradictory properties”. His stated purpose is to\nformulate a framework for quantum mechanics that is mathematically\nrigorous.", "\nWhat follows is a brief sketch of von Neumann’s strategy. First,\nhe recognized the mathematical framework of matrix mechanics as what\nwould now be characterized as an infinite dimensional, separable\nHilbert space. Here the term “Hilbert space” denotes\na complete vector space with an inner product; von Neumann imposed the\nadditional requirement of separability (having a countable basis) in\nhis definition of a Hilbert space. He then attempted to specify a set\nof functions that would instantiate an (infinite-dimensional)\nseparable Hilbert space and could be identified with\nSchrödinger’s wave mechanics. He began with the space of\nsquare-integrable functions on the real line. To satisfy the\ncompleteness condition, that all Cauchy sequences of functions\nconverge (in the mean) to some function in that space, he specified\nthat integration must be defined in the manner of Lebesgue. To define\nan inner product operation, he specified that the set of Lebesgue\nsquare-integrable functions must be partitioned into equivalence\nclasses modulo the relation of differing on a set of measure zero.\nThat the elements of the space are equivalence classes of functions\nrather than functions is sometimes overlooked, and it has interesting\nramifications for interpretive investigations. It has been argued in\nKronz (1999), for example, that separable Hilbert space is not a\nsuitable framework for quantum mechanics under Bohm’s\nontological interpretation (also known as\n Bohmian mechanics)." ], "subsection_title": "2.1 The Separable Hilbert Space Formulation of Quantum Mechanics" }, { "content": [ "\nIn a letter to Birkhoff from 1935, von Neumann says: “I would\nlike to make a confession which may seem immoral: I do not believe in\nHilbert space anymore”; the letter is published in von Neumann\n(2005). The confession is indeed startling since it comes from the\nchampion of the separable Hilbert space formulation of quantum\nmechanics and it is issued just three years after the publication of\nhis famous treatise, the definitive work on the subject. The irony is\ncompounded by the fact that less than two years after his confession\nto Birkhoff, his mathematical theorizing about the abstract\nmathematical structure that was to supersede the separable Hilbert\nspace, continuous geometries with a transition probability, turned out\nnot to provide a generalization of the separable Hilbert space\nframework. It is compounded again with interest in that subsequent\ndevelopments in mathematical physics initiated and developed by von\nNeumann ultimately served to strengthen the entrenchment of the\nseparable Hilbert space framework in mathematical physics (especially\nwith regards to quantum theory). These matters are explained in more\ndetail in Section 4.1.", "\nThree theoretical developments come together for von Neumann in his\ntheory of continuous geometries during the seven years following 1932:\nthe algebraic approach to quantum mechanics, quantum logics, and rings\nof operators. By 1934, von Neumann had already made substantial moves\ntowards an algebraic approach to quantum mechanics with the help of\nJordan and Wigner – their article, “On an Algebraic\nGeneralization of the Quantum Mechanical Formalism”,  is\nreprinted in von Neumann (1961–1963, Vol. II, No. 21). In 1936,\nhe published a second paper on this topic, “On an Algebraic\nGeneralization of the  Quantum Mechanical Formalism (Part\nI)”, which is reprinted in von Neumann (1961–1963, Vol.\nIII, No. 9). Neither work was particularly influential, as it turns\nout. A related paper by von Neumann and Birkhoff, “The Logic of\nQuantum Mechanics”, was also published in 1936, and it is\nreprinted in von Neumann (1961–1963, Vol. IV, No. 7). It was\nseminal to the development of a sizeable body of literature on\n quantum logics.\n It should be noted, however, that this happens only after modularity,\na key postulate for von Neumann, is replaced with orthomodularity (a\nweaker condition). The nature of the shift is clearly explained in\nHolland (1970): modularity is in effect a weakening of the\ndistributive laws (limiting their validity to certain selected triples\nof lattice elements), and orthomodularity is a weakening of modularity\n(limiting the validity of the distributive laws to an even smaller set\nof triples of lattice elements). The shift from modularity to\northomodularity was first made in (Loomis 1955). Rapid growth of\nliterature on orthomodular lattices and the foundations of quantum\nmechanics soon followed. For example, see Pavičić (1992) for\na fairly exhaustive bibliography of quantum logic up to 1990, which\nhas over 1800 entries.", "\nOf substantially greater note for the foundations of quantum theory\nare six papers by von Neumann (three jointly published with Murray) on\nrings of operators, which are reprinted in von Neumann\n(1961–1963, Vol. III, Nos 2–7). The first two, “On\nRings of Operators” and a sequel “On Rings of Operators\nII”, were published in 1936 and 1937, and they were seminal to\nthe development of the other four. The third, “On Rings of\nOperators: Reduction Theory”, was written during 1937–1938\nbut not published until 1949. The fourth, “On Infinite Direct\nProducts”, was published in 1938. The remaining two, “On\nRings of Operators III” and “On Rings of Operators\nIV” were published in 1941 and 1943, respectively. This massive\nwork on rings of operators was very influential and continues to have\nan impact in pure mathematics, mathematical physics, and the\nfoundations of physics. Rings of operators are now referred to as\n“von Neumann algebras” following Dixmier (1981), who first\nreferred to them by this name (stating that he did so following a\nsuggestion made to him by Dieudonné) in the introduction to his\n1957 treatise on operator algebras (Dixmier 1981).", "\nA von Neumann algebra is a \\(*\\)-subalgebra of the set\nof bounded operators B(H) on a Hilbert space H that is closed in the\nweak operator topology. It is usually assumed that the von Neumann\nalgebra contains the identity operator. A \\(*\\)-subalgebra\ncontains the adjoint of every operator in\nthe algebra, where the “\\(*\\)” denotes the\nadjoint. There are special types of von Neumann algebras that are\ncalled “factors”. A von Neumann algebra is a factor, if\nits center (which is the set of elements that commute with all\nelements of the algebra) is trivial, meaning that it only contains\nscalar multiples of the identity element. Moreover, von Neumann showed\nin his reduction-theory paper that all von Neumann algebras that are\nnot factors can be decomposed as a direct sum (or integral) of\nfactors. There are three mutually exclusive and exhaustive factor\ntypes: type-I, type-II, and type-III. Each type has been classified\ninto (mutually exclusive and exhaustive) sub-types: types I\\(_n\\) \\((n\n= 1,2,\\ldots ,\\infty),\\) II\\(_n\\) \\((n = 1,\\infty),\\) III\\(_z\\)\n\\((0\\le z\\le 1).\\) As mentioned above, type-I\\(_n\\) correspond to\nfinite dimensional Hilbert spaces, while type-I\\(_{\\infty}\\)\ncorresponds to the infinite dimensional separable Hilbert space that\nprovides the rigorous framework for wave and matrix mechanics. Von\nNeumann and Murray distinguished the subtypes for type-I and type-II,\nbut were not able to do so for the type-III factors. Subtypes were not\ndistinguished for these factors until the 1960s and 1970s – see\nChapter 3 of Sunder (1987) or Chapter 5 of Connes (1994) for\ndetails.", "\nAs a result of his earlier work on the foundations of quantum\nmechanics and his work on quantum logic with Birkhoff, von Neumann\ncame to regard the type-II\\(_1\\) factors as likely to be the most\nrelevant for physics. This is a substantial shift since the most\nimportant class of algebra of observables for quantum mechanics was\nthought at the time to be the set of bounded operators on an\ninfinite-dimensional separable Hilbert space, which is a\ntype-I\\(_{\\infty}\\) factor. A brief explanation for this shift is\nprovided below. See the well-informed and lucid account presented in\n(Rédei 1998) for a much fuller discussion of von\nNeumann’s views on fundamental connections between quantum\nlogic, rings of operators (particularly type-II\\(_1\\) factors),\nfoundations of probability theory, and quantum physics. It is worth\nnoting that von Neumann regarded the type-III factors as a catch-all\nclass for the “pathological” operator algebras; indeed, it\ntook several years after the classificatory scheme was introduced to\ndemonstrate the existence of such factors. It is ironic that the\npredominant view now seems to be that the type-III factors are the\nmost relevant class for physics (particularly for QFT and quantum\nstatistical mechanics). This point is elaborated further in Section\n4.1 after explaining below why von Neumann’s program never came\nto fruition.", "\nIn the introduction to the first paper in the series of four entitled\n“On Rings of Operators”, Murray and von Neumann list two\nreasons why they are dissatisfied with the separable Hilbert space\nformulation of quantum mechanics. One has to do with a property of the\ntrace operation, which is the operation appearing in the definition of\nthe probabilities for measurement results (the Born rule), and the\nother with domain problems that arise for unbounded observable\noperators. The trace of the identity is infinite when the separable\nHilbert space is infinite-dimensional, which means that it is not\npossible to define a correctly normalized a priori\nprobability for the outcome of an experiment (i.e., a measurement of\nan observable). By definition, the a priori probability for\nan experiment is that in which any two distinct outcomes are equally\nlikely. Thus, the probability must be zero for each distinct outcome\nwhen there is an infinite number of such outcomes, which can occur if\nand only if the space is infinite dimensional. It is not clear why von\nNeumann believed that it is necessary to have an a priori\nprobability for every experiment, especially since von Mises clearly\nbelieved that a priori probabilities (“uniform\ndistributions” in his terminology) do not always exist (von\nMises 1981, pp. 68 ff.) and von Neumann was influenced substantially\nby von Mises on the foundations of probability (von Neumann 1955, p.\n198 fn.). Later, von Neumann changed the basis for his expressed\nreason for dissatisfaction with infinite dimensional Hilbert spaces\nfrom probabilistic to algebraic considerations (Birkhoff and von\nNeumann 1936, p. 118); namely, that it violates Hankel’s\nprinciple of the preservation of formal law, which leads one to try to\npreserve modularity – a condition that holds in\nfinite-dimensional Hilbert spaces but not in infinite-dimensional\nHilbert spaces. The problem with unbounded operators arises from their\nonly being defined on a merely dense subset of the set elements of the\nspace. This means that algebraic operations of unbounded operators\n(sums and products) cannot be generally defined; for example, it is\npossible that two unbounded operators \\(A\\), \\(B\\)\nare such that the range of \\(B\\) and\nthe domain of \\(A\\) are disjoint, in which case the\nproduct \\(AB\\) is meaningless.", "\nThe problems mentioned above do not arise for type-I\\(_n\\) factors, if\n\\(n\\lt \\infty\\), nor do they arise for type-II\\(_1\\). That is to say,\nthese factor types have a finite trace operation and are not plagued\nwith the domain problems of unbounded operators. Particularly\nnoteworthy is that the lattice of projections of each of these factor\ntypes (type-I\\(_n\\) for \\(n\\lt \\infty\\) and type-II\\(_1)\\) is modular.\nBy contrast, the set of bounded operators on an infinite-dimensional\nseparable Hilbert space, a type-I\\(_{\\infty}\\) factor, is not modular;\nrather, it is only orthomodular. These considerations serve to explain\nwhy von Neumann regarded the type-II\\(_1\\) factor as the proper\ngeneralization of the type-I\\(_n\\) \\((n\\lt \\infty)\\) for quantum\nphysics rather than the type-I\\(_{\\infty}\\) factors. The shift in the\nliterature from modular to orthomodular lattices that was\ncharacterized above is in effect a shift back to von Neumann’s\nearlier position (prior to his confession). But, as was already\nmentioned, it now seems that this was not the best move either.", "\nIt was von Neumann’s hope that his program for generalizing\nquantum theory would emerge from a new mathematical structure known as\n“continuous geometry”. He wanted to use this structure to\nbring together the three key elements that were mentioned above: the\nalgebraic approach to quantum mechanics, quantum logics, and rings of\noperators. He sought to forge a strong conceptual link between these\nelements and thereby provide a proper foundation for generalizing\nquantum mechanics that does not make essential use of Hilbert space\n(unlike rings of operators). Unfortunately, it turns out that the\nclass of continuous geometries is too broad for the purposes of\naxiomatizing quantum mechanics. The class must be suitably restricted\nto those having a transition probability. It turns out that there is\nthen no substantial generalization beyond the separable Hilbert space\nframework. An unpublished manuscript that was finished by von Neumann\nin 1937 was prepared and edited by Israel Halperin, and then published\nas von Neumann (1981). A review of the manuscript by Halperin was\npublished in von Neumann (1961–1963, Vol. IV, No. 16) years\nbefore the manuscript itself was published. In that review, Halperin\nnotes the following:", "\nThe final result, after 200 pages of deep reasoning is (essentially):\nevery such geometry with transition probability can be identified with\nthe projection geometry of a finite factor in some finite or infinite\ndimensional Hilbert space (I\\(_m\\) or II\\(_1)\\). This result indicates\nthat continuous geometries do not provide new useful mathematical\ndescriptions of quantum mechanical phenomena beyond that already\navailable from rings of operators.\n", "\nThis unfortunate development does not, however, completely undermine\nvon Neumann’s efforts to generalize quantum mechanics. On the\ncontrary, his work on rings of operators does provide significant\nlight to the way forward. The upshot of subsequent developments is\nthat von Neumann settled on the wrong factor type for the foundations\nof physics." ], "subsection_title": "2.2 Rings of Operators, Quantum Logics, and Continuous Geometries" } ] }, { "main_content": [ "\nDirac’s formal framework for quantum mechanics was very useful\nand influential despite its lack of mathematical rigor. It was used\nextensively by physicists and it inspired some powerful mathematical\ndevelopments in functional analysis. Eventually, mathematicians\ndeveloped a suitable framework for placing Dirac’s formal\nframework on a firm mathematical foundation, which is known as a\nrigged Hilbert space (and is also referred to as a\nGelfand Triplet). This came about as follows. A rigorous\ndefinition of the \\(\\delta\\) function became possible in distribution\ntheory, which was developed by Schwartz from the mid-1940s to the\nearly 1950s. Distribution theory inspired Gelfand and collaborators\nduring the mid-to-late 1950s to formulate the notion of a rigged\nHilbert space, the firm foundation for Dirac’s formal framework.\nThis development was facilitated by Grothendiek’s notion of a\nnuclear space, which he introduced in the mid-1950s. The rigged\nHilbert space formulation of quantum mechanics was then developed\nindependently by Böhm and by Roberts in 1966. Since then, it has\nbeen extended to a variety of different contexts in the quantum domain\nincluding decay phenomena and the arrow of time. The mathematical\ndevelopments of Schwartz, Gelfand, and others had a substantial effect\non QFT as well. Distribution theory was taken forward by Wightman in\ndeveloping the axiomatic approach to QFT from the mid-1950s to the\nmid-1960s. In the late 1960s,  the axiomatic approach was\nexplicitly put into the rigged Hilbert space framework by Bogoliubov\nand co-workers.", "\nAlthough these developments were only indirectly influenced by Dirac,\nby way of the mathematical developments that are associated with his\nformal approach to quantum mechanics, there are other elements of his\nwork that had a more direct and very substantial impact on the\ndevelopment of QFT. In the 1930s, Dirac (1933) developed a Lagrangian\nformulation of quantum mechanics and applied it to quantum fields ,\nand the latter inspired Feynman (1948) to develop the path-integral\napproach to QFT. The mathematical foundation for path-integral\nfunctionals is still lacking (Rivers 1987, pp, 109–134), though\nsubstantial progress has been made (DeWitt-Morette et al.\n1979). Despite such shortcomings, it remains the most useful and\ninfluential approach to QFT to date. In the 1940s, Dirac (1943)\ndeveloped a form of quantum electrodynamics that involved an\nindefinite metric – see also Pauli (1943) in that connection.\nThis had a substantial influence on later developments, first in\nquantum electrodynamics in the early 1950s with the Gupta-Bluer\nformalism, and in a variety of QFT models such as vector meson fields\nand quantum gravity fields by the late 1950s – see Chapter 2 of\nNagy (1966) for examples and references." ], "section_title": "3. Dirac and the Foundations of Quantum Theory", "subsections": [ { "content": [ "\nDirac’s attempt to prove the equivalence of matrix mechanics and\nwave mechanics made essential use of the \\(\\delta\\) function, as\nindicated above. The \\(\\delta\\) function was used by physicists before\nDirac, but it became a standard tool in many areas of physics only\nafter Dirac very effectively put it to use in quantum mechanics. It\nthen became widely known by way of his textbook (Dirac 1930), which\nwas based on a series of lectures on quantum mechanics given by Dirac\nat Cambridge University. This textbook saw three later editions: the\nsecond in 1935, the third in 1947, and the fourth in 1958. The fourth\nedition has been reprinted many times. Its staying power is due, in\npart, to another innovation that was introduced by Dirac in the third\nedition, his bra-ket formalism. He first published this formalism in\n(Dirac 1939), but the formalism did not become widely used until after\nthe publication of the third edition of his book. There is no question\nthat these tools, first the \\(\\delta\\) function and then the bra-ket\nnotation, were extremely effective for physicists practicing and\nteaching quantum mechanics both with regards to setting up equations\nand to the performance of calculations. Most quantum mechanics\ntextbooks use \\(\\delta\\) functions and plane waves, which are key\nelements of Dirac’s formal framework, but they are not included\nin von Neumann’s rigorous mathematical framework for quantum\nmechanics. Working physicists as well as teachers and students of\nquantum mechanics often use Dirac’s framework because of its\nsimplicity, elegance, power, and relative ease of use. Thus, from the\nstandpoint of pragmatics, Dirac’s framework is much preferred\nover von Neumann’s. The notion of a rigged Hilbert space placed\nDirac’s framework on a firm mathematical foundation." ], "subsection_title": "3.1 Dirac’s \\(\\delta\\) Function, Principles, and Bra-Ket Notation" }, { "content": [ "\nMathematicians worked very hard to provide a rigorous foundation for\nDirac’s formal framework. One key element was Schwartz’s\n(1945; 1950–1951) theory of distributions. Another key element,\nthe notion of a nuclear space, was developed by Grothendieck (1955).\nThis notion made possible the generalized-eigenvector decomposition\ntheorem for self-adjoint operators in rigged Hilbert space – for\nthe theorem see Gelfand and Vilenken (1964, pp. 119–127), and\nfor a brief historical account of the convoluted path leading to it\nsee Berezanskii (1968, pp. 756–760). The decomposition principle\nprovides a rigorous way to handle observables such as position and\nmomentum in the manner in which they are presented in Dirac’s\nformal framework. These mathematical developments culminated in the\nearly 1960s with Gelfand and Vilenkin’s characterization of a\nstructure that they referred to as a rigged Hilbert space\n(Gelfand and Vilenkin 1964, pp. 103–127). It is unfortunate that\ntheir chosen name for this mathematical structure is doubly\nmisleading. First, there is a natural inclination to regard it as\ndenoting a type of Hilbert space, one that is rigged in some\nsense, but this inclination must be resisted. Second, the term\nrigged has an unfortunate connotation of illegitimacy, as in\nthe terms rigged election or rigged roulette table,\nand this connotation must be dismissed as prejudicial. There is\nnothing illegitimate about a rigged Hilbert space from the standpoint\nof mathematical rigor (or any other relevant standpoint). A more\nappropriate analogy may be drawn using the notion of a rigged ship:\nthe term rigged in this context means fully equipped. But\nthis analogy has its limitations since a rigged ship is a fully\nequipped ship, but (as the first point indicates) a rigged Hilbert\nspace is not a Hilbert space, though it is generated from a Hilbert\nspace in the manner now to be described.", "\nA rigged Hilbert space is a dual pair of spaces \\((\\Phi , \\Phi^x)\\)\nthat can generated from a separable Hilbert space \\(\\Eta\\) using a\nsequence of norms (or semi-norms); the sequence of norms is generated\nusing a nuclear operator (a good approximate meaning is an operator of\ntrace-class, meaning that the trace of the modulus of the operator is\nfinite). In the mathematical theory of topological vector spaces, the\nspace \\(\\Phi\\) is characterized in technical terms as a nuclear\nFréchet space. To say that \\(\\Phi\\) is a\nFréchet space means that it is a complete metric\nspace, and to say that it is nuclear means that it is the\nprojective limit of a sequence of Hilbert spaces in which the\nassociated topologies get rapidly finer with increasing n (i.e., the\nconvergence conditions are increasingly strict); the term\nnuclear is used because the Hilbert-space topologies are\ngenerated using a nuclear operator. In distribution theory, the space\n\\(\\Phi\\) is characterized as a test-function space, where a\ntest-function is thought of as a very well-behaved function (being\ncontinuous, n-times differentiable, having a bounded domain or at\nleast dropping off exponentially beyond some finite range, etc).\n\\(\\Phi^x\\) is a space of distributions, and it is the topological dual\nof \\(\\Phi\\), meaning that it corresponds to the complete space of\ncontinuous linear functionals on \\(\\Phi\\). It is also the inductive\nlimit of a sequence of Hilbert spaces in which the topologies get\nrapidly coarser with increasing n. Because the elements of \\(\\Phi\\)\nare so well-behaved, \\(\\Phi^x\\) may contain elements that are not so\nwell-behaved, some being singular or improper functions (such as\nDirac’s \\(\\delta\\) function). \\(\\Phi\\) is the topological\nanti-dual of \\(\\Phi^x\\), meaning that it is the complete set of\ncontinuous anti-linear functionals on \\(\\Phi^x\\); it is anti-linear\nrather than linear because multiplication by a scalar is defined in\nterms of the scalar’s complex conjugate.", "\nIt is worth noting that neither \\(\\Phi\\) nor \\(\\Phi^x\\) is a Hilbert\nspace in that each lacks an inner product that induces a metric with\nrespect to which the space is complete, though for each space there is\na topology with respect to which the space is complete. Nevertheless,\neach of them is closely related to the Hilbert space \\(\\Eta\\) from\nwhich they are generated: \\(\\Phi\\) is densely embedded in \\(\\Eta\\),\nwhich in turn is densely embedded in \\(\\Phi^x\\). Two other points are\nworth noting. First, dual pairs of this sort can also be generated\nfrom a pre-Hilbert space, which is a space that has all the features\nof a Hilbert space except that it is not complete, and doing so has\nthe distinct advantage of avoiding the partitioning of functions into\nequivalence classes (in the case of functions spaces). The term\nrigged Hilbert space is typically used broadly to include\ndual pairs generated from either a Hilbert space or a pre-Hilbert\nspace. Second, the term Gelfand triplet is sometimes used\ninstead of the term rigged Hilbert space, though it refers to\nthe ordered set \\((\\Phi , \\Eta , \\Phi^x)\\), where \\(\\Eta\\) is the\nHilbert space used to generate \\(\\Phi\\) and \\(\\Phi^x\\).", "\nThe dual pair \\((\\Phi , \\Phi^x)\\) possesses the means to represent\nimportant operators for quantum mechanics that are problematic in a\nseparable Hilbert space, particularly the unbounded operators that\ncorrespond to the observables position and momentum, and it does so in\na particularly effective and unproblematic manner. As already noted,\nthese operators have no eigenvalues or eigenvectors in a separable\nHilbert space; moreover, they are only defined on a dense subset of\nthe elements of the space and this leads to domain problems. These\nundesirable features also motivated von Neumann to seek an alternative\nto the separable Hilbert space framework for quantum mechanics, as\nnoted above. In a rigged Hilbert space, the\noperators corresponding to position and momentum can have a\ncomplete set of eigenfunctionals (i.e., generalized eigenfunctions).\nThe key result is known as the nuclear spectral theorem (and it is\nalso known as the Gelfand-Maurin theorem). One version of the theorem\nsays that if A is a symmetric linear operator defined on the space\n\\(\\Phi\\) and it admits a self-adjoint extension to the Hilbert space\nH, then A possesses a complete system of eigenfunctionals belonging to\nthe dual space \\(\\Phi^x\\) (Gelfand and Shilov 1977, chapter 4). That\nis to say, provided that the stated condition is satisfied, A can be\nextended by duality to \\(\\Phi^x\\), its extension \\(A^x\\) is continuous\non \\(\\Phi^x\\) (in the operator topology in \\(\\Phi^x)\\), and \\(A^x\\)\nsatisfies a completeness relation (meaning that it can be decomposed\nin terms of its eigenfunctionals and their associated eigenvalues).\nThe duality formula for extending \\(A\\) to \\(\\Phi^x\\)\nis \\(\\braket{\\phi}{A^x\\kappa} = \\braket{A\\phi}{\\kappa}\\), for all\n\\(\\phi \\in \\Phi\\) and for all \\(\\kappa \\in \\Phi^x\\). The completeness\nrelation says that for all \\(\\phi ,\\theta \\in \\Phi\\):", "\nwhere \\(v(A)\\) is the set of all generalized eigenvalues of \\(A^x\\)\n(i.e., the set of all scalars \\(\\lambda\\) for which there is \\(\\lambda\n\\in \\Phi^x\\) such that \\(\\braket{\\phi}{A^x\\lambda} = \\lambda\n\\braket{\\phi}{\\lambda}\\) for all \\(\\phi \\in \\Phi)\\).", "\nThe rigged Hilbert space representation of these observables is about\nas close as one can get to Dirac’s elegant and extremely useful\nformal representation with the added feature of being placed within a\nmathematically rigorous framework. It should be noted, however, that\nthere is a sense in which it is a proper generalization of\nDirac’s framework. The rigging (based on the choice of a nuclear\noperator that determines the test function space) can result in\ndifferent sets of generalized eigenvalues being associated with an\noperator. For example, the set of (generalized) eigenvalues for the\nmomentum operator (in one dimension) corresponds to the real line, if\nthe space of test functions is the set \\(S\\) of\ninfinitely differentiable functions of \\(x\\) which\ntogether with all derivatives vanish faster than any inverse power of\n\\(x\\) as \\(x\\) goes to infinity, whereas\nits associated set of eigenvalues is the complex plane, if the space\nof test functions is the set \\(D\\) of infinitely\ndifferentiable functions with compact support (i.e., vanishing outside\nof a bounded region of the real line). If complex eigenvalues are not\ndesired, then \\(S\\) would be a more appropriate choice\nthan \\(D\\) – see Nagel (1989) for a brief\ndiscussion. But there are situations in which it is desirable for an\noperator to have complex eigenvalues. This is so, for example, when a\nsystem exhibits resonance scattering (a type of decay phenomenon), in\nwhich case one would like the Hamiltonian to have complex eigenvalues\n– see Böhm & Gadella (1989). (Of course, it is\nimpossible for a self-adjoint operator to have complex eigenvalues in\na Hilbert space.)", "\nSoon after the development of the theory of rigged Hilbert spaces by\nGelfand and his associates, the theory was used to develop a new\nformulation of quantum mechanics. This was done independently by\nBöhm (1966) and Roberts (1966). It was later demonstrated that\nthe rigged Hilbert space formulation of quantum mechanics can handle a\nbroader range of phenomena than the separable Hilbert space\nformulation. That broader range includes scattering resonances and\ndecay phenomena (Böhm and Gadella 1989), as already noted.\nBöhm (1997) later extended this range to include a quantum\nmechanical characterization of the arrow of time. The Prigogine school\ndeveloped an alternative characterization of the arrow of time using\nthe rigged Hilbert space formulation of quantum mechanics (Antoniou\nand Prigogine 1993). Kronz (1998, 2000) used this formulation to\ncharacterize quantum chaos in open quantum systems. Castagnino and\nGadella (2003) used it to characterize\n decoherence\n in closed quantum systems." ], "subsection_title": "3.2 The Rigged Hilbert Space Formulation of Quantum Mechanics" } ] }, { "main_content": [], "section_title": "4 Mathematical Rigor: Two Paths", "subsections": [ { "content": [ "\nIn 1943, Gelfand and Neumark published an important paper on an\nimportant class of normed rings, which are now known as abstract\n\\(C^*\\)-algebras. Their paper was influenced by Murray and von\nNeumann’s work on rings of operators, which was discussed in the\nprevious section. In their paper, Gelfand and Neumark focus attention\non abstract normed \\(*\\)-rings. They show that any\n\\(C^*\\)-algebra can be given a concrete representation in a Hilbert\nspace (which need not be separable). That is to say, there is an\nisomorphic mapping of the elements of a \\(C^*\\)-algebra into the set\nof bounded operators of the Hilbert space. Four years later, Segal\n(1947a) published a paper that served to complete the work of Gelfand\nand Neumark by specifying the definitive procedure for constructing\nconcrete (Hilbert space) representations of an abstract\n\\(C^*\\)-algebra. It is called the GNS construction (after Gelfand,\nNeumark, and Segal). That same year, Segal (1947b) published an\nalgebraic formulation of quantum mechanics, which was substantially\ninfluenced by (though deviating somewhat from) von Neumann’s\n(1963, Vol. III, No. 9) algebraic formulation of quantum mechanics,\nwhich is cited in the previous section. It is worth noting that\nalthough \\(C^*\\)-algebras satisfy Segal’s postulates, the\nalgebra that is specified by his postulates is a more general\nstructure known as a Segal algebra. Every \\(C^*\\)-algebra is a Segal\nalgebra, but the converse is false since Segal’s postulates do\nnot require an adjoint operation to be defined. If a Segal algebra is\nisomorphic to the set of all self-adjoint elements of a\n\\(C^*\\)-algebra, then it is a special or exceptional Segal algebra.\nAlthough the mathematical theory of Segal algebras has been fairly\nwell developed, a \\(C^*\\)-algebra is the most important type of\nalgebra that satisfies Segal’s postulates.", "\nThe algebraic formulations of quantum mechanics that were developed by\nvon Neumann and Segal did not change the way that quantum mechanics\nwas done. Nevertheless, they did have a substantial impact in two\nrelated contexts: QFT and quantum statistical mechanics. The key\ndifference leading to the impact has to do with the domain of\napplicability. The domain of quantum mechanics consists of finite\nquantum systems, meaning quantum systems that have a finite number of\ndegrees of freedom. Whereas in QFT and quantum statistical mechanics,\nthe systems of special interest – i.e., quantum fields and\nparticle systems in the thermodynamic limit, respectively – are\ninfinite quantum systems, meaning quantum systems that have an\ninfinite number of degrees of freedom. Dirac (1927) was the first to\nrecognize the importance of infinite quantum systems for QFT, which is\nreprinted in Schwinger (1958).", "\nSegal (1959, p. 5) was the first to suggest that the beauty and power\nof the algebraic approach becomes evident when working with an\ninfinite quantum system . The key advantage of the algebraic approach,\naccording to Segal (1959, pp. 5–6), is that one may work in the\nabstract algebraic setting where it is possible to obtain interacting\nfields from free fields by an automorphism on the algebra, one that\nneed not be unitarily implementable. Segal notes (1959, p. 6) that von\nNeumann (1937) had a similar idea (that field dynamics are to be\nexpressed as an automorphism on the algebra) in an unpublished\nmanuscript. Segal notes this advantage in response to a result\nobtained by Haag (1955), that field theory representations of free\nfields are unitarily inequivalent to representations of interacting\nfields. Haag mentions that von Neumann (1938) first discovered\n‘different’ (unitarily inequivalent) representations much\nearlier. A different way of approaching unitarily equivalent\nrepresentations, by contrast with Segal’s approach, was later\npresented by Haag and Kastler (1964), who argued that unitarilty\ninequivalent representations are physically equivalent. Their notion\nof physical equivalence was based on Fell’s mathematical idea of\nweak equivalence (Fell 1960).", "\nAfter indicating important similarities between his and von\nNeumann’s approaches to infinite quantum systems, Segal draws an\nimportant contrast that serves to give the advantage to his approach\nover von Neumann’s. The key mathematical difference, according\nto Segal, is that von Neumann was working with a weakly closed ring of\noperators (meaning that the ring of operators is closed with respect\nto the weak operator topology), whereas Segal is working with a\nuniformly closed ring of operators (closed with respect to the uniform\ntopology). It is crucial because it has the following interpretive\nsignificance, which rests on operational considerations:", "\nThe present intuitive idea is roughly that the only measurable\nfield-theoretic variables are those that can be expressed in terms of\na finite number of canonical operators, or uniformly\napproximated by such; the technical basis is a uniformly\nclosed ring (more exactly, an abstract \\(C^*\\)-algebra). The crucial\ndifference between the two varieties of approximation arises from the\nfact that, in general, weak approximation has only analytical\nsignificance, while uniform approximation may be defined\noperationally, two observables being close if the maximum (spectral)\nvalue of the difference is small (Segal 1959, p. 7).\n", "\nInitially, it appeared that Segal’s assessment of the relative\nmerits of von Neumann algebras and \\(C^*\\)-algebras with respect to\nphysics was substantiated by a seminal paper, (Haag and Kastler 1964).\nAmong other things, Haag and Kastler introduced the key axioms of the\nalgebraic approach to QFT. They also argued that unitarily\ninequivalent representations are “physically equivalent”\nto each other. However, the use of physical equivalence to show that\nunitarily inequivalent representations are not physically significant\nhas been challenged; see Kronz and Lupher (2005), Lupher (2018), and\nRuetsche (2011). The prominent role of type-III factor von Neumann\nalgebras within the algebraic approach to quantum statistical\nmechanics and QFT raises further doubts about Segal’s\nassessment.", "\nThe algebraic approach has proven most effective in quantum\nstatistical mechanics. It is extremely useful for characterizing many\nimportant macroscopic quantum effects including crystallization,\nferromagnetism, superfluidity, structural phase transition,\nBose-Einstein condensation, and superconductivity. A good introductory\npresentation is Sewell (1986), and for a more advanced discussion see\nBratteli and Robinson (1979, 1981). In algebraic quantum statistical\nmechanics, an infinite quantum system is defined by specifying an\nabstract algebra of observables. A particular state may then be used\nto specify a concrete representation of the algebra as a set of\nbounded operators in a Hilbert space. Among the most important types\nof states that are considered in algebraic statistical mechanics are\nthe equilibrium states, which are often referred to as “KMS\nstates” (since they were first introduced by the physicists\nKubo, Martin, and Schwinger). There is a continuum of KMS states since\nthere is at least one KMS state for each possible temperature value\n\\(\\tau\\) of the system, for \\(0\\le \\tau \\le +\\infty\\). Given an\nautomorphism group, each KMS state corresponds to a representation of\nthe algebra of observables that defines the system, and each of these\nrepresentations is unitarily inequivalent to any other. It turns out\nthat each representation that corresponds to a KMS state is a factor:\nif \\(\\tau = 0\\) then it is a type-I factor, if \\(\\tau = +\\infty\\) then\nit is a type-II factor, and if \\(0\\lt \\tau \\lt +\\infty\\) then it is a\ntype-III factor. Thus, type-III factors play a predominant role in\nalgebraic quantum statistical mechanics.", "\nIn algebraic QFT, an algebra of observables is associated with bounded\nregions of Minkowski spacetime (and unbounded regions including all of\nspacetime by way of certain limiting operations) that are required to\nsatisfy standard axioms of local structure: isotony, locality,\ncovariance, additivity, positive spectrum, and a unique invariant\nvacuum state. The resulting set of algebras on Minkowski spacetime\nthat satisfy these axioms is referred to as the net of local\nalgebras. It has been shown that special subsets of the net of\nlocal algebras – those corresponding to various types of\nunbounded spacetime regions such as tubes, monotones (a tube that\nextends infinitely in one direction only), and wedges – are\ntype-III factors. Of particular interest for the foundations of\nphysics are the algebras that are associated with bounded spacetime\nregions, such as a double cone (the finite region of intersection of a\nforward and a backward light cone). As a result of work done over the\nlast thirty years, local algebras of relativistic QFT appear to be\ntype III von Neuman algebras see Halvorson (2007, pp. 749–752)\nfor more details.", "\nOne important area for interpretive investigation is the existence of\na continuum of unitarily inequivalent representations of an algebra of\nobservables. Attitudes towards unitarily inequivalent representations\ndiffer drastically in the philosophical literature. In (Wallace 2006)\nunitarily inequivalent representations are not considered a\nfoundational problem for QFT, while in Ruetsche (2011), Lupher (2018)\nand Kronz and Lupher (2005) unitarily inequivalent representations are\nconsidered physically significant." ], "subsection_title": "4.1 Algebraic Quantum Field Theory" }, { "content": [ "\nIn the early 1950s, theoretical physicists were inspired to axiomatize\nQFT. One motivation for axiomatizing a theory, not the one for the\ncase now under discussion, is to express the theory in a completely\nrigorous form in order to standardize the expression of the theory as\na mature conceptual edifice. Another motivation, more akin to the case\nin point, is to embrace a strategic withdrawal to the foundations to\ndetermine how renovation should proceed on a structure that is\nthreatening to collapse due to internal inconsistencies. One then\nlooks for existing piles (fundamental postulates) that penetrate\nthrough the quagmire to solid rock, and attempts to drive home others\nat advantageous locations. Properly supported elements of the\nsuperstructure (such as the characterization of free fields,\ndispersion relations, etc.) may then be distinguished from those that\nare untrustworthy. The latter need not be razed immediately, and may\nultimately glean supportive rigging from components not yet\nconstructed. In short, the theoretician hopes that the axiomatization\nwill effectively separate sense from nonsense, and that this will\nserve to make possible substantial progress towards the development of\na mature theory. Grounding in a rigorous mathematical framework can be\nan important part of the exercise, and that was a key aspect of the\naxiomatization of QFT by Wightman.", "\nIn the mid-1950s, Schwartz’s theory of distributions was used by\nWightman (1956) to develop an abstract formulation of QFT, which later\ncame to be known known as axiomatic quantum field theory.\nMature statements of this formulation are presented in Wightman and\nGårding (1964) and in Streater and Wightman (1964). It was\nfurther refined in the late 1960s by Bogoliubov, who explicitly placed\naxiomatic QFT in the rigged Hilbert space framework (Bogoliubov et\nal. 1975, p. 256). It is by now standard within the axiomatic\napproach to put forth the following six postulates: spectral condition\n(there are no negative energies or imaginary masses), vacuum state (it\nexists and is unique), domain axiom for fields (quantum fields\ncorrespond to operator-valued distributions), transformation law\n(unitary representation in the field-operator (and state) space of the\nrestricted inhomogeneous Lorentz group –\n“restricted” means inversions are excluded, and\n“inhomogeneous” means that translations are included),\nlocal commutativity (field measurements at spacelike separated regions\ndo not disturb one another), asymptotic completeness (the scattering\nmatrix is unitary – this assumption is sometimes weakened to\ncyclicity of the vacuum state with respect to the polynomial algebra\nof free fields). Rigged Hilbert space entered the axiomatic framework\nby way of the domain axiom, so this axiom will be discussed in more\ndetail below.", "\nIn classical physics, a field is is characterized as a scalar- (or\nvector- or tensor-) valued function \\(\\phi(x)\\) on a domain that\ncorresponds to some subset of spacetime points. In QFT, a field is\ncharacterized by means of an operator rather than a function. A\nfield operator may be obtained from a classical field\nfunction by quantizing the function in the canonical manner –\nsee Mandl (1959, pp. 1–17). For convenience, the field operator\nassociated with \\(\\phi(x)\\) is denoted below by the same expression\n(since the discussion below only concerns field operators). Field\noperators that are relevant for QFT are too singular to be regarded as\nrealistic, so they are smoothed out over their respective domains\nusing elements of a space of well-behaved functions known as test\nfunctions. There are many different test-functions spaces\n(Gelfand and Shilov 1977, Chapter 4). At first, the test-function\nspace of choice for axiomatic QFT was the Schwartz space\n\\(\\Sigma\\), the space of functions whose elements have partial\nderivatives of all orders at each point and such that each function\nand its derivatives decreases faster than \\(x^{-n}\\) for any \\(n\\in\nN\\) as \\(x\\rightarrow \\infty\\). It was later determined that some\nrealistic models require the use of other test-function spaces. The\nsmoothed field operators \\(\\phi[f\\)] for \\(f \\in \\Sigma\\) are known as\nquantum field operators, and they are defined as follows", "\nThe integral (over the domain of the field operator) of the product of\nthe test function \\(f(x)\\) and the field operator \\(\\phi(x)\\) serves\nto “smooth out” the field operator over its domain; a more\ncolloquial description is that the field is “smeared out”\nover space or spacetime. It is postulated within the axiomatic\napproach that a quantum field operator \\(\\phi[f\\)] may be represented\nas an unbounded operator on a separable Hilbert space \\(\\Eta\\), and\nthat \\(\\{\\phi[f]: f\\in \\Sigma \\}\\) (the set of smoothed field\noperators associated with \\(\\phi(x))\\) has a dense domain \\(\\Omega\\)\nin \\(\\Eta\\). The smoothed field operators are often referred to as\noperator-valued distributions, and this means that for every\n\\(\\Phi,\\Psi \\in \\Omega\\) there is an element of the space of\ndistributions \\(\\Sigma^x\\), the topological dual of \\(\\Sigma\\), that\nmay be equated to the expression \\(\\langle \\Phi {\\mid} \\phi[\\\n]{\\mid}\\Psi\\rangle\\). If \\(\\Omega'\\) denotes the set of functions\nobtained by applying all polynomials of elements of \\(\\{\\phi[f]: f\\in\n\\Sigma \\}\\) onto the unique vacuum state, then the axioms mentioned\nabove entail that \\(\\Omega'\\) is dense in \\(\\Eta\\) (asymptotic\ncompleteness) and that \\(\\Omega'\\subset \\Omega\\) (domain axiom). The\nelements of \\(\\Omega\\) correspond to possible states of the elements\nof \\(\\{\\phi[f]: f\\in \\Sigma \\}\\). Though only one field has been\nconsidered thus far, the formalism is easily generalizable to a\ncountable number of fields with an associated set of countably indexed\nfield operators \\(\\phi_k (x)\\) – cf. (Streater and Wightman\n1964).", "\nAs noted earlier, the appropriateness of the rigged Hilbert space\nframework enters by way of the domain axiom. Concerning that axiom,\nWightman says the following (in the notation introduced above, which\ndiffers slightly from that used by Wightman).", "\nAt a more advanced stage in the theory it is likely that one would\nwant to introduce a topology into \\(\\Omega\\) such that \\(\\phi[f\\)]\nbecomes a continuous mapping of \\(\\Omega\\) into \\(\\Omega\\). It is\nlikely that this topology has to be rather strong. We want to\nemphasize that so far we have only required that \\(\\langle\n\\Phi{\\mid}\\phi[f]{\\mid}\\Psi\\rangle\\) be continuous in \\(f\\)\nfor \\(\\Phi ,\\Psi\\) fixed; continuity in the\npair \\(\\Phi ,\\Psi\\) cannot be expected before we put a suitable strong\ntopology on \\(\\Omega\\) (Wightman and Gårding 1964, p. 137).\n", "\nIn Bogoliubov et al. (1975, p. 256), a topology is introduced\nto serve this role, though it is introduced on \\(\\Omega'\\) rather than\non \\(\\Omega\\). Shortly thereafter, they assert that it is not hard to\nshow that \\(\\Omega'\\) is a complete nuclear space with respect to this\ntopology. This serves to justify a claim they make earlier in their\ntreatise:", "\n… it is precisely the consideration of the triplet of spaces\n\\(\\Omega \\subset \\Eta \\subset \\Omega^*\\) which give a natural basis\nfor both the construction of a general theory of linear operators and\nthe correct statement of certain problems of quantum field theory\n(Bogoliubov et al. 1975, p. 34).\n", "\nNote that they refer to the triplet \\(\\Omega \\subset \\Eta \\subset\n\\Omega^*\\) as a rigged Hilbert space. In the terminology introduced\nabove, they refer in effect to the Gelfand triplet \\((\\Omega , \\Eta ,\n\\Omega^x )\\) or (equivalently) the associated rigged Hilbert space\n\\((\\Omega , \\Omega^x)\\) .", "\nFinally, it is worth mentioning that the status of the field in\nalgebraic QFT differs from that in Wightman’s axiomatic QFT. In\nboth approaches, a field is an abstract system having an infinite\nnumber of degrees of freedom. Sub-atomic quantum particles are field\neffects that appear in special circumstances. In algebraic QFT, there\nis a further abstraction: the most fundamental entities are the\nelements of the algebra of local (and quasi-local) observables, and\nthe field is a derived notion. The term local means bounded\nwithin a finite spacetime region, and an observable is not regarded as\na property belonging to an entity other than the spacetime region\nitself. The term quasi-local is used to indicate that we take\nthe union of all bounded spacetime regions. In short, the algebraic\napproach focuses on local (or quasi-local) observables and treats the\nnotion of a field as a derivative notion; whereas the axiomatic\napproach (as characterized just above) regards the field concept as\nthe fundamental notion. Indeed, it is common practice for proponents\nof the algebraic approach to distance themselves from the field notion\nby referring to their theory as “local quantum physics”.\nThe two approaches are mutually complementary – they have\ndeveloped in parallel and have influenced each other by analogy\n(Wightman 1976). For a discussion of the close connections between\nthese two approaches, see Haag (1996, p. 106)." ], "subsection_title": "4.2 Wightman’s Axiomatic Quantum Field Theory" } ] }, { "main_content": [], "section_title": "5 Philosophical Issues", "subsections": [ { "content": [ "\nMost physicists use Lagrangian QFT (LQFT) to make predictions that\nhave been experimentally verified with extraordinary precision in some\ncases. However, LQFT has been described as a “grab bag of\nconflicting mathematical ideas” that has not provided a sharp\nmathematical description of what counts as a QFT model (Swanson 2017,\npp. 1–2). Those criticisms motivated mathematically inclined\nphysicists to search for a mathematically rigorous formulation of QFT.\nAxiomatic versions of QFT have been favored by mathematical physicists\nand most philosophers. With greater mathematical rigor it is possible\nto prove results about the theoretical structure of QFT independent of\nany particular Lagrangian. Axiomatic QFT provides clear conceptual\nframeworks within which precise questions and answers to\ninterpretational issues can be formulated. There are three main\naxiomatic frameworks for QFT: Wightman QFT, Osterwalder-Schrader QFT,\nand algebraic QFT. In Wightman QFT, the axioms use functional analysis\nand operator algebras and is closer to LQFT since its axioms describe\ncovariant field operators acting on a fixed Hilbert space. The\nOsterwalder-Schrader axioms use a functional integration approach to\nQFT. The algebraic QFT axioms use \\(C^*\\)-algebras to model local\nobservables. However, axiomatic QFT approaches are sorely lacking with\nregards to building empirically adequate models. Unlike quantum\nmechanics which has a canonical mathematical framework in terms of von\nNeumann’s Hilbert space formulation, QFT has no canonical\nmathematical framework. Even though there is a canonical mathematical\nframework for quantum mechanics, there are many interpretations of\nthat framework, e.g., many-worlds, GRW, Copenhagen, Bohmian, etc...\nQFT has two levels that require interpretation: (1) which QFT\nframework should be the focus of these foundational efforts, if any,\nand (2) how that preferred framework should be interpreted. Since (1)\ninvolves issues about mathematical rigor and pragmatic virtues, it\ndirectly bears on the focus of this article. The lack of a canonical\nformulation of QFT threatens to impede any metaphysical or\nepistemological lessons that might be learned from QFT.", "\nOne view is that these two approaches to QFT, the mathematically\nrigorous axiomatic approach and the pragmatic / empirically adequate\nLQFT approach, are rival research programs (see David Wallace (2006,\n2011) and Doreen Fraser (2009, 2011)), though Swanson (2017) argues\nthat they are not rival programs. Fraser (2009, 2011) argues that the\ninterpretation of QFT should be based on the mathematically rigorous\napproach of axiomatic formulations of QFT. By contrast, Wallace (2006,\n2011) argues that an interpretation of QFT should be based on LQFT.\n(Wallace, in 2006, calls his preferred QFT framework conventional QFT\n(CQFT), but changes his terminology to LQFT in Wallace 2011). Swanson\n(2017) and Egg, Lam, and Oldofedi (2017) are good overviews of the\ndebate between Fraser and Wallace (for an extended analysis see James\nFraser 2016). The debate covers many different philosophical topics in\nQFT, which makes it more challenging to pin down exactly what is\nessential to the arguments for both sides (for one view of what is\nessential for the debate, see Egg, Lam, and Oldofedi 2017). One issue\nis the role of internal consistency established by mathematical rigor\nversus empirical adequacy. Wallace argues that LQFT is empirically\nadequate since it can describe the forces of the Standard Model. LQFT\nhas a collection of calculational techniques including perturbation\ntheory, path integrals, and renormalization group methods. One\ncriticism of LQFT is that the calculational techniques it uses are not\nmathematically rigorous. Wallace argues that renormalization group\nmethods puts perturbative QFT, an approach within LQFT, on\nmathematically rigorous ground and removes the main motivation for\naxiomatic QFT.", "\nWhat follows is a rough overview of perturbative QFT (see James Fraser\n2016 for more details). Since exactly solvable free QFT models are\nmore mathematically tractable than interacting QFT models,\nperturbative QFT treats interactions as perturbations to the free\nLagrangian assuming weak coupling. For strongly coupled theories like\nquantum chromodynamics that idealization fails. Using perturbation\ntheory, approximate solutions for interacting QFT models can be\ncalculated by expanding S-matrix elements in a power series in terms\nof a coupling parameter. However, the higher order terms will often\ncontain divergent integrals. Typically, renormalization of the higher\norder terms is required to get finite predictions. Two sources of\ndivergent integrals are infrared (long distance, low energy) and\nultraviolet (short distance, high energy) divergences. Infrared\ndivergences are often handled by imposing a long distance cutoff or\nputting a small non-zero lower limit for the integral over momentum. A\nsharp cutoff at low momentum is equivalent to putting the theory in a\nfinite volume box. Imposing asymptotic boundary conditions and\nrestricting the observables to long distance “friendly”\nobservables also help with infrared divergences. Ultraviolet\ndivergences are often handled by imposing a momentum cutoff to remove\nhigh momentum modes of a theory. That is equivalent to freezing out\nvariations in the fields at arbitrarily short length scales. Putting\nthe system on a lattice with some finite spacing can also help deal\nwith the high momentum. Dimensional regularization, where the integral\nmeasure is redefined to range over a fractional number of dimensions,\ncan help with both infrared and ultraviolet divergences. The last step\nin renormalization is to remove the cutoffs by taking the continuum\nlimit (i.e., removing the high momentum cutoff) and the infinite\nvolume limit (i.e., removing the low momentum cutoff). The hope is\nthat the limit is well-defined and there are finite expressions of the\nseries at each order.", "\nJames Fraser (2016) identifies three problems for perturbative QFT.\n(1) The rigor problem: perturbative QFT is not mathematically\nrigorous which makes it difficult to analyze and interpret. (2)\nThe consistency problem: perturbative calculations rest on\nthe interaction picture existing, but Haag’s theorem seems to\nshow that the interaction picture does not exist. (3) The\njustification problem: renormalization lacks physical motivation\nand appears ad hoc. James Fraser argues that (1) and (2) do not pose\nsevere problems for perturbative QFT because it is not attempting to\nbuild continuum QFT models. It is building approximate physical\nquantities – not mathematical structures that are to be\ninterpreted as physical systems.", "\nBaker (2016) and Swanson (2017) note that LQFT makes false or unproven\nassumptions such as the convergence of certain infinite sums in\nperturbation theory. Dyson (1952) gives a heuristic argument that\nquantum electrodynamic perturbation series do not converge. Baker and\nSwanson also argue that the use of long distance cutoffs is at odds\nwith cosmological theory and astronomical observations which suggest\nthat the universe is spatially infinite. Even in the weak coupling\nlimit where perturbation theory can be formally applied, it is not\nclear when the perturbative QFT gives an accurate approximation of the\nunderlying physics. In the interacting \\(\\phi^4\\) theory, when the\ndimension is less than 4 for Minkowski spacetime, the theory is\nnontrivial, but when the dimension is greater than 4, the renormalized\nperturbation series is asymptotic to a free field theory even though\nit appears to describe nontrivial interactions. When there are 4\ndimensions, the theory is also trivial if additional technical\nassumptions hold (see Swanson 2017 (p. 3) for more details).", "\nAnother area where questions of mathematical rigor arise within\nperturbative QFT is the use of path integrals. The S-matrix power\nseries expansion contains integrals over momentum space and this is\nwhere path integrals / Feynman diagrams have been helpful for making\ncalculations. The key concept is the partition function \\(Z\\),\nwhich is defined as a functional integral involving\nthe action, which is itself an integral of the Lagrangian. The\nfollowing details come mainly from Hancox-Li (2017). More\nspecifically, the action is a functional of quantum fields. The\nfunctional integral over the action ranges over all possible\ncombinations of the quantum fields values over spacetime. Informally,\nthe sum is being taken over all possible field configurations. As\nSwanson (2017) notes, the path integral requires choosing a measure\nover an infinite dimensional path space, which is only mathematically\nwell-defined in special cases. For example, if the system is\nformulated on a hypercubic lattice, then the measure can be defined\n(see section 1.2 of James Fraser 2016). Another way of having a\nwell-defined measure is to restrict attention to a finite dimensional\nsubspace. But if functions are allowed to vary arbitrarily on short\nlength scales, then the integral ceases to be well-defined (Wallace\n2006, p. 42). All of the correlation functions (i.e., vacuum state\nexpectation values of the fields at different spacetime points), can\nbe derived from the partition function \\(Z\\). So, given\n\\(Z\\), all empirical quantities associated with the\nLagrangian can be calculated, e.g., scattering cross-sections. Finding\n\\(Z\\) amounts to a solution of LQFT. \\(Z\\)\ncan be expanded in a Taylor series in the coupling\nconstant. When this is done, two types of divergences can occur: (1)\nindividual terms of the perturbation series can diverge and/or (2) the\nperturbation series itself is divergent, though the series may be an\nasymptotic series. To deal with (1), physicists do the following\nprocedures (Hancox-Li 2017, pp. 344–345): (i) regularization, which\ninvolves reducing the number of degrees of freedom via dimensional\nregularization, momentum cutoffs, or using a lattice formulation and\n(ii) add counterterms to compensate for the regularization in (i). But\nthis construction is purely formal and not mathematically defined. The\nrules used to manipulate the Lagrangian, and hence the partition\nfunction, are not well-defined.", "\nWallace (2011) argues that renormalization group techniques have\novercome the mathematical deficiencies of older renormalization\ncalculational techniques (for more details on the renormalization\ngroup see Butterfield and Bouatta 2015, Fraser 2016, Hancox-Li (2015a,\n2015b, 2017)). According to Wallace, the renormalization group methods\nput LQFT on the same level of mathematical rigor as other areas of\ntheoretical physics. It provides a solid theoretical framework that is\nexplanatorily rich in particle physics and condensed matter physics,\nso the impetus for axiomatic QFT has been resolved. Renormalization\ngroup techniques presuppose that QFT will fail at some short length\nscale, but the empirical content of LQFT is largely insensitive to the\ndetails at such short length scales. Doreen Fraser (2011) argues that\nrenormalization group methods help articulate the empirical content of\nQFT, but the renormalization group has no significance for the\ntheoretical content of QFT insofar as it does not tell us whether we\nshould focus on LQFT or AQFT. James Fraser (2016) and Hancox-Li\n(2015b) argue that the renormalization group does more than provide\nempirical predictions in QFT. The renormalization group gives us\nmethods for studying the behavior of physical systems at different\nenergy scales, namely how properties of QFT models depend or do not\ndepend on small scale structure. The renormalization group provides a\nnon-perturbative explanation of the success of perturbative QFT.\nHancox-Li (2015b) discusses how mathematicians working in constructive\nQFT use non-perturbative approximations with well controlled error\nbounds to prove the existence or non-existence of ultraviolet fixed\npoints. Hancox-Li argues that the renormalization group explains\nperturbative renormalization non-perturbatively. The renormalization\ngroup can tell us whether certain Lagrangians have an ultraviolet\nlimit that satisfies the axioms a QFT should satisfy. Thus, the use of\nthe renormalization group in constructive QFT can provide additional\ndynamical information (e.g., whether a certain dynamics can occur in\ncontinuous spacetime) that a pure axiomatic approach does not." ], "subsection_title": "5.1 Pragmatics versus Axiomatics " } ] } ]

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[ { "href": "../qm/", "text": "quantum mechanics" }, { "href": "../qm-bohm/", "text": "quantum mechanics: Bohmian mechanics" }, { "href": "../qm-decoherence/", "text": "quantum mechanics: the role of decoherence in" }, { "href": "../quantum-field-theory/", "text": "quantum theory: quantum field theory" }, { "href": "../qt-quantlog/", "text": "quantum theory: quantum logic and probability theory" } ]

[ "\nThis article is an overview of the philosophical issues raised by\nquantum theory, intended as a pointer to the more in-depth treatments\nof other entries in the Stanford Encyclopedia of Philosophy." ]

[ { "content_title": "1. Introduction", "sub_toc": [] }, { "content_title": "2. Quantum theory", "sub_toc": [ "2.1 Quantum states and classical states", "2.2 Quantum mechanics and quantum field theory", "2.3 Quantum state evolution" ] }, { "content_title": "3. Entanglement, nonlocality, and nonseparability", "sub_toc": [] }, { "content_title": "4. The measurement problem", "sub_toc": [ "4.1 The measurement problem formulated", "4.2 Approaches to the measurement problem", "4.3 Extended Wigner’s friend scenarios as a source of no-go theorems", "4.4 The role of decoherence", "4.5 Comparison of approaches to the measurement problem" ] }, { "content_title": "5. Ontological Issues", "sub_toc": [ "5.1 The question of quantum state realism.", "5.2 Ontological category of quantum states" ] }, { "content_title": "6. Quantum computing and quantum information theory", "sub_toc": [] }, { "content_title": "7. Reconstructions of quantum mechanics and beyond", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nDespite its status as a core part of contemporary physics, there is no\nconsensus among physicists or philosophers of physics on the question\nof what, if anything, the empirical success of quantum theory is\ntelling us about the physical world. This gives rise to the collection\nof philosophical issues known as “the interpretation of quantum\nmechanics”. One should not be misled by this terminology into\nthinking that what we have is an uninterpreted mathematical formalism\nwith no connection to the physical world. Rather, there is a common\noperational core that consists of recipes for calculating\nprobabilities of outcomes of experiments performed on systems\nsubjected to certain state preparation procedures. What are often\nreferred to as different “interpretations” of quantum\nmechanics differ on what, if anything, is added to the common core.\nTwo of the major approaches, hidden-variables theories and collapse\ntheories, involve formulation of physical theories distinct from\nstandard quantum mechanics; this renders the terminology of\n“interpretation” even more inappropriate.", "\nMuch of the philosophical literature connected with quantum theory\ncenters on the problem of whether we should construe the theory, or a\nsuitable extension or revision of it, in realist terms, and, if so,\nhow this should be done. Various approaches to what is called the\n“Measurement Problem” propose differing answers to these\nquestions. There are, however, other questions of philosophical\ninterest. These include the bearing of quantum nonlocality on our\nunderstanding of spacetime structure and causality, the question of\nthe ontological character of quantum states, the implications of\nquantum mechanics for information theory, and the task of situating\nquantum theory with respect to other theories, both actual and\nhypothetical. In what follows, we will touch on each of these topics,\nwith the main goal being to provide an entry into the relevant\nliterature, including the Stanford Encyclopedia entries on these\ntopics. Contemporary perspectives on many of the issues touched on in\nthis entry can be found in The Routledge Companion to Philosophy\nof Physics (Knox and Wilson, eds., 2021); The Oxford Handbook\nof the History of Quantum Interpretations (Freire, et al. eds.,\n2022) contains essays on the history of discussions of these\nissues." ], "section_title": "1. Introduction", "subsections": [] }, { "main_content": [ "\nIn this section we present a brief introduction to quantum theory; see\nthe entry on\n quantum mechanics\n for a more detailed introduction." ], "section_title": "2. Quantum Theory", "subsections": [ { "content": [ "\nIn classical physics, with any physical system is associated a state\nspace, which represents the totality of possible ways of assigning\nvalues to the dynamical variables that characterize the state of the\nsystem. For systems of a great many degrees of freedom, a complete\nspecification of the state of the system may be unavailable or\nunwieldy; classical statistical mechanics deals with such a situation\nby invoking a probability distribution over the state space of the\nsystem. A probability distribution that assigns any probability other\nthan one or zero to some physical quantities is regarded as an\nincomplete specification of the state of the system. In quantum\nmechanics, things are different. There are no quantum states that\nassign definite values to all physical quantities, and probabilities\nare built into the standard formulation of the theory.", "\nIn formulating a quantum theory of some system, one usually begins\nwith the Hamiltonian or Lagrangian formulation of the classical\nmechanical theory of that system. In the Hamiltonian formulation of\nclassical mechanics, the configuration of a system is represented by a\nset of coordinates. These could be, for example, the positions of each\nof a set of point particles, but one can also consider more general\ncases, such as angular coordinates that specify the orientation of a\nrigid body. For every coordinate there is an associated conjugate\nmomentum. If the coordinate indicates the position of some\nobject, the momentum conjugate to that coordinate may be what we\nusually call “momentum,” that is, the velocity of the body\nmultiplied by its mass. If the coordinate is an angle, the momentum\nconjugate to it is an angular momentum.", "\nConstruction of a quantum theory of a physical system proceeds by\nfirst associating the dynamical degrees of freedom with\noperators. These are mathematical objects on which operations\nof multiplication and addition are defined, as well as multiplication\nby real and complex numbers. Another way of saying this is that the\nset of operators forms an algebra. Typically, it is said that\nan operator represents an observable, and the result of an\nexperiment on a system is said to yield a value for some observable.\nTwo or more observables are said to be compatible if there is\nsome possible experiment that simultaneously yields values for all of\nthem. Others require mutually exclusive experiments; these are said to\nbe incompatible.", "\nOf course, in a classical theory, the dynamical quantities that define\na state also form an algebra also, as they can be multiplied and\nadded, and multiplied by real or complex numbers. Quantum mechanics\ndiffers from classical mechanics in that the order of multiplication\nof operators can make a difference. That is, for some operators\n\\(A\\),\\(B\\), the product \\(AB\\) is not equal to the product \\(BA.\\) If\n\\(AB = BA,\\) the operators are said to commute.", "\nThe recipe for constructing a quantum theory of a given physical\nsystems prescribes algebraic relations between the operators\nrepresenting the dynamical variables of the system. Compatible\nobservables are associated with operators that commute with each\nother. Operators representing conjugate variables are required to\nsatisfy what are called the canonical commutation relations.\nIf \\(q\\) is some coordinate, and \\(p\\) its conjugate\nmomentum, the operators \\(Q\\) and \\(P\\) representing them\nare required to not commute. Instead, the difference between\n\\(PQ\\) and \\(QP\\) is required to be a multiple of the\nidentity operator (that is, the operator \\(I\\) that satisfies,\nfor all operators \\(A\\), \\(IA = AI).\\)", "\nA quantum state is a specification, for every experiment that\ncan be performed on the system, of probabilities for the\npossible outcomes of that experiment. These can be summed up as an\nassignment of an expectation value to each observable. These states\nare required to be linear. This means that, if an operator\n\\(C\\), corresponding to some observable, is the sum of operators\n\\(A\\) and \\(B\\), corresponding to other observables, then\nthe expectation value that a quantum state assigns to \\(C\\) must\nbe the sum of the expectation values assigned to \\(A\\) and\n\\(B\\). This is a nontrivial constraint, as it is required to hold\nwhether or not the observables represented are compatible. A quantum\nstate, therefore, relates expectation values for quantities yielded by\nincompatible experiments.", "\nIncompatible observables, represented by noncommuting operators, give\nrise to uncertainty relations; see the entry on\n the uncertainty principle.\n These relations entail that there are no quantum states that assign\ndefinite values to the observables that satisfy them, and place bounds\non how close they can come to be simultaneously well-defined in any\nquantum state.", "\nFor any two distinct quantum states, \\(\\rho\\), \\(\\omega\\), and any\nreal number between 0 and 1, there is a corresponding mixed\nstate. The probability assigned to any experimental outcome by\nthis mixed state is \\(p\\) times the probability it is assigned by\n\\(\\rho\\) plus \\(1-p\\) times the probability assigned to it by\n\\(\\omega\\). One way to physically realize the preparation of a mixed\nstate is to employ a randomizing device, for example, a coin with\nprobability \\(p\\) of landing heads and probability \\(1-p\\) of\nlanding tails, and to use it to choose between preparing state\n\\(\\rho\\) and preparing state \\(\\omega\\). We will see another way to\nprepare a mixed state after we have discussed entanglement, in section\n3. A state that is not a mixture of any two distinct states is called\na pure state.", "\nIt is both useful and customary, though not strictly necessary, to\nemploy a Hilbert space representation of a quantum theory. In\nsuch a representation, the operators corresponding to observables are\nrepresented as acting on elements of an appropriately constructed\nHilbert space (see the entry on\n quantum mechanics\n for details). Usually, the Hilbert space representation is\nconstructed in such a way that vectors in the space represent pure\nstates; such a representation is called an irreducible\nrepresentation. Irreducible representations, in which mixed\nstates are also represented by vectors, are also possible.", "\nA Hilbert space is a vector space. This means that, for any two\nvectors \\(|\\psi\\rangle\\), \\(|\\phi\\rangle\\) , in the space,\nrepresenting pure states, and any complex numbers \\(a\\),\n\\(b\\), there is another vector, \\(a |\\psi\\rangle + b\n|\\phi\\rangle\\), that also represents a pure state. This is called a\nsuperposition of the states represented by \\(|\\psi\\rangle\\)\nand \\(|\\phi\\rangle\\) . Any vector in a Hilbert space can be written as\na superposition of other vectors in infinitely many ways. Sometimes,\nin discussing the foundations of quantum mechanics, authors fall into\ntalking as if some state are superpositions and others are not. This\nis simply an error. Usually what is meant is that some states yield\ndefinite values for macroscopic observables, and others cannot be\nwritten in any way that is not a superposition of macroscopically\ndistinct states.", "\nThe noncontroversial operational core of quantum theory consists of\nrules for identifying, for any given system, appropriate operators\nrepresenting its dynamical quantities. In addition, there are\nprescriptions for evolving the state of system when it is acted upon\nby specified external fields or subjected to various manipulations\n(see\n section 1.3).\n Application of quantum theory typically involves a distinction\nbetween the system under study, which is treated quantum mechanically,\nand experimental apparatus, which is not. This division is sometimes\nknown as the Heisenberg cut.", "\nWhether or not we can expect to be able to go beyond the\nnoncontroversial operational core of quantum theory, and take it to be\nmore than a means for calculating probabilities of outcomes of\nexperiments, remains a topic of contemporary philosophical\ndiscussion." ], "subsection_title": "2.1 Quantum states and classical states" }, { "content": [ "\nQuantum mechanics is usually taken to refer to the quantized\nversion of a theory of classical mechanics, involving systems with a\nfixed, finite number of degrees of freedom. Classically, a field, such\nas, for example, an electromagnetic field, is a system endowed with\ninfinitely many degrees of freedom. Quantization of a field theory\ngives rise to a quantum field theory. The chief philosophical\nissues raised by quantum mechanics remain when the transition is made\nto a quantum field theory; in addition, new interpretational issues\narise. There are interesting differences, both technical and\ninterpretational, between quantum mechanical theories and quantum\nfield theories; for an overview, see the entries on\n quantum field theory\n and\n quantum theory: von Neumann vs. Dirac.", "\nThe standard model of quantum field theory, successful as it is, does\nnot yet incorporate gravitation. The attempt to develop a theory that\ndoes justice both the quantum phenomena and to gravitational phenomena\ngives rise to serious conceptual issues (see the entry on\n quantum gravity)." ], "subsection_title": "2.2 Quantum mechanics and quantum field theory" }, { "content": [ "\nWhen constructing a Hilbert space representation of a quantum theory\nof a system that evolves over time, there are some choices to be made.\nOne needs to have, for each time t, a Hilbert space\nrepresentation of the system, which involves assigning operators to\nobservables pertaining to time t. An element of convention\ncomes in when deciding how the operators representing observables at\ndifferent times are to be related.", "\nFor concreteness, suppose that have a system whose observables include\na position, \\(x\\), and momentum, \\(p\\), with respect to some\nframe of reference. There is a sense in which, for two distinct times,\n\\(t\\) and \\(t'\\), position at time \\(t\\) and\nposition at time \\(t'\\) are distinct observables, and also\na sense in which they are values, at different times, of the same\nobservable. Once we have settled on operators \\(\\hat{X}\\) and\n\\(\\hat{P}\\) to represent position and momentum at time \\(t\\), we\nstill have a choice of which operators represent the corresponding\nquantities at time \\(t.\\) On the Schrödinger\npicture, the same operators \\(\\hat{X}\\) and \\(\\hat{P}\\) are used\nto represent position and momentum, whatever time is considered. As\nthe probabilities for results of experiments involving these\nquantities may be changing with time, different vectors must be used\nto represent the state at different times.", "\nThe equation of motion obeyed by a quantum state vector is the\nSchrödinger equation. It is constructed by first forming\nthe operator \\(\\hat{H}\\)corresponding to the Hamiltonian of the\nsystem, which represents the total energy of the system. The rate of\nchange of a state vector is proportional to the result of operating on\nthe vector with the Hamiltonian operator \\(\\hat{H}\\).", "\nThere is an operator that takes a state at time 0 into a state at time\n\\(t\\); it is given by", "\nThis operator is a linear operator that implements a one-one mapping\nof the Hilbert space to itself that preserves the inner product of any\ntwo vectors; operators with these properties are called unitary\noperators, and, for this reason, evolution according to the\nSchrödinger equation is called unitary evolution.", "\nFor our purposes, the most important features of this equation is that\nit is deterministic and linear. The state vector at\nany time, together with the equation, uniquely determines the state\nvector at any other time. Linearity means that, if two vectors\n\\(\\ket{\\psi_1(0)}\\) and \\(\\ket{\\psi_2(0)}\\) evolve into vectors\n\\(\\ket{\\psi_1(t) }\\) and \\(\\ket{\\psi_2(t)}\\), respectively, then, if\nthe state at time 0 is a linear combination of these two, the state at\nany time \\(t\\) will be the corresponding linear\ncombination of \\(\\ket{\\psi_1(t)}\\) and \\(\\ket{\\psi_2(t)}\\).", "\\[ a\\ket{\\psi_{1}(0)} + b\\ket{\\psi_{2}(0)} \\rightarrow a\\ket{\\psi_{1}(t)} + b\\ket{\\psi_{2}(t)} . \\]", "\nThe Heisenberg picture, on the other hand, employs different operators\n\\(\\hat{X}(t)\\), \\(\\hat{X}(t')\\) for position, depending on the time\nconsidered (and similarly for momentum and other observables). If\n\\(\\hat{A}(t)\\)is a family of Heisenberg picture operators representing\nsome observable at different times, the members of the family \nsatisfy the Heisenberg equation of motion,", "\nOne sometimes hears it said that, on the Heisenberg picture, the state\nof the system is unchanging. This is incorrect. It is true that there\nare not different state vectors corresponding to different times, but\nthat is because a single state vector serves for computing\nprobabilities for all observables pertaining to all times. These\nprobabilities do change with time.", "\nAs mentioned, standard applications of quantum theory involve a\ndivision of the world into a system that is treated within quantum\ntheory, and the remainder, typically including the experimental\napparatus, that is not treated within the theory. Associated with this\ndivision is a postulate about how to assign a state vector after an\nexperiment that yields a value for an observable, according to which,\nafter an experiment, one replaces the quantum state with an eigenstate\ncorresponding to the value obtained. Unlike the unitary\nevolution applied otherwise, this is a discontinuous change of the\nquantum state, sometimes referred to as collapse of the state\nvector, or state vector reduction. There are two\ninterpretations of the postulate about collapse, corresponding to two\ndifferent conceptions of quantum states. If a quantum state represents\nnothing more than knowledge about the system, then the collapse of the\nstate to one corresponding to an observed result can be thought of as\nmere updating of knowledge. If, however, quantum states represent\nphysical reality, in such a way that distinct pure states always\nrepresent distinct physical states of affairs, then the collapse\npostulate entails an abrupt, perhaps discontinuous, change of the\nphysical state of the system. Considerable confusion can arise if the\ntwo interpretations are conflated.", "\nThe collapse postulate occurs already in the general discussion at the\nfifth Solvay Conference in 1927 (see Bacciagaluppi and Valentini, 2009,\n437–450). It is also found in Heisenberg’s The\nPhysical Principles of the Quantum Theory, based on lectures\npresented in 1929 (Heisenberg, 1930a, 27; 1930b, 36). Von Neumann, in\nhis reformulation of quantum theory a few years later, distinguished\nbetween two types of processes: Process 1:, which occurs upon\nperformance of an experiment, and Process 2:, the unitary evolution\nthat takes place as long as no measurement is made (von Neumann, 1932;\n1955, §V.I). He does not take this distinction to be a difference\nbetween two physically distinct processes. Rather, the invocation of\none process or the other depends on a somewhat arbitrary division of\nthe world into an observing part and an observed part (see von\nNeumann,1932, 224; 1955, 420).", "\nThe collapse postulate does not appear in the first edition (1930) of\nDirac’s Principles of Quantum Mechanics; it is\nintroduced in the second edition (1935). Dirac formulates it as\nfollows.", "\n\n\nWhen we measure a real dynamical variable \\(\\xi\\), the disturbance\ninvolved in the act of measurement causes a jump in the state of the\ndynamical system. From physical continuity, if we make a second\nmeasurement of the same dynamical variable \\(\\xi\\) immediately after\nthe first, the result of the second measurement must be the same as\nthat of the first. Thus after the first measurement has been made,\nthere is no indeterminacy in the result of the second. Hence, after\nthe first measurement has been made, the system is in an eigenstate of\nthe dynamical variable \\(\\xi\\), the eigenvalue it belongs to being\nequal to the result of the first measurement. This conclusion must\nstill hold if the second measurement is not actually made. In this way\nwe see that a measurement always causes the system to jump into an\neigenstate of the dynamical variable that is being measured, the\neigenvalue this eigenstate belongs to being equal to the result of the\nmeasurement (Dirac 1935: 36).\n", "\nUnlike von Neumann and Heisenberg, Dirac is treating the\n“jump” as a physical process.", "\nNeither von Neumann nor Dirac take awareness of the result by a\nconscious observer to be a necessary condition for collapse. For von\nNeumann, the location of the cut between the “observed”\nsystem and the “observer”is somewhat arbitrary. It may be\nplaced between the system under study and the experimental apparatus.\nOn the other hand, we could include the experimental apparatus in the\nquantum description, and place the cut at the moment when light\nindicating the result hits the observer’s retina. We could also\ngo even further, and include the retina and relevant parts of the\nobserver’s nervous system in the quantum system. That the cut\nmay be pushed arbitrarily far into the perceptual apparatus of the\nobserver is required, according to von Neumann, by the principle\nof psycho-physical parallelism.", "\nA formulation of a version of the collapse postulate according to\nwhich a measurement is not completed until the result is observed is\nfound in London and Bauer (1939). For them, as for Heisenberg, this is\na matter of an increase of knowledge on the part of the observer.", "\nWigner (1961) combined elements of the two interpretations. Like those\nwho take the collapse to be a matter of updating of belief in light of\ninformation newly acquired by an observer, he takes collapse to take\nplace when a conscious observer becomes aware of an experimental\nresult. However, like Dirac, he takes it to be a real physical\nprocess. His conclusion is that consciousness has an influence on the\nphysical world not captured by the laws of quantum mechanics. This\ninvolves a rejection of von Neumann’s principle of\npsycho-physical parallelism, according to which it must be possible to\ntreat the process of subjective perception as if it were a physical\nprocess like any other.", "\nThere is a persistent misconception that, for von Neumann, collapse is\nto be invoked only when a conscious observer becomes aware of the\nresult. As noted, this is the opposite of his view, as the cut may be\nplaced between the observed system and the experimental apparatus, and\nit is for him an important point that the location of the cut be\nsomewhat arbitrary. In spite of this, von Neumann’s position is\nsometimes conflated with Wigner’s speculative proposal, and\nWigner’s proposal is sometimes erroneously referred to as the\nvon Neumann-Wigner interpretation.", "\nNone of the standard formulations are precise about when the collapse\npostulate is to be applied; there is some lee-way as to what is to\ncount as an experiment, or (for versions that require reference to an\nobserver) what is to count as an observer. Some, including von Neumann\nand Heisenberg, have taken it to be a matter of principle that there\nbe some arbitrariness in where to apply the postulate. It is common\nwisdom that, in practice, this arbitrariness is innocuous. The rule of\nthumb that seems to be applied, in practice, in setting the split\nbetween the parts of the world treated quantum-mechanically and things\ntreated as classical objects has been formulated by J. S. Bell as,\n“[w]hen in doubt enlarge the quantum system,” to the point\nat which including more in the quantum system makes negligible\ndifference to practical predictions (Bell 1986, 362; Bell 2004, 189).\nIf anything is to be counted as “standard” quantum\nmechanics, it is the operational core we have discussed, supplemented\nby a heuristic rule of application of this sort. Standard quantum\nmechanics works very well. If, however, one seeks a theory that is\ncapable of describing all systems, including macroscopic ones, and can\nyield an account of the process by which macroscopic events, including\nexperimental outcomes, come about, this gives rise to the so-called\n“measurement problem”, which we will discuss after we have\nintroduced the notion of entanglement (see \n section 3).", "\nAmong the Hilbert-space representations of a quantum theory are\nwave-function representations.", "\nAssociated with any observable is its spectrum, the range of\npossible values that the observable can take on. Given any\nphysical system and any observable for that system, one can always\nform a Hilbert-space representation for the quantum theory of that\nsystem by considering complex-valued functions on the spectrum of that\nobservable. The set of such functions form a vector space. Given\na measure on the spectrum of the observable, we can form a Hilbert space\nout of the set of complex-valued square-integrable functions on the\nspectrum by treating functions that differ only on a set of zero\nmeasure as equivalent (that is, the elements of our Hilbert space are\nreally equivalence classes of functions), and by using the measure to\ndefine an inner product (see\n entry on Quantum Mechanics\n if this terminology is unfamiliar).", "\nIf the spectrum of the chosen observable is a continuum (as it is, for\nexample, for position or momentum), a Hilbert-space representation of\nthis sort is called a wave function representation, and the\nfunctions that represent quantum states, wave functions (also\n“wave-functions,” or “wavefunctions”). The\nmost familiar representations of this form are position-space wave\nfunctions, which are functions on the set of possible configurations\nof the system, and momentum-space wave functions, which are functions\nof the momenta of the systems involved." ], "subsection_title": "2.3 Quantum state evolution" } ] }, { "main_content": [ "\nGiven two disjoint physical systems, \\(A\\) and \\(B\\),\nwith which we associate Hilbert spaces \\(H_{A}\\) and\n\\(H_{B}\\), the Hilbert space associated with the composite system is\nthe tensor product space, denoted \\(H_{A} \\otimes H_{B}\\).", "\nWhen the two systems are independently prepared in pure states\n\\(\\ket{\\psi}\\) and \\(\\ket{\\phi}\\), the state of the composite system\nis the product state \\(\\ket{\\psi} \\otimes \\ket{\\phi}\\)\n(sometimes written with the cross, \\(\\otimes\\), omitted).", "\nIn addition to the product states, the tensor product space contains\nlinear combinations of product states, that is, state vectors of the\nform", "\nThe tensor product space can be defined as the smallest Hilbert space\ncontaining all of the product states. Any pure state represented by a\nstate vector that is not a product vector is an entangled\nstate.", "\nThe state of the composite system assigns probabilities to outcomes of\nall experiments that can be performed on the composite system. We can\nalso consider a restriction to experiments performed on system \\(A\\),\nor a restriction to experiments performed to \\(B\\). Such restrictions\nyields states of \\(A\\) and \\(B\\), respectively, called the reduced\nstates of the systems. When the state of the composite system\n\\(AB\\) is an entangled state, then the reduced states of \\(A\\) and\n\\(B\\) are mixed states. To see this, suppose that in the above state\nthe vectors \\(\\ket{\\phi_{1}}\\) and \\(\\ket{\\phi_{2}}\\) represent\ndistinguishable states. If one confines one’s attention to\nexperiments performed on \\(A\\), it makes no difference whether an\nexperiment is also performed on \\(B\\). An experiment performed on\n\\(B\\) that distinguishes \\(\\ket{\\phi_{1}}\\) and \\(\\ket{\\phi_{2}}\\)\nprojects the state of \\(A\\) into either \\(\\ket{\\psi_{1}}\\) or\n\\(\\ket{\\psi_{2}}\\), with probabilities \\(\\abs{a}^{2}\\) and\n\\(\\abs{b}^{2}\\), respectively, and probabilities for outcomes of\nexperiments performed on \\(A\\) are the corresponding averages of\nprobabilities for states \\(\\ket{\\psi_{1}}\\) and\n\\(\\ket{\\psi_{2}}\\). These probabilities, as mentioned, are the same as\nthose for the situation in which no experiment is performed on\n\\(B\\). Thus, even if no experiment is performed on \\(B\\), the\nprobabilities of outcomes of experiments on \\(A\\) are exactly as if\nsystem \\(A\\) is either in the state represented by \\(\\ket{\\psi_{1}}\\)\nor the state represented by \\(\\ket{\\psi_{2}}\\), with probabilities\n\\(\\abs{a}^{2}\\) and \\(\\abs{b}^{2}\\), respectively.", "\nIn general, any state, pure or mixed, that is neither a product state\nnor a mixture of product states, is called an entangled\nstate.", "\nThe existence of pure entangled states means that, if we consider a\ncomposite system consisting of spatially separated parts, then, even\nwhen the state of the system is a pure state, the state is not\ndetermined by the reduced states of its component parts. Thus, quantum\nstates exhibit a form of nonseparability. See the entry on\n holism and nonseparability in physics\n for more information.", "\nQuantum entanglement results in a form of nonlocality that is alien to\nclassical physics. Even if we assume that the reduced states of \\(A\\)\nand \\(B\\) do not completely\ncharacterize their physical states, but must be supplemented by some\nfurther variables, there are quantum correlations that cannot be\nreduced to correlations between states of \\(A\\) and \\(B\\);\nsee the entries on\n Bell’s Theorem\n and\n action at a distance in quantum mechanics." ], "section_title": "3. Entanglement, nonlocality, and nonseparability", "subsections": [] }, { "main_content": [], "section_title": "4. The measurement problem", "subsections": [ { "content": [ "\nIf quantum theory is meant to be (in principle) a universal theory, it\nshould be applicable, in principle, to all physical systems, including\nsystems as large and complicated as our experimental apparatus. It is\neasy to show that linear evolution of quantum states, when applied to\nmacroscopic objects, will routinely lead to superpositions of\nmacroscopically distinct states. Among the circumstances in which this\nwill happen are experimental set-ups, and much of the early\ndiscussions focussed on how to construe the process of measurement in\nquantum-mechanical terms. For this reason, the interpretational issues\nhave come to be referred to as the measurement problem. In\nthe first decades of discussion of the foundations of quantum\nmechanics, it was commonly referred to as the problem of\nobservation.", "\nConsider a schematized experiment. Suppose we have a quantum system\nthat can be prepared in at least two distinguishable states, \\(\\ket{0}\n_{S}\\) and \\(\\ket{1} _{S}\\). Let \\(\\ket{R} _{A}\\) be a ready state of\nthe apparatus, that is, a state in which the apparatus is ready to\nmake a measurement.", "\nIf the apparatus is working properly, and if the measurement is a\nminimally disturbing one, the coupling of the system \\(S\\)\nwith the apparatus \\(A\\) should result\nin an evolution that predictably yields results of the form", "\nwhere \\(\\ket{“0” } _{A}\\) and \\(\\ket{“1”}\n_{A}\\) are apparatus states indicating results 0 and 1,\nrespectively.", "\nNow suppose that the system \\(S\\) is prepared in a\nsuperposition of the states \\(\\ket{0} _{S}\\) and \\(\\ket{1}_{S}\\).", "\nwhere \\(a\\) and \\(b\\) are both nonzero.\nIf the evolution that leads from the pre-experimental state to the\npost-experimental state is linear Schrödinger evolution, then we\nwill have", "\nThis is not an eigenstate of the instrument reading variable, but is,\nrather, a state in which the reading variable and the system variable\nare entangled with each other. The eigenstate-eigenvalue link, applied\nto a state like this, does not yield a definite result for the\ninstrument reading. The problem of what to make of this is called the\n“measurement problem” which is discussed in more detail\nbelow." ], "subsection_title": "4.1 The measurement problem formulated" }, { "content": [ "\nIf quantum state evolution proceeds via the Schrödinger equation\nor some other linear equation, then, as we have seen in the previous\nsection, typical experiments will lead to quantum states that are\nsuperpositions of terms corresponding to distinct experimental\noutcomes. It is sometimes said that this conflicts with our\nexperience, according to which experimental outcome variables, such as\npointer readings, always have definite values. This is a misleading\nway of putting the issue, as it is not immediately clear how to\ninterpret states of this sort as physical states of a system that\nincludes experimental apparatus, and, if we can’t say what it\nwould be like to observe the apparatus to be in such a state, it makes\nno sense to say that we never observe it to be in a state like\nthat.", "\nNonetheless, we are faced with an interpretational problem. If we take\nthe quantum state to be a complete description of the system, then the\nstate is, contrary to what would antecedently expect, not a state\ncorresponding to a unique, definite outcome. This is what led J.S.\nBell to remark, “Either the wavefunction, as given by the\nSchrödinger equation, is not everything, or it is not\nright” (Bell 1987: 41, 2004: 201). This gives us a (prima\nfacie) tidy way of classifying approaches to the measurement\nproblem:", "\nWe include in the first category approaches that deny that a quantum\nstate should be thought of as representing anything in reality at all.\nThese include variants of the Copenhagen interpretation, as well as\npragmatic and other anti-realist approaches. Also in the first\ncategory are approaches that seek a completion of the quantum state\ndescription. These include hidden-variables approaches and modal\ninterpretations. The second category of interpretation motivates a\nresearch programme of finding suitable indeterministic modifications\nof the quantum dynamics. Approaches that reject both horns of\nBell’s dilemma are typified by Everettian, or\n“many-worlds” interpretations.", "\nSince the mid-1950’s, the term “Copenhagen\ninterpretation” has been commonly used for whatever it is that\nthe person employing the term takes to be the ‘orthodox’\nviewpoint regarding the philosophical issues raised by quantum\nmechanics. According to Howard (2004), the phrase was first used by\nHeisenberg (1955, 1958), and is intended to suggest a commonality of\nviews among Bohr and his associates, included Born and Heisenberg\nhimself. Recent historiography has emphasized diversity of viewpoints\namong the figures associated with the Copenhagen interpretation; see\nthe entry on\n Copenhagen interpretation of quantum mechanics,\n and references therein. Readers should be aware that the term is not\nunivocal, and that different authors might mean different things when\nspeaking of the“Copenhagen interpretation.”", "\nFrom the early days of quantum mechanics, there has been a strain of\nthought that holds that the proper attitude to take towards quantum\nmechanics is an instrumentalist or pragmatic one. On such a view,\nquantum mechanics is a tool for coordinating our experience and for\nforming expectations about the outcomes of experiments. Variants of\nthis view include some versions of the Copenhagen interpretation. More\nrecently, views of this sort have been advocated by physicists,\nincluding QBists, who hold that quantum states represent subjective or\nepistemic probabilities (see Fuchs et al., 2014). The\nphilosopher Richard Healey defends a related view on which quantum\nstates, though objective, are not to be taken as\nrepresentational (see Healey 2012, 2017a, 2020). For more on\nthese approaches, see entry on\n Quantum-Bayesian and pragmatist views of quantum theory.", "\nTheories whose structure include the quantum state but include\nadditional structure, with an aim of circumventing the measurement\nproblem, have traditionally been called “hidden-variables\ntheories”. That a quantum state description cannot be regarded\nas a complete description of physical reality was argued for in a\nfamous paper by Einstein, Podolsky and Rosen (EPR) and by Einstein in\nsubsequent publications (Einstein 1936, 1948, 1949). See the entry on\nthe\n Einstein-Podolsky-Rosen argument in quantum theory.", "\nThere are a number of theorems that circumscribe the scope of possible\nhidden-variables theories. The most natural thought would be to seek a\ntheory that assigns to all quantum observables definite values that\nare merely revealed upon measurement, in such a way that any\nexperimental procedure that, in conventional quantum mechanics, would\ncount as a “measurement” of an observable yields the\ndefinite value assigned to the observable. Theories of this sort are\ncalled noncontextual hidden-variables theory. It was shown by\nBell (1966) and Kochen and Specker (1967) that there are no such\ntheories for any system whose Hilbert space dimension is greater than\nthree (see the entry on\n the Kochen-Specker theorem).", "\nThe Bell-Kochen-Specker Theorem does not rule out hidden-variables\ntheories tout court. The simplest way to circumvent it is to\npick as always-definite some observable or compatible set of\nobservables that suffices to guarantee determinate outcomes of\nexperiments; other observables are not assigned definite values and\nexperiments thought of as “measurements” of these\nobservables do not reveal pre-existing values.", "\nThe most thoroughly worked-out theory of this type is the pilot wave\ntheory developed by de Broglie and presented by him at the Fifth\nSolvay Conference held in Brussels in 1927, revived by David Bohm in\n1952, and currently an active area of research by a small group of\nphysicists and philosophers. According to this theory, there are\nparticles with definite trajectories, that are guided by the quantum\nwave function. For the history of the de Broglie theory, see the\nintroductory chapters of Bacciagaluppi and Valentini (2009). For an\noverview of the de Broglie-Bohm theory and philosophical issues\nassociated with it see the entry on\n Bohmian mechanics.", "\nThere have been other proposals for supplementing the quantum state\nwith additional structure; these have come to be called modal\ninterpretations; see the entry on\n modal interpretations of quantum mechanics.", "\nAs already mentioned, Dirac wrote as if the collapse of the\nquantum state vector precipitated by an experimental intervention on\nthe system is a genuine physical change, distinct from the usual\nunitary evolution. If collapse is to be taken as a genuine physical\nprocess, then something more needs to be said about the circumstances\nunder which it occurs than merely that it happens when an experiment\nis performed. This gives rise to a research programme of formulating a\nprecisely defined dynamics for the quantum state that approximates the\nlinear, unitary Schrödinger evolution in situations for which\nthis is well-confirmed, and produces collapse to an eigenstate of the\noutcome variable in typical experimental set-ups, or, failing that, a\nclose approximation to an eigenstate. The only promising collapse\ntheories are stochastic in nature; indeed, it can be shown that a\ndeterministic collapse theory would permit superluminal signalling.\nSee the entry on\n collapse theories\n for an overview, and Gao, ed. (2018) for a snapshot of contemporary\ndiscussions.", "\nPrima facie, a dynamical collapse theory of this type can be\na quantum state monist theory, one on which, in Bell’s words,\n“the wave function is everything”. In recent years, this\nhas been disputed; it has been argued that collapse theories require\n“primitive ontology” in addition to the quantum state. See\nAllori et al. (2008), Allori (2013), and also the entry on\n collapse theories,\n and references therein. Reservations about this approach have been\nexpressed by Egg (2017, 2021), Myrvold (2018), and Wallace \n(2020).", "\nIn his doctoral dissertation of 1957 (reprinted in Everett 2012), Hugh\nEverett III proposed that quantum mechanics be taken as it is, without\na collapse postulate and without any “hidden variables”.\nThe resulting interpretation he called the relative state\ninterpretation.", "\nThe basic idea is this. After an experiment, the quantum state of the\nsystem plus apparatus is typically a superposition of terms\ncorresponding to distinct outcomes. As the apparatus interacts with\nits environment, which may include observers, these systems become\nentangled with the apparatus and quantum system, the net result of\nwhich is a quantum state involving, for each of the possible\nexperimental outcomes, a term in which the apparatus reading\ncorresponds to that outcome, there are records of that outcome in the\nenvironment, observers observe that outcome, etc.. Everett\nproposed that each of these terms be taken to be equally real. From a\nGod’s-eye-view, there is no unique experimental outcome, but one\ncan also focus on a particular determinate state of one subsystem,\nsay, the experimental apparatus, and attribute to the other systems\nparticipating in the entangled state a relative state,\nrelative to that state of the apparatus. That is, relative to the\napparatus reading ‘+’ is a state of the environment\nrecording that result and states of observers observing that result\n(see the entry on\n Everett’s relative-state formulation of quantum mechanics,\n for more detail on Everett’s views).", "\nEverett’s work has inspired a family of views that go by the\nname of “Many Worlds” interpretations; the idea is that\neach of the terms of the superposition corresponds to a coherent\nworld, and all of these worlds are equally real. As time goes on,\nthere is a proliferation of these worlds, as situations arise that\ngive rise to a further multiplicity of outcomes (see the entry\n many-worlds interpretation of quantum mechanics,\n and Saunders 2007, for overviews of recent discussions; Wallace 2012\nis an extended defense of an Everettian interpretation of quantum\nmechanics).", "\nThere is a family of distinct, but related views, that go by the name\nof “Relational Quantum Mechanics”. These views agree with\nEverett in attributing to a system definite values of dynamical\nvariables only relative to the states of other systems; they differ in\nthat, unlike Everett, they do not take the quantum state as their\nbasic ontology (see the entry on\n relational quantum mechanics\n for more detail)." ], "subsection_title": "4.2 Approaches to the measurement problem" }, { "content": [ "\nAs mentioned, quantum theory, as standardly formulated, employs a\ndivision of the world into a part that is treated with the theory, and\na part that is not. Both von Neumann and Heisenberg emphasized an\nelement of arbitrariness in the location of the division. In some\nformulations, the division was thought of as a distinction between\nobserver and observed, and it became common to say that quantum\nmechanics requires reference to an observer for its formulation.", "\nThe founders of quantum mechanics tended to assume implicitly that,\nthough the “cut” is somewhat moveable, in any given\nanalysis a division would be settled on, and one would not attempt to\ncombine distinct choices of the cut in one analysis of an experiment.\nIf, however, one thinks of the cut as marking the distinction between\nobserver and observed, one is led to ask about situations involving\nmultiple observers. Is each observer permitted to treat the other as a\nquantum system?", " \nThe consideration of such scenarios was initiated by Wigner\n(1961). Wigner considered a hypothetical scenario in which a friend\nconducts an observation, and he himself treats the joint system,\nconsisting of the friend and the system experimented upon, as a\nquantum system. For this reason, scenarios of this sort have come to\nbe known as “Wigner’s friend” scenarios. Wigner was\nled by consideration of such scenarious to hypothesize that conscious\nobservers cannot be in a superposition of states corresponding to\ndistinct perceptions; the introduction of conscious observers\ninitiates a physical collapse of the quantum state; this involves,\naccording to Wigner, “a violation of physical laws where\nconsciousness plays a role” (Wigner 1961, 294 ;167, 181). ", " \nFrauchiger and Renner (2018) initiated the discussion of scenarios\nof this sort involving more than two observers, which have come to be\ncalled “extended Wigner’s friend” scenarios. Further\nresults along these lines include Brukner (2018), Bong et al. (2020),\nand Guérin et al. (2021). The strategy of these investigations\nis to present some set of plausible-seeming assumptions (a different\nset, for each of the works cited), and to show, via consideration of a\nhypothetical situation involving multiple observers, the inconsistency\nof that set of assumptions. The theorems are, therefore, no-go\ntheorems for approaches to the measurement problem that would seek to\nsatisfy all of the members of the set of assumptions that has been\nshown to be inconsistent.", "\nAn assumption common to all of these investigations is that it is\nalways permissible for one observer to treat systems containing other\nobservers within quantum mechanics and to employ unitary evolution for\nthose systems. This means that collapse is not regarded as a physical\nprocess. It is also assumed that each observer always perceives a\nunique outcome for any experiment performed by that observer; this\nexcludes Everettian interpretations. Where the works cited vary is in\nthe other assumptions made.", "\n\nIt should be noted that each of the major avenues of approach to the\nmeasurement problem is capable of giving an account of goings-on in\nany physical scenario, including the ones considered in these works.\nEach of them, therefore, must violate some member of the set of\nassumptions shown to be inconsistent. These results do not pose\nproblems for existing approaches to the measurement problem; rather,\nthey are no-go theorems for approaches that might seek to satisfy all\nof the set of assumptions shown to be inconsistent. As the assumptions\nconsidered include both unitary evolution and unique outcomes of\nexperiments, and the scenarios considered involved situations\ninvolving superpositions of distinct experimental outcomes, these\nresults concern theories on which the quantum state, as given by the\nSchrödinger equation, is not a complete description of reality,\nas it fails to determine the unique outcomes perceived by the\nobservers. These preceptions could be thought of as supervening on\nbrain states, in which case there is physical structure not included\nin the quantum state, or as attributes of immaterial minds. On either\ninterpretation, the sorts of theories ruled out fall under the first\nhorn of Bell’s dilemma, mentioned in section 4.2, and these\nno-go results in part reproduce, and in part extend, no-go results for\ncertain sorts of modal interpretations (see entry on\n modal interpretations of quantum mechanics).", "\nThese results involving extended Wigner’s friend scenarios have engendered\nconsiderable philosophical discussion; see Sudbery (2017, 2019),\nHealey (2018, 2020), Dieks (2019), Losada et al. (2019), Dascal\n(2020), Evans (2020), Fortin and Lombardi (2020), Kastner (2020),\nMuciño & Okon (2020), Bub (2020, 2021), Cavalcanti (2021),\nCavalcanti and Wiseman (2021), and Żukowski and Markiewicz\n(2021)." ], "subsection_title": "4.3 Extended Wigner’s friend scenarios as a source of no-go theorems" }, { "content": [ "\nA quantum state that is a superposition of two distinct terms, such\nas", "\nwhere \\(\\ket{\\psi_{1}}\\) and \\(\\ket{\\psi_{2}}\\) are distinguishable\nstates, is not the same state as a mixture of \\(\\ket{\\psi_{1}}\\) and\n\\(\\ket{\\psi_{2}}\\), which would be appropriate for a situation in\nwhich the state prepared was either \\(\\ket{\\psi_{1}}\\) or\n\\(\\ket{\\psi_{2}}\\), but we don’t know which. The difference\nbetween a coherent superposition of two terms and a mixture has\nempirical consequences. To see this, consider the double-slit\nexperiment, in which a beam of particles (such as electrons, neutrons,\nor photons) passes through two narrow slits and then impinges on a\nscreen, where the particles are detected. Take \\(\\ket{\\psi_{1}}\\) to\nbe a state in which a particle passes through the top slit, and\n\\(\\ket{\\psi_{2}}\\), a state in which it passes through the bottom\nslit. The fact that the state is a superposition of these two\nalternatives is exhibited in interference fringes at the screen,\nalternating bands of high and low rates of absorption.", "\nThis is often expressed in terms of a difference between classical and\nquantum probabilities. If the particles were classical particles, the\nprobability of detection at some point \\(p\\) of the\nscreen would simply be a weighted average of two conditional\nprobabilities: the probability of detection at \\(p\\),\ngiven that the particle passed through the top slit, and the\nprobability of detection at \\(p\\), given that the\nparticle passed through the bottom slit. The appearance of\ninterference is an index of nonclassicality.", "\nSuppose, now, that the electrons interact with something else (call it\nthe environment) on the way to the screen, that could serve\nas a “which-way” detector; that is, the state of this\nauxiliary system becomes entangled with the state of the electron in\nsuch a way that its state is correlated with \\(\\ket{\\psi_{1}}\\) and\n\\(\\ket{\\psi_{2}}\\). Then the state of the quantum system, \\(s\\),\nand its environment, \\(e\\), is", "\nIf the environment states \\(\\ket{\\phi_{1}} _{e}\\) are\n\\(\\ket{\\phi_{2}}_{e}\\) are distinguishable states, then this\ncompletely destroys the interference fringes: the particles interact\nwith the screen as if they determinately went through one slit or the\nother, and the pattern that emerges is the result of overlaying the\ntwo single-slit patterns. That is, we can treat the particles as if\nthey followed (approximately) definite trajectories, and apply\nprobabilities in a classical manner.", "\nNow, macroscopic objects are typically in interaction with a large and\ncomplex environment—they are constantly being bombarded with air\nmolecules, photons, and the like. As a result, the reduced state of\nsuch a system quickly becomes a mixture of quasi-classical states, a\nphenomenon known as decoherence.", "\nA generalization of decoherence lies at the heart of an approach to\nthe interpretation of quantum mechanics that goes by the name of\ndecoherent histories approach (see the entry on\n the consistent histories approach to quantum mechanics\n for an overview).", "\nDecoherence plays important roles in the other approaches to quantum\nmechanics, though the role it plays varies with approach; see the\nentry on\n the role of decoherence in quantum mechanics\n for information on this." ], "subsection_title": "4.4 The role of decoherence" }, { "content": [ "\nMost of the above approaches take it that the goal is to provide an\naccount of events in the world that recovers, at least in some\napproximation, something like our familiar world of ordinary objects\nbehaving classically. None of the mainstream approaches accord any\nspecial physical role to conscious observers. There have,\nhowever, been proposals in that direction (see the entry on\n quantum approaches to consciousness\n for discussion).", "\nAll of the above-mentioned approaches are consistent with observation.\nMere consistency, however, is not enough; the rules for connecting\nquantum theory with experimental results typically involve nontrivial\n(that is, not equal to zero or one) probabilities assigned to\nexperimental outcomes. These calculated probabilities are confronted\nwith empirical evidence in the form of statistical data from repeated\nexperiments. Extant hidden-variables theories reproduce the quantum\nprobabilities, and collapse theories have the intriguing feature of\nreproducing very close approximations to quantum probabilities for all\nexperiments that have been performed so far but departing from the\nquantum probabilities for other conceivable experiments. This permits,\nin principle, an empirical discrimination between such theories and\nno-collapse theories.", "\nA criticism that has been raised against Everettian theories is that\nit is not clear whether they can even make sense of statistical\ntesting of this kind, as it does not, in any straightforward way, make\nsense to talk of the probability of obtaining, say, a ‘+”\noutcome of a given experiment when it is certain that all possible\noutcomes will occur on some branch of the wavefunction. This has been\ncalled the “Everettian evidential problem”. It has been\nthe subject of much recent work on Everettian theories; see Saunders\n(2007) for an introduction and overview.", "\nIf one accepts that Everettians have a solution to the evidential\nproblem, then, among the major lines of approach, none is favored in a\nstraightforward way by the empirical evidence. There will not be space\nhere to give an in-depth overview of these ongoing discussions, but a\nfew considerations can be mentioned, to give the reader a flavor of\nthe discussions; see entries on particular approaches for more\ndetail.", "\nEverettians take, as a virtue of the approach, the fact that it does\nnot involve an extension or modification of the quantum formalism.\nBohmians claim, in favor of the Bohmian approach, that a theory on\nthese lines provides the most straightforward picture of events;\nontological issues are less clear-cut when it comes to Everettian\ntheories or collapse theories.", "\nAnother consideration is compatibility with relativistic causal\nstructure. See Myrvold (2021) for an overview of relavistic\nconstraints on approaches to the measurement problem.The de\nBroglie-Bohm theory requires a distinguished relation of distant\nsimultaneity for its formulation, and, it can be argued, this is an\nineliminable feature of any hidden-variables theory of this sort, that\nselects some observable to always have definite values (see Berndl\net al. 1996; Myrvold 2002, 2021). On the other hand, there\nare collapse models that are fully relativistic. On such models,\ncollapses are localized events. Though probabilities of collapses at\nspacelike separation from each other are not independent, this\nprobabilistic dependence does not require us to single one out as\nearlier and the other later. Thus, such theories do not require a\ndistinguished relation of distant simultaneity. There remains,\nhowever, some discussion of how to equip such theories with beables\n(or “elements of reality”). See the entry on\n collapse theories\n and references therein; see also, for some recent contributions to\nthe discussion, Fleming (2016), Maudlin (2016), and Myrvold\n(2016). In the case of Everettian theories, one must first think\nabout how to formulate the question of relativistic locality. Several\nauthors have approached this issue in somewhat different ways, with a\ncommon conclusion that Everettian quantum mechanics is, indeed, local.\n(See Vaidman 1994; Bacciagaluppi 2002; Chapter 8 of Wallace 2012; Tipler\n2014; Vaidman 2016; and Brown and Timpson 2016.)" ], "subsection_title": "4.5 Comparison of approaches to the measurement problem" } ] }, { "main_content": [ "\nAs mentioned, a central question of interpretation of quantum\nmechanics concerns whether quantum states should be regarded as\nrepresenting anything in physical reality. If this is answered in the\naffirmative, this gives rise to new questions, namely, what sort of\nphysical reality is represented by the quantum state, and whether a\nquantum state could in principle give an exhaustive account of\nphysical reality." ], "section_title": "5. Ontological Issues", "subsections": [ { "content": [ "\nHarrigan and Spekkens (2010) have introduced a framework for\ndiscussing these issues. In their terminology, a complete\nspecification of the physical properties is given by the ontic\nstate of a system. An ontological model posits a space of ontic\nstates and associates, with any preparation procedure, a probability\ndistribution over ontic states. A model is said to be\n\\(\\psi\\)-ontic if the ontic state uniquely determines the\nquantum state; that is, if there is a function from ontic states to\nquantum states (this includes both cases in which the quantum state\nalso completely determines the physical state, and cases, such as\nhidden-variables theories, in which the quantum state does not\ncompletely determine the physical state). In their terminology, models\nthat are not \\(\\psi\\)-ontic are called \\(\\psi\\)-epistemic. If\na model is not \\(\\psi\\)-ontic, this means that it is possible for some\nontic states to be the result of two or more preparations that lead to\ndifferent assignments of pure quantum states; that is, the same ontic\nstate may be compatible with distinct quantum states.", "\nThis gives a nice way of posing the question of quantum state realism:\nare there preparations corresponding to distinct pure quantum states\nthat can give rise to the same ontic state, or, conversely, are there\nontic states compatible with distinct quantum states? Pusey, Barrett,\nand Rudolph (2012) showed that, if one adopts a seemingly natural\nindependence assumption about state preparations—namely, the\nassumption that it is possible to prepare a pair of systems in such a\nway that the probabilities for ontic states of the two systems are\neffectively independent—then the answer is negative; any\nontological model that reproduces quantum predictions and satisfies\nthis Preparation Independence assumption must be a \\(\\psi\\)-ontic\nmodel.", "\nThe Pusey, Barrett and Rudolph (PBR) theorem does not close off all\noptions for anti-realism about quantum states; an anti-realist about\nquantum states could reject the Preparation Independence assumption,\nor reject the framework within which the theorem is set; see\ndiscussion in Spekkens (2015): 92–93. See Leifer (2014) for a\ncareful and thorough overview of theorems relevant to quantum state\nrealism, and Myrvold (2020) for a presentation of a case for quantum\nstate realism based on theorems of this sort." ], "subsection_title": "5.1 The question of quantum state realism." }, { "content": [ "\nThe major realist approaches to the measurement problem are all, in\nsome sense, realist about quantum states. Merely saying this is\ninsufficient to give an account of the ontology of a given\ninterpretation. Among the questions to be addressed are: if quantum\nstates represent something physically real, what sort of thing is it?\nThis is the question of the ontological construal of quantum states.\nAnother question is the EPR question, whether a description in terms\nof quantum states can be taken as, in principle, complete, or whether\nit must be supplemented by different ontology.", "\nDe Broglie’s original conception of the “pilot wave”\nwas that it would be a field, analogous to an electromagnetic field.\nThe original conception was that each particle would have its own\nguiding wave. However, in quantum mechanics as it was developed at the\nhands of Schrödinger, for a system of two or more particles there\nare not individual wave functions for each particle, but, rather, a\nsingle wave function that is defined on \\(n\\)-tuples of\npoints in space, where \\(n\\) is the number of\nparticles. This was taken, by de Broglie, Schrödinger and others,\nto militate against the conception of quantum wave functions as\nfields. If quantum states represent something in physical reality,\nthey are unlike anything familiar in classical physics.", "\nOne response that has been taken is to insist that quantum wave\nfunctions are fields nonetheless, albeit fields on a space of\nenormously high dimension, namely, \\(3n\\), where \\(n\\)\nis the number of elementary particles in the universe. On this view,\nthis high-dimensional space is thought of as more fundamental than the\nfamiliar three-dimensional space (or four-dimensional spacetime) that\nis usually taken to be the arena of physical events. See Albert (1996,\n2013), for the classic statement of the view; other proponents include\nLoewer (1996), Lewis (2004), Ney (2012, 2013a,b, 2021), and North\n(2013). Most of the discussion of this proposal has taken place within\nthe context of nonrelativistic quantum mechanics, which is not a\nfundamental theory. It has been argued that considerations of how the\nwave functions of nonrelativistic quantum mechanics arise from a\nquantum field theory undermines the idea that wave functions are\nrelevantly like fields on configuration space, and also the idea that\nconfiguration spaces can be thought of as more fundamental than\nordinary spacetime (Myrvold 2015).", "\nA view that takes a wave function as a field on a high-dimensional\nspace must be distinguished from a view that takes it to be what Belot\n(2012) has called a multi-field, which assigns properties to\n\\(n\\)-tuples of points of ordinary three-dimensional\nspace. These are distinct views; proponents of the \\(3n\\)-dimensional\nconception make much of the fact that it restores Separability: on\nthis view, a complete specification of the way the world is, at some\ntime, is given by specification of local states of affairs at each\naddress in the fundamental (\\(3n\\)-dimensional) space. Taking a wave\nfunction to be a multi-field, on the other hand, involves accepting\nnonseparability. Another difference between taking wave-functions as\nmulti-fields on ordinary space and taking them to be fields on a\nhigh-dimensional space is that, on the multi-field view, there is no\nquestion about the relation of ordinary three-dimensional space to\nsome more fundamental space.­ Hubert and Romano (2018) argue that\nwave-functions are naturally and straightforwardly construed as\nmulti-fields.", "\nIt has been argued that, on the de Broglie-Bohm pilot wave theory and\nrelated pilot wave theories, the quantum state plays a role more\nsimilar to that of a law in classical mechanics; its role is to\nprovide dynamics for the Bohmian corpuscles, which, according to the\ntheory, compose ordinary objects. See Dürr, Goldstein, and\nZanghì (1997), Allori et al. (2008), Allori\n(2021).", "\nDürr, Goldstein, and Zanghì (1992) introduced the term\n“primitive ontology” for what, according to a physical\ntheory, makes up ordinary physical objects; on the de Broglie-Bohm\ntheory, this is the Bohmian corpuscles. The conception is extended to\ninterpretations of collapse theories by Allori et al. (2008).\nPrimitive ontology is to be distinguished from other ontology, such as\nthe quantum state, that is introduced into the theory to account for\nthe behavior of the primitive ontology. The distinction is meant to be\na guide as to how to conceive of the nonprimitive ontology of the\ntheory." ], "subsection_title": "5.2 Ontological category of quantum states" } ] }, { "main_content": [ "\nQuantum mechanics has not only given rise to interpretational\nconundrums; it has given rise to new concepts in computing and in\ninformation theory. Quantum information theory is the study\nof the possibilities for information processing and transmission\nopened up by quantum theory. This has given rise to a different\nperspective on quantum theory, one on which, as Bub (2000, 597) put\nit, “the puzzling features of quantum mechanics are seen as a\nresource to be developed rather than a problem to be solved”\n(see the entries on\n quantum computing\n and\n quantum entanglement and information)." ], "section_title": "6. Quantum computing and quantum information theory", "subsections": [] }, { "main_content": [ "\nAnother area of active research in the foundations of quantum\nmechanics is the attempt to gain deeper insight into the structure of\nthe theory, and the ways in which it differs from both classical\nphysics and other theories that one might construct, by characterizing\nthe structure of the theory in terms of very general principles, often\nwith an information-theoretic flavour.", "\nThis project has its roots in early work of Mackey (1957, 1963),\nLudwig (1964), and Piron (1964) aiming to characterize quantum\nmechanics in operational terms. This has led to the development of a\nframework of generalized probabilistic model. It also has connections\nwith the investigations into quantum logic initiated by Birkhoff and\nvon Neumann (1936) (see the entry\n quantum logic and probability theory\n for an overview).", "\nInterest in the project of deriving quantum theory from axioms with\nclear operational content was revived by the work of Hardy (2001\n[2008], Other Internet Resources). Significant results along these\nlines include the axiomatizations of Masanes and Müller (2011)\nand Chiribella, D’Ariano, and Perinotti (2011). See Chiribella\nand Spekkens (2015) for an overview of this burgeoning research\narea." ], "section_title": "7. Reconstructions of quantum mechanics and beyond", "subsections": [] } ]

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A Study in Mythology”, Philosophy of\nScience, 71: 669–682.", "Hubert, Mario, and Davide Romano, 2018, “The wave-function\nas a multi-field”, European Journal for the Philosophy of\nScience, 8: 521–537.", "Kastner, Ruth, 2020, “Unitary‑Only Quantum Theory\nCannot Consistently Describe the Use of Itself: On the\nFrauchiger–Renner Paradox”, Foundations of\nPhysics, 50: 441–456.", "Knox, Eleanor, and Alastair Wilson (eds.), 2021, The Routledge\nCompanion to Philosophy of Physics, London: Routledge.", "Kochen, Simon and Ernst Specker, 1967, “The Problem of\nHidden Variables in Quantum Mechanics”, Journal of\nMathematics and Mechanics, 17: 59–87.", "Lazarovici, Dustin, and Mario Hubert, 2019, “How Quantum\nMechanics can consistently describe the use of itself”,\nScientific Reports, 9: 470.", "Leifer, Matthew Saul, 2014, “Is the Quantum State Real? An\nExtended Review of \\(\\psi\\)-ontology Theorems”, Quanta,\n3: 67–155.", "Lewis, Peter J., 2004, “Life in configuration space”,\nThe British Journal for the Philosophy of Science, 55:\n713–729. doi:10.1093/bjps/55.4.713", "Loewer, B., 1996, “Humean supervenience”,\nPhilosophical Topics, 24: 101–127.", "London, Fritz and Edmond Bauer, 1939, La théorie de\nl’observation en mécanique quantique, Paris:\nHermann. English translation, “The theory of observation in\nquantum mechanics”, in Quantum Theory and Measurement,\nJ.A. Wheeler and W.H. Zurek (eds.), Princeton: Princeton University\nPress, 1983, 217–259.", "Losada, Marcelo, Roberto Laura, and Olimpia Lombardi, 2019,\n“Frauchiger-Renner argument and quantum histories”,\nPhysical Review A, 100: 052114.", "Ludwig, G., 1964, “Versuch einer axiomatischen Grundlegung\nder Quantenmechanik und allgemeinerer physikalischer Theorien”,\nZeitschrift für Physik, 181: 233–260.", "Mackey, George W. 1957, “Quantum Mechanics and Hilbert\nSpace”, American Mathematical Monthly, 64:\n45–57.", "–––, 1963, The Mathematical Foundations of\nQuantum Mechanics: A lecture-note volume, New York: W.A.\nBenjamin.", "Masanes, Lluís and Markus P. Müller, 2011, “A\nderivation of quantum theory from physical Requirements”,\nNew Journal of Physics, 13: 063001.", "Maudlin, Tim, 2016, “Local Beables and the Foundations of\nPhysics”, in Bell and Gao (eds.) 2016: 317–330.", "Muciño, R., and E. Okon, 2020, “Wigner’s\nconvoluted friends”, Studies in History and Philosophy of\nModern Physics, 72: 87–90.", "Myrvold, Wayne C., 2002, “Modal Interpretations and\nRelativity”, Foundations of Physics, 32:\n1773–1784.", "–––, 2015, “What is a Wavefunction?”\nSynthese, 192: 3247–3274.", "–––, 2016, “Lessons of Bell”s\nTheorem: Nonlocality, Yes; Action at a Distance, Not\nNecessarily”, in Bell and Gao (eds.) 2016: 237–260.", "–––, 2018, “Ontology for Collapse\nTheories,” in Gao (ed.) 2018: 97–123.", "–––, 2020, “On the Status of Quantum State\nRealism,” in French and Saatsi (eds.), 2020: 229–251.", "–––, 2021, “Relativistic Constraints on\nInterpretations of Quantum Mechanics”, in Knox and Wilson (eds.)\n2021: 99–121.", "Ney, Alyssa, 2012, “The status of our ordinary three\ndimensions in a quantum universe”, Noûs, 46:\n525–560.", "–––, 2013a, “Introduction”, in Ney\nand Albert (eds.) 2013: 1–51.", "–––, 2013b, “Ontological\nreduction and the wave function ontology”, in Ney and Albert\n(eds.) 2013: 168– 183.", "–––, 2021, The World in the Wave Function: A\nMetaphysics for Quantum Physics, Oxford, Oxford University\nPress.", "Ney, Alyssa and David Z. Albert (eds.), 2013, The Wave\nFunction: Essays on the Metaphysics of Quantum Mechanics, Oxford:\nOxford University Press.", "North, Jill, 2013, “The structure of a quantum world”,\nin Ney and Albert (eds.) 2013: 184–202.", "Piron, Constantin, 1964, “Axiomatique quantique”,\nHelvetica Physica Acta, 37: 439–468.", "Pusey, Matthew F., Jonathan Barrett, and Terry Rudolph, 2012,\n“On the Reality of the Quantum State”, Nature\nPhysics, 8: 475–478.", "Saunders, Simon, 2007. “Many Worlds? An Introduction”,\nin S. Saunders, J. Barrett, A. Kent, and D. Wallace (eds.), Many\nWorlds? Everett, Quantum Theory, and Reality, Oxford: Oxford\nUniversity Press, 1–50.", "Spekkens, Robert W., 2007, “Evidence for the Epistemic view\nof Quantum States: A Toy Theory”, Physical Review A,\n75: 032110.", "–––, 2015, “Quasi-Quantization: Classical\nStatistical Theories with an Epistemic Restriction”, in\nChiribella and Spekkens 2015: 83–135.", "Sudbery, Anthony, 2017, “Single-world theory of the extended\nWigner’s friend experiment”, Foundations of\nPhysics, 47: 658–669.", "–––, 2019, “The Hidden Assumptions of\nFrauchiger and Renner”, International Journal of Quantum\nFoundations, 5: 98-109.", "Tipler, Frank J., 2014, “Quantum nonlocality does not\nexist”, Proceedings of the National Academy of\nSciences, 111: 11281–6.", "Vaidman, Lev, 1994, “On the paradoxical aspects of new\nquantum experiments”, in D. Hull, M. Forbes and R.M. Burian\n(eds.), PSA 1994 (Volume 1), Philosophy of Science\nAssociation, 211–17.", "–––, 2016, “The Bell Inequality and the\nMany-Worlds Interpretation”, in Bell and Gao (eds.) 2016:\n195–203.", "von Neumann, John, 1932, Mathematische Grundlagen der\nQuantenmechanik, Berlin, Springer Verlag.", "–––, 1955, Mathematical Foundations of\nQuantum Mechanics, Robert T. Beyer (trans.), Princeton: Princeton\nUniversity Press.", "Wallace, David, 2012, The Emergent Multiverse: Quantum Theory\naccording to the Everett interpretation, Oxford: Oxford\nUniversity Press.", "–––, 2020, “On the Plurality of Quantum\nTheories: Quantum Theory as a Framework, and its Implications for the\nQuantum Measurement Problem”, in French and Saatsi (eds.) 2020:\n78–102.", "Wigner, Eugene P., 1962, “Remarks on the Mind-Body\nProblem”, in I.J. Good (ed.), The Scientist Speculates: An\nAnthology of Partly-Baked Ideas, London: William Heinemann,\n284–320; reprinted in Wigner (1967), 171–184.", "–––, 1967, Symmetries and Reflections:\nScientific Essays of Eugene P. Wigner, Bloomington, Indiana\nUniversity Press.", "Żukowski, Marek, and Marcin Markiewicz, 2021, “Physics\nand Metaphysics of Wigner’s Friends: Even Performed\nPre-measurements Have No Results”, Physical Review\nLetters, 126: 130402." ]

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[ "\nCombining physics, mathematics and computer science, quantum computing\nand its sister discipline of\n quantum information\n have developed in the past few decades from visionary ideas to two of\nthe most fascinating areas of quantum theory. General interest and\nexcitement in quantum computing was initially triggered by Peter Shor\n(1994) who showed how a quantum algorithm could exponentially\n“speed-up” classical computation and factor large numbers\ninto primes far more efficiently than any (known) classical algorithm.\nShor’s algorithm was soon followed by several other algorithms\nthat aimed to solve combinatorial and algebraic problems, and in the\nyears since theoretical study of quantum systems serving as\ncomputational devices has achieved tremendous progress. Common belief\nhas it that the implementation of Shor’s algorithm on a large\nscale quantum computer would have devastating consequences for current\ncryptography protocols which rely on the premise that all known\nclassical worst-case algorithms for factoring take time\nexponential in the length of their input (see, e.g., Preskill 2005).\nConsequently, experimentalists around the world are engaged in\nattempts to tackle the technological difficulties that prevent the\nrealisation of a large scale quantum computer. But regardless whether\nthese technological problems can be overcome (Unruh 1995; Ekert and\nJozsa 1996; Haroche and Raimond 1996), it is noteworthy that no proof\nexists yet for the general superiority of quantum computers\nover their classical counterparts.", "\nThe philosophical interest in quantum computing is manifold. From a\nsocial-historical perspective, quantum computing is a domain where\nexperimentalists find themselves ahead of their fellow theorists.\nIndeed, quantum mysteries such as\n entanglement\n and\n nonlocality\n were historically considered a philosophical quibble, until\nphysicists discovered that these mysteries might be harnessed to\ndevise new efficient algorithms. But while the technology for\nharnessing the power of 50–100 qubits (the basic unit of information\nin the quantum computer) is now within reach (Preskill 2018), only a\nhandful of quantum algorithms exist, and the question of whether these\ncan truly outperform any conceivable classical alternative is still\nopen. From a more philosophical perspective, advances in quantum\ncomputing may yield foundational benefits. For example, it may turn\nout that the technological capabilities that allow us to isolate\nquantum systems by shielding them from the effects of\n decoherence\n for a period of time long enough to manipulate them will also allow\nus to make progress in some fundamental problems in the foundations of\nquantum theory itself. Indeed, the development and the implementation\nof efficient quantum algorithms may help us understand better the\nborder between classical and quantum physics (Cuffaro 2017, 2018a; cf.\nPitowsky 1994, 100), and perhaps even illuminate fundamental concepts\nsuch as\n measurement\n and\n causality.\n Finally, the idea that abstract mathematical concepts such as\ncomputability and complexity may not only be\ntranslated into physics, but also re-written by physics bears\ndirectly on the autonomous character of computer science and the\nstatus of its theoretical entities—the so-called\n“computational kinds”. As such it is also relevant to the\nlong-standing philosophical debate on the relationship between\nmathematics and the physical world." ]

[ { "content_title": "1. A Brief History of the Field", "sub_toc": [ "1.1 Physical Computational Complexity", "1.2 Physical “Short-cuts” of Computation", "1.3 Milestones" ] }, { "content_title": "2. Basics", "sub_toc": [ "2.1 The Qubit", "2.2 Quantum Gates", "2.3 Quantum Circuits" ] }, { "content_title": "3 Quantum Algorithms", "sub_toc": [ "3.1 Quantum-Circuit-Based Algorithms", "3.2 Adiabatic Algorithms", "3.3 Measurement-Based Algorithms", "3.4 Topological-Quantum-Field-Theory (TQFT) Algorithms" ] }, { "content_title": "4 Realisations", "sub_toc": [] }, { "content_title": "5. Philosophical Questions", "sub_toc": [ "5.1 What is Quantum in Quantum Computing?", "5.2 Experimental Metaphysics?", "5.3 Quantum Causality", "5.4 (Quantum) Computational Perspectives on Physical Science", "5.5 The Church-Turing Thesis and Deutsch’s Principle", "5.6 (Quantum) Computation and Scientific Explanation", "5.7 Are There Computational Kinds?" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [ "Online Papers", "Web sites of interest" ] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. A Brief History of the Field", "subsections": [ { "content": [ "\nThe mathematical model for a “universal” computer was\ndefined long before the invention of computers and is called the\n Turing machine\n (Turing 1936). A Turing machine consists of an unbounded tape, a head\ncapable of reading from and writing to it which can occupy one of a\npotentially infinite number of possible states, and an instruction\ntable (i.e. a transition function). This table, given the head’s\ninitial state and the input it reads from the tape in that state,\ndetermines (a) the symbol that the head will write on the tape, (b)\nthe internal state it will occupy, and (c) the displacement of the\nhead on the tape. In 1936 Turing showed that since one can encode the\ninstruction table of a Turing machine \\(T\\) and express it as a binary\nnumber \\(\\#(T)\\), there exists a universal Turing machine \\(U\\) that\ncan simulate the instruction table of any Turing machine on any given\ninput. That the Turing machine model captures the concept of\ncomputability in its entirety is the essence of the\n Church-Turing thesis,\n according to which any effectively calculable function can be\ncomputed using a Turing machine. Admittedly, no counterexample to this\nthesis (which is the result of convergent ideas of Turing, Post,\nKleene and Church) has yet been found. But since it identifies the\nclass of computable functions with the class of those functions which\nare computable using a Turing machine, this thesis involves both a\nprecise mathematical notion and an informal and intuitive notion,\nhence cannot be proved or disproved. Simple cardinality considerations\nshow, however, that not all functions are Turing-computable (the set\nof all Turing machines is countable, while the set of all functions\nfrom the natural numbers to the natural numbers is not), and the\ndiscovery of this fact came as a complete surprise in the 1930s (Davis\n1958).", "\nComputability, or the question whether a function can be computed, is\nnot the only question that interests computer scientists. Beginning\nespecially in the 1960s (Cobham 1965; Edmonds 1965; Hartmanis and\nStearns 1965), the question of the cost of computing a\nfunction (which was to some extent already anticipated in 1956 by\nGödel) also came to be of great importance. This cost, also known\nas\n computational complexity,\n is measured naturally in the physical resources (e.g., time, space,\nenergy) invested in order to solve the computational problem at hand.\nComputer scientists classify computational problems according to the\nway their cost function behaves as a function of their input size,\n\\(n\\) (the number of bits required to store the input) and in\nparticular, whether it increases exponentially or polynomially with\n\\(n\\). Tractable problems are those which can be solved in\npolynomial cost, while intractable problems are those which\ncan only be solved with exponential cost (the former solutions are\ncommonly regarded as efficient although an exponential-time\nalgorithm could turn out to be more efficient than a polynomial-time\nalgorithm for some range of input sizes).", "\nSo far, the Turing machines we have been discussing have been\ndeterministic; for such machines, their behaviour at any given time is\nwholly determined by their state plus whatever their input happens to\nbe. In other words such machines have a unique “instruction\ntable” (i.e. transition function). We can generalise the Turing\nmodel, however, by allowing a machine to instantiate more than one\ntransition function simultaneously. A nondeterministic Turing\nmachine (NTM), upon being presented with a given input in a given\nstate, is allowed to ‘choose’ which of its transition\nfunctions to follow, and we say that it solves a given problem\nwhenever, given some input, there exists at least one path through its\nstate space leading to a solution. Exactly how an NTM\n“chooses” whether to follow one transition function rather\nthan another is left undefined (in his 1936 paper, Turing originally\nconceived these choices as those of an external operator). In\nparticular, we do not assume that any probabilities are attached to\nthese choices. In a probabilistic Turing machine (PTM), on\nthe other hand, we characterise the computer’s choices by\nassociating a particular probability with each of its possible\ntransitions.", "\nProbabilistic and deterministic Turing machines (DTMs) have different\nsuccess criteria. A successful deterministic algorithm for a given\nproblem is guaranteed to yield the correct answer given its input. Of\na successful probabilistic algorithm, on the other hand, we only\ndemand that it yield a correct answer with “high”\nprobability (minimally, we demand that it be strictly greater than\n1/2). It was believed, until relatively recently, that for some\nproblems (see, e.g. Rabin 1976) probabilistic algorithms are\ndramatically more efficient than any deterministic alternatives; in\nother words that the set or “class” of problems\nefficiently solvable by PTM is larger than the class of problems\nefficiently solvable by DTM. Fascinatingly, evidence has been mounting\nin recent years (e.g. Agrawal, Kayal, and Saxena 2004) that this is\nnot the case, and it is now believed that the PTM model in fact does\nnot offer a computational advantage in this sense over the DTM model\n(Arora and Barak 2009 Ch. 20). Probabilistic (Turing) computation is\nnevertheless interesting to consider, because abstractly a\nquantum computer is just a variation on the PTM which\ndoes appear to offer computational advantages over\ndeterministic computation, although as already mentioned this\nconjecture still awaits a proof. See Hagar (2007) and Cuffaro (2018b)\nfor divergent opinions over what this purported quantum computational\nadvantage tells us about the theory of computational complexity as a\nwhole.", "\nThe class \\(\\mathbf{P}\\) (for Polynomial) is the class containing all\nthe computational decision problems that can be solved by a DTM in\npolynomial time. The class NP (for Non-deterministic\nPolynomial) is the class containing all the computational decision\nproblems that can be solved by an NTM in polynomial\n time.[1]\n The most famous problems in NP are called\n“NP-complete”, where\n“complete” designates the fact that these problems stand\nor fall together: Either they are all tractable, or none of them is!\nIf we knew how to solve an NP-complete problem\nefficiently (i.e., with polynomial cost) we could use it to\nefficiently solve any other problem in NP (Cook\n1971). Today we know of hundreds of examples of\nNP-complete problems (Garey and Johnson 1979), all of\nwhich are reducible one to another with polynomial slowdown, and since\nthe best known algorithm for any of these problems is exponential, the\nwidely believed conjecture is that there is no polynomial algorithm\nthat can solve them. Clearly \\(\\mathbf{P} \\subseteq \\mathbf{NP}\\).\nProving or disproving the conjecture that \\(\\mathbf{P} \\ne\n\\mathbf{NP}\\), however, remains perhaps one of the most important open\nquestions in computer science and complexity theory.", "\nAlthough the original Church-Turing thesis involves the\nabstract mathematical notion of computability, physicists as\nwell as computer scientists often interpret it as saying something\nabout the scope and limitations of physical computing\nmachines. Wolfram (1985) claims that any physical system can be\nsimulated (to any degree of approximation) by a universal Turing\nmachine, and that complexity bounds on Turing machine simulations have\nphysical significance. For example, if the computation of the minimum\nenergy of some system of \\(n\\) particles requires at least an\nexponentially increasing number of steps in \\(n\\), then the actual\nrelaxation of this system to its minimum energy state will also take\nexponential time. Aharonov (1999) strengthens this thesis (in the\ncontext of showing its putative incompatibility with quantum\nmechanics) when she says that a PTM can simulate any reasonable\nphysical device at polynomial cost. In order for the physical\nChurch-Turing thesis to make sense we have to relate physical space\nand time parameters to their computational counterparts: memory\ncapacity and number of computation steps, respectively. There are\nvarious ways to do that, leading to different formulations of the\nthesis (Pitowsky 1990). For example, one can encode the set of\ninstructions of a universal Turing machine and the state of its\ninfinite tape in the binary development of the position coordinates of\na single particle. Consequently, one can physically\n‘realise’ a universal Turing machine as a billiard ball\nwith hyperbolic mirrors (Moore 1990; Pitowsky 1996). For the most\nintuitive connection between abstract Turing machines and physical\ndevices see the pioneering work of Gandy (1980), simplified later by\nSieg and Byrnes (1999), and discussed, for example, in Copeland\n(2018). It should be stressed that there is no relation between the\noriginal Church-Turing thesis and its physical version (Pitowsky and\nShagrir 2003), and while the former concerns the concept of\ncomputation that is relevant to logic (since it is strongly tied to\nthe notion of proof which requires validation), it\ndoes not analytically entail that all computations should be\nsubject to validation. Indeed, there is a long historical tradition of\nanalog computations which use continuous physical processes (Dewdney\n1984), and the output of these computations is validated either by\nrepetitive “runs” or by validating the physical theory\nthat presumably governs the behaviour of the analog computer." ], "subsection_title": "1.1 Physical Computational Complexity" }, { "content": [ "\nDo physical processes exist which contradict the physical\nChurch-Turing thesis? Apart from analog computation, there exist at\nleast two main kinds of example purporting to show that the notion of\nrecursion, or Turing-computability, is not a natural physical\nproperty (Pour-el and Richards 1981; Pitowsky 1990; Hogarth 1994).\nAlthough the physical systems involved (a specific initial condition\nfor the wave equation in three dimensions and an exotic solution to\nEinstein’s field equations, respectively) are somewhat\ncontrived, a thriving school of “hypercomputation” that\naspires to extend the limited examples of physical\n“hypercomputers” and in so doing to physically\n“compute” the non-Turing-computable has nevertheless\nemerged (for a review see Copeland (2002); for a criticism: Davis\n(2003); for a recent proposal and response to criticisms see\nAndréka et al. (2018)). Quantum hypercomputation is\nrarely discussed in the literature (see, e.g., Adamyan, Calude, and\nPavlov 2004), but the most concrete attempt to harness quantum theory\nto compute the non-computable is the suggestion to use the quantum\nadiabatic algorithm (see below) to solve Hilbert’s Tenth Problem\n(Kieu 2002, 2004)—a Turing-undecidable problem equivalent to the\nhalting problem. Criticism, however, has exposed the unphysical\ncharacter of the alleged quantum adiabatic hypercomputer (see Hodges\n2005; Hagar and Korolev 2007).", "\nSetting aside “hypercomputers”, even if we restrict\nourselves only to Turing-computable functions, one can still find many\nproposals in the literature that purport to display\n“short-cuts” in computational resources. Consider, e.g.,\nthe DNA model of computation that was claimed (Adleman 1994; Lipton\n1995) to solve NP-complete problems in polynomial\ntime. A closer inspection shows that the cost of the computation in\nthis model is still exponential since the number of molecules in the\nphysical system grows exponentially with the size of the problem. Or\ntake an allegedly instantaneous solution to another\nNP-complete problem using a construction of rods and\nballs (Vergis, Steiglitz, and Dickinson 1986) that unfortunately\nignores the accumulating time-delays in the rigid rods that result in\nan exponential overall slowdown. It appears that these and other\nsimilar models cannot serve as counter-examples to the physical\nChurch-Turing thesis (as far as complexity is concerned) since they\nall require some exponential physical resource. Note, however, that\nall these models are based on classical physics, hence the unavoidable\nquestion: Can the shift to quantum physics allow us to find\n“short-cuts” in computational resources? The quest for the\nquantum computer began with the possibility of giving a positive\nanswer to this question." ], "subsection_title": "1.2 Physical “Short-cuts” of Computation" }, { "content": [ "\nThe idea of a computational device based on quantum mechanics was\nexplored already in the 1970s by physicists and computer scientists.\nAs early as 1969 Steven Wiesner suggested quantum information\nprocessing as a possible way to better accomplish cryptologic tasks.\nBut the first four published papers on quantum information (Wiesner\npublished his only in 1983), belong to Alexander Holevo (1973), R. P.\nPoplavskii (1975), Roman Ingarden (1976), and Yuri Manin (1980).\nBetter known are contributions made in the early 1980s by Charles H.\nBennett of the IBM Thomas J. Watson Research Center, Paul A. Benioff\nof Argonne National Laboratory in Illinois, David Deutsch of the\nUniversity of Oxford, and Richard P. Feynman of the California\nInstitute of Technology. The idea emerged when scientists were\ninvestigating the fundamental physical limits of computation. If\ntechnology continued to abide by “Moore’s Law” (the\nobservation made in 1965 by Gordon Moore, co-founder of Intel, that\nthe number of transistors per square inch on integrated circuits had\ndoubled every 18 months since the integrated circuit was invented),\nthen the continually shrinking size of circuitry packed onto silicon\nchips would eventually reach a point where individual elements would\nbe no larger than a few atoms. But since the physical laws that govern\nthe behaviour and properties of the putative circuit at the atomic\nscale are inherently quantum mechanical in nature, not classical, the\nnatural question arose whether a new kind of computer could be devised\nbased on the principles of quantum physics.", "\nInspired by Ed Fredkin’s ideas on reversible computation (see\nHagar 2016), Feynman was among the first to attempt to provide an\nanswer to this question by producing an abstract model in 1982 that\nshowed how a quantum system could be used to do computations. He also\nexplained how such a machine would be able to act as a simulator for\nquantum physics, conjecturing that any classical computer could do the\nsame task only inefficiently. In 1985 David Deutsch proposed the first\nuniversal quantum Turing machine and paved the way to the quantum\ncircuit model (Deutsch 1989). The young and thriving domain also\nattracted philosophers’ attention. In 1983 David Albert showed\nhow a quantum mechanical automaton behaves remarkably differently from\na classical automaton, and in 1990 Itamar Pitowsky raised the question\nof whether the superposition principle may allow quantum computers to\nefficiently solve NP-complete problems. He also\nstressed that although one could in principle ‘squeeze’\ninformation of exponential complexity into polynomially many quantum\nstates, the real problem lay in the efficient retrieval of this\ninformation.", "\nProgress in quantum algorithms began in the 1990s, with the discovery\nof the Deutsch-Josza algorithm (1992) and of Simon’s algorithm\n(1994). The latter supplied the basis for Shor’s algorithm for\nfactoring. Published in 1994, this algorithm marked a\n‘phase transition’ in the development of quantum computing\nand sparked a tremendous interest even outside the physics community.\nIn that year the first experimental realisation of the quantum\nCNOT gate with trapped ions was proposed by Cirac and Zoller\n(1995). In 1995, Peter Shor and Andrew Steane proposed (independently)\nthe first scheme for quantum error-correction. In that same year the\nfirst realisation of a quantum logic gate was done in Boulder,\nColorado, following Cirac and Zoller’s proposal. In 1996, Lov\nGrover from Bell Labs invented a quantum search algorithm which yields\na provable (though only quadratic) “speed-up” compared to\nits classical counterparts. A year later the first model for quantum\ncomputation based on nuclear magnetic resonance (NMR) techniques was\nproposed. This technique was realised in 1998 with a 2-qubit register,\nand was scaled up to 7 qubits in the Los Alamos National Lab in\n2000.", "\nSince 2000 the field has seen tremendous growth. New paradigms of\nquantum algorithms have appeared, such as adiabatic algorithms,\nmeasurement-based algorithms, and\ntopological-quantum-field-theory-based algorithms, as well as new\nphysical models for realising a large scale quantum computer with cold\nion traps, quantum optics (using photons and optical cavity),\ncondensed matter systems and solid state physics (meanwhile, the first\nNMR model had turned out to be a dead-end with respect to scaling; see\nDiVincenzo (2000)). The basic questions, however, remain open even\ntoday: (1) theoretically, can quantum algorithms efficiently solve\nclassically intractable problems? (2) operationally, can we actually\nrealise a large scale quantum computer to run these algorithms?" ], "subsection_title": "1.3 Milestones" } ] }, { "main_content": [ "\nIn this section we review the basic paradigm for quantum algorithms,\nnamely the quantum circuit model, which is composed of the basic\nquantum units of information (qubits) and the basic logical\nmanipulations thereof (quantum gates). For more detailed introductions\nsee Nielsen and Chuang (2000) and Mermin (2007)." ], "section_title": "2. Basics", "subsections": [ { "content": [ "\nThe qubit is the quantum analogue of the bit, the classical\nfundamental unit of information. It is a mathematical object with\nspecific properties that can be realised in an actual physical system\nin many different ways. Just as the classical bit has a state\n(either 0 or 1), a qubit also has a state. Yet contrary to the\nclassical bit, \\(\\lvert 0\\rangle\\) and \\(\\lvert 1\\rangle\\) are but two\npossible states of the qubit, and any linear combination\n(superposition) thereof is also physically possible. In\ngeneral, thus, the physical state of a qubit is the superposition\n\\(\\lvert\\psi \\rangle = \\alpha \\lvert 0\\rangle + \\beta \\lvert\n1\\rangle\\) (where \\(\\alpha\\) and \\(\\beta\\) are complex numbers). The\nstate of a qubit can be described as a vector in a two-dimensional\nHilbert space, a complex vector space (see the entry on\n quantum mechanics).\n The special states \\(\\lvert 0\\rangle\\) and \\(\\lvert 1\\rangle\\) are\nknown as the computational basis states, and form an\northonormal basis for this vector space. According to quantum theory,\nwhen we try to measure the qubit in this basis in order to determine\nits state, we get either \\(\\lvert 0\\rangle\\) with probability \\(\\lvert\n\\alpha\\rvert^2\\) or \\(\\lvert 1\\rangle\\) with probability \\(\\lvert\n\\beta\\rvert^2\\). Since \\(\\lvert \\alpha\\rvert^2 + \\lvert\\beta\\rvert^2 =\n1\\) (i.e., the qubit is a unit vector in the aforementioned\ntwo-dimensional Hilbert space), we may (ignoring the overall phase\nfactor) effectively write its state as \\(\\lvert \\psi \\rangle =\\)\ncos\\((\\theta)\\lvert 0\\rangle + e^{i\\phi}\\)sin\\((\\theta)\\lvert\n1\\rangle\\), where the numbers \\(\\theta\\) and \\(\\phi\\) define a point\non the unit three-dimensional sphere, as shown here. This sphere is\noften called the Bloch sphere, and it provides a useful means\nto visualise the state of a single qubit.", "\nSince \\(\\alpha\\) and \\(\\beta\\) are complex and therefore continuous\nvariables one might think that a single qubit is capable of storing an\ninfinite amount of information. When measured, however, it yields only\nthe classical result (0 or 1) with certain probabilities specified by\nthe quantum state. In other words, the measurement changes\nthe state of the qubit, “collapsing” it from a\nsuperposition to one of its terms. In fact one can prove (Holevo 1973)\nthat the amount of information actually retrievable from a single\nqubit (what Timpson (2013, 47ff.) calls its “accessible\ninformation”) is no more than one bit. If the qubit is\nnot measured, however, the amount of “hidden”\ninformation it “stores” (what Timpson calls its\n“specification information”) is conserved under its\n(unitary) dynamical evolution. This feature of quantum mechanics\nallows one to manipulate the information stored in unmeasured qubits\nwith quantum gates (i.e. unitary transformations), and is one of the\nsources for the putative power of quantum computers.", "\nTo see why, let us suppose we have two qubits at our disposal. If\nthese were classical bits, then they could be in four possible states\n(00, 01, 10, 11). Correspondingly, a pair of qubits has\nfour computational basis states (\\(\\lvert 00\\rangle\\),\n\\(\\lvert 01\\rangle\\), \\(\\lvert 10\\rangle\\), \\(\\lvert 11\\rangle)\\). But\nwhile a single classical two-bit register can store these numbers\nonly one at a time, a pair of qubits can also exist in a\nsuperposition of these four basis states, each with its own complex\ncoefficient (whose mod square, being interpreted as a probability, is\nnormalised). For example, using a “Hadamard\ngate”—which unitarily transforms a single qubit to the\nstate \\(\\frac{\\lvert 0\\rangle + \\lvert 1\\rangle}{\\sqrt 2}\\) whenever\nit is in the state \\(\\lvert 0\\rangle\\), and to the state\n\\(\\frac{\\lvert 0\\rangle - \\lvert 1\\rangle}{\\sqrt 2}\\) whenever it is\nin the state \\(\\lvert 1\\rangle\\)—we can transform the\n\\(n\\)-qubit state \\(\\lvert 0...01 \\rangle\\) as\nfollows:", "\nwhere \\(\\lvert - \\rangle =_{df} \\frac{| 0 \\rangle - | 1 \\rangle}{\\sqrt\n2}\\). The resulting state is a superposition of \\(2^n\\) terms and can\nbe imagined to “store” that many bits of (specification)\ninformation. The difficult task, however, is to use this information\nefficiently in light of the bound on the state’s accessible\ninformation." ], "subsection_title": "2.1 The Qubit" }, { "content": [ "\nClassical computational gates are Boolean logic gates that manipulate\ninformation stored in bits. In quantum computing such gates are\nrepresented by matrices, and can be visualised as rotations over the\nBloch sphere. This visualisation represents the fact that quantum\ngates are unitary operators, i.e., they preserve the norm of the\nquantum state (if \\(U\\) is a matrix describing a single qubit gate,\nthen \\(U^{\\dagger}U=I\\), where \\(U^{\\dagger}\\) is the adjoint\nof \\(U\\), obtained by transposing and then complex-conjugating \\(U)\\).\nIn classical computing some gates are “universal”. For\nexample the NAND gate is a gate that evaluates the function\n“not both A and B” over its two inputs. By stringing\ntogether a number of NAND gates it is possible to compute any\ncomputable function. Another universal gate is the NOR gate,\nwhich evaluates the function “not (A or B)”. In the\ncontext of quantum computing it was shown (DiVincenzo 1995) that\ntwo-qubit gates (i.e. which transform two qubits) are sufficient to\nrealise a general quantum circuit, in the sense that a circuit\ncomposed exclusively from a small set of one- and two-qubit gates can\napproximate to arbitrary accuracy any unitary transformation of \\(n\\)\nqubits. Barenco et. al. (1995) showed in particular that any\nmultiple qubit logic gate may be composed in this sense from a\ncombination of single-qubit gates and the two-qubit controlled-not\n(CNOT) gate, which either flips or preserves its\n“target” input bit depending on the state of its\n“control” input bit (specifically: in a CNOT gate\nthe output state of the target qubit is the result of an operation\nanalogous to the classical exclusive-OR (XOR) gate on the\ninputs). One general feature of quantum gates that distinguishes them\nfrom classical gates is that they are always reversible: the inverse\nof a unitary matrix is also a unitary matrix, and thus a quantum gate\ncan always be inverted by another quantum gate.", "\nUnitary gates manipulate information stored in the “quantum\nregister”—a quantum system—and in this sense\nordinary (unitary) quantum evolution can be regarded as a computation.\nIn order to read the result of this computation, however, the quantum\nregister must be measured. The measurement gate is a non-unitary gate\nthat “collapses” the quantum superposition in the register\nonto one of its terms with a probability corresponding to its complex\ncoefficient. Usually this measurement is done in the computational\nbasis (see the previous section), but since quantum mechanics allows\none to express an arbitrary state as a linear combination of basis\nstates, provided that the states are orthonormal (a condition that\nensures normalisation) one can in principle measure the\nregister in any arbitrary orthonormal basis. This, however,\ndoesn’t mean that measurements in different bases are equivalent\ncomplexity-wise. Indeed, one of the difficulties in constructing\nefficient quantum algorithms stems exactly from the fact that\nmeasurement collapses the state, and some measurements are much more\ncomplicated than others." ], "subsection_title": "2.2 Quantum Gates" }, { "content": [ "\nQuantum circuits are similar to classical computer circuits in that\nthey consist of wires and logical gates. The wires\nare used to carry the information, while the gates manipulate it (note\nthat the wires are abstract and do not necessarily correspond to\nphysical wires; they may correspond to a physical particle, e.g. a\nphoton, moving from one location to another in space, or even to\ntime-evolution). Conventionally, the input of the quantum circuit is\nassumed to be a number of qubits each initialised to a computational\nbasis state (typically \\(\\lvert 0\\rangle\\)). The output state of the\ncircuit is then measured in the computational basis, or in any other\narbitrary orthonormal basis. The first quantum algorithms (i.e.\nDeutsch-Jozsa, Simon, Shor and Grover) were constructed in this\nparadigm. Additional paradigms for quantum computing exist today that\ndiffer from the quantum circuit model in many interesting ways. So\nfar, however, they all have been demonstrated to be computationally\nequivalent to the circuit model (see below), in the sense that any\ncomputational problem that can be solved by the circuit model can be\nsolved by these new models with only a polynomial overhead in\ncomputational resources. This is analogous to the fact that in\nclassical computation every “reasonable” model can be\nefficiently simulated by any other. For discussion see Cuffaro (2018b,\n274)." ], "subsection_title": "2.3 Quantum Circuits" } ] }, { "main_content": [ "\nAlgorithm design is a highly complicated task, and in quantum\ncomputing, delicately leveraging the features of quantum mechanics in\norder to make our algorithms more efficient makes the task even more\ncomplicated. But before discussing this aspect of quantum algorithm\ndesign, let us first convince ourselves that quantum computers can be\nharnessed to perform standard, classical, computation without any\ncomputational speed-up. In some sense this is obvious, given the\nbelief in the universal character of quantum mechanics, and the\nobservation that any quantum computation that is diagonal in the\ncomputational basis, i.e., that involves no interference between the\nqubits, is effectively classical. Yet the demonstration that quantum\ncircuits can be used to simulate classical circuits is not\nstraightforward (recall that the former are always reversible while\nthe latter use gates which are in general irreversible). Indeed,\nquantum circuits cannot be used directly to simulate\nclassical computation, but the latter can still be simulated on a\nquantum computer using an intermediate gate, namely the\nToffoli gate. This universal classical gate has three input\nbits and three output bits. Two of the input bits are control bits,\nunaffected by the action of the gate. The third input bit is a target\nbit that is flipped if both control bits are set to 1, and otherwise\nis left alone. This gate is reversible (its inverse is itself), and by\nstringing a number of such gates together one can simulate any\nclassical irreversible circuit.", "\nConsequently, using the quantum version of the Toffoli gate\n(which by definition permutes the computational basis states similarly\nto the classical Toffoli gate) one can simulate, although\nrather tediously, irreversible classical logic gates with quantum\nreversible ones. Quantum computers are thus capable of performing any\ncomputation which a classical deterministic computer can do.", "\nWhat about probabilistic computation? Not surprisingly, a quantum\ncomputer can also simulate this type of computation by using another\nfamous quantum gate, namely the Hadamard gate, a single-qubit gate\nwhich receives as input the state \\(\\lvert 0\\rangle\\) and produces the\nstate \\(\\frac{\\lvert 0\\rangle + \\lvert 1\\rangle}{\\sqrt{2}}\\).\nMeasuring this output state yields \\(\\lvert 0\\rangle\\) or \\(\\lvert\n1\\rangle\\) with 50/50 probability, which can be used to simulate a\nfair coin toss.", "\nObviously, if quantum algorithms could be used only to simulate\nclassical algorithms, then the technological advancement in\ninformation storage and manipulation, encapsulated in\n“Moore’s law”, would have only trivial consequences\non computational complexity theory, leaving the latter unaffected by\nthe physical world. But while some computational problems will always\nresist quantum “speed-up” (in these problems the\ncomputation time depends on the input, and this feature will lead to a\nviolation of unitarity hence to an effectively classical computation\neven on a quantum computer—see Myers (1997) and Linden and\nPopescu (1998)), the hope is, nonetheless, that quantum algorithms may\nnot only simulate classical ones, but that they will actually\noutperform the latter in some cases, and in so doing help to\nre-define the abstract notions of tractability and intractability and\nviolate the physical Church-Turing thesis, at least as far as\ncomputational complexity is concerned." ], "section_title": "3 Quantum Algorithms", "subsections": [ { "content": [ "\nThe first quantum algorithms were designed to solve problems which\nessentially involve the use of an “oracle”, so let us\nbegin by explaining this term. Oracles are used by computer scientists\nas conceptual aids in the complexity-theoretic analysis of algorithms.\nWe can think of an oracle as a kind of imaginary magic black box\n(Arora and Barak (2009, 72–73); Aaronson (2013a, 29ff.)) to\nwhich, like the famous oracle at Delphi, one poses (yes or no)\nquestions. Unlike that ancient oracle, the oracles considered in\ncomputer science always return an answer in a single time\nstep. For example, we can imagine an oracle to determine whether a\ngiven Boolean formula is satisfiable or not: Given as input the\ndescription of a particular propositional formula, the oracle\noutputs—in a single time step—a single bit indicating\nwhether or not there is a truth-value assignment satisfying that\nformula. Obviously such a machine does not really\nexist—SAT is an NP-complete problem—but\nthat is not the point. The point of using such imaginary devices is to\nabstract away from certain “implementational details”\nwhich are for whatever reason deemed unimportant for the\ncomplexity-theoretic analysis of a given problem. For example,\nSimon’s problem (Simon 1994, see below) is that of determining\nthe period of a given function \\(f\\) that is periodic under bit-wise\nmodulo-2 addition. Relative to Simon’s problem, we judge the\ninternal complexity of \\(f\\) to be unimportant, and so abstract away\nfrom it by imagining that we have an oracle to evaluate it in a single\nstep. As useful as these conceptual devices are, however, their\nusefulness has limitations. To take one example, there are oracles\nrelative to which P = NP, as well as\noracles relative to which P \\(\\not =\\)\nNP. This (and many other) questions are not clarified\nby oracles (see Fortnow 1994).", "\nDeutsch (1989) asks the following question: Suppose we have a function\n\\(f\\) which can be either constant—i.e. such that it produces\nthe same output value for each of its possible inputs, or\nbalanced—i.e. such that the output of one half of its possible\ninputs is the opposite of the output of the other half. The particular\nexample considered is the function \\(f : \\{0,1\\} \\rightarrow\n\\{0,1\\}\\), which is constant if \\(f\\)(0) \\(= f\\)(1) and balanced if\n\\(f\\)(0) \\(\\ne f\\)(1). Classically it would take two\nevaluations of the function to tell whether it is one or the other.\nQuantumly, we can answer this question in one evaluation. For\nDeutsch, the explanation for this complexity reduction involves an\nappeal to “many computational worlds” (see section 5.1.1).\n Arguably, however, a fully satisfactory answer appeals only to the\nsuperposition principle and entanglement (Bub 2010).", "\nAfter initially preparing the first and second qubits of the computer\nin the state \\(\\lvert 0\\rangle\\lvert 0\\rangle\\), one then\n“flips” the second qubit using a “NOT” gate\n(i.e. a Pauli X operation) to \\(\\lvert 1 \\rangle\\),\nand then subjects each qubit to a Hadamard gate. We now send the two\nqubits through an oracle or ‘black box’ which we imagine\nas a unitary gate, \\(\\mathbf{U}_f\\), representative of the function\nwhose character (of being either constant or balanced) we wish to\ndetermine. We define \\(\\mathbf{U}_f\\) so that it takes inputs like\n\\(\\lvert x,y\\rangle\\) to \\(\\lvert x, y\\oplus f (x)\\rangle\\), where\n\\(\\oplus\\) is addition modulo two (i.e. exclusive-or). The first qubit\nis then fed into a further Hadamard gate, and the final output of the\nalgorithm (prior to measurement) is the state: \\[\\pm\\lvert f(0)\\oplus\nf(1)\\rangle~\\lvert - \\rangle,\\] where \\(\\lvert - \\rangle =_{df}\n\\frac{| 0 \\rangle - | 1 \\rangle}{\\sqrt 2}\\). Since \\(f\\)(0)\\(\\oplus\nf\\)(1) is 0 if the function is constant and 1 if the function is\nbalanced, a single measurement of the first qubit suffices to retrieve\nthe answer to our original question regarding the function’s\nnature. And since there are two possible constant functions and two\npossible balanced functions from \\(f : \\{0,1\\} \\rightarrow \\{0,1\\}\\),\nwe can characterise the algorithm as distinguishing, using only one\noracle call, between two quantum disjunctions without finding out the\ntruth values of the disjuncts themselves, i.e. without\ndetermining which balanced or which constant\nfunction \\(f\\) is (Bub 2010).", "\nA generalisation of Deutsch’s problem, called the Deutsch-Jozsa\nproblem (Deutsch and Jozsa 1992), enlarges the class of functions\nunder consideration so as to include all of the functions\n\\(f:\\{0,1\\}^n\\to\\{0,1\\}\\), i.e. rather than only considering \\(n =\n1\\). The best deterministic classical algorithm for determining\nwhether a given such function is constant or balanced requires\n\\(\\frac{2^{n}}{2}+1\\) queries to an oracle in order to solve this\nproblem. In a quantum computer, however, we can answer the question\nusing one oracle call. Generalising our conclusion regarding\nthe Deutsch algorithm, we may say that the Deutsch-Jozsa algorithm\nallows one to evaluate a global property of the function in one\nmeasurement because the output state is a superposition of balanced\nand constant states such that the balanced states all lie in a\nsubspace orthogonal to the constant states and can therefore be\ndistinguished from the latter in a single measurement (Bub 2006a)", "\nSuppose we have a Boolean function \\(f\\) on \\(n\\) bits that is 2-to-1,\ni.e. that takes \\(n\\) bits to \\(n-1\\) bits in such a way that for\nevery \\(n\\)-bit integer \\(x_1\\) there is an \\(n\\)-bit integer \\(x_2\\)\nfor which \\(f (x_{1}) = f (x_{2})\\). The function is moreover periodic\nin the sense that \\(f(x_1)\\) = \\(f(x_2)\\) if and only if \\(x_1 = x_2\n\\oplus a\\), where \\(\\oplus\\) designates bit-wise modulo 2 addition and\n\\(a\\) is an \\(n\\)-bit nonzero number called the period of\n\\(f\\). Simon’s problem is the problem to find \\(a\\) given \\(f\\).\nRelative to an oracle \\(U_f\\) which evaluates \\(f\\) in a single step,\nSimon’s quantum algorithm (Simon 1994) finds the period of \\(f\\)\nin a number of oracle calls that grows only linearly with the length\nof \\(n\\), while the best known classical algorithm requires an\nexponentially greater number of oracle calls. Simon’s algorithm\nreduces to Deutsch’s algorithm when \\(n=2\\), and can be regarded\nas an extension of the latter, in the sense that in both cases a\nglobal property of a function is evaluated in no more than a\n(sub-)polynomial number of oracle invocations, owing to the fact that\nthe output state of the computer just before the final measurement is\ndecomposed into orthogonal subspaces, only one of which contains the\nproblem’s solution. Note that one important difference between\nDeutsch’s and Simon’s algorithms is that the former yields\na solution with certainty, whereas the latter only yields a solution\nwith probability very close to 1. For more on the logical analysis of\nthese first quantum-circuit-based algorithms see Bub (2006a) and Bub\n(2010).", "\nThe algorithms just described, although demonstrating the potential\nsuperiority of quantum computers over their classical counterparts,\nnevertheless deal with apparently unimportant computational problems.\nMoreover the speed-ups in each of them are only relative to their\nrespective oracles. It is doubtful whether research into quantum\ncomputing would have attracted so much attention and evolved to its\ncurrent status if its merit could be demonstrated only with these\nproblems. But in 1994, Peter Shor realised that Simon’s\nalgorithm could be harnessed to solve a much more interesting and\ncrucial problem, namely factoring, which lies at the heart of\ncurrent cryptographic protocols such as RSA (Rivest, Shamir, and\nAdleman 1978). Shor’s algorithm has turned quantum computing\ninto one of the most exciting research domains in quantum\nmechanics.", "\nShor’s algorithm exploits the ingenious number theoretic\nargument that two prime factors \\(p,q\\) of a positive integer \\(N=pq\\)\ncan be found by determining the period of a function \\(f(x) = y^x\n\\textrm{mod} N,\\) for any \\(y < N\\) which has no common factors\nwith \\(N\\) other than 1 (Nielsen and Chuang 2000 App. 4). The period\n\\(r\\) of \\(f(x)\\) depends on \\(y\\) and \\(N\\). Once one knows it, one\ncan factor \\(N\\) if \\(r\\) is even and \\(y^{\\,\\frac{r}{2}} \\neq -1\\)\nmod \\(N\\), which will be jointly the case with probability greater\nthan \\(\\frac{1}{2}\\) for any \\(y\\) chosen randomly (if not, one\nchooses another value of \\(y\\) and tries again). The factors of \\(N\\)\nare the greatest common divisors of \\(y^{\\,\\frac{r}{2}} \\pm 1\\) and\n\\(N\\), which can be found in polynomial time using the well known\nEuclidean algorithm. In other words, Shor’s remarkable result\nrests on the discovery that the problem of factoring reduces\nto the problem of finding the period of a certain periodic function\n\\(f: Z_{n} \\rightarrow Z_{N}\\), where \\(Z_{n}\\) is the additive group\nof integers mod \\(n\\) (Note that \\(f(x) = y^{x}\\ \\textrm{mod}\\ N\\) so\nthat \\(f(x+r) = f(x)\\) if \\(x+r \\le n\\). The function is periodic if\n\\(r\\) divides \\(n\\) exactly, otherwise it is almost periodic). That\nthis problem can be solved efficiently by a quantum computer is hinted\nat by Simon’s algorithm, which considers the more restricted\ncase of functions periodic under bit-wise modulo-2 addition as opposed\nto the periodic functions under ordinary addition considered here.", "\nShor’s result is the most dramatic example so far of quantum\n“speed-up” of computation, notwithstanding the fact that\nfactoring is believed to be only in NP and\nnot in NP-complete (see Aaronson 2013a, 64–66).\nTo verify whether \\(n\\) is prime takes a number of steps which is a\npolynomial in \\(\\log_{2}n\\) (the binary encoding of a natural number\n\\(n\\) requires \\(\\log_{2}n\\) resources). But nobody knows how to\nfactor numbers into primes in polynomial time, and the best classical\nalgorithms we have for this problem are sub-exponential. This is yet\nanother open problem in the theory of computational complexity. Modern\ncryptography and Internet security protocols are based on these facts\n(Giblin 1993): It is easy to find large prime numbers fast, and it is\nhard to factor large composite numbers in any reasonable amount of\ntime. The discovery that quantum computers can solve\nfactoring in polynomial time has had, therefore, a dramatic\neffect. The implementation of the algorithm on a physical machine\nwould have economic, as well as scientific consequences (Alléaume\net al. 2014).", "\nIn a brilliant undercover operation, Agent 13 has managed to secure\ntwo crucial bits of information concerning the whereabouts of the\narch-villain Siegfried: the phone number of the secret hideout from\nwhich he intends to begin carrying out KAOS’s plans for world\ndomination, and the fact that the number is a listed one (apparently\nan oversight on Siegfried’s part). Unfortunately you and your\ncolleagues at CONTROL have no other information besides this. Can you\nfind Siegfried’s hideout using only this number and a phone\ndirectory? In theoretical computer science this task is known as an\nunstructured search. In the worst case, if there are \\(n\\) entries in\nthe directory, the computational resources required to find the entry\nwill be linear in \\(n\\). Grover (1996) showed how this task could be\ndone with a quantum algorithm using computational resources on the\norder of only \\(\\sqrt{n}\\). Agreed, this “speed-up” is\nmore modest than Shor’s since unstructured search belongs to the\nclass \\(\\mathbf{P}\\), but contrary to Shor’s case, where the\nclassical complexity of factoring is still unknown, here the\nsuperiority of the quantum algorithm, however modest, is definitely\nprovable. That this quadratic “speed-up” is also\nthe optimal quantum “speed-up” possible for this\nproblem was proved by Bennett, Bernstein, Brassard, & Vazirani\n(1997).", "\nAlthough the purpose of Grover’s algorithm is usually described\nas “searching a database”, it may be more accurate to\ndescribe it as “inverting a function”. Roughly speaking,\nif we have a function \\(y=f(x)\\) that can be evaluated on a quantum\ncomputer, Grover’s algorithm allows us to calculate \\(x\\) given\n\\(y\\). Inverting a function is related to searching a database because\nwe could come up with a function that produces a particular value of\n\\(y\\) if \\(x\\) matches a desired entry in a database, and another\nvalue of \\(y\\) for other values of \\(x\\). The applications of this\nalgorithm are far-reaching (even more so than foiling\nSiegfried’s plans for world domination). For example, it can be\nused to determine efficiently the number of solutions to an \\(N\\)-item\nsearch problem, hence to perform exhaustive searches on a class of\nsolutions to an NP-complete problem and substantially\nreduce the computational resources required for solving it." ], "subsection_title": "3.1 Quantum-Circuit-Based Algorithms" }, { "content": [ "\nMany decades have passed since the discovery of the first quantum\nalgorithm, but so far little progress has been made with respect to\nthe “Holy Grail” of solving an\nNP-complete problem with a quantum-circuit. In 2000 a\ngroup of physicists from MIT and Northeastern University (Farhi et al.\n2000) proposed a novel paradigm for quantum computing that differs\nfrom the circuit model in several interesting ways. Their goal was to\ntry to solve with this algorithm an instance of the\nsatisfiability problem (see above), one of the most famous\nNP-complete problems (Cook 1971).", "\nAccording to the adiabatic theorem (e.g. Messiah 1961) and given\ncertain specific conditions, a quantum system remains in its lowest\nenergy state, known as the ground state, along an adiabatic\ntransformation in which the system is deformed slowly and smoothly\nfrom an initial Hamiltonian to a final Hamiltonian (as an\nillustration, think of moving a sleeping baby in a cradle from the\nliving room to the bedroom. If the transition is done slowly and\nsmoothly enough, and if the baby is a sound sleeper, then it will\nremain asleep during the whole transition). The most important\ncondition in this theorem is the energy gap between the ground state\nand the next excited state (in our analogy, this gap reflects how\nsound asleep the baby is). Being inversely proportional to the\nevolution time \\(T\\), this gap controls the latter. If this gap exists\nduring the entire evolution (i.e., there is no level crossing between\nthe energy states of the system), the theorem dictates that in the\nadiabatic limit (when \\(T\\rightarrow \\infty)\\) the system will remain\nin its ground state. In practice, of course, \\(T\\) is always finite,\nbut the longer it is, the less likely it is that the system will\ndeviate from its ground state during the time evolution.", "\nThe crux of the quantum adiabatic algorithm which rests on this\ntheorem lies in the possibility of encoding a specific instance of a\ngiven decision problem in a certain Hamiltonian (this can be done by\ncapitalising on the well-known fact that any decision problem can be\nderived from an optimisation problem by incorporating into it a\nnumerical bound as an additional parameter). One then starts the\nsystem in a ground state of another Hamiltonian which is easy to\nconstruct, and slowly evolves the system in time, deforming it towards\nthe desired Hamiltonian. According to the quantum adiabatic theorem\nand given the gap condition, the result of such a physical process is\nanother energy ground state that encodes the solution to the desired\ndecision problem. The adiabatic algorithm is thus a rather ‘laid\nback’ algorithm: one needs only to start the system in its\nground state, deform it adiabatically, and measure its final ground\nstate in order to retrieve the desired result. But whether or not this\nalgorithm yields the desired “speed-up” depends crucially\non the behaviour of the energy gap as the number of degrees of freedom\nin the system increases. If this gap decreases exponentially with the\nsize of the input, then the evolution time of the algorithm will\nincrease exponentially; if the gap decreases polynomially, the\ndecision problem so encoded could be solved efficiently in polynomial\ntime. Although physicists have been studying spectral gaps for almost\na century, they have never done so with quantum computing in mind. How\nthis gap behaves in general remains thus far an open\nempirical question.", "\nThe quantum adiabatic algorithm holds much promise (Farhi et al.\n2001). It has been shown (Aharonov et al. 2008) to be polynomially\nequivalent to the circuit model (that is, each model can simulate the\nother with only polynomial overhead in the number of qubits and\ncomputational steps), but the caveat that is sometimes left\nunmentioned is that its application to an intractable computational\nproblem may sometimes require solving another, as intractable a task\n(this general worry was first raised by a philosopher; see Pitowsky\n(1990)). Indeed, Reichardt (2004) has shown that there are simple\nproblems for which the algorithm will get stuck in a local minimum, in\nwhich there are exponentially many eigenvalues all exponentially close\nto the ground state energy, so applying the adiabatic theorem, even\nfor these simple problems, will take exponential time, and we are back\nto square one." ], "subsection_title": "3.2 Adiabatic Algorithms" }, { "content": [ "\nMeasurement-based algorithms differ from circuit algorithms in that\ninstead of employing unitary evolution as the basic mechanism for the\nmanipulation of information, these algorithms essentially make use of\nnon-unitary measurements in the course of a computation. They are\nespecially interesting from a foundational perspective because they\nhave no evident classical analogues and because they offer new insight\non the role of\n entanglement\n in quantum computing (Jozsa 2006). They may also have interesting\nengineering-related consequences, suggesting a different kind of\ncomputer architecture which is more fault tolerant (Nielsen and Dawson\n2005).", "\nMeasurement-based algorithms fall into two categories. The first is\nteleportation quantum computing (based on an idea of Gottesman and\nChuang (1999), and developed into a computational model by Nielsen\n(2003) and Leung (2004)). The second is the “one way quantum\ncomputer”, known also as the “cluster state” model\n(Raussendorf and Briegel 2002). The interesting feature of these\nmodels is that they are able to simulate arbitrary quantum dynamics,\nincluding unitary dynamics, using basic non-unitary measurements. The\nmeasurements are performed on a pool of highly entangled states and\nare adaptive, i.e., each measurement is done in a different basis\nwhich is calculated classically, given the result of earlier\nmeasurements.", "\nExotic models such as these might seem redundant, especially since\nthey have been shown to be polynomially equivalent to the standard\ncircuit model in terms of computational complexity (Raussendorf,\nBrowne, and Briegel 2003). Their merit, however, lies in the\nfoundational lessons they drive home: with these models the separation\nbetween the classical (i.e., the calculation of the next\nmeasurement-basis) and quantum (i.e., measurements on the entangled\nqubits) parts of the computation becomes evident, hence it may be\neasier to pinpoint the quantum resources that are responsible for the\nputative “speed-up”." ], "subsection_title": "3.3 Measurement-Based Algorithms" }, { "content": [ "\nAnother exotic model for quantum computing which has attracted a lot\nof attention, especially from Microsoft inc. (Freedman 1998), is the\nTopological Quantum Field Theory model. In contrast to the easily\nvisualisable circuit model, this model resides in the most abstract\nreaches of theoretical physics. The exotic physical systems TQFT\ndescribes are topological states of matter. That the formalism of TQFT\ncan be applied to computational problems was shown by Witten (1989)\nand the idea was later developed by others. The model has been proved\nto be efficiently simulatable on a standard quantum computer\n(Freedman, Kitaev, and Wang 2002; Aharonov, Jones, and Landau 2009).\nIts main merit lies in its high tolerance to the errors which are\ninevitably introduced in the implementation of a large scale quantum\ncomputer (see below). Topology is especially helpful here because many\nglobal topological properties are, by definition, invariant under\ndeformation, and given that most errors are local, information encoded\nin topological properties is robust against them." ], "subsection_title": "3.4 Topological-Quantum-Field-Theory (TQFT) Algorithms" } ] }, { "main_content": [ "\nThe quantum computer might be the theoretician’s dream, but as\nfar as experimentalists are concerned, its realisation is a nightmare.\nThe problem is that while some prototypes of the simplest elements\nneeded to build a quantum computer have already been implemented in\nthe laboratory, it is still an open question how to combine these\nelements into scalable systems (see Van Meter and Horsman 2013).\nShor’s algorithm may break RSA encryption, but it will remain an\nanecdote if the largest number that it can factor is 15. In the\ncircuit-based model the problem is to achieve a scalable quantum\nsystem that at the same time will allow one to (1) robustly represent\nquantum information with (2) a time to decoherence significantly\nlonger than the length of the computation, (3) implement a universal\nfamily of unitary transformations, (4) prepare a fiducial initial\nstate, and (5) measure the output result (these are DiVincenzo\n(2000)’s five criteria). Alternative paradigms may trade some of\nthese requirements with others, but the gist will remain the same,\ni.e., one would have to achieve control of one’s quantum system\nin such a way that the system will remain “quantum” albeit\nmacroscopic or at least mesoscopic in its dimensions.", "\nIn order to deal with these challenges, several ingenious solutions\nhave been devised, including quantum error correction codes and fault\ntolerant computation (Shor 1995; Shor and DiVincenzo 1996; Aharonov\nand Ben-Or 1997; Raussendorf, Harrington, and Goyal 2008; Horsman et\nal. 2012; De Beaudrap and Horsman 2019) which can dramatically reduce\nthe spread of errors during a ‘noisy’ quantum computation.\nAn important criticism of these active error correction schemes,\nhowever, is that they are devised for a very unrealistic noise model\nwhich treats the computer as quantum and the environment as classical\n(Alicki, Lidar, and Zinardi 2006). Once a more realistic noise model\nis allowed, the feasibility of large scale, fault tolerant and\ncomputationally superior quantum computers is less clear (Hagar 2009;\nTabakin 2017).", "\nIn the near term, a promising avenue for realising a quantum advantage\nin a limited number of problem domains is the Noisy Intermediate-Scale\nQuantum (NISQ) paradigm (Preskill 2018). The NISQ paradigm does not\nemploy any error correction mechanisms (postponing the problem to\nimplement scalable versions of these to the future) but rather focuses\non building computational components, and on tackling computational\nproblems, which are inherently more resilient to noise. These include,\nfor example, certain classes of optimisation problems, quantum\nsemidefinite programming, and digital quantum simulation (Tacchino et\nal. 2019). A caveat here is that as the resiliency to noise of a\ncircuit increases, the more classically it behaves. Nevertheless,\nresearch into NISQ computing is believed to be on track to realise a\n50–100 qubit machine—large enough to achieve a quantum advantage\nover known classical alternatives for the envisioned\napplications—within the next 5–10 years.", "\nAs mentioned, one of the envisioned applications of NISQ computing is\nfor digital quantum simulation (i.e. simulation using a gate-based\nprogrammable quantum computer). There is an older tradition of\nanalog quantum simulation, however, wherein one utilises a\nquantum system whose dynamics resemble the dynamics of a particular\ntarget system of interest. Although it is believed that digital\nquantum simulation will eventually supersede it, the field of analog\nquantum simulation has progressed substantially in the years since it\nwas first proposed, and analog quantum simulators have already been\nused to study quantum dynamics in regimes thought to be beyond the\nreach of classical simulators (see, e.g., Bernien et al. (2017); for\nfurther discussion of the philosophical issues involved, see\nHangleiter, Carolan, and Thébault (2017))." ], "section_title": "4 Realisations", "subsections": [] }, { "main_content": [], "section_title": "5. Philosophical Questions", "subsections": [ { "content": [ "\nNotwithstanding the excitement around the discovery of Shor’s\nalgorithm, and putting aside the presently insurmountable problem of\npractically realising and implementing a large scale quantum computer,\na crucial theoretical question remains open: What physical resources\nare responsible for quantum computing’s putative power? Put\nanother way, what are the essential features of quantum mechanics that\nwould in principle allow one to solve problems or simulate certain\nsystems more efficiently than on a classical computer? A number of\ncandidates have been put forward. Fortnow (2003) posits interference\nas the key, though it has been suggested that this is not truly a\nquantum phenomenon (Spekkens 2007). Jozsa (1997) and many others point\nto entanglement, although there are purported counter-examples to this\nthesis (see, e.g., Linden and Popescu (1999), Gottesman (1999), Biham\net al. (2004), and finally see Cuffaro (2017) for a philosophical\ndiscussion). Howard et al. (2014) appeal to quantum contextuality. For\nBub (2010) the answer lies in the logical structure of quantum\nmechanics (cf. Pitowsky 1989). Duwell (2018) argues for quantum\nparallelism, and for Deutsch (1997) and Hewitt-Horsman (2009) it is\n“parallel worlds” which are the resource.", "\nSpeculative as it may seem, the question “what is\nquantum in quantum computing?” has significant\npractical consequences. One of the embarrassments of quantum computing\nis the paucity of quantum algorithms which have actually been\ndiscovered. It is almost certain that one of the reasons for this is\nthe lack of a full understanding of what makes a quantum computer\nquantum (see also Preskill (1998) and Shor (2004)). As an ultimate\nanswer to this question one would like to have something similar to\nBell’s famous\n theorem,\n i.e., a succinct crisp statement of the fundamental difference\nbetween quantum and classical systems. Quantum computers,\nunfortunately, do not seem to allow such a simple characterisation\n(see Cuffaro 2017, 2018a). Quantum computing skeptics (Levin 2003)\nhappily capitalise on this puzzle: If no one knows why\nquantum computers are superior to classical ones, how can we be sure\nthat they are, indeed, superior?", "\nThe answer that has tended to dominate the popular literature on\nquantum computing is motivated by evolutions such as: ", "\nwhich were common to many early quantum algorithms. Note the\nappearance that \\(f\\) is evaluated for each of its possible inputs\nsimultaneously. The idea that we should take this at face\nvalue—that quantum computers actually do compute a\nfunction for many different input values simultaneously—is what\nDuwell (2018) calls the Quantum Parallelism Thesis\n(QPT). For Deutsch, who accepts it as true, the only reasonable\nexplanation for the QPT is that the many\nworlds interpretation (MWI) of quantum mechanics is also true. For\nDeutsch, a quantum computer in superposition, like any other quantum\nsystem, exists in some sense in many classical universes\nsimultaneously. These provide the physical arena within which the\ncomputer effects its parallel computations. This conclusion is\ndefended by Hewitt-Horsman (2009) and by Wallace (2012). Wallace\nnotes, however, that the QPT—and hence the explanatory need for\nmany worlds—may not be true of all or even most quantum\nalgorithms.", "\nFor Steane (2003), in contrast, quantum computers are not well\ndescribed in terms of many worlds or even quantum parallelism. Among\nother things, Steane argues that the motivation for the QPT is at\nleast partly due to misleading aspects of the standard quantum\nformalism. Additionally, comparing the information actually produced\nby quantum and classical algorithms (state collapse entails that only\none evaluation instance in (2) is ever accessible, while a classical\ncomputer must actually produce every instance) suggests that quantum\nalgorithms perform not more but fewer, cleverer, computations than\nclassical algorithms (see, also, section 5.1.2 below).", "\nAnother critic is Duwell, who (contra Steane) accepts the QPT (Duwell\n2018a), but nevertheless denies that it uniquely supports the MWI\n(Duwell 2007). Considering the phase relations between the terms in a\nsuperposition such as (2) is crucially important when evaluating a\nquantum algorithm’s computational efficiency. Phase relations,\nhowever, are global properties of a state. Thus a quantum computation,\nDuwell argues, does not consist solely of local parallel\ncomputations. But in this case, the QPT does not uniquely support the\nMWI over other explanations.", "\nDefending the MWI, Hewitt-Horsman (2009) argues (contra Steane) that\nto state that quantum computers do not actually generate each of the\nevaluation instances represented in (2) is false according to the\nview: on the MWI such information could be extracted in principle\ngiven sufficiently advanced technology. Further, Hewitt-Horsman\nemphasises that the MWI is not motivated simply by a suggestive\nmathematical representation. Worlds on the MWI are defined according\nto their explanatory usefulness, manifested in particular by their\nstability and independence over the time scales relevant to the\ncomputation. Wallace (2012) argues similarly.", "\nCuffaro (2012) and Aaronson (2013b) point out that the Many Worlds\nExplanation of Quantum Computing (MWQC) and the MWI are not actually\nidentical. The latter employs\n decoherence\n as a criterion for distinguishing macroscopic worlds from one\nanother. Quantum circuit model algorithms, however, utilise\ncoherent superpositions. To distinguish computational worlds,\ntherefore, one must weaken the decoherence criterion, but Cuffaro\nargues that this move is ad hoc. Further, Cuffaro argues that the MWQC\nis for all practical purposes incompatible with\n measurement based computation,\n for even granting a weakened world identification criterion, there is\nno natural way in this model to identify worlds that are stable and\nindependent in the way required.", "\nEven if we could rule out the MWQC, the problem of finding the\nphysical resource(s) responsible for quantum “speed-up”\nwould remain a difficult one. Consider a solution of a decision\nproblem, say satisfiability, with a quantum algorithm based\non the circuit model. What we are given here as input is a proposition\nin the propositional calculus and we have to decide whether it has a\nsatisfying truth assignment. As Pitowsky (2002) shows, the quantum\nalgorithm appears to solve this problem by testing all \\(2^{n}\\)\nassignments “at once” as suggested by (2), yet this\nquantum ‘miracle’ helps us very little since, as\npreviously mentioned, any measurement performed on the output state\ncollapses it, and if there is one possible truth assignment that\nsolves this decision problem, the probability of retrieving it is\n\\(2^{-n}\\), just as in the case of a classical probabilistic Turing\nmachine which guesses the solution and then checks it.\nPitowsky’s conclusion (echoed, as we saw, by Steane (2003) and\nDuwell (2007)) is that in order to enhance computation with quantum\nmechanics we must construct ‘clever’ superpositions that\nincrease the probability of successfully retrieving the result far\nmore than that of a pure guess. Shor’s algorithm and the class\nof algorithms that evaluate a global property of a function\n(this class is known as the hidden subgroup class of\nalgorithms) are (so far) a unique example of both a construction of\nsuch ‘clever’ superpositions and a retrieval of the\nsolution in polynomial time. The quantum adiabatic algorithm may give\nus similar results, contingent upon the existence of an energy gap\nthat decreases polynomially with the input.", "\nThis question also raises important issues about how to measure the\ncomplexity of a given quantum algorithm. The answer differs, of\ncourse, according to the particular model at hand. In the adiabatic\nmodel, for example, one needs only to estimate the energy gap\nbehaviour and its relation to the input size (encoded in the number of\ndegrees of freedom of the Hamiltonian of the system). In the\nmeasurement-based model, one counts the number of measurements needed\nto reveal the solution that is hidden in the input cluster state\n(since the preparation of the cluster state is a polynomial process,\nit does not add to the complexity of the computation). But in the\ncircuit model things are not as straightforward. After all, the whole\nof the quantum-circuit-based computation can be be simply represented\nas a single unitary transformation from the input state to\nthe output state.", "\nThis feature of the quantum circuit model supports the conjecture that\nthe power of quantum computers, if any, lies not in quantum dynamics\n(i.e., in the Schrödinger equation), but rather in the quantum\nstate, or the wave function. Another argument in favour of this\nconjecture is that the Hilbert subspace “visited” during a\nquantum computational process is, at any moment, a linear space\nspanned by all of the vectors in the total Hilbert space which have\nbeen created by the computational process up to that moment. But this\nHilbert subspace is thus a subspace spanned by a polynomial number of\nvectors and is thus at most a polynomial subspace of the total Hilbert\nspace. A classical simulation of the quantum evolution on a Hilbert\nspace with polynomial number of dimensions (that is, a Hilbert space\nspanned by a number of basis vectors which is polynomial in the number\nof qubits involved in the computation), however, can be carried out in\na polynomial number of classical computations. Were quantum\ndynamics the sole ingredient responsible to the efficiency of\nquantum computing, the latter could be mimicked in a polynomial number\nof steps with a classical computer (see, e.g. Vidal 2003).", "\nThis is not to say that quantum computation is no more powerful than\nclassical computation. The key point, of course, is that one does not\nend a quantum computation with an arbitrary superposition, but aims\nfor a very special, ‘clever’ state—to use\nPitowsky’s term. Quantum computations may not always be\nmimicked with a classical computer because the characterisation of the\ncomputational subspace of certain quantum states is difficult, and it\nseems that these special, ‘clever’, quantum states cannot\nbe classically represented as vectors derivable via a quantum\ncomputation in an optimal basis, or at least that one cannot do so in\nsuch way that would allow one to calculate the outcome of the final\nmeasurement made on these states.", "\nConsequently, in the quantum circuit model one should count the number\nof computational steps in the computation not by counting the number\nof transformations of the state, but by counting the number of one- or\ntwo-qubit local transformations that are required to create the\n‘clever’ superposition that ensures the desired\n“speed-up”. (Note that Shor’s algorithm, for\nexample, involves three major steps in this context: First, one\ncreates the ‘clever’ entangled state with a set of unitary\ntransformations. The result of the computation—a global property\nof a function—is now ‘hidden’ in this state; second,\nin order to retrieve this result, one projects it on a subspace of the\nHilbert space, and finally one performs another set of unitary\ntransformations in order to make the result measurable in the original\ncomputational basis. All these steps count as\ncomputational steps as far as the efficiency of the algorithm\nis concerned. See also Bub (2006b).) The trick is to perform these\nlocal one- or two-qubit transformations in polynomial time, and it is\nlikely that it is here where the physical power of quantum computing\nmay be found." ], "subsection_title": "5.1 What is Quantum in Quantum Computing?" }, { "content": [ "\nThe quantum information revolution has prompted several physicists and\nphilosophers to claim that new insights can be gained from the rising\nnew science into conceptual problems in the foundations of quantum\nmechanics (see, e.g., Bub (2016), Chiribella and Spekkens (2016); for\nresponses and commentaries, see, e.g., Myrvold (2010), Timpson (2013),\nFelline (2016), Cuffaro (forthcoming), Duwell (forthcoming), Felline\n(forthcoming-a), Henderson (forthcoming), Koberinski and Müller\n(2018)). Yet while one of the most famous foundational problems in\nquantum mechanics, namely\n the quantum measurement problem,\n remains unsolved even within quantum information theory (see Hagar\n (2003), Hagar and Hemmo (2006), and Felline (forthcoming-b) for a\n critique of the quantum information theoretic approach to the\n foundations of quantum mechanics and the role of the quantum\n measurement problem in this context), some quantum information\n theorists dismiss it as a philosophical quibble (Fuchs 2002). Indeed,\n in quantum information theory the concept of\n “measurement” is taken as a primitive, a “black\n box” which remains unanalysed. The measurement problem itself,\n furthermore, is regarded as a misunderstanding of quantum theory. But\n recent advances in the realisation of a large scale quantum computer\n may eventually prove quantum information theorists wrong: Rather than\n supporting the dismissal of the quantum measurement problem, these\n advances may surprisingly lead to its empirical solution.", "\nThe speculative idea is the following. As it turns\nout, collapse theories—one form of\nalternatives to quantum theory which aim to solve the measurement\nproblem—modify Schrödinger’s equation and give\ndifferent predictions from quantum theory in certain specific\ncircumstances. These circumstances can be realised, moreover,\nif decoherence effects can be\nsuppressed (Bassi, Adler, & Ippoliti 2004). Now one of the most\ndifficult obstacles that await the construction of a large scale\nquantum computer is its robustness against decoherence effects (Unruh\n1995). It thus appears that the technological capabilities required\nfor the realisation of a large scale quantum computer are potentially\nrelated to those upon which the distinction between “true”\nand “false” collapse (Pearle 1997), i.e., between collapse\ntheories and environmentally induced decoherence, is\ncontingent. Consequently the physical realisation of a large-scale\nquantum computer, if it were of the right architecture, could\npotentially shed light on one of the long standing conceptual problems\nin the foundations of the theory, and if so this would serve as yet\nanother example of experimental metaphysics (the term was coined by\nAbner Shimony to designate the chain of events that led\nfrom the EPR argument\nvia Bell’s theorem to\nAspect’s experiments). Note, however, that as just mentioned,\none would need to consider the computer’s architecture before\nmaking any metaphysical conclusions. The computer architecture is\nimportant because while dynamical collapse theories tend to collapse\nsuperpositions involving the positions of macroscopic quantities of\nmass, they tend not to collapse large complicated superpositions of\nphoton polarisation or spin." ], "subsection_title": "5.2 Experimental Metaphysics?" }, { "content": [ "\nIs quantum mechanics compatible with the principle of causality? This\nis an old question—indeed one of the very first interpretational\nquestions confronted by the early commentators on the theory (Hermann\n2017; Schlick 1961, 1962). The contemporary literature continues to\nexhibit considerable skepticism in regards to the prospects of\nexplaining quantum phenomena causally (Hausman & Woodward 1999;\nVan Fraassen 1982; Woodward 2007), or at any rate locally\ncausally, especially in the wake\nof Bell’s theorem (Myrvold\n2016). As a result of some fascinating theoretical work (Allen,\nBarrett, Horsman, Lee, & Spekkens 2017; Costa & Shrapnel 2016;\nShrapnel 2017), however, it seems that the prospects for a locally\ncausal explanation of quantum phenomena are not quite as hopeless as\nthey may initially have seemed, at least in the context of\nan interventionist theory of\ncausation. This is not to say that decades of physical and\nphilosophical investigations into the consequences of Bell’s\ntheorem have all been mistaken, of course. For one thing, the\ninterventionist frameworks utilised in this new work are\noperationalist, thus the relevance of this work to so-called hidden\nvariables theories of quantum mechanics is unclear. Second, the\ninterventionist frameworks utilised are not classical, and neither is\nthe kind of causality they explicate. Indeed, in regard to the latter\npoint, it is arguably the key insight emerging from this work that the\nframeworks previously utilised for analysing interventionist causation\nin the quantum context are inappropriate to that context. In contrast\nto a classical interventionist framework in which events are thought\nof as primitive (i.e. as not further analysable), events in these\ngeneralised frameworks are characterised as processes with\nassociated inputs and outputs. Specifically, one characterises quantum\nevents using a concept from quantum computation and information theory\ncalled a quantum channel. And within this generalised\ninterventionist framework, causal models of quantum phenomena can be\ngiven which do not need to posit non-local causal influences, and\nwhich satisfy certain other desiderata typically required in a causal\nmodel (in particular that such a model respect the causal Markov\ncondition and that it not require ‘fine-tuning’; see\nShrapnel (2017))." ], "subsection_title": "5.3 Quantum Causality" }, { "content": [ "\nPhysics is traditionally conceived as a primarily\n“theoretical” activity, in the sense that it is generally\nthought to be the goal of physics to tell us, even if only indirectly\n(Fuchs (2002), pp. 5–6, Fuchs (2010), pp. 22–3), what the world is\nlike independently of ourselves. This is not the case with every\nscience. Chemistry, for example, is arguably best thought of as a\n“practically” oriented discipline concerned with the ways\nin which systems can be manipulated for particular purposes\n(Bensaude-Vincent (2009)). Even within physics, there are\nsub-disciplines which are best construed in this way (Myrvold 2011;\nWallace 2014; Ladyman 2018), and indeed, some (though at present these\nare still a minority) have even sought to (re-)characterise physics as\na whole in something like this way, i.e. as a science of possible as\nopposed to impossible transformations (Deutsch 2013).", "\nElaborating upon ideas which one can glean from Pitowsky’s work\n(1990, 1996, 2002), Cuffaro argues at length that quantum computation\nand information theory (QCIT) are practical sciences in this sense, as\nopposed to the “theoretical sciences” exemplified by\nphysics under its traditional characterisation; further that\nrecognising this distinction illuminates both areas of activity. On\nthe one hand (Cuffaro 2017), practical investigators attempting to\nisolate and/or quantify the computational resources made available by\nquantum computers are in danger of conceptual confusion if they are\nnot cognisant of the differences between practical and traditional\nsciences. On the other hand (Cuffaro 2018a), one should be wary of the\nsignificance of classical computer simulations of quantum mechanical\nphenomena for the purposes of a foundational analysis of the latter.\nFor example, certain mathematical results can legitimately be thought\nof as no-go theorems for the purposes of foundational analysis, and\nyet are not really relevant for the purpose of characterising the\nclass of efficiently simulable quantum phenomena." ], "subsection_title": "5.4 (Quantum) Computational Perspectives on Physical Science" }, { "content": [ "\nThe Church-Turing thesis, which asserts that every function naturally\nregarded as computable is Turing-computable, is argued by Deutsch to\npresuppose a physical principle, namely that:", "\n\n\n[DP]: Every finitely realisable physical system can be perfectly\nsimulated by a universal model computing machine operating by finite\nmeans. (Deutsch 1985)\n", "\nSince no machine operating by finite means can simulate classical\nphysics’ continuity of states and dynamics, Deutsch argues that\nDP is false in a classical world. He argues that it is true for\nquantum physics, however, owing to the existence of the universal\nquantum Turing machine he introduces in the same paper, which thus\nproves both DP and the Church-Turing thesis it underlies to be sound.\nThis idea—that the Church-Turing thesis requires a physical\ngrounding—is set into historical context by Lupacchini (2018),\nwho traces its roots in the thought of Gödel, Post, and Gandy. It\nis criticised by Timpson (2013), who views it as methodologically\nfruitful, but as nevertheless resting on a confusion regarding the\nmeaning of the Church-Turing thesis, which in itself has nothing to do\nwith physics." ], "subsection_title": "5.5 The Church-Turing Thesis and Deutsch’s Principle" }, { "content": [ "\nIn the general philosophy of science literature on\n scientific explanation\n there is a distinction between so-called “how-actually”\nand “how-possibly” explanation, where the former aims to\nconvey how a particular outcome actually came about, and the latter\naims to convey how the occurrence of an event can have been possible.\nThat how-actually explanation actually explains is uncontroversial,\nbut the merit (if any) of how-possibly explanation has been debated.\nWhile some view how-possibly explanation as genuinely explanatory,\nothers have argued that how-possibly ‘explanation’ is\nbetter thought of as, at best, a merely heuristically useful\nexercise.", "\nIt turns out that the science of quantum computation is able to\nilluminate this debate. Cuffaro (2015) argues that when one examines\nthe question of the source of quantum “speed-up”, one sees\nthat to answer this question is to compare algorithmic processes of\nvarious kinds, and in so doing to describe the possibility spaces\nassociated with these processes. By doing so one explains how it is\npossible for one process to outperform its rival. Further, Cuffaro\nargues that in examples like this, once one has answered the\nhow-possibly question, nothing is actually gained by subsequently\nasking a how-actually question." ], "subsection_title": "5.6 (Quantum) Computation and Scientific Explanation" } ] } ]

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[ "\nQuantum Gravity, broadly construed, is a physical theory (still\n‘under construction’) incorporating both the principles of\ngeneral relativity and quantum theory. Such a theory is expected to be\nable to provide a satisfactory description of the microstructure of\nspacetime at the so-called\n Planck scale,\n at which all fundamental constants of the ingredient theories,\nc (the velocity of light in vacuo), ℏ (the reduced\nPlanck’s constant), and G (Newton’s constant), come\ntogether to form units of mass, length, and time. This scale is so\nremote from current experimental capabilities that the empirical\ntesting of quantum gravity proposals along standard lines is rendered\nnear-impossible.", "\nIn most, though not all, theories of quantum gravity, the\ngravitational field itself is also quantized. Since the contemporary\ntheory of gravity, general relativity, describes gravitation as the\ncurvature of spacetime by matter and energy, a quantization of gravity\nseemingly implies some sort of quantization of spacetime geometry:\nquantum spacetime. Insofar as all extant physical theories rely on a\nclassical (non-quantum) spacetime background, this presents not only\nextreme technical difficulties, but also profound methodological and\nontological challenges for the philosopher and the physicist. Though\nquantum gravity has been the subject of investigation by physicists\nfor almost a century, philosophers have only just begun to investigate\nits philosophical implications." ]

[ { "content_title": "1. Introduction", "sub_toc": [] }, { "content_title": "2. Gravity Meets Quantum Theory", "sub_toc": [] }, { "content_title": "3. Theoretical Frameworks", "sub_toc": [ "3.1 String theory", "3.2 Canonical and loop quantum gravity", "3.3 Other approaches" ] }, { "content_title": "4. Methodology", "sub_toc": [ "4.1 Theory", "4.2 Experiment" ] }, { "content_title": "5. Philosophical Issues", "sub_toc": [ "5.1 Time", "5.2 Ontology", "5.3 Status of quantum theory", "5.4 The Planck Scale", "5.5 Background Structure", "5.6 Necessity of Quantization" ] }, { "content_title": "6. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nDutch artist M.C. Escher’s elegant pictorial paradoxes are\nprized by many, not least by philosophers, physicists, and\nmathematicians. Some of his work, for example Ascending and\nDescending, relies on optical illusion to depict what is actually\nan impossible situation. Other works are paradoxical in the broad\nsense, but not impossible: Relativity depicts a\ncoherent arrangement of objects, albeit an arrangement in which the\nforce of gravity operates in an unfamiliar fashion. (See the\n Other Internet Resources\n section below for images.) Quantum gravity itself may be like this:\nan unfamiliar yet coherent arrangement of familiar elements. Or it may\nbe more like Ascending and Descending, an impossible\nconstruction which looks sensible in its local details but does not\nfit together into a coherent whole when using presently existing\nbuilding materials. If the latter is true, then the construction of a\nquantum theory of gravity may demand entirely unfamiliar elements.\nWhatever the final outcome, the situation at present is one of flux,\nwith a great many competing approaches vying for the prize. However,\nit is also important to note that the prize is not always the same:\nstring theorists seek a unified theory of all four interactions that\nhas the power of explaining such things as the numbers of generations\nof elementary particles and other previous inexplicable properties.\nOther approaches are more modest, and seek only to bring general\nrelativity in line with quantum theory, without necessarily invoking\nthe other interactions. Hence, the problem of quantum gravity\ncan mean very different things to different researchers and what\nconstitutes a possible solution to one group might not qualify as such\nto another.", "\nGiven that quantum gravity does not yet exist as a working physical\ntheory, one might legitimately question whether philosophers have any\nbusiness being involved at this stage. Certainly the\nphilosopher’s task will be somewhat different from that faced\nwhen dealing with a more-or-less settled body of theory such as\nclassical Newtonian mechanics, general relativity, or quantum\nmechanics. In such cases, one typically proceeds by assuming the\nphysical soundness of the theory or theoretical framework and drawing\nout the ontological and perhaps epistemological consequences of the\ntheory, trying to understand what it is that the theory is telling us\nabout the nature of space, time, matter, causation, and so on.\nTheories of quantum gravity, on the other hand, are bedeviled by a\nhost of technical and conceptual problems, questions, and issues that\nmake them largely unsuited to this kind of interpretive approach. In\nthe case of string theory, there isn’t even really a\n‘theory’ to speak of, so much as several clues pointing to\nwhat many hope will some day be an applicable, consistent physical\ntheory. However, philosophers who have a taste for a broader and more\nopen-ended form of inquiry will find much to think about, and it is\nentirely possible that future philosophers of physics will be faced\nwith problems of a very different flavour as a result of the peculiar\nnature of quantum gravity. Indeed, Tian Cao argues that quantum\ngravity offers up a unique opportunity for philosophers of\nphysics, leaving them “with a good chance to make some positive\ncontributions, rather than just analysing philosophically what\nphysicists have already established” (Cao, 2001, p. 138). This\nsentiment has in fact been echoed by several physicists, not least by\nCarlo Rovelli (a central architect of the approach known as loop\nquantum gravity), who complains that he wishes philosophers would not\nrestrict themselves to “commenting and polishing the present\nfragmentary physical theories, but would take the risk of trying to\nlook ahead” (Rovelli, 1997, p. 182). This raises an\nimportant point: though we think of general relativity and quantum\ntheory as ‘nice’ theories from the point of view of\nphilosophical investigation, in a very real sense they are not the\nwhole story and break down at extreme scales. " ], "section_title": "1. Introduction", "subsections": [] }, { "main_content": [ "\nThe difficulties in reconciling quantum theory and gravity into some\nform of quantum gravity come from the prima facie\nincompatibility of general relativity, Einstein’s relativistic\ntheory of gravitation, and quantum field theory, the framework for the\ndescription of the other three forces (electromagnetism and the strong\nand weak nuclear interactions). Whence the incompatibility? General\nrelativity is described by Einstein’s equations, which amount to\nconstraints on the curvature of spacetime (the Einstein tensor on the\nleft-hand side) due to the presence of mass and other forms of energy,\nsuch as electromagnetic radiation (the stress-energy-momentum tensor\non the right-hand side). (See John Baez’s webpages in\n Other Internet Resources\n for an excellent introduction.) In doing so, they manage to encompass\ntraditional, Newtonian gravitational phenomena such as the mutual\nattraction of two or more massive objects, while also predicting new\nphenomena such as the bending and red-shifting of light by these\nobjects (which have been observed) and the existence of gravitational\nradiation (until very recently, with the direct detection of\ngravitational waves by LIGO, this was, of course, only indirectly\nobserved via the decrease in the period of binary pulsars-see the\n 1993 Physics Nobel Prize presentation speech by Carl Nordling.)", "\nIn general relativity, mass and energy are treated in a purely\nclassical manner, where ‘classical’ means that physical\nquantities such as the strengths and directions of various fields and\nthe positions and velocities of particles have definite values. These\nquantities are represented by tensor fields, sets of (real) numbers\nassociated with each spacetime point. For example, the stress, energy,\nand momentum\nTab(x,t) of the\nelectromagnetic field at some point\n(x,t), are functions of the three\ncomponents Ei, Ej,\nEk, Bi,\nBj, Bk of the electric and\nmagnetic fields E and\nB at that point. These quantities in turn\ndetermine, via Einstein’s equations, an aspect of the\n‘curvature’ of spacetime, a set of numbers\nGab(x,t) which\nis in turn a function of the spacetime metric. The metric\ngab(x,t) is a\nset of numbers associated with each point which gives the distance to\nneighboring points. A model of the world according to general\nrelativity consists of a spacetime manifold with a metric, the\ncurvature of which is constrained by the stress-energy-momentum of the\nmatter distribution. All physical quantities — the value of the\nx-component of the electric field at some point, the scalar\ncurvature of spacetime at some point, and so on — have definite\nvalues, given by real (as opposed to complex or imaginary) numbers.\nThus general relativity is a classical theory in the sense given\nabove.", "\nThe problem is that our fundamental theories of matter and energy, the\ntheories describing the interactions of various particles via the\nelectromagnetic force and the strong and weak nuclear forces, are all\nquantum theories. In\n quantum theories,\n these physical quantities do not in general have definite\nvalues. For example, in quantum mechanics, the position of an electron\nmay be specified with arbitrarily high accuracy only at the cost of a\nloss of specificity in the description of its momentum, hence its\nvelocity. At the same time, in the quantum theory of the\nelectromagnetic field known as quantum electrodynamics (QED), the\nelectric and magnetic fields associated with the electron suffer an\nassociated uncertainty. In general, physical quantities are described\nby a quantum state which gives a probability distribution over many\ndifferent values, and increased specificity (narrowing of the\ndistribution) of one property (e.g., position, electric field) gives\nrise to decreased specificity of its canonically conjugate property\n(e.g., momentum, magnetic field). This is an expression of\nHeisenberg’s\n Uncertainty Principle.\n In the context of quantum gravity the fluctuating geometry is known\nas “spacetime foam”. Likewise, if one focusses in on the\nspatial geometry, it will not have a definite trajectory.", "\nOn the surface, the incompatibility between general relativity and\nquantum theory might seem rather trivial. Why not just follow the\nmodel of QED and quantize the gravitational field, similar to the way\nin which the electromagnetic field was quantized? This is more or less\nthe path that was taken, but it encounters extraordinary difficulties.\nSome physicists consider these to be ‘merely’ technical\ndifficulties, having to do with the non-renormalizability of the\ngravitational interaction and the consequent failure of the\nperturbative methods which have proven effective in ordinary quantum\nfield theories. However, these technical problems are closely related\nto a set of daunting conceptual difficulties, of interest to\nboth physicists and philosophers.", "\nThe conceptual difficulties basically follow from the nature of the\ngravitational interaction, in particular the equivalence of\ngravitational and inertial mass, which allows one to represent gravity\nas a property of spacetime itself, rather than as a field propagating\nin a (passive) spacetime background. When one attempts to\nquantize gravity, one is subjecting some of the properties of\nspacetime to quantum fluctuations. For example, in canonical\nquantizations of gravity one isolates and then quantizes geometrical\nquantities (roughly the intrinsic and extrinsic curvature of three\ndimensional space) functioning as the position and momentum variables.\nGiven the uncertainty principle and the probabilistic nature of\nquantum theory, one has a picture involving fluctuations of the\ngeometry of space, much as the electric and magnetic fields fluctuate\nin QED. But ordinary quantum theory presupposes a well-defined\nclassical background against which to define these\nfluctuations (Weinstein, 2001a, b), and so one runs into trouble not\nonly in giving a mathematical characterization of the quantization\nprocedure (how to take into account these fluctuations in the\neffective spacetime structure?) but also in giving a conceptual and\nphysical account of the theory that results, should one succeed. For\nexample, a fluctuating metric would seem to imply a fluctuating causal\nstructure and spatiotemporal ordering of events, in which case, how is\none to define equal-time commutation relations in the quantum theory?\n(See the section on the Lagrangian formulation in the entry on\n quantum field theory.)\n ", "\nCao (2001) believes that the conceptual nature of the problem demands\na conceptual resolution. He advocates what he calls ‘ontological\nsynthesis’. This approach asks for an analysis of the\nontological pictures of the two ingredient theories of quantum\ngravity, so that their consistency (the consistency of the resulting\nsynthesis) can be properly assessed. Ontology for Cao refers to the\nprimary, autonomous structures from which all other properties and\nrelations in a theory are constructed. A fairly simple inspection of\nthe respective ontological constraints imposed by general relativity\nand quantum field theory reveals serious tension: general relativity\ndiscards the fixed kinematical structure of spacetime, so that\nlocalization is rendered relational, but in quantum field theory a\nfixed flat background is part of its ontological basis, from which the\nstandard features of the theory are derived. On the other hand, as we\nhave seen, quantum field theory involves quantum fluctuations in the\nvicinity of a point, while general relativity involves the use of a\nsmooth point neighbourhood. Either way, in order to bring the two\nontological bases together, some piece of either edifice must be\ndemolished. Cao proposes that the tension can best be resolved by\nfocussing firmly on those sine qua non principles of the\nrespective theories. Cao views the gravitational property of universal\ncoupling as essential, but notes that this does not require\ncontinuity, so that the former could be retained while discarding the\nlatter, without rendering the framework inconsistent, thus allowing\nfor quantum theory’s violent fluctuations (Cao’s prime\ncandidate for an essential quantum field theoretic concept). Likewise,\nhe argues that quantum field theory requires a fixed background in\norder to localize quantum fields and set up causal structure. But he\nnotes that a relational account of localization could perform such a\nfunction, with fields localized relative to each other. In so doing,\none could envisage a diffeomorphism covariant quantum field theory\n(i.e. one that does not involve reference to fields localized at\npoints of the spacetime manifold). The resulting synthesized entity (a\nviolently fluctuating, universally coupled quantum gravitational\nfield) would then be what a quantum theory of gravity ought to\ndescribe.", "\nWhile such an approach sounds sensible enough on the surface, to\nactually put it into practice in the constructive stages of\ntheory-building (rather than a retrospective analysis of a completed\ntheory) is not going to be easy—though it has to be said, the\nmethod Cao describes bears close resemblance to the way loop quantum\ngravity has developed. Lucien Hardy (2007) has developed a novel\napproach to quantum gravity that shares features of Cao’s\nsuggestion, though the principles isolated are different from\nCao’s. The causaloid approach is intended to provide a\nframework for quantum gravity theories, where idea is to\ndevelop a general formalism that respects the key features of both\ngeneral relativity, which he takes to be the dynamical\n(non-probabilistic) causal structure, and quantum theory, which he\ntakes to be the probabilistic (nondynamical) dynamics. The causaloid\n(of some theory) is an entity that encodes all that can be calculated\nin the theory. Part of the problem here is that Cao’s (and\nHardy’s) approach assumes that the ontological principles hold\nat the Planck scale. However, it is perfectly possible that both of\nthe input theories break down at higher energies. Not only that, the\ntechnical difficulties of setting up the kind of (physically\nrealistic) diffeomorphism-invariant quantum field theory he suggests\nhave so far proven to be an insurmountable challenge. One crucial\naspect that is missing from Cao’s framework is a notion of what\nthe observables might be. Of course, they must be relational,\nbut this still leaves the problem very much open. (The idea of making\nprogress by isolating appropriate principles of quantum gravity\nforms the basis of a special issue: Crowther and Rickles, eds,\n2014.)", "\nWe will look in more detail at how various conceptual and\nmethodological problems arise in two different research programs\nbelow. But first, we introduce some key features of the leading\nresearch programs." ], "section_title": "2. Gravity Meets Quantum Theory", "subsections": [] }, { "main_content": [ "\nAll approaches to the problem of quantum gravity agree that something\nmust be said about the relationship between gravitation and quantized\nmatter. These various approaches can be catalogued in various ways,\ndepending on the relative weight assigned to general relativity and\nquantum field theory. Some approaches view general relativity as in\nneed of correction and quantum field theory as generally applicable,\nwhile others view quantum field theory as problematic and general\nrelativity as having a more universal status. Still others view the\ntheories in a more even-handed manner, perhaps with both simply\namounting to distinct limits of a deeper theory. It has often been\nsuggested, since the earliest days of quantum gravity research, that\nbringing quantum field theory and general relativity together might\nserve to cure their respective singularity problems (the former\nresulting from bad high frequency behaviour of fields; the latter\nresulting from certain kinds of gravitational collapse). This hope\ndoes seem to have been borne out in many of the current approaches.\nRoger Penrose has even argued that the joint consideration of\ngravitation and quantum theory could resolve the infamous quantum\nmeasurement problem (see Penrose 2001; see also the section on the\nmeasurement problem in the entry on\n philosophical issues in quantum theory).\n The basic idea of Penrose’s proposal is fairly simple to grasp:\nwhen there is wave-packet spreading of the centre of mass of some\nbody, there results a greater imprecision in the spacetime structure\nassociated with the spreading wave-packet, and this destroys the\ncoherence of the distant parts of the wave-function. There are\ndifficulties in distinguishing the gravitationally induced collapse\nthat Penrose proposes from the effective collapse induced by quantum\ntheory itself, thanks to decoherence—Joy Christian (2005) has\nsuggested that by observing oscillations in the flavor ratios of\nneutrinos originating at cosmological distances one could eliminate\nthe confounding effects of environmental decoherence.", "\nBy far the two most popular approaches are string theory and loop\nquantum gravity. The former is an example of an approach to quantum\ngravity in which the gravitational field is not quantized; rather, a\ndistinct theory is quantized which happens to coincide with general\nrelativity at low energies. The latter is an approach involving\n(constrained) canonical quantization, albeit of a version of general\nrelativity based on a different choice of variables than the usual\ngeometrodynamical, metric-based variables. We cover the basic details\nof each of these in the following subsections." ], "section_title": "3. Theoretical Frameworks", "subsections": [ { "content": [ "\nKnown variously as string theory, superstring theory, and M-theory,\nthis program (qua theory of quantum gravity) has its roots,\nindirectly, in the observation, dating back to at least the 1930s,\nthat classical general relativity looks in many ways like the theory\nof a massless ‘spin-two’ field propagating on the flat\nMinkowski spacetime of special relativity. [See Cappelli et\nal. (eds.) 2012, and Gasperini and Maharana (eds.) 2008, for\ncollections of essays covering the early history of string theory;\nRickles 2014 offers a conceptually-oriented history of the earlier\ndays of string theory; Rovelli 2001b (Other Internet Resources section\nbelow) and 2006 offer a capsule history, and Greene 2000 provides a\npopular account.] This observation led to early attempts to formulate\na quantum theory of gravity by “quantizing” this spin-two\ntheory. However, it turned out that the theory is not perturbatively\nrenormalizable, meaning that there are ineliminable infinities.\nAttempts to modify the classical theory to eliminate this problem led\nto a different problem, non-unitarity, and so this general approach\nwas moribund until the mid-1970s, when it was discovered that a theory\nof one-dimensional “strings” developed around 1970 to\naccount for the strong interaction, actually provided a framework for\na unified theory which included gravity, because one of the modes of\noscillation of the string corresponded to a massless spin-two particle\n(the ‘graviton’).", "\nThe original and still prominent idea behind string theory was to\nreplace the point particles of ordinary quantum field theory\n(particles like photons, electrons, etc) with one-dimensional extended\nobjects called strings. (See Weingard, 2001 and Witten, 2001 for\noverviews of the conceptual framework.) In the early development of\nthe theory, it was recognized that construction of a consistent\nquantum theory of strings required that the strings “live”\nin a larger number of spatial dimensions than the observed three.\nString theories containing fermions as well as bosons must be\nformulated in nine space dimensions and one time dimension. Strings\ncan be open or closed, and have a characteristic tension and hence\nvibrational spectrum. The various modes of vibration correspond to\nvarious particles, one of which is the graviton (the hypothetical\nmassless, spin-2 particle responsible for mediating gravitational\ninteractions). The resulting theories have the advantage of being\nperturbatively renormalizable. This means that perturbative\ncalculations are at least mathematically tractable. Since perturbation\ntheory is an almost indispensable tool for physicists, this is deemed\na good thing.", "\nString theory has undergone several mini-revolutions over the last\nseveral years, one of which involved the discovery of various duality\nrelations, mathematical transformations connecting, in this case, what\nappear to be physically distinct string theories — type I, type\nIIA, type IIB, (heterotic) SO(32) and (heterotic)\nE8×E8 — to one another and to\neleven-dimensional supergravity (a particle theory). The discovery of\nthese connections led to the conjecture that all of the string\ntheories are really aspects of a single underlying theory, which was\ngiven the name ‘M-theory’ (though M-theory is also used\nmore specifically to describe the unknown theory of which\neleven-dimensional supergravity is the low energy limit). The\nrationale, according to one kind of duality (S-duality), is that one\ntheory at strong coupling (high energy description) is physically\nequivalent (in terms of physical symmetries, correlation functions and\nall observable content) to another theory at weak coupling (where a\nlower energy means a more tractable description), and that if all the\ntheories are related to one another by dualities such as this, then\nthey must all be aspects of some more fundamental theory. Though\nattempts have been made, there has been no successful formulation of\nthis theory: its very existence, much less its nature, is still\nlargely a matter of conjecture.", "\nThere has been some recent interest in dualities by philosophers,\ngiven their clear links to standard philosophical issues such as\nunderdetermination, conventionalism, and emergence/reduction. The link\ncomes about because in a dual pair (of theories) one has a observable\nequivalence combined with what appears to be radical physical (and\nmathematical) differences. These differences can be as extreme as\ndescribing spacetimes of apparently different topological structures,\nincluding different numbers of dimensions. This has led some\nphysicists to speak of spacetime emerging, depending on such\nthings as the coupling strength governing physical interactions. This\ncan be seen most clearly in the context of the AdS/CFT duality in\nwhich a ten dimensional string theory is found to be observationally\nequivalent (again covering physical symmetries, observables and their\ncorrelation functions) to a four dimensional gauge theory — this\nis sometimes called a ‘gauge/gravity’ duality since the\nstring theory contains gravity (all string theories contain\ngravitons) while the gauge theory does not. Since there is an\nequivalence between these descriptions, it makes sense to say that\nneither is fundamental, and so (elements of) the spacetimes they\napparently describe are also not fundamental; thus implying that the\nspacetime we observe at low-energies is an emergent phenomenon —\nVistarini 2013 is a recent discussion of spacetime emergence in string\ntheory. One way to view such dual pairs is in terms of the two\ntheories (the gauge theory and a gravitational theory) being distinct\nclassical limits of a more all-encompassing quantum theory. In this\ncase, the classical emergent structures also include the specific\ngauge symmetries and degrees of freedom of the limiting theories. A\nproblem remains of making sense of the more fundamental theory (and\nthe associated physical structure it describes) from which these\nspacetimes and gauge symmetries emerge. ", "\nPhilosophically speaking, there is a large question mark over whether\nthe dual pair should be seen as genuinely distinct in a physical sense\nor as mere notational variants of the same theory — talk of a\n“dictionary” relating the theories makes the latter more\npalatable and suggests that the choice of physical interpretation\nmight be conventional. However, if we view the theories as notational\nvariants, then our sense of theory-individuation is seemingly\ncompromised, since the dual pairs involve different dynamics and\ndegrees of freedom. (See Joseph Polchinski 2014, for a thorough\naccount of the various kinds of dualities along with some of their\ninterpretive quirks; Rickles 2011 provides a philosophical examination\nof string dualities.) " ], "subsection_title": "3.1 String Theory" }, { "content": [ "\nWhereas (perturbative) string theory and other so-called\n‘covariant’ approaches view the curved spacetime of\ngeneral relativity as an effective modification of a flat (or other\nfixed) background geometry by a massless spin-two field, the canonical\nquantum gravity program treats the full spacetime metric itself as a\nkind of field, and attempts to quantize it directly without splitting\nit apart into a flat part and a perturbation. However, spacetime\nitself is split apart into a stack of three dimensional slices (a\nfoliation) on which is defined a spatial geometry. Technically, work\nin this camp proceeds by writing down general relativity in so-called\n‘canonical’ or ‘Hamiltonian’ form, since there\nis a more-or-less clearcut way to quantize theories once they are put\nin this form (Kuchar, 1993; Belot & Earman, 2001). In a canonical\ndescription, one chooses a particular set of configuration variables\nxi and canonically conjugate momentum variables\npi which describe the state of a system at some\ntime, and can be encoded in a phase space. Then, one obtains the\ntime-evolution of these variables from the Hamiltonian\nH(xi,pi), which\nprovides the physically possible motions in the phase space a a family\nof curves. Quantization proceeds by treating the configuration and\nmomentum variables as operators on a quantum state space (a Hilbert\nspace) obeying certain commutation relations analogous to the\nclassical Poisson-bracket relations, which effectively encode the\nquantum fuzziness associated with Heisenberg’s uncertainty\nprinciple. The Hamiltonian operator, acting on quantum states, would\nthen generate the dynamical evolution.", "\nWhen one attempts to write general relativity down in this way, one\nhas to contend with the existence of constraints on the\ncanonical variables that are inherited from the diffeomorphism\ninvariance of the spacetime formulation of the theory. The single\ntensorial equation that we see in standard presentations of the\nEinstein field equations is translated into 10 scalar equations in the\ncanonical formulation, with constraints accounting for four of these\nequations (the remaining six are genuine evolutionary equations).\nThree of the constraints (known as the momentum or diffeomorphism\nconstraints) are responsible for shifting data tangential to the\ninitial surface and, thus, are related to the shift vector field. The\nremaining constraint, known as the Hamiltonian (or scalar) constraint,\nis responsible for pushing data off the initial surface, and thus is\nrelated to the lapse function. If the constraints are not satisfied by\nthe canonical initial data then the development of the data with\nrespect to the evolution equations, will not generate a physically\npossible spacetime for choices of lapse and shift. However, when the\nconstraints are satisfied then the various choices of lapse and\nshift will always grow the same 4D spacetime (that it, the same\nspacetime metric). However, to extract a notion of time from this\nformulation demands that one first solve for the spacetime metric,\nfollowed by a singling out of a specific solution. This is a kind of\nclassical problem of time in that since the spacetime geometry is a\ndynamical variable, time is something that also must be solved for.\nFurther, there is arbitrariness in the time variable as a result of\nthe arbitrariness encoded in the constraints, stemming from the fact\nthat time is essentially a freely chosen label of the three\ndimensional slices and so is not a physical parameter. However, one\ncan extract a time for each solution to the Einstein equations\nby ‘deparametrizing’ the theory (i.e. isolating a variable\nfrom within the phase space that is to play the role of time). Below\nwe see that things become more problematic in the shift to quantum\ntheory.", "\nAlthough advocates of the canonical approach often accuse string\ntheorists of relying too heavily on classical background spacetime,\nthe canonical approach does something which is arguably quite similar,\nin that one begins with a theory that conceives time-evolution in\nterms of evolving some data specified on an a priori given\nspacelike surface, and then quantizing the theory. However, this does\nnot imply any breaking of spacetime diffeomorphism invariance (or\ngeneral covariance) since the constraints that must be satisfied by\nthe data on the slice mean that the physical observables of the theory\nwill be independent of whatever foliation one chooses. However, the\nproblem is that if spacetime is quantized along these lines, the\nassumption (of evolving then quantizing) does not make sense in\nanything but an approximate way. That is, the evolution does not\ngenerate a classical spacetime! Rather, solutions will be\nwave-functions (solutions of some Schrödinger-type equation).\nThis issue in particular is decidedly neglected in both the physical\nand philosophical literature (but see Isham, 1993), and there is more\nthat might be said. We return to the issue of time in quantum gravity\nbelow.", "\nEarly attempts at quantizing general relativity by Bergmann, Dirac,\nPeres, Wheeler, DeWitt and others in the 1950s and 1960s worked with a\nseemingly natural choice for configuration variables, namely geometric\nvariables gij corresponding to the various\ncomponents of the ‘three-metric’ describing the intrinsic\ngeometry of the given spatial slice of spacetime. One can think about\narriving at this via an arbitrary slicing of a 4-dimensional\n“block” universe by 3-dimensional spacelike hypersurfaces.\nThe conjugate momenta πij then effectively\nencode the time rate-of-change of the metric, which, from the\n4-dimensional perspective, is directly related to the extrinsic\ncurvature of the slice (meaning the curvature relative to the\nspacetime in which the slice is embedded). This approach is known as\n‘geometrodynamics’ since it views general relativity as\ndescribing the dynamics of spatial geometry.", "\nAs mentioned above, in these geometric variables, as in any other\ncanonical formulation of general relativity, one is faced with\nconstraints, which encode the fact that the canonical variables cannot\nbe specified independently. A familiar example of a constraint is\nGauss’s law from ordinary electromagnetism, which states that,\nin the absence of charges,\n∇·E(x)\n− 4πρ = 0 at every point x. It\nmeans that the three components of the electric field at every point\nmust be chosen so as to satisfy this constraint, which in turn means\nthat there are only two “true” degrees of freedom\npossessed by the electric field at any given point in space.\n(Specifying two components of the electric field at every point\ndictates the third component.) Thus, not all components of the Maxwell\nequations propagate the fields in a physical sense. ", "\nThe constraints in electromagnetism may be viewed as stemming from the\nU(1) gauge invariance of Maxwell’s theory, while the\nconstraints of general relativity stem from the diffeomorphism\ninvariance of the theory.\n Diffeomorphism invariance\n means, informally, that one can take a solution of Einstein’s\nequations and drag it (meaning the metric and the matter fields)\naround on the spacetime manifold and obtain a mathematically distinct\nbut physically equivalent solution. The three\n‘supermomentum’ constraints in the canonical theory\nreflect the freedom to drag the metric and matter fields around in\nvarious directions on a given three-dimensional spacelike\nhypersurface, while the ‘super-Hamiltonian’ constraint\nreflects the freedom to drag the fields in the “time”\ndirection, and so to the “next” hypersurface. (Each\nconstraint applies at each point of the given spacelike hypersurface,\nso that there are actually 4 × ∞3 constraints:\nfour for each point.) In the classical (unquantized) canonical\nformulation of general relativity, the constraints do not pose any\nparticular conceptual problems (though one does face a problem in\ndefining suitable observables that commute with the constraints, and\nthis certainly has a conceptual flavour). One effectively chooses a\nbackground space and time (via a choice of the lapse and shift\nfunctions) “on the fly”, and one can be confident that the\nspacetime that results is independent of the particular choice.\nEffectively, different choices of these functions give rise to\ndifferent choices of background against which to evolve the\nforeground. However, the constraints pose a serious problem (as much\nconceptual as technical) when one moves to quantum theory.", "\nAll approaches to canonical quantum gravity face the so-called\n“problem of time” in one form or another (Kuchař\n(1992) and Isham (1993) are still excellent reviews; Rickles, 2006,\noffers a more philosophical guide). The problem stems from the fact\nthat in preserving the diffeomorphism-invariance of general relativity\n— depriving the coordinates of the background manifold of any\nphysical meaning — the “slices” of spacetime one is\nconsidering inevitably include time, just as they include space. In\nthe canonical formulation, the diffeomorphism invariance is reflected\nin the constraints, and the inclusion of what would ordinarily be a\n‘time’ variable in the data is reflected in the existence\nof the super-Hamiltonian constraint. The difficulties presented by\nthis latter constraint constitute the problem of time.", "\nAttempts to quantize general relativity in the canonical framework\nproceed by turning the canonical variables into operators on an\nappropriate state space (e.g., the space of square-integrable\nfunctions over three-metrics), and dealing somehow with the\nconstraints. When quantizing a theory with constraints, there are two\npossible approaches. The approach usually adopted in gauge theories is\nto deal with the constraints before quantization, so that only\ntrue degrees of freedom are promoted to operators when passing to the\nquantum theory. There are a variety of ways of doing this so-called\n‘gauge fixing’, but they all involve removing the extra\ndegrees of freedom by imposing some special conditions. In general\nrelativity, fixing a gauge is tantamount to specifying a particular\ncoordinate system with respect to which the “physical”\ndata is described (spatial coordinates) and with respect to which it\nevolves (time coordinate). This is difficult already at the classical\nlevel, since the utility and, moreover, the very tractability of any\nparticular gauge generally depends on the properties of the solution\nto the equations, which of course is what one is trying to find in the\nfirst place. But in the quantum theory, one is faced with the\nadditional concern that the resulting theory may well not be\nindependent of the choice of gauge. This is closely related to the\nproblem of identifying true, gauge-invariant observables in the\nclassical theory (Torre 2005, in the Other Internet Resources\nsection).", "\nThe preferred approach in canonical quantum gravity is to impose the\nconstraints after quantizing. In this ‘constraint\nquantization’ approach, due to Dirac, one treats the constraints\nthemselves as operators A, and demands that\n“physical” states ψ be those which are solutions to\nthe resulting equations A ψ = 0. The problem of time is\nassociated with the super-Hamiltonian constraint, as mentioned above.\nThe super-Hamiltonian H is responsible for describing\ntime-evolution in the classical theory, yet its counterpart in the\nconstraint-quantized theory, H ψ = 0, would prima\nfacie seem to indicate that the true physical states of the\nsystem do not evolve at all: there is no t. Trying to\nunderstand how, and in what sense, the quantum theory describes the\ntime-evolution of something, be it states or observables, is the\nessence of the problem of time (on which, more below).", "\nIn geometrodynamics, all of the constraint equations are difficult to\nsolve (though the super-Hamiltonian constraint, known as the\nWheeler-DeWitt equation, is especially difficult), even in the absence\nof particular boundary conditions. Lacking solutions, one does not\nhave a grip on what the true, physical states of the theory are, and\none cannot hope to make much progress in the way of predictions. The\ndifficulties associated with geometric variables are addressed by the\nprogram initiated by Ashtekar and developed by his collaborators (for\na review and further references see Rovelli 2001b (Other Internet\nResources), 2001a). Ashtekar used a different set of variables, a\ncomplexified ‘connection’ (rather than a three-metric) and\nits canonical conjugate, which made it simpler to solve the\nconstraints. This change of variables introduces an additional\nconstraint into the theory (the Gauss law constraint generating SO(3)\ntransformations) on account of the freedom to rotate the vectors\nwithout disturbing the metric. The program underwent further\nrefinements with the introduction of the loop transform, and further\nrefinements still when it was understood that equivalence classes of\nloops could be identified with spin networks. One is able to recover\nall the standard geometrical features of general relativity from this\nformulation. (See Smolin (2001, 2004) for a popular introduction;\nRovelli, 2004, offers a physically intuitive account; Thiemann, 2008,\nprovides the mathematical underpinnings; Rickles, 2005, offers a\nphilosophically-oriented review.) Note that the problems of time and\nobservables afflict the loop approach just as they did the earlier\ngeometrodynamical approach. The difference is that one has more\n(mathematical) control over the theory (and its quantization), in\nterms of a definable inner product, a separable state space, and more.\nThere is still a question mark over the construction of the full\nphysical Hilbert space, since the solution of the Hamiltonian\nconstraint remains a problem. However, some progress is being made in\nvarious directions, e.g. Thomas Thiemann’s master constraint\nprogramme (see Thiemann, 2006)." ], "subsection_title": "3.2 Canonical and Loop Quantum Gravity" }, { "content": [ "\nThough the impression often painted of the research landscape in\nquantum gravity is an either/or situation between string theory and\nloop quantum gravity, in reality there are very many more options on\nthe table. Some (e.g., Callender and Huggett 2001, Wüthrich 2004\n(Other Internet Resources section); J. Mattingly 2005) have argued\nthat semiclassical gravity, a theory in which matter is quantized but\nspacetime is classical, is at least coherent, though not quite an\nempirically viable option (we discuss this below). Other approaches\ninclude twistor theory (currently enjoying a revival in conjunction\nwith string theory), Bohmian approaches (Goldstein & Teufel,\n2001), causal sets (see Sorkin 2003, in the Other Internet Resources\nsection) in which the universe is described as a set of discrete\nevents along with a stipulation of their causal relations, and other\ndiscrete approaches (see Loll, 1998). Causal set theory has begun to\nstimulate some philosophical interest on account of the claims, by\nphysicists, to the effect that the theory embodies a notion of\nobjective becoming or temporal passage based on the notion of the\n‘birth’ of spacetime atoms (see, e.g., Dowker 2014; for a\nskeptical response, see Huggett 2014; Wüthrich, 2012, pursues\ninstead the structuralist leanings of causal set theory). ", "\nAlso of interest are arguments to the effect that gravity itself may\nplay a role in quantum state reduction (Christian, 2001; Penrose,\n2001; also briefly discussed below). A fairly comprehensive overview\nof the current approaches to quantum gravity can be found in Oriti\n(2009). In this entry we have chosen to focus upon those approaches\nthat are both the most actively pursued and that have received\nmost attention from philosophers. Let us now turn to several\nmethodological and philosophical issues that arise quantum gravity\nresearch." ], "subsection_title": "3.3 Other Approaches" } ] }, { "main_content": [ "\nResearch in quantum gravity has always had a rather peculiar flavor,\nowing to both the technical and conceptual difficulty of the field and\nthe remoteness from experiment. Yoichiro Nambu (1985) wryly labels\nresearch on quantum gravity “postmodern physics” on\naccount of its experimental remoteness. Thus conventional notions of\nthe close relationship between theory and experiment have but a\ntenuous foothold, at best, in quantum gravity. However, since there\nis a rudimentary ‘pecking order’ amongst the\nvarious approaches to quantum gravity, and since the history of\nquantum gravity contains various fatalities, there clearly are\nsome methods of theory evaluation in operation, there are\nconstraints functioning in something like the way experiment and\nobservation function. Investigating these methods and constraints\nconstitutes an open research problem for philosophers of\nscience—for initial investigations along these lines, see James\nMattingly (2005a and 2009) and Rickles (2011). Audretsch (1981) argues\nthat quantum gravity research conflicts with Kuhn’s account of\nscientific development since it stems from the desire to unify (for\nreasons not based on any empirical tension) multiple paradigms, both\nof which are well-confirmed and both of which make claims to\nuniversality. One might easily question Audretsch’s focus on\ndirect empirical tensions here. Given, as he admits, both general\nrelativity and quantum theory claim to be universal theories,\nany conceptual or formal tension that can be found to hold between\nthem must point to either or both theories being in error in their\nclaims to universality—this is an empirical claim of sorts. In\nthe context of string theory, Peter Galison (1995) argues that\nmathematical constraints take the place of standard empirical\nconstraints. James Cushing (1990) also considers some of the potential\nmethodological implications of string theory (though he deals with\nstring theory in its earliest days, when it underwent a transition\nfrom the dual resonance model of hadrons into a theory of quantum\ngravity). Dawid (2014) focuses in more detail on methodological issues\nin string theory and defends the idea that string theory is\ncharacterised by a uniqueness claim (the no-alternatives argument)\naccording to which string theory is the only way to unify\ngravity and the other fundamental interactions, thus grounding\nphysicists’ strong belief in the theory; however, that is a\nrather different problem (that of constructing a theory of everything)\nthan the more restricted problem of quantum gravity — quantum\ngravity researchers from other approaches might simply reject the need\nfor such a unified theory (e.g., as opposed to a theory that is\ncompatible with the inclusion other interactions). " ], "section_title": "4. Methodology", "subsections": [ { "content": [ "\nAs remarked in the introduction, there is no single, generally\nagreed-upon body of theory in quantum gravity. The majority of the\nphysicists working in the field focus their attention on string\ntheory, an ambitious program which aims at providing a unified theory\nof all four interactions. A non-negligible minority work on what is\nnow called loop quantum gravity, the goal of which is simply to\nprovide a quantum theory of the gravitational interaction\nsimpliciter. There is also significant work in other areas,\nincluding approaches that don’t really involve the quantization\nof a theory at all. [Good recent reviews of the theoretical landscape\ninclude Carlip 2001, Smolin 2001 (Other Internet Resources section\nbelow), 2003, Penrose 2004, and Oriti, ed, 2009.] But there is no real\nconsensus, for at least two reasons.", "\nThe first reason is that it is extremely difficult to make any\nconcrete predictions in these theories. String theory, in particular,\nis plagued by a lack of experimentally testable predictions because of\nthe tremendous number of distinct ground or vacuum states in the\ntheory, with an absence of guiding principles for singling out the\nphysically significant ones (including our own). Though the string\ncommunity prides itself on the dearth of free parameters in the theory\n(in contrast to the nineteen or so free parameters found in the\nstandard model of particle physics), the problem arguably resurfaces\nin the huge number of vacua associated with different\ncompactifications of the nine space dimensions to the three we\nobserve. These vacua are either viewed as distinct string theories, or\nelse as solutions of one and the same theory (though some deeper,\nunknown theory, as mentioned above). Attempts to explain why we live\nin the particular vacuum that we do have recently given rise to\nappeals to the infamous anthropic principle (Susskind, 2003), whereby\nthe existence of humans (or observers) is invoked to, in some sense,\n“explain” the fact that we find ourselves in a particular\nworld by restricting the possible ground states to those that could\nsupport such creatures in which we should expect our universe’s\nobserved features to be typical. (See Weinstein, 2006, for a\nphilosophical discussion of the usage of anthropic reasoning in string\ntheory, including an ambiguity in the meaning of\n‘typicality’ in this context; Azhar, 2013, further\ndevelops this discussion.)", "\nLoop quantum gravity is seemingly less plagued by a lack of\npredictions, and indeed it is often claimed that the discreteness of\narea and volume operators are concrete predictions of the theory, with\npotentially testable consequences. Proponents of this approach argue\nthat this makes the theory more susceptible to falsification, and thus\nmore scientific (in the sense of Popper; see the entry on\n Karl Popper)\n than string theory (see Smolin 2006 for this line of argument).\nHowever, it is still quite unclear, in practice and even in principle,\nhow one might actually observe these quantities. There have been\nrecent suggestions that in order to probe the effects of the Planck\nscale (discreteness, or minimal length in particular) one needs to\nlook to the cosmological level for tiny violations of Lorentz\ninvariance. Rovelli and Speziale (2003) have argued that, in fact, the\nexistence of a minimal length does not imply a violation of the\nLorentz symmetry (a conclusion seconded by the proponents of the\ncausal set programme). Their argument turns on the fact that in the\ncontext of quantum theory, symmetries act on states (and so on mean\nvalues) rather than eigenvalues (representing the discrete quantities\nin the theory). However, in any case, there remains a question mark\nover the theoretical status of the discreteness result which has been\nshown to hold only for operators on the kinematical Hilbert\nspace, that is, for gauge-variant quantities. It is still an open\nquestion whether this result transfers to genuine observables (i.e.\noperators that satisfy all of the constraints and are defined on the\nphysical Hilbert space: that gauge-invariant quantities). See\nDittrich and Thiemann (2009) for a detailed investigation of the\nproblem and a possible resolution employing suitably gauge-fixed (by\nmatter) Dirac observables. Even if one overcomes this problem, and\ncould observe evidence of the discreteness of space, so many\napproaches involve such discreteness that one would face a further\nproblem in using this new data to decide between the discrete\napproaches. For a philosophical discussion of this and related issues\n(including the question of whether the proposed discreteness breaks\nLorentz invariance), see Hagar (2009) — Hagar (2014) considers\nthese and related issues in a book-length treatment." ], "subsection_title": "4.1 Theory" }, { "content": [ "\nThe second reason for the absence of consensus is that there are no\nexperiments in quantum gravity, and little in the way of observations\nthat might qualify as direct or indirect data or empirical evidence.\nThis stems in part from the lack of theoretical predictions,\nsince it is difficult to design an observational test of a theory if\none does not know where to look or what to look at. But it also stems\nfrom the fact that most theories of quantum gravity appear to predict\ndepartures from classical relativity only at energy scales on the\norder of 1019 GeV. (By way of comparison, the proton-proton\ncollisions at Fermilab have an energy on the order of 103\nGeV.) Whereas research in particle physics proceeds in large part by\nexamining the data collected in large particle accelerators, which are\nable to smash particles together at sufficiently high energies to\nprobe the properties of atomic nuclei in the fallout, gravity is so\nweak that there is no physically realistic way to do a comparable\nexperiment that would reveal properties at the energy scales at which\nquantum gravitational effects are expected to be\nimportant—it would take a particle accelerator of galactic size\nto even approach the required energies. (In a little more detail, the\nweakness of gravity can be compared to the strength of the\nelectromagnetic interaction — cf. Callender and Huggett (eds.)\n2001, p. 4. An electron couples to the electromagnetic field with a\nstrength of 10−2, while the coupling of a mass to the\ngravitational field is 10−22. Feynman (1963, p. 697)\ngives an example that highlights this difference in magnitudes more\ndramatically by showing how the gravitational coupling between a\nproton and an electron in a hydrogen atom would shift the\nwave-function of an electron by just 43 arcseconds over a time period\nof 100 times the age of the Universe! Hence, quantum gravity is more\nof a theorist’s problem.)", "\nThough progress is being made in trying to at least draw observational\nconsequences of loop quantum gravity, a theory of quantum gravity\nwhich arguably does make predictions (Amelino-Camelia, 2003,\nin the Other Internet Resources section below; D. Mattingly, 2005), it\nis remarkable that the most notable “test” of quantum\ntheories of gravity imposed by the community to date involves a\nphenomenon which has never been observed, the so-called Hawking\nradiation from black holes. Based on earlier work of Bekenstein (1973)\nand others, Hawking (1974) predicted that black holes would radiate\nenergy, and would do so in proportion to their gravitational\n“temperature,” which was in turn understood to be\nproportional to their mass, angular momentum, and charge. Associated\nwith this temperature is an entropy (see the entry on\n the philosophy of statistical mechanics),\n and one would expect a theory of quantum gravity to allow one to\ncalculate the entropy associated with a black hole of given mass,\nangular momentum, and charge, the entropy corresponding to the number\nof quantum (micro-)states of the gravitational field having the same\nmass, charge, and angular momentum. (See Unruh, 2001, and references\ntherein.) In their own ways, string theory and loop quantum gravity\nhave both passed the test of predicting an entropy for black holes\nwhich accords with Hawking’s calculation, using very different\nmicroscopic degrees of freedom. String theory gets the number right\nfor a not-particularly-physically-realistic subset of black holes\ncalled near-extremal black holes, while loop quantum gravity gets it\nright for generic black holes, but only up to an overall constant.\nMore recently, the causal set approach has also managed to derive the\ncorrect value. If the Hawking effect is real, then this\nconsonance could be counted as evidence in favor of either or both/all\ntheories.", "\nErik Curiel (2001) has argued against the manner in which the ability\nto derive the Bekenstein-Hawking result as a theorem of an approach is\nused as evidence for that approach in much the same way that\nempirical evidence is used to justify a theory in normal\ncircumstances, say predicting the value of a well-confirmed\nexperimental result. It is true that black hole physics is used as\ntesting ground for quantum gravity and the Bekenstein-Hawking result\ndoes not have the status of an empirical fact. However, it is a strong\ndeduction from a framework that is fairly mature, namely\nquantum field theory on a curved spacetime background. In this sense,\nalthough it does not provide a constraint as strong as an\nexperimentally observed phenomenon, it might legitimately function as\na constraint on possible theories. Constraints on theory construction\ncome in a variety of shapes and sizes, and not all take the form of\nempirical data — thought experiments are a case in point. In the\ncontext of quantum gravity it is especially important that one have\nsome agreed upon constraints to guide the construction. Without them,\nwork would halt. It also seems reasonable to insist that a full theory\nof quantum gravity be able to reproduce predictions of the\nsemi-classical theory of gravity, since this will be one of its\npossible limits. Still, Curiel is right that researchers ought to be\nrather more wary of attributing too much evidential weight to such\nfeatures that remain empirically unconfirmed.", "\nCuriel goes on to question, more generally, the ranking of approaches\nto quantum gravity given what he views as the absence of demonstrated\nscientific merit in any of them: elegance and consistency might well\nbe merits of a scientific theory, but they do not count as\nscientific. (ibid, p. S437). However, this claim hinges on the\ndirect alignment of scientific merit and empirical clout; but this\nrequires an argument, for it is far from obvious: from whence this\nprescription? Surely if a theory is mathematically inconsistent that\nsays something about its physical status too? Moreover, the\nrelationship between experimental and observational data and theories\nis not a simple matter. Finally, it is perhaps too quick to say that\napproaches do not have empirical consequences. Already known empirical\ndata can confirm the predictions of a theory; therefore, it is clear\nthat we can judge the extent to which the various contenders satisfy\nthis old evidence, and how they do so. For example, string theory at\nleast has the potential of explaining why there are three generations\nof elementary particles by invoking the Euler characteristic of the\ncompact spaces it employs—the Euler characteristic is equal to\ntwice the number of generations (see Seifert, 2004, for details).\nWhatever one might think about string theory’s relationship with\nanthropic reasoning, we do have here a potential explanation of a\npreviously inexplicable piece of old empirical data, which ought to\nlend some credence to the theory. There is also the not inconsiderable\nfact that string theory is able to derive general relativity (and all\nthe physically observed facts that are associated with this theory) as\na low energy feature. This is not a novel fact, but it is an\nphysical, empirical consequence of the theory nonetheless.", "\nHowever, it should be noted, finally, that to date neither of the main\nresearch programs has been shown to properly reproduce the world we\nsee at low energies. Indeed, it is a major challenge of loop quantum\ngravity to show that it indeed has general relativity as a low-energy\nlimit, and a major challenge of string theory to show that it has the\nstandard model of particle physics plus general relativity as a\nlow-energy limit. There are promising indications that both theories\nmight be able to overcome this challenge (see Thiemann for the loop\nquantum gravity case; for the string theoretic case, see Graña,\n2006). A similar problem faces causal set theory in the form of the\n‘inverse problem’, which roughly amounts to the difficulty\nof getting continuous manifolds (with their corresponding symmetries)\nfrom a fundamentally discrete theory (see Wallden, 2010, for a good\nrecent review of causal sets, including a discussion of this problem,\non which progress has also been made)." ], "subsection_title": "4.2 Experiment" } ] }, { "main_content": [ "\nQuantum gravity raises a number of difficult philosophical questions.\nTo date, it is the ontological aspects of quantum gravity that have\nattracted the most interest from philosophers, and it is these we will\ndiscuss in the first five sections below. In the final section,\nthough, we will briefly discuss some further methodological and\nepistemological issues which arise.", "\nFirst, however, let us discuss the extent to which ontological\nquestions are tied to a particular theoretical framework. In its\ncurrent stage of development, string theory unfortunately provides\nlittle indication of the more fundamental nature of space, time, and\nmatter. Despite the consideration of ever more exotic objects —\nstrings, p-branes, D-branes, etc. — these objects are\nstill understood as propagating in a background spacetime. Since\nstring theory is supposed to describe the emergence of classical\nspacetime from some underlying quantum structure, these objects are\nnot to be regarded as truly fundamental. Rather, their status in\nstring theory is analogous to the status of particles in quantum field\ntheory (Witten, 2001), which is to say that they are relevant\ndescriptions of the fundamental physics only in situations in which\nthere is a background spacetime with appropriate symmetries. While\nthis suggests tantalising links to issues of emergence, it is\ndifficult to pursue them without knowing the details of the more\nfundamental theory. As already mentioned, the duality relations\nbetween the various string theories suggest that they are all\nperturbative expansions of some more fundamental, non-perturbative\ntheory known as ‘M-theory’ (Polchinski, 2002, see the\nOther Internet Resources section below). This, presumably, is the most\nfundamental level, and understanding the theoretical framework at that\nlevel is central to understanding the underlying ontology of the\ntheory (and so the manner in which any other structures might emerge\nfrom it). ‘Matrix theory’ is an attempt to do just this,\nto provide a mathematical formulation of M-theory, but it remains\nhighly speculative. Thus although string theory purports to be a\nfundamental theory, the ontological implications of the theory are\nstill very obscure — though this could be viewed as a challenge\nrather than a reason to ignore the theory.", "\nCanonical quantum gravity, in its loop formulation or otherwise, has\nto date been of greater interest to philosophers because it appears to\nconfront fundamental questions in a way that string theory, at least\nin its perturbative guise, does not — certainly, it does so more\nexplicitly and in language more amenable to philosophers. Whereas\nperturbative string theory treats spacetime in an essentially\nclassical way, canonical quantum gravity treats it as\nquantum-mechanical entity, at least to the extent of treating the\ngeometric structure (as opposed to, say, the topological or\ndifferential structure) as quantum-mechanical. Furthermore, many of\nthe issues facing canonical quantum gravity are also firmly rooted in\nconceptual difficulties facing the classical theory, which\nphilosophers are already well acquainted with (e.g. via the\n hole argument)." ], "section_title": "5. Philosophical Issues", "subsections": [ { "content": [ "\nAs noted in\n Section 3.2.2\n above, the treatment of time presents special difficulties in\ncanonical quantum gravity, though they easily generalise to many other\napproaches to quantum gravity. These difficulties are connected with\nthe special role time plays in physics, and in quantum theory in\nparticular. Physical laws are, in general, laws of motion, of change\nfrom one time to another. They represent change in the form of\ndifferential equations for the evolution of, as the case may be,\nclassical or quantum states; the state represents the way the system\nis at some time, and the laws allow one to predict how it\nwill be in the future (or retrodict how it was in the past). It is not\nsurprising, then, that a theory of quantum spacetime would have a\nproblem of time, because there is no classical time against which to\nevolve the “state”. The problem is not so much that the\nspacetime is dynamical; there is no problem of time in classical\ngeneral relativity (in the sense that a time variable is present).\nRather, the problem is roughly that in quantizing the structure of\nspacetime itself, the notion of a quantum state, representing the\nstructure of spacetime at some instant, and the notion of the\nevolution of the state, do not get any traction, since there\nare no real “instants”. (In some approaches to canonical\ngravity, one fixes a time before quantizing, and quantizes the\nspatial portions of the metric only. This approach is not without its\nproblems, however; see Isham (1993) for discussion and further\nreferences.)", "\nOne can ask whether the problem of time arising from the canonical\nprogram tells us something deep and important about the nature of\ntime. Julian Barbour (2001a,b), for one, thinks that it tells us that\ntime is illusory (see also Earman, 2002, in this connection). It is\nargued that the fact that quantum states do not evolve under the\nsuper-Hamiltonian means that there is no change. However, it can also\nbe argued (Weinstein, 1999a,b) that the super-Hamiltonian itself\nshould not be expected to generate time-evolution; rather, one or more\n“true” Hamiltonians should play this role, though\nuncovering such Hamiltonians is no easy matter. (See Butterfield &\nIsham (1999) and Rovelli (2006) for further discussion.)", "\nBradley Monton (2006) has argued that a specific version of canonical\nquantum gravity – that with a so-called constant mean\nextrinsic curvature [CMC] (or fixed) foliation – has the\nnecessary resources to render presentism (the view that all and only\npresently existing things exist) a live possibility (see the section\non Presentism, Eternalism, and The Growing Universe Theory in the\nentry on\n time\n for more on presentism). The reason is that with such a fixed\nfoliation one has at one’s disposal some spacelike hypersurface\nthat contains a set of well-defined events that can be viewed through\nthe lens of presentism, such that this set of events at this\nparticular instant (or ‘thin-sandwich’) changes over time.\nThough he readily admits that CMC formulations are outmoded in the\ncontemporary theoretical landscape, he nonetheless insists that given\nthe lack of experimental evidence one way or the other, it stands as a\nviable route to quantum gravity, and therefore presentism remains as a\npossible theory of time that is compatible with frontier theoretical\nphysics. Christian Wüthrich (2010) takes Monton to task on a\nvariety of both technical and non-technical grounds. He rightly\nquestions Monton’s claim that the CMC approach really is an\napproach to quantum gravity, in the same sense as string theory\nand loop quantum gravity. It is more of a piece of machinery that is\nused within a pre-existing approach (namely, the canonical\napproach). He also questions Monton’s claim, inasmuch as it does\nconstitute an approach of sorts, that it is viable. Simply not\nbeing ruled out on experimental grounds does not thereby render an\napproach viable. Besides, if anything has the prospect of saving\npresentism, then surely it is Julian Barbour’s position\nmentioned above. This at least has the added benefit of being a\nresearch programme that is being actively pursued.", "\nA common claim that appears in many discussions of the problem of time\n(especially amongst philosophers) is that it is restricted to\ncanonical formulations of general relativity, and has something to do\nwith the Hamiltonian formalism (see Rickles 2008a, pp. 340–1 for\nmore details). The confusion lies in the apparently very different\nways that time is treated in general relativity as standardly\nformulated, and as it appears in a canonical, Hamiltonian formulation.\nIn the former there is no preferred temporal frame, whereas the latter\nappears to demand such a frame in order to get off the ground\n(cf. Curiel, 2009, p. 59; Tim Maudlin (2004) tells a broadly similar\nstory).", "\nHowever, this encodes several pieces of misinformation making it hard\nto make sense of the claim that general relativity and canonical\ntheories cannot be “reconciled”. The canonical framework\nis simply a tool for constructing theories, and one that makes\nquantization an easier prospect. As a matter of historical fact the\ncanonical formulation of general relativity is a completed project,\nand has been carried out in a variety of ways, using compact spaces\nand non-compact spaces, and with a range of canonical variables. Of\ncourse, general relativity, like Maxwell’s theory of\nelectromagnetism, possesses gauge symmetries, so it is a constrained\ntheory that results, and one must employ the method of constrained\nHamiltonian systems. However, there is no question that general\nrelativity is compatible with the canonical analysis of theories, and\nthe fact that time looks a little strange in this context is simply\nbecause the formalism is attempting to capture the dynamics of general\nrelativity. In any case, the peculiar nature of general relativity and\nquantum gravity, with respect to the treatment of time, resurfaces in\narguably the most covariant of approaches, the Feynman path-integral\napproach. In this case that central task is to compute the amplitude\nfor going from an initial state to a final state (where these states\nwill be given in terms of boundary data on a pair of initial and final\nhypersurfaces). The computation of this propagator proceeds à\nla sum-over-histories: one counts to the number of possible spacetimes\nthat might interpolate between the initial and final hypersurfaces.\nHowever, one cannot get around the fact that general relativity is a\ntheory with gauge freedom, and so whenever one has diffeomorphic\ninitial and final hypersurfaces, the propagator will be trivial.", "\nA similar confusion can be found in discussions of the related problem\nof defining observables in canonical general relativity. The claim\ngets its traction from the fact that it is very difficult to construct\nobservables in canonical general relativity, while (apparently) it is\nrelatively straightforward in the standard Lagrangian description.\n(See, e.g., Curiel, 2009, pp. 59–60, for an explicit statement\nof this claim. Curiel cites a theorem of Torre, 1993, to the effect\nthat there can be no local observables in compact spacetimes, to argue\nthat the canonical formulation is defective somehow.) Again, this\nrests on a misunderstanding over what the canonical formalism is and\nhow it is related to the standard spacetime formulation of general\nrelativity. That there are no local observables is not an artefact of\ncanonical general relativity. The notion that observables have to be\nnon-local (in this case, relational) is a generic feature that results\nprecisely from the full spacetime diffeomorphism invariance of general\nrelativity (and is, in fact, implicit in the theorem of Torre\nmentioned earlier). It receives a particularly transparent description\nin the context of the canonical approach because one can define\nobservables as quantities that commute with all of the constraints.\nThe same condition will hold for the four-dimensional versions, only\nthey will have to be spacetime diffeomorphism invariant in that case.\nThis will still rule out local observables since any quantities\ndefined at points or regions of the spacetime manifold will clearly\nfail to be diffeomorphism invariant. Hence, the problems of\nobservables (and the result that they must be either global or\nrelational in general relativity) is not a special feature of the\ncanonical formulation, but a generic feature of theories possessing\ndiffeomorphism invariance. As Ashtekar and Geroch point out,\n“[s]ince time is essentially a geometrical concept [in general\nrelativity], its definition must be in terms of the metric. But the\nmetric is also the dynamical variable, so the flow of time becomes\nintertwined with the flow of the dynamics of the system” (1974,\np. 1215)." ], "subsection_title": "5.1 Time" }, { "content": [ "\nThe problem of time is closely connected with a general puzzle about\nthe ontology associated with “quantum spacetime”. Quantum\ntheory in general resists any straightforward ontological reading, and\nthis goes double for quantum gravity. In quantum mechanics,\none has particles, albeit with indefinite properties. In quantum field\ntheory, one again has particles (at least in suitably symmetric\nspacetimes), but these are secondary to the fields, which again are\nthings, albeit with indefinite properties. On the face of it, the only\ndifference in quantum gravity is that spacetime itself becomes a kind\nof quantum field, and one would perhaps be inclined to say that the\nproperties of spacetime become indefinite. But space and time\ntraditionally play important roles in individuating objects and their\nproperties—in fact a field is in some sense a set of properties\nof spacetime points — and so the quantization of such raises\nreal problems for ontology.", "\nOne area that philosophers might profit from is in the investigation\nof the relational observables that appear to be necessitated by\ndiffeomorphism invariance. For example, since symmetries (such as the\ngauge symmetries associated with the constraints) come with quite a\nlot of metaphysical baggage attached (as philosophers of physics know\nfrom the\n hole argument),\n such a move involves philosophically weighty assumptions. For\nexample, the presence of symmetries in a theory would appear to allow\nfor more possibilities than one without, so eradicating the symmetries\n(by solving the constraints and going to the reduced, physical phase\nspace) means eradicating a chunk of possibility space: in particular,\none is eradicating states that are deemed to be physically equivalent,\ndespite having some formal differences in terms of representaton.\nHence, imposing the constraints involves some serious modal\nassumptions. Belot and Earman (2001) have argued that since the\ntraditional positions on the ontology of spacetime (relationalism and\nsubstantivalism) involve a commitment to a certain way of counting\npossibilities, the decision to eliminate symmetries can have serious\nimplications for the ontology one can then adopt. Further, if some\nparticular method (out of retaining or eliminating symmetries) were\nshown to be successful in the quest for quantizing gravity, then, they\nargue, one could have good scientific reasons for favouring one of\nsubstantivalism or relationalism. (See Belot, 2011a, for more on this\nargument; Rickles, 2008c, explicitly argues against the idea that\npossibility spaces have any relevance for spacetime ontology.)", "\nIn the loop quantum gravity program, the area and volume operators\nhave discrete spectra. Thus, like electron spins, they can\nonly take certain values. This suggests (but does not imply) that\nspace itself has a discrete nature, and perhaps time as well\n(depending on how one resolves the problem of time). This in turn\nsuggests that space does not have the structure of a differential\nmanifold, but rather that it only approximates such a manifold on\nlarge scales, or at low energies. A similar idea, that classical\nspacetime is an emergent entity, can be found in several\napproaches to quantum gravity (see Butterfield and Isham, 1999 and\n2001, for a discussion of emergence in quantum gravity). The\npossibility that a continuous structure (with continuous symmetries)\ncould emerge from a fundamentally discrete structure is a problem with\na clear philosophical flavour —Huggett and Wüthrich, eds.\n(2013) contains a variety of papers investigating this issue, with\ntheir own contribution focusing on the notion of recovering\n‘local beables’ from such emergent theories. " ], "subsection_title": "5.2 Ontology" }, { "content": [ "\nWhether or not spacetime is discrete, the quantization of spacetime\nentails that our ordinary notion of the physical world, that of matter\ndistributed in space and time, is at best an approximation. This in\nturn implies that ordinary quantum theory, in which one calculates\nprobabilities for events to occur in a given world, is inadequate as a\nfundamental theory. As suggested in the\n Introduction,\n this may present us with a vicious circle. At the very least, one\nmust almost certainly generalize the framework of quantum theory. This\nis an important driving force behind much of the effort in quantum\ncosmology to provide a well-defined version of the\n many-worlds\n or\n relative-state\n interpretations. Much work in this area has adopted the so-called\n‘decoherent histories’ or ‘consistent\nhistories’ formalism, whereby quantum theories are understood to\nmake probabilistic predictions about entire (coarse-grained)\n‘histories’. Almost all of this work to date construes\nhistories to be histories of spatiotemporal events, and thus\npresupposes a background spacetime; however, the incorporation of a\ndynamical, quantized spacetime clearly drives much of the\ncosmology-inspired work in this area.", "\nMore generally, one might step outside the framework of canonical,\nloop quantum gravity, and ask why one should only quantize the metric.\nAs pointed out by Isham (1994, 2002), it may well be that the\nextension of quantum theory to general relativity requires one to\nquantize, in some sense, not only the metric but also the underlying\ndifferential structure and topology. This is somewhat unnatural from\nthe standpoint where one begins with classical, canonical general\nrelativity and proceeds to “quantize” (since the\ntopological structure, unlike the metric structure, is not represented\nby a classical variable). But one might well think that one should\nstart with the more fundamental, quantum theory, and then investigate\nunder which circumstances one gets something that looks like a\nclassical spacetime.", "\nOne final issue we might mention here is whether there is a conflict\nbetween the superposition principle and general relativity. Curiel\nclaims that “[t]here exists no physical phenomenon well\ncharacterized by experiment that cannot be accurately described by one\nof the two theories, and no physical phenomenon that suggests that one\nof the two is correct to the detriment of the other’s\naccuracy” (2001, p. S432). However, Roger Penrose (2004, Chapter\n30) has forcefully argued that the superposition principle can, in\nsome circumstances, threaten the principle of general covariance,\nsurely a core principle of general relativity! The idea is that if we\nprepare a lump of matter in a superposition of two position states\n(stationary in their ambient spacetime), χ and φ, a state\nPenrose labels a “Schrödinger’s Lump” state,\nthen the superposition is represented by: |Ψ〉 =\nw|χ〉 + z|φ〉. Penrose then shows that a\nstationary gravitational field does nothing to affect the fact that\nany superposition of the (stationary) position states χ and φ\nwill also be stationary. But then introducing the gravitational field\nof the lump itself raises a problem. By themselves, the components of\nthe superposition would not seem to raise problems, and we can simply\nthink of the field around the location associated with the\nlump’s states individually as being nearly classical. Given the\nstationarity of the states χ and φ, there will be a distinct\nKilling vector (i.e. a metric preserving vector field) associated with\neach them. The problem then arises: what of superpositions of these\nlump states? Are they stationary? Since the Killing vector fields of\nthe two component stationary states live on different spacetimes, with\ndifferent structures, it seems we don’t have the invariant\nspatiotemporal structure needed to answer the question. To try and say\nthat the spacetime is really the same (the obvious answer) would\nconflict with general covariance since then one would be supposing a\nrobust notion of spacetime points which enables one to match up the\ntwo spacetimes. As we have seen above, Penrose’s proposed\nsolution is to consider such superpositions as generating a kind of\ngeometric instability which causes the collapse of the\nsuperposition.", "\nOf course, one might question various moves in Penrose’s\nreasoning here (especially as regards the nature of the gravitational\nfields of stationary quantum states), so there is clearly more to be\nsaid. But there is potentially a conflict (and a measurable one at\nthat: see Penrose, 2002) between the superposition principle and\nprinciples of general relativity. Those with experience of the\nstandard quantum measurement problem will find much to interest them\nin this problem." ], "subsection_title": "5.3 Status of quantum theory" }, { "content": [ "\nIt is almost Gospel that quantum gravity is what happens when you\nreach the Planck scale. The standard refrain is that ‘something\npeculiar’ happens to our concepts of space, time, and causality\nat such such scales requiring radical revisions that must be described\nby the quantum theory of gravity (see, e.g., Rovelli, 2007, p. 1287).\nHowever, the arguments underlying this orthodoxy have not been\nrigorously examined. The usual motivation involves a dimensional\nanalysis argument. The scales at which theories make their mark are\nset by the values of the fundamental constants. In this way the\nconstants demarcate the domains of applicability of theories: c\ntells us when specially relativistic effects will become apparent,\nℏ tells us when quantum effects will become apparent, and G\ntells us when gravitational effects will become apparent. As Planck\nwas able to demonstrate in 1899, these constants can be combined so as\nto uniquely determine a natural, absolute family of units that are\nindependent of all human and terrestrial baggage. The Planck length\ncan be written as\n(Gℏ/c3)½ and has the\nvalue 10−33 in centimeters. Planck was not aware of\nthe relevance of the scale set by the constants to the applicability\nof general relativity, of course, but Arthur Eddington seems to have\nbeen aware (though getting a different value as a result of using\nOsborn Reynold’s determination for the finest grain believed\npossible), writing in the March edition of Nature in 1918:", "\nFrom the combination of the fundamental constants, G, c,\nand h it is possible to form a new fundamental unit of length\nLmin = 7 × 10−28cm. It seems to be\ninevitable that this length must play some role in any complete\ninterpretation of gravitation. ... In recent years great progress has\nbeen made in knowledge of the excessively minute; but until we can\nappreciate details of structure down to the quadrillionth or\nquintillionth of a centimetre, the most sublime of all the forces of\nNature remains outside the purview of the theories of physics.\n(Eddington, 1918, p. 36)\n", "\nThe idea that the Planck length amounts to a minimal length in\nnature follows from the argument that if distances smaller than this\nlength are resolved (say in the measurement of the position of a\nmass), then it would require energies concentrated in a region so\nsmall that a mini-black hole would form, taking the observed system\nwith it – see Rovelli (2007, p. 1289) for this argument.\nMeschini (2007) is not convinced by such arguments, and doesn’t\nsee that the case for the relevance of the Planck scale to quantum\ngravity research has been properly made. He is suspicious of the\nclaims made on behalf of dimensional analysis. There is something to\nMeschini’s claims, for if the dimensional argument were true\nthen, without realising it, Planck would have stumbled upon the\nbeginnings of quantum gravity before either quantum field theory or\ngeneral relativity were devised! However, Meschini speculates that the\nfinal theory of quantum gravity “has nothing to do with one or\nmore of the above-mentioned constants” (p. 278). This seems too\nstrong a statement, since a core condition on a theory of quantum\ngravity will be to reduce to general relativity and quantum field\ntheory as we know it, according to limits involving these constants.\nNonetheless, Meschini is surely right that the details of these\ndimensional arguments, and the role of the Planck scale are calling\nout for a closer analysis." ], "subsection_title": "5.4 The Planck Scale" }, { "content": [ "\nIn non-generally relativistic theories the spacetime metric is frozen\nto a single value assignment for all times and all solutions: it is\nmodel independent. Of course, in general relativity the metric is what\none solves for: the metric is a dynamical variable, which implies that\nthe geometry of spacetime is dynamical. This intuitive notion is\nbundled into the concept of background freedom, or background\nindependence. In general, background independence is understood to be\nthe freedom of a theory from background structures, where the latter\namount to some kind of absolute, non-dynamical objects in a theory.\nThe extent to which their respective theories incorporate background\nstructures has recently proven to be a divisive subject amongst string\ntheorists and loop quantum gravity theorists and others. It is often\nclaimed that the central principle that distinguishes general\nrelativity from other theories is its (manifest) background\nindependence. But background independence is a slippery notion meaning\ndifferent things to different people. We face a series of questions\nwhen considering background independence: What, exactly, is it (beyond\nthe simple intuitive notion)? Why is it considered to be such an\nimportant principle? What theories incorporate it? To what\nextent do they incorporate it?", "\nThe debate between strings and loops on this matter is severely\nhampered by the fact that there is no firm definition of background\nindependence on the table and, therefore, the two camps are almost\ncertainly talking past each other when discussing this issue. It seems\nprima facie reasonable to think that in order to reproduce a\nmanifestly background independent theory like general relativity, a\nquantum theory of gravity should be background independent too, and so\nbackground independence has begun to function as a constraint on\nquantum gravity theories, in much the same way that renormalizability\nused to constrain the construction of quantum field theories.\nAdvocates of loop quantum gravity often highlight the background\nindependence of their theory as a virtue that it has over string\ntheory. However, there is no proof of this implication, and aspects of\nthe so-called ‘holographic principle’ seem to suggest that\na background independent theory could be dual to a background\ndependent theory (see the contributions to Biquard, ed., 2005).\nFurthermore, depending on how we define the intuitive notion of\nbackground independence, and if ‘clues’ from the duality\nsymmetries of M-theory are anything to go by, it looks like string\ntheory might even be more background independent than loop\nquantum gravity, for the dimensionality of spacetime becomes a\ndynamical variable too (cf. Stelle, 2000, p. 7).", "\nIndeed, various string theorists claim that their theory is background\nindependent. In many cases it seems that they have a different\nunderstanding of what this entails than loop quantum gravity\nresearchers—this takes us to the first, definitional, question.\nIn particular some seem to think that the ability to place a general\nmetric in the Lagrangian amounts to background independence. This\nfalls short of the mark for how the majority of physicists understand\nit, namely as a reactive dynamical coupling between spacetime and\nmatter. Though one can indeed place a variety of metrics in the\nstringy Lagrangian, one does not then vary the metric in the action.\nThere is no interaction between the strings and the ambient spacetime.\nIndeed, this is not really distinct from quantum field theory of point\nparticles in curved spacetimes: the same freedom to insert a general\nmetric appears there too.", "\nThere is an alternative argument for the background independence of\nstring theory that comes from the field theoretic formulation of the\ntheory: string field theory. The idea is that classical spacetime\nemerges from the two dimensional conformal field theory on the strings\nworldsheet. However, in this case one surely has to say something\nabout the target space, for the worldsheet metric takes on a metric\ninduced from the ambient target spacetime. Yet another argument for\nthe background independence of string theory might point to the fact\nthat the dimensionality of spacetime in string theory has to satisfy\nan equation of motion (a consistency condition): this is how the\ndimensionality comes out (as 26 or 10, depending on whether one\nimposes supersymmetry). One contender for the definition of background\nindependence is a structure that is dynamical in the sense that one\nhas to solve equations of motion to get at its values. In this case we\nwould have extreme background independence stretching to the structure\nof the manifold itself. However, the problem with this is that this\nstructure is the same in all models of the theory; yet we intuitively\nexpect background independent theories to be about structures that can\nvary across a theory’s models.", "\nThe issues here are clearly subtle and complex, and philosophers have\nonly just begun to consider them. The central problem faced, as a\nphilosopher, when trying to make sense of claims such as these is that\nthere is no solid, unproblematic definition of background structure\n(and therefore background independence and dependence) on the table.\nWithout this, one simply cannot decide who is right; one cannot decide\nwhich theories are background independent and which are not. Hence, an\nurgent issue in both physics and the philosophy of physics is to work\nout exactly what is meant by ‘background independence’ in\na way that satisfies all parties, that is formally correct, and that\nsatisfies our intuitive notions of the concept. Until this is\nachieved, background independence cannot be helpfully used to\ndistinguish the approaches, nor can we profitably discuss its merits.\nA serious attempt to define background independence in such a way as\nto make these tasks possible has been made by Domenico Giulini (2007).\nBut Giulini admits that a general definition still eludes us. The\nstumbling block might be that background independence simply\nisn’t a formal property of theories at all. Gordon Belot (2011b)\nhas recently argued that background independence is partly an\ninterpretive matter, and that one can have varying levels of\nbackground independence (the latter notion is also defended by Lee\nSmolin, 2006). Rickles (2008b) argues that the place to seek a notion\nof background independence that can be put to use in the quantum\ngravitational context is by focusing on the kinds of\nobservables that an approach employs, rather than squarely on\nproperties of the equations of motion." ], "subsection_title": "5.5 Background Structure" }, { "content": [ "\nIn earlier research on quantum gravity it was often supposed that if\nthere was at least one quantum field in the world together with the\ngravitational field, then given the universal coupling of the\ngravitational field, it must follow that the quantization of the one\nfield somehow infects the gravitational field, implying that it must\nnecessarily have quantum properties too. The arguments basically\ninvolve the consideration of a mass prepared in a superposition of\nposition eigenstates. If the gravitational field remained classical\n(and, therefore, not constrained by the uncertainty relations) then\none could violate the uncertainty relations by simply making\nmeasurements of the gravitational field, discovering the properties of\nthe quantized matter to which it was coupled. However, all attempts at\nmaking this argument stick have so far failed, meaning that there is\nno logical necessity demanding that we quantize the gravitational\nfield. Given that we also seemingly lack experimental reasons for\nquantization of the gravitational field (since we have not observed\nevidence of its quantum properties), several physicists (and\nphilosophers) have questioned the programme as it stands. It is, they\nargue, a matter for experiment to decide, not logic. Note, however,\nthat this does not mean that the project of quantum gravity itself\nrests on unsteady ground: if there are quantum fields and\ngravitational fields in the world, then given the nature of gravity,\nwe need to say something about the manner in which they\ninteract. What is being questioned is whether this means that gravity\ncannot itself remain fundamentally classical while interacting with\nquantum fields. After all, as far as all our experiments show: gravity\nis classical and matter is quantum. This pessimistic argument is\nusually traced back to Rosenfeld, though he wavered somewhat on the\nmatter (see DeWitt and Rickles, 2011, p. 164 and p. 170, for\nRosenfeld’s original arguments).", "\nIf it is to remain fundamentally classical, then there is the simple\nquestion of what such a classical gravitational field would couple to:\nthe quantum properties? That seems problematic for the reasons given\nabove. Moreover, given the form of the Einstein field equations, with\na classical c-number on the left hand side, that would mean equating a\nc-number with a q-number (i.e. a quantum operator). The standard way\nout of this problem is to couple the gravitational field instead to\nthe expectation value of the stress-energy tensor of some quantized\nmatter field. The expectation value is a c-number. There have been a\nvariety of arguments and no-go theorems against this so-called\nsemi-classical gravitational theory, most of which replay the kind of\nargument invoking violations of the uncertainty relations sketched\nabove (see Eppley and Hannah 1977, and Page and Geilker 1981).\nBasically, the upshot of the Eppley and Hannah paper is that, given\nthe coexistence of classical gravity and quantum fields, two things\ncan happen upon a gravitational field measurement: on the one hand the\nquantum wavefunction could collapse, in which case there momentum\nnon-conservation. On the other hand, the measurement could leave the\nquantum wavefunction in a coherent state, in which case signals can be\nsent faster than light. Mattingly (2006) argues that, when properly\nanalyzed, the thought experiments employed by Eppley and Hannah\nviolate basic physical principles involving the construction of the\nequipment that would be needed to make the necessary field\nmeasurements — however, while not viewing the original\nsemi-classical approach as a viable option, Mattingly argues that an\nextension of the approach has the potential to reveal a viable theory\nof micro-gravity (see Mattingly 2010 and 2014). Adrian Kent has\nrecently argued that general hybrid classical/quantum theories\n(including those involving gravity) need not allow superluminal\nsignalling or violate relativity (Kent 2018).", "\nA batch of new approaches based on analogies with condensed matter\nphysics and hydrodynamics point to another way in which gravity can\nescape quantization, though not in a truly fundamental sense.\nAccording to such approaches, gravity is emergent in the sense that\nthe metric (or connection) variables, and other variables representing\ngravitational features, are collective variables that only appear at\nenergies away from the Planck scale. In other words, gravity is a\npurely macroscopic, low energy phenomenon and general relativity is an\neffective field theory. This leaves the task of actually filling in\nthe details of the microscopic structure of spacetime (the\n‘atoms of spacetime’) out of which the low energy\ncollective variables emerge (see Hu, 2009, for a conceptually oriented\nreview of such approaches; Crowther 2014 provides a detailed\nphilosophical analysis). As Rovelli notes (2007, p. 1304), the mere\nfact that the gravitational field is an emergent, collective variable\ndoes not thereby imply an absence of quantum effects, and it is\npossible that collective variables too are governed by quantum\ntheory.", "\nWüthrich (2005, pp. 779–80) has argued that the very\nexistence of approaches to quantum gravity that do not involve the\nquantization of the gravitational field means that quantization of the\ngravitational field has to be a contingent matter. However,\nthis seems to rest on a mistake. It might still be the case that there\nare reasons of logical consistency forbidding the union of a classical\nand quantum field even though there are entirely distinct\nnon-quantization approaches. For example, string theory does not\nquantize the gravitational field; however, it is clearly wrong to say\nthat the existence of this position would be ruled out if the various\nno-go theorems outlawing hybrid classical-quantum theories were true.\nThe fact that one can isolate states corresponding to gravitons in the\nstring spectrum stands quite independent from issues over the\ninteraction of classical and quantum field. The question of the\nnecessity of quantization (as a result of coupling a classical\ngravitational field to quantum fields) should be held separate from\nthe prospect of producing a quantum theory of gravity that does not\ninvolve gravitational field quantization, for both input theories, for\ndescribing the classical and quantum fields, could be fundamentally\nwrong at high energies, requiring entirely new principles. However, a\nstronger argument against the impossibility hybrids is provided by\nJames Mattingly, who points out that since there are satisfiable\naxioms for semiclassical theories, inconsistency cannot be established\nin general (2009, p. 381)." ], "subsection_title": "5.6 Necessity of Quantization" } ] }, { "main_content": [ "\nResearch on quantum gravity is beset by a combination of formal,\nexperimental, and conceptual difficulties. It is inevitable that the\nquest for a quantum theory of gravity will continue – whether\nfor reasons of necessity or not – and it seems that the\nresolution of the problem will require an equivalent combination of\nformal, experimental, and conceptual expertise. Given this, and given\nthe central position quantum gravity research occupies in theoretical\nphysics, it makes good sense for philosophers of physics (and general\nphilosophers of science) to do their best to acquaint themselves with\nthe central details of the problem of quantum gravity and the main\napproaches that are seeking to crack the problem. Beyond this, quantum\ngravity research has the potential to invigorate several standard\nareas of philosophical inquiry, including our standard notions of\ntheory construction, selection and justification; the nature of space,\ntime, matter, and causality, and it also introduces a new case study\nin emergence, with entirely novel features." ], "section_title": "6. Conclusion", "subsections": [] } ]

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[ { "href": "../popper/", "text": "Popper, Karl" }, { "href": "../qm/", "text": "quantum mechanics" }, { "href": "../qm-everett/", "text": "quantum mechanics: Everett’s relative-state formulation of" }, { "href": "../qm-manyworlds/", "text": "quantum mechanics: many-worlds interpretation of" }, { "href": "../quantum-field-theory/", "text": "quantum theory: quantum field theory" }, { "href": "../spacetime-theories/", "text": "space and time: absolute and relational space and motion, post-Newtonian theories" }, { "href": "../spacetime-singularities/", "text": "space and time: singularities and black holes" }, { "href": "../spacetime-holearg/", "text": "space and time: the hole argument" }, { "href": "../time-machine/", "text": "time machines" }, { "href": "../qt-uncertainty/", "text": "Uncertainty Principle" } ]

[ "\nMathematically, quantum mechanics can be regarded as a non-classical\nprobability calculus resting upon a non-classical propositional logic.\nMore specifically, in quantum mechanics each probability-bearing\nproposition of the form “the value of physical quantity \\(A\\)\nlies in the range \\(B\\)” is represented by a projection operator\non a Hilbert space \\(\\mathbf{H}\\). These form a non-Boolean—in\nparticular, non-distributive—orthocomplemented lattice.\nQuantum-mechanical states correspond exactly to probability measures\n(suitably defined) on this lattice.", "\nWhat are we to make of this? Some have argued that the empirical\nsuccess of quantum mechanics calls for a revolution in logic itself.\nThis view is associated with the demand for a realistic interpretation\nof quantum mechanics, i.e., one not grounded in any primitive notion\nof measurement. Against this, there is a long tradition of\ninterpreting quantum mechanics operationally, that is, as being\nprecisely a theory of measurement. On this latter view, it is not\nsurprising that a “logic” of measurement-outcomes, in a\nsetting where not all measurements are compatible, should prove not to\nbe Boolean. Rather, the mystery is why it should have the\nparticular non-Boolean structure that it does in quantum\nmechanics. A substantial literature has grown up around the programme\nof giving some independent motivation for this\nstructure—ideally, by deriving it from more primitive and\nplausible axioms governing a generalized probability theory." ]

[ { "content_title": "1. Quantum Mechanics as a Probability Calculus", "sub_toc": [ "1.1 Quantum Probability in a Nutshell", "1.2 The “Logic” of Projections", "1.3 Probability Measures and Gleason’s Theorem", "1.4 The Reconstruction of QM" ] }, { "content_title": "2. Interpretations of Quantum Logic", "sub_toc": [ "2.1 Realist Quantum Logic", "2.2 Operational Quantum Logic" ] }, { "content_title": "3. Generalized Probability Theory", "sub_toc": [ "3.1 Discrete Classical Probability Theory", "3.2 Test Spaces", "3.3 Kolmogorovian Probability Theory", "3.4 Quantum Probability Theory" ] }, { "content_title": "4. Logics associated with probabilistic models", "sub_toc": [ "4.1 Operational Logics", "4.2 Orthocoherence", "4.3 Lattices of Properties" ] }, { "content_title": "5. Piron’s Theorem", "sub_toc": [ "5.1 Conditioning and the Covering Law" ] }, { "content_title": "6. Classical Representations", "sub_toc": [ "6.1 Classical Embeddings", "6.2 Contextual Hidden Variables" ] }, { "content_title": "7. Composite Systems", "sub_toc": [ "7.1 The Foulis-Randall Example", "7.2 Aerts’ Theorem", "7.3 Ramifications" ] }, { "content_title": "8. Effect Algebras", "sub_toc": [ "8.1 Quantum effects and Naimark’s Theorem", "8.2 Sequential Effect Algebras" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nIt is uncontroversial (though remarkable) that the formal apparatus of\nquantum mechanics reduces neatly to a generalization of classical\nprobability in which the role played by a Boolean algebra of events in\nthe latter is taken over by the “quantum logic” of\nprojection operators on a Hilbert\n space.[1]\n Moreover, the usual statistical interpretation of quantum mechanics\nasks us to take this generalized quantum probability theory quite\nliterally—that is, not as merely a formal analogue of its\nclassical counterpart, but as a genuine doctrine of chances. In this\nsection, I survey this quantum probability theory and its supporting\nquantum\n logic.[2]", "\n[For further background on Hilbert spaces, see the entry on\n quantum mechanics.\n For further background on ordered sets and lattices, see the\nsupplementary document:\n The Basic Theory of Ordering Relations.\n Concepts and results explained these supplements will be used freely\nin what follows.] " ], "section_title": "1. Quantum Mechanics as a Probability Calculus", "subsections": [ { "content": [ "\nThe quantum-probabilistic formalism, as developed by von Neumann\n[1932], assumes that each physical system is associated with a\n(separable) Hilbert space \\(\\mathbf{H}\\), the unit vectors of which\ncorrespond to possible physical states of the system. Each\n“observable” real-valued random quantity is represented by\na self-adjoint operator \\(A\\) on \\(\\mathbf{H}\\), the spectrum of which\nis the set of possible values of \\(A\\). If \\(u\\) is a unit vector in\nthe domain of \\(A\\), representing a state, then the expected value of\nthe observable represented by \\(A\\) in this state is given by the\ninner product \\(\\langle Au,u\\rangle\\). The observables represented by\ntwo operators \\(A\\) and \\(B\\) are commensurable iff \\(A\\) and \\(B\\)\ncommute, i.e., AB = BA. (For further discussion, see the\n entry on quantum mechanics.)" ], "subsection_title": "1.1 Quantum Probability in a Nutshell" }, { "content": [ "\nAs stressed by von Neumann, the \\(\\{0,1\\}\\)-valued observables may be\nregarded as encoding propositions about—or, to use his phrasing,\nproperties of—the state of the system. It is not difficult to\nshow that a self-adjoint operator \\(P\\) with spectrum contained in the\ntwo-point set \\(\\{0,1\\}\\) must be a projection; i.e., \\(P^2 = P\\).\nSuch operators are in one-to-one correspondence with the closed\nsubspaces of \\(\\mathbf{H}\\). Indeed, if \\(P\\) is a projection, its\nrange is closed, and any closed subspace is the range of a unique\nprojection. If \\(u\\) is any unit vector, then \\(\\langle Pu,u\\rangle =\n\\llvert Pu\\rrvert ^2\\) is the expected value of the corresponding\nobservable in the state represented by \\(u\\). Since this observable is\n\\(\\{0,1\\}\\)-valued, we can interpret this expected value as the\nprobability that a measurement of the observable will produce\nthe “affirmative” answer 1. In particular, the affirmative\nanswer will have probability 1 if and only if Pu = u; that\nis, \\(u\\) lies in the range of \\(P\\). Von Neumann concludes that ", "\n\n\n… the relation between the properties of a physical system on\nthe one hand, and the projections on the other, makes possible a sort\nof logical calculus with these. However, in contrast to the concepts\nof ordinary logic, this system is extended by the concept of\n“simultaneous decidability” which is characteristic for\nquantum mechanics. (1932: 253) \n", "\nLet’s examine this “logical calculus” of\nprojections. Ordered by set-inclusion, the closed subspaces of\n\\(\\mathbf{H}\\) form a complete lattice, in which the meet (greatest\nlower bound) of a set of subspaces is their intersection, while their\njoin (least upper bound) is the closed span of their union. Since a\ntypical closed subspace has infinitely many complementary closed\nsubspaces, this lattice is not distributive; however, it is\northocomplemented by the mapping ", "\n In view of the\nabove-mentioned one-one correspondence between closed subspaces and\nprojections, we may impose upon the set \\(L(\\mathbf{H})\\) the\nstructure of a complete orthocomplemented lattice, defining \\(P\\le\nQ\\), where \\(\\rran (P) \\subseteq \\rran (Q)\\) and \\(P' = 1 - P\\) (so\nthat \\(\\rran (P') = \\rran (P)^{\\bot})\\). It is straightforward that\n\\(P\\le Q\\) just in case \\(PQ = QP = P\\). More generally, if PQ =\nQP, then \\(PQ = P\\wedge Q\\), the meet of \\(P\\) and \\(Q\\) in\n\\(L(\\mathbf{H})\\); also in this case their join is given by \\(P\\vee Q\n= P+Q - PQ\\).", "\nAdhering to the idea that commuting observables—in particular,\nprojections—are simultaneously measurable, we conclude that the\nmembers of a Boolean sub-ortholattice of \\(L(\\mathbf{H})\\) are\nsimultaneously testable. This suggests that we can maintain a\nclassical logical interpretation of the meet, join and orthocomplement\nas applied to commuting projections." ], "subsection_title": "1.2 The “Logic” of Projections" }, { "content": [ "\nThe foregoing discussion motivates the following. Call projections\n\\(P\\) and \\(Q\\) orthogonal, and write \\(P\\binbot Q\\) iff \\(P\n\\le Q'\\). Note that \\(P\\binbot Q\\) iff \\(PQ = QP = 0\\). If \\(P\\) and\n\\(Q\\) are orthogonal projections, then their join is simply their sum;\ntraditionally, this is denoted \\(P\\oplus Q\\). We denote the identity\nmapping on \\(\\mathbf{H}\\) by \\(\\mathbf{1}\\).", "\nHere is one way in which we can manufacture a probability measure on\n\\(L(\\mathbf{H})\\). Let \\(u\\) be a unit vector of \\(\\mathbf{H}\\), and\nset \\(\\mu_u (P) = \\langle Pu,u\\rangle\\). This gives the usual\nquantum-mechanical recipe for the probability that \\(P\\) will have\nvalue 1 in the state \\(u\\). Note that we can also express \\(\\mu_u\\) as\n\\(\\mu_u(P) = Tr(P P_u)\\), where \\(P_u\\) is the one-dimensional\nprojection associated with the unit vector \\(u\\), i.e., \\(P_u(x) =\n\\langle x, u \\rangle u\\) for all \\(x \\in \\mathbf{H}\\). ", "\nMore generally, if \\(\\mu_i, i=1,2,\\ldots\\), are probability measures\non \\(L(\\mathbf{H})\\), then so is any “mixture”, or convex\ncombination \\(\\mu = \\sum_i t_i\\mu_i\\) where \\(0\\le t_i\\le 1\\) and\n\\(\\sum_i t_i = 1\\). Given any sequence \\(u_1, u_2,\\ldots\\), of unit\nvectors, let \\(\\mu_i = \\mu_{u_{ i}}\\) and let \\(P_i = P_{u_{ i}}\\).\nForming the operator ", " one sees that ", "\nAn operator expressible in this way as a convex combination of\none-dimensional projections in is called a density operator.\nDensity operators are the standard mathematical representation for\ngeneral (pure or “mixed”) quantum-mechanical states. We\nhave just seen that every density operator \\(W\\) gives rise to a\ncountably additive probability measure on \\(L(\\mathbf{H})\\). The\nfollowing striking converse, due to A. Gleason [1957], shows that the\ntheory of probability measures on \\(L(\\mathbf{H})\\) is co-extensive\nwith the theory of (mixed) quantum mechanical states on\n\\(\\mathbf{H}\\):", "\nAn important consequence of Gleason’s Theorem is that\n\\(L(\\mathbf{H})\\) does not admit any probability measures having only\nthe values 0 and 1. To see this, note that for any density operator\n\\(W\\), the mapping \\(u \\rightarrow \\langle Wu,u\\rangle\\) is continuous\non the unit sphere of \\(\\mathbf{H}\\). But since the latter is\nconnected, no continuous function on it can take only the two values 0\nand 1. This result is often taken to rule out the possibility of\n“hidden variables”—an issue taken up in more detail\nin section 6." ], "subsection_title": "1.3 Probability Measures and Gleason’s Theorem" }, { "content": [ "\nFrom the single premise that the “experimental\npropositions” associated with a physical system are encoded by\nprojections in the way indicated above, one can reconstruct the rest\nof the formal apparatus of quantum mechanics. The first step, of\ncourse, is Gleason’s theorem, which tells us that probability\nmeasures on \\(L(\\mathbf{H})\\) correspond to density operators. There\nremains to recover, e.g., the representation of\n“observables” by self-adjoint operators, and the dynamics\n(unitary evolution). The former can be recovered with the help of the\nSpectral theorem and the latter with the aid of a deep theorem of E.\nWigner on the projective representation of groups. See also R. Wright\n[1980]. A detailed outline of this reconstruction (which involves some\ndistinctly non-trivial mathematics) can be found in the book of\nVaradarajan [1985]. The point to bear in mind is that, once the\nquantum-logical skeleton \\(L(\\mathbf{H})\\) is in place, the remaining\nstatistical and dynamical apparatus of quantum mechanics is\nessentially fixed. In this sense, then, quantum mechanics—or, at\nany rate, its mathematical framework—reduces to quantum\nlogic and its attendant probability theory." ], "subsection_title": "1.4 The Reconstruction of QM" } ] }, { "main_content": [ "\nThe reduction of QM to probability theory based on \\(L(\\mathbf{H})\\)\nis mathematically compelling, but what does it tell us about\nQM—or, assuming QM to be a correct and complete physical theory,\nabout the world? How, in other words, are we to interpret the quantum\nlogic \\(L(\\mathbf{H})\\)? The answer will turn on how we unpack the\nphrase, freely used above,", "\nOne possible reading of (*) is operational:\n“measurement of the observable \\(A\\) would yield (or will yield,\nor has yielded) a value in the set \\(B\\)”. On this view,\nprojections represent statements about the possible results of\nmeasurements. This sits badly with realists of a certain stripe, who,\nshunning reference to “measurement”, prefer to understand\n(*) as a property ascription: ", "\n\n\nthe system has a certain categorical property, which corresponds to\nthe observable \\(A\\) having, independently of any measurement, a value\nin the set \\(B\\). \n", "\n(One must be careful in how one understands this last phrase, however:\nconstrued incautiously, it seems to posit a hidden-variables\ninterpretation of quantum mechanics of just the sort ruled out by\nGleason’s Theorem. I will have more to say about this\nbelow.)" ], "section_title": "2. Interpretations of Quantum Logic", "subsections": [ { "content": [ "\nThe interpretation of projection operators as representing the\nproperties of a physical system is already explicit in von\nNeumann’s Grundlagen.. However, the logical operations\ndiscussed there apply only to commuting projections, which are\nidentified with simultaneously decidable propositions. In 1936\nBirkhoff and von Neumann took a step further, proposing to interpret\nthe lattice-theoretic meet and join of projections as their\nconjunction and disjunction, whether or not they commute.\nImmediately this proposal faces the problem that the lattice\n\\(L(\\mathbf{H})\\) is not distributive, making it impossible to give\nthese “quantum” connectives a truth-functional\ninterpretation. Undaunted, von Neumann and Birkhoff suggested that the\nempirical success of quantum mechanics as a framework for physics\ncasts into doubt the universal validity of the distributive laws of\npropositional logic. Their phrasing remains cautious:", "\nWhereas logicians have usually assumed that properties … of\nnegation were the ones least able to withstand a critical analysis,\nthe study of mechanics points to the distributive identities …\nas the weakest link in the algebra of logic. (1936: 837)\n", "\nIn the 1960s and early 1970s, this thesis was advanced rather more\naggressively by a number of authors, including especially David\nFinkelstein and Hilary Putnam, who argued that quantum mechanics\nrequires a revolution in our understanding of logic per se.\nAccording to Putnam, “Logic is as empirical as geometry.\n… We live in a world with a non-classical logic” ([1968]\n1979: 184).", "\nFor Putnam, the elements of \\(L(\\mathbf{H})\\) represent categorical\nproperties that an object possesses, or does not, independently of\nwhether or not we look. Inasmuch as this picture of physical\nproperties is confirmed by the empirical success of quantum mechanics,\nwe must, on this view, accept that the way in which physical\nproperties actually hang together is not Boolean. Since logic is, for\nPutnam, very much the study of how physical properties actually hang\ntogether, he concludes that classical logic is simply mistaken: the\ndistributive law is not universally valid.", "\nClassically, if \\(S\\) is the set of states of a physical system, then\nevery subset of \\(S\\) corresponds to a categorical property\nof the system, and vice versa. In quantum mechanics, the state space\nis the (projective) unit sphere \\(S = S(\\mathbf{H})\\) of a Hilbert\nspace. However, not all subsets of \\(S\\) correspond to\nquantum-mechanical properties of the system. The latter correspond\nonly to subsets of the special form \\(S \\cap \\mathbf{M}\\), for\n\\(\\mathbf{M}\\) a closed linear subspace of \\(\\mathbf{H}\\). In\nparticular, only subsets of this form are assigned probabilities. This\nleaves us with two options. One is to take only these special\nproperties as “real” (or “physical”, or\n“meaningful”), regarding more general subsets of \\(S\\) as\ncorresponding to no real categorical properties at all. The other is\nto regard the “quantum” properties as a small subset of\nthe set of all physically (or at any rate, metaphysically) reasonable,\nbut not necessarily observable, properties of the system. On\nthis latter view, the set of all properties of a physical\nsystem is entirely classical in its logical structure, but we decline\nto assign probabilities to the non-observable\n properties.[3]", "\nThis second position, while certainly not inconsistent with realism\nper se, turns upon a distinction involving a notion of\n“observation”, “measurement”,\n“test”, or something of this sort—a notion that\nrealists are often at pains to avoid in connection with fundamental\nphysical theory. Of course, any realist account of a statistical\nphysical theory such as quantum mechanics will ultimately have to\nrender up some explanation of how measurements are supposed to take\nplace. That is, it will have to give an account of which physical\ninteractions between “object” and “probe”\nsystems count as measurements, and of how these interactions cause the\nprobe system to evolve into final “outcome-states” that\ncorrespond to—and have the same probabilities as—the\noutcomes predicted by the theory. This is the notorious\nmeasurement problem.", "\nIn fact, Putnam advanced his version of quantum-logical realism as\noffering a (radical) dissolution of the measurement problem: According\nto Putnam, the measurement problem (and indeed every other\nquantum-mechanical “paradox”) arises through an improper\napplication of the distributive law, and hence disappears\nonce this is recognized. This proposal, however, is widely regarded as\n mistaken.[4]\n ", "\nAs mentioned above, realist interpretations of quantum mechanics must\nbe careful in how they construe the phrase “the observable \\(A\\)\nhas a value in the set \\(B\\)”. The simplest and most traditional\nproposal—often dubbed the “eigenstate-eigenvalue\nlink” (Fine [1973])—is that (*) holds if and only if a\nmeasurement of \\(A\\) yields a value in the set \\(B\\) with certainty,\ni.e., with (quantum-mechanical!) probability 1. While this certainly\ngives a realist interpretation of\n (*),[5]\n it does not provide a solution to the measurement problem. Indeed, we\ncan use it to give a sharp formulation of that problem: even though\n\\(A\\) is certain to yield a value in \\(B\\) when measured, unless the\nquantum state is an eigenstate of the measured observable \\(A\\), the\nsystem does not possess any categorical property corresponding to\n\\(A\\)’s having a specific value in the set \\(B\\). Putnam seems\nto assume that a realist interpretation of (*) should consist in\nassigning to \\(A\\) some unknown value within \\(B\\), for which quantum\nmechanics yields a non-trivial probability. However, an attempt to\nmake such assignments simultaneously for all observables runs afoul of\nGleason’s\n Theorem.[6]" ], "subsection_title": "2.1 Realist Quantum Logic" }, { "content": [ "\nIf we put aside scruples about “measurement” as a\nprimitive term in physical theory, and accept a principled distinction\nbetween “testable” and non-testable properties, then the\nfact that \\(L(\\mathbf{H})\\) is not Boolean is unremarkable, and\ncarries no implication about logic per se. Quantum mechanics\nis, on this view, a theory about the possible statistical\ndistributions of outcomes of certain measurements, and its\nnon-classical “logic” simply reflects the fact that not\nall observable phenomena can be observed simultaneously. Because of\nthis, the set of probability-bearing events (or propositions) is\nless rich than it would be in classical probability theory,\nand the set of possible statistical distributions, accordingly, less\ntightly constrained. That some “non-classical” probability\ndistributions allowed by this theory are actually manifested in nature\nis perhaps surprising, but in no way requires any deep shift in our\nunderstanding of logic or, for that matter, of probability.", "\nThis is hardly the last word, however. Having accepted all of the\nabove, there still remains the question of why the logic of\nmeasurement outcomes should have the very special form\n\\(L(\\mathbf{H})\\), and never anything more\n general.[7]\n This question entertains the idea that the formal structure of\nquantum mechanics may be uniquely determined by a small\nnumber of reasonable assumptions, together perhaps with certain\nmanifest regularities in the observed phenomena. This possibility is\nalready contemplated in von Neumann’s Grundlagen (and\nalso his later work in continuous geometry), but first becomes\nexplicit—and programmatic—in the work of George Mackey\n[1957, 1963]. Mackey presents a sequence of six axioms, framing a very\nconservative generalized probability theory, that underwrite the\nconstruction of a “logic” of experimental propositions,\nor, in his terminology, “questions”, having the structure\nof a sigma-orthomodular partially-ordered set (see Section 4 and the\nsupplement document\n The Basic Theory of Ordering Relations\n for definitions of these terms). The outstanding problem, for Mackey,\nwas to explain why this poset ought to be isomorphic to\n\\(L(\\mathbf{H})\\):", "\nAlmost all modern quantum mechanics is based implicitly or explicitly\non the following assumption, which we shall state as an axiom:\n\n\nAxiom VII: The partially ordered set of all questions in quantum\nmechanics is isomorphic to the partially ordered set of all closed\nsubspaces of a separable, infinite dimensional Hilbert space.\n\n\n\nThis axiom has rather a different character from Axioms I through VI.\nThese all had some degree of physical naturalness and plausibility.\nAxiom VII seems entirely ad hoc. Why do we make it? Can we justify\nmaking it? … Ideally, one would like to have a list of\nphysically plausible assumptions from which one could deduce Axiom\nVII. Short of this one would like a list from which one could deduce a\nset of possibilities for the structure … all but one of which\ncould be shown to be inconsistent with suitably planned experiments.\n[Mackey 1963: 71–72]\n", "\nSince Mackey’s writing there has grown up an extensive technical\nliterature exploring variations on his axiomatic framework in an\neffort to supply the missing assumptions. The remainder of this\narticle presents a brief survey of the current state of this\nproject." ], "subsection_title": "2.2 Operational Quantum Logic" } ] }, { "main_content": [ "\nRather than restate Mackey’s axioms verbatim, I shall paraphrase\nthem in the context of an approach to generalized probability theory\ndue to D. J. Foulis and C. H. Randall having—among the many more\nor less analogous approaches\n available[8]—certain\n advantages of simplicity and flexibility. References for this section\nare Foulis, Greechie, and Rüttimann [1992]; Foulis, Piron and\nRandall [1983]; Randall and Foulis [1983]; see also Gudder [1989];\nWilce [2000b] and Wilce [2009] for surveys." ], "section_title": "3. Generalized Probability Theory", "subsections": [ { "content": [ "\nIt will be helpful to begin with a review of classical probability\ntheory. In its simplest formulation, classical probability theory\ndeals with a (discrete) set \\(E\\) of mutually exclusive outcomes, as\nof some measurement, experiment, etc., and with the various\nprobability weights that can be defined thereon—that\nis, with mappings \\(\\omega : E \\rightarrow[0,1]\\) summing to 1 over\n \\(E\\).[9]", "\nNotice that the set \\(\\Delta(E)\\) of all probability weights on \\(E\\)\nis convex, in that, given any sequence\n\\(\\omega_1,\\omega_2,\\ldots\\) of probability weights and any sequence\n\\(t_1,t_2,\\ldots\\) of non-negative real numbers summing to one, the\nconvex sum or “mixture” \\(t_1\\omega_1 + t_2\\omega_2\n+\\ldots\\) (taken pointwise on \\(E)\\) is again a probability weight.\nThe extreme points of this convex set are exactly the\n“point-masses” \\(\\delta(x)\\) associated with the outcomes\n\\(x \\in E\\): ", "\n Thus, \\(\\Delta(E)\\) is a simplex:\neach point \\(\\omega \\in \\Delta(E)\\) is representable in a unique way\nas a convex combination of extreme points, namely: ", "\n We also\nneed to recall the concept of a random variable. If \\(E\\) is\nan outcome set and \\(V\\), some set of “values” (real\nnumbers, pointer-readings, or what not), a \\(V\\)-valued random\nvariable is simply a mapping \\(f : E \\rightarrow V\\). The\nheuristic (but it need only be taken as that) is that one\n“measures” the random variable \\(f\\) by\n“performing” the experiment represented by \\(E\\) and, upon\nobtaining the outcome \\(x \\in E\\), recording \\(f(x)\\) as the measured\nvalue. Note that if \\(V\\) is a set of real numbers, or, more\ngenerally, a subset of a vector space, we may define the expected\nvalue of \\(f\\) in a state \\(\\omega \\in \\Delta(E)\\) by:" ], "subsection_title": "3.1 Discrete Classical Probability Theory" }, { "content": [ "\nA very natural direction in which to generalize discrete classical\nprobability theory is to allow for a multiplicity of outcome-sets,\neach representing a different “experiment”. To formalize\nthis, let us agree that a test space is a non-empty\ncollection A of non-empty sets \\(E,F,\\ldots\\), each construed as a\ndiscrete outcome-set as in classical probability theory. Each set \\(E\n\\in \\mathcal{A}\\) is called a test. The set \\(X = \\cup\n\\mathcal{A}\\) of all outcomes of all tests belonging to\n\\(\\mathcal{A}\\) is called the outcome space of\n\\(\\mathcal{A}\\). Notice that we allow distinct tests to overlap, i.e.,\nto have outcomes in\n common.[10]", "\nIf \\(\\mathcal{A}\\) is a test space with outcome-space \\(X\\), a\nstate on \\(\\mathcal{A}\\) is a mapping \\(\\omega : X\n\\rightarrow\\) [0,1] such that \\(\\sum_{x\\in E} \\omega(x) = 1\\) for\nevery test \\(E \\in \\mathcal{A}\\). Thus, a state is a consistent\nassignment of a probability weight to each test—consistent in\nthat, where two distinct tests share a common outcome, the state\nassigns that outcome the same probability whether it is secured as a\nresult of one test or the other. (This may be regarded as a normative\nrequirement on the outcome-identifications implicit in the structure\nof \\(\\mathcal{A}\\): if outcomes of two tests are not equiprobable in\nall states, they ought not to be identified.) The set of all states on\n\\(\\mathcal{A}\\) is denoted by \\(\\Omega(\\mathcal{A})\\). This is a\nconvex set, but in contrast to the situation in discrete classical\nprobability theory, it is generally not a simplex.", "\nThe concept of a random variable admits several generalizations to the\nsetting of test spaces. Let us agree that a simple (real-valued)\nrandom variable on a test space \\(\\mathcal{A}\\) is a mapping \\(f\n: E \\rightarrow \\mathbf{R}\\) where \\(E\\) is a test in \\(\\mathcal{A}\\).\nWe define the expected value of \\(f\\) in a state \\(\\omega \\in\n\\Omega(\\mathcal{A})\\) in the obvious way, namely, as the expected\nvalue of \\(f\\) with respect to the probability weight obtained by\nrestricting \\(\\omega\\) to \\(E\\) (provided, of course, that this\nexpected value exists). One can go on to define more general classes\nof random variables by taking suitable limits (for details, see Younce\n[1987]).", "\nIn classical probability theory (and especially in classical\nstatistics) one usually focuses, not on the set of all possible\nprobability weights, but on some designated subset of these (e.g.,\nthose belonging to a given family of distributions). Accordingly, by a\nprobabilistic model, I mean pair \\((\\mathcal{A},\\Delta)\\)\nconsisting of a test space \\(\\mathcal{A}\\) and a designated set of\nstates \\(\\Delta \\subseteq \\Omega(\\mathcal{A})\\) on \\(\\mathcal{A}\\).\nI’ll refer to \\(\\mathcal{A}\\) as the test space and to\n\\(\\Delta\\) as the state space of the model.", "\nI’ll now indicate how this framework can accommodate both the\nusual measure-theoretic formalism of full-blown classical probability\ntheory and the Hilbert-space formalism of quantum probability\ntheory." ], "subsection_title": "3.2 Test Spaces" }, { "content": [ "\nLet \\(S\\) be a set, understood for the moment as the state-space of a\nphysical system, and let \\(\\Sigma\\) be a \\(\\sigma\\)-algebra of subsets\nof \\(S\\). We can regard each partition \\(E\\) of \\(S\\) into countably\nmany pair-wise disjoint \\(\\Sigma\\)-measurable subsets as representing\na “coarse-grained” approximation to an imagined perfect\nexperiment that would reveal the state of the system. Let\n\\(\\mathcal{A}_{\\Sigma}\\) be the test space consisting of all such\npartitions. Note that the outcome set for \\(\\mathcal{A}_{\\Sigma}\\) is\nthe set \\(X = \\Sigma \\setminus \\{\\varnothing \\}\\) of non-empty\n\\(\\Sigma\\)-measurable subsets of \\(S\\). Evidently, the probability\nweights on \\(\\mathcal{A}_{\\Sigma}\\) correspond exactly to the\ncountably additive probability measures on \\(\\Sigma\\). " ], "subsection_title": "3.3 Kolmogorovian Probability Theory" }, { "content": [ "\nLet \\(\\mathbf{H}\\) denote a complex Hilbert space and let\n\\(\\mathcal{A}_{\\mathbf{H}}\\) denote the collection of (unordered)\northonormal bases of \\(\\mathbf{H}\\). Thus, the outcome-space \\(X\\) of\n\\(\\mathcal{A}_{\\mathbf{H}}\\) will be the unit sphere of\n\\(\\mathbf{H}\\). Note that if \\(u\\) is any unit vector of\n\\(\\mathbf{H}\\) and \\(E \\in \\mathcal{A}_{\\mathbf{H}}\\) is any\northonormal basis, we have ", "\nThus, each unit vector of \\(\\mathbf{H}\\) determines a probability\nweight on \\(\\mathcal{A}_{\\mathbf{H}}\\). Quantum mechanics asks us to\ntake this literally: any “maximal” discrete\nquantum-mechanical observable is modeled by an orthonormal basis, and\nany pure quantum mechanical state, by a unit vector in exactly this\nway. Conversely, every orthonormal basis and every unit vector are\nunderstood to correspond to such a measurement and such a state.", "\nGleason’s theorem can now be invoked to identify the states on\n\\(\\mathcal{A}_{\\mathbf{H}}\\) with the density operators on\n\\(\\mathbf{H}\\): to each state \\(\\omega\\) in\n\\(\\Omega(\\mathcal{A}_{\\mathbf{H}})\\) there corresponds a unique\ndensity operator \\(W\\) such that, for every unit vector \\(x\\) of\n\\(\\mathbf{H}, \\omega(x) = \\langle Wx,x\\rangle = Tr(WP_x), P_x\\) being\nthe one-dimensional projection associated with \\(x\\). Conversely, of\ncourse, every such density operator defines a unique state by the\nformula above. We can also represent simple real-valued random\nvariables operator-theoretically. Each bounded simple random variable\n\\(f\\) gives rise to a bounded self-adjoint operator \\(A = \\sum_{x\\in\nE} f(x)P_x\\). The spectral theorem tells us that every self-adjoint\noperator on \\(\\mathbf{H}\\) can be obtained by taking suitable limits\nof operators of this form." ], "subsection_title": "3.4 Quantum Probability Theory" } ] }, { "main_content": [ "\nAssociated with any probabilistic model \\((\\mathcal{A},\\Delta)\\) are\nseveral partially ordered sets, each of which has some claim to the\nstatus of an “empirical logic” associated with the model.\nIn this section, I’ll discuss two: the so-called operational\nlogic \\(\\Pi(\\mathcal{A})\\) and the property lattice\n\\(\\mathbf{L}(\\mathcal{A},\\Delta)\\). Under relatively benign conditions\non \\(\\mathcal{A}\\), the former is an orthoalgebra. The latter\nis always a complete lattice, and under plausible further assumptions,\natomic. Moreover, there is a natural order preserving mapping from\n\\(\\Pi\\) to \\(\\mathbf{L}\\). This is not generally an order-isomorphism,\nbut when it is, we obtain a complete orthomodular lattice, and thus\ncome a step closer to the projection lattice of a Hilbert space. " ], "section_title": "4. Logics associated with probabilistic models", "subsections": [ { "content": [ "\nIf \\(\\mathcal{A}\\) is a test space, an \\(\\mathcal{A}\\)-event\nis a set of \\(\\mathcal{A}\\)-outcomes that is contained in some test.\nIn other words, an \\(\\mathcal{A}\\)-event is simply an event in the\nclassical sense for any one of the tests belonging to \\(\\mathcal{A}\\).\nNow, if \\(A\\) and \\(B\\) are two \\(\\mathcal{A}\\)-events, we say that\n\\(A\\) and \\(B\\) are orthogonal, and write \\(A\\binbot B\\), if\nthey are disjoint and their union is again an event. We say that two\northogonal events are complements of one another if their\nunion is a test. We say that events \\(A\\) and \\(B\\) are\nperspective, and write \\(A\\sim B\\), if they share any common\ncomplement. (Notice that any two tests \\(E\\) and \\(F\\) are\nperspective, since they are both complementary to the empty\nevent.)", "\nWhile it is possible to construct perfectly plausible examples of test\nspaces that are not algebraic, many test spaces that one encounters in\nnature do enjoy this property. In particular, the Borel and quantum\ntest spaces described in the preceding section are algebraic. The more\nimportant point is that, as an axiom, algebraicity is relatively\nbenign, in the sense that many test spaces can be\n“completed” to become algebraic. In particular, if every\noutcome has probability greater than 1/2 in at least one state, then\n\\(\\mathcal{A}\\) is contained in an algebraic test space\n\\(\\mathcal{B}\\) having the same outcomes and the same states as\n\\(\\mathcal{A}\\) (see Gudder [1989] for details).", "\nIt can be\n shown[11]\n that test space \\(\\mathcal{A}\\) is algebraic if and only if it\nsatisfies the condition", "\nFor all events \\(A, B\\) of \\(\\mathcal{A}\\), if \\(A\\sim B\\), then any\ncomplement of \\(B\\) is a complement of \\(A\\). ", "\nFrom this, it is not hard to see that, for an algebraic test space\n\\(\\mathcal{A}\\), the relation \\(\\sim \\) of perspectivity is then an\nequivalence relation on the set of \\(\\mathcal{A}\\)-events. More than\nthis, if \\(\\mathcal{A}\\) is algebraic, then \\(\\sim \\) is a\ncongruence for the partial binary operation of forming unions\nof orthogonal events: in other words, for all \\(\\mathcal{A}\\)-events\n\\(A, B\\), and \\(C, A\\sim B\\) and \\(B\\binbot C\\) imply that \\(A\\binbot\nC\\) and \\(A\\cup C \\sim B\\cup C\\).", "\nLet \\(\\Pi(\\mathcal{A})\\) be the set of equivalence classes of\n\\(\\mathcal{A}\\)-events under perspectivity, and denote the equivalence\nclass of an event \\(A\\) by \\(p(A)\\); we then have a natural partial\nbinary operation on \\(\\Pi(\\mathcal{A})\\) defined by \\(p(A)\\oplus p(B)\n= p(A\\cup B)\\) for orthogonal events \\(A\\) and \\(B\\). Setting 0 :\\(=\np(\\varnothing)\\) and 1 :\\(= p(E), E\\) any member of \\(\\mathcal{A}\\),\nwe obtain a partial-algebraic structure \\((\\Pi(\\mathcal{A}),\\oplus\n,0,1)\\), called the logic of \\(\\mathcal{A}\\). This satisfies\nthe following conditions:", "\nWe may now define: ", "\nThus, the logic of an algebraic test space is an orthoalgebra. One can\nshow that, conversely, every orthoalgebra arises as the logic\n\\(\\Pi(\\mathcal{A})\\) of an algebraic test space \\(\\mathcal{A}\\)\n(Golfin [1988]). Note that non-isomorphic test spaces can have\nisomorphic logics." ], "subsection_title": "4.1 Operational Logics" }, { "content": [ "\nAny orthoalgebra \\(\\mathbf{L}\\) is partially ordered by the relation\n\\(a\\le b\\) iff \\(b = a\\oplus c\\) for some \\(c\\binbot a\\). Relative to\nthis ordering, the mapping \\(a\\rightarrow a'\\) is an\northocomplementation and \\(a\\binbot b\\) iff \\(a\\le b'\\). It can be\nshown that \\(a\\oplus b\\) is always a minimal upper bound for \\(a\\) and\n\\(b\\), but it is generally not the least upper bound. Indeed,\nwe have the following (Foulis, Greechie and Ruttimann [1992], Theorem 2.12):", "\nAn orthoalgebra satisfying condition (b) is said to be\northocoherent. In other words: an orthoalgebra is\northocoherent if and only if finite pairwise summable subsets of\n\\(\\mathbf{L}\\) are jointly summable. The lemma tells us that every\northocoherent orthoalgebra is, inter alia, an orthomodular\nposet. Conversely, an orthocomplemented poset is orthomodular iff\n\\(a\\oplus b = a\\vee b\\) is defined for all pairs with \\(a\\le b'\\) and\nthe resulting partial binary operation is associative—in which\ncase the resulting structure \\((\\mathbf{L},\\oplus ,0,1)\\) is an\northocoherent orthoalgebra, the canonical ordering on which agrees\nwith the given ordering on \\(\\mathbf{L}\\). Thus, orthomodular posets\n(the framework for Mackey’s version of quantum logic) are\nequivalent to orthocoherent orthoalgebras.", "\nA condition related to, but stronger than, orthocoherence is that any\npairwise compatible propositions should be jointly\ncompatible. This is sometimes called regularity. Most\nnaturally occurring orthomodular lattices and posets are regular. In\nparticular, Harding (1996, 1998) has shown that the direct-product\ndecompositions of any algebraic, relational or topological structure\ncan be organized in a natural way into a regular orthomodular\n poset.[12]\n ", "\nSome version of orthocoherence or regularity was taken by Mackey and\nmany of his successors as an axiom. (Orthocoherence appears, in an\ninfinitary form, as Mackey’s axiom V; regularity appears in the\ndefinition of a partial Boolean algebra in the work of Kochen and\nSpecker (1965).) However, it is quite easy to construct simple model\ntest spaces, having perfectly straightforward—even\nclassical—interpretations, the logics of which are not\northocoherent. There has never been given any entirely compelling\nreason for regarding orthocoherence as an essential feature of all\nreasonable physical models. Moreover, certain apparently quite\nwell-motivated constructions that one wants to perform with test\nspaces tend to destroy orthocoherence (see\n section 7)." ], "subsection_title": "4.2 Orthocoherence" }, { "content": [ "\nThe decision to accept measurements and their outcomes as primitive\nconcepts in our description of physical systems does not mean that we\nmust forgo talk of the physical properties of such a system. Indeed,\nsuch talk is readily accommodated in the present formalism.[13]\n In the approach we have been pursuing, a physical system is\nrepresented by a probabilistic model \\((\\mathcal{A},\\Delta)\\), and the\nsystem’s states are identified with the probability weights in\n\\(\\Delta\\). Classically, any subset \\(\\Gamma\\) of the\nstate-space \\(\\Delta\\) corresponds to a categorical property of the\nsystem. However, in quantum mechanics, and indeed even classically,\nnot every such property will be testable (or “physical”).\nIn quantum mechanics, only subsets of the state-space corresponding to\nclosed subspaces of the Hilbert space are testable; in classical\nmechanics, one usually takes only, e.g., Borel sets to correspond to\ntestable properties: the difference is that the testable properties in\nthe latter case happen still to form a Boolean algebra of sets, where\nin the former case, they do not.", "\nOne way to frame this distinction is as follows. The support\nof a set of states \\(\\Gamma \\subseteq \\Delta\\) is the set ", "\nof outcomes that are possible when the property \\(\\Gamma\\) obtains.\nThere is a sense in which two properties are empirically\nindistinguishable if they have the same support: we cannot distinguish\nbetween them by means of a single execution of a single test. We might\ntherefore wish to identify physical properties with classes of\nphysically indistinguishable classical properties, or, equivalently,\nwith their associated supports. However, if we wish to adhere to the\nprogramme of representing physical properties as subsets (rather than\nas equivalence-classes of subsets) of the state-space, we can do so,\nas follows. Define a mapping \\(F : \\wp(X) \\rightarrow \\wp(\\Delta)\\) by\n\\(F(J) = \\{\\omega \\in \\Delta \\mid S(\\omega) \\subseteq J \\}\\). The\nmapping \\(\\Gamma \\rightarrow F(S(\\Gamma))\\) is then a closure\noperator on \\(\\wp(\\Delta)\\), and the collection of closed sets\n(that is, the range of \\(F)\\) is a complete lattice of sets, closed\nunder arbitrary\n intersection.[14]\n Evidently, classical properties—subsets of\n\\(\\Delta\\)—have the same support iff they have the same closure,\nso we may identify physical properties with closed subsets of the\nstate-space:", "\nWe now have two different “logics” associated with a probabilistic model \\((\\mathcal{A},\\Delta)\\) with \\(\\mathcal{A}\\) algebraic: a\n“logic” \\(\\Pi(\\mathcal{A})\\) of experimental propositions\nthat is an orthoalgebra, but generally not a lattice, and a\n“logic” \\(\\mathbf{L}(\\mathcal{A},\\Delta)\\) of properties\nthat is a complete lattice, but rarely orthocomplemented in any\nnatural way (Randall and Foulis [1983]). The two are connected by a\nnatural mapping [ ] : \\(\\Pi \\rightarrow \\mathbf{L}\\), given by\n\\(p \\rightarrow[p] = F(J_p)\\) where for each \\(p\\in \\Pi\\), \\(J_p =\n\\{x\\in X \\mid p(x) \\nleq p' \\}\\). That is, \\(J_p\\) is the set of\noutcomes that are consistent with \\(p\\), and [\\(p\\)] is the largest\n(i.e., weakest) physical property making \\(p\\) certain to be confirmed\nif tested.", "\nThe mapping \\(p \\rightarrow[p\\)] is order preserving. For both the\nclassical and quantum-mechanical models considered above, it is in\nfact an order-isomorphism. Whenever this is the case, \\(\\Pi\\) will\ninherit from \\(\\mathbf{L}\\) the structure of a complete lattice, which\nwill then automatically be orthomodular by Lemma 4.3. In other words,\nin such cases we have only one logic, which is a complete\northomodular lattice. While it is surely too much to expect that [ ]\nwill be an order-isomorphism every conceivable physical\nsystem—indeed, we can easily construct toy examples to the\ncontrary—the condition is at least reasonably transparent in its\nmeaning." ], "subsection_title": "4.3 Lattices of Properties" } ] }, { "main_content": [ "\nSuppose that the logic and property lattices of a model are\nisomorphic, so that the logic of propositions/properties is a complete\northomodular lattice. The question then arises: how close does this\nbring us to quantum mechanics—that is, to the projection lattice\n\\(L(\\mathbf{H})\\) of a Hilbert space? ", "\nThe answer is: without additional assumptions, not very. The lattice\n\\(L(\\mathbf{H})\\) has several quite special order-theoretic features.\nFirst it is atomic—every element is the join of minimal\nnon-zero elements (i.e., one-dimensional subspaces). Second, it is\nirreducible—it can not be expressed as a non-trivial\ndirect product of simpler\n OMLs.[16]\n Finally, and most significantly, it satisfies the so-called\natomic covering law: if \\(p \\in L(\\mathbf{H})\\) is an atom\nand \\(p\\nleq q\\), then \\(p \\vee q\\) covers \\(q\\) (no element\nof \\(L(\\mathbf{H})\\) lies strictly between \\(p \\vee q\\) and\n\\(q)\\).", "\nThese properties still do not quite suffice to capture\n\\(L(\\mathbf{H})\\), but they do get us into the right ballpark. Let\n\\(\\mathbf{V}\\) be any inner product space over an involutive division\nring \\(D\\). A subspace \\(\\mathbf{M}\\) of \\(\\mathbf{V}\\) is said to be\n\\(\\bot\\)-closed iff \\(\\mathbf{M} = \\mathbf{M}^{\\bot \\bot}\\),\nwhere \\(\\mathbf{M}^{\\bot} = \\{v\\in \\mathbf{V} \\mid \\forall m\\in\n\\mathbf{M}( \\langle v,m\\rangle = 0)\\}\\). Ordered by set-inclusion, the\ncollection \\(L(\\mathbf{V})\\) of all \\(\\bot\\)-closed subspaces of\n\\(\\mathbf{V}\\) forms a complete atomic lattice, orthocomplemented by\nthe mapping \\(\\mathbf{M} \\rightarrow \\mathbf{M}^{\\bot}\\). A theorem of\nAmemiya and Araki (1966) shows that a real, complex or quaternionic\ninner product space \\(\\mathbf{V}\\) with \\(L(\\mathbf{V})\\)\northomodular, is necessarily complete. For this reason, an inner\nproduct space \\(\\mathbf{V}\\) over an involutive division ring is\ncalled a generalized Hilbert space if its\nlattice\\(L(\\mathbf{V})\\) of \\(\\bot\\)-closed subspaces is orthomodular.\nThe following representation theorem is due to C. Piron [1964]:", "\nIt should be noted that generalized Hilbert spaces have been\nconstructed over fairly exotic division\n rings.[17]\n Thus, while it brings us tantalizingly close, Piron’s theorem\ndoes not quite bring us all the way back to orthodox quantum\nmechanics." ], "section_title": "5. Piron’s Theorem", "subsections": [ { "content": [ "\nLet us call a complete orthomodular lattice satisfying the hypotheses\nof Piron’s theorem a Piron lattice. Can we give any\ngeneral reason for supposing that the logic/property lattice of a\nphysical system (one for which these are isomorphic) is a Piron\nlattice? Or, failing this, can we at least ascribe some clear physical\ncontent to these assumptions? The atomicity of \\(L\\) follows if we\nassume that every pure state represents a “physical\nproperty”. This is a strong assumption, but its content seems\nclear enough. Irreducibility is usually regarded as a benign\nassumption, in that a reducible system can be decomposed into its\nirreducible parts, to each of which Piron’s Theorem applies.", "\nThe covering law presents a more delicate problem. While it is\nprobably safe to say that no simple and entirely compelling argument\nhas been given for assuming its general validity, Piron [1964, 1976]\nand others (e.g., Beltrametti and Cassinelli [1981] and Guz [1978])\nhave derived the covering law from assumptions about the way in which\nmeasurement results warrant inference from an initial state to a final\nstate. Here is a brief sketch of how this argument goes. Suppose that\nthere is some reasonable way to define, for an initial state \\(q\\) of\nthe system, represented by an atom of the logic/property lattice\n\\(L\\), a final state \\(\\phi_p (q)\\)—either another atom, or\nperhaps 0—conditional on the proposition \\(p\\) having been\nconfirmed. Various arguments can be adduced suggesting that the only\nreasonable candidate for such a mapping is the Sasaki\nprojection \\(\\phi_p : L \\rightarrow L\\), defined by", "\n\\(\\phi_p (q) = (q \\vee p') \\wedge\n p\\).[18]", "\nIt can be shown that an atomic OML satisfies the atomic covering law\njust in case Sasaki projections take atoms again to atoms, or to 0.\nAnother interesting view of the covering law is developed by Cohen and\nSvetlichny [1987]." ], "subsection_title": "5.1 Conditioning and the Covering Law" } ] }, { "main_content": [ "\nThe perennial question in the interpretation of quantum mechanics is\nthat of whether or not essentially classical explanations are\navailable, even in principle, for quantum-mechanical phenomena.\nQuantum logic has played a large role in shaping (and clarifying) this\ndiscussion, in particular by allowing us to be quite precise about\nwhat we mean by a classical explanation. " ], "section_title": "6. Classical Representations", "subsections": [ { "content": [ "\nSuppose we are given a statistical model \\((\\mathcal{A},\\Delta)\\). A\nvery straightforward approach to constructing a “classical\ninterpretation” of \\((\\mathcal{A},\\Delta)\\) would begin by\ntrying to embed \\(\\mathcal{A}\\) in a Borel test space \\(\\mathcal{B}\\),\nwith the hope of then accounting for the statistical states in\n\\(\\delta\\) as averages over “hidden” classical—that\nis, dispersion-free—states on the latter. Thus, we’d want\nto find a set \\(S\\) and a mapping \\(X \\rightarrow \\wp(S)\\) assigning\nto each outcome \\(x\\) of \\(\\mathcal{A}\\) a set \\(x* \\subseteq\nS\\) in such a way that, for each test \\(E \\in \\mathcal{A}, \\{x* \\mid x\n\\in E\\}\\) forms a partition of \\(S\\). If this can be done, then each\noutcome \\(x\\) of \\(\\mathcal{A}\\) simply records the fact that the\nsystem is in one of a certain set of states, namely, \\(x\\)*. If we let\n\\(\\Sigma\\) be the \\(\\sigma\\)-algebra of sets generated by sets of the\nform \\(\\{x* \\mid x \\in X\\}\\), we find that each probability measure\n\\(\\mu\\) on \\(\\Sigma\\) pulls back to a state \\(\\mu\\)* on\n\\(\\mathcal{A}\\), namely, \\(\\mu *(x) = \\mu(x\\)*). So long as every\nstate in \\(\\delta\\) is of this form, we may claim to have given a\ncompletely classical interpretation of the model\n\\((\\mathcal{A},\\Delta)\\).", "\nThe minimal candidate for \\(S\\) is the set of all\ndispersion-free states on \\(\\mathcal{A}\\). Setting \\(x* = \\{s\\in S\n\\mid s(x) = 1\\}\\) gives us a classical interpretation as above, which\nI’ll call the classical image of \\(\\mathcal{A}\\). Any\nother classical interpretation factors through this one. Notice,\nhowever, that the mapping \\(x \\rightarrow x\\)* is injective only if\nthere are sufficiently many dispersion-free states to separate\ndistinct outcomes of \\(\\mathcal{A}\\). If \\(\\mathcal{A}\\) has \\(no\\)\ndispersion-free states at all, then its classical image is\nempty. Gleason’s theorem tells us that this is the case\nfor quantum-mechanical models. Thus, this particular kind of classical\nexplanation is not available for quantum mechanical models.", "\nIt is sometimes overlooked that, even if a test space \\(\\mathcal{A}\\)\ndoes have a separating set of dispersion-free states, there may exist\nstatistical states on \\(\\mathcal{A}\\) that can not be\nrealized as mixtures of these. The classical image provides no\nexplanation for such states. For a very simple example of this sort of\nthing, consider the the test space: ", "\n and the state\n\\(\\omega(a) = \\omega(b) = \\omega(c) = \\frac{1}{2}\\), \\(\\omega(x) =\n\\omega(y) = \\omega(z) = 0\\). It is a simple exercise to show that\n\\(\\omega\\) cannot be expressed as a weighted average of\n\\(\\{0,1\\}\\)-valued states on \\(\\mathcal{A}\\). For further examples and\ndiscussion of this point, see Wright [1980]." ], "subsection_title": "6.1 Classical Embeddings" }, { "content": [ "\nThe upshot of the foregoing discussion is that most test spaces\ncan’t be embedded into any classical test space, and that even\nwhere such an embedding exists, it typically fails to account for some\nof the model’s states. However, there is one very important\nclass of models for which a satisfactory classical interpretation is\nalways possible. Let us call a test space \\(\\mathcal{A}\\)\nsemi-classical if its tests do not overlap; i.e., if \\(E \\cap\nF = \\varnothing\\) for \\(E, F \\in \\mathcal{A}\\), with \\(E\\ne F\\).", "\nAs long as \\(\\mathcal{A}\\) is locally countable (i.e., no test \\(E\\)\nin \\(\\mathcal{A}\\) is uncountable), every state can be represented as\na convex combination, in a suitable sense, of extreme states (Wilce\n[1992]). Thus, every state of a locally countable semi-classical test\nspace has a classical interpretation.", "\nEven though neither Borel test spaces nor quantum test spaces are\nsemi-classical, one might argue that in any real laboratory situation,\nsemi-classicality is the rule. Ordinarily, when one writes down in\none’s laboratory notebook that one has performed a given test\nand obtained a given outcome, one always has a record of which test\nwas performed. Indeed, given any test space \\(\\mathcal{A}\\), we may\nalways form a semi-classical test space simply by forming the\nco-product (disjoint union) of the tests in \\(\\mathcal{A}\\). More\nformally:", "\nWe can regard \\(\\mathcal{A}\\) as arising from \\(\\mathcal{A}^{\\sim}\\)\nby deletion of the record of which test was performed to secure a\ngiven outcome. Note that every state on \\(\\mathcal{A}\\) defines a\nstate \\(\\omega^{\\sim}\\) on \\(\\mathcal{A}^{\\sim}\\) by \\(\\omega^{\\sim}\n(x,E) = \\omega(x)\\). The mapping \\(\\omega \\rightarrow \\omega^{\\sim}\\)\nis plainly injective; thus, we may identify the state-space of\n\\(\\mathcal{A}\\) with a subset of the state-space of\n\\(\\mathcal{A}^{\\sim}\\). Notice that there will typically be many\nstates on \\(\\mathcal{A}^{\\sim}\\) that do not descend to\nstates on \\(\\mathcal{A}\\). We might wish to think of these as\n“non-physical”, since they do not respect the (presumably,\nphysically motivated) outcome-identifications whereby \\(\\mathcal{A}\\)\nis defined.", "\nSince it is semi-classical, \\(\\mathcal{A}^{\\sim}\\) admits a classical\ninterpretation, as per Lemma 7.1. Let’s examine this. An element\nof \\(S(\\mathcal{A}^{\\sim}\\)) amounts to a mapping \\(f :\n\\mathcal{A}^{\\sim} \\rightarrow X\\), assigning to each test \\(E \\in\n\\mathcal{A}\\), an outcome \\(f(E) \\in E\\). This is a (rather brutal)\nexample of what is meant by a contextual (dispersion-free) hidden\nvariable. The construction above tells us that such contextual\nhidden variables will be available for statistical models quite\ngenerally. For other results to the same effect, see Kochen and\nSpecker [1967], Gudder [1970], Holevo [1982], and, in a different\ndirection, Pitowsky\n [1989].[19]", "\nNote that the simple random variables on \\(\\mathcal{A}\\) correspond\nexactly to the simple random variables on \\(\\mathcal{A}^{\\sim}\\), and\nthat these, in turn, correspond to some of the simple random\nvariables (in the usual sense) on the measurable space\n\\(S(\\mathcal{A}^{\\sim}\\)). Thus, we have the following picture: The\nmodel \\((\\mathcal{A},\\Delta)\\) can always be obtained from a classical\nmodel simply by omitting some random variables, and identifying\noutcomes that can no longer be distinguished by those that remain.", "\nAll of this might suggest that our generalized probability theory\npresents no significant conceptual departure from classical\nprobability theory. On the other hand, models constructed along the\nforegoing lines have a distinctly ad hoc character. In particular, the\nset of “physical” states in one of the classical (or\nsemi-classical) models constructed above is determined not by any\nindependent physical principle, but only by consistency with the\noriginal, non-semiclassical model. Another objection is that the\ncontextual hidden variables introduced in this section are badly\nnon-local. It is by now widely recognized that this non-locality is\nthe principal locus of non-classicality in quantum (and more general)\nprobability models. (For more on this, see the entry on\n Bell’s theorem.)" ], "subsection_title": "6.2 Contextual Hidden Variables" } ] }, { "main_content": [ "\nSome of the most puzzling features of quantum mechanics arise in\nconnection with attempts to describe compound physical systems. It is\nin this context, for instance, that both the measurement problem and\nthe non-locality results centered on Bell’s theorem arise. It is\ninteresting that coupled systems also present a challenge to the\nquantum-logical programme. I will conclude this article with a\ndescription of two results that show that the coupling of\nquantum-logical models tends to move us further from the realm of\nHilbert space quantum mechanics. " ], "section_title": "7. Composite Systems", "subsections": [ { "content": [ "\nA particularly striking result in this connection is the observation\nof Foulis and Randall [1981a] that any reasonable (and reasonably\ngeneral) tensor product of orthoalgebras will fail to preserve\northo-coherence. Consider the test space ", "\n consisting of\nfive three-outcome tests pasted together in a loop. This test space is\nby no means pathological; it is both ortho-coherent and algebraic, and\nits logic is an orthomodular lattice. Moreover, it admits a separating\nset of dispersion-free states and hence, a classical interpretation.\nIt can also be embedded in the test space \\(\\mathcal{A}_{\\mathbf{H}}\\)\nof any 3-dimensional Hilbert space \\(\\mathbf{H}\\). Now consider how we\nmight model a compound system consisting of two separated sub-systems\neach modeled by \\(\\mathcal{A}_5\\). We would need to construct a test\nspace \\(\\mathcal{B}\\) and a mapping \\(\\otimes : X \\times X \\rightarrow\nY = \\cup \\mathcal{B}\\) satisfying, minimally, the following;", "\nFoulis and Randall show that no such embedding exists for which\n\\(\\mathcal{B}\\) is orthocoherent. Indeed, suppose we have a test space\n\\(\\mathcal{B}\\) and an embedding satisfying conditions (a) and (b).\nConsider the set of outcomes ", "\n By (a), this set is pairwise\northogonal. Now let \\(\\alpha\\) be the state on \\(\\mathcal{A}_5\\)\ntaking the value 1/2 on outcomes \\(a, b, c, d\\) and \\(e\\), and the\nvalue 0 on \\(x, y, z, w\\) and \\(v\\). By condition (b), there exists\nstate \\(\\omega\\) on \\(\\mathcal{B}\\) such that ", "\n for all\noutcomes \\(s, t\\) in \\(X\\). But this state takes the constant value\n1/4 on the set \\(S\\), whence, it sums over this set to \\(5/4 \\gt 1\\).\nHence, \\(S\\) is not an event, and \\(\\mathcal{B}\\) is not\northocoherent.", "\nIt is important to emphasize here that the test space\n\\(\\mathcal{A}_5\\) has a perfectly unproblematic quantum-mechanical\ninterpretation, as it can be realized as a set of orthonormal bases in\na 3-dimensional Hilbert space \\(\\mathbf{H}\\). However, the\nstate \\(\\omega\\) figuring in the Foulis-Randall example\ncannot arise quantum-mechanically (much less classically). (Indeed,\nthis follows from the example itself: the canonical mapping\n\\(\\mathbf{H} \\times \\mathbf{H} \\rightarrow \\mathbf{H} \\otimes\n\\mathbf{H}\\) provides a mapping satisfying the conditions (a) and (b)\nabove. Since \\(\\mathbf{L}(\\mathbf{H} \\otimes \\mathbf{H})\\) is\northocoherent, the set S corresponds to a pairwise orthogonal family\nof projections, over which a quantum-mechanical state would have to\nsum to no more than 1.) " ], "subsection_title": "7.1 The Foulis-Randall Example" }, { "content": [ "\nAnother result having a somewhat similar force is that of Aerts\n[1981]. If \\(L_1\\) and \\(L_2\\) are two Piron lattices, Aerts\nconstructs in a rather natural way a lattice \\(L\\) representing two\nseparated systems, each modeled by one of the given lattices.\nHere “separated” means that each pure state of the larger\nsystem \\(L\\) is entirely determined by the states of the two component\nsystems \\(L_1\\) and \\(L_2\\). Aerts then shows that \\(L\\) is again a\nPiron lattice iff at least one of the two factors \\(L_1\\) and \\(L_2\\)\nis classical. (This result has recently been strengthened by Ischi\n[2000] in several ways.)" ], "subsection_title": "7.2 Aerts’ Theorem" }, { "content": [ "\nThe thrust of these no-go results is that straightforward\nconstructions of plausible models for composite systems destroy\nregularity conditions (ortho-coherence in the case of the\nFoulis-Randall result, orthomodularity and the covering law in that of\nAerts’ result) that have widely been used to underwrite\nreconstructions of the usual quantum-mechanical formalism. This puts\nin doubt whether any of these conditions can be regarded as having the\nuniversality that the most optimistic version of Mackey’s\nprogramme asks for. Of course, this does not rule out the possibility\nthat these conditions may yet be motivated in the case of especially\nsimple physical systems.", "\nIn some quarters, the fact that the most traditional models of quantum\nlogics lack a reasonable tensor product have have been seen as\nheralding the collapse of the entire quantum-logical enterprise. This\nreaction is premature. The Foulis-Randall example, for instance, shows\nthat there can be no general tensor product that behaves properly on\nall orthomodular lattices or orthomodular posets (that is,\northocoherent orthoalgebras), and on all states\nthereon. But this does not rule out the existence of a satisfactory tensor\nproduct for classes of structures larger than that of\northomodular posets, or smaller than that of orthomodular\nlattices, or for classes of orthomodular lattices or posets with\nrestricted state spaces. Quantum Mechanics itself provides one example. \nFor another, as Foulis and Randall showed in\nFoulis and Randall [1981a], the class of unital\northoalgebras—that is, orthoalgebras in which every proposition\nhas probability 1 in some state—does support a\ncanonical tensor product satisfying their conditions (a) and (b). ", "\nMoving in the opposite direction, one can take it as an axiomatic\nrequirement that a satisfactory physical theory be closed under some\nreasonable device for coupling separated systems. This suggests taking\nclasses of systems, i.e., physical theories, as distinct from\nindividual systems, as the focus of attention. And in fact, this is\nexactly the trend in much current work on the foundations of quantum\nmechanics. ", "\nA particularly fruitful approach of this kind, due to Abramsky and\nCoecke [2009] takes a physical theory to be represented by a symmetric\nmonoidal category—roughly, a category equipped with a naturally\nsymmetric and associative tensor product. Subject to some further\nconstraints (e.g., compact closure), such categories exhibit formal\nproperties strikingly reminiscent of quantum mechanics. Interestingly,\nit has recently been shown by Harding [2009] that, in every strongly\ncompact closed category with biproducts, every object is associated\nwith an orthomodular poset Proj\\((A)\\) of “weak\nprojections”, and that Proj\\((A \\otimes B)\\) behaves in many\nrespects as a sensible tensor product for Proj\\((A)\\) and Proj\\((B)\\).\nFrom this perspective, the FR example simply exhibits a pathological\nexample — \\(A_5\\) and the state \\(\\alpha\\) — that can not\nbe accommodated in such a theory, establishing that the monoidality\nrequirement imposes a nontrivial restriction on the structure of\nindividual systems.\n", "\nThis recent emphasis on systems in interaction is part of a more\ngeneral shift of attention away from the static structure of states\nand observables and towards the processes in which physical\nsystems can participate. This trend is evident not only in the\ncategory-theoretic formulation of Abramsky and Coecke (see also Coecke\n[2011]), but also in several recent axiomatic reconstructions of\nquantum theory (e.g., Hardy [2001, Other Internet Resources], Rau\n[2009], Dakic-Brukner [2011], Massanes and Mueller [2011],\nChiribella-D’Ariano-Perinotti [2011], Wilce [2018]), most of\nwhich involve assumptions about how physical systems combine. In a\ndifferent direction, Baltag and Smets [2005] enrich a Piron-style\nlattice-theoretic framework with an explicitly dynamical element,\narriving at a quantum analogue of propositional dynamical logic." ], "subsection_title": "7.3 Ramifications" } ] }, { "main_content": [ " \nAnother recent development was the introduction in the early 1990s of\nstructures called effect algebras (Foulis and Bennett\n[1994]) generalizing the orthoalgebras discussed in sect 4.1. The\ndefinition is almost identical, except that the weaker condition \\(a\n\\perp a \\Rightarrow a = 0\\) is replaced by the weaker condition \\(a\n\\perp 1 \\ \\Rightarrow \\ a = 0\\). Like orthoalgebras, effect algebras\nare partially ordered by setting \\(a \\leq b\\) iff \\(b = a \\oplus c\\)\nfor some \\(c \\perp \na\\).[20]\n", "\nA simple but important example is the effect algebra \\([0,1]^{E}\\) of\nfunctions \\(\\,f : E \\rightarrow [0,1]\\), with \\(f \\perp g\\) iff \\(f + g\n\\leq 1\\) and, in that case, \\(f \\oplus g = f + g\\). One can regard\nelements of \\([0,1]^{E}\\) as “unsharp” or\n“fuzzy” versions of indicator functions \\(f : E\n\\rightarrow \\{0,1\\}\\). The set \\(\\{0,1\\}^{E}\\) of indicator\nfunctions, regarded as a subeffect algebra of \\([0,1]^{E}\\), is an\northoalgebra and, of course, isomorphic to the boolean algebra of\nsubsets of \\(E\\).[21]", "\nEffect algebras exist in great abundance. In particular, if \\(\\Omega\\)\nis a convex set arising as the state-space of a probabilistic model,\nthen the set \\({\\mathcal E}(\\Omega)\\) of bounded affine\n(convex-linear) functions \\(f : \\Omega \\rightarrow [0,1]\\) form an\neffect algebra, with \\(f \\oplus g = f + g\\) if \\(f + g \\leq 1\\). The\nidea is that a function \\(\\,f \\in {\\mathcal E}(\\Omega)\\) represents an\n\"in principle\" measurement outcome, with probability \\(f(\\alpha)\\) in\nstate \\(\\alpha \\in \\Omega\\). If \\(f_0,...,f_n \\in {\\mathcal\nE}(\\Omega)\\) with \\(f_0 + \\cdots + f_n = 1\\), then the sequence\n\\((f_0,...,f_n)\\) rpresents an “in principle” observable with values\n\\(i = 0,...,n\\), taking value \\(i\\) with probability\n\\(f_i(\\alpha)\\)." ], "section_title": "8. Effect Algebras ", "subsections": [] }, { "main_content": [ "\nIn the special case where \\(\\Omega = \\Omega(\\mathbf{H})\\), the set of\ndensity operators on a Hilbert space \\(\\mathbf{H}\\), one can show\nthat every effect \\(f\\) on \\(\\Omega\\) has the form \\(\\,f(W) =\n\\textrm{Tr}(W a)\\) for a unique positive self-adjoint operator \\(a\\)\nwith \\(a \\leq 1\\). Conversely, such an operator\ndefines an effect through the formula just given. One therefore\nidentifies \\(\\mathcal{E}(\\Omega(\\mathbf{H}))\\) with the set\n\\(\\mathcal{E}(\\mathbf{H})\\) of all positive self-adjoint operators on\n\\(\\mathbf{H})\\) with \\(0 \\leq a \\leq 1\\), referring to these also as\neffects.", "\nArbitrary quantum effects, and arbitrary effect-valued observables,\narise quite naturally as models of actual experimental\noutcomes. Consider an isolated quantum system \\(A\\) with Hilbert space\n\\(\\mathbf{H}_A\\), and an ancillary system \\(B\\), with Hilbert space\n\\(\\mathbf{H}_{B}\\), maintained in a reference state represented by a\ndensity operator \\(W^{B}_o\\). If \\(A\\) is in the state represented by\na density operator \\(W^{A}\\) on \\(\\mathbf{H}_A\\), thet state of the\njoint system is represented by \\(W^{A} \\otimes W^{B}_o\\). If we make a\nyes-no measurement on \\(AB\\) represented by a projection operator\n\\(P_{AB}\\) on \\(\\mathbf{H}_{AB} = \\mathbf{H}_{A} \\otimes\n\\mathbf{H}_{B}\\) then the probability of obtaining a positive result\nis \\(\\textrm{Tr}(P_{AB}(W^{A} \\otimes W^{B}_{o}))\\). This defines a\nbounded convex-linear function of \\(W^{A}\\), and hence, there is a\nunique effect \\(a\\) with \\(\\textrm{Tr}((W^{A} \\otimes\nW^{B}_{o})P_{AB}) = \\textrm{Tr}(W^{A} a)\\). This effect \\(a\\) is\ncalled the compression of \\(P_{AB}\\) onto \\(\\mathbf{H}_{A}.\\)\nIn other words, we can understand \\(a\\) as representing the result of\nmeasuring \\(P_{AB}\\) on the combined system \\(AB\\), holding \\(B\\) in\nstate \\(W^{B}_o\\), and then “forgetting about” the\nancillary system \\(B\\).\n\nIt is not difficult to show that every every effect on \\(A\\) arises in\nthis way from a projection on \\(\\mathbf{H}_{A} \\otimes\n\\mathbf{H}_{B}\\) for a suitable Hilbert space \\(\\mathbf{H}_{B}\\). More\ngenerally, a classic result in operator theory known as Naimark’s\nTheorem asserts that any effect-valued observable\n\\(a_1,...,a_n\\) on \\(A\\) arises by compression of an ordinary\nprojection-valued observable \\(P_1,...,P_n\\) on \\(AB\\) for a suitable\nquantum system \\(B\\). Thus, all effects, and indeed all effect-valued\nobservables, on \\(A\\) are physically realizable. In view of this, it\nis difficult to see why effect algebras should have any less claim to\nthe status of a “quantum logic” than do, say, orthomodular posets.\n" ], "section_title": "8.1 Quantum Effects and Naimark’s Theorem ", "subsections": [] }, { "main_content": [ " \nA natural question is whether one can characterize those effect\nalgebras of the special form \\(\\mathcal{E}(\\mathbf{H})\\). One way in\nwhich effects arise naturally is in the context of sequential\nmeasurements. If \\(P\\) is a projection, a measurement of \\(P\\) in\nstate corresponding to the density operator \\(W\\) leaves the system in\nthe state corresponding to the density operator", "\nA subsequent measurement of \\(q\\) in this\nstate then yields a positive result with probability \\begin{equation}\n\\textrm{Tr}(W_{P} Q) = \\frac{\\textrm{Tr}(QP W PQ)}{\\textrm{Tr}(W P)} =\n\\frac{\\textrm{Tr}(W PQP)}{\\textrm{Tr}(W P)}. \\end{equation} The\noperator \\(PQP\\) is not a projection unless \\(P\\) and \\(Q\\) commute,\nbut is always an effect. If we write \\(\\Pr(a|W)\\) for\n\\(\\textrm{Tr}(Wa)\\) for arbitrary effects \\(a\\), then the above can be\nrewritten, perhaps more transparently, as", "\nThus, \\(PQP\\) represents the “(yes,yes)”-outcome in a\nsequential measurement of \\(P\\) and \\(Q\\) (in that order).\n", "\nMore generally, the sequential product \\(a \\odot b :=\n\\sqrt{a}b\\sqrt{a}\\) of two effects is another effect, representing the\nresult of observing first \\(a\\) and then \\(b\\) in a sequential\nmeasurement (and assuming the state updates according to \\(W \\mapsto\n(\\textrm{Tr}(Wa))^{-1} \\sqrt{a} W \\sqrt{a}\\) after measurement of\n\\(a\\)). Abstracting from this example, S. Gudder and R. J. Greechie\n([2002]) defined a sequential effect algebra to be an effect\nalgebra \\((\\mathbf{L},\\oplus,0,1)\\) equipped with a binary operation\n\\(\\odot : \\mathbf{L} \\times \\mathbf{L} \\rightarrow \\mathbf{L}\\)\nsatisfying the following conditions for all \\(a,b,c \\in \\mathbf{L}\\),\nwhere \\(a | b\\) means \\(a \\odot b = b \\odot a\\):\n", "\nA remarkable recent result of J. van de Wetering ([2019]) shows that\nany finite-dimensional order-unit space whose order interval \\([0,u]\\)\nis an SEA under a binary operation continuous in the first variable,\nis a euclidean (equivalently, formally real) Jordan algebra in a\nnatural\n way.[22]\n" ], "section_title": "8.2 Sequential effect algebras ", "subsections": [] } ]

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[ "\nMany scientists, philosophers, and laypersons have regarded science as\nthe one human enterprise that successfully escapes the contingencies\nof history to establish eternal truths about the universe, via a\nspecial, rational method of inquiry. Historicists oppose this view. In\nthe 1960s several historically informed philosophers of science\nchallenged the then-dominant accounts of scientific method advanced by\nthe Popperians and the positivists (the logical positivists and\nlogical empiricists) for failing to fit historical scientific practice\nand failing particularly to account for deep scientific change. While\nseveral strands of historicism originated in nineteenth-century\nhistoriography, this article focuses, first, on the historicist\nconceptions of scientific rationality that became prominent in the\n1960s and 1970s, as the maturation of the field of historiography of\nscience began to suggest competing models of scientific development,\nand, second, on recent approaches such as historical epistemology.", "\nThe “Battle of the Big Systems” of the 1960s and\n‘70s, involving historicists such as Thomas Kuhn, Imre Lakatos,\nPaul Feyerabend, and Larry Laudan, eventually gave way to a realist\nreaction, as many philosophers rejected the perceived skepticism and\npotential relativism of the historicist movement, now reinforced by\nnew-wave sociology of science. The 1990s featured the so-called\nScience Wars, as philosophers attempted to defend truth, rationality,\nobjectivity, and scientific progress (and their own turf) from the\nperceived threats of rapidly developing, sociology-inspired science\nand technology studies and (other) postmodern influences. Since then,\na group of interdisciplinary scholars have attempted to reimagine ways\nin which historical and philosophical work can be brought together\nfruitfully." ]

[ { "content_title": "1. Historicist Conceptions of Rationality: The Battle of the Big Systems", "sub_toc": [ "1.1 Overview", "1.2 The Historical Turn in Philosophy of Science", "1.3 The Methodology of Scientific Research Programs", "1.4 Methodological Anarchism", "1.5 The Pragmatic, Problem-Solving Approach", "1.6 Evolutionary Models of Scientific Development", "1.7 New-Wave Sociology of Science and the Realist Reaction" ] }, { "content_title": "2. Rationality and History: Some Basic Questions", "sub_toc": [] }, { "content_title": "3. Historicism Then and Now", "sub_toc": [] }, { "content_title": "4. Related Developments and Further Challenges", "sub_toc": [] }, { "content_title": "5. Integrated HPS and Historical Epistemology: What Good Are They Regarding Scientific Rationality?", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Historicist Conceptions of Rationality: The Battle of the Big Systems", "subsections": [ { "content": [ "\nWhat good is appeal to history when it comes to evaluating the\nrationality of decisions and actions? Since the past is already over,\nisn’t history simply “bunk”? A couple of everyday\nlocutions suggest otherwise. It is commonly held that\n“history” (meaning historiography, the disciplined study\nof what happened in history) is a debunker of myths. And politicians\nare not the only people worried about “the judgment of\nhistory”. Both these ideas came into play in the new\nhistorically-oriented philosophy of science that began to emerge at\nthe end of the 1950s. The “new historicists” (as we may\ncall them) included Thomas Kuhn, N.R. Hanson, Mary Hesse, Imre\nLakatos, Paul Feyerabend, Stephen Toulmin, Dudley Shapere, Larry\nLaudan, Ernan McMullin, and Michael Ruse. They claimed that the\nthen-dominant positivist and Popperian accounts of science were\nthemselves bunk—myths about how science is done. Some new\nhistoricists claimed to find larger units and a hitherto unnoticed\ndynamic in the time-series of the historical record—long-term,\nforward-looking research programs that included evolving series of\nrelated theoretical moments. Above all, the historicists stressed the\ndepth of major historical changes and the resulting challenges to\ncumulative scientific progress. They argued that there was nothing in\nthe traditional “logic of science” that could rationalize\nsuch changes. The problem was to produce a new dynamical model of\nscience that would capture these patterns and rationally motivate\nthem.", "\nHistoricist philosophers did a convincing job of showing that\nhistorical evidence called the received views into question. Most\nphilosophers today accept that verdict of history. Less successful was\nthe attempt to formulate an adequate positive theory of rationality,\nboth at the first-order level of scientific methodological norms\n(e.g., “Reject a hypothesis that makes clearly false\npredictions” or “Use double-blind experimental methods\nwhen dealing with cognitive agents”) and at the\nmetamethodological level, where they faced the problem of how to\nrationally select among competing theories of scientific rationality,\nwithout circularity. The disagreements here raised the question of\nwhether there is a general theory of scientific rationality\nto be found, or a need for one.", "\n(For accessible, critical summaries of the “Big Systems”\ndebate, see Suppe 1974, Newton-Smith 1981, McGuire 1992, and Zammito\n2004. Space limitations have forced the omission of important\ndevelopments, including the Marxist dialectical tradition, e.g., Nowak\n1980, and recent work on stance and rationality, e.g., van Fraassen\n2002, Rowbottom & Bueno 2011.) " ], "subsection_title": "1.1 Overview" }, { "content": [ "\nKuhn’s Structure of Scientific Revolutions (1962/1970a)\nwas the original manifesto of historicist philosophy of science and\nremains the primary reference point. His work thus provides the most\nuseful platform for recounting early historicist efforts—and the\ndifficulties they faced. We shall then take a briefer look at other\nmajor contributors. Kuhn had been anticipated in quite diverse ways by\nKant, Hegel, William Whewell, Émile Meyerson, Ernst Cassirer,\nAlexandre Koyré, Philipp Frank, Gaston Bachelard, Ludwik Fleck,\nHans Reichenbach, Rudolf Carnap, W.V. Quine, Michael Polanyi, Hesse,\nToulmin, and Hanson and was immediately followed by Lakatos,\nFeyerabend, Shapere, Laudan, and others (see the entry on\n Thomas Kuhn;\n also Hoyningen-Huene [1989] 1993 and Rheinberger [2007] 2010b).", "\nThe famous opening sentence of Structure was:", "\n\n\nHistory, if viewed as a repository for more than anecdote or\nchronology, could produce a decisive transformation in the image of\nscience by which we are now possessed. That image has previously been\ndrawn, even by scientists themselves, mainly from the study of\nfinished scientific achievements as these are recorded in the classics\nand, more recently, in the textbooks from which each new scientific\ngeneration learns to practice its trade. Inevitably, however, the aim\nof such books is persuasive and pedagogic; a concept of science drawn\nfrom them is no more likely to fit the enterprise that produced them\nthan an image of a national culture drawn from a tourist brochure or a\nlanguage text. This essay attempts to show that we have been misled by\nthem in fundamental ways. Its aim is a sketch of the quite different\nconcept of science that can emerge from the historical records of the\nresearch activity itself.\n", "\nKuhn modeled the history of a science as a succession of dogmatic\nperiods of “normal science” under a\n“paradigm”, separated by “revolutionary”\ntransitions to the next paradigm. According to Kuhn such a break from\nthe past rejuvenates a field that had stagnated under the weight of\nanomalies that it no longer seemed to have the resources to solve. A\nnew paradigm introduces changes at all levels, from established\ndatabases and instrumentation to the conceptual framework, goals,\nstandards, institutional organization, and research culture—so\nmuch so that some older practitioners can hardly recognize the new\nparadigm as their field. This disconnect produces\n“incommensurability” across paradigm change, ranging from\ncommunication failure to problems of rational choice between the two,\nsince there exists no fixed measure of success. At his most radical,\nKuhn modeled revolutionary decisions on political revolution at the\ncommunity level and on religious conversion at the individual level,\nadding that scientists on different sides of a paradigm debate\n“live in different worlds” ([1962] 1970a: ch. 10). Under\ncritical pressure, he subsequently softened his position. In fact, he sought\nto clarify the notion of incommensurability to the end of his life\n(Sankey 1997). Kuhn exemplifies the irony that, while historicists\nused deep change as a weapon to beat up traditionalists, it presented\nserious problems for the historicists themselves as well.", "\nKuhn’s book was his attempt to answer the question posed by the\nabove quotation. This question immediately raised another: How can\nappeal to history achieve that transformative change? In particular,\nhow can descriptive claims about the past (or present\nscience, for that matter) affect our normative judgments\nabout rational beliefs and behaviors? How can history inform a\nmethodology of science? This is a version of the so-called\n“is-ought” problem. Can there really be a\n“judgment” of history?", "\nOver the next decade or two, most philosophers of science came to\nagree that there was a disconnect between science as historically\npracticed and the normative models of the received philosophers. The\nhistoricists therefore presented the philosophical community with a\nmomentous dilemma: either reject most of science to date as irrational\nor else accept that science is generally rational and use the\nhistorical information to revise our deeply entrenched logical and\nprobabilistic conception of rationality. Some positivists and Popperians\nattempted to finesse option one by arguing that the history of science\napproximated the traditional view of rationality closely enough if we\ntreated their sanitized, abstract models of science as regulative\nideals. Kuhn and other historicists defended option two, taking the\nrationality of science to be practically axiomatic. Wrote Kuhn,", "\n\n\nI do not for a moment believe that science is an intrinsically\nirrational enterprise …. I take this assertion not as a matter\nof fact, but rather of principle. Scientific behavior, taken as a\nwhole, is the best example we have of rationality. (1971: 143f; quoted\nby Hoyningen-Huhne [1989] 1993: 251f.)\n", "\nWhat was Kuhn’s revised conception of rationality and how was it\nbased on history (to the degree that it was)? While he provided no\nexplicit, general theory of rationality, Kuhn’s challenge here\nwas greater than many appreciate. The positivists and Popperians had\npractically invented modern, academic philosophy of science. For them,\nscientific rationality was wholly a matter of making correct theory\nacceptance decisions in context of justification, where the hypotheses\nand test data are already on the table, the data are theory-neutral,\nand the goals and standards are logically independent of theory. To\nKuhn this picture of science was more like a photographic negative in\nwhich light and dark are reversed. Let us count the ways.", "\n(1) Although his work deepened the problem of underdetermination by\ninsisting that logic plus data is insufficient to determine theory\nchoice, Kuhn reduced the magnitude of the problem of justifying\nscientific claims by rejecting traditional realism and the\ncorrespondence theory of truth. No longer must scientists justify a\ntheoretical claim as true. Instead, he adopted the Kantian critical\nposition that no enterprise, including science, has the ability to\nestablish the final, metaphysical truth about the world. Instead,\nscience is largely a problem-solving enterprise, and scientists\nare in position to evaluate the goodness of proposed problem\nsolutions, relative to previous attempts. “[T]he unit of\nscientific achievement is the solved problem” ([1962] 1970a:\n169). What demarcates science from nonscience and pseudoscience is\nsustained support (over historical time) of a puzzle-solving\ntradition, not the application of a nonexistent “scientific\nmethod” to determine whether the claims are true or false or\nprobable to some degree. With justified truth claims gone, new\naccounts of scientific discovery, knowledge, explanation, and progress\nwill also be needed.", "\n(2) Contrary to most empiricist views, the data are not\ntheory-neutral, hence not cumulative from one period of science to\nanother. ", "\n(3) Moreover, Kuhn extended the claim that observation is theory laden\nto say that all major aspects of a science are laden by the\nothers. Substantive data and theoretical claims, methodological\nstandards, goals, and even the social institutions of science are all\nbound up in mutual dependence. (The received view had kept them\nseparate and independent in order to avoid mutual contamination\nallegedly leading to circularity; see Scheffler 1967.) It is this\ninternal feedback that introduces the interesting, nonlinear dynamics\ninto Kuhn’s model, since the feedback produces coupled\ninteraction terms (Kuhn 1977: 336; Nickles 2013b; De Langhe\n2014b).", "\n(4) This tight coherence implies that normal science is conservative\nand closed, in contrast to Popper’s science as an “open\nsociety” (Popper 1945). Contrary to tradition, said Kuhn,\nscientific rationality does not consist in advancing hypotheses and\ntesting them severely. To challenge the constitutive pillars of a\nscientific field, as Popper and the positivists advocated, would\ndestroy it, for all theories and conceptual frameworks face\npotentially falsifying anomalies at all times (Kuhn [1962] 1970a and\n1970b; Lakatos 1970 agreed). Popper’s “critical\nrationalism”, the key to Popper’s Enlightenment conception\nof political democracy as well as scientific advance, is actually\nirrational; for such criticism would undercut the\nresearchers’ reason for being.", "\n(5) Kuhn claimed that Popper and others had missed the existence of\nkey structures in the history of science—the longer-term\napproaches that he called paradigms and hence both normal and truly\nrevolutionary science. There are different historical scales in play:\nindividual theories, paradigms, and the still longer-term perspective\nof a succession of paradigms. So Kuhn adopted a two-tiered or\ndouble-process conception of science in which there is, first, a\nconstitutive framework (the paradigm), held immune to revision during\nperiods of normal science, and, second, change from one framework to\nanother. For these frameworks are historically contingent and are\neventually displaced by others. Kuhn’s two-process account\nsharply clashed with the one-process account of Popper (1963) and many\nothers. Ironically, given that Kuhn was also attacking positivist\npositions, and given his greater sympathy for Popper, the two-process\naccount was closer to the “positivists” Reichenbach and\nCarnap than to Popper (see Reisch 1991; Carnap 1950; De Langhe\n2014a,b; Nickles 2013a).", "\n(6) Thus two different accounts of scientific rationality are\nrequired, not one: one to cover the relatively smooth change within\nnormal science under a single paradigm and the other to handle radical\nparadigm change. This immediately implies that there are two basic\ntypes of scientific change, hence two problems of scientific change\nand/or two problems of progress to be solved, hence two accounts of\nscientific rationality needed to solve them. What were Kuhn’s\nconstructive claims?", "\n(7) We should seek neither a single, neutral method of all science at\nall times nor an account based on explicit methodological rules. Most\nnormal scientific decisions are based on skilled judgments, not rules\n(Kuhn [1962] 1970a: chs. 5, 10). The appearance of rules in scientific\npractice is a sign of crisis, of breakdown. Contrary to tradition,\nneither rationality within a paradigm nor rational choice between\nparadigms is a matter of following rules. It is not the application of\na formal, logic- or probability-based algorithm. In both cases it is a\nmatter of skilled judgment (of different kinds).", "\n(8) Informal scientific judgment depends heavily upon rhetoric and\njudgments of heuristic fertility in the context of discovery—the\nvery items that had been expressly excluded from the context of\nrational justification by the dominant tradition. For Kuhn, normal\nproblem solving is a matter of modeling new puzzles solutions on\nestablished precedents, the exemplars, where modeling crucially\ninvolves judgments of similarity, analogy, or metaphor. (Whereas\nPopper’s methodology is a learning theory in which we learn only\nfrom our mistakes, in Kuhn’s we learn also (mainly) from our\nsuccesses—the exemplars, which, over time ratchet up our\nknowledge within normal science.) In paradigm change, the rhetorical\ntropes used in persuasion are typically more abstract and tenuous than\nin normal science. Kuhn’s account of the rational acceptance of\nparadigm change had to remain thin because of incommensurability. Here\nthe justification problem was all the more difficult because new\nparadigms generally lose some of the successes of their predecessors\n(so called “Kuhn loss” of problem solutions but also data,\ntheory, goals, and standards).", "\n(9) Kuhn’s novel constructive move in dealing with the\nrationality of paradigm change was to bring in a prospective dimension\nof heuristic fertility judgments. From the point of view of key,\ncreative scientists, the old paradigm has exhausted its resources,\nwhereas radical new ideas and practices can not only resolve some old\nanomalies (retrospective confirmation) but, equally importantly, can\nreinvent and thereby preserve the field by opening up new frontiers\nwith much interesting new work to be done. For them the field now had\na future. To be sure, heuristic guidance was also a feature of normal\nscience, but there it was built in implicitly.", "\nIn sum, Kuhn turned the traditional ideas of scientific justification,\nbased on the discovery-justification-context distinction, on their\nhead. Ironically, once we take the research scientists’ points\nof view, the more interesting forms of scientific cognition, including\njustification, occur in contexts of discovery. All of this according to Kuhn.", "\nCritics countered that, while the historicist upstarts had scored some\ndamaging critical points, their positive accounts of scientific\nrationality were underdeveloped, vague, and unconvincing. Political\nrevolution and religious conversion as models of rational\nbehavior?! Clark Glymour (1980: 7, 96ff) called the new approach\n“the new fuzziness”. Could intuitive judgment really\nreplace standard confirmation theory? And what would be the analogous\nrelation of evidence to theory at the metamethodological level, where\nnow “theory” was the set of methodological rules or theory\nof rationality itself? (Historicists replied that it is not their fault\nif real-life decision-making is a messy business that often outruns\navailable formal rules.) Shapere (1984: chs. 3–5) was a severe\nearly critic of Kuhn, and Lakatos (1970: 178) reported that Kuhn had\nreplaced rationality with “mob rule”. Since Shapere and\nLakatos were historicists, we see that the historicists could disagree\nsharply among themselves. Feyerabend will provide the most vivid\nexample.", "\nKuhn’s insightful treatment of science from the working\nscientists’ point of view provided a microlevel conception of\nrational decision-making. But did he have a metamethodological account\nof how to decide among competing theories of scientific rationality?\nAgain, not an explicit and comprehensive account, only some\nconstructive suggestions. Like all historicists, he said that a\nrationality theory must fit the history of science and that the\ntraditional accounts failed this history test. An adequate theory must\nalso be progressive and avoid epistemological relativism. Kuhn (and\nmany others) simply built in these norms from the outset. Such a move\nworks well among most friends of historicism but not well for critics,\nwho think these presuppositions simply beg the normativity of history\nquestion. Given incommensurability, are not rationality,\nprogressiveness, and denial of relativism key items that must be\nargued for? In other passages, Kuhn did argue for them, but few\ncritics were convinced.", "\nOn the positive side, Kuhn made an epistemological economy claim. ", "\n\n\n[I]n its normal state … a scientific community is an immensely\nefficient instrument for solving the problems or puzzles that its\nparadigms define. ([1962] 1970a: 166; cf. Wray 2011: ch. 7) \n", "\nIt is clear that Kuhn considered science more\nefficient on his own account than on Popper’s, because the double process enables\nextreme specialization (Wray 2011; De Langhe 2014c). Indeed,\ntraditional accounts fail Kuhn’s demarcation\ncriterion—that a genuine science supports a puzzle-solving\ntradition. Given Kuhn’s conviction that science is progressive\nin terms of problem-solving success, predictive accuracy, simplicity\n(the reworking and streamlining of problem-solving efficiency over\ntime), and so on, it supposedly follows that his account makes science\nboth rational and non-relativistic. Critics disagreed.", "\nThere also seems to be a kind of transcendental argument strategy\nbehind Kuhn’s approach, as a response to the quasi-Kantian\nquestion: Given that science, as historically practiced, is\nlargely rational and progressive, but not in the standard way, how are\nits rationality and progress possible? Supposedly, the study of the\nhistorical patterns will show the way.", "\nKuhn often described his two-process view as “Kant with moveable\ncategories”. Accordingly, there is also a dialectical,\nquasi-Hegelian reading: from the myriad of micro-decisions by the\ncommunity of scientists in a given field over time, with lots of fits\nand starts, a progressive enterprise emerges, although not one that is\nteleologically converging on the metaphysical truth about the universe\nor on any other “end”. However, on this view we have\nabandoned the idea that individual scientific decisions are typically\ndriven by an explicit concern for rationality. In several areas of\nphilosophy there are heated controversies about whether higher-order\nemergents have genuine causal power and hence genuine explanatory\nforce. To that degree, it remains unclear what role the desire to be\nrational plays, as opposed to more mundane motives. This problem\narises for other historicists as well, as David Hull will note. (See\nthe entries on\n mental causation\n and on\n internalist vs. externalist conceptions of epistemic justification.)", "\nOn rationality as socially emergent, we may jump ahead here to note that feminist\nphilosophers of science such as Helen Longino and Miriam Solomon have\ndefended scientific rationality as a socially emergent norm (Longino\n1990, 2001; Solomon\n2001). They thereby address the question of how a naturalistic,\nscience-as-practiced approach to scientific knowledge can nonetheless\nhave normative implications. However, they do not shy away from making\npolicy proposals for changing (improving) scientific\npractices and their supporting institutions. On their accounts, some\nother factors, such as political/ideological ones, also socially\nemerge and can have top-down causal efficacy on individual\npractitioners but without negating the agency and autonomy of those\nindividuals. Here familiar issues of “methodological\nindividualism” come into play. (See the entries on\n feminist epistemology and philosophy of science,\n feminist perspectives on science,\n feminist social epistemology,\n and\n feminist political philosophy.)", "\nThe vigorous attacks on Kuhn as a radical subjectivist and\nirrationalist who was undermining not only philosophy but the Western\nintellectual tradition now look exaggerated, but it is fair to say\nthat the five big problem-complexes of normativity, incommensurability\n(including meaning change), relativism, social knowledge, and deep but\nrational progressive change are extremely difficult and remain open to\ndebate today. For many philosophers of science, relativism is the big\nbugaboo that must be defeated at all costs. For them, any view that\nleads to even a moderate relativism is thereby reduced to absurdity.\nHistoricist philosophers have insisted on relativity to historical\ncontext but, with few exceptions, have made a sharp distinction\nbetween relativity and outright relativism. Some\ncritics have not found this distinction convincing (see the entry on\n relativism,\n Kindi & Arabatzis 2012 and Richards & Daston 2016)." ], "subsection_title": "1.2 The Historical Turn in Philosophy of Science" }, { "content": [ "\nCriticism and the Growth of Knowledge (1970), edited by\nLakatos and Alan Musgrave, was a second major contribution to the\nhistoricism debate. This collection of articles, originating from a\n1965 London conference, was in significant respects a reaction to\nKuhn; but it is especially important for Lakatos’s own\ncontribution to the volume, “Falsification and the Methodology\nof Scientific Research Programmes” (MSRP), an attempt to\naccommodate a broadly Popperian perspective to some of Kuhn’s\nideas and thereby to diverge from Popperian orthodoxy. Lakatos had\nlong favored an historical approach to the philosophy of mathematics\nand science (see his 1976). One of his central concerns was to defend\nthe rational continuity and progressiveness of modern science from the\nchallenge of radical change. Another was to fend off charges of\nhistorical relativism.", "\nLike Kuhn’s paradigms and Laudan’s research traditions\n(see below), the unit of rational appraisal for Lakatos is not a\nsingle theory at a point in time; instead, it is a series of theories\nthat are rationally-connected moments in the development of an\nidentifiable research program. In MSRP these theories share a\nnegative heuristic containing inviolable principles and a\npositive heuristic that both provides a “protective\nbelt” around the negative heuristic and guides future research.\nThe forward-looking heuristic element was, as for Kuhn, an important\nfeature missing from traditional accounts of science. In MSRP,\nresearch programs are evaluated as to their progressiveness\nover historical time, i.e., which grows knowledge fastest.\nLakatos’s measure of knowledge growth is novel prediction, the\nadvantage going to which program yields more novel\ntheoretical predictions and more confirmed novel\npredictions than its competitors. This is a historicist position since\ndetermining whether something is a novel prediction requires detailed\nknowledge of the historical context of discovery in which the\npredictive theory was produced (Lakatos & Zahar 1976).\nUnfortunately, however, Lakatos’s falsificationism had become so\nsophisticated that he could provide no rule for when it was rational\nto abandon a degenerating research program that was being outstripped\nby a more progressive one; for scientists, he said, may legitimately\nmake risky choices. In any case, contrary to Kuhn, two or more\nresearch programs may exist side-by-side. Lakatosian rationality does\nnot dictate that researchers all join the same program.", "\nWhat is the relation between a theory of scientific rationality and a\ngeneral methodology of science? Like the Popperians from which he\ndiverged, Lakatos held that methodologies are theories of\nscientific rationality (Curtis 1986). Similarly, a metamethodology\n(tasked with determining which methodology outperforms others) is\nidentical with a metatheory of scientific rationality. Lakatos’s\nmetatheory recapitulates MSRP at the metalevel. According to Lakatos,\nhis meta-MSRP shows that MSRP defeats competing methodologies, because\nit provides the best fit with the history of science in the sense that\nit renders the history of science maximally rational. That is, MSRP\nmakes rational sense of both the intuitively rational episodes and\nsome that its competitors have to exclude as externally caused\ndeviations from the rational ideal. Indeed, it predicts that\nsome counterintuitive cases will be seen to be rational when examined\nclosely.", "\nLakatos’s paper, “The History of Science and Its Rational\nReconstructions” (1971: 91) opens with a promising paraphrase of\nKant (previously used by Hanson (1962: 575, 580) and by Herbert Feigl\n(1970: 4): “Philosophy of science without history of science is\nempty; history of science without philosophy of science is\nblind”. However, his use of rational reconstructions of\nsupporting historical episodes—the science as it allegedly could\nhave been done or should have been done—made the actual\nscience look more internally correct (according to MSRP) than it was.\nHistorians and philosophical critics replied sharply that this was not\ngenuine history and hence not a fair test (see Arabatzis forthcoming).", "\nLakatos and his followers (e.g., Worrall 1988, 1989) conceived MSRP as\na fixed and final methodology by contrast with Kuhn’s,\nToulmin’s, and (eventually) Laudan’s changing\nmethodologies. The idea that all previous history of science was\nworking up to this final methodology that Lakatos was first to\ndivine—the end-of-history for methodology, so to speak—was\none of the broadly Hegelian themes in Lakatos’s work. Another\nwas that there is no instant rationality as proposed by the formal\napproaches of standard confirmation theory. Writes Daniel Little (in\nthe entry on\n philosophy of history)\n “Hegel finds reason in history; but it is a latent reason, and\none that can only be comprehended when the fullness of history’s\nwork is finished… ”. The owl of Minerva flies out at\ndusk. For Lakatos rational judgments can only be made retrospectively.\nFor example, one cannot judge an experiment as crucial at the time it\noccurs, only in historical retrospect (1970: 154ff). Appraisals are\nmade with hindsight. (See the entry on\n Lakatos.)" ], "subsection_title": "1.3 The Methodology of Scientific Research Programs" }, { "content": [ "\nIn his early work Feyerabend (1962) appealed to historical cases to\nreject Hempel’s account of explanation and Nagel’s\nparallel account of intertheoretic reduction (traditionally postulated\nmechanisms of cumulative progress), on the ground that in actual\nhistorical practice meaning change occurs from one major theory to its\nsuccessor. Deducibility thus fails. It also more obviously fails because\nthe two theories are typically mutually inconsistent. Accordingly, one\ncannot reason by traditional logical argument from one to the other.\nFeyerabend introduced his own conception of incommensurability into\nthis work. Anticipating his later broad pluralism, early Feyerabend\nalso extended the Popperian line on testing to a full-blown\nproliferationist methodology. Competing theories should be multiplied\nand tested against each other, because more empirical content is\nthereby brought to light than in testing theories in isolation. In his\nlater work, Feyerabend (1975, 1987, 1989) moved vehemently away from\nthe positions of the Popper school. He vigorously rejected the idea of\na scientific method that makes science superior to other cultural\nenterprises. According to his “methodological anarchism”,\nany so-called methodological rule, including logical consistency,\ncould be fruitfully violated in some contexts. That said, his\nwell-known slogan, “Anything goes”, was widely read as\nmore radical than he intended, given his playful interactions with his\nfriend Lakatos.", "\nThis later Feyerabend declared that his primary aim was humanitarian,\nnot epistemological, so it was not his purpose to defend the rationality\nof science. His attack on dogmatic, scientistic conservatism, both\nwithin and without scientific communities, has methodological import,\nalbeit negative import. Feyerabend was one of the first to stress the\nstrong historical contingency of scientific work, in context of\njustification as well as discovery, and he defended this contingency\nat the methodological level as well. Thus there is no fixed\nrationality of science. For example, Galileo (he argued in historical\ndetail) introduced a new sort of methodology, a new kind of\nrationality, partly via rhetorical deception, partly with arresting\napplications of mathematics to basic mechanical phenomena.\nGalileo’s new vision happened to win out, but there is no point\nin calling it either rational or irrational in any absolute sense.", "\nPhilosophers, retreating from concrete detail to their abstract\nformalisms, make science look far more rational than it is, stressed\nFeyerabend. “[H]istory, not argument, undermined the\ngods”, and also undermined Aristotelian science and several\nlater scientific orthodoxies (1989: 397, his emphasis). Feyerabend\nrejected “the separability thesis”, according to which a\nhighly contingent historical processes can furnish scientific products\nthat are true and non-contingent, products that have achieved escape\nvelocity from history as it were (my expression). However, although\nnot as pronounced as in Lakatos, there remain traces of historicist\nconsequentialism in Feyerabend’s view, as when he wrote that\n“scientific achievements can be judged only after the\nevent” ([1975] 1993: 2). There is no “theory” of\nscientific rationality in Feyerabend, only a historicist anti-theory,\nas it were; but he was not quite the irrationalist that critics took\nhim to be. (See the entry on\n Feyerabend.\n For recent work on historical contingency, see Stanford 2006 and\nSoler et al. 2015.)", "\nFeyerabend embraced the relativism implied by the positions just\ndescribed. In a late work, Science as Art, influenced by the\nprominent Viennese art historian Alois Riegl, he spoke of distinct,\nself-contained scientific styles at different periods that are much\nlike the distinct styles in art (Ginzburg 1998). Such a view fit well\nwith his sometime assertion that there is no scientific progress, just\na succession or multiplicity of styles. Here there is a faint\nconnection to Kuhn’s early views, although the two men\nreportedly did not interact as much as one might expect while both\nwere at Berkeley." ], "subsection_title": "1.4 Methodological Anarchism" }, { "content": [ "\nLaudan opened Progress and Its Problems (1977) with the claim\nthat providing an adequate model of rationality is the primary\nbusiness of the philosopher of science but that no extant\nmethodologies fit actual science. In this book his idea of good fit\nwas fit with a selection of intuitively strong historical instances\nthat any adequate theory must explain. (Laudan 1984 and 1996: ch. 7,\nlater rejected the intuitionistic elements that gave normative punch\nto this model.) His response to the rationality question was to\npropose a thoroughgoing, explicitly pragmatic, problem-solving account\nof science. Problem-solving had been an important element in previous\naccounts, notably those of Kuhn and Popper, but Laudan\nreversed the usual account of scientific progress as a\ntemporal succession of atemporal rational decisions. Instead of\ndefining progress in terms of rationality, we should define\nrationality in terms of progress. We cannot measure progress in terms\nof approach to an unknowable, final, metaphysical truth, but we do\nhave reliable markers of progress in terms of numbers and relative\nimportance of both empirical and conceptual problems solved by\nlong-term “research traditions”. Just as Lakatos’s\nresearch programs were a compromise between Popper and Kuhn, we can\nread Laudan’s “research traditions” as incorporating\nelements of his major historicist predecessors, while departing\nsharply from other tenets of their work.", "\nMany analysts have played with possible relationships between the\nsciences’ assumed rationality and assumed progressiveness. The\ncentral issue for them is analogous to the question in Rodgers and\nHammerstein’s Cinderella: Is science progressive\nbecause it’s rational, or is it rational because it’s\nprogressive? (Kuhn [1962] 1970a: 162, had asked: Does a field make\nprogress because it is a science, or is it a science because it makes\nprogress?”) The underlying question is whether rationality is\nbasic and fundamental rather than derivative to something else. Those\nlike Laudan who make it derivative need to defend their position\nagainst the objection that they are committing a verificationist\nfallacy of confusing rationality itself (its constitutive nature) with\nthe criteria for applying the term ‘rational’. Are\nmomentary success or longer-term progress constitutive of\nrationality or merely consequential indicators of it (or neither)?", "\nBe that as it may, since progress is a historical (history-laden)\nconcept, so is rationality on Laudan’s conception, as it was on\nLakatos’s. The temporality of his account led Laudan to\nintroduce an important distinction between acceptance of a\ntheory and pursuit that would explain how rational\ntransitions to a new research tradition are possible. Scientists\nshould accept the theory that, pro tem, has the greatest\noverall problem-solving success, but pursue the tradition that now\nenjoys a higher rate of success. Nearly everyone today\naccepts a distinction of this sort, although not necessarily\nLaudan’s criteria of success.", "\nLike Structure and MSRP, Laudan’s model of science\nreceived much discussion, both constructive and critical. It faced the\nusual difficulties of how we are to count and weigh the importance of\nproblems in order to have a viable accounting scheme. Historicists can\nreply that it is not their fault if this is a messy task, since that\nis just historical reality, a reality that, if anything, favors expert\njudgment over tidy decision algorithms.", "\nLaudan (1984) agreed with Kuhn that the goals, standards, and methods\nof science change historically as well as the theoretical and\nobservational claims, but his “reticulationist model”\nrejected as historically inaccurate Kuhn’s claim that sometimes they all\nchange together to constitute a (Kuhnian) revolution. Dramatic change in one\nplace need not seriously disturb fixity elsewhere and rarely or never does. Hence,\nincommensurability is a pseudo-problem. Moreover, Laudan contended, his\nreticulationist model overcomes the hierarchical problem that has led\nthinkers such as Poincaré and Popper to make the goals of\nscience arbitrary (the top of the hierarchy and hence the unjustified\njustifier of what comes below), e.g., mere conventions. These authors have no\nway to rationally appraise the goals themselves, leaving their positions stuck\nwith an account of merely instrumental reason: efficiency relative to\na given, arbitrary goal. By contrast, in Laudan’s model, the\nelements are mutually constraining, mutually adjusting, an idea\nprominent in Dewey’s attack on hierarchy in his 1939. None takes\nabsolute precedence over the others. Thus, some goals are irrational\nbecause present and foreseeable knowledge and methods have no way to\nachieve them or to measure progress toward them. (Laudan thereby\nrejected strong realist goals as irrational.) An advance in substantive\nor methodological expertise can make it rational to embrace new\nstandards and also new goals.", "\nThe debate between Laudan and Worrall over the value of a fixed\nmethodology of science wonderfully exemplifies the persistence of the\nancient problem of change (Laudan 1989; Worrall 1989). How is it\npossible to explain, or even to measure, change except in terms of an\nunderlying fixity? Doesn’t allowing change at all three of\nLaudan’s levels—matters of scientific fact and theory,\nmethod and standards, and goals—leave us with a damaging\nrelativism? Worrall defends the fixity of Lakatos’s MSRP but\nagrees that it cannot be established a priori. Laudan’s\nreticulated model retains a more piecemeal and historically contingent fixity, as described\nabove.", " With all that said, the threat of relativism remains, for how can\na good, non-whiggish historicist have a trans-historical measure of\nprogress? Laudan’s answer was that we can whiggishly measure\nscientific progress by our own standards, regardless of what the goals\nof the historical investigators were. This sounds right about what we\ndo. But if the reasons why the historical scientists in the trenches\nmade the decisions they did do not really matter to us (or to any\ngiven generation), retrospectively, then how is rationality providing\na methodological guide or causal explanation why historical scientists\nmade the decisions they did? Their individual rationality would seem\nto become irrelevant. And why, then, is rationality the central\nproblem of philosophy of science?", "\nDeparting sharply from traditional, non-naturalistic treatments of\nnorms, Laudan addressed the is-ought problem head-on by advancing an\nimportant and influential, pragmatic “normative\nnaturalism” whereby the acceptable norms are those best\nsupported by successful historical practice—where, again,\nsuccess is as we judge it today. On this view, norms have empirical\ncontent. They are winnowed from the history of successful practice,\nagain a broadly Deweyan idea (e.g., Dewey 1929). At Virginia Tech\nLaudan and colleagues initiated a program to test the individual norms\npresent in various philosophical models of science against the history\nof science (Laudan 1977: 7; Donovan et al. 1988). Like every major\nphilosophical proposal, this one came under critical fire, in this\ncase, e.g., for isolating individual methodological rules from their\nhistorical contexts and for reverting to a traditional, positivistic,\nhypothetico-deductive model of testing. In short, critics complained\nthat Laudan’s metatheory of rationality did not match his\nfirst-order, problem-solving-progress theory of rationality. And\nprofessional historians did not welcome this invitation to\ncooperation, since the project implied a division of labor that\nregarded philosophers as the theoreticians proposing rules to test,\nwhile the historians were relegated to fact-grubbing handmaidens doing\nthe testing. To be fair, as a historicist philosopher, Laudan himself\nhad done a good deal of historical work.", "\nOn another front, Laudan’s (1981) attempt to\n“confute” scientific realism on the basis of historical\nexamples of major scientific change stimulated much discussion, since\nthe status of realism had become a central issue in philosophy of\nscience. Indeed, Laudan’s article helped to make it so." ], "subsection_title": "1.5 The Pragmatic, Problem-Solving Approach" }, { "content": [ "\nToulmin (1972) produced an evolutionary model of scientific\ndevelopment in terms of populations of concepts, a gradualist account\nof scientific change that he considered more historically accurate and\nphilosophically defensible than Kuhn’s discontinuous model.\nToulmin’s “concepts” are historically malleable, yet they are\ncharacterized by historicity. He quotes Kierkegaard: “Concepts,\nlike individuals, have their histories, and are just as incapable of\nwithstanding the ravages of time as are individuals” (1972:\nfrontispiece). Toulmin held that biological, social, and conceptual\nevolution, including scientific development, are all instances of the\nsame generalized variation-selection-transmission schema, albeit with\nquite different concrete implementations. For Toulmin, disciplines\n(specialties) are analogous to biological species. He touted his model\nas naturalistic, indeed ecological, but not in a way that excludes\nrationality. Rationality enters primarily at the selection level,\ndetermining which families of concepts (including methodological ones)\nget selected and reproduced. Rationality is not a matter of\n“logicality”, i.e., of sticking to a given logical or\nKuhnian framework through thick and thin. Rather, it is a matter of\nadapting appropriately to changing circumstances. Like Newtonian\nforce, rationality has to do with change, not maintenance of the same\nstate. Thus no Kuhnian revolution is needed in order to break out of\nan old conceptual framework.", "\nAs for the descriptive-normative problem, thinkers from Kuhn to Robert\nBrandom (e.g., 2002: 13, 230ff) have appealed to the common law\ntradition as an instructive analogy, and Toulmin was no exception.\nPublished legal cases provide legal precedents that later legal\nargumentation can cite for support. Over time, normative traditions\nemerge. Explicit rules may be formulated by reflecting on the history\nof precedents, but the practices typically remain implicit. There is a\nwhiff of Hegelian, retrospective reconstruction in this idea of\nextracting norms from patterned historical practices that embody them\nimplicitly and contingently. The main trouble with Toulmin’s\naccount, said critics, is that it is so vague and abstract that it\ntells us little about how science works. It would seem to apply to\njust about everything.", "\nDonald Campbell (1960, 1974) had previously defended the generalized\nvariation plus selective retention schema, which he traced back to\nWilliam James. Popper regarded his own evolutionary account of\nscientific development as similar to Campbell’s (1974). Ditto\nfor David Hull (1988) with his more detailed evolutionary model.\nHowever, Hull rejected evolutionary epistemology, as such,\nand denied that he was doing epistemology at all. (Evolutionary\nepistemologies face the problem of why we should expect a contingent\nselectionist process to be truth-conducive: see the entry on\n evolutionary epistemology.\n Assuming that it is can also tempt one to fall into whiggism\nregarding the past in a social Darwinist sort of way.) Hull rejected\nToulmin’s biological species analogy, as based only on\nfeature-similarity rather than on the historical-causal continuity of\ngenuine biological species. Hull’s book reflected his own deep\ninvolvement in the controversy between cladists, evolutionary\nsystematicists, and pheneticists over biological classification. (He\nserved terms as president of both the Society for Systematic Biology\nand the Philosophy of Science Association.) Hull generalized his\nimportant biological concepts of replicator (gene) and interactor\n(organism) to scientists and communities. His central unit of and for\nanalysis was the deme, or research group, in its competition with\nothers.", "\nHull (1988) argued that the success of science can be explained by an\ninvisible hand mechanism rather than in terms of rational\ndecision-making. He did not deny that most scientists regard\nthemselves as rational truth seekers, but on his account the primary\nmotivation is the drive for professional recognition and credit via\npositive citation by others, and avoidance of violations of\ninstitutionalized standards. The term ‘rationality’ does\nnot even appear in the book’s index. Nonetheless, the\ninstitutional incentive structure of science works to produce\ngenerally reliable results and scientific progress, so that, to\nrationality-minded philosophers, science looks as if it is\ndriven by the intentional rationality of its practitioners. We might\nsay that, for Hull, rationality explains nothing without causal\nbacking, but once we bring the causal mechanisms into play, there is\nno longer a need to foreground rationality, at least not intentional\nrationality.", "\n\n\nThe better [scientists] are at evaluating the work of others when it\nis relevant to their own research, the more successful they will be.\nThe mechanism that has evolved in science that is responsible for its\nunbelievable success may not be all that “rational”, but\nit is effective, and it has the same effect that advocates of science\nas a totally rational enterprise prefer. (1988: 4)\n", "\nLike Adam Smith’s view of the invisible hand regarding altruism\nand the public good, rationalists can interpret Hull’s account\nas broadly Hegelian in the sense that the rationality of science\nemerges (insofar as it does) from the complex social interactions of scientists\nand groups of scientists going about their normal business in ordinary\nways that satisfy community norms and incentive structures, not from\ntheir explicit intentions to make rational decisions. While Hull gave\nclose attention to these social interactions and to the institutions\nthat enable them, he claimed that his appeal to social factors was\ninternal to science rather than external." ], "subsection_title": "1.6 Evolutionary Models of Scientific Development" }, { "content": [ "\nLeft relatively untouched by historicist philosophers during the\nBattle of the Big Systems was the internal/external distinction. The\nphilosophers, consonant with traditional sociology of science (e.g.,\nMerton 1973) and sociology of knowledge more generally, defended a\nkind of “inertial principle” (Fuller 1989: xiii et\npassim): social and psychological factors such as economic and\npolitical interests and psychological dispositions should be brought\ninto play only to explain deviation from the rational path. This\ndistinction began to erode already in Kuhn, who stressed the social\nfactors internal to the organization of science itself:\nscience education, the strong role of scientific communities with\ntheir distinctive cultures, etc. (See also Lakatos on comprehensive\ntheories of rationality that can turn apparent external considerations\ninto internal ones, and Hull 1988 on career advancement.)", "\nIn the 1970s, new-wave sociologists of science quickly rejected the\ndivision of labor implied by the inertial principle and took sociology\nfar beyond where Kuhn had left it (much to his chagrin). These\nsociologists insisted that sociology, via social interests and other\nsocial motivational causes, had much to say about the internal,\ntechnical content of science—so much, in fact, that it was not\nclear that there was any room left for the rational explanations of\nthe philosophers. The Edinburgh Strong Programme founded by David\nBloor and Barry Barnes (see Bloor 1976), the Bath relativist school of\nHarry Collins and Trevor Pinch (Collins 1981), and later\nconstructivist work of Bruno Latour and Steve Woolgar (1979), Karin\nKnorr-Cetina (1981), Steve Shapin (1982), Shapin and Simon Schaffer\n(1985), and Andy Pickering (1984) were important early developments.\n(See Shapin 1982 for a helpful discussion.)", "\nSince the new sociology of science was also heavily based on\nhistorical case studies, we find more radical historicisms challenging\nless radical ones. Although the sociologists often disagreed among\nthemselves, as the philosophers did, the general thrust of their work\nwas that the philosophical historicists had failed to take\nsocio-political context into account and thus were still too much\nwedded to the old, abstract, acausal ideals of rationality,\nobjectivity, and progress toward truth. Much sociological work was\nexplicitly anti-realist and relativist, at least as a methodology.", "\nMost philosophers of science strongly rejected the new sociology as\nrelativist and irrationalist, the non-historicists among them adopting\nversions of strong realism, according to which mature science can\nknowingly, on internalist grounds, arrive at theoretical truth and\ngenuine reference to theoretical entities, or closely enough. The\neventual upshot was “the Science Wars” of the 1990s. By\nnow (2017), the sides in this dispute have mellowed, fruitful\nconversations are taking place, and some degree of reconciliation has\noccurred (see Labinger & Collins 2001). Work by feminists in\nscience studies such as Donna Haraway (2004) and feminist philosophers\nof science such as Helen Longino (1990, 2001) and Miriam Solomon\n(2001) have rejected assumptions common to both sides in the debate,\nthereby opening the way to their more pluralistic, interactive, and\nless hierarchical options. Distinct prominent approaches to social\nepistemology by philosophers include Fuller 1988, Goldman 1999, and\nRouse 2002. (See the entries on\n social epistemology,\n scientific method,\n scientific realism,\n and the\n social dimensions of science\n as well as the feminist entries referenced above.)", "\nSome of the sociological work had a postmodern cast, and so did\ncontributions by some philosophers. For example, Richard Rorty’s\nversion of historicist pragmatism rejected correspondence theories of\ntruth and the related idea that we humans have some\nnaturalized-theological obligation faithfully to represent\nmetaphysical nature with our science. He spoke suggestively but\nvaguely of major transformations in the sciences (or anywhere else in\nculture), such as that achieved by Galileo, as the invention of a new\n“vocabulary” that worked well enough for certain purposes\nto catch on, but not as new truths established by logical reasoning. As\nfor rationality itself, it is a matter of maintaining an honest, civil\n“conversation”:", "\n\n\nOn a pragmatist view, rationality is not the exercise of a faculty\ncalled “reason”—a faculty which stands in some\ndeterminate relation to reality. Nor is [it] the use of a method. It\nis simply a matter of being open and curious, and of relying\non persuasion rather than force. (1991: 62).\n", "\nSo rationality is not the key to scientific success, and it has as\nmuch to do with rhetoric as with logic. Pragmatists, he said, prefer\nto speak of the success or failure of problem-solving efforts, rather\nthan rationality or irrationality (1991: 66).", "\nA view sometimes ascribed to Rorty’s hero Dewey is that\nrationality is not an a priori, universal method of thinking\nand acting properly; rather, it is like a box of intellectual tools,\neach of which, as humans have learned from craft experience, work better than\nothers in various situations, the result being what might be called a\n“teleonormative” conception of rationality." ], "subsection_title": "1.7 New-Wave Sociology of Science and the Realist Reaction" } ] }, { "main_content": [ "\nMany of the issues raised by and about historicist conceptions of\nrationality remain unresolved, but the approach has the merit of\nbringing back into discussion several interrelated questions." ], "section_title": "2. Rationality and History: Some Basic Questions", "subsections": [] }, { "main_content": [ "\nNineteenth-century philosophers and (especially) historians are\ncommonly credited with the modern “discovery” of history,\nespecially political history, via developing the discipline of\nevidence-based, interpretive and explanatory historiography. Hegel\nhistoricized Kant at the beginning of that century, but it was\nprimarily German historians such as Ranke, Droysen, Windelband,\nDilthey, Rickert, and Weber who developed competing conceptions of\nwhat is required for rigorous historical research. (For an in-depth\nsurvey, see Beiser 2011.) These historians were concerned to develop\nhistoriography as wissenschaftlich but autonomous from the\nnatural sciences, where positivism reigned. They also rejected the\ngrand, Hegel-type philosophies of history. Toward the end of the\ncentury, this opposition produced the Methodenstreit, the\nvehement debate over differences between the natural sciences\n(Naturwissenschaften) and the socio-historical sciences\n(Geisteswissenschaften). Historicists saw naturalism and\nmaterialistic mechanism as threats.", "\nThe connection of the historicization of philosophy of science in the\n1960s to the German historicist tradition is indirect, given the\ntime-gap of decades. However, the historicists of scientific\nrationality discussed in this article did (or do) agree to several of\nthe following (overlapping) tenets, most of them traceable to\nnineteenth-century antecedents. There exist tensions among the\nfollowing claims, so internal disagreement among historicists is to be\nexpected.", "\n1. The historicity of all things. Virtually all things come\ninto existence and pass away in historical time. Nothing is guaranteed\nto be fixed and permanent, written in the stone of the universe.", "\n2. History vs. a priori reason or logic alone. Human beings\ndo not possess a faculty of a priori reason capable of\nsurveying the space of all logical possibilities. The emergence of\nnon-Euclidean geometry illustrates this point. Human inconceivability\nis not an adequate criterion of either logical or historical\npossibility.", "\n3. Our historical boundedness: anti-whiggism and the principle of\nno privilege. We inquirers are also historically situated. While\nwe are not slaves to our cultural context, we can escape it only\npartially and with difficulty. Our horizons sometimes prevent us from\nrecognizing our own presuppositions, not to mention future\npossibilities. Wrote Mary Hesse: “our own scientific theories\nare held to be as much subject to radical change as past theories are\nseen to be” (1976: 264). Although we have good reason to hold\nthat our science is superior to that of the past, this does not confer\nan absolute, ahistorical privilege on our science. Rather than succumb\nto this perspectival illusion, we must imagine that our successors may\nlook at us as we see our predecessors. We, too, are just a\ntransitional stage into a future that is likely to include much that\nis beyond our present horizon of imagination. We must avoid the flat\nfuture illusion that sees the future a tame continuation of the\npresent (Nickles forthcoming).", "\n4. History as endlessly creative, thus an endless frontier.\nStrong historicists think an endless frontier is likely, history as\nopen, and productive of perpetual novelty (no agency intended).", "\n5. Historical content of theory of justification: The complexity\nof history. History is too complex and too subtle to be captured\nby a fixed, formal system or in terms of the dynamical relationships\nof a set of “state variables”. Logical and probabilistic\nsystems alone are crude tools for capturing the reasoning of real\npeople, scientists included. Besides the subtle, contextual reasons,\ninnovative scientists work at moving research frontiers\n(“context of discovery”) and, so, must make many decisions\nunder uncertainty (not only under mere risk). Rationality has more to do with\nappropriate response to change than with sticking rigidly to\none’s initial standpoint. This challenge strikes at the heart of\ntraditional accounts of context of justification, hence at the heart\nof traditional philosophy of science. Thinkers from Kuhn to van\nFraassen (2002: 125) have taken a dim view of confirmation theory,\nalthough Bayesians have made valiant attempts to capture historicist\ninsights. (For examples, see Salmon 1990 and Howson & Urbach\n1993).", "\n6. Consequentialism and history as a judge. Frontier\nepistemology teaches that we can often only learn which modes of\naction are successful via historical experience of the consequences.\n(Non-historicists can reply that the eventual judgment is not itself\nhistorical but only delayed, because based on evidence gathered over\ntime.) In its strongest form, historical judgment replaces “the\nLast Judgment”, the judgment of God, as reflected in the common\nexpression “the judgment of history”. (Of course, this\nview is itself anti-historicist in its conception of finality.)", "\n7. Genetic, genealogical understanding. Since nearly\neverything is the product of historical development or disintegration,\nstudying its historical genesis and dissolution is key to\nunderstanding it. Genetic fallacies are avoidable by including\ndevelopment and maintenance as part of the narrative, since\ndevelopment can be transformative. Today many writers are exploring\nthe biological and socio-cultural evolutionary origins of human\nrationality, going far deeper, historically, than to recent historical\ndevelopments such as the so-called Scientific Revolution.", "\n8. Historical skepticism, incommensurability, and relativism.\nOne role of historiography is to debunk myths. As such, it can be\nliberating, as when we see that institutions and conceptual frameworks\nare, to a large degree, human constructions with a historical origin,\nnot things irremediably fixed in the foundation of the universe. For that\nvery reason it produces a degree of skepticism toward all human\nthings. Although the natural world shapes human cultures, including\nscientific ones, it far from dictates a single, fixed culture.\nHistoriography discloses that human enterprises, including the\nsciences, are imbedded in deep cultures with their distinctive norms.\nThere is no “God’s-eye”, history-neutral set of\nmeta-norms, no “Archimedean point” from which these\ncultures can be objectively compared. Thus it is difficult or\nimpossible to evaluate all science with a single standard. Here lurks\nthe problems of cultural incommensurability and relativism.", "\n9. Pluralism. Methodological pluralism is a natural\nconsequence of historicist approaches. Historical study discloses that\nthe various sciences employ quite different methods and often harbor\ncompeting research programs. The emergence of philosophy of biology as\na specialty area in the wake of the 1959 Darwin centennial added\nsubstance to this claim. (For entries into the pluralism literature,\nsee Dupré 1993; Galison & Stump 1996; Mitchell 2003; and\nKellert et al. 2006.)", "\n10. Science as a model of rationality. On this theme,\nhistoricists are divided. Some strong historicists, especially\nFeyerabend, Hull, and thoroughgoing social constructivists, deny that\nscience is rationally or methodologically special among human\nenterprises.", "\n11. Science as a model of progress. This, too, is practically\naxiomatic among philosophers of science. The idea of history\n“itself” as progressive came in with the Enlightenment and\nwas severely challenged by the world wars.", "\n12. Historicism as half-naturalistic. Historicist accounts do\nnot appeal to supernatural factors or to factors beyond the\npossibility of human cognition such as clairvoyance or the\nmetaphysical truth about reality. Historicists usually take a second\nstep toward naturalism in considering humans as biologically limited\nbeings, but they resist reduction to the natural science brand of\nnaturalism. Philosophical historicists also reject the reduction of\nnorms to facts. (But, late in life, R.G. Collingwood may have come to hold a\nstrong version of historicism according to which philosophy reduces to\nhistory: see the entry on\n Collingwood.\n Some new-wave sociologists may have held a parallel reductionist view\nabout philosophy and sociology, insofar as philosophy was worth\nsaving.)", "\n13. Major historical change as emergent—against intelligent\ndesign and the conscious model. Many historical developments are\nnot deliberately chosen or designed but emerge from numbers of people\ncarrying out their individual and collective activities. The rise of the nation-state\nand of the international capitalist economic system were not the\nproducts of centralized, rational planning, nor were modern science\nand technology, although there were, of course, many micro-instances\nof such planning. This point applies to the idea of scientific method,\nwhich tradition often depicted as clairvoyantly, intelligently guiding\nscientific innovation. But as Hume already anticipated, no method is\nguaranteed in advance to work in a novel domain. Methodological\ninnovation typically follows rather than precedes innovative work\n(Hull 1988; Dennett 1995; Nickles 2009, forthcoming). This is a\nbroadly Hegelian idea.", "\n14. Strong historical determinism is mistaken. A controversy\namong historicists of various stripes is whether there are “iron\nlaws of historical development”. Hegel and Marx, in quite\ndifferent but related ways, believed in a teleological conception of\nhistory, that “it” was working its way inevitably through\nknown stages toward a final goal that would amount to “the end\nof history” in the sense that deep historical change would now\ncease. This is the view that Popper termed “historicism”\nin The Poverty of Historicism (1957; see also his 1945).\nPopper vehemently rejected this version of historicism, as do\nvirtually all historicist philosophers of science today. For them,\nhistory is non-teleological and highly contingent. This includes\nKuhn’s ([1962] 1970a) model, although the latter does posit an\nalmost inevitable, unending alternation of normal and revolutionary\nperiods—a final pattern without end, as it were.", "\n15. Hermeneutic interpretation. The received, covering-law\nmodel of explanation is inadequate to explain historical action,\nincluding that of scientists and communities of scientists. Kuhn\ndescribed his method as hermeneutic, but few historicist philosophers\nof science are full-blown hermeneuticists or as fully committed to\nempathic understanding as were some of the classic German\nhistoricists. Most or all historicists are somewhat partial to\nnarrative forms of explanation. (See the entry on\n scientific explanation.)" ], "section_title": "3. Historicism Then and Now", "subsections": [] }, { "main_content": [ "\nThe battle of the big systems seems to be over, and likewise for the\nheyday of interdisciplinary departments and programs of history and\nphilosophy of science (but see below). So are historicist conceptions\nof rationality dead? Despite claims that historicist philosophy of\nscience has been “withering on the vine” (Fuller 1991), it\nis fair to say that historicist influences remain important, but in a\nsubtler way. Most philosophers of science are more historically\nsensitive than before, whether or not they identify as historicists.\nHistoricist interests have expanded into “the naturalistic\nturn”, “the models turn”, and “the practice\nturn”, which includes interest in contemporary practices, and,\nto a lesser degree, in future history (Nickles forthcoming).", "\nMoreover, in parallel developments, the classical conception of\nrationality is under attack on many fronts. Herbert Simon (1947)\nintroduced the ideas of bounded rationality and satisficing. Simon\nlater championed the need for a heuristic approach to problem solving\nby humans and computers (Newell & Simon 1972). Various flavors of\nartificial intelligence then led the way in the methodology of problem\nsolving, with heuristics as a central topic and no longer the temporary\nscaffolding of positivism and Popper. Simon’s program in\nadaptive, “ecological rationality” is now being expanded\nby Gerd Gigerenzer and the Adaptive Behavior and Cognition group in\nBerlin (Gigerenzer et al. 1999). Simon’s approach and the\n“heuristics and biases” program of Daniel\nKahneman and Amos Tversky (Kahneman et al. 1982), plus work by the\nlatter on prospect theory, triggered the emergence of behavioral\neconomics, which rejects the neo-classical homo economicus\nrationality model. Philosopher Christopher Cherniak’s\nMinimal Rationality (1986) also brought out sharply how\nidealized were traditional philosophical assumptions about\nrationality. In other directions, some computer scientists are\nchallenging the anthropocentrism of received conceptions of rational\ninference by asking why artificial intelligence, including deep\nlearning, should be restricted to human forms of reasoning. Meanwhile,\nbiologists and philosophers are studying the evolution of rationality\n(Okasha & Binmore 2012), and ethologists ask why we should\nwithhold attributions of rationality to animals from chimps and\nelephants to octopuses, simply because they seem to lack a human sort\nof conceptual language.", "\nNonetheless, there is wide agreement that historicist accounts of\nscientific rationality cannot fully supplant traditional views. For\nexample, there surely does exist some “instant\nrationality” even at research frontiers. One finds a wide\nvariety of decision contexts there, and some of these decisions will\nbe uncontroversially warranted at that time and in that context, while\nothers will not be. Hesse (1980) and many others (see Radnitzky &\nAndersson 1978) raised the issue of how to generalize from historical\ncase studies, for citing case studies can be like citing the\nBible. One can cherry-pick one’s case studies to\nsupport most any position. In any case it is fallacious to generalize\nfrom a few, highly contextualized case studies to conclusions about\nall science at all times. Early historical work in social studies of\nscience faced the same problem. Ironically, such generalization\nabstracts away from the historicity of the case studies themselves.\nThe attempt to replace inductive generalization by testing via an H-D\nmodel also runs into trouble, as we noted in connection to the\nVirginia Tech project. And why should case studies from two or three\nhundred years ago be taken seriously when science itself has changed\nsignificantly in the meantime? Partly for this reason Ronald Giere\n(1973) contended that it was necessary to study only today’s\nscientific practices, that philosophers had no special need of\nconsulting historians.", "\nLate in life, Kuhn himself, surprisingly, rejected the case-study method as too\nwedded to the traditional view of science as a direct search for the\ntruth about the universe. The first generations of historical inquiry\nby philosophers and sociologists so shockingly revealed the presence\nof many non-epistemic factors and the general failure of any method\nfully to justify scientific beliefs, he said, that skepticism was the\nresult. The more people learned about how science is actually done,\nthe more skeptical they became. Declared Kuhn, we can more securely\nderive historical patterning “from first principles” and\n“with scarcely a glance at the historical record itself”\n(1991: 111ff). This is not a complete departure from history, however,\nfor it begins from what he termed “the historical\nperspective”, a non-whiggish understanding of the decisions\nactually available to the historical actors in their own context.\nKuhn’s main point is that such decisions should be considered\ncomparative (“Is this item better than that one, given the\ncontextual knowledge and standards?”), not as judgments of truth\nor probability. This move reduces the problem of understanding\nbehavior in rational terms to something manageable, he explained.\nDeveloping this point, Kuhn said, will bring the only defensible sort\nof rationality back into scientific practice in a way that largely\navoids the old problems of incommensurability. It will also provide a\ndefensible concept of scientific progress and of scientific\nknowledge (almost by definition)—knowledge as what the\nscientific process produces. This historical perspective was part of\nKuhn’s project of developing a biological analogy for the\ndevelopment of science, wherein disciplinary speciation events\ncorrespond to revolutions. Kuhn held that his approach applied to all\nhuman enterprises, not just science (Kuhn 2000).", "\nRecently, Rogier De Langhe (2014a,b,c, 2017) has been developing a\nbroadly Kuhnian, two-process account of science from an economics\nstandpoint. Instead of doing a series of historical cases, De Langhe\nand colleagues are developing algorithms to detect subtle patterns in\nthe large citation databases now available. In sum, both late Kuhn and\nearly De Langhe are now appealing to the history of science in a more\nabstract, or perhaps comprehensive, manner, a manner complementary to the two-process approach of\nMichael Friedman (below).", "\nAnother general challenge for historicists and others concerned with\nthe rationality of science is how to factor the division of labor in\nscience into a model of scientific rationality. How does individual\nrationality (the traditional focus of economists as well as\nphilosophers) relate to the collective rationality of working groups\nor entire specialist communities? (See Sarkar 1983; Kitcher 1993;\nMirowski 1996; Downes 2001; De Langhe 2014b; Latour 1987 and later for his\nactor-network theory; and the entry on\n social epistemology.)\n Feminist philosophers such as Longino (1990, 2001) and Solomon (2001)\nhave proposed more thoroughgoing social epistemologies of science that\ngo beyond the problem of division of labor, which, in their view, is\nstill often treated individualistically." ], "section_title": "4. Related Developments and Further Challenges", "subsections": [] }, { "main_content": [ "\nThe attempt to integrate historiography and philosophy of science has\na troubled history. Several joint departments and programs were formed\nin the heady 1960s, just as much historiography of science was turning\naway from internalist approaches. As professional historians and\nphilosophers came to realize that their interests differed, many of\nthese programs did wither.", "\nIn the meantime, several philosophers have engaged in serious\ninternalist studies for philosophical purposes, usually focusing on\n“big names” such as Galileo, Newton, Lavoisier, Darwin,\nand Einstein, or big developments such as the route to the double\nhelix. More recently, scholars such as Nancy Nersessian with her\n“cognitive history” project (1995) have employed new\nresources from the cognitive sciences in this regard, a move neglected\nby Kuhn himself and resisted by sociologists concerned by the\nphilosophers’ neglect of the social basis of the knowledge\nenterprise. (See also Giere 1988; Bechtel & Richardson 1993;\nDarden 2006; Andersen et al. 2006; Thagard, e.g., 2012.) Historians,\nmeanwhile, have focused on social history and, more recently, on\nsocial microhistory and lesser-known figures, including women, rather\nthan on the internalist moves of big-name scientists. Consequently,\nhistoricists today still feel the need to respond to Giere’s\n(1973) question of whether history and philosophy of science can be an\nintimate marriage.", "\nSince 1990 promising new movements have emerged that bring together\nphilosophy of science and historiography of science. First,\nphilosophers of science became interested in the historical emergence\nand professionalization of their own field. Early work quickly\ndestroyed some myths about the Vienna Circle, for example. The primary\norganization here is the International Society for the History of\nPhilosophy of Science (HOPOS), with its own journal and regular\nmeetings. More recently, the Integrated History and Philosophy of\nScience (&HPS) organization has sponsored several conferences with\nthe goal of maintaining the standards of both fields rather than\ncompromising one for the supposed advantage of the other. (For\nbackground, see Schickore 2011, 2017. Consult the &HPS website for\nother contributors.)", "\nTheodore Arabatzis (forthcoming) distinguishes two ways of integrating\nhistory and philosophy of science: the familiar “historical\nphilosophy of science” (HPS), usually based on\n“historical” case studies; and the less familiar\n“philosophical history of science” (PHS). It is well known\nthat historians have found most philosophical work of little use, and\nArabatzis aims to help correct the asymmetric relationship between\nhistory and philosophy.", "\n\n\n[P]hilosophical reflection on these concepts can be\nhistoriographically fruitful: it can elucidate historiographical\ncategories, justify historiographical choices and, thereby, enrich and\nimprove the stories that historians tell about past science as a\nknowledge-producing enterprise. \n", "\nLabels for movements can be arbitrary and misleading, but several of\nthe authors cited by Arabatzis have been identified with a movement\nusually called “historical epistemology”, the goal of\nwhich is to combine excellent history of science with philosophical\nsophistication or excellent philosophy with more historical\nsophistication than is usually found in case-studies approaches. Given\nthe epistemological focus, here is where we might expect to find the\ngreater concentration of work relevant to questions of scientific\nrationality. The epicenter of the movement is the Max Planck Institute\nfor the History of Science in Berlin, whose directors over the years,\nLorenz Krüger (who died before he could assume the post),\nLorraine Daston, Hans-Jörg Rheinberger, and Jürgen Renn,\nhave promoted historical epistemology. A recent, special issue of\nErkenntnis (Sturm & Feest (eds.) 2011) on historical\nepistemology derives from a conference at the Institute. In their\nintroductory essay to the special issue, the co-editors, Uljana Feest\nand Thomas Sturm, ask “What (Good) is Historical\nEpistemology?” (Feest & Sturm 2011). The special issue\nincludes a baker’s dozen authors who develop and/or critique\nvarious approaches to historical epistemology. The participants range\nfrom older hands such as Philip Kitcher, Michael Friedman, and Mary\nTiles to more recent contributors such as Jutta Schickore and\nFeest. (See Tiles & Tiles 1993 for an early philosophical\nintroduction to the field.)", "\nFeest & Sturm (2011) divide the movement into three streams. One stream\nstudies historical changes in epistemology-laden concepts\nsuch as objectivity, observation, evidence, experimentation,\nexplanation, and probability. How do new concepts emerge? How are they\nstabilized? At what point do they become conscious rather than\nremaining implicit in practice? How do they shift over time and how\nwell do they travel to different scientific contexts (cf. Howlett\n& Morgan 2011)? Insofar as they are initially metaphorical, how do\nthey become dead metaphors? How do they fade out of use? Lorraine\nDaston’s work is a good example of this approach (e.g., 1988,\n1991; Daston & Galison 2007; Daston & Lunbeck 2011). This\nmeans looking at the evolution of concepts or organizing\n“categories” of action and thought within a historically\nconfined project, however interdisciplinary it might\nbe—something between the eternal, global, and maximal often\nfavored by philosophers and the evanescent, local, and contingent\nfavored by many historians. Gone is the old-fashioned\n“conceptual history” of the sort exemplified by Max\nJammer’s (1957),\nwhich traces “the concept” of force from ancient Egypt to\nthe twentieth century. Wrote Daston in an early paper:", "\n\n\nTo my mind, the most able practitioners of historical epistemology\nthese days are philosophers rather than historians—I think of\nthe remarkable recent work of Ian Hacking and Arnold\nDavidson—although I think they, intellectual historians, and\nhistorians of science might well make common cause in such a venture.\n(1991: 283, footnote omitted; see also Davidson 2002)\n", "\nDaston then asks, “What good is historical epistemology?”\nHer opening (but later qualified) suggestion is that it goes part way\ntoward “releasing us from our bondage to the past by hauling\nthat past into conscious view”, although we must recognize that\ncalling attention to the contingent origins of something is not\nsufficient to debunk it, upon pain of committing a genetic fallacy.\nNor can we simply reject something without having an alternative to\nput in its place. “That is, historicizing is not identical to\nrelativizing, much less to debunking”.", "\nThe second strand of historical epistemology identified by Feest and\nSturm in their introduction to the special issue focuses on the trajectories of the objects of\nresearch—“epistemic things”—rather than on\nconcepts, and here the well-known work of Rheinberger (1997, [2006]\n2010a, [2007] 2010b) is emblematic. Renn (1995, 2004) represents the\nthird approach, an attempt to understand the longer-term dynamics of\nscience. For example, Renn attempts to solve several mysteries about\nhow Einstein was able to accomplish the relativity revolution. His\nanswer takes into account the long history of developments in distinct\nfields that Einstein was able to bring together, partly because of his\nwide philosophical and other cultural interests. Renn looks at\nlong-term developments by analogy with biological development. Norton\nWise (2011) also brings biological metaphor into play. He observes\nthat historical narrative as a form of explanation is now making\nserious incursions into physics, in the physics of complex or highly\nnonlinear systems. “Covering law” explanations are not\navailable there, he says, and sometimes we must resort to simulations\nin order to understand how systems evolve. “We know what we can\ngrow”.", "\nRunning through much historical epistemology is a century-long line of\nneo-Kantian thinking, from Ernst Cassirer and the Marburg school to\nReichenbach and Carnap and then to Kuhn, Ian Hacking, Michael\nFriedman, Daston, Renn, and others. Theirs are diverse versions of the\ntwo-process view introduced in\n Section 1.2\nabove. On this view, there are long-term socio-cognitive stabilities\n(not necessarily the paradigms or research programs discussed above)\nthat have a beginning, middle, and end in historical time. They are\nhistoricized Archimedean points or platforms that organize\nhuman experience, rather than fixed Kantian categories. But, like\nKant’s categories, they are presuppositions that define how\ncoherent perception and the formation of true or false propositions\nare possible.", "\nFriedman speaks of these as “historically contingent but constitutive\na prioris”. His 2011 takes first steps beyond the two-process\ndynamic of his 2001 to address the problem of changing conceptions of\nrationality (i.e., intersubjective objectivity) and to bring in a\nwider social dimension. Like Renn, Friedman makes philosophical\nreflection a key to understanding changes so rapid that they amount to\ndiscontinuities. Up to a point he defends Kuhn on the existence of\nscientific revolutions and incommensurability. Kuhn ran into trouble\nwith incommensurability and relativism, he says, for failing to\ninclude the history of scientific philosophical reflection\nthat parallels the first-order, technical scientific work itself.\nFriedman’s leading example is also the relativity\nrevolution.", "\nWhy do philosophers need to appeal to serious history of science? From\nthe beginning, Friedman has answered this question by insisting on the\nimportance of the history of science to locate the emergence of\nphilosophical ideas in their historical scientific context and vice\nversa—thus to understand the interaction between what\nis commonly called scientific work and philosophical work (Domski\n& Dickson 2010: 4). For example, Newton’s mechanical system\nof the world was shaped by philosophical and theological interests\nthat Newton and his contemporaries considered directly relevant\n(internal not external), as well as socio-political interests. And\nlikewise for Kant and Poincaré and Einstein and many other\nthinkers, great and small. To the degree that we retain an\ninternal/external distinction, it is historically relative. Unlike\nmost other historical philosophers, Friedman furnishes the intricate\ntechnical and contextual detail to support such claims.", "\nInspired by Friedman’s approach is the rich collection,\nDiscourse on a New Method: Reinvigorating the Marriage of History\nand Philosophy of Science (2010), edited by Mary Domski and\nMichael Dickson, and containing a book-length response (Friedman\n2010). Their introduction to the volume is a “manifesto”\nfor “synthetic history” (2010: 11ff, 572ff). This sense of\n‘synthetic’ is not opposed to ‘analytic’, they\ninsist. For example, rather than separating out the mathematical,\nphysical, philosophical, theological and other social-contextual\nconstituents of Newton’s work for separate disciplinary\ntreatment, synthetic history follows Friedman in exploring the ways\nthese relate to one another to achieve an outcome with a satisfying\nconvergence (2010: 15ff). Although inspired by Friedman’s work,\nthe manifesto denies that Friedman’s two-process view is\nessential to synthetic history. (See also the extensive discussion of\nFriedman by Menachem Fisch (forthcoming), a work centered on George\nPeacock’s struggle with rational consistency that helped produce\na transformation in nineteenth-century mathematics.)", "\nA somewhat different sort of two-levels position is the\n“historical ontology” of Ian Hacking. Hacking (2002, 2012)\ncites Foucault’s “discursive formations”\n(epistèmes) and Alistair Crombie’s “styles\nof scientific thinking” (Crombie 1994) as inspirations. Examples\nof such styles are the Greek discovery or invention of axiomatic\ngeometry, the laboratory science that emerged in the Scientific\nRevolution (Shapin & Schaffer 1985), and modern probability theory\nand statistical inference (Hacking 1975). Hacking returns to\nKant’s “how possible?” question, the answer to which\nestablishes the necessary conditions for a logical space of reasons in\nwhich practitioners can make true or false claims about objects and\npose research questions about them. And Hacking also historicizes the\nKantian conception.", "\n\n\nThe historical a priori points at conditions whose dominion\nis as inexorable, there and then, as Kant’s synthetic a\npriori. Yet they are at the same time conditioned and formed in\nhistory, and can be uprooted by later, radical, historical\ntransformations. T.S. Kuhn’s paradigms have some of the\ncharacter of a historical a priori. (Hacking 2002: 5)\n\n\n…\n\n\n[S]cientific styles of thinking & doing are not good\nbecause they find out the truth. They have become part of our\nstandards for what it is, to find out the truth. They establish\ncriteria of truthfulness. … Scientific reason, as manifested in\nCrombie’s six genres of inquiry, has no foundation. The styles\nare how we reason in the sciences. To say that these styles\nof thinking & doing are self-authenticating is to say that they\nare autonomous: they do not answer to some other, higher, or deeper,\nstandard of truth and reason than their own. To repeat: No foundation.\nThe style does not answer to some external canon of truth independent\nof itself. (2012: 605; Hacking’s emphasis)\n", "\nAs in early Kuhn, there is a kind of circularity here that is perhaps not\nvicious but, quite the contrary, bootstraps the whole enterprise.\nHacking describes changes in historical a prioris as\n“significant singularities during which the coordinates of\n‘scientific objectivity’ are rearranged” (2002:\n6).", "\nUnlike Kuhnian paradigms, several of Hacking’s styles of\nthinking and doing can exist side by side, e.g., the laboratory and\nhypothetical modeling traditions. Yet people living before and after\nthe historical crystallization of a style would find each other\nmutually unintelligible. Hacking recognizes that Kuhnian problems of\nrelativism lurk in such positions. “Just as statistical reasons\nhad no force for the Greeks, so one imagines a people for whom none of\nour reasons for belief have force” (2002: 163). This sort of\nincommensurability is closer to Feyerabend’s extreme cases (as\nin the ancient Greek astronomers versus their Homeric predecessors)\nthan to Kuhn’s “no common measure” (2002: chap. 11).\nWrites Hacking,", "\n\n\nMany of the recent but already “classical” philosophical\ndiscussions of such topics as incommensurability, indeterminacy of\ntranslation, and conceptual schemes seem to discuss truth where they\nought to be considering truth-or-falsehood. (2002: 160)\n", "\nFor an illuminating exposition and critique of Hacking’s\nposition, see Kusch (2010, 2011).", " A still more integrative role for historical epistemology is\narticulated by Hasok Chang (2004, 2012). Chang is a nonrealist who\nboldly goes beyond the case-study genres of both philosophers and\nprofessional historians to propose what he terms “complementary\nscience”, a fully integrated historical and philosophical\napproach that does not stop with pointing out historical contingencies\nbut also investigates them scientifically, e.g., by repeating and\nextending historical experimental practices. Chang’s idea is\nthat complementary science can preserve previously gained knowledge\nand unanswered questions now in danger of becoming lost, and can even\nbuild upon them as a complement to today’s highly specialized\nscientific disciplines. The results can be published as genuine, if\nnon-mainstream, scientific contributions. For example, in his own work\nhe tries to bring the debate over phlogiston to life as well as that\nover the nature of water and the question of its boiling point. For\nhis work, Chang leaves both his armchair and the library, for he needs\nscientific equipment and laboratory space in addition to the usual\nscholarly materials.", "\nHistorical epistemology faces a variety of criticisms, including some\ninherited from the Battle of the Big Systems, e.g., whether\nrationality and objectivity can be locally preserved during major\ntransformations and how to have thoroughgoing historicity, including\nhistorical relativity, without full-blown relativism. Generalization\nproblems still lurk at the meso-scale of historical epistemology. Some\ncritics question whether historical epistemology is anything new,\nsometimes complaining that it just revives traditional history of\nideas. Some would question its neo-Kantian underpinnings. For example,\nhow can we really identify and individuate the\n“categories” employed by scholars such as Hacking and\nDaston? (See Kusch 2010, 2011 and Sciortino 2017.) Skeptics ask what\ndifference historical epistemology makes to science, history, or\nphilosophy of science. Is it more than a faddish relabeling of work\nalready well underway? Are new historical and/or philosophical methods\nrequired to conduct such a study? Given its different strands, is it\ncoherent as a movement? Various adherents disagree on what it includes\nand even what to call it. Although Daston declares that\nHacking’s work provided much of her original inspiration,\nHacking denies that he is doing historical epistemology, preferring\n“meta-epistemology”. He also says that he is doing\nwhiggish “history of the present”. Scholars such as\nNersessian, ABC (Andersen, Barker, & Chen 2006), and Renn rely\nheavily on recent work in cognitive science, whereas sociologists\nstill tend to shun cognitive psychology.", "\nHow significant can we expect historical epistemology to be in the\nlonger run? History will be the judge!" ], "section_title": "5. Integrated HPS and Historical Epistemology: What Good Are They Regarding Scientific Rationality?", "subsections": [] } ]

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Reprinted in Lakatos\n1978: 102–138.", "–––, 1976, Proofs and Refutations,\n(edited by John Worrall & Elie Zahar from previously published\narticles in The British Journal for the Philosophy of\nScience), Cambridge: Cambridge University Press.", "–––, 1978, The Methodology of Scientific\nResearch Programmes: Philosophical Papers, vol. 1, John Worrall\n& Gregory Currie (eds.), Cambridge: Cambridge University\nPress.", "Lakatos, Imre & Alan Musgrave (eds.), 1970, Criticism and\nthe Growth of Knowledge, Cambridge: Cambridge University\nPress.", "Lakatos, Imre & Elie Zahar, 1976, “Why did\nCopernicus’s Programme Supersede Ptolemy’s?”, in\nLakatos 1978: 168–192.", "Latour, Bruno, 1987. Science in Action: How to Follow\nScientists and Engineers through Society, Cambridge, MA: Harvard\nUniversity Press.", "Latour, Bruno & Steve Woolgar, 1979, Laboratory Life: The\nConstruction of Scientific Facts, Beverly Hills: Sage\nPublications.", "Laudan, Larry, 1977, Progress and Its Problems, Berkeley,\nCA: University of California Press.", "–––, 1981, “A Confutation of Convergent\nRealism”, Philosophy of Science, 48(1): 19–49.\ndoi:10.1086/288975", "–––, 1984, Science and Values: The Aims of\nScience and Their Role in Scientific Debate, Berkeley, CA:\nUniversity of California Press.", "–––, 1989, “Discussion: If It Ain’t\nBroke, Don’t Fix It”, British Journal for the\nPhilosophy of Science, 40(3):\n369–375. doi:10.1093/bjps/40.3.369", "–––, 1990, “Normative Naturalism”\n(reply to the preceding articles by Doppelt, Leplin, & Rosenberg),\nPhilosophy of Science, 57(1): 44–59.\ndoi:10.1086/289530", "–––, 1996, Beyond Positivism and Relativism:\nTheory, Method, and Evidence, Boulder, CO: Westview.", "Longino, Helen E., 1990, Science as Social Knowledge: Values\nand Objectivity in Scientific Inquiry, Princeton, NJ: Princeton\nUniversity Press.", "–––, 2001, The Fate of Knowledge,\nPrinceton, NJ: Princeton University Press.", "McGuire, J.E., 1992, “Scientific Change”, chapter 4 of\nMerrilee Salmon et al., Introduction to the Philosophy of\nScience, Englewood Cliffs, NJ: Prentice-Hall, pp.\n132–178.", "Merton, Robert King, 1973, The Sociology of Science,\nChicago: University of Chicago Press.", "Mirowski, Philip, 1996, “The Economic Consequences of Philip\nKitcher”, Social Epistemology, 10(2): 153–169.\ndoi:10.1080/02691729608578812", "Mitchell, Sandra D., 2003, Biological Complexity and\nIntegrative Pluralism, New York: Cambridge University Press.", "Nersessian, Nancy J., 1995, “Opening the Black Box:\nCognitive Science and History of Science”, Osiris,\n10(1): 194–2011. doi:10.1086/368749", "Newell, Allen & Herbert A. Simon, 1972, Human Problem\nSolving, Englewood Cliffs, NJ: Prentice-Hall.", "Newton-Smith, W., 1981, The Rationality of Science,\nLondon: Routledge.", "Nickles, Thomas, 2009, “The Strange Story of Scientific\nMethod”, in Joke Meheus & Thomas Nickles (eds.), Models\nof Discovery and Creativity (Origins: Studies in the Sources of\nScientific Creativity 3), Dordrecht: Springer, pp. 167–207.", "–––, 2013a, “Tempo and Mode in Scientific\nand Technological Innovation: Thomas Kuhn and Nonlinear\nDynamics”, in González 2013: 187–212.", "–––, 2013b, “Creativity, Nonlinearity, and\nthe Sustainability of Scientific Progress”, in González\n2013: 143–172.", "–––, forthcoming, “Strong Realism as\nScientism: Are We at the End of History?”, in Maarten Boudry\n& Massimo Pigliucci (eds.), Science Unlimited? 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Wade\nSavage (ed.), Scientific Theories, (Minnesota Studies in the\nPhilosophy of Science, Vol. 14), Minneapolis, MN: University of\nMinnesota Press, pp. 175–204.", "Sankey, Howard, 1997, Rationality, Relativism and\nIncommensurability, Aldershot, UK: Ashgate.", "Sarkar, Husain, 1983, A Theory of Method, Berkeley, CA:\nUniversity of California Press.", "Scheffler, Israel, 1967, Science and Subjectivity,\nIndianapolis, IN: Bobbs-Merrill.", "Schickore, Jutta, 2011, “More Thoughts on HPS: Another 20\nYears Later”, Perspectives on Science, 19(4):\n453–481. doi:10.1162/POSC_a_00049", "–––, 2017, About Method: Experimenters,\nSnake Venom, and the History of Writing Scientifically, Chicago:\nUniversity of Chicago Press.", "Sciortino, Luca, 2017, “On Ian Hacking’s Notion of\nStyle of Reasoning, Erkenntnis, 82(2): 243–264,\ndoi:10.1007/s10670-016-9815-9.", "Shapere, Dudley, 1984, Reason and the Search for Knowledge:\nInvestigations in the Philosophy of Science, Dordrecht:\nReidel.", "Shapin, Steven, 1982, “History of Science and Its\nSociological Reconstructions”, History of Science,\n20(3): 157–211.", "Shapin, Steven & Simon Schaffer, 1985, Leviathan and the\nAir-Pump: Hobbes, Boyle, and the Experimental Life, Princeton,\nNJ: Princeton University Press.", "Simon, Herbert Alexander, 1947, Administrative Behavior: A\nStudy of Decision-Making Processes in Administrative\nOrganization, New York: Macmillan.", "Soler, Léna, Emiliano Trizio, & Andrew Pickering\n(eds.), 2015, Science as it Could Have Been: Discussing the\nContingency/Inevitability Problem, Pittsburgh, PA: University of\nPittsburgh Press.", "Solomon, Miriam, 2001, Social Empiricism, Cambridge, MA:\nMIT Press.", "Stanford, P. Kyle, 2006, Exceeding Our Grasp: Science,\nHistory, and the Problem of Unconceived Alternatives, New York:\nOxford University Press.", "Sturm, Thomas & Uljana Feest (eds.), 2011, “What (Good) Is\nHistorical Epistemology?”, Erkenntnis, 75(3), special\nissue.", "Suppe, Frederick, 1974, “The Search for Philosophic\nUnderstanding of Scientific Theories”, in Frederick Suppe (ed.),\nThe Structure of Scientific Theories, Urbana, IL: University\nof Illinois Press, pp. 1–232.", "Thagard, Paul, 2012, The Cognitive Science of Science:\nExplanation, Discovery, and Conceptual Change, Cambridge, MA: MIT\nPress.", "Tiles, Mary & Jim E. Tiles, 1993, An Introduction to\nHistorical Epistemology: The Authority of Knowledge, Oxford:\nBlackwell.", "Toulmin, Stephen Edelston, 1972, Human Understanding, vol. 1:\nThe Collective Use and Evolution of Concepts, Oxford: Clarendon\nPress.", "van Fraassen, Bas C., 2002, The Empirical Stance, New\nHaven, CT: Yale University Press.", "Wise, Norton, 2011, “Science as (Historical)\nNarrative”, Erkenntnis, 75(3): 349–376.", "Worrall, John, 1988, “The Value of a Fixed\nMethodology”, British Journal for the Philosophy of\nScience, 39(2): 263–275. doi:10.1093/bjps/39.2.263", "–––, 1989, “Fix It and Be Damned: A Reply\nto Laudan”, British Journal for the Philosophy of\nScience, 40(3): 376–388. doi:10.1093/bjps/40.3.376", "Wray, K. Brad, 2011, Kuhn’s Evolutionary Social\nEpistemology, New York: Cambridge University Press.\ndoi:10.1017/CBO9780511997990", "Zammito, John H., 2004, A Nice Derangement of Epistemes,\nChicago: University of Chicago Press." ]

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[ "\nAccording to metaphysical realism, the world is as it is independent\nof how humans or other inquiring agents take it to be. The objects the\nworld contains, together with their properties and the relations they\nenter into, fix the world’s nature and these objects [together\nwith the properties they have and the relations they enter into] exist\nindependently of our ability to discover they do. Unless this is so,\nmetaphysical realists argue, none of our beliefs about our world could\nbe objectively true since true beliefs tell us how things are and\nbeliefs are objective when true or false independently of what anyone\nmight think.", "\nMany philosophers believe metaphysical realism is just plain common\nsense. Others believe it to be a direct implication of modern science,\nwhich paints humans as fallible creatures adrift in an inhospitable\nworld not of their making. Nonetheless, metaphysical realism is\ncontroversial. Besides the analytic question of what it means to\nassert that objects exist independently of the mind, metaphysical\nrealism also raises epistemological problems: how can we obtain\nknowledge of a mind-independent world? There are also prior semantic\nproblems, such as how links are set up between our beliefs and the\nmind-independent states of affairs they allegedly represent. This is\nthe Representation Problem.", "\nAnti-realists deny the world is mind-independent. Believing the\nepistemological and semantic problems to be insoluble, they conclude\nrealism must be false. The first anti-realist arguments based on\nexplicitly semantic considerations were advanced by Michael Dummett\nand Hilary Putnam. These are:", "\nWe’ll proceed by first defining metaphysical realism,\nillustrating its distinctive mind-independence claim with some\nexamples and distinguishing it from other doctrines with which it is\noften confused, in particular factualism. We’ll then outline the\nRepresentation Problem in the course of presenting the anti-realist\nchallenges to metaphysical realism that are based on it. We discuss\nmetaphysical realist responses to these challenges, indicating how the\ndebates have proceeded, suggesting various alternatives and\ncountenancing anti-realist replies. We finish with a brief review of\nrecent realist/anti-realist debates in meta-ontology." ]

[ { "content_title": "1. What is Metaphysical Realism?", "sub_toc": [] }, { "content_title": "2. Mind-Independent Existence", "sub_toc": [] }, { "content_title": "3. The Anti-Realist Challenges to Metaphysical Realism", "sub_toc": [ "3.1 Language Use and Understanding", "3.2 Language Acquisition", "3.3 Radical Skepticism", "3.4 Models and Reality", "3.5 Conceptual Schemes and Pluralism" ] }, { "content_title": "4. Realist Responses", "sub_toc": [ "4.1 Language Use and Understanding", "4.2 Language Acquisition", "4.3 Radical Skepticism", "4.4 Models and Reality", "4.5 Conceptual Schemes and Pluralism" ] }, { "content_title": "5. Realism and Anti-Realism in Meta-Ontology", "sub_toc": [] }, { "content_title": "6. Summary", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nMetaphysical realism is the thesis that the objects, properties and\nrelations the world contains, collectively: the structure of the world\n[Sider 2011], exists independently of our thoughts about it or our\nperceptions of it. Anti-realists either doubt or deny the existence of\nthe structure the metaphysical realist believes in or else doubt or\ndeny its independence from our conceptions of it. Realists about\nnumbers, for example, hold that numbers exist mind-independently. This\nview is opposed by Nominalists who deny the existence of abstract\nobjects and Intuitionists who agree numbers exist, but as mental\nconstructions, denying their mind-independence. Some realists about\nlaws of nature, to take an empirical example, hold that laws are\nrelations between universals [Armstrong 1983], others that laws are\nontologically primitive entities [Maudlin 2007]. Anti-realists about\nlaws of nature, on the other hand, either deny there are any laws at\nall [Cartwright 1983; van Fraassen 1989] or else discern a dependence\non human concepts in the nature of these laws, interpreting them as\nexpressing certain expectations we have about regularities that we\nunconsciously project onto the world [Blackburn 1986]. ", "\nMetaphysical realism is not the same as scientific realism. That the\nworld’s constituents exist mind-independently does not entail\nthat its constituents are as science portrays them. One could adopt an\ninstrumentalist attitude toward the theoretical entities posited by\nscience, continuing to believe that whatever entities the world\nactually does contain exist independently of our conceptions and\nperceptions of them. For the same reason, metaphysical realists need\nnot accept that the entities and structures ontologists posit exist\nmind-independently.", "\nHenceforth, we shall often just use the term ‘realism’ to\nmean metaphysical realism. Opposition to realism can take many forms\nso there is no single theoretical view denoted by the term\n‘anti-realism’. In particular, anti-realism is not\nIdealism, even though Idealism is its most recognised form. One\napproach, popular in Continental Philosophy, rejects realism on the\ngrounds that words can only acquire their meaning\nintra-linguistically, through their semantic relations with\nother words, where these relations are grounded in our linguistic and\ncultural practices, rather than through referential relations to the\nworld outside of language. This view, Anti-Representationalism as it\nis sometimes called, has gained traction in analytic philosophy also\n[See Price 2009]. ", "\nWithin the ranks of Analytic Philosophy, Verificationists and\nPragmatists also reject realism, though for different reasons. We\nshall mainly focus in this entry on the types of criticism voiced by\nthese two groups of Analytic philosophers with Michael Dummett\nadvocating a certain kind of Verificationism and Hilary Putnam a\ncertain kind of Pragmatism. While accepting Representationalism, both\nDummett and Putnam rejected realism by deploying semantic\nconsiderations in arguments designed to show that realism is\nuntenable. The main goal of this entry is to outline these\n‘semantic’ challenges to realism and to review realist\nresponses to them.", "\nThe characterization of realism in terms of mind-independence above is\nnot universally accepted. Some object that mind-independence is\nobscure [e.g. Chalmers 2009; for relevant discussion, see the entry\n ontological dependence].\n Others maintain that realism is committed, in addition, to a\ndistinctive (and tendentious) conception of truth [Putnam 1981, 1985,\n1992; Wright 1993; Button 2013; Taylor 2006] or, more radically, that\nrealism just is a thesis about the nature of truth—that truth\ncan transcend the possibility of verification, ruling statements for\nwhich we can gather no evidence one way or the other to be\ndeterminately either true or false. An example would be “Julius\nCaesar’s heart skipped a beat as he crossed the Rubicon.”\nThus the realist on this view is one who believes the law of bivalence\n(every statement is either true or false) holds for all meaningful\n(non-vague) statements [Dummett 1978, 1991, 1993]. ", "\nIn the same vein, Crispin Wright [1992a, 2003] presents a nuanced\nalethic analysis according to which discourses may be more or less\nrealist depending on which distinctive ‘marks of truth’\nthey satisfy. ", "\nThese semantic formulations of metaphysical realism are unacceptable\nto realists who are deflationists about truth, denying that truth is a\nsubstantive notion that can be used to characterise alternative\nmetaphysical views [see the entry on the\n deflationary theory of truth].\n Realists collectively complain, with some justice, that the\nanti-realist arguments are really arguments against the correspondence\n(or other substantive) theory of truth rather than realism [Devitt\n1983, 1991; Millikan 1986]. This is an important reason for preferring\nan ontological construal of realism rather than a semantic one. ", "\nThere is, in fact, an obvious worry about using the notion of\nmind-independence to characterise realism: it appears to consign\nmental states and events to irreality. Surely your savouring the taste\nof espresso, say, is dependent on your mind if anything is? Moreover,\njust as certainly the nature and content of the experience of tasting\nespresso depends upon one’s beliefs and expectations. Indeed,\nbut this is not what the ‘mind-independence’\ncharacterisation of realism means to exclude. Rather, it is the\nexistence of conscious events that is deemed to be\nindependent of the particular opinions or theories we might hold about\ntheir existence —given conscious events do exist, were our\ndescendants to uniformly dismiss them as illusory, they would be\nmistaken. The ‘mind-independence’ at issue is epistemic\nrather than ontological.", "\nOn this understanding of realism, it is an error to identify realism\nwith factualism, the view that sentences in some discourse or theory\nare to be construed literally as fact-stating ones. The anti-realist\nviews discussed below are factualist about discourse describing\ncertain contentious domains. Adopting a non-factualist or\nerror-theoretic interpretation of some domain of discourse commits one\nto anti-realism about its entities. Factualism is thus a necessary\ncondition for realism. But it is not sufficient. Verificationists such\nas Dummett reject the idea that something might exist without our\nbeing able to recognize its existence. They can be factualists about\nentities such as numbers and quarks while anti-realists about their\nnature since they deny any entities can exist mind-independently.", "\nTo elaborate the notion of mind-independent existence, consider Peter\nvan Inwagen’s argument for the existence of numbers [van Inwagen\n2016], which he describes as “a typical neo-Quinean\nargument”. The argument rests on two Quinean theses, van Inwagen\nrelays. Firstly, that there is only one kind of variable, a variable\nthat occupies nominal position, the range of which is unrestricted.\nSecondly, that the meanings of the quantifiers are\n univocal.[1]", "\nGiven these two background assumptions, the argument he gives is this:\n", "\n(3) follows from (1) and (2), with the conclusion (5) deducible from\n(1), (2) and (4). Moreover, both (2) and (4) are, if not analytically\ntrue, simple mathematical truths. (1), on the other hand, is an\nempirical fact, van Inwagen notes. The argument is clearly valid and\nthe three premises that support the conclusion are all highly\nplausible. Should we not just accept that numbers exist? Many\nphilosophers think so but some philosophers demur. Amongst the latter\nare those who think that the meaning of ‘there exists’\nvaries from context to context [Hilary Putnam and Eli Hirsch are two\nprominent advocates whose ideas we review]. There are others who think\nthat the existential quantifier carries no ontological import\n[Azzouni, J. 1997]. If one accepts Quine’s two assumptions about\nthe existential quantifier, however, and regards the argument as\nsound, hasn’t one thereby accepted realism about numbers? ", "\nNo. For, while the argument establishes the existence of numbers, if\nit is indeed sound, it leaves their nature unspecified. Hence, it does\nnot prove that numbers exist independently of human (or other) minds.\nMoreover, since the inferences are intuitionistically valid,\nanti-realists can accept it. The argument gives Intuitionists who\nbelieve numbers are mental constructs just as much as Platonists who\nbelieve they are eternal abstract objects a reason to believe numbers\nexist. " ], "section_title": "1. What is Metaphysical Realism?", "subsections": [] }, { "main_content": [ "\nWhy do some find the notion of mind-independent existence inadequate\nfor the task of formulating metaphysical realism? The most common\ncomplaint is that the notion is either obscure, or, more strongly,\nincoherent or cognitively meaningless. An eloquent spokesman for this\nstrong view was Rudolf Carnap: “My friends and I have maintained\nthe following theses,” Carnap announces [Carnap 1963,\np.868]:", "\n(1) The statement asserting the reality of the external world\n(realism) as well as its negation in various forms, e.g. solipsism and\nseveral forms of idealism, in the traditional controversy are\npseudo-statements, i.e., devoid of cognitive content. (2) The\nsame holds for the statements about the reality or irreality of\nother minds (3) and for the statements of the reality or\nirreality of abstract entities (realism of universals or\nPlatonism, vs. nominalism).\n", "\nIn spite of his finding these disputes meaningless, Carnap indicates\nhow he thinks we could reconstruct them (sic.) so as to make some\nsense of them: if we were to “replace the ontological theses\nabout the reality or irreality of certain entities, theses which we\nregard as pseudo-theses, by proposals or decisions concerning the use\nof certain languages. Thus realism is replaced by the practical\ndecision to use the reistic language”.", "\nCarnap does not have in mind a factualist reformulation of\nmetaphysical realism here—his “reistic” language is\nstrictly limited to the description of “intersubjectively\nobservable, spatio-temporally localized things or events”.", "\nWhat matters here is not Carnap’s sense of a commensurability\nbetween a metaphysical thesis about reality and a practical decision\nto speak only about observable things, but rather that he thinks he\ncan explain how the illusion of meaningfulness arises for the\nmetaphysical theses he declares “devoid of cognitive\ncontent”. His explanation has to do with a distinction between\ntwo types of questions — internal and external\nquestions: ", "\nAn existential statement which asserts that there are entities of a\nspecified kind can be formulated as a simple existential statement in\na language containing variables for these entities. I have called\nexistential statements of this kind, formulated within a\ngiven language, internal existential statements. [Carnap\n1963, p. 871]\n", "\nWhereas internal questions about the existence of physical objects are\nto be answered by observations that confirm or disconfirm sentences\nasserting their existence, existential statements about abstract\nobjects are analytic, Carnap contends:", "\nJust because internal statements are usually analytic and trivial, we\nmay presume that the theses involved in the traditional philosophical\ncontroversies are not meant as internal statements, but rather as\nexternal existential statements; they purport to assert the\nexistence of entities of the kind in question not merely within a\ngiven language, but, so to speak, before a language has been\nconstructed. [1963, p. 871]\n", "\nHaving dismissed all external existential questions as devoid of\ncognitive content, Carnap decides that both realism which asserts the\nontological reality of abstract entities and nominalism which asserts\ntheir irreality are “pseudo-statements if they claim to be\ntheoretical statements” (ibid).", "\nWhere Carnap could make no sense of the notion of mind-independent\nreality, Albert Einstein had no such difficulty. For, together with\nPodolsky and Rosen, Einstein famously proposed a test for elements of\nreality in their EPR paper [Einstein, Podolsky and Rosen 1935:\n777–8]:", "\nIf, without in any way disturbing a system, we can predict with\ncertainty (i.e. with probability equal to unity) the value of a\nphysical quantity, then there exists an element of physical reality\ncorresponding to this physical quantity.\n", "\nTim Maudlin [2014, p.7] explains the significance of the EPR criterion\nthus:", "\nSuppose … I can without in any way disturbing a system\npredict with certainty the value of a physical quantity … then the\nrelevant element of reality obtained … independently of the\ndetermination being made. Because, as we have said, the means of\ndetermination did not (by hypothesis) disturb the system.\n", "\nRealists might wish to endorse the EPR criterion as an idealized test\nfor the mind-independent reality of (macro-)physical quantities\n— even if we rarely (if at all) are able to “predict with\ncertainty” the outcome of an experiment, we can, some would\nargue, approach near-certainty in a significant class of cases without\ndisturbing the system. Carnapian anti-realists, however, will deny the\nEPR criterion validates any external notion of mind-independent\nexistence, regarding it instead as a means of settling internal\nexistence questions about physical quantities." ], "section_title": "2. Mind-Independent Existence", "subsections": [] }, { "main_content": [], "section_title": "3. The Anti-Realist Challenges to Metaphysical Realism", "subsections": [ { "content": [ "\nThe first anti-realist challenge to consider focuses on the use we\nmake of our words and sentences. The challenge is simply this: what\naspect of our linguistic use could provide the necessary evidence for\nthe realist’s correlation between sentences and mind-independent\nstates of affairs? Which aspects of our semantic behaviour manifest\nour grasp of these correlations, assuming they do hold?", "\nFor your representations of the world to be reliable, there must be a\ncorrelation between these representations and the states of affairs\nthey portray. So the cosmologist who utters the statement “the\nentropy of the Big Bang was remarkably low” has uttered a truth\nif and only if the entropy of the Big Bang was remarkably low.", "\nA natural question to ask is how the correlation between the statement\nand the mind-independent state of affairs which makes it true is\nsupposed to be set up. One suggestive answer is that the link is\neffected by the use speakers make of their words, the statements they\nendorse and the statements they dissent from, the rationalizations\nthey provide for their actions and so forth; cognitively, it will be\nthe functional role of mental symbols in thought, perception and\nlanguage learning etc. that effects these links.", "\nHowever, when we look at how speakers actually do use their sentences,\nanti-realists argue, we see them responding not to states of affairs\nthat they cannot in general detect but rather to agreed upon\nconditions for asserting these sentences. Scientists assert “the\nentropy of the Big Bang was remarkably low” because they all\nconcur that the conditions justifying this assertion have been\nmet.", "\nWhat prompts us to use our sentences in the way that we do are the\npublic justification conditions associated with those sentences,\njustification conditions forged in linguistic practices which imbue\nthese sentences with meaning.", "\nThe realist believes we are able to mentally represent\nmind-independent states of affairs. But what of cases where everything\nthat we know about the world leaves it unsettled whether the relevant\nstate of affairs obtains? Did Socrates sneeze in his sleep the night\nbefore he took the hemlock or did he not? How could we possibly find\nout? Yet realists hold that the sentence “Socrates sneezed in\nhis sleep the night before he took the hemlock” will be true if\nSocrates did sneeze then and false if he did not and that this is a\nsignificant semantic fact.", "\nThe Manifestation challenge to realism is to isolate some feature of\nthe use agents make of their words, or their mental symbols, which\nforges the link between mind-independent states of affairs and the\nthoughts and sentences that represent them. Nothing in the\nthinker’s linguistic behaviour, according to the anti-realist,\nprovides evidence that this link has been forged—linguistic use\nis keyed to public assertibility conditions, not undetectable\ntruth-conditions. In those cases, such as the Socrates one, where we\ncannot find out whether the truth-condition is satisfied or not, it is\nsimply gratuitous to believe that there is anything we can think or\nsay or do which could provide evidence that the link has been set up\nin the first place. So the anti-realist claims [Dummett 1978, 1991,\n1993; Tennant 1987, 1997; Wright 1993].", "\nWhy should we expect the evidence to be behavioural rather than, say,\nneurophysiological? The reason anti-realists give is that the meanings\nof our words and (derivatively for them) the contents of our thoughts\nare essentially communicable and thus must be open for all speakers\nand thinkers to see [Dummett 1978, 1993]." ], "subsection_title": "3.1 Language Use and Understanding" }, { "content": [ "\nThe second challenge to be considered concerns our acquisition of\nlanguage. The challenge to realism is to explain how a child could\ncome to know the meanings of certain sentences within his/her\nlanguage: the ones which the realist contends have undetectable\ntruth-makers associated with them. How could the child learn the\nmeanings of such sentences if these meanings are determined by states\nof affairs not even competent speakers can detect?", "\nConsider the sentence (S) once more:", "\nRealists say (S) is either true or false even though we may (and\nalmost certainly will) never know which it is. The state of affairs\nwhich satisfies (S)’s truth-condition when it is true, its\n‘truthmaker’, and the state of affairs which satisfies the\ntruth-condition of the negation of (S) when (S) is false are supposed\nto be able to hold even though competent speakers cannot detect\nwhether they do. How could the child ever learn about this\nundetectable relation?", "\nSuppose God (or nature) had linked our mental representations to just\nthe right states of affairs in the way required by the realist. If so,\nthis is a semantically significant fact. Anyone learning their native\nlanguage would have to grasp these correspondences between sentences\nand states of affairs. How can they do this if even the competent\nspeakers whom they seek to emulate cannot detect when these\ncorrespondences hold? In short, competence in one’s language\nwould be impossible to acquire if realism were true [Dummett 1978,\n1993; Wright 1993]. This is the Language Acquisition challenge.", "\nThis challenge is exacerbated by the anti-realist’s assumption\nthat since the linguistic meaning of an expression \\(E\\) is determined\nsolely by competent speakers’ use of \\(E\\) the child’s\ntask in all cases is to infer the meaning of \\(E\\) from its use. Thus\nDummett [1978 pp. 216–217], in discussing the meaning of\nmathematical statements, proposes a thesis he argues holds for the\nmeanings of every kind of statement:", "\n\n\nThe meaning of a mathematical statement determines and is exhaustively\ndetermined by its use. The meaning of a mathematical statement cannot\nbe, or contain as an ingredient, anything which is not manifest in the\nuse made of it, lying solely in the mind of the individual who\napprehends that meaning: if two individual agree completely about the\nuse to be made of the statement, then they agree about its meaning.\nThe reason is that the meaning of a statement consists solely in its\nrole as an instrument of communication between individuals, just as\nthe powers of a chess-piece consist solely in its role in the game\naccording to the rules.\n", "\nW.V.O. Quine is even more insistent on the public nature of linguistic\nmeaning. Displaying his unshakable faith in Skinnerian models of\nlanguage-learning he writes [1992, pp. 37–38]:", "\nIn psychology one may or may not be a behaviourist, but in linguistics\none has no choice … There is nothing in linguistic meaning\nbeyond what is to be gleaned from overt behaviour in observable\ncircumstances.\n" ], "subsection_title": "3.2 Language Acquisition" }, { "content": [ "\nAccording to Hilary Putnam, the metaphysical realist subscribes not\njust to the belief in a mind-independent world but also to the thesis\nthat truth consists in a correspondence relation between words (or\nmental symbols) and things in that mind-independent world. Call this\nthesis correspondence truth (after Devitt 1991). More\nimportantly, metaphysical realists aver that an ideal theory of the\nworld could be radically false, Putnam contends:\n‘radical’ in the sense that all (or\nalmost all) of the theory’s theses could fail to hold. Such a\nglobal failure would result if we were to be\n‘brains-in-a-vat’ our brains manipulated by mad scientists\n(or machines, as in the movie The Matrix) so as to dream of\nan external world that we mistake for reality. Call this thesis\nradical skepticism.", "\nIt is widely believed that states of affairs that are truly\nmind-independent do engender radical skepticism. The skeptic contends\nthat for all we could tell we could be brains in a vat—brains\nkept alive in a bath of nutrients by mad alien scientists. All our\nthoughts, all our experience, all that passed for science would be\nsystematically mistaken if we were. We’d have no bodies although\nwe thought we did, the world would contain no physical objects, yet it\nwould seem to us that it did, there’d be no Earth, no Sun, no\nvast universe, only the brain’s deluded representations of such.\nAt least this could be the case if our representations derived even\npart of their content from links with mind-independent objects and\nstates of affairs. Since realism implies that such an absurd\npossibility could hold without our being able to detect it, it has to\nbe rejected, according to anti-realists.", "\nA much stronger anti-realist argument due to Putnam uses the\nbrain-in-a-vat hypothesis to show that realism is internally\nincoherent rather than, as before, simply false. A crucial assumption\nof the argument is semantic externalism, the thesis that the reference\nof our words and mental symbols is partially determined by contingent\nrelations between thinkers and the world. This is a semantic\nassumption many realists independently endorse.", "\nGiven semantic externalism, the argument proceeds by claiming that if\nwe were brains in a vat we could not possibly have the thought that we\nwere. For, if we were so envatted, we could not possibly mean by\n‘brain’ and ‘vat’ what unenvatted folk mean by\nthese words since our words would be connected only to neural impulses\nor images in our brains where the unenvatteds’ words are\nconnected to real-life brains and real-life vats. Similarly, the\nthought we pondered whenever we posed the question “am I a brain\nin a vat?” could not possibly be the thought unenvatted folk\npose when they ask themselves the same-sounding question in English.\nBut realism entails that we could indeed be brains in a vat. As we\nhave just shown that were we to be so, we could not even entertain\nthis as a possibility, Putnam concludes that realism is incoherent\n[Putnam 1981]. For this argument to work, however, Putnam must be\nassuming a rather restrictive form of modal rationalism: we could be\nbrains in a vat only if in the circumstance that we were envatted, we\ncould conceive that we were envatted." ], "subsection_title": "3.3 Radical Skepticism" }, { "content": [ "\nPutnam’s Model-Theoretic Argument is the most technical of the\narguments we have so far considered although we shall not reproduce\nall the technicalities here. The central ideas can be conveyed\ninformally, although some technical concepts will be mentioned where\nnecessary. The argument purports to show that the Representation\nProblem—to explain how our mental symbols and words get hooked\nup to mind-independent objects and how our sentences and thoughts\ntarget mind-independent states of affairs—is insoluble.", "\nAccording to the Model-Theoretic Argument, there are simply too many\nways in which our mental symbols can be mapped onto items in the\nworld. The consequence of this is a dilemma for the realist. The first\nhorn of the dilemma is that s/he must accept that what our symbols\nrefer to is massively indeterminate. The second horn is that s/he must\ninsist that even an ideal theory, whose terms and predicates can\ndemonstrably be mapped veridically onto objects and properties in the\nworld might still be false, i.e., that such a mapping might not be the\nright one, the one ‘intended’.", "\nNeither alternative can be defended, according to anti-realists.\nConcerning the first alternative, massive indeterminacy for perfectly\ndeterminate terms is absurd. As for the second, for realists to\ncontend that even an ideal theory could be false is to resort to\nunmotivated dogmatism, since on their own admission we cannot tell\nwhich mapping the world has set up for us. Such dogmatism leaves the\nrealist with no answer to a skepticism which undermines any capacity\nto reliably represent the world, anti-realists maintain.", "\nNow, in logic theories are treated as sets of sentences and the\nobjects (if any) that sentences talk about appear as elements of the\ndomain of set-theoretic entities called structures. Associated\nwith these structures are interpretation functions that map\nindividual constants onto individual objects of the domain and n-place\npredicates onto n-tuples of elements in the domain. When a structure\nmakes all the sentences of a given theory true it is called a\nmodel of the theory. By demonstrating that there is a model of\nT we show theory T is consistent. If T turns out to be true in its\nintended model, then T is true simpliciter. ", "\n\n\nFor an informal illustration of the basic ideas of model theory, see\nthe supplementary document,\n Model Theory: Core Ideas.\n \n", "\nLet us call structures whose domains consist of numbers\n‘numeric’ structures. The nub of Putnam’s\nModel-Theoretic Argument against realism is that the realist cannot\ndistinguish the intended model for his/her total theory of the world\nfrom non-standard interlopers such as permuted models or ones derived\nfrom numeric models, even when total theory is a rationally optimal\none that consists, as it must do, of an infinite set of\nsentences and the realist is permitted to impose the most exacting\nconstraints to distinguish between models. This is a very surprising\nresult if true! How does Putnam arrive at it? ", "\nPutnam actually uses a number of different arguments to establish the\nconclusion above. Of prime concern to realists, as Taylor (2006)\nemphasises, is the argument based on Gödel’s Completeness\nTheorem, GCT. For, following Lewis [Lewis, 1984], realists might\nconcede to Putnam that they cannot single out the intended model or\ndistinguish it from various ersatz models, but argue that this is not\nnecessary since it suffices that an intended model exists,\neven if we cannot specify it. This response does not answer the GCT\nargument, however. For this argument purports to prove directly that\nan ideal theory of the world could not be false, a conclusion flatly\ninconsistent with realism. See the supplementary document\n The Model-Theoretic Argument and the Completeness Theorem\n for an outline of this argument. ", "\nPutnam has another argument, the Permutation Argument:", "\nSuppose that the realist is able to somehow specify the intended\nmodel. Call this intended model \\(W''\\). Then nothing the realist can\ndo can possibly distinguish \\(W''\\) from a permuted variant \\(W^*\\)\nwhich can be specified following Putnam 1994b, 356–357:", "\nWe define properties of being a cat* and being a mat* such that:\n\n\n\nIn the actual world cherries are cats* and trees are mats*.\n\nIn every possible world the two sentences “A cat is on a\nmat” and “A cat* is on a mat*” have precisely the\nsame truth value.\n\n", "\nInstead of considering two sentences “A cat is on a mat”\nand “A cat* is on a mat*” now consider only the one\n“A cat is on a mat”, allowing its interpretation to change\nby first adopting the standard interpretation for it and then adopting\nthe non-standard interpretation in which the set of cats* are assigned\nto ‘cat’ in every possible world and the set of mats* are\nassigned to ‘mat’ in every possible world. The result will\nbe the truth-value of “A cat is on a mat” will not change\nand will be exactly the same as before in every possible world.\nSimilar non-standard reference assignments could be constructed for\nall the predicates of a language. [See Putnam 1985, 1994b.] However,\nunlike the GCT argument, the Permutation Argument is susceptible to\nthe Lewis-styled reply above." ], "subsection_title": "3.4 Models and Reality" }, { "content": [ "\nAccording to conceptual pluralists, there can no more be an answer to\nthe question “What is the structure of the world?” outside\nof some scheme for classifying entities than there can be an answer to\nthe question of whether two events \\(A\\) and \\(B\\) are simultaneous\noutside of some inertial frame for dating those events. The objects\nthat exist are the objects some conceptual scheme says\nexists—‘mesons exist’ really means ‘mesons\nexist relative to the conceptual scheme of current physics’.", "\nRealists think there is a unitary sense of ‘object’,\n‘property’ etc., for which the question “what\nobjects and properties does the world contain?” makes sense. Any\nanswer which succeeded in listing all the objects, properties, events\netc. which the world contains would comprise a privileged description\nof that totality [Putnam 1981]. Anti-realists reject this. For them\n‘object’, ‘property’ etc., shift their senses\nas we move from one conceptual scheme to another. Some anti-realists\nargue that there cannot be a totality of all the objects the world\ncontains since the notion of ‘object’ is indefinitely\nextensible and so, trivially, there cannot be a privileged description\nof any such totality. [For discussions of indefinite extensibility see\nDummett 1978, 1991; Linnebo 2018; Warren 2017].", "\nHow does the anti-realist defend conceptual relativity? One way is by\narguing that there can be two complete theories of the world which are\ndescriptively equivalent yet logically incompatible from the\nrealist’s point of view. For example, theories of space-time can\nbe formulated in one of two mathematically equivalent ways: as an\nontology of points, with spatiotemporal regions being defined as sets\nof points; or as an ontology of regions, with points being defined as\nconvergent sets of regions. Such theories are descriptively equivalent\nsince mathematically equivalent and yet are logically incompatible\nfrom the realist’s point of view, anti-realists contend [Putnam\n1985, 1990]." ], "subsection_title": "3.5 Conceptual Schemes and Pluralism" } ] }, { "main_content": [], "section_title": "4. Realist Responses", "subsections": [ { "content": [ "\nWe now turn to some realist responses to these challenges. The\nManifestation and Language Acquisition arguments allege there is\nnothing in an agent’s cognitive or linguistic behaviour that\ncould provide evidence that s/he had grasped what it is for a sentence\nto be true in the realist’s sense of ‘true’. How can\nyou manifest a grasp of a notion which can apply or fail to apply\nwithout you being able to tell which? How could you ever learn to use\nsuch a concept?", "\nOne possible realist response is that the concept of truth is actually\nvery simple, and it is spurious to demand that one always be able to\ndetermine whether a concept applies. As to the first part, it is often\nargued that all there is to the notion of truth is what is given by\nthe formula “‘\\(p\\)’ is true if and only if\n\\(p\\)”. The function of the truth-predicate is to disquote\nsentences in the sense of undoing the effects of quotation—thus\nall that one is saying in calling the sentence “Yeti are\nvicious” true is that Yeti are vicious.", "\nIt is not clear that this response really addresses the\nanti-realist’s worry, however. It may well be that there is a\nsimple algorithm for learning the meaning of ‘true’ and\nthat, consequently, there is no special difficulty in learning to\napply the concept. But that by itself does not tell us whether the\npredicate ‘true’ applies to cases where we cannot\nascertain that it does. All the algorithm tells us, in effect, is that\nif it is legitimate to assert \\(p\\) it is legitimate to assert that\n‘\\(p\\)’ is true. So are we entitled to assert\n‘either Socrates did or did not sneeze in his sleep the night\nbefore he took the hemlock’ or are we not? Presumably that will\ndepend on what we mean by the sentence, whether we mean to be\nadverting to two states of affairs neither of which we have any\nprospect of ever confirming.", "\nAnti-realists follow verificationists in rejecting the intelligibility\nof such states of affairs and tend to base their rules for assertion\non intuitionistic logic, which rejects the universal applicability of\nthe Law of Bivalence (the principle that every statement is either\ntrue or false). This law is thought to be a foundational semantic\nprinciple for classical logic. However, some question whether\nclassical logic requires bivalence [e.g. Sandqvist 2009]. Others\ndispute the idea that acceptance or rejection of bivalence has any\nmetaphysical (rather than meaning-theoretic) consequences\n[Edgington, 1981; McDowell 1976; Pagin 1998; Gaiffman 1996]. There is,\nin addition, a question as to whether the anti-realist’s\npreferred substitute for realist truth-conditions in\nverification-conditions (or proof-conditions) satisfies the\nrequirement of exhaustive manifestability [Pagin 2009]. ", "\nA more direct realist response to the Manifestation challenge points\nto the prevalence in our linguistic practices of realist-inspired\nbeliefs to which we give expression in what we say and do [McDowell\n1976]. We assert things like “either there were an odd or an\neven number of dinosaurs on this planet independently of what anyone\nbelieves” and all our actions and other assertions confirm that\nwe really do believe this. Furthermore, the overwhelming acceptance of\nclassical logic by mathematicians and scientists and their rejection\nof intuitionistic logic for the purposes of mainstream science\nprovides very good evidence for the coherence and usefulness of a\nrealist understanding of truth [Edgington 1981; Burgess 1984; Hellman\n1989, 1992]. ", "\nAnti-realists reject this reply. They argue that all we make manifest\nby asserting things like “either there were an odd or an even\nnumber of dinosaurs on this planet independently of what anyone\nbelieves” is our pervasive misunderstanding of the notion of\ntruth. They apply the same diagnosis to the realist’s belief in\nthe mind-independence of entities in the world and to counterfactuals\nwhich express this belief. We overgeneralize the notion of truth,\nbelieving that it applies in cases where it does not, they contend\n[Tennant 1987, 1997; Wright 1993]. ", "\nAn apparent consequence of their view is that reality is indeterminate\nin surprising ways—we have no grounds for asserting that\nSocrates did sneeze in his sleep the night before he took the hemlock\nand no grounds for asserting that he did not and no prospect of ever\nfinding out which. Does this mean that for anti-realists the world\ncontains no such fact as the fact that Socrates did one or the other\nof these two things? Not necessarily. For anti-realists who subscribe\nto intuitionistic principles of reasoning, the most that can be said\nis that there is no present warrant to assert \\(S \\lor \\neg S\\): that\nSocrates either did or did not sneeze in his sleep the night before he\ntook the hemlock.", "\nPerhaps anti-realists are right. But if so, they need to explain how a\npractice based on a pervasive illusion can be as successful as modern\nscience. Anti-realists perturbed by the manifestability of realist\ntruth are revisionists about parts of our linguistic practice, and the\nconsequence of this revisionist stance is that mathematics and science\nrequire extensive and non-trivial revision. The debate about whether\nclassical logic should (or can) be rejected on meaning-theoretic\ngrounds is ongoing: Burgess 1984, Hellman 1989, Michael 1999 and Read\n2000 are critical of Dummett’s case for rejecting classical\nlogic, whereas Cogburn 2005, Cozzo 1994, Prawitz 1977, 1987, 1994 and\nTennant 1997 are, in varying degrees, supportive. " ], "subsection_title": "4.1 Language Use and Understanding" }, { "content": [ "\nThe challenge to realism posed by language acquisition is to explain\nhow a child (or novice) could come to know the meanings of certain\nsentences within his/her language: the ones the realist contends have\nundetectable truth-makers associated with them. How could the child\nlearn the meanings of such sentences if these meanings are determined\nby states of affairs not even competent speakers can detect?", "\nA straightforward realist reply is that knowledge of the meanings of\nsentences with undetectable truth-conditions is acquired in the same\nway as knowledge of the meanings of sentences with recognisable\ntruth-conditions: namely, compositionally by acquiring knowledge of\nthe lexicon and the relevant compositional principles [Pagin\n 2009].[2]\n Anti-realists respond by contesting the interpretation of the\ncompositional principles that generate sentences with undetectable\ntruth-conditions — where realists assert \\(S \\lor \\neg S\\) is\ntrue (\\(S\\) being the Socrates sentence), anti-realists maintain there\nis no ground for asserting this disjunction [e.g. Tennant 1987].", "\nSome realists reject the publicity of meaning principle as it applies\nto language learning. While many accept that the meaning of a word is\ndetermined by its use in a given language, not all do [e.g. Chomsky\n1986; Fodor and Lepore 2002]. Realists who think of semantic\nunderstanding as a mental state reject the idea that a speaker’s\nunderstanding of meaning is exhaustively manifest in its use as an\ninstrument of communication rather than in its internal use in\nexpressing thought. If Dummett’s manifestation requirement is a\ndemand for a behaviouristic reduction of semantic knowledge, they\nargue, it should be rejected [Burgess 1984; Chomsky 1986]. However,\nsome sympathetic to the demand for full manifestability of semantic\nknowledge reject the behaviouristic construal and instead justify it\non conceptual grounds [e.g. Shieh 1998, McGee\n 2015].[3]\n ", "\nThe Acquisition Challenge is a vexed one for realists because Dummett\nshares little common ground with the many (realist) philosophers,\nlinguists and cognitive scientists who believe language acquisition is\neffected by a dedicated language module [Fodor 1975, 1983, 2008;\nChomsky 1986, 2006; Crain 2012; Pinker 1994] or even with those who\ndisavow modularity but agree that semantic knowledge is partly\nunconscious. Thus, Dummett rejected Chomsky’s thesis that\nspeakers have unconscious knowledge of the rules of Universal Grammar\non the Wittgensteinian grounds that it was, at best “an\nexplanatory hypothesis, not a systematisation of facts open to\nview.” [Dummett 1981]. Dummett apparently took this\n“systemisation of facts” to be satisfied by an account\nthat pairs knowledge of meaning with recognitional\n abilities.[4]", "\nIt is worth noting that evidence from developmental psychology\nindicates some meaning is pre-linguistic and that some pre-linguistic\nmeaning or conceptual content relate to situations that are not\ndetectable by the child. For example, psychologists have discovered\nsystems of core knowledge activated in infancy that govern the\nrepresentation of, inter alia concrete objects and human\nagents [see Spelke 2003; Spelke and Kinzler 2007]. An interesting\nfinding from preferential gaze experiments suggests 4 month old\ninfants represent occluded objects as continuing behind their\n barriers.[5]", "\nWhile these findings do not by themselves show that the meanings of\nmental symbols is not determined by public use, they do provide\nevidence that ‘verification-transcendent’ conceptual\ncontent is laid down in the earliest stages of cognitive development.\n" ], "subsection_title": "4.2 Language Acquisition" }, { "content": [ "\nThe Brains-in-a-Vat argument purports to show that, given semantic\nexternalism, realism is incoherent on the grounds that it is both\ncommitted to the genuine possibility of our being brains in a vat and\nyet entails something that anti-realists judge to be inconsistent with\nthis: namely, that were we to be so envatted we could not possibly\nhave the thought that we were.", "\nRealists have three obvious responses.", "\nAs for (i), one might question the coherence of the idea of our being\nbrains in a vat on the grounds that the skeptical hypothesis uses\nterms which derive their meaning from successful theory to pose a\nproblem which, if intelligible, would rob those very terms of meaning.\n", "\nWhat of option (ii)—denying semantic externalism? Is this really\na live prospect for realists? Semantic externalism no longer commands\nthe consensus amongst realists that it did when Putnam formulated his\nBrains-in-a-Vat argument. David Lewis, a prominent realist, rejected\nexternalism in favour of a sophisticated semantic internalism based on\na ‘Two-Dimensional’ analysis of modality proposed by\nStalnaker [Lewis 1994]. Frank Jackson [Jackson 2000] contributed to\nthe development of internalist 2D semantics and used it to formulate a\nversion of materialism grounded on conceptual analysis that provides a\nuseful model of a physicalistic realist’s metaphysics.", "\nOther realists reject externalism because they think that the\nRepresentation Problem is just a pseudo-problem. When we say things\nlike “‘cat’ refers to cats” or\n“‘quark’ refers to quarks” we are simply\nregistering our dispositions to call everything we consider\nsufficiently cat-like/quark-like,\n‘cat’/’quark’ [Horwich, 1990; Resnick,\n1990].", "\nAccording to these semantic deflationists, it is just a confusion to\nask how the link was set up between our use of the term ‘the Big\nBang’ and the event of that name which occurred some fourteen\nbillion years ago. Yet, if all there is to the story are our\nlinguistic dispositions and the conditions to which they are presently\nattuned, the case has effectively been ceded to the anti-realist who\ndenies it is possible to set up a correlation between our utterances\nor thoughts and mind-independent states of affairs. ", "\nPerhaps the most effective realist rejoinder is (iii). We shall return\nto this response after we have reviewed Putnam’s Brains-in-a-Vat\nArgument, BIVA.", "\nHow does Putnam prove we can know we are not brains in a vat? To\nunderstand Putnam’s argument, we need to first recall the\n‘Twin-Earth’ considerations used to support Semantic\nExternalism: on Twin-Earth things are exactly as they are here on\nEarth except for one difference—whereas for Earthly humans water\nhas the chemical composition H2O, for our\ndöppelgangers on Twin-Earth, twumans, water is instead composed\nof some substance unknown to us on Earth, XYZ. Now when you and your\ntwuman counterpart say (or think) “‘Water’ refers to\nwater” both of you utter (or think) truths. But which truth you\nboth think or utter differs. For humans “‘Water’\nrefers to water” expresses the truth that the term\n‘water’ in English refers to that substance whose chemical\ncomposition is H2O. For our twuman Twin-Earth counterparts,\nhowever, their sentence “‘Water’ refers to\nwater” expresses the truth that their term ‘water’\nin Twenglish refers to that substance whose chemical composition is\nXYZ.", "\nWith these points about Externalism in mind, consider Putnam’s\nBIVA [we follow the formulation section 7 of the entry\n skepticism and content externalism].\n Let us call whatever it is that an envatted brain’s symbol\n‘tree’ refers to, if it refers at all,\n\\(v\\)-trees. Then the BIVA is: ", "\nNow (1) seems correct: if I am a brain-in-a-vat then, given\nexternalism, my symbol ‘tree’ cannot refer to trees since\nthere aren’t any trees in the vat-world—a BIV’s\n‘tree’ symbol refers to \\(v\\)-trees, not\ntrees. But what reason do we have to believe (2)? If we are BIVs\nwon’t our ‘tree’ symbols refer to v-trees rather\nthan trees? Crispin Wright [1992b] argues that all language-users,\nwhether humans or brains-in-a-vat, can be certain of (2) since they\ncan know they use language meaningfully and thus can know that their\nlanguage disquotes. Graeme Forbes [1995] questions Wright’s\nargument. ", "\nDiscussion of the brains-in-a-vat hypothesis has been extensive. Early\ncontributions by Brueckner 1986, 1992; David 1991; Ebbs 1992; Forbes\n1995 reconstruct Putnam’s argument and assess it from a realist\nperspective. Important defences of the BIVA are provided by Wright\n1992b; Tymoczko 1989; Button 2013, 2015. Some recent discussions bring\nBayesian [Huemer 2016] or psychological [Jackson 2015] considerations\nto bear on Putnam’s BIV hypothesis. A valuable collection of\nessays is Goldberg 2015.", "\nEven if it were to turn out that the BIVA is not sound, Putnam’s\nchallenge to the realist remains unanswered. This was to show how\nrealism could be coherent if it is committed both to:", "\nand to the consequence that:", "\nWhile it is usually not remarked upon, there is no logical\nincoherence in accepting both (I) and (II)—as the figure below\nillustrates. There is thus no logical incoherence in believing both\nthat it is possible that one is a BIV and that if one is a BIV one\ncould never come to know this. ", "\nNick Bostrom has recently argued it is quite likely that we humans are\nactually virtual humans: computer simulations of flesh and\nblood creatures. Bostrom reasons that if our mental lives can be\nsimulated then it is highly probable that our distant descendants\n(more intelligent or at least more technologically advanced\n‘post-human’ successors) will eventually create such a\nsimulation in which case it is more likely that we are the unwitting\ndenizens of a simulated world than the flesh and blood inhabitants of\nthe real world we take ourselves to be. At least this will be so\nunless the chances that creatures of our intelligence are doomed to\nbecome extinct before reaching the technological sophistication to\ncreate simulations are overwhelmingly large or else almost no such\ntechnologically capable civilizations have any interest in simulating\nminds like ours in the first place [Bostrom, N., 2003]. ", "\nBostrom’s position owes nothing to skepticism, he is concerned\nsolely with the question of whether virtual humans are empirically\npossible and, if so, how likely it is that we might be such beings.\nHis argument, if sound, makes it look very doubtful that we can know\na priori that we are not brains-in-a-vat,\nwhen BIVs are understood to be virtual humans in a\n simulation.[6]\n If Bostrom is correct, Putnam’s attempt to prove we cannot\nbe BIVs must be flawed. However, the Simulation Argument is\nnothing if not controversial: it has provoked interest from\ncosmologists as well as philosophers [For discussion of the Simulation\nHypothesis see Bostrom, 2005; Brueckner 2008; Chalmers 2010;\nWeatherson 2003]. " ], "subsection_title": "4.3 Radical Skepticism" }, { "content": [ "\nIf metaphysical realism is to be tenable, it must be possible for even\nthe best theories to be mistaken. Or so metaphysical realists have\nthought. Whence, such realists reject the Model-Theoretic Argument MTA\nwhich purports to show that this is not possible. Here is an informal\nsketch of the MTA due to van Fraassen [1997]:", "\nLet \\(T\\) be a theory that contains all the sentences we insist are\ntrue, and that has all other qualities we desire in an ideal theory.\nSuppose moreover that there are infinitely many things, and that \\(T\\)\nsays so. Then there exist functions (interpretations) which assign to\neach term in \\(T\\)’s vocabulary an extension, and which satisfy\n\\(T\\). So we conclude, to quote Putnam, “\\(T\\) comes out true,\ntrue of the world, provided we just interpret ‘true’ as\nTRUE(SAT)”.\n", "\nHere ‘TRUE(SAT)’ means “true relative to a mapping\nof the terms of the language of \\(T\\) onto (sets of) items in the\nworld”.", "\nBut why should we interpret ‘true’ as TRUE(SAT)? Because\ntruth is truth in an intended model and, Putnam argues, amongst all\nthe models of \\(T\\) that make all its theses come out true there is\nguaranteed to be at least one that passes all conceivable constraints\nwe can reasonably impose on a model in order for it to be an intended\nmodel of \\(T\\). ", "\nRealists have responded to the argument by rejecting the claim that a\nmodel \\(M\\) of the hypothetical ideal theory \\(T\\) passes every\ntheoretical constraint simply because all of the theory’s theses\ncome out true in it. For there is no guarantee, they claim, that terms\nstand in the right relation of reference to the objects to which \\(M\\)\nlinks them. To be sure, if we impose another theoretical constraint,\nsay:", "\nRight Reference Constraint (RRC): Term \\(t\\) refers to object \\(x\\) if\nand only if \\(Rtx\\) where \\(R\\) is the right relation of reference,\n", "\nthen \\(M\\) (or some model based on it) can interpret this RRC\nconstraint in such a way as to make it come out true.", "\nBut there is a difference between a model’s making some\ndescription of a constraint come out true and its actually conforming\nto that constraint, metaphysical realists insist [Devitt 1983, 1991;\nLewis 1983, 1984].", "\nFor their part, anti-realists have taken the metaphysical\nrealist’s insistence on a Right Reference Constraint to be\n‘just more theory’—what it is for a model to conform\nto a constraint is for us to be justified in asserting that it does.\nUnfortunately, this has led to something of a stand-off. Metaphysical\nrealists think that anti-realists are refusing to acknowledge a clear\nand important distinction. Anti-realists think realists are simply\nfalling back on dogmatism at a crucial point in the argument.", "\nOn the face of it, the Permutation Argument presents a genuine\nchallenge to any realist who believes in determinate reference. But it\ndoes not refute metaphysical realism unless such realism is committed\nto determinate reference in the first place and it is not at all\nobvious that this is so.", "\nRealist responses to this argument vary widely. At one extreme are the\n‘determinatists’, those who believe that Nature has set up\nsignificant, determinate referential connections between our mental\nsymbols and items in the world. They contend that all the argument\nshows is that the distribution of truth-values across possible worlds\nis not sufficient to determine reference [van Cleve 1992].", "\nAt another extreme are ‘indeterminatists’, realists who\nconcede the conclusion, agreeing that it demonstrates that word-world\nreference is massively indeterminate or ‘inscrutable’. The\nlocus classicus for inscrutability of reference is Quine 1964 [See\nalso Quine 1969, 1992; Davidson 1979]. ", "\nSome infer from this that reference could not possibly consist in\ncorrespondences between mental symbols and objects in the world. For\nthem all that makes ‘elephant’ refer to elephants is that\nour language contains the word ‘elephant’. This is\nDeflationism about reference. Vann McGee presents a strong case for\ninscrutability on a deflationary view of reference, one that is\ngrounded in a “… peculiarly egocentric conception of\nsemantics—questions of others’ meanings are settled by\nasking what I mean by the words of my language” [McGee\n2015].", "\nIn between these two extremes are those prepared to concede the\nargument establishes the real possibility of a significant and\nsurprising indeterminacy in the reference of our mental symbols but\nwho take it to be an open question whether other constraints can be\nfound which pare down the range of reference assignments to just the\nintuitively acceptable\n ones.[7]\n ", "\nThe simplest and most direct response to the MTA questions its\nvalidity. Thus Devitt and Lewis claim that Putnam’s alternative\nmodel \\(M\\) has not been shown to satisfy every theoretical\nconstraint merely by making some description of each\ntheoretical constraint true.", "\nSkolem’s Paradox in set theory seems to present a striking\nillustration of Lewis’s distinction. The Löwenheim-Skolem\nTheorem states that every consistent, countable set of first-order\nformulae has a denumerable model, in fact a model in the set of\nintegers \\(\\mathbb{Z}\\). Now in ZF one can prove the existence of sets\nwith a non-denumerable number of elements such as the set\n\\(\\mathbb{R}\\) of real numbers. Yet the ZF axioms comprise a\nconsistent, countable set of first-order formulae and thus by the\nLöwenheim-Skolem Theorem has a model in \\(\\mathbb{Z}\\). So\nZF’s theorem \\(\\phi\\) stating that \\(\\mathbb{R}\\) is\nnon-denumerable will come out true in a denumerable model \\(\\mu\\) of\nZF.", "\nHow can this be? One explanation is that \\(\\mu\\) makes \\(\\phi\\) true\nonly at the cost of re-interpreting the term\n‘non-denumerable’ so that it no longer means\nnon-denumerable. Thus \\(\\mu\\) is not the intended model\n\\(M^*\\) of ZF. It looks as if the metaphysical realist has a clear\nillustration of Lewis’s distinction at hand in set theory.", "\nUnfortunately for the realist, this is not the only explanation. In\nfact, Putnam used this very example in an early formulation of the\nMTA. Just because there are different models that satisfy \\(\\phi\\) in\nsome of which \\(\\mathbb{R}\\) is non-denumerable but in others of which\n(such as \\(\\mu\\)) \\(\\mathbb{R}\\) is denumerable, Putnam argued, it is\nimpossible to pin down the intended interpretation of\n‘set’ via first-order axioms. Moreover, well before\nPutnam, Skolem and his followers had taken the moral of Skolem’s\nParadox to be that set-theoretic notions are indeterminate [For\nfurther discussion, see the entry on\n Skolem’s paradox].", "\nThe question of how to interpret Skolem’s Paradox merely raises\nanew the question of what it is for a theory such as the hypothesized\nideal theory \\(T\\) to satisfy a right reference constraint, (RRC).", "\nPutnam [1985] regards it as simply question-begging for a realist to\nassume her notion of an intended model is determinate: i.e. that terms\nsuch as ‘satisfaction’ or ‘correspondence’\nrefer to those relations to which she wishes them to refer. That her\nterm ‘refers’ refers to her desired reference relation is\n‘just more theory’. Realists have responded that Putnam is\nwilfully re-interpreting their semantic terms as he sees\n fit.[8]\n ", "\nIs there some independent way to validate Lewis’s distinction?\nMichael Resnick thinks so [Resnick 1987]. Putnam maintained that\n\\(M\\), the model he constructs of the ideal theory \\(T\\), is an\nintended model because it passes every operational and theoretical\nconstraint we could reasonably impose. It passes every theoretical\nconstraint, he argues, simply because it makes every thesis of \\(T\\)\ntrue. But unless the Reflection Principle (RP) below\nholds, Resnick argues, this inference is just a\nnon-sequitur:", "\nHowever, this principle is false. The simplest counterexample to it,\nResnick points out, is Tarskian truth. Suppose we impose on\n\\(T\\)’s model \\(M\\) a condition \\(f^*\\) that \\(M\\) makes all of\n\\(T\\)’s theses come out true. Then, unless \\(T\\) is either\ninconsistent or too weak to express elementary arithmetic no truth\npredicate will be definable in \\(T\\). Whence there will be no\ncondition \\(C\\) expressible in \\(T\\) corresponding to this condition\n\\(f^*\\) on \\(T\\)’s model(s) \\(M\\).", "\nResnick concludes (ibid):", "\nAny true interpretation of \\(T\\) whatsoever—even one which does\nnot satisfy \\(C\\)—will make true every thesis of \\(T\\),\nincluding T’s assertion that \\(C\\) is satisfied. Which suffices\nto block the ‘just more theory’ gambit.\n", "\nThe philosophical consensus appears to be that Lewis and Resnick are\nright. Apart from the authors already discussed, important criticisms\nof the MTA were advanced in Hale and Wright 1997, van Cleve 1992 and\nBays 2008. However, some very sophisticated anti-realist attempts to\nbuttress the Model-Theoretic Argument against Lewis-styled criticisms\nhave appeared. Igor Douven reconstructs Putnam’s argument,\ndefending it against standard objections [Douven 1999]. Barry Taylor\npresents a detailed explication and defence of Putnam’s Just\nMore Theory reply [Taylor 2006], as does Tim Button [Button 2013].\nWhether these newer formulations of the MTA succeed in answering the\nLewis/Resnick objection is an open\n question.[9]\n " ], "subsection_title": "4.4 Models and Reality" }, { "content": [ "\nTo the extent it makes the existence of all things relative to the\nclassificatory skills of minds, conceptual relativism appears highly\ncounter-intuitive to realists. Whilst it may seem plausible to some\nthat moral values or perhaps even colours might disappear with the\nextinction of sentient life on Earth, it is not at all plausible to\nthink that trees, rocks and microbes would follow in their train. ", "\nThis is not how Putnam understands his idea of conceptual relativity,\nhowever, which thesis he distinguishes from conceptual relativism. As\nhe sees things, we accept a theory which licenses us to assert\n“Electrons exist” and also licenses us to assert “if\nhumans were to disappear from this planet, electrons need not follow\nin their train” since the theory assures us that the existence\nof electrons in no way causally depends on the existence of humans.\nFor the anti-realist our well-founded practices of assertion ground at\none and the same time our conception of the world and our conception\nof humanity’s place within it.", "\nRealists might still worry that whether there are to be any electrons\nin the anti-realist’s ontology apparently depends upon the\nconceptual schemes humans happen to chance upon and Putnam himself\nencourages this interpretation: “‘objects’ do not\nexist independently of conceptual schemes” [Putnam 1981]. The\nrelativity of existence to conceptual scheme is, in this respect,\nquite unlike the relativity of simultaneity to frame of reference.", "\nStill, anti-realists maintain that there are actual instances of\nconceptual schemes that explain the same phenomena equally well,\nschemes which, they aver, realists must judge to be logically\nincompatible. The earlier example of competing theories of space-time\nwas a case in point. On one theory, \\(T_1\\), space-time consists of\nunextended spatiotemporal points and regions of space-time are sets of\nthese points. According to the second theory, \\(T_2\\), space-time\nconsists of extended spatiotemporal regions and points are logical\nconstructions—convergent sets of regions. Realists will judge\nthat only one of the two theories can be true if they really are\nlogically incompatible. Anti-realists respond that the two theories\n\\(T_1\\) and \\(T_2\\) cannot differ in truth-value since they are\ndescriptively equivalent. ", "\nAnti-realists regard two theories as descriptively equivalent if each\ntheory can be interpreted in the other and both theories explain the\nsame phenomena. Is there nothing more to the notion of descriptive\nequivalence than this? Realists might not accept that there\nisn’t.", "\nConsider our two competing theories of space-time \\(T_1\\) and \\(T_2\\)\nagain. Are \\(T_1\\) and \\(T_2\\) descriptively equivalent? At the stroke\nof midnight Cinderella’s carriage changes into a\npumpkin—it is a carriage up to midnight, a pumpkin thereafter.\nAccording to the region-based theory \\(T_2\\) which takes temporal\nintervals as its primitives, that’s all there is to it. But if\nthere are temporal points, instants, as \\(T_1\\) affirms, there is a\nfurther issue left undecided by this story—viz, at the moment of\nmidnight is the carriage still a carriage or is it a pumpkin?", "\nSo does the region-based theory fail to recognize certain facts or are\nthese putative facts merely artefacts of the punctate theory’s\ndescriptive resources, reflecting nothing in reality? We cannot\ndeclare the two theories \\(T_1\\) and \\(T_2\\) descriptively equivalent\nuntil we resolve this question at least.", "\nIn fact, there is no reason why realists cannot agree with\nanti-realists in regarding the conflict between a punctate geometry\nand a region-based geometry as merely apparent. Thomas\nWilliam Barrett and Hans Halvorson argue that the two theories “\n… are simply convenient ways of expressing the geometric facts that\nare more fully expressed by a comprehensive theory” that\nquantifies over both points and lines. \\(T_1\\) and \\(T_2\\) cannot be\nincompatible according to Barrett and Halvorson because they are in\nessence the same theory [Barrett and Halvorson 2017].\nHowever, the geometric case is a rather special one.", "\nConsider another Putnam-styled case [Putnam 2004]. Ernie looks into\nhis bag and sees there are 3 coins and nothing else and announces\n“There are exactly 3 objects in my bag.” Maxi looks into\nErnie’s bag and shakes her head “No Ernie there are 7\nobjects in your bag!” she corrects him. The Carnapian pluralist\nfeels she can defuse the conflict and accommodate both points of view\nby maintaining that whilst 3 objects exist-in-\\(E\\) (where \\(E\\) is\nErnie’s everyday framework), 7 objects exist-in-\\(M\\) (with\n\\(M\\) Maxi’s mereological framework). But even if Maxi can\nendorse both of these claims (since the mereological objects include\nErnie’s 3 coins), it is not at all certain Ernie can do so. If\nErnie is unpersuaded that mereological fusions of objects are\nthemselves objects, then Maxi’s putative truthmaker for her\nframework-relative existence claim “7 objects\nexist-in-\\(M\\)” will be unconvincing to him.", "\nFor this case, the pluralist’s suggestion that 3 objects\nexist-in-\\(E\\) but 7 objects exist-in-\\(M\\) is not clearly warranted.\nThere are simpler explanations: one is that by ‘object’\nErnie means ordinary object, by ‘object’ Maxi means\nmereological object. Nothing deeper than that is required to explain\ntheir disagreement. Rather than existence or truth that is\nrelativized, the meanings of their terms differ. On this account,\npluralists have mistaken a plurality of meanings for a plurality of\nmodes of being. However, other explanations are also possible: for\ninstance, it may be that Ernie and Maxi do mean the same thing by\n‘object’ but hold incompatible theories about what counts\nas an object. More importantly, as a reviewer noted, the debate\nneed not turn on the notion of an object: it can proceed with\nquantifiers, for example. The disagreement then would arise from\ndivergent interpretations of those quantifiers.", "\nPutnam’s pluralism has provoked very different reactions from\nrealists. Some argue that conceptual pluralism is consistent with\nrealism [Lynch 1998; Horgan and Timmons 2002; Sosa 2003], others take\nPutnam’s pluralism to amount to the claim that ontological\nexpressions are either indeterminate or that alternative ontologies\nare equally good, both alternatives being problematic [Eklund 2008].\nRealists cannot make sense of the Carnapian idea that existence and\ntruth are relative to a conceptual scheme [Brueckner 1998]. Peter van\nInwagen provides a trenchant criticism of Putnam’s claims [van\nInwagen 2002]: ", "\nI cannot grant that ‘Carnap’s’ [DK: Ernie’s]\nand ‘The Polish logician’s’ [DK: Maxi’s]\ndescriptions are equally good or equivalent descriptions of the\npopulation of a world [DK: e.g. the contents of Ernie’s\nbag]—not at least if Carnap’s description is ‘a\nworld that contains three mereological simples and nothing\nelse’. I cannot grant that they could be ‘equally\ngood or equivalent descriptions of the population of a world’\nsince they are straightforwardly incompatible.\n", "\nRecently, however, some impressive neo-Carnapian defences of\nconceptual pluralism have been proposed that bring new considerations\nto bear on these debates. We briefly review some of these in section\n5." ], "subsection_title": "4.5 Conceptual Schemes and Pluralism" } ] }, { "main_content": [ "\nDebates in meta-ontology (analytic ontology) over the last twenty\nyears have sparked renewed interest in realism. They have also seen a\nmarked shift in how realism, i.e. ontological realism, is understood.\n“The central question of metaontology”, Theodore Sider, a\nprominent ontological realist, contends, “is that of whether\nthere are many equally good quantifier meanings, or whether there is a\nsingle best quantifier meaning.” [Sider 2009, p.397]. Where\nSider argues for a single best quantifier meaning, Eli Hirsch believes\nthere are a multiplicity of possible quantifier meanings that are\nequally good, a thesis he calls Quantifier Variance. This\nmeaning-theoretic focus is something\n new.[10]\n ", "\nIt is no surprise, then, to find that the positions marked out as\n‘realist’ and ‘anti-realist’ by those engaged\nin ontological disputes do not always coincide with realism and\nanti-realism as we have explained these metaphysical\n views.[11]", "\nA more significant division is between metaontologists who accept a\nrobust conception of ontology, and deflationists about\nontology who don’t. Sider defends robust ontology [Sider 2009,\n385–386]:", "\n“ontological deflationists”… have said … when some\nparticles are arranged tablewise, there is no\n“substantive” question of whether there also exists a\ntable composed of those particles. There are simply different —\nand equally good — ways to talk. I, on the other hand, accept a\nvery strong realism about ontology. I think that questions about the\nexistence of composite objects are substantive, just as substantive as\nthe question of whether there are extra-terrestrials.\n", "\nNeo-Carnapians such as Putnam, Eli Hirsch, David Chalmers, Amie\nThomasson, and Huw Price are ontological deflationists who embrace\nconceptual pluralism about ontological matters. Hirsch, however,\nthinks conceptual pluralism is perfectly consistent with realism\n[Hirsch, E. 2002]. Matti Eklund understands Hirsch to mean that he\nconsiders the world to be an amorphous lump [Eklund, M., 2008] (citing\nMichael Dummett), a ‘lump’ that alternative and equally\nfeasible conceptual schemes serve to make intelligible. For Sider, in\ncontrast, rejecting an intrinsic structure to the world is to reject\n realism.[12]\n ", "\nCompeting views about temporal persistence do not seem to be semantic\nin nature. While Perdurantists believe that things persist through\ntime by virtue of having temporal parts that perdure,\nEndurantists reject the notion of temporal parts as incoherent\n—things persist by enduring: they are wholly present\nwhenever they exist. As observed in the entry on\n temporal parts:", "\nThis looks like a straightforward ontological disagreement, a dispute\nabout what exists.\n", "\nEli Hirsch is not convinced, however:", "\nI claim that the dispute between Endurantists and Perdurantists is\nverbal … each party ought to agree the other party speaks a truth in\nhis own language. [Hirsch 2011, 229]\n", "\nHow can this be? Endurantists think perdurantists are guilty of\nspatializing time when they talk about temporal parts; perdurantists\nthink enduring objects cannot explain change. How can there be a\nrapprochement of the sort Hirsch has in mind?", "\nHirsch’s novel and intriguing idea is that what makes the\nendurantist/perdurantist temporal parts debate and the\nnihilist/universalist mereological debate merely verbal ones is the\nfact that the protagonists in these debates mean different things by\ntheir quantifiers, in particular their existential quantifiers, in\ntheir ontological assertions. While both protagonists speak a common\nlanguage, here English, in which certain ontological claims such as\n‘there are tables’ happen to come out true, this is a\nsuperficial socio-linguistic fact about English that might not have\nbeen so: we and they could just as easily have spoken English* (an\nontological nihilist language) in which the sentence ‘there are\ntables’ came out false. Protagonists in these ontological\ndisputes are, unwittingly, engaged in a ‘merely verbal’\ndebate and are thus talking past each\n other.[13]\n ", "\nHow does the deflationist tell that an ontological dispute is a\n‘merely verbal’ one? Hirsch thinks that when we interpret\nthe words of another, we assign truth-conditions to their sentences by\nmatching those sentences with sets of possible worlds, guided by the\nmetasemantic maxim that the speaker’s assertion of those\nsentences should come out true. The maxim applies to ontological\ndisputes such as the Ernie/Maxi dispute about mereology — there\nare possible languages in which both speakers’ assertions come\nout true. Hirsch contends: “speakers of either language should\nallow that speakers of the other language assert sentences that have\nthe same characters (DK: functions from contexts of utterance to\ntruth-conditions) and the same truth-values as they themselves\nassert.” [Hirsch 2009, p.242]. ", "\nIn this way Ernie should attribute the same set of possible worlds\n(intensions) to Maxi’s sentence ‘There are seven objects\nin your bag’ as he associates with his own sentence ‘There\nare three objects in my bag’ and Ernie should interpret Maxi as\nuttering a truth in so doing. Ernie and Maxi are asserting the very\nsame proposition but are using different words to express it. They\nare, as a result, simply talking past each other. ", "\nHirsch’s doctrine of quantifier variance QV dominates current\nmetaontological debate. Some have questioned whether interpreters on\none side of an ontological dispute can admit that the language of\nthose on the other side is possible. For to do so each interpreter\nmust be able to provide a Tarskian semantics for the other’s\nlanguage. But an Endurantist won’t be able to do this for the\nPerdurantist’s sentence such as ‘Alicet is a\ntemporal part of Alice’ since the predicate ‘is a temporal\npart of’ has an empty extension in the Endurantist’s\nlanguage [Hawthorne 2006; Eklund 2009]. Others suspect QV is an\ninternally unstable position: how can an Endurantist speaking her\nlanguage E allow that a sentence like ‘Alicet is a\ntemporal part of Alice’ is a true sentence of the\nPerdurantist’s language P without admitting that there are\ntemporal parts [e.g. Hale and Wright 2009; Dorr 2014]? Warren 2015\nprovides a convincing QV response to this ‘Collapse’\nargument. An important resource, containing papers by some of the\nauthors cited, is the collection of essays anthologised in Chalmers et\nal 2009 [For background on mereology see the entry\n mereology\n and for discussion of whether there are composite objects, see the\nentry\n material constitution\n and the entry\n ordinary objects].\n ", "\nThe meaning-theoretic focus on Quantifier Variance in metaontology\nrepresents a fascinating development. The implications for ontological\nrealism are as yet undecided." ], "section_title": "5. Realism and Anti-Realism in Meta-Ontology", "subsections": [] }, { "main_content": [ "\nWe have considered a number of challenges to realism, the thesis that\nthe objects and properties that the world contains, its nature and\nstructure, exist independently of our conception or perception of\nthem. Historically, these challenges came from two camps: (1)\nneo-verificationists led by Dummett who assimilate belief in\nmind-independent world to a belief in a verification-transcendent\nconception of truth which they profess to find unintelligible, and (2)\npragmatists and pluralists led by Putnam who also question the\nintelligibility of the realist’s mind-independent world but for\nreasons independent of any commitment to verificationism. While\nneo-verificationism today claims few adherents, within the ranks of\nanalytic ontologists, pluralism and Carnap’s version of it in\nparticular, has enjoyed something of a revival. Today, the most active\nand engaging debates about realism are meta-ontological ones that\ninvolve neo-Carnapian pluralists and their ontological realist\nopponents. ", "\nBoth the historical debate between realists and their anti-realist\nopponents and the meta-ontological debate are still very much open. If\nrealists could provide a plausible theory about how correspondences\nbetween mental symbols and the items in the world to which they refer\nmight be set up, many of these challenges could be met. Alternatively,\nif they could explain how, consistently with our knowledge of a\nmind-independent world, no such correspondences are required to begin\nwith, many of the anti-realist objections would fall away as\nirrelevant. In the absence of such explanations it is still entirely\nreasonable for realists to believe that the correspondences are in\nplace, however, and there can, indeed, be very good evidence for\nbelieving this. Ignorance of Nature’s reference-fixing mechanism\nis no reason for denying it exists." ], "section_title": "6. Summary", "subsections": [] } ]

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[ { "href": "../mental-representation/", "text": "mental representation" }, { "href": "../realism/", "text": "realism" }, { "href": "../truth/", "text": "truth" }, { "href": "../truth-coherence/", "text": "truth: coherence theory of" }, { "href": "../truth-deflationary/", "text": "truth: deflationation about" } ]

[ "\nScientific theories seem to have an expiry date. If we look at the\nhistory of science, a number of theories that once were dominant and\nwidely accepted are currently taught in history of science courses.\nWill this be the fate of current scientific theories? Is there a\npattern of radical theory-change as science grows? Are theories\nabandoned en bloc? Or are there patterns of retention in\ntheory-change? That is, are some parts of theories more likely to\nsurvive than other parts? And what are the implications of all this\nfor the scientific image of the world?", "\nThese kinds of question have played a major role in the scientific\nrealism debate. The challenge to scientific realism is supposed to\ncome directly from the history of science. The history of science, it\nis claimed, is at odds with scientific realism’s epistemic\noptimism. It is full of theories which were shown to be false and\nabandoned, despite their empirical successes. Hence, it is claimed,\nrealists cannot be warrantedly optimistic about the (approximate)\ntruth of currently empirically successful theories. If we take the\nhistorical evidence seriously, it is claimed, current theories too\nwill, sooner or later, be abandoned and take their place in future\nhistory-of-science courses. This anti-realist line of argument has\nbecome known as ‘the pessimistic induction’ (aka\npessimistic meta-induction)—henceforth PI. Without\ndenying that theories change over time, scientific realists have tried\nto block this line of argument by showing either that it is fallacious\nor that there is substantive continuity in theory-change which\nwarrants the realist’s optimism that current science is on the\nright track.", "\nThis entry discusses the origin and current state of the historical\nchallenge to realism and the various realist reactions to it. The\nfirst part focuses on the first enactment of arguments based on\nhistorical pessimism, as these appeared in the so-called\n‘bankruptcy of science controversy’ in the end of the\nnineteenth century.", "\nThe second part deals with the historical challenge to scientific\nrealism as this is currently formulated and the various lines of\ndefense of the claim that scientific knowledge grows despite\ntheory-change." ]

[ { "content_title": "1. The History of the Historical Challenge", "sub_toc": [ "1.1 The Bankruptcy-of-science Debate", "1.2 Duhem on Continuity", "1.3 Poincaré’s Relationism", "1.4 Boltzmann Against Historical Pessimism" ] }, { "content_title": "2. Scientific Realism and the Pessimistic Induction", "sub_toc": [ "2.1 The ‘Disastrous Meta-Induction’", "2.2 The Principle of No Privilege", "2.3 Getting Nearer to the Truth", "2.4 The Plethora of False Theories", "2.5 The Divide et Impera Strategy", "2.6 Criticisms of Divide et Impera", "2.7 Structural Realism", "2.8 Induction or Deduction?", "2.9 A New Induction" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. The History of the Historical Challenge", "subsections": [ { "content": [ "\nThe issue of theory-change in science was debated in the context of\nthe ‘bankruptcy of science’ controversy that was raging in\nParis in the last decade of the nineteenth century and the first\ndecade of the twentieth. A claim of growing popular reputation among\nvarious public intellectuals, spearheaded by Ferdinand\nBrunetière and Leo Tolstoy, was that scientific theories are\nephemeral; and this was supposed to prove that science has at best no\nmore than predictive value with no legitimate claim to showing what\nthe world is like—especially in its unobservable aspects. In\nlight of a growing interest in the history of science among scientists\nand philosophers, it was pointed out that science has had a poor track\nrecord: it has gone through many radical theory-changes in the past;\nhence, there is reason to believe that what is currently\naccepted will be overturned in the future.", "\nIn his essay “The Non-Acting”, published in French in\nAugust 1893, the Russian novelist Tolstoy (1828–1910) noted:", "\n\n\nLastly, does not each year produce its new scientific discoveries,\nwhich after astonishing the boobies of the whole world and bringing\nfame and fortune to the inventors, are eventually admitted to be\nridiculous mistakes even by those who promulgated them? (…)\nUnless then our century forms an exception (which is a supposition we\nhave no right to make), it needs no great boldness to conclude by\nanalogy that among the kinds of knowledge occupying the attention of\nour learned men and called science, there must necessarily be some\nwhich will be regarded by our descendants much as we now regard the\nrhetoric of the ancients and the scholasticism of the Middle Ages.\n(1904: 105)\n", "\nA few years earlier, in 1889, Ferdinand Brunetière\n(1849–1906), Professor at the École Normale\nSupérieure and editor of the prestigious journal Revue\ndes Deux Mondes, noted in his review of Paul Bourget’s play\n‘Le Disciple’:", "\n\n\nWe differ from animals in recognizing that humans have to be first\n(i.e., they have value). The laws of nature, the ‘struggle for\nlife’ or ‘natural selection’, do not show what we\nhave in common. Are these the only laws? Do we know whether perhaps\ntomorrow they will not join in the depths of oblivion the Cartesian\nvortices or the ‘quiddities’ of scholasticism? (1889: 222,\nauthor’s translation)\n", "\nThis history-fed pessimism about science, which seemed to capture the\npublic mood, led to a spirited reaction by the scientific community.\nIn an anonymous article that appeared in Revue Scientifique,\na prestigious semi-popular scientific journal, in August 17 1889, the\nfollowing questions were raised: Is the history of science the history\nof human error? Will what theories affirm today be affirmed in a\ncentury or two? The reply was:", "\n\n\nWe will say to savants, philosophers and physicists, physicians,\nchemists, astronomers or geologists: Go forward boldly, without\nlooking behind you, without caring for the consequences, reasonable or\nabsurd, that can be drawn from your work. Seek the truth, without the\nworry of its applications. (Anonymous 1889: 215, author’s\ntranslation)\n", "\nA few years later, in 1895, Brunetière strikes back with an\narticle titled ‘Après Une Visite Au\nVatican’, published in Revue des Deux Mondes, by\nclaiming that science is bankrupt:", "\n\n\nScience has failed to deliver on its promise to change ‘the face\nof the world’. (...) Even if this is not a total bankruptcy, it\nis certainly a partial bankruptcy, enough to shake off the credit from\nscience. (1895: 98, 103)\n", "\nThe eminent scientist Charles Richet (1850–1935), Professor of\nPhysiology at the Collège de France, Editor of Revue\nScientifique and Nobel Laureate for Medicine in 1913, replied\nwith an article titled ‘La Science a-t-elle fait\nbanqueroute?’ (Revue Scientifique, 12 January\n1895), which appeared in the section: Histoire des Sciences.\nIn this, he did three things. Firstly, he noted that science can never\nunderstand the ‘why’ (‘le pourquoi’)\nof things, especially when it comes to the infinitely small and the\ninfinitely large. Science “attends only to the phenomena. The\nintimate nature of things escapes from us” (1895: 34). Secondly,\nhe stressed that “science has not promised anything”, let\nalone the discovery of the essence of things. Thirdly, he added that\ndespite the fact that science has made no promises, it has changed the\nworld, citing various scientific, industrial and technological\nsuccesses (from the invention of printing and the microscope to the\nrailways, the electric battery, the composition of the air, and the\nnature of fermentation).", "\nTurning Brunetière’s argument on its head, Richet\nformulated what might be called an ‘optimistic induction’\nbased on the then recent history of scientific successes. To those who\nclaim that science has failed in the past, his reply is that history\nshows that it is unreasonable to claim for any scientific question\nthat we will always fail to answer it. Far from warranting epistemic\npessimism, the history of science is a source of cognitive optimism.\nRichet referred to a few remarkable cases, the most striking of which\nis the case of Jean Louis Prevost and Jean Baptiste Dumas, who had\nwritten in 1823:", "\n\n\nThe pointlessness of our attempts to isolate the colouring matter of\nthe blood gives us almost the certainty that one will never be able to\nfind it. (1823, 246, author’s translation)\n", "\nForty years after their bold statement, Richet exclaimed, this\ncoloured matter (haemoglobin) had been isolated, analysed and\nstudied.", "\nRichet’s reply to the historical challenge suggested lowering\nthe epistemic bar for science: science describes the phenomena and\ndoes not go beyond them to their (unobservable) causes. This attitude\nwas echoed in the reply to the ‘bankruptcy charge’ issued\nby the eminent chemist and politician of the French Third Republic,\nMarcelin Berthelot (1827–1907) in his pamphlet Science et\nMorale in 1897. He was firm in his claim that the alleged\nbankruptcy of science is an illusion of the non-scientific mind. Like\nRichet, he also argued that science has not pretended to have\npenetrated into the essence of things: “under the words\n‘essence’, ‘the nature of things’, we hide the\nidols of our own imagination” (1897: 18, author’s\ntranslation). Science, he noted, has as its starting point the study\nof facts and aims to establish general relations, that is,\n‘scientific laws’, on their basis. If science does not aim\nfor more, we cannot claim that it is bankrupt; we cannot accuse it for\n“affirmations it did not make, or hopes it has not\n aroused”.[1]", "\nBerthelot, who objected to atomism, captured a broad positivist trend\nin French science at the end of the nineteenth century, according to\nwhich science cannot offer knowledge of anything other than the\nphenomena. In light of this view, the history-fed pessimism is\nmisguided precisely because there has been substantial continuity at\nthe level of the description of the phenomena, even if explanatory\ntheories have come and gone." ], "subsection_title": "1.1 The Bankruptcy-of-science Debate" }, { "content": [ "\nThis kind of attitude was captured by Pierre Duhem’s (1906)\ndistinction between two parts of a scientific theory: the\nrepresentative part, which classifies a set of experimental laws; and\nthe explanatory part, which “takes hold of the reality\nunderlying the phenomena” (1906 [1954: 32]). Duhem understood\nthe representative part of a theory as comprising the empirical laws\nand the mathematical formalism, which is used to represent,\nsystematize and correlate these laws, while he thought that the\nexplanatory part relates to the construction of physical (and in\nparticular, mechanical) models and explanatory hypotheses about the\nnature of physical processes which purport to reveal underlying\nunobservable causes of the phenomena. For him, the explanatory part is\nparasitic on the representative. To support this view, he turned to\nthe history of science, especially the history of optical theories and\nof mechanics. He argued that when a theory is abandoned because it\nfails to cover new experimental facts and laws, its representative\npart is retained, partially or fully, in its successor theory, while\nthe attempted explanations offered by the theory get abandoned. He\nspoke of the “constant breaking-out of explanations which arise\nto be quelled” (1906 [1954: 33]).", "\nThough Duhem embedded this claim for continuity in theory-change in an\ninstrumentalist account of scientific theories, he also took it that\nscience aims at a natural classification of the phenomena, where a\nclassification (that is the representation of the phenomena within a\nmathematical system) is natural if the relations it\nestablishes among the phenomena gathered by experiments\n“correspond to real relations among things” (1906 [1954:\n26–27]). Hence, scientific knowledge does go beyond the\nphenomena but in doing so, that is, in tending to be a natural\nclassification, it can extend only up to relations among “hidden\nrealities whose essence cannot be grasped” (1906 [1954: 297]). A\nclear mark of the naturalness of a classification is when it issues in\nnovel predictions (1906 [1954: 28]). Hence, successful novel\npredictions issued by a theory are a mark for the theory getting some\naspects of reality right, viz. real relations among unobservable\n entities.[2]" ], "subsection_title": "1.2 Duhem on Continuity" }, { "content": [ "\nThis kind of relationism became a popular middle way between\npositivism and what may be called full-blown realism. Duhem himself,\njustly, traced it back to his contemporary Henri Poincaré. He\nnoted with approval that Poincaré “felt a sort of\nrevolt” against the proposition that “theoretical physics\nis a mere collection of recipes” and he “loudly proclaimed\nthat a physical theory gives us something else than the mere knowledge\nof the facts, that it makes us discover the real relations among\nthings ([1906] 2007: 446; improved translation from the French\noriginal by Marie Guegeun and the author).", "\nIn his address to the 1900 International Congress of Physics in Paris,\nPoincaré made a definitive intervention in the\nbankruptcy-of-science debate and its history-fed pessimism. He\ndescribed the challenge thus:", "\n\n\nThe people of world [les gens du monde] are struck to see how\nephemeral scientific theories are. After some years of prosperity,\nthey see them successively abandoned; they see ruins accumulated on\nruins; they predict that the theories in fashion today will quickly\nsuccumb in their turn, and they conclude that they are absolutely\nfutile. This is what they call the bankruptcy of science\n(1900: 14, author’s translation).\n", "\nThe view of ‘the people of the world’ is not right:", "\n\n\nTheir scepticism is superficial; they understand none of the aim and\nthe role of scientific theories; otherwise they would understand that\nruins can still be good for something.\n", "\nBut unlike the positivist trend around him, Poincaré took it\nthat scientific theories offer knowledge of the relational structure\nof the world behind the phenomena. In the Introduction to La\nScience et l’Hypothése in 1902, he made clear what\nhe took to be the right answer to the historical challenge:", "\n\n\nWithout doubt, at first, the theories seem to us fragile, and the\nhistory of science proves to us how ephemeral they are; yet they do\nnot entirely perish, and of each of them something remains. It is this\nsomething we must seek to unravel, since there and there alone is the\ntrue reality. (1902: 26, author’s translation)\n", "\nPoincaré argued that what survives in theory-change are\nrelations among physical magnitudes, expressed by mathematical\nequations within theories. His prime example was the reproduction of\nFresnel’s laws concerning the relations of amplitudes of\nreflected rays vis-à-vis the amplitude of incident rays in the\ninterface of two media within Maxwell’s theory of\nelectromagnetism, although in this transition, the interpretation of\nthese laws changed dramatically, from an ether-based account to an\nelectromagnetic-field-based account. For Poincaré", "\n\n\nThese equations express relations, and if the equations remain true it\nis because these relations preserve their reality. They teach us,\nbefore and after, that there is such and such a relation between some\nthing and some other thing; only this something we used to call\nmotion, we now call it electric current. But these\nnames were only images substituted for the real objects which nature\nwill eternally hide from us. The true relations between these real\nobjects are the only reality we can attain to, and the only condition\nis that the same relations exist between these objects as between the\nimages by which we are forced to replace them. If these relations are\nknown, what does it matter if we deem it convenient to replace one\nimage by another? (1900: 15, author’s translation.\n", "\nIn recent literature, Poincaré’s line of thought has come\nto be known as structural realism, though it may be best if\nwe describe it as ‘relationism’. In the Introduction to\nLa Science et l’Hypothése, he noted that", "\n\n\nthe things themselves are not what it [science] can reach, as the\nnaive dogmatists think, but only the relations between things. Apart\nfrom these relations there is no knowable reality. (1902: 25,\nauthor’s translation)\n", "\nIt should be stressed that Poincaré does not deny that there is\nreality outside relations; but he does deny that this reality is\nknowable. Note also that Poincaré does not use the\nexpression ‘things in themselves’ (choses en soi)\nbut the expression ‘things themselves’ (chose\nelles-memes). Elsewhere he talks about the “nature of\nthings” or “real objects”. It is quite clear that he\nwanted to draw a distinction between how things are—what their\nnature is—and how they are related to each other (and\nto us qua knowers). A plausible way to draw this distinction\nis to differentiate between the intrinsic and perhaps fully\nqualitative properties of things—what he plausibly calls\n‘nature’ of things—and their relations. The former\nare unknowable, whereas the latter are\n knowable.[3]", "\nSo, Poincaré and Duhem initiated a strategy for dealing with\ntheory-change in science which pointed to substantial continuities\namong successive theories. For them, the continuity is, by and large,\nrelational (and in this sense mathematical). Hence,\nmathematically-convergent scientific theories reveal the relational\nstructure of the world." ], "subsection_title": "1.3 Poincaré’s Relationism" }, { "content": [ "\nThis relational answer to historical pessimism was motivated, at least\npartly, by the widespread scepticism towards the atomic theory of\nmatter. Atomism posited the existence of unobservable\nentities—the atoms—to account for a host of observable\nphenomena (from chemical bonding to Brownian motion). A trend among\nscientists opposed to the explanation of the visible in terms of the\ninvisible was what Ludwig Boltzmann called\n“phenomenologists” (which included the early Max Planck),\naccording to whom the aim of science was to “write down for\nevery group of phenomena the equations by means of which their\nbehavior could be quantitatively calculated” (Boltzmann 1901:\n249). The theoretical hypotheses from which the equations might have\nbeen deduced were taken to be the scaffolding that was discarded after\nthe equations were arrived at. For phenomenologists, then, hypotheses\nare not unnecessary or useless—rather they have only a\nheuristic value: they lead to stable (differential) equations\nand that’s it.", "\nAccording to Boltzmann, a motivation for this phenomenological\nattitude was the “historical principle”, viz., that\nhypotheses are essentially insecure because they tend to be abandoned\nand replaced by others, “totally different” ones. As he\nput it:", "\n\n\nfrequently opinions which are held in the highest esteem have been\nsupplanted within a very short space of time by totally different\ntheories; nay, even as St. Remigius the heathens, so now they [the\nphenomenologists] exhorted the theoretical physicists to consign to\nthe flames the idols that but a moment previously they had worshipped\n(1901: 252–253).\n", "\nLike Poincaré, Boltzmann’s answer to historical pessimism\nwas that despite the presence of “revolutions” in science,\nthere is enough continuity in theory change to warrant the claim that\nsome “achievements may possibly remain the possession of science\nfor all time” (1901: 253). But unlike Poincaré, Boltzmann\ndid not restrict the criterion of invariance-in-theory-change to\nrelations only: The answer to the historical challenge is to look\nfor patterns of continuity in theory change. In fact, as\nBoltzmann noted, if the historical principle is correct at all, it\ncuts also against the equations of the phenomenologists. For unless\nthese very equations remain invariant through theory-change, there\nshould be no warrant for taking them to be accurate descriptions of\nworldly relations (cf. 1901: 253). Besides, Boltzmann noted, the very\nconstruction of the differential equations of the phenomenologists\nrequires commitment to substantive atomistic assumptions. Hence, the\nphenomenologists are not merely disingenuous when they jettison the\natomistic assumptions after the relevant differential equations have\nbeen arrived at. Their move is self-undermining. In light of the\nhistorical principle, the success of the mathematical equations would\nlead to their defeat, since the very theory that led to this success\nwould fall foul of the historical principle: it would have to be\nabandoned.", "\nThe history-based pessimism (and the relevant debate) came to an end\nby the triumph of atomism in the first decade of the twentieth\ncentury. Due to the work of Albert Einstein and the French physicist\nJean Perrin on the atomic explanation of Brownian motion, one after\nthe other of major scientists who were initially sceptical about the\natomic conception of matter came to accept\n atomism.[4]\n The French philosopher André Lalande captured this point in\nhis 1913 (pp. 366–367) thus:", "\n\n\nM. Perrin, professor of physics at the Sorbonne, has described in\nLes Atomes, with his usual lucidity and vigour, the recent\nexperiments (in which he has taken so considerable a part) which prove\nconclusively that the atoms are physical realities and not symbolical\nconceptions as people have for a long time been fond of calling them.\nBy giving precise and concordant measures for their weights and\ndimensions, it is proved that bodies actually exist which, though\ninvisible, are analogous at all points to those which we see and\ntouch. An old philosophical question thus receives a positive\nsolution.\n", "\nBe that as it may, what this brief account of the history of the\nhistorical challenge to realism reveals are the two major lines of\ndefense of realism at play. Both lines of defense are based on the\npresence of substantial continuity in theory-change in the history of\nscience. This continuity suggests that the disruption of the\nscientific image of the world, as theories change, is less radical\nthan is assumed by the historical challenge to realism. But the two\nlines of defense (the Poincaré-Duhem and the Boltzmann one)\ndisagree over what is retained when theories change. The\nPoincaré-Duhem line of defense focuses on mathematical\nequations (which express relations) and claims that only relations\namong unobservable things are knowable, whereas the Boltzmann line of\ndefense focuses on whatever theoretical elements (including entities\nlike atoms) are retained while theories change; hence, it does not\nlimit scientific knowledge to the knowledge of relations only. Both\nlines have resurfaced in the current debate." ], "subsection_title": "1.4 Boltzmann Against Historical Pessimism" } ] }, { "main_content": [], "section_title": "2. Scientific Realism and the Pessimistic Induction", "subsections": [ { "content": [ "\nCapitalizing on the work of Richard Boyd, the early Hilary Putnam took\nscientific realism to involve three theses:", "\nPutnam argued that the failure of the third thesis would lead to a\ndisastrous “meta-induction”:", "\n\n\njust as no term used in the science of more than fifty (or\nwhatever) years ago referred, so it will turn out that no term\nused now (except maybe observation terms, if there are such)\nrefers (1978: 25) (emphasis in the original).\n", "\nAn answer to this ‘disastrous’ history-fed argument was\nthe development of a causal theory of reference, which allows for\nreferential continuity in theory-change. This theory was first\nsuggested by Saul Kripke (1972) as an alternative to the then dominant\ndescriptive theories of reference of proper names and was extended by\nPutnam (1973, 1975) to cover natural kind terms and theoretical terms.\nAccording to the causal theory, the reference of a theoretical term\nt is fixed during an introducing event in which an entity or\na physical magnitude is posited as the cause of various observable\nphenomena. The term t, then, refers to the posited entity.\nThough some kind of descriptions of the posited entity will be\nassociated with t, they do not play a role in reference\nfixing. The referent has been fixed existentially: it is the\nentity causally responsible for certain effects.", "\nThe causal theory of reference makes it possible that the same term\nfeaturing in different theories refers to the same worldly entity. If,\nfor instance, the referent of the term ‘electricity’ is\nfixed existentially, all different theories of electricity refer to,\nand dispute over, the same ‘existentially given’\nmagnitude, viz. electricity; better, the causal agent of\nsalient electrical effects. Hence, the causal theory makes available a\nway to compare past and present theories and to claim that the\nsuccessor theory is more truthlike than its predecessors since it says\ntruer things of the same entities. It turns out, however, that the\ncausal theory faces a number of conceptual problems, most notable of\nwhich is that it makes referential success inevitable insofar as the\nphenomena which lead to the introduction of a new theoretical term do\nhave a cause (see Psillos 1999: chapter 11 for a discussion).\nPhilosophers of science have tried to put forward a causal-descriptive\ntheory of reference which makes referential continuity possible whilst\nallowing room for causal descriptions in fixing the reference of a\ntheoretical\n term.[5]" ], "subsection_title": "2.1 The ‘Disastrous Meta-Induction’" }, { "content": [ "\nAn analogous history-fed pessimistic argument can be based on the\nso-called “principle of no privilege”, which was advanced\nby Mary Hesse in her 1976. According to this principle:", "\n\n\nour own scientific theories are held to be as much subject to radical\nconceptual change as past theories are seen to be. (1976: 266)\n", "\nThis principle can be used for the derivation of the strong conclusion\nthat all theories are false. As Hesse put it:", "\n\n\nEvery scientific system implies a conceptual classification of the\nworld into an ontology of fundamental entities and properties—it\nis an attempt to answer the question “What is the world really\nmade of?” But it is exactly these ontologies that are most\nsubject to radical change throughout the history of science. Therefore\nin the spirit of the principle of no privilege, it seems that we must\nsay either that all these ontologies are true, ie: we must give a\nrealistic interpretation of all of them or we must say they are all\nfalse. But they cannot all be true in the same world, because they\ncontain conflicting answers to the question “What is the world\nmade of?” Therefore they must all be false. (1976: 266)\n", "\nThis argument engages the history of theory-change in science in a\nsubstantial way. As Hesse admitted, the Principle of No Privilege\narises “from accepting the induction from the history of\nscience” (1976: 271). Hesse’s argument starts with the\nhistorical premise that, as science grows over time, there has been a\nrecognizable pattern of change in the ‘ontology of fundamental\nentities and properties’ posited by scientific theories.\nAssuming, then, the Principle of No Privilege, it is argued that\ncurrent theories too will be subjected to a radical change in the\nontology of the entities and properties they posit. Hence, current\ntheories are as false as the past ones.", "\nThe problem with this kind of argument is that the historical premise\nshould be borne out by the actual history of theory-change in science.\nIt’s not enough to say that scientific theories change over\ntime; these changes should be such that the newer theories are\nincompatible with the past ones. Or, to use Hesse’s idiom, it\nshould be shown that past and current scientific\n‘ontologies’ are incompatible with each other. Showing\nincompatibility between the claims made by current theory T\nand a past theory T′ requires a theory of reference of\ntheoretical terms which does not allow that terms featuring\nin different theories can nonetheless refer to the same entity in the\nworld. Hence, it is question-begging to adopt a theory of reference\nwhich makes it inevitable that there is radical-reference variance in\ntheory-change.", "\nReferential stability, as noted already, makes possible the claim that\npast and present ontologies are compatible, even if there have been\nchanges in what current theories say of the posited entities. The\n“revolutionary induction from the history of science about\ntheory change” (Hesse 1976: 268) can be blocked by pointing to a\npattern of substantial continuity in theory change." ], "subsection_title": "2.2 The Principle of No Privilege" }, { "content": [ "\nCan a history-fed argument be used in defence of realism?\nWilliam Newton-Smith (1981) was perhaps the first in the recent debate\nto answer positively this question. Scientific realism is committed to\nthe two following theses:", "\nAccording to Newton-Smith, (2) is under threat “if we reflect on\nthe fact that all physical theories in the past have had their heyday\nand have eventually been rejected as false”. And he added:", "\n\n\nIndeed, there is inductive support for a pessimistic induction: any\ntheory will be discovered to be false within, say 200 years of being\npropounded. We may think of some of our current theories as being\ntrue. But modesty requires us to assume that they are not so. For what\nis so special about the present? We have good inductive grounds for\nconcluding that current theories—even our most favourite\nones—will come to be seen to be false. Indeed the evidence might\neven be held to support the conclusion that no theory that will ever\nbe discovered by the human race is strictly speaking true. So how can\nit be rational to pursue that which we have evidence for thinking can\nnever be reached? (1981: 14)\n", "\nThe key answer to this question is that even if truth cannot be\nreached, it is enough for the defense of realism to posit “an\ninterim goal for the scientific enterprise”, viz., “the\ngoal of getting nearer the truth”. If this is the goal, the\n“sting” of the preceding induction “is\nremoved”. Accepting PI “is compatible with maintaining\nthat current theories, while strictly speaking false, are getting\nnearer the truth” (1981: 14).", "\nBut aren’t all false theories equally false? The standard\nrealist answer is based on what Newton-Smith called “the animal\nfarm move” (1981: 184), viz., that though all theories are\nfalse, some are truer than others. Hence, what was needed to be\ndefended was the thesis that if a theory \\(T_2\\) has greater\nverisimilitude than a theory \\(T_1\\), \\(T_2\\) is likely to have\ngreater observational success than \\(T_1\\). The key argument was based\non the “undeniable fact” that newer theories have yielded\nbetter predictions about the world than older ones (cf. Newton-Smith\n1981: 196). But if the ‘greater verisimilitude’ thesis is\ncorrect (that is, if theories “are increasing in truth-content\nwithout increasing in falsity-content”), then the increase in\npredictive power would be explained and rendered expectable. This\nincrease in predictive power “would be totally mystifying\n(…) if it were not for the fact that theories are capturing\nmore and more truth about the world” (1981: 196).", "\nThe key point, then, is that the defense of realism against the\nhistorical induction requires showing that there is, indeed, a\nprivilege that current theories enjoy over past ones, which is strong\nenough to block transferring, on inductive grounds, features of past\ntheories to current ones. For most realists, the privilege current\ntheories enjoy over past ones is not that they are true while the past\ntheories are false. Rather, the privilege is that they are more\ntruthlike than past theories because they have had more predictive\npower than past theories. The privilege is underpinned by an\nexplanatory argument: the increasing truthlikeness of current theories\nbest explains their increasing predictive and empirical\nsuccess.", "\nBut there is a way to see the historical challenge to realism which\nmakes it have as its target precisely to undercut the explanatory link\nbetween empirical success and truthlikeness. This was brought\nunder sharp relief in the subsequent debates." ], "subsection_title": "2.3 Getting Nearer to the Truth" }, { "content": [ "\nThe most famous history-based argument against realism, issued by\nLarry Laudan (1981), was meant to show how the explanatory link\nbetween success and truthlikeness is undermined by taking seriously\nthe history of science. It should be noted that Laudan’s\nargument has been subjected to several diverging interpretations,\nwhich will be the focus of section 2.8. For the time being let’s\nstick to a particularly popular one, according to which Laudan argues\ninductively from the falsity of past theories to the falsity of\ncurrent ones. This argument may be put thus:", "\nLaudan substantiated (L) by means of what he has called “the\nhistorical gambit”: the following list—which “could\nbe extended ad nauseam”—gives theories which were\nonce empirically successful and fruitful, yet just false.", "\nLaudan’s list of successful-yet-false theories", "\nThis is a list of a dozen of cases, but Laudan boldly noted the famous\n6 to 1 ratio:", "\n\n\nI daresay that for every highly successful theory in the past of\nscience which we now believe to be a genuinely referring theory, one\ncould find half a dozen once successful theories which we now regard\nas substantially non-referring. (1981: 35)\n", "\nIf we are to take seriously this “plethora” of theories\nthat were both successful and false, it appears that (L) is meant to\nbe a genuinely inductive argument.", "\nAn argument such as (I) has obvious flaws. Two are the most important.\nThe first is that the basis for induction is hard to assess. This does\nnot just concern the 6:1 ratio, of which one may ask: where does\nit come from? It also concerns the issue of how we individuate\nand count theories as well as how we judge success and referential\nfailure. Unless we are clear on all these issues in advance of the\ninductive argument, we cannot even start putting together the\ninductive evidence for its conclusion (cf. Mizrahi 2013).", "\nThe second flaw of (I) is that the conclusion is too strong.\nIt is supposed to be that there is rational warrant for the judgment\nthat current theories are not truthlike. The flaw with this\nkind of sweeping generalization is precisely that it totally\ndisregards the fresh strong evidence there is for current\ntheories—it renders current evidence totally irrelevant to the\nissue of their probability of being true. Surely this is unwarranted.\nNot only because it disregards potentially important differences in\nthe quality and quantity of evidence there is for current theories\n(differences that would justify treating current theories as more\nsupported by available evidence than past theories were by the then\navailable evidence); but also because it makes a mockery of looking\nfor evidence for scientific theories! If I know that X is\nmore likely than Y and that this relation cannot change by\ndoing Z, there is no point in doing Z. ", "\nThe second flaw of (I) becomes (even more) apparent when one takes a\ncloser look at the successful-yet-false theories in Laudan’s\nlist. Would anyone be willing to insist that, say, the humoral theory\nof medicine, the vital force theory of physiology or the theory of\ncrystalline spheres are on a par with our current scientific theories\nwith the same domain of application? The difference between their\nrespective evidence is undoubtedly enormous. Nevertheless, it would\nrather be mistaken to restrict our attention to those theories\ncomprising Laudan’s own list. Indeed, subsequent\nscholars have provided new lists of cases where admittedly false\ntheories had been used in the derivation of impressive empirical\npredictions. Most notably, Timothy Lyons (2002: 70–72) and Peter\nVickers (2013: 191–194) suggest the following (partly overlapping)\nlists:", "\nLyons’s list", "\nVickers’s list", "\nThese lists summarize much of the work done by historians of science\nand historically informed philosophers of science. They are meant to\npresent cases of empirical successes that were (supposedly) brought\nabout by false theoretical hypotheses, hence offering a fresh source\nof historical challenges to realism. At first sight, the cases\nprovided look substantially different from the majority of\nLaudan’s examples (viz. the successes, in at least some of them,\nare more impressive). Yet, it remains to be seen whether they are more\ntroublesome for scientific realism." ], "subsection_title": "2.4 The Plethora of False Theories" }, { "content": [ "\nIf we think of the pessimistic argument not as inductive but as a\nwarrant-remover argument and if we also think that the fate\nof (past) theories should have a bearing on what we are warranted in\naccepting now, we should think of its structure differently. It has\nbeen argued by Psillos (1999: chapter 5) that we should think of the\npessimistic argument as a kind of reductio. Argument (L)\nabove aimed to “discredit the claim that there is an explanatory\nconnection between empirical success and truth-likeness” which\nwould warrant the realist view that current successful theories are\ntruthlike. If we view the historical challenge this way, viz., as a\npotential warrant-remover argument, the past record of science does\nplay a role in it, since it is meant to offer this\nwarrant-remover.", "\nPsillos’s (1996) reconstruction of Laudan’s argument was\nas follows:", "\n\n\nArgument (P):\n\n\n(A) Currently successful theories are truthlike.\n\n\n(B) If currently successful theories are truthlike, then past theories\nare not.\n\n\n(C) These characteristically false past theories were, nonetheless,\nempirically successful. (The ‘historical gambit’)\n\n\nHence, empirical success is not connected with truthlikeness and\ntruthlikeness cannot explain success: the realist’s potential\nwarrant for (A) is defeated.\n", "\nPremise (B) of argument (P) is critical. It is meant to capture\nradical discontinuity in theory-change, which was put thus (stated in\nthe material mode):", "\n\n\nPast theories are deemed not to have been truth-like because the\nentities they posited are no longer believed to exist and/or because\nthe laws and mechanisms they postulated are not part of our current\ntheoretical description of the world. (Psillos 1999: 97).\n", "\nIn this setting, the ‘historical gambit’ (C) makes perfect\nsense. Unless there are past successful theories which are\nwarrantedly deemed not to be truthlike, premise (B) cannot be\nsustained and the warrant-removing reductio of (A) fails. If (C) can\nbe substantiated, success cannot be used to warrant the claim that\ncurrent theories are true. The realists’ explanatory link\nbetween truthlikeness and empirical success is undercut. (C) can be\nsubstantiated only by examining past successful theories and their\nfate. History of science is thereby essentially engaged.", "\nThe realist response has come to be known as the divide et\nimpera strategy to refute the pessimistic argument. The focus of\nthis strategy was on rebutting the claim that the truth of current\ntheories implies that past theories cannot be deemed truthlike. To\ndefend realism, realists needed to be selective in their commitments.\nThis selectivity was developed by Kitcher (1993) and (independently)\nby Psillos (1994).", "\nOne way to be selective is to draw a distinction between working\nposits of a theory (viz., those theoretical posits that occur\nsubstantially in the explanatory schemata of the theory) and\npresuppositional posits (putative entities that apparently\nhave to exist if the instances of the explanatory schemata of the\ntheory are to be true) (cf. Kitcher 1993: 149). Another way is to draw\na distinction between the theoretical claims that essentially or\nineliminably contribute to the generation of successes of a theory and\nthose claims that are ‘idle’ components that have had no\ncontribution to the theory’s success (cf. Psillos 1994, 1996).\nThe underlying thought is that the empirical successes of a theory do\nnot indiscriminably support all theoretical claims of the theory, but\nrather the empirical support is differentially distributed among the\nvarious claims of the theory according to the contribution they make\nto the generation of the successes. Generally, Kitcher (1993) and\nPsillos (1996, 1999) have argued that there are ways to distinguish\nbetween the ‘good’ and the ‘bad’\nparts of past abandoned theories and to show that the\n‘good’ parts—those that enjoyed evidential support,\nwere not idle components and the like—were retained in\nsubsequent theories.", "\nIt is worth-noting that, methodologically, the divide et\nimpera strategy recommended that the historical challenge to\nrealism can only be met by looking at the actual successes of past\nsuccessful theories and by showing that those parts of past theories\n(e.g., the caloric theory of heat or the optical ether theories) that\nwere fuelling theory successes were retained in subsequent theories\nand those theoretical terms which were central in the relevant past\ntheories were referential. In fact, Vickers has recently made the\nmethodological suggestion that if one’s sole aim is to\ncope with a historical challenge, then it is sufficient that one shows\nthat the abandoned hypotheses were not essential for the\nrelevant theory’s empirical success, without at the same time\ntaking side on which are the essential theoretical\nhypotheses. As Vickers claims, in order to respond to a PI-style\nchallenge, “all the realist needs to do is show that the\nspecific assumptions identified by the antirealist do not\nmerit realist commitment. And she can do this without saying anything\nabout how to identify the posits which do merit realist\ncommitment” (2017: 3224). Besides, according to Vickers’s\nconception of the dialectic of the PI-debate, the onus of proof lies\nwith the antirealist: the antirealist has to reconstruct the\nderivation of a prediction, identify the assumptions that merit\nrealist commitments and then show that at least one of them is not\ntruthlike by our current lights; and then all the realists need to\nshow is that the specific assumptions were inessential. In sum,\nVickers argues that “the project of responding to the historical\nchallenge” and “the project of explaining what realists\nshould commit to” have to be kept distinct (2017: 3222). ", "\nAt any rate, either employed in the identification of the trustworthy\ntheoretical parts or in the (mere) handling of a historical challenge,\nthe divide et impera move suggests that there has been enough\ntheoretical continuity in theory-change to warrant the realist claim\nthat science is ‘on the right track." ], "subsection_title": "2.5 The Divide et Impera Strategy" }, { "content": [ "\nThe realist move from substantive continuity in theory-change to\ntruthlikeness has been challenged on grounds that there is no\nentitlement to move from whatever preservation in theoretical\nconstituents there is in theory-change to these constituents’\nbeing truthlike (Chang 2003: 910–12; Stanford 2006). Against\nthis point it has been argued that the realist strategy proceeds in\ntwo steps (cf. Psillos 2009: 72). The first is to make the claim of\ncontinuity (or convergence) plausible, viz., to show that there is\ncontinuity in theory-change: substantive theoretical claims that\nfeatured in past theories and played a key role in their successes\n(especially novel predictions) have been incorporated in subsequent\ntheories and continue to play an important role in making them\nempirically successful. But this first step does not establish that\nthe convergence is to the truth. For this claim to be made\nplausible a second argument is needed, viz., that the emergence of\nthis evolving-but-convergent network of theoretical assertions is best\nexplained by the assumption that it is, by and large, truthlike. So\nthere is, after all, entitlement to move from convergence to\ntruthlikeness, insofar as truthlikeness is the best explanation of\nthis convergence.", "\nAnother critical point was that the divide et impera strategy\ncannot offer independent support to realism since it is tailor-made to\nsuit realism: it is the fact that the very same present theory is used\nboth to identify which parts of past theories were\nempirically successful and which parts were (approximately)\ntrue that accounts for the realists’ wrong impression that these\nparts coincide (Stanford 2006). He says:", "\n\n\nWith this strategy of analysis, an impressive retrospective\nconvergence between our judgements of the sources of a past\ntheory’s success and the things it ‘got right’ about\nthe world is virtually guaranteed: it is the very fact that some\nfeatures of a past theory survive in our present account of nature\nthat leads the realist both to regard them as true\nand to believe that they were the sources of the rejected\ntheory’s success or effectiveness. So the apparent convergence\nof truth and the sources of success in past theories is easily\nexplained by the simple fact that both kinds of retrospective\njudgements have a common source in our present beliefs about nature.\n(2006: 166)\n", "\nIt has been claimed by Psillos (2009) that the foregoing objection is\nmisguided. The problem is this. There are the theories scientists\ncurrently endorse and there are the theories that had been endorsed in\nthe past. Some (but not all) of them were empirically successful\n(perhaps for long periods of time). They were empirically successful\nirrespective of the fact that, subsequently, they came to be replaced\nby others. This replacement was a contingent matter that had to do\nwith the fact that the world did not fully co-operate with the then\nextant theories: some of their predictions failed; or the theories\nbecame overly ad hoc or complicated in their attempt to accommodate\nanomalies, or what have you. The replacement of theories by others\ndoes not cancel out the fact that the replaced theories were\nempirically successful. Even if scientists had somehow failed to come\nup with new theories, the old theories would not have ceased to be\nsuccessful. So success is one thing, replacement is another.", "\nHence, it is one thing to inquire into what features of some past\ntheories accounted for their success and quite another to ask whether\nthese features were such that they were retained in\nsubsequent theories of the same domain. These are two independent\nissues and they can be dealt with (both conceptually and historically)\nindependently. One should start with some past theories\nand—bracketing the question of their replacement—try to\nidentify, on independent grounds, the sources of their empirical\nsuccess; that is, to identify those theoretical constituents of the\ntheories that fuelled their successes. When a past theory has been, as\nit were, anatomised, we can then ask the independent question\nof whether there is any sense in which the sources of success of a\npast theory that the anatomy has identified are present in our current\ntheories. It’s not, then, the case that the current theory is\nthe common source for the identification of the successful parts of a\npast theory and of its truthlike parts.", "\nThe transition from Newton’s theory of gravity to\nEinstein’s illustrates this point. Einstein took it for granted\nthat Newton’s theory of gravity (aided by perturbation theory)\ncould account for 531 arc-second per century of the perturbation of\nMercury’s perihelion. Not only were the empirical successes of\nNewton’s theory identified independently of the successor\ntheory, but also some key theoretical components of Newton’s\ntheory—the law of attraction and the claim that the\ngravitational effects from the planets on each other were a\nsignificant cause of the deviations from their predicted\norbits—were taken to be broadly correct and explanatory (of at\nleast part) of the successes. Einstein could clearly identify the\nsources of successes of Newton’s theory independently of his own\nalternative theory and it is precisely for this reason that he\ninsisted that he had to recover Newton’s law of attraction (a\nkey source of the Newtonian success) as a limiting case of his own\nGTR. He could then show that his new theory could do both: it could\nrecover the (independently identified) sources of successes of\nNewton’s theory (in the form of the law of attraction)\nand account for its failures by identifying further causal\nfactors (the curvature of space-time) that account for the\ndiscrepancies between the predicted orbits of planets (by\nNewton’s theory of gravity) and the observed\n trajectories.[6]", "\nApart from Stanford’s case against the divide et impera\nmove, the latter has become the target of criticism—among\nothers—by Timothy Lyons.\n [7]\n Lyons (2006) focuses his critique on Psillos’s criterion\nfor the conditions under which a hypothesis indispensably contributes\nto the derivation of novel predictions. In his (1999: 100) Psillos\nsays:", "\n\nSuppose that \\(H\\) together with another set of hypotheses \\(H'\\)\n(and some auxiliaries A) entail a\nprediction \\(P\\). \\(H\\) indispensably contributes to the\ngeneration of \\(P\\) if \\(H'\\) and A alone cannot\nyield \\(P\\) and no other available hypothesis \\(H^*\\) which\nis consistent with \\(H'\\) and A can replace \\(H\\) without\nloss in the relevant derivation of \\(P\\). \n", "\nLyons interprets this passage—as well as Psillos’s\nsubsequent claim that \\(H^*\\) must satisfy some “natural epistemic\nconstraints”, such as being “independently motivated, non\nad hoc, potentially explanatory etc.” (ibid.)—as providing\nthe following criterion for the essential role of hypothesis \\(H\\) in the\nderivation of prediction \\(P\\):", "\nFor \\(H\\) to be essential [for the derivation of \\(P\\)]:", "\nThus construed, Lyons criticizes Psillos’ criterion for\nessentiality, as being “superfluous, unmotivated, and therefore\ninappropriate” (2006: 541). Briefly put, his point is that\ncondition 3 “unacceptably overshoots” the realist’s\ngoal, since the absence of an alternative \\(H^*\\) has “no bearing\nwhatsoever on whether \\(H\\) itself contributed to, was deployed\nin, the derivation of a given prediction” (2006: 540). Besides,\nLyons states that condition 3 is so vague that it is “simply\ninapplicable” (2006: 542). According to Mario Alai’s\n(2021) summary of Lyons’s point, condition 3 doesn’t\nspecify (a) when the alternative hypothesis \\(H^*\\) must\nor must not be available, (b) what ‘potentially\nexplanatory etc.’ means and (c) whether\n\\(H'\\) and \\(A\\) must be essential too. In addition;\n(d) it doesn’t state whether \\(H^*\\) is allowed to lead to\nlosses of other confirmed predictions and (e) whether \\(H^*\\)\nshould be consistent with those elements of \\(H'\\)\nand \\(A\\), which, though they are ‘essential’ for other\npredictions, they are dispensable when it comes to the derivation of\nthe prediction under scrutiny. Based on these points, Lyons suggests\nthat even if realists might hold onto conditions 1 and 2 above,\ncondition 3 has to be abandoned, thereby isolating “the\ndeployment realist’s fundamental insight”, viz., that\ncredit should be attributed to those posits that\nactually—as opposed to essentially—have\nbeen deployed in the derivation of empirical predictions (2006,543).\n", "\nIn reply to Lyons, Peter Vickers (2017) and Alai (2021) have defended\nthe divide et impera move against the PI by suggesting the\nfollowing refinement of condition 3 (let’s call it\n3′):", "\nAccording to Vickers, when realists are presented with an instance of\na (seemingly) success-inducing-yet-false hypothesis, all they need to\ndo is to show that the specific hypothesis does not satisfy the above\ncondition. It should be noted, however, that this, in essence, is the\nstrategy recommended by Psillos in his 1994, where he aimed to show,\nusing specific cases, that various assumptions such as that heat is a\nmaterial substance in the case of the caloric theory of heat, do not\nmerit realist commitment, because there are weaker assumptions that\nfuel the derivation of successful predictions. ", "\nAlai claims that substituting condition 3′ for\ncondition 3 is an improvement of the divide et impera move,\nfor not only does condition 3′ perform the task\nthat Psillos had in mind, but also escapes from Lyons’\ncriticisms (2021: 188). To begin with, condition\n3′ is said not to suffer from\nthe (alleged) vagueness of condition 3, for according to Alai:\n(a) there is no question about when the alternative\n\\(H^*\\) is available; (b) there is no need to specify\nwhat ‘explanatory’ means; and (c) it is not\nrequired that \\(H'\\) and \\(A\\) are also essential. In\naddition, (d) condition 3′ allows that\n\\(H^*\\) may lead to losses of other confirmed predictions and (e),\nsince 3′ excludes only hypotheses \\(H^*\\) which are\nentailed by \\(H\\), \\(H^*\\) are ipso facto consistent with\n\\(H'\\) and \\(A\\).", "\nNow, it is rather evident that condition 3′ is neither\nsuperfluous nor unmotivated, since as Alai (2021, 188) stressed it is\nmotivated by a plausible epistemic principle associated with the\nOccam’s razor:", "\n\nin abductions we can assume only what is essential, i.e., the weakest\nhypothesis sufficient to explain a given effect; but if a hypotheses\n[sic], although deployed, was not essential in deriving [the novel\nprediction at hand], it is not essential in explaining its derivation\neither; therefore deployment realists need not (and must not) be\ncommitted to its truth. \n", "\nIn sum, contra Lyons, condition 3΄ is both\nepistemologically motivated as well as indispensable for the proper\napplication of the divide et impera move. ", "\nThe ‘Vickers-Alai’ refinement of the divide et\nimpera move has not been uncontested. It has been criticized on\nprincipled grounds, as well as for not being sufficient in dealing\nwith PI-style challenges. For instance, Dean Peters (2014) argues\ninter alia that Vickers’ criterion for essentiality\ncannot account for the unificatory aspect of scientific theorizing,\nwhereas Florian Boge (2021) and Dana Tulodziecki (2021) have provided\nnew historical counterexamples—within the field of nuclear\nphysics and phychometry, and the 19th century miasma theory\nof disease, respectively—that cannot be handled, or so it is\nargued, by the ‘Vickers-Alai’ criterion. ", "\nIt should also be noted that, according to Vickers himself, the\nemployment of condition 3′ in dealing with PI\nseems to bring scientific realism dangerously close to structural\nrealism. As has already been said, Vickers’s recipe for handling\na PI-style challenge is roughly the following: take the (false)\nhypothesis \\(H\\) that, according to the anti-realist, is employed\nin the derivation of a prediction \\(P\\), identify an\n(uncontested) \\(H^*\\) which is entailed by \\(H\\) and show\nthat \\(H^*\\) is enough for the derivation of \\(P\\). This\nrecipe goes a long way in disarming Lyon’s objection. And yet,\nVickers notes, an even weaker hypothesis \\(H^{**}\\) is available, viz., that\nfor the prediction of P only the mathematical structure of \\(H^*\\) is\nrequired. But then, “only the very abstract\n‘structure’ truly merits realist commitment, as structural\nrealists like to claim” (2017: 3227). If we take\n‘structure’ to be identified with the Ramsey sentence of a\ngiven theory (see the next section), then Vickers’ concern is,\nat least prima facie, a plausible one. For the Ramsey\nsentence of a theory is obviously entailed by the latter and, as is\nwell known, any theory and its Ramsey sentence have exactly the same\nobservational consequences. Hence, it seems that the employment of\ncondition 3′ forces realists to restrict their\ncommitment solely towards the Ramsey sentences of their favoured\ntheories. In reply, however, it should be stressed that though\nVickers’s concern is prima facie warranted, it is far\nfrom conclusive. In fact, after raising his concern, Vickers\ndoesn’t further explore it, whereas Alai (2021: 211–212) has\nargued that from the mere application of condition\n3′ “it doesn’t follow that every\nhypothesis is dispensable in favor of its Ramsey sentence”." ], "subsection_title": "2.6 Criticisms of Divide et Impera" }, { "content": [ "\nAn instance of the divide et impera strategy is structural\nrealism. This view has been associated with John Worrall (1989), who\nrevived the relationist account of theory-change that emerged in the\nbeginning of the twentieth century. In opposition to scientific\nrealism, structural realism restricts the cognitive content of\nscientific theories to their mathematical structure together with\ntheir empirical consequences. But, in opposition to instrumentalism,\nstructural realism suggests that the mathematical structure of a\ntheory represents the structure of the world (real relations between\nthings). Against PI, structural realism contends that there is\ncontinuity in theory-change, but this continuity is (again) at the\nlevel of mathematical structure. Hence, the ‘carried over’\nmathematical structure of the theory correctly represents the\nstructure of the world and this best explains the predictive success\nof a\n theory.[8]", "\nStructural realism was independently developed in the 1970s by Grover\nMaxwell (1970a, 1970b) in an attempt to show that the Ramsey-sentence\napproach to theories need not lead to instrumentalism.\nRamsey-sentences go back to a seminal idea by Frank Ramsey (1929). To\nget the Ramsey-sentence \\(^{R}T\\) of a (finitely axiomatisable) theory\nT we conjoin the axioms of T in a single sentence,\nreplace all theoretical predicates with distinct variables \\(u_i\\),\nand bind these variables by placing an equal number of existential\nquantifiers \\(\\exists u_i\\) in front of the resulting formula. Suppose\nthat the theory T is represented as T\n(\\(t_1\\),…, \\(t_n\\); \\(o_1\\),…, \\(o_m\\)), where\nT is a purely logical \\(m+n\\)-predicate. The Ramsey-sentence\n\\(^{R}T\\) of T is:", "\nThe Ramsey-sentence \\(^{R}T\\) that replaces theory T has\nexactly the same observational consequences as T; it can play\nthe same role as T in reasoning; it is truth-evaluable if\nthere are entities that satisfy it; but since it dispenses altogether\nwith theoretical vocabulary and refers to whatever entities satisfy it\nonly by means of quantifiers, it was taken to remove the issue of the\nreference of theoretical terms/predicates. ‘Structural\nrealism’ was suggested to be the view that: i) scientific\ntheories issue in existential commitments to unobservable entities and\nii) all non-observational knowledge of unobservables is structural\nknowledge, i.e., knowledge not of their first-order (or\nintrinsic) properties, but rather of their higher-order (or\nstructural) properties. The key idea here was that a Ramsey-sentence\nsatisfies both conditions (i) and (ii). So we might say that, if true,\nthe Ramsey-sentence \\(^{R}T\\) gives us knowledge of the structure of\nthe world: there is a certain structure which satisfies the\nRamsey-sentence and the structure of the world (or of the relevant\nworldly domain) is isomorphic to this structure.", "\nThough initially Worrall’s version of structural realism was\ndifferent from Maxwell’s, being focused on—and motivated\nby—Poincaré’s argument for structural\ncontinuity in theory-change, in later work Worrall came to adopt the\nRamsey-sentence version of structural realism (see appendix IV of\nZahar 2001).", "\nA key problem with Ramsey-sentence realism is that though a\nRamsey-sentence of a theory may be empirically inadequate, and hence\nfalse, if it is empirically adequate (if, that is, the\nstructure of observable phenomena is embedded in one of its models),\nthen it is bound to be true. For, as Max Newman (1928) first noted in\nrelation to Russell’s (1927) structuralism, given some\ncardinality constraints, it is guaranteed that there is an\ninterpretation of the variables of \\(^{R}T\\) in the theory’s\nintended\n domain.[9]", "\nMore recently, David Papineau (2010) has argued that if we identify\nthe theory with its Ramsey-sentence, it can be argued that past\ntheories are approximately true if there are entities which satisfy,\nor nearly satisfy, their Ramsey-sentences. The advantage of this move,\naccording to Papineau, is that the issue of referential failure is\nbypassed when assessing theories for approximate truth, since the\nRamsey sentence replaces the theoretical terms with existentially\nbound variables. But as Papineau (2010: 381) admits, the force of the\nhistorical challenge to realism is not thereby thwarted. For it may\nwell be the case that the Ramsey-sentences of most past theories are\nnot satisfied (not even nearly\n so).[10]" ], "subsection_title": "2.7 Structural Realism" }, { "content": [ "\nIn the more recent literature, there has been considerable debate as\nto how exactly we should understand PI. There are those, like Anjan\nChakravartty who take it that PI is an Induction. He says:", "\n\n\nPI can … be described as a two-step worry. First, there is an\nassertion to the effect that the history of science contains an\nimpressive graveyard of theories that were previously believed [to be\ntrue], but subsequently judged to be false … Second, there is\nan induction on the basis of this assertion, whose conclusion is that\ncurrent theories are likely future occupants of the same graveyard.\n(2008: 152)\n", "\nYet, it is plausible to think that qua an inductive argument,\nhistory-based pessimism is bound to fail. The key point here is that\nthe sampling of theories which constitute the inductive evidence is\nneither random nor otherwise representative of theories in\ngeneral.", "\nIt has been argued that, seen as an inductive argument, PI is\nfallacious: it commits the base-rate fallacy (cf. Lewis 2001). If in\nthe past there have been many more false theories than true ones, (if,\nin other words, truth has been rare), it cannot be concluded that\nthere is no connection between success and truth. Take S to\nstand for Success and not-S to stand for failure.\nAnalogously, take T to stand for truth of theory T\nand not-T for falsity of theory T. Assume also that\nthe probability that a theory is unsuccessful given that it is true is\nzero \\((\\textrm{Prob}({\\textrm{not-}S}\\mid T)=0)\\) and that the\nprobability that a theory is successful given that it is false is\n0.05 \\((\\textrm{Prob}(S\\mid {\\textrm{not-}T})=0.05)\\). Assume that is,\nthat there is a very high True Positives (successful but true) rate\nand a small False Positives (successful but false theories) rate. We\nmay then ask the question: How likely is it that a theory is true,\ngiven that it is successful? That is, what is the posterior\nprobability \\(\\textrm{Prob}(T\\mid S)\\)?", "\nThis answer is indeterminate if we don’t take into account the\nbase-rate of truth, viz., the incidence rate of truth in the\npopulation of theories. If the base rate is very low (let’s\nassume that only 1 in 50 theories have been true), then it is\nunlikely that T is true given success.\n\\(\\textrm{Prob}(T\\mid S)\\) would be around 0.3. But this does not imply\nsomething about the connection between success and truth. It is still\nthe case that the false positives are low and that the true positives\nhigh. The low probability is due to the fact that truth is rare (or\nthat falsity is much more frequent). For \\(\\textrm{Prob}(T\\mid S)\\) to be\nhigh, it must be the case that \\(\\textrm{Prob}(T)\\) is not too small.\nBut if \\(\\textrm{Prob}(T)\\) is low, it can dominate over a high\nlikelihood of true positives and lead to a very low posterior\nprobability \\(\\textrm{Prob}(T\\mid S)\\). Similarly, the probability that a\ntheory is false given that it is successful (i.e.,\n\\(\\textrm{Prob}({\\textrm{not-}T}\\mid S))\\) may be high simply because\nthere are a lot more false theories than true ones. As Peter Lewis put\nit:", "\n\n\nAt a given time in the past, it may well be that false theories vastly\noutnumber true theories. In that case, even if only a small proportion\nof false theories are successful, and even if a large proportion of\ntrue theories are successful, the successful false theories may\noutnumber the successful true theories. So the fact that successful\nfalse theories outnumber successful true theories at some time does\nnothing to undermine the reliability of success as a test for truth at\nthat time, let alone at other times (2001: 376–7).\n", "\nSeen in this light, PI does not discredit the reliability of success\nas a test for truth of a theory; it merely points to the fact that\ntruth is scarce among past\n theories.[11]", "\nChallenging the inductive credentials of PI has acquired a life of its\nown. A standard objection (cf. Mizrahi 2013) is that theories are not\nuniform enough to allow an inductive generalization of the form\n“seen one, seen them all”. That is, theories are diverse\nenough over time, structure and content not to allow us to take a few\nof them—not picked randomly—as representative of all and\nto project the characteristics shared by those picked to all theories\nin general. In particular, the list that Laudan produced is not a\nrandom sample of theories. They are all before the twentieth century\nand all have been chosen solely on the basis that they had had some\nsuccesses (irrespective of how robust these successes were). An\nargument of the form:", "\nwould be a weak inductive argument because", "\n\n\nit fails to provide grounds for projecting the property of the\nobserved members of the reference class to unobserved members of the\nreference class. (Mizrahi 2013: 3219)\n", "\nThings would be different, if we had a random sampling of theories.\nMizrahi (2013: 3221–3222) collected 124 instances of\n‘theory’ from various sources and picked at random 40 of\nthem. These 40 were then divided into three groups: accepted theories,\nabandoned theories and debated theories. Of those 40 theories, 15%\nwere abandoned and 12% debated. Mizrahi then notes that these randomly\nselected data cannot justify an inductively drawn conclusion that most\nsuccessful theories are false. On the contrary, an optimistic\ninduction would be more warranted:", "\nMizrahi has come back to the issue of random sampling and has\nattempted to show that the empirical evidence is against PI:", "\n\n\nIf the history of science were a graveyard of dead theories and\nabandoned posits, then random samples of scientific theories and\ntheoretical posits would contain significantly more dead theories and\nabandoned posits than live theories and accepted posits.\n\n\nIt is not the case that random samples of scientific theories and\ntheoretical posits contain significantly more dead theories and\nabandoned posits than live theories and accepted posits.\n\n\nTherefore, It is not the case that the history of science is a\ngraveyard of dead theories and abandoned posits. (2016: 267)\n", "\nA similar argument has been defended by Park (2011). We may call it,\nthe explosion argument: Most key theoretical terms of successful\ntheories of the twentieth century refer “in the light of current\ntheories”. But then, “most central terms of successful\npast theories refer”, the reason being that there are far more\ntwentieth century theories than theories in total. This is because\n“the body of scientific knowledge exploded in the twentieth\ncentury with far more human and technological resources” (2011:\n79).", "\nLet’s call this broad way to challenge the inductive credentials\nof the pessimistic argument ‘the Privilege-for-current-theories\nstrategy’. This has been adopted by Michael Devitt (2007) too,\nthough restricted to entities. Devitt, who takes realism to be a\nposition concerning the existence of unobservables, noted that the\nright question to ask is this: ‘What is the “success\nratio” of past theories?’, where the “success\nratio” is “the ratio of the determinately existents to the\ndeterminately nonexistents + indeterminates”. Asserting a\nprivilege for current science, he claims that “we are now\nmuch better at finding out about unobservables”.\nAccording to him, then, it is “fairly indubitable” that\nthe historical record shows “improvement over time in our\nsuccess ratio for unobservables’.", "\nIn a similar fashion but focusing on current theories, Doppelt (2007)\nclaims that realists should confine their commitment to the\napproximate truth of current best theories, where best theories are\nthose that are both most successful and well established. The\nasymmetry between current best theories and past ones is such that the\nsuccess of current theories is of a different kind than the\nsuccess of past theories. The difference, Doppelt assumes, is so big\nthat the success of current theories can only be explained by assuming\nthat they are approximately true, whereas the explanation of the\nsuccess of past theories does not require this commitment.", "\nIf this is right, there is sufficient qualitative distance between\npast theories and current best ones to block", "\n\n\nany pessimistic induction from the successful-but-false superseded\ntheories to the likelihood that our most successful and\nwell-established current theories are also probably false. (Doppelt\n2007: 110).\n", "\nThe key difference, Doppelt argues, is that", "\n\n\nour best current theories enjoy a singular degree of empirical\nconfirmation impossible for their predecessors, given their ignorance\nof so many kinds of phenomena and dimensions of nature discovered by\nour best current theories.\n", "\nThis singular degree of empirical confirmation amounts to raising the\nstandards of empirical success to a level unreachable by past theories\n(cf. 2007: 112).", "\nThe advocate of PI can argue that past ‘best theories’\nalso raised and met the standards of empirical success, which\ninductively supports the conclusion that current best theories will be\nsuperseded by others which will meet even higher standards of success.\nDoppelt’s reply is that this new version of PI “should not\nbe given a free pass as though it were on a par with the original\npessimistic induction” the reason being that “in the\nhistory of the sciences, there is greater continuity in standards of\nempirical success than in the theories taken to realize them”.\nHence, the standards of empirical success change slower than theories.\nHence, it is not very likely that current standards of empirical\nsuccess will change any time soon.", "\nIt has been argued, however, that Doppelt cannot explain the novel\npredictive success of past theories without arguing that they had\ntruthlike constituents (cf. Alai 2017). Besides, as Alai puts it,\n“current best theories explain the (empirical) success of\ndiscarded ones only to the extent that they show that the latter were\npartly true” (2017: 3282).", "\nThe ‘Privilege-for-current-theories strategy’ has been\nsupported by Ludwig Fahrbach (2011). The key point of this strategy is\nthat the history of science does not offer a representative sample of\nthe totality of theories that should be used to feed the historical\npessimism of PI. In order to substantiate this, Fahrbach suggested,\nbased on extensive bibliometric data, that over the last three\ncenturies the number of papers published by scientists as well as the\nnumber of scientists themselves have grown exponentially,\nwith a doubling rate of 15–20 years. Hence, he claims, the past\ntheories that feed the historical premise of PI were produced during\nthe time of the first 5% of all scientific work ever done by\nscientists. As such the sample is totally unrepresentative of theories\nin total; and hence the pessimistic conclusion, viz., that current\ntheories are likely to be false and abandoned in due course, is\ninductively unwarranted. Moreover, Fahrbach argues, the vast majority\nof theories enunciated in the last 50–80 years, (which\nconstitute the vast majority of scientific work ever produced) are\nstill with us. Hence, as he puts it,", "\n\n\n(t)he anti-realist will have a hard time finding even one or two\nconvincing examples of similarly successful theories that were\naccepted in the last 50–80 years for some time, but later\nabandoned. (2011: 152)\n", "\nSince there have been practically no changes “among our best\n(i.e., most successful) theories”, Fahrbach suggests", "\n\n\nan optimistic meta-induction to the effect that they will remain\nstable in the future, i.e., all their empirical consequences which\nscientists will ever have occasion to compare with results from\nobservation at any time in the future are true. (2011: 153)\n", "\nThe conclusion is that the PI is unsound: “its conclusion that\nmany of our current best scientific theories will fail empirically in\nthe future cannot be drawn” (2011: 153).", "\nA key assumption of the foregoing argument is that there is a strong\nconnection between the amount of scientific work (as measured by the\nnumber of journal articles) and the degree of success of the best\nscientific theories. But this can be contested on the grounds that\nit’s a lot easier to publish currently than it was in the\nseventeenth century and that current research is more tightly\nconnected to the defense of a single theoretical paradigm than before.\nThis might well be a sign of maturity of current science but, as it\nstands, it does not show that the present theoretical paradigm is not\nsubject to radical change. Florian Müller (2015) put the point in\nterms of decreasing marginal revenues. The correlation between\nincreased scientific work and scientific progress, which is assumed by\nFahrbach may not be strong enough:", "\n\n\nIt seems more plausible to expect decreasing marginal revenues of\nscientific work since it usually takes much less time to establish\nvery basic results than to make progress in a very advanced state of\nscience. (Müller 2015: 404)\n", "\nThe ‘Privilege-for-current-theories strategy’ can be\nfurther challenged on the grounds that it requires some\n“fundamental difference between the theories we currently\naccept, and the once successful theories we have since rejected”\n(Wray 2013: 4325). As Brad Wray (2013) has argued Fahrbach’s\nstrategy is doomed to fail because the argument from exponential\ngrowth could be repeated at former periods too, thereby undermining\nitself. Imagine that we are back in 1950 and we look at the period\nbetween 1890 and 1950. We could then argue, along Farhbach’s\nlines, that the pre-1890 theories (which were false and abandoned)\nwere an unrepresentative sample of all theories and that the recent\ntheories (1890–1950) are by far the most theories until 1950 and\nthat, since most of them have not been abandoned (by 1950), they are\nlikely to remain impervious to theory-change. Or imagine that we are\nfurther back in 1890 and look at the theories of the period\n1830–1890. We could run the same argument about those theories,\nviz, that they are likely to survive theory change. But if we look at\nthe historical pattern, they did not survive; nor did the\ntheories between 1890–1950. By the same token, we should not\nexpect current theories to survive theory-change.", "\nIs there room for defending an epistemic privilege for current\nscience? Two points are worth making. The first is that it’s\nhard to defend some kind of epistemic privilege of current science if\nthe realist argument against PI stays only at a level of statistics\n(even assuming that there can be statistics over theories). If there\nis an epistemic privilege of current science in relation to past\nscience, it is not a matter of quantity but of quality. The\nissue is not specifying how likely it is that an arbitrary current\ntheory T be true, given the evidence of the past record of\nscience. The issue, instead, is how a specific scientific\ntheory—a real theory that describes and explains certain\nwell-founded worldly phenomena—is supported by the evidence\nthere is for it. If we look at the matter from this perspective, we\nshould look at case-histories and not at the history of science at\nlarge. The evidence there is for specific theory T (e.g., the\nDarwinian synthesis or GTR etc.) need not be affected by past failures\nin the theoretical understanding of the world in general. The reason\nis that there is local epistemic privilege, that is, privilege over\npast relevant theories concerning first-order evidence and specific\nmethods.", "\nThe second point is this. Wray’s argument against Fahrbach is,\nin effect, that there can be a temporal meta-(meta-)induction which\nundermines at each time t (or period Dt) the\nprivilege that scientific theories at t or Dt are\nsupposed to have. So Wray’s point is this: at each time\n\\(t_{i}\\) (or period \\(Dt_{i}\\)), scientists claim that their theories\nare not subject to radical change at subsequent times; but if we look\nat the pattern of theory change over time, the history of science\nshows that there have been subsequent times \\(t_{i}+1\\) (or periods\n\\({Dt}_{i}+1\\)) such that the theories accepted at \\(t_{i}\\) were\nconsidered false and abandoned. Hence, he takes it that at no time\n\\(t_{i}\\) are scientists justified in accepting their theories as not\nbeing subject to radical change in the future. But this kind of\nargument is open to the following criticism. It assumes, as it were,\nunit-homogeneity, viz., that science at all times \\(t_{i}\\) (and all\nperiods \\({Dt}_{i}\\)) is the same when it comes to how far it is from\nthe truth. Only on this assumption can it be argued that at\nno time can scientists claim that their theories are not subject to\nradical change. For if there are senses in which subsequent theories\nare closer to the truth than their predecessors, it is not equally\nlikely that they will be overturned as their predecessors were.", "\nThe point, then, is that though at each time \\(t_{i}\\) (or period\n\\({Dt}_{i}\\)) scientists might well claim that their theories are not\nsubject to radical change at subsequent times, they are not equally\njustified in making this claim! There might well be times\n\\(t_{i}\\) (or periods \\({Dt}_{i}\\)) in which scientists are more\njustified in making the claims that their theories are not subject to\nradical change at subsequent times simply because they have reasons to\nbelieve that their theories are truer than their predecessors. To give\nan example: if Wray’s argument is right then Einstein’s\nGTR is as likely to be overthrown at future time \\(t_{2100}\\) as was\nAristotle’s crystalline spheres theory in past time\n\\(t_{-300}\\). But this is odd. It totally ignores the fact that all\navailable evidence renders GTR closer to the truth than the simply\nfalse Aristotelian theory. In other words, that GTR has substantial\ntruth-content makes it less likely to be radically revised in the\nfuture.", "\nAn analogous point was made by Park (2016). He defined what he called\nProportional Pessimism as the view that “as theories\nare discarded, the inductive rationale for concluding that the next\ntheories will be discarded grows stronger” (2016: 835). This\nview entails that the more theories have been discarded before\nT is discarded, the more justified we are in thinking that\nT is likely to be discarded. However, it is also the case\nthat based on their greater success, we are more justified to take\nnewer theories to be more likely to be truthlike than older ones. We\nthen reach a paradoxical situation: we are justified to take newer\ntheories to be both more probable than older ones and more likely to\nbe abandoned than older ones.", "\nIf an inductive rendering of historical pessimism fails, would a\ndeductive rendering fare better? Could PI be considered at least as a\nvalid deductive argument? Wray (2015: 65) interprets the\noriginal argument by Laudan as being deductive. And he notes", "\n\n\nas far as Laudan is concerned, a single successful theory that is\nfalse would falsify the realist claim that (all) successful theories\nare true; and a single successful theory that refers to a non-existent\ntype of entity would falsify the realist claim that (all) successful\ntheories have genuinely referring theoretical terms.\n", "\nBut if this is the intent of the argument, history plays no\nrole in it. All that is needed is a single counterexample, past\nor present. This, it should be noted, is an endemic problem with all\nattempts to render PI as a deductive argument. Müller, for\ninstance, notes that the fundamental problem raised by PI is\n“simply that successful theories can be false”. He\nadds:", "\n\n\nEven just one counterexample (as long as it is not explained away)\nundermines the claim that truth is the best explanation for the\nsuccess of theories as it calls into question the explanatory\nconnection in general. (2015: 399)\n", "\nThus put, the history of past failures plays no role in PI. Any\ncounterexample, even one concerning a current theory, will do.", "\nHow is it best to understand the realist theses that the history of\nscience is supposed to undermine? Mizrahi (2013: 3224) notes that the\nrealist claim is not meant to be a universal statement. As he puts\nit:", "\n\n\nSuccess may be a reliable indicator of (approximate) truth, but this\nis compatible with some instances of successful theories that turn out\nnot to be approximately true. In other words, that a theory is\nsuccessful is a reason to believe that it is approximately true, but\nit is not a conclusive proof that the theory is approximately\ntrue.\n", "\nThe relation between success and (approximate) truth, in this sense,\nis more like the relation between flying and being a bird: flying\ncharacterizes birds even if kiwis do not fly. If this is so, then\nthere is need for more than one counter-example for the realist thesis\nto be undermined.", "\nA recent attempt to render PI as a deductive argument is by Timothy\nLyons. He (2016b) takes realism to issue in the following\nmeta-hypothesis: “our successful scientific theories\nare (approximately) true”. He then reconstructs PI thus:", "\nThis is supposed to be a deductive argument against the ‘meta\nhypothesis’. But in his argument the history of science plays no\nrole. All that is needed for the argument above to be sound is a\nsingle instance of a successful theory that is not true. A\nsingle non-white swan is enough to falsify the hypothesis ‘All\nswans are white’—there is no point in arguing here: the\nmore, the merrier! In a similar fashion, it doesn’t add much to\nargument (D) to claim", "\n\n\nthe quest to empirically increase the quantity of instances (…)\nis rather to secure the soundness of the modus tollens, to\nsecure the truth of the pivotal second premise, the claim that there\nare counterinstances to the realist meta-hypothesis. (Lyons 2016b:\n566)\n", "\nIn any case, a critical question is: can some\nfalse-but-rigorously-empirically-successful theories justifiably be\ndeemed truthlike from the point of view of successor theories? This\nquestion is hard to answer without looking at actual cases in the\nhistory of science. The general point, made by Vickers (2017) is that\nit is not enough for the challenger of realism to identify some\ncomponents of past theories which were contributing to their successes\nsuch that they were not retained in subsequent theories. The\nchallenger of realism should show that false components “merit\nrealist commitment”. If they do not, “ (…) that is\nenough to answer the historical challenge”.", "\nMore generally, the search for a generic form of the pessimistic\nX-duction (In-duction or De-duction) has yielded the\nfollowing problem: If the argument is inductive, it is at best weak.\nIf the argument is deductive, even if it is taken to be sound, it\nmakes the role of the history of science\n irrelevant.[12]" ], "subsection_title": "2.8 Induction or Deduction?" } ] } ]

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[ "\nWhy are you always lying? Why did the Ancient Egyptians mummify their\ndead? Should Huck Finn have turned Jim in? Why is she selling her car?\nQuestions that ask for reasons, and in particular, reasons for action,\nare among the commonest questions humans have. Philosophers have\nsought to understand the nature of such reasons. Most contemporary\nphilosophers start by distinguishing two types of reason for action:\n“normative” reasons—that is, reasons which, very\nroughly, favour or justify an action, as judged by a well-informed,\nimpartial observer; and “motivating” reasons—which,\nagain roughly, are reasons the “agent” (that is, the\nperson acting) takes to favour and justify her action and that guides\nher in acting. But there are, in addition, “explanatory”\nreasons, reasons that explain an action without necessarily justifying\nit and without being the reasons that motivated the agent.", "\nA clear understanding of reasons for action in their justifying,\nmotivating and explanatory functions is of relevance to the philosophy\nof action, to ethics, political philosophy and the philosophy of law.\nThe essential issues about reasons—what they are, and how they\nrelate to human actions—are of wider concern.", "\nThis entry examines the various accounts that philosophers have given\nof these different kinds of reasons and their interconnections, as\nwell as the disagreements among them about these matters. The focus\nwill be on reasons for acting—what are commonly called\n“practical reasons”, leaving aside questions that are\nspecific to other reasons, for instance, reasons for believing,\nwanting, feeling emotions, and having attitudes, such as hope or\nresentment." ]

[ { "content_title": "1. The Variety of Reasons", "sub_toc": [] }, { "content_title": "2. Normative Reasons", "sub_toc": [] }, { "content_title": "3. Motivating and Explanatory Reasons", "sub_toc": [ "3.1 Motivating Reasons", "3.2 Explanatory Reasons" ] }, { "content_title": "4. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nHumans engage in practical reasoning: they deliberate about what to do\nand how to do it. And they often act in light of reasons which can\nthen explain their actions, and may also justify them.\nThese ideas go back to Plato (Protagoras and\nRepublic, Book 4) and Aristotle (De Anima, see esp.\nIII.10; see also Price 2011). They have been a constant theme in\ndiscussions of the character of human behaviour in the history of\nphilosophy. In the 18th century, David Hume and Immanuel\nKant offered radically different views about the role and importance\nof Reason (the faculty of reason) in guiding and justifying human\nactions. Their contributions remain influential today, but in the\nsecond half of the 20th century, the focus shifted from\ndiscussion of the faculty of reason to discussion of the very concept\nof a reason and to questions about different kinds of reasons and\ntheir interconnections.", "\nAs mentioned in the introduction, a distinction is commonly drawn in\ncontemporary debates between two kinds of reason:\n“normative” and “motivating” reasons. Jonathan\nDancy (2000: 20ff. and Appendix) discusses the history of this\ndistinction. It is sometimes said to date back to Francis Hutcheson\n(1730), though Dancy notes that the modern distinction does not\nclearly map on to earlier ones. Whatever its history, the distinction\nis now accepted by most if not all contemporary philosophers who write\non this topic (Raz 1975; Smith 1994; Parfit 1997; and Dancy 1995\nand 2000 are representative examples).", "\nA normative reason is a reason (for someone) to act—in T. M.\nScanlon’s phrase, “a consideration that counts in favour\nof” someone’s acting in a certain way (1998 and 2004). A\nmotivating reason is a reason for which someone does something, a\nreason that, in the agent’s eyes, counts in favour of her acting\nin a certain way. When an agent acts motivated by a reason, she acts\n“in light of that reason” and the reason will be a premise\nin the practical reasoning, if any, that leads to the action.\nMotivating reasons can also figure in explanations of actions that\ncite agents’ reasons, what are called “reason\nexplanations” of actions. Because of that, they are sometimes\ncalled “explanatory” reasons, though we shall scrutinize\nthis description more carefully below.", "\nDancy suggests that the distinction between different types of reason\nis best understood as one between questions we can ask about them (a\nview that he finds also in Baier 1958):", "\n\nIf we do speak in this way, of motivating and normative reasons, this\nshould not be taken to suggest that there are two sorts of reason, the\nsort that motivate and the sort that are good. There are not. There\nare just two questions that we use the single notion of a reason to\nanswer. When I call a reason “motivating”, all that I am\ndoing is issuing a reminder that the focus of our attention is on\nmatters of motivation, for the moment. When I call it\n“normative”, again all that I am doing is stressing that\nwe are currently thinking about whether it is a good reason, one that\nfavours acting in the way proposed (Dancy 2000: 2–3).\n", "\nAccording to this suggestion, there is a single notion of a reason\nthat is used to answer different questions: the question whether there\nis a reason for someone to do something (normative) and the question\nwhat someone’s reason for acting is (motivating). For instance,\nwe can ask whether there is a reason for the government of a country\nto tax sugary drinks (normative), and ask also for the\ngovernment’s reason for actually taxing the drinks (motivating).\nThe same reason may answer both questions: the reason that favours\ntaxing the drink may be that the tax will help reduce child obesity;\nand that may also be the government’s reason for taxing the\ndrinks. In that case, the government is motivated to tax drinks by a\nreason that there is for it to do so, the reason that may justify its\ndoing so. But we don’t always act for the reasons that favour\nour actions. For instance, the government may tax sugary drinks\nbecause (or in part because) some of its members own shares in a\ncompany that sells low-sugar drinks. In that case, the reason for\nwhich the government decides to tax sugary drinks is not, or not\nsolely, the reason that favours its doing so. The distinction between\nnormative and motivating reasons, therefore, enables us to separate\nthe question what reasons motivate agents to act (a psychological\nquestion) and the question whether those are good reasons: reasons\nthat favour and justify their acting thus.", "\nIf this way of understanding talk about different kinds of reasons is\nright, perhaps the picture is more complex than the dichotomy of\n“normative vs. motivating” suggests. For there seem to be\nat least three distinct questions about the relation between reasons\nand actions. There are questions about whether there is a reason that\nfavours someone’s action; questions about what reason motivates\nsomeone to act; and also questions about what reasons explain his\naction. Consider the behaviour of Othello in Shakespeare’s play\nof the same name. Othello kills Desdemona in the belief, induced by\nIago, that she has been unfaithful to him. The tragedy, however, is\nthat she has not: Desdemona is innocent, she loves Othello and is\nfaithful to him. Clearly, there is no reason that justifies the\nmurder: no normative reason. But there are two things we can say about\nOthello’s reason for acting and his action. One is that Othello\nis motivated to kill Desdemona by the (putative) fact that Desdemona\nhas been unfaithful. The other is that we can explain his action of\nkilling her by citing the fact that he believes that Desdemona has\nbeen unfaithful. So here we seem to have two different reasons: one\nthat motivates—the (putative) fact that Desdemona has been\nunfaithful; and one that explains—the (actual) fact that Othello\nbelieves that she has. We can distinguish, then, between the reason\nthat explains Othello’s action (the fact that he believes that\nDesdemona has been unfaithful) and the reason that motivates him to\nact (the alleged infidelity itself). It might be tempting to think\nthat Othello’s motivating reason is just the fact that he\nbelieves that Desdemona has been unfaithful. We shall examine below\nreasons why the temptation should be resisted. Because of this, the\naccount that follows proceeds by dividing reasons for action initially\ninto two categories: normative and motivating-explanatory. It will\nthen present the case for treating motivating and explanatory reasons\nseparately.", "\nUntil relatively recently, the distinction between different kinds of\nreasons was assumed, whether explicitly or not, to imply that these\nreasons were things of different kinds. Normative reasons were\nconceived of as facts, and so were regarded as mind-independent: the facts\nare what they are independently of whether anyone knows them or thinks\nabout them. By contrast, motivating and explanatory reasons were\nconceived of as mental states of agents and, as such, as entities\nwhich depend on someone’s thinking or believing certain things\n(Audi 2001 and Mele 2003 are representative examples—but see\nalso Mele 2013). In recent years, however, this assumption has been\nchallenged, giving rise to a number of disputes about the ontology of\nreasons—that is, disputes about what kind of thing or things\nreasons are. As we examine different kinds of reasons, we shall\nencounter some of these ontological debates. We start with normative\nreasons." ], "section_title": "1. The Variety of Reasons", "subsections": [] }, { "main_content": [ "\nA reason is said to be a “normative reason” for acting\nbecause it favours someone’s acting. But what does it mean to\nsay that a reason “favours” an action? One way of\nunderstanding this claim is in terms of justification: a reason\njustifies or makes it right for someone to act in a certain way. This\nis why normative reasons are also called “justifying”\nreasons.", "\nThe term “normative reason” derives from the idea that\nthere are norms, principles or codes that prescribe actions: they make\nit right or wrong to do certain things. To take a relatively trivial,\nculturally-determined example, the norms of etiquette in some\ncountries say that when meeting someone for the first time, the right\nthing to do is to shake hands, whereas in other countries, the right\nthing to do is to kiss them on both cheeks. So the fact that in the UK\nshaking hands is the norm of etiquette is a reason that makes it right\nto do so in the UK when you meet someone for the first time. There are\nmany other, often more important, norms, principles and values,\nimplicit or explicit, that make it right to do or not do certain\nthings. The existence of these norms or values depends on a variety of\nthings: logical and natural relations, conventions, rules and\nregulations, etc. And the norms or values may be moral, prudential,\nlegal, hedonic (relating to pleasure) or of some other kind. There are\nnormative reasons, therefore, corresponding to the variety of values\nand norms: normative reasons that are moral, prudential, legal,\nhedonic, etc.", "\nThe variety of norms or values that underpin normative reasons\nrequires some modification of the claim that reasons that favour\nactions make those actions right. If a reason favours my doing\nsomething, then I have a “pro-tanto” reason to do\nit: it is pro tanto (i.e., to that extent) right for me to do\nit. But there may be a reason against my doing it: a\npro-tanto reason not to do it. The fact that a joke is funny\nmay be a reason to tell it; but the fact that it’ll embarrass\nsomeone may be a reason against doing so. In that case, I have a\npro-tanto reason to tell the joke and a different\npro-tanto reason not to tell it. Whether it would be right\nfor me to tell the joke, whether I have an\n“all-things-considered” reason to tell it, will depend on\nwhether either of the reasons is stronger than the other. If so, that\nreason will override or “defeat” the other reason. Only if\nthe pro-tanto reason for telling the joke is undefeated will\nit be right or justified all things considered for me to tell the\njoke.", "\nBut what sort of thing is a normative reason? What gives reasons their\nnormative force, so that they can make it right for someone to do\nsomething? And what determines whether there is such a reason and to\nwhom it applies? These and related questions have received much\nphilosophical attention in recent years.", "\nThere is consensus that normative reasons are facts (Raz 1975; Scanlon\n1998), though the consensus is not universal. The question is\ncomplicated by disagreement about what facts of any kind are: are they\nconcrete or abstract entities? Is a fact the same as the corresponding\ntrue proposition, or is the fact the “truth-maker” of the\nproposition? Are there any facts other than empirical facts, e.g.,\nlogical, mathematical, moral or aesthetic facts? For instance, it has\nbeen argued, notably by John Mackie, that there are no moral facts.\nMackie argued against the existence of moral facts partially on the\ngrounds that they would be metaphysically “queer”. He held\nthat, if there are any moral facts, they would have to be both\nobjective and necessarily motivating to those who are aware of them,\nand he claimed that it was wholly implausible that anything could have\nsuch properties (Mackie 1977). If Mackie is right that there are no\nmoral facts, then either moral reasons are not normative reasons; or\nat least some normative reasons namely, moral reasons, are not\nfacts.", "\nAmong those who hold that normative reasons are facts, some hold that\nfacts are true propositions and hence that reasons are also true\npropositions (Darwall 1983; Smith 1994; Scanlon 1998). Others reject\nthe idea that normative reasons could be true propositions; for\ninstance, Dancy (2000) does so on the grounds that propositions are\nabstract and representational (they represent the way the world is)\nbut reasons must be concrete and non-representational (they are ways\nthe world is). These problems are complex and have many ramifications\nbut we cannot and perhaps need not resolve them here because the view\nthat normative reasons are facts is generally meant to imply a very\nundemanding notion of facts. Thus Raz says that, “when saying\nthat facts are reasons” he is using the term “fact”\nto designate ", "\n\nthat in virtue of which true or justified statements are true or\njustified. By “fact” is meant simply that which can be\ndesignated by the use of the operator “the fact that\n…”. (1975: 17–18)\n", "\nThere is less consensus about the basis of the normativity of\npractical reasons: the capacity of reasons to justify actions. On one\nproposal, the normativity of practical reasons depends on the\ngoodness, intrinsic or instrumental, of doing what there is reason to\ndo. This view is associated with Aristotle who, in the Nicomachean\nEthics, links what is right to do (what one has reason to do)\nwith what is conducive to the good (whether intrinsically or\ninstrumentally). The idea was prevalent among medieval philosophers,\nfor example Thomas Aquinas (Summa Theologiae, 1a, q.82), and\nin the 20th century it was central to Elizabeth\nAnscombe’s discussion of intentional actions (1957). Many\ncontemporary philosophers (e.g., Raz 1999 and Dancy 2000) have offered\naccounts of the normativity of reasons in line with this idea, so a\nreason is a normative reason to do something because it picks the\ngood-making features or value of the relevant action. As Raz puts it,\n“reasons are facts in virtue of which (…) actions are\ngood in some respect and to some degree” (1999: 23). There are\nother accounts that ground the normativity of reasons on the concept of\nrationality (e.g., Korsgaard 1996, who is influenced by Kant; and\nSmith 1994 and Gert 2004, who base their accounts on the concept of\nthe “ideally rational agent”). A different proposal, which\nechos Hume’s views about the relation between reason and\npassions, claims that the normativity of reasons is based on their\nrelation to our desires. Accordingly, what one has reason to do\ndepends ultimately on one’s desires and motivations. Roughly,\nsomeone’s having a reason to act requires their having some\nmotivation that would be served by acting in the way favoured by the\nputative reason. The motivation may be such things as desires, plans,\nlong-standing projects or values. And it may be something the agent\nactually has, or something she would have if she reasoned properly\nfrom her current motivations. Desire-based accounts of this sort have\nbeen defended recently by Williams 1979 and 1989, Schroeder 2008, and\nGoldman 2009.", "\nHowever we explain their normativity, normative reasons should be\ncapable of motivating agents to act—though of course they may\noften fail to do so. Therefore, any account of normative reasons must\noffer a plausible explanation of the relationship between the\nnormativity of reasons and the capacity that reasons have to motivate\nagents to act. An account must explain how thinking that there is a\nreason for me to do something can motivate me to act, and to act\nfor that reason. Desire-based accounts of reasons might seem\nto have the edge here. If the reasons that apply to me depend on my\nantecedent motivations (desires, plans), then it is plausible that I\nshall be motivated to do what I believe will contribute to the\nsatisfaction or furthering of those motivations. But desire-based\naccounts fare less well in accommodating another central claim about\nnormative reasons. For it seems equally plausible that there are\nreasons (for instance, moral reasons) that apply to agents regardless\nof their motivations. Arguably, we all have reason to do what morality\ndictates, whether or not we are (or would be, if we reasoned\nconsistently from our current motivations), motivated by those\nreasons. (For a detailed discussion of these issues, see the entry on\n reasons for action: internal vs. external.)", "\nThe claim that something is a normative reason for action is generally\nthought to be a “relational” claim: it establishes a\nrelation between a fact, an agent, and an action kind. The relation is\nthat of “being a reason for” (see Raz 1975 and 1998, Dancy\n2004, Cuneo 2007). For example, the fact that a person has ingested a\nlethal poison may be a reason for the paramedics to give the person an\nantidote. According to some, the relation involves not just a person,\na reason and an action, but more aspects: a time, circumstances, etc.\n(Skorupski 2010 and Scanlon 2014). This relational view of reasons\ngives a minimal sense in which claims about normative reasons are\n“agent-relative”: they relate agents to reasons (a more\nsubstantial sense is developed in Nagel 1970 and 1986 and discussed in\nthe entry\n reasons for action: agent-neutral vs. agent-relative).\n But even in the minimal sense, the agent-relativity of reasons raises\nquestions about the conditions that determine when a reason for acting\napplies to a particular agent. One such question, mentioned in the\nprevious paragraph, is whether the reasons that apply to you depend on\nyour desires and motivations. Another question is whether they depend\non your knowledge and beliefs. To go back to the example of Othello:\non the one hand it seems clear that Othello has no reason to kill\nDesdemona, and the reason he thinks he has—that she is\nunfaithful—is no reason at all. On the other hand, it might seem\nthat Othello does have a reason, for he believes that Desdemona is\nunfaithful and believes, moreover, that his reputation has been\ndamaged and needs to be restored with her death. And those beliefs\nappear to give him a reason to do what he does, at least from his\nperspective.", "\nPhilosophers disagree about how to reconcile these competing claims.\nOne way of resolving the tension between them is to say that Othello\nhas no normative reason to kill Desdemona but has a\nmotivating reason: viz., the falsehood he believes. Smith\n(1994) and Dancy (2000) both offer suggestions of this sort (though\nSmith calls Othello’s beliefs “his normative\nreasons”). Others, e.g., Schroeder (2008), talk about\n“objective” and “subjective” normative\nreasons, so that Othello would have a subjective normative reason but\nno objective normative reason to kill Desdemona. These positions are\nall “objectivist” in that they presuppose that whether an\nagent has an (objective) normative reason to act depends solely on the\nfacts and not on the agent’s beliefs (see Williams 1979).\n“Perspectivists” take a different view. They claim that\nwhether someone has a normative reason to do something is not\nindependent of her perspective, which includes her beliefs (see Fantl\nand McGrath 2009 and Gibbons 2010). Certain cases of ignorance and\nmistake help to bring out their view. A much discussed case introduced\nby Williams (1979) concerns an agent, call him Sam, who orders a gin\nand tonic and, when served a glass with a liquid that looks like gin\nand tonic, forms the belief that it is gin and tonic, when in fact the\nglass contains petrol and ice. Does Sam have a normative reason to\ndrink what’s in the glass? The objectivists say that the answer\ndepends solely on the facts, so Sam has no normative reason to drink\nthe liquid. Perspectivists, by contrast, say that given Sam’s\nperspective, which includes a reasonable (though false) belief that\nthe liquid is gin and tonic, Sam does have a normative reason to drink\nwhat’s in the glass.", "\nPerspectivists tend to defend their position by reference to\nconsiderations of rationality. Agents are often in situations in which\nthey don’t know all the relevant facts. And yet, perspectivists\nsay, these agents often do what is reasonable or rational for them to\ndo, given their perspective. If, as seems plausible, one acts\nrationally when one acts for reasons that make it rational for one to\nso act, then perspectivism must be right: agents who act in error or\nignorance often act rationally and, when they do, they act for reasons\nthey have to do what they do. In short, as perspectivism says, the\nnormative reasons an agent has depend in an important sense on his\nepistemic perspective, and so an agent can have a normative reason\nthat is a false belief. Similar arguments are articulated in relation\nto justification (though often questions about rationality and\njustification are run together). Surely, the argument goes, what an\nagent is justified in doing depends on whether he has reasons that\njustify his doing that thing. But, again, there are cases where an\nagent would surely be justified in doing something even though there\nare conclusive reasons against doing it; and he would be justified\nprecisely because he doesn’t know about those reasons. For\nexample, the fact that the cake is poisoned is a conclusive reason not\nto offer it to your guests. But you might be justified in offering it\nto them, the perspectivist says, if you don’t know about the\npoison. So considerations about the justification of action also seem\nto support perspectivism because they show that what reasons you have\ndepends on your perspective.", "\nThere are several moves that an opponent of perspectivism can make in\nresponse here. She can concede that an agent who acts according to his\nepistemic perspective but guided by a false belief acts rationally,\nbut deny that acting rationally requires that the agent act for\nnormative reasons. Instead, the objectivist may say, acting rationally\nonly requires acting in a way that is consistent with one’s\nbeliefs, so long as these are themselves rational. This response could\nrely on, e.g., Derek Parfit’s conception of rationality, which\nrequires acting guided by one’s real or apparent reasons (Parfit\n2001, an “apparent reason” is a falsehood that an agent\nbelieves to be true, and treats as a normative reason but which is not\na normative reason; see also Kolodny 2005). As for the justification\nof action, the objectivist can deny that the actions of agents who act\nin ignorance or guided by a mistaken belief are justified. Whether the\naction is justified, the objectivist will say, depends purely on\nwhether the facts make it the right thing to do, and not on the\nagent’s beliefs. So in the cake example above, the action of\noffering the poisoned cake to his guests is not justified: there is no\nnormative reason that makes it the right thing to do. And that is so\nregardless of what the agent knows or believes. A different question,\nthe objectivist will say, is whether an agent who does something wrong\nbecause of his false beliefs or ignorance is himself justified and/or\nblameworthy for so acting. If our host’s ignorance about the\npoison is not culpable, he will most likely not be blameworthy and the\nagent may be justified. But in saying this, the objectivist need not\nbe conceding that the action was justified, i.e., done for a\nnormative reason, only that the host may be exculpated for doing the\nwrong thing. As Austin noted (1957), we must distinguish between a\njustification and an excuse. When accused of wrongdoing, one may offer\na justification, which aims to show that in fact the thing done was\nright because there was reason for doing it. Alternatively, one may\noffer an excuse: admit that one did the wrong thing but plead to be\npartly or wholly exculpated—for instance, because it was done\nout of ignorance or mistake. (There are other excuses, such as\naccidents or coercion but those need not concern us here.) To return\nto the cake example, our agent might be excused for doing the wrong\nthing (poisoning the guests) if he was non-culpably ignorant about the\npoison. By contrast, it might be possible to give a justification for\npoisoning the guests: for instance, that they were in fact some\npsychopaths intent on causing his family mortal harm. If so, poisoning\nthem with the cake may have been the right thing to do and, depending\non whether our agent was aware of the relevant facts and acted guided\nby them, it may be that he was justified in poisoning them.\nThis example shows how questions about normative reasons bear directly\non the justification of agents, as distinct from the justification of\ntheir actions, by raising questions about motivating reasons, to which\nwe now turn." ], "section_title": "2. Normative Reasons", "subsections": [] }, { "main_content": [ "\nIt was suggested above that although reasons are traditionally divided\ninto two kinds: normative and motivating/explanatory, there may be a\ncase for distinguishing between motivating reasons and explanatory\nreasons. The basis for doing so was said to be the existence of three\ndistinct questions about reasons: whether a reason favours an\naction; whether a reason motivates an agent; and whether a\nreason explains an agent’s action. Accordingly, the\nthought goes, we should recognise three kinds of reasons: normative,\nmotivating and explanatory. This way of classifying reasons is\nexplicitly accepted and/or defended by various authors (Baier 1958;\nAlvarez 2007, 2009a, 2010; Hieronymi 2011); and it is hinted at, using\ndifferent terminology, by others (Smith 1994; Darwall 2003; Mantel\n2014).", "\nThis three-part classification may seem excessively refined: is it\nreally necessary or advantageous to distinguish motivating and\nexplanatory reasons? After all, a motivating reason can always explain\nthe action that it motivates, so the question of what reason motivates\nan agent and what reason explains her action are, one might think,\nfundamentally the same. If so, “motivating” and\n“explanatory” are surely just different labels for the\nsame kind of reason, at least in contexts of intentional actions. And\nthere appears to be no obvious advantage in regarding motivating and\nexplanatory reasons as distinct kinds.", "\nThese considerations against a three-part classification of reasons,\nthough plausible, are not decisive. First, the fact that the same\nreason can answer different questions does not show that the questions\nare not importantly different and, consequently that the reasons that\nanswer those questions are not of different kinds. We saw that to be\nso for normative and motivating reasons: the same reason can answer a\nquestion about motivation and one about justification. And yet, that\ndoes not blur the difference between those questions, nor does it\nundermine the importance of recognising the corresponding two kinds of\nreasons. So the same may be true for motivating and explanatory\nreasons.", "\nSecond, even if the same reason sometimes answers the two questions\nabout motivation and explanation, this is not always so. Although a\nreason that motivates an action can always explain it, a reason that\ncan explain the action is not always the reason that motivates it. For\nexample, that he is jealous is a reason that explains why Othello\nkills Desdemona. But that is not the reason that motivates him to kill\nher. This example may appear not to be to the point because an\nexplanation that refers to his jealousy is not a\nrationalisation of Othello’s action: it doesn’t\nexplain his action by citing his reason. That is right and\nyet the example still shows that not all reasons that explain by\nciting psychological factors, e.g., jealousy, are reasons that\nmotivate. Moreover, knowing that Othello acted out of jealousy gives\nan indication of Othello’s reason (Desdemona’s suspected\nunfaithfulness) and yet the reason of jealousy is not Othello’s\nmotivating reason. Besides, the explaining and motivating reasons may\ndiffer even in cases where the reason that explains makes reference to\nthe reason that motivates. For suppose that John punches Peter because\nhe finds out that Peter has betrayed him. The fact that John knows\nthat Peter has betrayed him is a reason that explains John’s\naction. This is an explanatory reason. But that fact about\nJohn’s mental state of knowledge is not the reason for which\nJohn punches Peter. That reason is a fact about Peter, namely that he\nhas betrayed John. That is the reason that motivates John to punch\nPeter—his motivating reason. So in this case we have two\ndifferent (though related) reasons: that Peter has betrayed John and\nthat John knows that Peter has betrayed him, which play different\nroles. One reason motivates John to punch Peter (the betrayal); and\nthe other explains why he does it (the knowledge of the betrayal). To\nbe sure, the latter reason explains by reference to the former.\nNonetheless, these are different reasons that answer different questions about\nmotivation and explanation, respectively.", "\nBut isn’t this distinction superficial? After all, the fact that\nmotivates John, i.e., that Peter has betrayed him, can also explain\nJohn’s action—we need not cite John’s knowledge of\nthis fact. As we shall see below\n (3.2),\n this is controversial: some philosophers think that all reason\nexplanations require reference to psychological states of the agent.\nBe that as it may, consider a different example. The fact that Othello\nbelieves that Desdemona is unfaithful explains why he kills her. But\nthe fact that he believes in her infidelity is not the reason in light\nof which he kills her, the reason that, in his eyes, favours killing\nher. What he takes to favour killing her is the (putative) fact that\nshe is unfaithful. Again, these are importantly different reasons: for\nit can be the case that Othello believes that Desdemona is unfaithful\nwithout it being the case that she is, and vice versa.\nMoreover, since Desdemona is not unfaithful, that putative fact cannot\nbe what explains Othello’s action because something that is not\nthe case cannot explain anything—though, as we shall see below\n(also\n 3.2),\n this view of explanation has proved controversial too.", "\nThe intricacies of these controversies suggest that it may indeed be\nhelpful to keep apart questions of motivation and questions of\nexplanation even when we are dealing with reason explanations of\naction. The advantages of drawing this distinction will be spelled out\nin examining debates concerning motivating reasons and the explanation\nof action. We shall see there that apparently competing claims about\nmotivating reasons and the explanation of action are often best\nunderstood and resolved as claims about motivating or explanatory\nreasons, respectively. The following passage, in which Stephen Darwall\ncomments on a putative disagreement between Dancy and Michael Smith,\nhelps to illustrate the point of the distinction:", "\n\n“Motivating reason” in Dancy’s pen means the\nagent’s reason, the (believed, putative) fact in light of which\nthe agent acted. Smith, however, uses “the agent’s\nnormative reason” to refer to this and “motivating\nreason” to refer to the desire/belief combination necessary to\nexplain behavior teleologically. (Darwall 2003: 442–3)\n", "\nUsing the terminology introduced above, we can reframe Darwall’s\npoint as follows. When Dancy says that reasons are (putative) facts\nthat agents take to favour their actions, he is talking about\nmotivating reasons. By contrast, when Smith says that reasons are\ncombinations of mental states of believing and desiring, he is talking\nabout explanatory reasons. So Dancy and Smith may not be disagreeing\nbut, rather, using the same term, “motivating reason” for\ntwo different concepts: Dancy is using it to refer to the reasons in\nlight of which an agent acts, while Smith is using it to refer to the\nreasons that explain an agent’s act.", "\nOne of the most intensely debated issues concerning both motivating\nand explanatory reasons is their ontology: what kind of thing are\nthese reasons? The philosophical literature of the last half of the\n20th century was premised on the more or less explicit\nassumption that motivating and explanatory reasons, which at the time\nwere not normally explicitly distinguished, were psychological\nentities, in particular, mental states of agents, such as\nOthello’s believing that Desdemona is unfaithful to him. This\nview of the ontology of reasons is often called “Psychologism”.\nThat consensus began to dissolve at the turn of the century and\npsychologism came under sustained attack. Opposition to it is\nvariously labelled “non-psychologism”,\n“externalism” and “objectivism”. The last two\nlabels are also used for a variety of other philosophical views so, to\navoid confusion, I will stick with the term\n“Non-psychologism”.", "\nDonald Davidson’s 1963 paper, “Actions, Reasons, and\nCauses” is often cited as the locus classicus of\npsychologism. In that paper he characterises a reason as follows:", "\n\nC1. R is a primary reason why an agent performed the action\nA under the description d only if R consists of a\npro attitude of the agent toward actions with a certain property, and\na belief of the agent that A, under the description d,\nhas that property. (1963: 687)\n", "\nA primary reason is a combination of two mental states: a pro-attitude\nand a belief. These “primary reasons” are, in effect,\nexplanatory reasons: reasons that explain actions. Davidson defended\nthe “desire-belief” model of action explanation, according\nto which reasons are states of believing and desiring that explain\nactions because they cause them. This model is at the centre of\nDavidson’s account of intentional action, which he characterises\nas an event caused “in the right way” by a primary reason.\nDavidson’s paper was highly influential; as a result,\npsychologism became the dominant view for both motivating and\nexplanatory reasons, which, as noted above, were then not explicitly\ndistinguished.", "\nPsychologism is very appealing. For it seems right that when an agent\nacts for a reason, he acts motivated by an end that he desires (an end\ntowards which he has a “pro-attitude”) and guided by a\nbelief about how to achieve that end. Because of this, it is possible\nto explain his action by citing his desiring and his believing the\nrelevant things. To return to our example, we can explain why Othello\nkills Desdemona by citing his wanting to defend his honour and his\nbelieving that, given that Desdemona has been unfaithful, killing her\nis the only way to do so. And this sort of explanation in terms of\nstates of belief and desire supports the relevant counterfactuals: had\nOthello not believed that she had been unfaithful or had he not\nbelieved that killing her was the only way to defend his honour, he\nwouldn’t have killed her, even if he had still wanted to restore\nhis reputation; and had he not cared about his reputation, he\nwouldn’t have killed her, despite his beliefs about her betrayal\nand what was necessary to defend his honour. This sort of\nconsideration led to widespread acceptance of the view that\nexplanatory reasons are mental states and, since the latter were not\ndistinguished from motivating reasons, it also led to the view that\nmotivating reasons are mental states.", "\nAmong psychologists, some say that motivating and explanatory reasons\nare mental or psychological facts, rather than mental states.\nThis is because psychologism holds that reasons are mental states such\nas “an agent’s believing (or wanting, or knowing)\nsomething”, and it is easy to move from the claim that\nsomeone’s reason is his believing something (a mental\nstate) to the claim that his reason is that he believes\nsomething (a psychological fact). For instance, it is easy to move\nfrom saying that Joe’s reason for running is his believing that\nhe’s late (a mental state) to saying that Joe’s reason is\n(the fact) that he believes that he’s late.", "\nThese defenders of psychologism do not on the face of it disagree with\nchampions of non-psychologism about the ontology of these reasons. For\npsychological facts are not themselves mental states, though they are\nfacts about mental states. But they still disagree with non-psychologists about\nwhat these reasons are. Because of this, we need a way to\ndistinguish between psychologism and non-psychologism other than in terms of\nontology—the kind of thing that each camp says reasons\nare—in order to capture the deeper disagreement between them.\nPerhaps a better way to do so is to say that psychologism holds that\nmotivating and explanatory reasons are mental states or facts about\nmental states of agents, whereas non-psychologism says that\nmotivating and explanatory reasons, like normative reasons, are facts\nabout all sorts of things, including mental states of agents.", "\nThe following sections examine current debates about psychologism, and\nother issues, concerning motivating and explanatory reasons. It\ndoes so separately for reasons of each kind, as that will facilitate\nclarity in the various debates. We start with motivating reasons." ], "section_title": "3. Motivating and Explanatory Reasons", "subsections": [ { "content": [ "\nThe term “motivating reason” is a semi-technical\nphilosophical term. As we saw above, the phrase is now generally used\nin the literature to refer to a reason that the agent takes to favour\nher action, and in light of which she acts. Motivating reasons are\nalso considerations that can figure as premises in the practical\nreasoning, if any, that leads to action. The terms “agential\nreason”, “the agent’s normative reason”,\n“subjective (normative) reasons”, “the agent’s\noperative reason” and “possessed reasons” are\nsometimes also used to capture this notion of a reason. Because the\nconcept is somewhat technical, further clarification is needed.", "\nFirst, the current use of the term excludes some otherwise plausible\ncandidates from being motivating reasons. For instance,\nsomeone’s goal or intention in acting, which is something the\nagent desires (to grow vegetables; to kill Desdemona) seem to be\nmotivating factors in acting. But because these are not considerations\nin light of which one acts, they do not fall under the category\n“motivating reasons” as currently understood (but see Audi\n1993). Similarly, a state of desiring (wanting to have one’s\nrevenge), or a motive or emotion (for instance, jealousy) can be\nstates “that encompass motivation”, to use Mele’s\nphrase, 2003: if one is in any such a mental state, one is thereby\nmotivated to act. But again, these are not motivating reasons in the\nsense at issue because they are not considerations that the agent\ntakes to favour acting. Moreover, many hold that states of desiring\nare often grounded in considerations about the goodness or value of\nwhat is desired—a view defended by Anscombe 1957, Nagel 1970,\nQuinn 1993, Raz 1999, and Schueler 2003, among others. When this is\nso, the motivating reasons both for wanting and for acting accordingly\nare the considerations about the goodness or rightness of what is\ndesired. To continue with our example, Othello’s desire to kill\nDesdemona is grounded in the thoughts that she is unfaithful to him\nand that killing her is a fitting way to restore his reputation (even\nif the desire is intensified by his jealousy). These considerations\nare his reason for wanting to kill her and his reason for doing so. In\nshort, what Othello desires (to kill Desdemona), his goal (to redress\nher betrayal), his state of desiring those things, or his motive\n(jealousy) are things that motivate him to kill Desdemona but they are\nnot his motivating reasons in the semi-technical sense of the phrase\nstipulated above. His motivating reasons, if we agree he has any, are,\nrather, the putative facts that she is unfaithful to him and that\nkilling her is a fitting way to restore his reputation.", "\nSecond, talk of an agent’s motivating reason, or of “the\nagent’s reason”, always involves some simplification.\nIt’s a simplification because an agent may be motivated to act\nby more than one reason: I may hoover the house early in the morning\nboth because I won’t have time to do it later and because it\nwill annoy my inconsiderate neighbour. Moreover, a fact will seem a\nreason for me to act only in combination with other facts: that I\nwon’t have time to hoover later will seem a reason to do it now\nonly if the house needs hovering. So my reason is, arguably, a\ncombination of at least two facts: that the house needs hovering and\nthat I won’t be able to do it later. Finally, I may consider a\nfact that counts against acting, for instance, that hoovering early\nwill also disturb my other neighbour, who is very considerate. If I\nstill decide to hoover, I do not act for that “con-reason”\nbut, arguably, I am still guided by it if I give it some weight in my\ndeliberation (see Ruben 2009 for a discussion of\n“con-reasons”).", "\nSince motivating reasons are considerations that an agent takes to\nfavour acting, and since the reasons that favour acting are facts, it\nmight seem that motivating reasons are also facts or at least putative\nfacts, rather than mental states. However, the view that they are\nmental states was, as noted earlier, the dominant view till the turn\nof the 20th century, and it is still very popular today. A\nseemingly compelling argument for adopting psychologism for motivating\nreasons is the following. For a reason to motivate you it must be a\nreason you have. This does not require that the reason should\ngenuinely apply to you. But it requires that you “possess”\nthe reason: you must know or believe the consideration that\nconstitutes the reason. And this appears to support the view that\nreasons are mental states of agents, or facts about those states. The\nopponent of psychologism about motivating reasons can respond by\nnoting that, while it is true that, for it to motivate you to act, you\nmust know or believe the thing that constitutes a reason, that\ndoesn’t imply that the reason that motivates you is your knowing\nor believing what you do. Rather your reason is what is known or\nbelieved: a (putative) fact. To put the point differently, motivating\nreasons are the contents of mental states but not mental states\nthemselves. This argument about motivating reasons is not, therefore,\ndecisive for psychologism. And in fact, there are several compelling\narguments against psychologism.", "\nA very influential argument, found in Dancy 1995 and 2000, focuses on\nthe relation between normative and motivating reasons. The argument\nhinges on Dancy’s claim that any account of motivating reasons\nmust meet what he calls “the normative constraint”:", "\n\nThis [normative constraint] requires that a motivating reason, that in\nthe light of which one acts, must be the sort of thing that is capable\nof being among the reasons in favour of so acting; it must, in this\nsense, be possible to act for a good reason. (2000: 103)\n", "\nDancy’s charge against psychologism about motivating reasons is\nthat it fails to meet the constraint because, if psychologism is\nright, we can never act for a good reason. Why? In order to act for a\ngood reason, we need to act for a reason that is or could be a fact.\nHowever, according to psychologism, motivating reasons are mental\nstates. If so, the reasons for which we act are mental states, and not\nfacts. If, by contrast, motivating reasons were, say facts and\nputative facts, then some of the reasons for which we act would be\nfacts, and it would follow that we can, and sometimes do, act for a\ngood reason. But in saying that motivating reasons are mental states,\npsychologism eliminates this possibility, for a mental state can never\nbe a fact. As Dancy puts it, psychologism has the consequence that\n“the reasons why we act can never be among the reasons in favour\nof acting” (2000: 105). The argument relies on the\n“identity thesis” about reasons: the thesis that you act\nfor a good reason, only if your motivating reason is identical to the\nnormative reason that favours your action (see Heuer 2004 for a\nhelpful explanation).", "\nDancy (2000: 106ff.) considers a possible response: that acting for a\ngood reason may simply require your motivating reason to be a mental\nstate whose content is a good reason. So, you act for a good reason if\nyour motivating reason for, say, taking your umbrella is your\nbelieving that it is raining, which is a mental state whose\ncontent—“it is raining”—is a good reason to\ntake your umbrella. The success of this response to Dancy’s\nargument is unclear. On the one hand, if the response is that the\nreasons that motivate us are the contents of our mental\nstates of believing, this meets the normative constraint but it does\nnot favour psychologism. It meets the normative constraint because the\ncontent is the fact that it is raining and that is a good\nreason. But this interpretation amounts to abandoning psychologism\nbecause the contents of mental states are not themselves mental\nstates. On the other hand, the response might be just the assertion\nthat a mental state with the right content can be a good reason for\nacting. But this does not seem so much a response to Dancy’s\nargument as a refusal to engage with it. For it remains unclear how,\naccording to this response, we can ever act for a good (i.e., a\nnormative) reason (but see Mantel 2014 for an attempt to develop the\nobjection by rejecting the identity thesis).", "\nThis brings us to another, related argument against psychologism,\nwhich is simply that consideration of what agents take their reasons\nfor acting to be, and of what they typically give and accept as their\nreasons for acting, count against psychologism. Thus, as Othello\nconsiders what to do, even while in the grip of his jealousy, his\nreasoning does not include considerations about whether he believes\nthis or that but rather considerations about what Desdemona has or has\nnot done. The things that Othello considers, then, are not his mental\nstates but rather facts, or alleged facts, about the world around him,\nin particular about Desdemona. This argument is reinforced by\nconsidering that motivating reasons are the reasons that would figure\nas premises in a reconstruction of the agent’s practical\nreasoning, if any. Again, these premises are sometimes considerations\nto the effect that one believes this or that; but much more often,\nthey are considerations about the world, about the value or goodness\nof things and people around us, the means of achieving those things,\netc. In short, although practical reasoning sometimes includes\npsychological facts about oneself among its premises, much more often\nthese premises refer to (perceived or real) facts about the world\nbeyond our minds.", "\nThese arguments lend substantial support to non-psychologism and\nsuggest that being motivated by a reason is not acting in light of, or\nguided by, a mental state, or by a fact about one’s mental\nstates. Along with other arguments, they have led many philosophers (see Alvarez 2008, 2009b, 2010; Bittner 2001; Dancy 2000, 2008; Hornsby 2007, 2008: Hyman 1999, 2015;\nMcDowell 2013; Raz 1999; Schueler 2003; Stout 1996; Stoutland 1998;\nWilliamson 2000, among others) to reject psychologism. But non-psychologism is not free from difficulties. A central problem for non-psychologism is presented by\n“error cases”. If motivating reasons are facts, then\nwhat is the agent’s reason in cases, like\nOthello’s, where the agent is in error and is motivated to act\nby a false consideration? In such a case, what the agent would give as\nhis reason—say, that Desdemona has been unfaithful—is\nfalse. So, Othello cannot act in light of the fact that Desdemona has\nbeen unfaithful. And non-psychologism does not seem to have a ready\nanswer to what the motivating reason is in these cases.", "\nNon-psychologists have offered different proposals to accommodate\nerror cases. One proposal is to say that in error cases agents act for\na reason that is a falsehood that the agent believes. So, in the\nexample above, Othello’s reason is his false belief about\nDesdemona. Note—not his believing that she’s unfaithful,\nwhich would bring us back to psychologism, but his false belief (the\ncontent). According to this proposal, then, Othello did act for a\nreason: a false belief, which is a putative fact that the agent takes\nto be a fact. The view is defended or at least endorsed by many, among\nothers: Dancy (2000, 2008, 2014), Hornsby (2007, 2008), McDowell\n(2013), Schroeder (2008), Setiya (2007), and Comesaña and\nMcGrath (2014). Jennifer Hornsby defends the view in the process of\noffering a disjunctive conception of a reason for acting, analogous to\nMcDowell’s “disjunctive conception of appearances”\n(Hornsby 2008: 251), summarized in the following passage:", "\n\nWe now have the two answers to the question What is a reason for\nacting? Reasons for acting are given when facts are\nstated: let us call these “(F)-type reasons”. Reasons for\nacting are given when it is said what an agent believes: let\nus call these “(B)-type reasons”. (2008: 247)\n", "\nThis response to problem of error cases is plausible but there are\nalso considerations against it. One such consideration is that stating\nthese alleged reasons often leads to paradox or infelicitous claims.\nFor many would argue that a claim such as “Ellie’s reason\nfor stepping on your toes is that you are stepping on her toes,\nalthough you are not stepping on her toes” is paradoxical. By\ncontrast, there is no air of paradox whatsoever in the corresponding\nclaim about Ellie’s beliefs: “Ellie believes that\nyou’re stepping on her toes although you are not”. Thus,\nUnger writes: ", "\n\nit is inconsistent to say “His reason was that the store was\ngoing to close, but it wasn’t going to close”. (1975: 208)\n", "\nIf this is right, then the operator “her reason is that\n…”, unlike “her belief is that …” is\nfactive: the truth of the propositions expressed by sentences formed\nwith “her reason is that…” requires the truth of\nthe proposition expressed with the “that” clause. This\nresponse to the error cases—that a reason can be a\nfalsehood—is therefore problematic.", "\nA related difficulty is that this view commits one to awkward claims\nabout reasons, such as Dancy’s claim that one’s reason for\nacting may be “a reason that is no reason” (Dancy 2000: 3;\nhe qualifies this with the parenthesis “no good reason, that\nis”), or Hornsby’s claim that sometimes it is the case\nthat “there was no reason to do what he did, even though he did\nit for a reason” (Hornsby 2008: 249; though again, she clarifies\nthat the first clause denies that there is an “F-type”\nreason, a fact, while the second asserts that the agent had a\n“B-type”). The awkwardness of these claims is further\nsupported by considerations about usage, for it seems that claims\nabout what someone’s reason is are often retracted and qualified\non learning that the person was mistaken concerning what he or she\nbelieved. If I say that Lisa’s reason for attending the party is\nthat James will be there, and you tell me that he won’t be at\nthe party, it would sound paradoxical if I insist that her reason is\nthat James will be at the party.", "\nThe fact that these claims about reasons are prima facie\nparadoxical or infelicitous is not a decisive argument against the\nviews that generate them, but it has led some non-psychologists to\noffer alternative accounts of error cases. One such alternative says\nthat, in error cases, an agent acts on something that he treats as a\nreason and in light of which he acts but which is in fact not a\nreason. So, in these cases an agent acts for an “apparent\nreason” (Alvarez 2010 and Williamson forthcoming). The view is\nalso defended by Parfit, who characterizes apparent reasons as\nfollows: “We have some apparent reason when we have some belief\nwhose truth would give us that reason” (2001: 25). On this view,\nan apparent motivating reason is not merely a bad reason but simply\nnot a reason. So according to this alternative, agents who act on\nfalse beliefs are motivated by something, a false belief. They treat\nthat belief as a reason and are guided by it in acting. Nonetheless,\nthat false belief is not a motivating reason because it is not a fact,\nbut merely an apparent fact, and hence only an apparent reason.", "\nIt might appear that the difference between these two\nnon-psychological alternatives boils down to just a terminological\ndispute: some philosophers choose to call these false beliefs\n“false”, “subjective”, or “bad\nreasons”, etc., while others choose to call them “apparent\nreasons”. Surely, the thought would go, terminology is a matter\nof choice and nothing of substance depends on this choice. What\nmatters is that every proposal contains clear definitions of how terms\nare being used. A response would be that some terminological choices\nare more apt than others because they reflect a more nuanced or\nprecise understanding of the relevant concept. The substantial issue\nbehind this debate seems to be whether the notion of a reason we apply\nin different contexts is a unified notion. If it is, the choice\nbetween the alternative non-psychological views outlined in the\nprevious paragraphs will depend largely on what features are taken to\nbe essential to that notion.", "\nWe noted above that most if not all accounts of acting for a\nmotivating reason require as a condition that the agent be in some\nkind of epistemic relation to the reason that motivates her. And we\nsaw also that a widespread view is that this epistemic relation is one\nof belief: for an agent to act for the reason that p, the agent must\nbelieve that p. It is this thought that led many to endorse the view\nthat reasons are mental states (often as part of the\n“desire-belief” conception of reasons for action described\nabove). But the view that mere belief is not sufficient to act for a\nreason has gained popularity in recent years. And many have argued\nthat, in order to act in light of a fact that is a reason, an agent needs to\n know the relevant fact. The view is explicitly\ndefended by Unger (1975), Hyman (1999, 2011 and 2015), Williamson\n(2000 and forthcoming), Hornsby (2007 and 2008 (as part of her\ndisjunctive conception mentioned above)), and McDowell\n(2013)—but many others also endorse it. The basic idea behind\nthis position is that an agent may act on the basis of a belief merely\nby treating that belief (i.e., what she believes) as a reason for\nacting. However, if there is a fact in virtue of which her belief is\ntrue, then she acts in light of that fact, or is guided by that fact,\nonly if she knows that fact. If the agent does not know the fact, we\ncannot say that she was guided by it (Hyman), or that she was\nresponding rationally to it (McDowell). If the agent does not know the\nfact, the argument goes, the relationship between the agent’s\nacting as she did and the fact is fortuitous, a matter of luck or\ncoincidence, and hence not sufficient for the fact to be her reason\nfor acting. And this, they argue, is so even in cases where an agent\nacts motivated by a belief that is both true and justified. For just\nas Gettier (1963) showed that having a justified true belief is not\nsufficient for having knowledge of the corresponding fact, so, these\nauthors argue, acting on a justified true belief is not enough for\nacting in light of the corresponding fact: the connection between the\nfact and the action is fortuitous. (See entries on\n the analysis of knowledge\n and\n epistemology\n for discussions of Gettier’s arguments).", "\nThose who think that acting for a reason requires merely treating\nsomething one believes as a ground, e.g., using it as a premise in\none’s reasoning, reject this characterisation of acting for a\nreason—Dancy (2011 and 2014) is an example. But defenders of the\nknowledge condition complain that Dancy’s remarks are\noff-target. For their point is that there is a notion of acting for a\nreason—arguably, the central notion—that involves the idea\nof acting guided by a fact. This notion requires not mere belief but\nknowledge of the fact that is a reason. Others have argued that it is,\nhowever, possible to accept that there is this distinctive, central\nnotion of acting for a reason but still deny that an agent needs to\nknow a fact in order to act guided by it. Dustin Locke (2015), for\nexample, argues that it is possible for someone to act guided by a\nfact that he does not know. Locke uses so-called\n“fake-barn” cases to make his point against the knowledge\ncondition. These cases are due to Alvin Goldman (1967) who developed\nthem in his defence of his theory of knowledge. Suppose that a man is\ndriving in the countryside and sees a barn. Unbeknown to him,\nhe’s driving in “fake-barn country”, which is\nlittered with fake barns: barn façades designed to look like\nreal barns. The widely held consensus is that a person in a fake-barn\nsituation who, on seeing a real barn, forms the belief that there is a\nbarn, does not know that there is a barn, even though he has a\njustified true belief to that effect. Locke uses this sort of case to\nargue that a person in this situation could, for instance, drive\ntowards a barn guided by the fact that there is a barn over there,\nwithout knowing that there is. If so, Locke claims, the agent acts for\nthe reason that there is a barn over there, since he is guided by that\nfact. Nonetheless, he doesn’t know that there is a barn. (For\nfurther discussion of practical reasoning, the knowledge condition and\nfake-barn situations see Hawthorne 2004, Brown 2008 and Neta\n2009.)", "\nThese debates about motivating reasons focus primarily on what sort of\nthing motivating reasons are and what it takes for an agent to act for\na reason. We now turn to when and how reasons explain actions." ], "subsection_title": "3.1 Motivating Reasons" }, { "content": [ "\nA person’s action may be explained in a variety of ways: by\nreference to the agent’s goal, or habits, or character traits,\nor to her reasons for acting. For instance, we may say that Jess went\nto the hospital in order to reassure her father, or that she went\nbecause she always goes on Tuesdays, or because she is a dutiful\ndaughter, or because her father was in intensive care. These\nstatements explain why Jess went to the hospital because, given\ncertain background assumptions, they enable a third person to\nunderstand Jess’s action: they make it intelligible. In the\nexamples just given, the first explanation gives us Jess’s goal\nin going to the hospital (to reassure her father), the second and\nthird place her action in the context of her habits (she does it every\nTuesday) and her character (she’s dutiful), respectively, and\nthe fourth explanation gives a reason why she did it that was\nher reason for doing it: a reason that, from her perspective,\nspoke in favour of going to the hospital (that her father was in\nintensive care). Among this variety of possible explanations (and\nthere are more), the last one is a distinctive type that is of\nparticular interest here because it is an explanation of an\nintentional action that rationalises the action: it explains the\naction by citing the agent’s reason for acting. In\nDavidson’s words:", "\n\nA reason rationalizes an action only if it leads us to see something\nthe agent saw, or thought he saw, in his action—some feature,\nconsequence, or aspect of the action the agent wanted, desired,\nprized, held dear, thought dutiful, beneficial, obligatory, or\nagreeable. (Davidson 1963: 685)\n", "\nOne argument in favour of psychologism for explanatory reasons that\nrationalise actions depends on the following idea. For a reason to be\nable to rationalise your action, that reason must be part of your\npsychology: a fact that is merely “out there” cannot\nexplain why you do anything. Your believing or knowing that fact, by\ncontrast, can explain why you act. So the reasons that explain your\nactions must be mental states (believings, knowings, etc.).", "\nIt might be responded that, although a fact cannot be a reason that\nexplains one’s action unless the person is aware of it, it does\nnot follow that the explanation of the action must mention their\nawareness of the reason. For instance, we can explain why\nJess went to the hospital by citing her reason for going, namely that\nher father had been admitted to the intensive care unit—this\npoints to something she saw in the action that made it desirable:\ne.g., that she could then be with her father in this difficult moment.\nThe explanation does not need to mention any psychological fact, such\nas the fact that she knew that her father had been admitted, even\nthough the explanation presupposes this fact. Against this suggestion,\na defender of psychologism for explanatory reasons might urge that\nthese explanations are elliptical and when fully spelled out their\nexplanans (the part of the explanation that does the explaining)\ncontains facts about what she knew or believed. But are these\nexplanations really elliptical? It seems undeniable that a person\ncannot act for the reason that p, or on the grounds that p, unless she\nstands in some epistemic relation to p: she needs to believe, know,\naccept, etc. that p. However, it does not follow that all full\nrationalisations need mention psychological facts and that, when they\ndon’t, this is because they’ve been given in elliptical\nform. Perhaps the fact that the agent knows the relevant things is\nsimply a necessary condition for her reason to be the explanans in a\nreason explanation. Or as Dancy suggests, her knowing or believing may be an\n“enabling condition” for the explanation (Dancy 2000:\n127).", "\nHowever that issue about rationalisations is decided, two things\nshould be noted. First, in “error cases”—cases when\nan agent acts on the basis of a falsehood that he believes and treats\nas a reason for acting—the explanans of a true explanation must\nbe a psychological fact. For instance, the explanation of why Othello\nkills Desdemona cannot be what he believes, that Desdemona has been\nunfaithful, but rather the fact that he believes it. This is because\nexplanations are, it is generally thought, factive: a true explanation cannot have a falsehood as its explanans: we cannot say that Othello kills Desdemona because\nshe has been unfaithful when she hasn’t. The second thing to\nnote is that, even if psychologism is right for explanatory reasons\n(that is, even if all reason explanations cite psychological facts),\nit does not follow that psychologism is right for motivating reasons\nbecause these reasons need not be the same. In other words, if one\nattends to the distinction between the roles of motivation and\nexplanation that reasons can play, there should be no temptation to\nmove from psychologism concerning explanatory reasons in some or in\nall cases, to psychologism concerning motivating reasons.", "\nNot all opponents of psychologism accept the suggestion that\nexplanatory reasons in rationalisations are mental states, or facts\nabout them, even for error cases. For example, in his 2000 book, Dancy\ndenies this and argues that we can always explain an action by\nspecifying the reason for which it was done, even when an agent acted\non a false consideration. The problem with this view is that it\ncommits Dancy to the conclusion that some reason explanations are\nnon-factive: an explanation may be true even though what does the\nexplaining is not. For instance, it commits him to saying that what\nexplains why I took my umbrella is that it was raining, even though it\nwas not raining. To most philosophers this is an unacceptable\nconclusion: surely true explanations require the truth of both the\nexplanandum (what is explained: that I took my umbrella) and the\nexplanans (that it was raining). In a recent paper (2014), Dancy has\nabandoned his earlier view that reason explanations can be non-factive\nbut he still retains his opposition to psychologism for explanatory\nreasons. So he still maintains that we can always explain an action by\nspecifying the reason for which it was done, even when the\n“reason” is some falsehood that the agent believed and in\nlight of which he acted. In those cases, he says,", "\n\nwe can say that what explains the action is that it was done for the\nreason that p, without committing ourselves to saying that\nwhat explains the action is that p. (2014: 90)\n", "\nHe adds that in such cases the reason itself “need not be the\ncase and does not make the sort of distinct contribution to the\nexplanation that would enable us to think of it as the\nexplanans” (2014: 91). Philosophers may disagree about whether\nthis new suggestion is satisfactory. Some may think that\n“Othello killed Desdemona for the reason that Desdemona had been\nunfaithful to him, although she had not been unfaithful to him”\nsounds paradoxical. Moreover, to say that the reason that explains an\naction is (the fact) that it was done for the reason that p\nenables Dancy to accommodate the view that explanations are factive.\nBut it does so at the expense of undermining his claim that the\nreasons that explain are also the reasons that motivate. For Dancy\nsays that the reason that motivates Othello is that Desdemona is\nunfaithful, while, according to this new suggestion, the reason that\nexplains his action (i.e., the explanans) is that it was done for\nthe reason that she is unfaithful.", "\nWhatever one thinks about Dancy’s new proposal it is worth\nemphasizing again that the distinction between explanatory and\nmotivating reasons enables one to bypass these issues. For one can say\nthat the reason that explains why Othello kills Desdemona is the\npsychological fact that he believes that she has been unfaithful\nwithout accepting that that is the reason that motivates him. His\nmotivating reason for killing her is the putative fact that she has\nbeen unfaithful (which, as we saw above, some would describe as merely\nan apparent reason). In short, even if some form of psychologism is\nright for explanatory reasons, it does not follow that it is right for\nmotivating reasons: the two may differ from each other in some\ncases." ], "subsection_title": "3.2 Explanatory Reasons" } ] }, { "main_content": [ "\nSpace limitations preclude detailed examination of other debates about\npractical reasons. We shall close the entry with a\nbrief description of a relatively new debate about reasons for action\nthat derives from work in the social sciences. The debate relates to\nwork in experimental psychology (some of it dating from the 1970s,\ne.g., Nisbett and Wilson 1977) that claims to identify our “real\nreasons” for acting. Briefly, experiments have shown that\nfactors such as the way items are presented in a situation of choice\ninfluence people’s choices without their being aware of this\ninfluence. For example, in some of these experiments, when faced with\na choice among what in fact are identical options, agents tend to\nchoose the item on the right. This appears to be in fact the result of\na right-hand bias in most humans. However, since people are not aware\nof this bias, when asked to justify their choice, agents cite reasons\nconcerning some alleged superior feature of their chosen option. These\nand other phenomena, such as implicit bias (which occurs when agents\ndisplay bias based on race, gender, etc. in their behaviour, while\nexplicitly denying that they endorse such bias) and others, seem to show that agents\nare motivated by reasons they are not aware of, and in ways that they are not aware of, even\nafter careful reflection on their reasons and motivations. The general\nclaim, then, is that these phenomena undermine many of our ordinary\nand philosophical assumptions about our reasons for acting, for they\nshow, it is said, that agents are often ignorant of their real reasons\nfor acting, and as a result they often “confabulate” when\nexplaining and attempting to justify their behaviour (see Hirstein\n2009). These conclusions, if right, would appear to threaten\nfundamentally the authority we seem to enjoy about our own reasons for\nacting, as well as the explanatory power of the ordinary explanations\nof action that cite the agent’s reasons for acting.", "\nThe plausibility of these conclusions depends to a large extent on\nwhether the notion of “the agent’s real reason” that\nthese studies claim to uncover is the same as the notion of a\nmotivating reason that has been examined in this entry. One suggestion\nmight be that these so-called “real reasons” are\nexplanatory but not motivating reasons. And, it has been argued that,\nwhile these explanatory reasons might make important contributions to\nexplaining our actions, in a variety of ways, this fact is compatible\nwith our ordinary psychological explanations in terms of agents’\nmotivating reasons. For instance, it may be that the sorts of reasons\nuncovered by these experiments help explain why agents are motivated\nby the reasons that they avow are their reasons for acting: the\nprevalence of a right-hand bias in most humans may explain why the\nitem on the right seems more appealing to an agent. But this is\nconsistent with the truth of the agent’s claim that her reason\nfor choosing the item is the (putative) fact that it is better than the other items\n(see Sandis 2015 for\nsuggestions along these lines).", " \nThe above is an overview of a range of\nproblems about practical reasons and their widespread significance. It\nshould be sufficient to show how the problems and their many\nramifications reach into many aspects of our lives and have important\nconsequences for our understanding of ourselves as rational\nagents." ], "section_title": "4. Conclusion", "subsections": [] } ]

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(ed.),\n1997, Indianapolis: Hackett.", "Price, A., 2011, Virtue and Reason in Plato and\nAristotle, Oxford: Oxford University Press.", "Quinn, W., 1993, “Putting Rationality in its Place”,\nreprinted in his 1994, Morality and Action, Cambridge:\nCambridge University Press, 228–255.", "Raz, J., 1975, Practical Reasoning and Norms, London:\nHutchinson & Co., reprinted, Oxford University Press, 1990 and\n1999.", "–––, 1997, “When We Are Ourselves: The\nActive and the Passive”, revised and reprinted in Engaging\nReason, J. Raz, Oxford: Oxford University Press, 1999,\n5–22.", "–––, 1999, Engaging Reason: On the Theory\nof Value and Action, Oxford: Oxford University Press.", "Ruben, D.H., 2009, “Con Reasons as Causes”, in C.\nSandis (ed.), New Essays on the Explanation of Action,\nLondon: Palgrave Macmillan, 62–74.", "Sandis, C., 2015, “Verbal Reports and “Real Reasons”: Confabulation and Conflation”, Ethical Theory and Moral Practice, 18: 267–280.", "Scanlon, T.M., 1998, What We Owe to Each Other,\nCambridge, MA: Belknap Press of Harvard University Press. ", "–––, 2004, “Reasons: A Puzzling\nDuality”, in R.J. Wallace, S. Scheffler, and M. Smith (eds.),\nReason and Value: Themes from the Moral Philosophy of Joseph\nRaz, Oxford: Oxford University Press, 231–246.", "–––, 2014, Being Realistic About\nReasons, Oxford: Oxford University Press.", "Schroeder, M., 2007, Slaves of the Passions, Oxford:\nOxford University Press.", "–––, 2008, “Having Reasons”,\nPhilosophical Studies, 139: 57–71.", "Schueler, G.F., 2003, Reasons and Purposes: Human Rationality\nand the Teleological Explanation of Action, Oxford: Oxford\nUniversity Press.", "Setiya, K., 2007, Reasons without Rationalism,\nPrinceton, NJ: Princeton University Press.", "Skorupski, J., 2002, “The Ontology of Reasons”,\nTopoi 21: 113–124.", "–––, 2010, The Domain of Reasons,\nOxford: Oxford University Press.", "Smith, M., 1994, The Moral Problem, Oxford:\nBlackwell.", "Stout, R. , 1996, Things that Happen Because They Should: A\nTeleological Approach to Action, Oxford: Oxford University\nPress.", "Stoutland, F., 1998, “The Real Reasons”, in Human\nAction, Deliberation and Causation, J. Bransen and S.E. Cuypers\n(eds.), Dordrecht: Kluwer Academic Publishers, 43–66.", "Strawson, P.F., 1949, “Truth”, Analysis,\n9(6): 83–97.", "–––, 1987, “Causation and\nExplanation”, reprinted in his 1992, Analysis and\nMetaphysics, Oxford: Oxford University Press, 109–31.", "Unger, P., 1975, Ignorance. A Case for Scepticism,\nOxford: Clarendon Press.", "Williams, B.A.O, 1979, “Internal and External\nReasons”, reprinted in his 1981, Moral Luck, Cambridge:\nCambridge University Press, 101–113.", "–––, 1989, “Internal Reasons and the\nObscurity of Blame”, in reprinted in his 1995, Making Sense\nof Humanity, Cambridge: Cambridge University Press,\n35–45.", "Williamson, T., 2000, Knowledge and its Limits, Oxford:\nOxford University Press.", "–––, forthcoming, “Acting on\nKnowledge”, in J.A. Carter, E. Gordon, and B. Jarvis (eds.),\nKnowledge-First, Oxford: Oxford University Press.", "Wilson, T.D. and R.E. Nisbett, 1978, “The Accuracy of\nVerbal Reports About the Effects of Stimuli on Evaluations and\nBehavior”, Social Psychology, 41(2):\n118–131." ]

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[ "\nWe are often told that the moral theories defended by modern\nphilosophers fall into two types. On the one hand are rationalist\npositions developed by thinkers such as Samuel Clarke, William\nWollaston, and Richard Price. The rationalists, it is said, believe\nthat reason is the basis of morality, as morality is (in some sense)\nboth grounded in and grasped by reason. On the other hand are\nsentimentalist positions championed by philosophers such as the Third\nEarl of Shaftesbury, Francis Hutcheson, and David Hume. The\nsentimentalists, it is claimed, hold that affect is the basis of\nmorality. According to the standard classification, the\nsentimentalists believe that morality has relatively little to do with\nreason, as it is (in some sense) both grounded in and discerned by\nsentiment.", "\nThomas Reid’s (1710–1796) moral philosophy does not neatly\nfit into this scheme of classification. To be sure, some characterize\nReid as a rationalist working within the tradition of Clarke and Price\n(see MacIntyre 1966 and Rawls 2000, Introduction). One can see why.\nReid, after all, affirms core rationalist claims, such as that there\nis a body of necessary moral principles that are self-evident to the\nordinary person. But there are important elements of Reid’s\nthought that do not fit the rationalist paradigm. For example, Reid\ndefends the view that all normal, mature human beings are endowed with\na moral sense. Like philosophers such as Hutcheson and Hume, Reid\nclaims that the moral sense yields sentiments of various sorts that\nthemselves occasion “our first moral conceptions,” such as\nthe apprehension that an act is approbation-worthy (EAP V.ii: 279).\nThis account of concept formation, according to some philosophers,\nwould make Reid’s position a version of sentimentalism (see\nD’Arms 2005). In this respect, Reid’s position resembles\nnot Clarke’s and Price’s but Hutcheson’s and\nHume’s.", "\nThere is, then, a sense in which Reid’s moral philosophy resists\nready categorization. It is neither a version of rationalism nor\nsentimentalism, but an attempt to blend those features from both these\ntraditions that Reid found most attractive. This presents a challenge\nto the contemporary interpreter of Reid’s moral philosophy. One\nwonders: Is Reid’s theory of morals an exotic hybrid, one which\neludes the categories used by contemporary philosophers to describe\nethical theories?", "\nNot exactly. Anyone familiar with contemporary moral philosophy could\nnot fail to miss the resemblance that Reid’s position bears to\nthe view defended some one hundred and fifty years later by W. D. Ross\n(see Ross 2002). Although Ross never mentions Reid as an influence,\nboth thinkers operate within a broadly non-naturalist framework\naccording to which the sciences offer us limited insight into the\nnature of moral reality. In so doing, they both stood against powerful\ntrends in their day to “naturalize” ethics. Moreover, both\nreject monistic accounts of the moral domain, such as those defended\nby Kantians and consequentialists, according to which there is one\nmaster ethical principle from which all others are derived. According\nto both Reid and Ross, there is instead a plurality of self-evident\nmoral first principles, none of which is reducible to another.", "\nIn light of this, we might describe Reid’s position as a\nproto-Rossian version of ethical intuitionism. While such a\ndescription is tempting, it would probably be misleading. For the\nparallels between Reid and Ross extend only so far. The most important\ndifference between the two thinkers is this: Ross frames his project\nin the light of G. E. Moore’s Open Question Argument and\nMill’s utilitarianism—two philosophical topics about which\nReid knew nothing. Reid, by contrast, developed his version of ethical\nintuitionism within the context of a defense of a certain account of\nhuman agency, according to which each of us is endowed with\n“active power” which we can freely exercise. Reid believed\nthat this account of human agency, when coupled with our best\nscientific knowledge, yields a form of non-naturalist ethical\nintuitionism. Call a position that grounds many of its core\nmetaethical claims about the nature of moral reality in a particular\nview of human agency an agency-centered account.\nAgency-centered views tell us that in order to understand the nature\nof moral reality we must first examine the nature of agency.\nReid’s is an agency-centered version of ethical intuitionism.\nRoss’s, by contrast, is not.", "\nThe project of this essay is to present both the motivations for and\nfundamental contours of Reid’s agency-centered intuitionist\nview. Before diving into the details of Reid’s position,\nhowever, it may be worth saying a word about the influence of\nReid’s views in contemporary ethics. If one were to gauge this\ninfluence by the number of books or articles written in the last one\nhundred years about Reid’s ethics, one would have to conclude\nthat his influence is negligible. Very little has been written about\nReid’s moral philosophy. Indeed, Reid is not even included in\nwhat is perhaps the standard anthology on the British Moralists, the\ntwo-volume work edited by Selby-Bigge of the same title (Selby-Bigge\n1965). Moreover, one would also have to conclude that Reid’s\ninfluence on moral philosophers who receive a great deal of attention,\nsuch as Moore, is marginal. For example, in the flurry of work\nproduced in 2003 on the centenary of the publication of Moore’s\nPrincipia Ethica, no one mentions Reid as an influence on\nMoore’s ethical views.", "\nThe reality of the matter, however, is that Reid has indeed exercised\nconsiderable influence on contemporary moral philosophy, albeit\nindirectly. This influence runs primarily through Henry Sidgwick, who\nknew Reid’s work well (see Sidgwick 2000, Ch. 16). Sidgwick, it\nseems, exposed his student, G. E. Moore, to Reid’s views (see\nBeanblossom 1983). Reid’s broadly common sense methodology and\nhis positive views were subsequently taken up by Moore. Among the more\nsalient similarities one finds in their ethical views is that both\nthinkers are interested in whether the fundamental moral properties\nare definable. Reid claims they are not; fundamental moral properties\nare, in Reid’s estimation, simple, indefinable, and sui generis\n(EAP III.iii.v). Famously, Moore said the same, although for somewhat\ndifferent reasons. And the rest, as they say, is history. Depending on\none’s views, one might view this history as one in which Moore\nfinally put ethical theory on the right track or, alternatively,\npushed it off the rails. Whatever one’s opinion on this issue,\nReid seems to have had a role in its direction." ]

[ { "content_title": "1. The System of Necessity", "sub_toc": [ "1.1 Reid’s alternative", "1.2 Reid’s moral non-naturalism" ] }, { "content_title": "2. The Rational Principles of Action", "sub_toc": [ "2.1 Reid’s defense of The Hierarchy Thesis" ] }, { "content_title": "3. Moral Principles", "sub_toc": [ "3.1 Reid’s defense of the objectivity of moral first principles" ] }, { "content_title": "4. The Moral Sense", "sub_toc": [ "4.1 Reid’s view compared with Hutcheson’s", "4.2 Reid’s defense of the reliability of the moral sense" ] }, { "content_title": "5. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Primary Literature", "Secondary Literature" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nReid’s moral philosophy, according to the gloss offered thus\nfar, is an agency-centered intuitionist position, which also blends\ntogether both rationalist and sentimentalist influences. Given its\nsynthetic character, it is natural to ask how best to enter into\nReid’s thought. A promising avenue is to note a pattern of\nthought present in Reid’s work. In his work in epistemology and\nphilosophy of mind, which is found primarily in An Inquiry into\nthe Human Mind (IHM) and Essays on the Intellectual Powers of\nMan (EIP), Reid frames his project as a response to a general\nposition that he calls the Way of Ideas. This position, which Reid\nsays unites philosophers as diverse as Aristotle, Locke, Berkeley, and\nHume, holds that we are never acquainted with the external world but\nonly with “images” or sense data in the mind. What Reid\nsays positively about our perception of the external world is couched\nas a response to this view. Although it is rarely noted, Reid’s\nwork in ethics in Essays on the Active Powers of Man (EAP) is\nalso framed as a response to a general position, which he claims is\nadopted by philosophers as diverse as Spinoza, Leibniz, and Hume. This\nposition Reid ordinarily calls the System of Necessity. Reid’s\nown positive views about the nature of agency and the moral domain are\nbest viewed as a response to the System of Necessity. Let us, then,\nenter Reid’s moral philosophy by having before us the rudiments\nof the System of Necessity.", "\nSuppose you have fallen asleep in your bed after a long day of work.\nYou briefly wake during the night, noting that someone has left a\nkitchen light on. You do not want, however, to get out of bed at this\nhour. Still, after pondering the issue for a moment, you know that you\nshould do so. So, you drag yourself out of bed and turn the light off.\nHow should we describe your behavior?", "\nAccording to advocates of the System of Necessity, there is a sense in\nwhich the performance of this action is up to you. No one forced you\nto get up out of bed. There is also a sense in which you did it\nbecause you believed you should. It is this belief, coupled with a\ndesire—perhaps to do what is right—that moved you to get\nout of bed. Finally, there is a sense in which there is an explanation\nof your action that is perfectly law-like. Because your desire (let us\nsuppose) to do what is right was stronger than your desire to stay in\nbed, it won out. Under the supposition that stronger motivations win,\nwe have a perfectly general, law-like explanation of why you acted as\nyou did.", "\nIn Reid’s view, then, proponents of the System of Necessity\naffirm these three claims:", "\nViewed from on angle, these claims appear not to fit tightly together.\nOne could accept any one and reject the others. Viewed from another\nangle, however, they express a unified picture of human action, one\naccording to which human action is a natural phenomenon that is\nsubsumable under laws in much the same way that other ordinary natural\nevents are. If one is attracted to this broadly naturalistic position,\nas Reid claims that figures such as Spinoza, Hume, Priestley, and\nKames were, then these claims form a natural package (see Cuneo\n2011a).", "\nReid, however, believed that this package of claims provides a deeply\ndistorted picture of human action. Why did he believe this? In large\npart because he could not see how it could account for genuinely\nautonomous human agency in at least two senses of this multivalent\nterm. In the first place, autonomous actions are ones that can be\nproperly ascribed to an agent. But if the System of Necessity were\ntrue, Reid claimed, there is no proper sense in which actions that\nappear to be performed by an agent could justly be attributed to that\nagent—the human agent being simply a theater in which various\ndrives and impulses vie for dominance. One could, if the System of\nNecessity were right, attribute actions to mental states such as\ndesires. And this might be adequate to describe the behavior of\nanimals and addicts. But, Reid claims, it is not adequate to describe\npurposeful human action. For human action, in Reid’s view, must\nbe attributable to the person as a whole, not some force working in or\non her (see Korsgaard 2009, xii).", "\nSecondly, autonomous agency is such that an agent can exercise a\ncertain type of control over the various impulses that present\nthemselves when deliberating. Suppose, to return to our earlier case,\nthat you briefly wake during the night, noting that someone has left a\nkitchen light on. You want not to get out of bed at this hour. Must\nyou capitulate to your strongest desire? Not if you are autonomous.\nFor genuinely autonomous agents, according to Reid, are reflective.\nAny desire is such that an autonomous agent can direct his attention\nnot only to its object, but also to the desire itself, asking: Should\nI act on it? That is, any such agent can ask these two questions:\nFirst, would acting on this desire contribute to my genuine\nwell-being? And, second, is there a sufficient moral reason or\nobligation for acting on or ignoring it? These two questions advert to\nwhat Reid calls the rational principles of action (see EAP,\nIII.iii.i). The first principle Reid calls the principle with\n“regard to our good on the whole,” the second the\n“principle of duty.” The fact that you needn’t\ncapitulate to your desire to stay in bed but can step back and\ncritically assess it with reference to these two rational principles\nof action, in Reid’s estimation, is what separates normal,\nmature human beings from the rest of the natural order.", "\nThis point was important enough to Reid that he highlights it in the\nIntroduction to Essays on the Active Powers and\nelsewhere:", "\n\n\nThe brutes are stimulated to various actions by their instincts, by\ntheir appetites, by their passions: but they seem to be necessarily\ndetermined by the strongest impulse, without any capacity of\nself-government…. They may be trained up by discipline, but\ncannot be governed by law. There is no evidence that they have the\nconception of a law, or of its obligation.\n\n\nMan is capable of acting from motives of a higher nature. He perceives\na dignity and worth in one course of conduct, a demerit and turpitude\nin another, which brutes have not the capacity to discern….\n\n\n[Men] judge what ends are most worthy to be pursued, how far every\nappetite and passion may be indulged, and when it ought to be\nresisted…. In them [the brutes] we may observe one passion\ncombating another, and the strongest prevailing; but we perceive no\ncalm principle in their constitution that is superior to every\npassion, and able to give law to it. (EAP, 5 and II.ii: 57)\n", "\nWhen Reid talks about our capacity to be governed by law he has in\nmind our capacity to regulate our behavior by assessing it in terms of\nthe two rational principles of action. Reid, then, champions what we\nmight call a regulation account of autonomy. We are\nautonomous, rational agents, in Reid’s estimation, in virtue of\nthe fact that we can regulate or govern our behavior by stepping back\nfrom our various impulses, desires, instincts, and assess prospective\nactions in light of the two rational principles of action. It is this\ndimension of human action, according to Reid, that is missing\naltogether from the description of agency offered by advocates of the\nSystem of Necessity." ], "section_title": "1. The System of Necessity", "subsections": [ { "content": [ "\nIn Reid’s view, then, the System of Necessity fails to offer an\naccurate account of human agency. What alternative account of agency\ndid Reid propose? One that accepts the following three claims:", "\n\n\n(1′) Every human action has a cause, which in the case of free\nhuman action is not itself a motive, but the agent himself.\n\n\n(2′) Motives are not mental states but the ends for which an\nagent acts.\n\n\n(3′) Human action is nomic only to this extent: If an agent\nfails to exercise autonomy when deliberating (and he is not in a state\nof indifference), then his strongest desire to act in a certain way\nwill prevail. If he exercises autonomy when deliberating, however,\nthen he will act on the motive that seems to him most rationally\nappropriate.\n", "\nLet us consider these three claims in turn.", "\nThe first statement, (1′), expresses Reid’s commitment to\nan agent causal account of human free action. Reid presents various\narguments for this view in Essays on the Active Powers of\nMan, but it is worth emphasizing that a central consideration\nthat Reid furnishes in its favor appeals not to common sense but to\nwhat science appears to tell us. Reid, like most of his\ncontemporaries, was a Newtonian. In Reid’s judgment, however,\nNewtonian science is committed to the claim “that matter is a\nsubstance altogether inert, and merely passive; that gravitation, and\nthe other attractive or repulsive powers … are not inherent in\nits nature, but impressed upon it by some external cause” (EAP\nI.vi: 34). Matter, according to this view, does not cause anything. On\nthe assumptions that there is genuine causality in the world and that\nagents are causes, it follows that agents, who are not material\nthings, in Reid’s view, are the only causes. Reid takes\nNewtonian science to imply a mitigated version of occasionalism\naccording to which the only genuine causation in the world is agent\ncausation.", "\nThe second statement above, (2′), expresses Reid’s\ncommitment to a broadly teleological account of human agency,\naccording to which autonomous human action is explained not by the\nimpulses that present themselves to an agent when deliberating but by\nthe ends for which she acts. In his defense of this view, Reid argues\nthat, contrary to the adherents of the System of Necessity, motives\nare not mental states that cause us to act, for motives are not the\nright sort of thing to be causes: They are not agents. In some places,\nin fact, Reid says that motives (as he thinks of them) have no\n“real existence,” by which he seems to mean (at least)\nthat they are not part of the spatio-temporal manifold but are\nabstracta (see EAP IV.iv: 214).", "\nThese claims might take us aback: Motives are not causes and have no\nreal existence? How could that be? When evaluating these claims, two\nthings should be noted. First, Reid is working with a rather narrow\nunderstanding of what it is for something to be a cause (and to\nexist)—an understanding, we’ve seen, he thinks fits best\nwith a Newtonian understanding of the world. Second, Reid’s\nconsidered view about the role of motives is actually more complicated\nthan (2′) would have us believe. (2′) expresses the view\nthat Reid defends in Essay IV of Essays on the Active Powers,\n“Of the Liberty of Moral Agents.” But anyone who has read\nEssay III, “Of the Principles of Action,” knows that Reid\nclaims that motives or “principles of action” divide into\nthree kinds: mechanical, animal, and rational. Mechanical principles\nof action are what we would call instincts, such as the unreflective\nimpulse to protect oneself from perceived harm. Animal principles of\naction are a more varied lot. Under this category, Reid places the\nso-called benevolent affections, such as the affection felt between\nkin, gratitude to benefactors, pity and compassion, friendship, public\nspirit, and the like (see EAP III.iii.iv). He also includes the\nso-called malevolent affections, such as resentment and the desire to\ndominate others. (In section III, we will see a reason to believe that\nsome animal principles, by Reid’s own lights, are not ones that\ncould be had by the animals.)", "\nAll this complicates Reid’s picture. Reid seems to want to allow\nthat motives come in two varieties. On the one hand, Reid says that\nrational motives function as “advice” or\n“exhortation” which do not push but pull us to action. On\nthe other, he describes the mechanical and animal motives as\n“impulses,” which do not pull but push us to action (EAP\nII.ii and IV.iv). How best to understand what Reid is saying? Perhaps\nthe best conclusion to draw is that Reid does not have a unified\naccount of motives. Some of the rational motives are best described as\nbeing either those ends for which we act or principles by which we\nevaluate those ends for which we act. Other motives—the\nmechanical and a range of the animal ones—are not; they are what\npush or impel us to action (see Cuneo and Harp 2016).", "\nAre these latter motives best described as having a causal influence\non behavior? Perhaps they are, according to a more relaxed\nunderstanding of causality than that with which Reid officially works.\nFor suppose we agree that there are processes that are instigated by\nthe exercise of active power, such as the process that is instigated\nby an agent’s willing to raise her arm. In Reid’s view,\nthis process includes the exercise of active power, which is the\nagent’s willing to raise her arm, the activity of nerves and\nmuscles and, finally, the raising of her arm. If we allow ourselves to\ntalk of elements of this process as causes in a “lax and popular\nsense,” then perhaps some motives, in Reid’s view, could\nbe called causes. Of course Reid would have to say that in some cases\nthe motives that “cause” us to act are not part of a\ncausal process that we ourselves instigate. Not every desire or mental\nstate we have is the causal consequence of the exercise of our active\npower in a given way. (That I desire to eat an ice cream cone, for\nexample, appears to be a causal consequence not of the exercise of my\nactive power but of your handing me an ice cream cone.) Reid would\nhave to say, then, that those mental states and events that are not\nsimply the causal consequence of the exercise of active power are\nparts of processes instigated by some other agent cause, such as God.\nThis may seem odd. But it seems to be the broader picture within which\nReid operated. All causal processes in nature (which are not due to\nus) are instigated by the exercise of God’s active power. A\ntypical case of human action involves the coincidence of the exercise\nof our active power with God’s (see EAP I.vi and Cuneo\n2011a).", "\nLet us now turn to the third statement above, namely, (3′). This\nclaim expresses Reid’s two-fold conviction that free human\naction is (i) not in any interesting sense nomic, and (ii) that we can\nassess our motives along two dimensions. We can assess them, first,\naccording to their psychological strength and, second, according to\ntheir rational authority.", "\nThat free human action is not nomic is simply an implication of\nReid’s conviction that we are endowed with libertarian free\nwill, the exercise of which does not fall under any natural law in the\nsense described by Newtonian science. That our motives can be assessed\nalong two dimensions, by contrast, is an implication of Reid’s\nregulation account of autonomy.", "\nTo see how Reid is thinking about the strength of motives, consider a\ncase in which you are moved to action by some animal principle of\naction. Imagine, for example, you are incited to reprimand someone in\nyour family because you believe that he or she has acted irresponsibly\nby leaving a kitchen light on during the night. One way to assess this\naction would be to ask whether it conforms to the rational principles\nof action. Let us suppose that, in the case we are considering, by\nreprimanding you risk alienating yourself from those with whom you\nlive; the circumstances you’re in call for a calm and measured\nresponse. While there may be good reasons to alienate yourself from\nothers, expressing your anger in these circumstances is not one of\nthem. This motive in these circumstances, then, has no rational\nauthority.", "\nNow consider the same motive not with respect to its rational\nauthority but with regard to its psychological strength. Is this\nmotive the strongest of your motives? Reid maintains that this is a\ndifficult question to answer. One of the complaints Reid raises about\nthe System of Necessity is that it sheds no light on the matter.\nAlthough advocates of the System of Necessity claim that human actions\ncan be subsumed under natural laws, the laws to which they appeal in\norder to assess the strength of motives are either false or trivial.\nFor recall that, according to the System of Necessity:", "\n(3) Every human action is subsumable under a law, which specifies that\nfor any agent S, set of motives M, and action\nA at t, necessarily, if S performs\nA, then there is some member of M that is\nS’s strongest motive, which causes S to\nperform A at t.\n", "\nReid finds this claim totally unpersuasive. It is worth quoting at\nlength what he has to say about it:", "\nIt is a question of fact, whether the influence of motives be fixed by\nlaws of nature, so that they shall always have the same effect in the\nsame circumstance. Upon this, indeed, the question about liberty and\nnecessity hangs. But I have never seen any proof that there are such\nlaws of nature, far less any proof that the strongest motive always\nprevails. However much our late fatalists have boasted of this\nprinciple as of a law of nature, without telling us what they mean by\nthe strongest motive, I am persuaded that, whenever they shall be\npleased to give us any measure of the strength of motives distinct\nfrom their prevalence, it will appear, from experience, that the\nstrongest motive does not always prevail. If no other test or measure\nof the strength of motives can be found but their prevailing, then\nthis boasted principle will be only an identical proposition, and\nsignify only that the strongest motive is the strongest motive\n… which proves nothing. (C, 176–77)\n", "\nAccording to Reid, (3), then, is either false or trivial (for\ndiscussion, see Yaffe 2004, Ch. 6).", "\nWe should now have a better picture of Reid’s favored account of\nhuman agency. It is one according to which agents are causes, at least\nsome motives are not causes but ends, and autonomous action is\nnon-nomic. Earlier I said that this picture of agency grounds his\nnon-naturalist account of the ethical domain. Let me now explain\nhow." ], "subsection_title": "1.1 Reid’s alternative" }, { "content": [ "\nLike most of his contemporaries, Reid’s worldview was Newtonian.\nWhile he was convinced that the natural sciences should conform to\nNewtonian methods, Reid held that these methods have their\nlimitations. In a passage from an unpublished review composed toward\nthe end of his life, Reid writes:", "\nThere are many important branches of human knowledge, to which Sir\nIsaac Newton’s rules of Philosophizing have no relation, and to\nwhich they can with no propriety be applied. Such are Morals,\nJurisprudence, Natural Theology, and the abstract Sciences of\nMathematicks and Metaphysicks; because in none of those Sciences do we\ninvestigate the physical laws of Nature. There is therefore no reason\nto regret that these branches of knowledge have been pursued without\nregard to them. (AC, 186)\n", "\nIn this passage, Reid tells us that Newton’s rules pertain only\nto the physical laws of nature and what is subsumable under them. But\nthe rational principles of action, we have seen, are not themselves\nthe physical laws of nature. They do not concern how the universe in\nfact operates. Rather, they concern how rational agents ought to\nconduct their behavior. Nor are these principles subsumable under\nNewton’s laws (EAP IV.ix: 251). They are, in Reid’s view,\nnot part of the space/time manifold. It follows that Newton’s\nmethods should not guide our theorizing about the rational principles\nof action. Since moral principles are among the rational principles of\naction, it follows that they are not identical with or subsumable\nunder Newton’s laws. Given the additional assumption that\nnatural science must conform to Newton’s rules, Reid concludes\nthat morality is not the subject matter of natural science. That this\nis so, Reid continues, is “no reason to regret.” It is a\nmatter of simply acknowledging the implications of Newton’s\nsystem—implications, Reid maintains, that philosophers such as\nHume and Priestley, who also took themselves to be followers of\nNewton, had failed to appreciate.", "\nIn sum: Suppose we understand moral naturalism to be the view that\nmoral facts are natural. And suppose we say, in a rough and ready way,\nthat a fact is natural just in case it pulls its explanatory weight in\nthe natural sciences (see Wiggins 1993). Reid maintains that Newtonian\nmethods exhaust the limits of natural science. Newtonian science,\nhowever, does not investigate the ends or rational principles for\nwhich we act. The ends for which we act neither fall under Newtonian\nlaws nor are identical with them. But moral facts, Reid says, are\namong the ends or rational principles for which we act. It follows\nthat, in Reid’s view, moral facts are not the proper object of\nscientific inquiry. The moral domain is autonomous." ], "subsection_title": "1.2 Reid’s moral non-naturalism" } ] }, { "main_content": [ "\nPhilosophers such as Hume and Priestly were eager to apply\nNewton’s methods to the moral domain. Reid, however, viewed\nattempts to use Newtonian methods to understand the moral domain as\nmistaken—not, once again, because he viewed Newtonian science as\nsuspect, but because he held that Newton’s methods themselves\nrequire this. That said, we have seen that there is a sense in which\nReid believes that human action is law-governed. We can regulate our\nbehavior by reference to the rational principles of action. Earlier we\nsaw that these principles are of two kinds: They concern our good on\nthe whole and duty. Reid holds that these principles stand in a\ncertain kind of relation to one another. We can better identify this\nrelation by having the notion of motivational primacy before\nus.", "\nSuppose we say that a state of affairs P has motivational\nprimacy for an (ordinary adult) agent S just in case three\nconditions are met. First, in a wide range of ordinary cases,\nP is a type of consideration in light of which S\nwould act. Accordingly, were S to deliberate about what to\ndo, P is a type of state of affairs that S would, in\na wide range of cases, not only use to “frame” his\npractical deliberations, but also endeavor to bring about. That my\nloved ones flourish is such a state of affairs for many of\nus.", "\nSecond, P is a sufficient reason for S to act.\nRoughly put, P is a sufficient reason for S to act\njust in case were S to deliberate about what to do, then (in\na wide range of ordinary cases) S would take P to be\na reason to act and would endeavor to bring about P even if\nhe believed (or presupposed) that his doing so would not bring about\n(or increase the likelihood of his bringing about) any further state\nof affairs that he values. Imagine, for example, S is like\nmany of us inasmuch as he takes himself to have a reason to bring\nabout the flourishing of his loved ones. This is a sufficient reason\nfor S to act since he would endeavor to bring about the\nflourishing of his loved ones even if he believed that his doing so\nwould not bring about any further state of affairs that he values,\nsuch as his gaining increased notoriety among his peers.", "\nThird, P has deliberative weight for S. For our\npurposes, we can think of this as the claim that P is a\nreason of such a type that, in a wide range of circumstances, were S\nto deliberate about what to do, then S would take P\nto trump other types of reasons, even other sufficient reasons. Many\nof us, for example, hold that there is a beautiful sunset on the\nhorizon is a sufficient reason to stop whatever we are doing and\nenjoy it. Still, for most of us, that an act would bring about or\npreserve the flourishing of our loved ones has greater deliberative\nweight than this. If a person had to choose between enjoying a\nbeautiful sunset, on the one hand, or protecting her child from\ndanger, on the other, then the latter reason trumps." ], "section_title": "2. The Rational Principles of Action", "subsections": [ { "content": [ "\nHaving introduced the notion of motivational primacy, we can now\nidentify a claim that is arguably the centerpiece of Reid’s\ndiscussion of rational motivation, namely:", "\nThe Hierarchy Thesis: In any case in which an agent\nmust decide what to do, considerations of what is morally required\nshould have motivational primacy. Specifically, what is morally\nrequired of an agent should have motivational primacy over what he\ntakes to be his good on the whole.\n", "\nEudaimonist positions, such as those defended in the broadly\nAristotelian tradition, reject The Hierarchy Thesis. They maintain\nthat when an agent deliberates about what to do he assumes, or ought\nto assume, that considerations concerning his own well-being or\neudaimonia have motivational primacy in a very robust sense. Every act\nthat an agent performs, say eudaimonists, either is or should be taken\nfor the sake of his own happiness. Accordingly, if eudaimonism is\ntrue, an agent operates, or ought to operate, with the following\nprinciple of action selection: Perform only those actions that, to the\nbest of one’s knowledge, positively contribute to one’s\nown well-being or eudaimonia. Moreover, in so doing, an agent treats,\nor ought to treat, considerations concerning his own well-being as\nbeing both a sufficient reason to act and having deliberative weight.\nWhen asked: “Why did you do that?” an agent’s\nultimate justification will, or ought to, appeal to the way in which\nacting in that fashion contributes to her own well-being.", "\nReid rejects eudaimonism thus understood. It is safe to assume that\nReid took Butler’s attack on what we might call descriptive\neudaimonism to be decisive: There is no plausibility to the idea\nthat agents necessarily will their own happiness, as they understand\nit, for they can knowingly act in self-destructive ways (cf. EAP\nIII.ii.i: 95). But Reid realized that Butler’s attack left\nprescriptive eudaimonism, or the view that the\npractically rational agent takes her own well-being to have\nmotivational primacy, relatively untouched. According to this view,\nwhatever may be the case about how agents actually act, they ought to\nview their own well-being as having motivational primacy.", "\nLike Butler, Reid did not wish to recommend a picture of agency\naccording to which agents should disregard or ignore their own\nwell-being. “To serve God and be useful to mankind, without any\nconcern about one’s own good and happiness,” Reid writes,\nis “beyond the pitch of human nature” (EAP III.iii.iv:\n166). Indeed, Reid holds that, when properly understood, a concern for\none’s good on the whole naturally leads to the acquisition of\nthe moral virtues, such as justice and benevolence (EAP III.iii.iii:\n163; see also EAP V.i). Still, Reid insists that our good on the whole\nought not to be the “only regulating principle of human\nconduct” (EAP III.iii.iv: 164). Why?", "\nFor four main reasons. First, Reid claims that “the greater part\nof mankind can never attain such extensive views of human life, and so\ncorrect a judgment of good and ill, as the right application of this\nprinciple requires” (EAP III.iii.iv: 164). Reid’s point\nhere is that a principle of action should be action-guiding. It should\nbe the sort of thing that, in a wide range of cases, an agent could\nconsult when determining what to do and thereby come to understand\nwhat she morally ought to do. The principles of morality are\naction-guiding. “Every man of common understanding,” says\nReid, is such that he is capable of knowing his duty (EAP V.i: 277).\nBut gaining a conception of one’s good on the whole, let alone\nan accurate one, and an understanding of what genuinely contributes to\nit, is something that is very difficult to do. It requires that one\n“observe the connections of things, and the consequences of our\nactions,” thereby “taking an extended view of our\nexistence, past, present, and future” (EAP III.iii.i: 153). Many\nordinary persons will have neither the time nor the ability to do\nthis, let alone actually gain an accurate notion of that in which\ntheir good on the whole consists. If this is right, however, then\none’s good on the whole is not sufficiently action-guiding to be\nthe most general and fundamental principle of action, as eudaimonists\nclaim.", "\nSecond, since one’s good on the whole is concerned not only with\npresent satisfaction, but also with the enjoyment of future goods, it\nproves not to be as motivationally charged as one might hope. We would\nlike to have a clearer and more efficacious guide to conduct. Reid\nputs the point thus:", "\nMen stand in need of a sharper monitor to their duty than a dubious\nview of distant good. There is reason to believe, that a present sense\nof duty has, in many cases a stronger influence than the apprehension\nof distant good would have of itself. And it cannot be doubted, that a\nsense of guilt and demerit is a more pungent reprover than the bare\napprehension of having mistaken our true interest. (EAP III.iii.iv:\n165)\n", "\nDuty is, then, according to Reid, in many cases, a better guide to\naction than interest. Moreover, it is often motivationally more\npowerful than an appeal to interest, as it connects more intimately\nwith powerful motivating considerations such as one’s own\nguilt.", "\nThe third point that Reid makes is that “a steady pursuit of our\nown good may, in an enlightened mind, produce a kind of virtue which\nis entitled to some degree of approbation, yet it can never produce\nthe noblest kind of virtue, which claims our highest love and\nesteem” (EAP III.iii.iv: 165). So, Reid’s view is not that\na concern for one’s own well-being is crass egoism or\nself-centeredness. To the contrary, there is something admirable about\nit; to pursue one’s own well-being properly requires virtue. For\nexample, if concern for one’s self is such that it helps one to\ndiscount temptations to a life of ease, leisure, or frivolity, then it\nis much to be admired (cf. EAP III.iii.iv: 165; but also cf. EAP V.vi:\n272). That said, to be genuinely dedicated to the moral life, one\ncannot grant motivational primacy to one’s good on the whole.\nFor our esteem, Reid writes, “is due only to the man whose soul\nis not contracted within itself, but embraces a more extensive object:\nwho loves virtue, not for her dowry only, but for her own sake: whose\nbenevolence is not selfish, but generous and disinterested” (EAP\nIII.iii.iv: 166). For Reid, then, virtue requires caring not only\nabout particular persons (they are, according to Reid, the objects of\nbenevolence), but also about virtue itself. Being virtuous requires\nbeing committed to the idea that the moral life is, in and for itself,\nworth living. It is not to be made subordinate to considerations about\none’s well-being.", "\nReid’s fourth point echoes one of Butler’s most famous\nobservations regarding the pursuit of happiness: If one primarily aims\nto secure one’s own happiness, one often increases the risk of\nnot obtaining it. This is not only because directly aiming for\none’s own happiness can “fill the mind with fear, and\ncare, and anxiety” (EAP III.iii.iv: 167). It is also because a\n“concern for our own good is not a principle that, of itself,\ngives any enjoyment” (EAP III.iii.iv: 166). What does give\nenjoyment, however, are those particular activities and objects to\nwhich our affections are directed, such as friendship and the common\ngood. To achieve one’s good on the whole, then, one must, at\nleast part of the time, be focused on and motivated by considerations\nthat are not identical with it.", "\nEarlier we said that a consideration has motivational primacy for an\nagent just in case the following three conditions are met: First, it\nis a type of consideration in light of which an ordinary adult agent\nwould act in a wide array of cases; second, it is a sufficient reason\nfor that agent; and, third it has deliberative weight for him.\nEudaimonists believe that one’s good on the whole has\nmotivational primacy. Indeed, they believe that one’s good on\nthe whole has motivational primacy in a very robust sense.\nEudaimonists hold that every act that an agent performs is,\nor should be, taken for the sake of his own happiness and that there\nis, or should be, no deeper practical justification for so acting.\nReid maintains that eudaimonism thus understood is false. In many\ncases, agents do not act for the sake of their good on the whole. Nor,\nin many cases, should they do so. For one thing, appealing to\none’s good on the whole is insufficiently action-guiding, since\nmany agents simply do not have an adequate understanding of that in\nwhich it consists. For another, to make happiness the final court of\nappeal when deliberating is to undermine the rightful primacy of\nvirtue.", "\nThere is a substantial challenge facing views such as Reid’s.\nConsider a case in which considerations of well-being conflict with\nduty, such as when moral duty requires that one stand up for the\ninnocent at the cost of one’s life and those of one’s\nfamily. Reid is committed to the claim that, in a case such as this,\none is required to surrender one’s life. Could that be right?\nReid insists that it is. For any such conflict, Reid says, is\n“imaginary” (EAP III.iii.viii: 194). So long as “the\nworld is under a wise and benevolent administration, it is impossible,\nthat any man should … be a loser by doing his duty.”\nReid’s theism, in short, grounds his allegiance to The Hierarchy\nThesis. God guarantees that the two principles of action never come\ninto genuine conflict since performing one’s duty will not\ndetract from one’s good on the whole in the long run (see Cuneo\n2010)." ], "subsection_title": "2.1 Reid’s defense of The Hierarchy Thesis" } ] }, { "main_content": [ "\nAccording to the picture sketched thus far, Reid’s account of\nautonomous action is as follows: We human beings can act from a great\nvariety of principles, including the so-called mechanical and animal\nprinciples. What renders us rational agents distinct from the rest of\nthe animals is our ability to gain critical distance from these\nincentives and regulate our conduct by appeal to the two rational\nprinciples of action, asking whether a given course of action truly\ncontributes to our good on the whole and is consonant with moral duty.\nFinally, the principle of duty enjoys motivational primacy. Although I\nhave not yet emphasized the point, the similarities between\nReid’s and Kant’s thought in these respects are\nunmistakable. (We have, however, no evidence that Reid was aware of\nKant’s work.) According to both Reid and Kant, we are rational\nbeings not primarily because we can engage in means-end practical\nreasoning. Rather, we are practically rational agents primarily\nbecause we can assess the various impulses to act by appeal to a\n“certain general principle” or law – this law\nconsisting, in Reid’s view, in the rational principles of\naction. Indeed, if J. B. Schneewind is correct, Reid and Kant were\nunique among the moderns inasmuch as that they conceived of morality\nprimarily in terms of rational self-governance (see Schneewind\n1998).", "\nStill, we saw earlier that there is an important difference between\nReid and Kant. Kant is an ethical monist, holding that there is one\nmaster principle of morality—the categorical\nimperative—which is fundamental and from which all our\nparticular duties can be derived. Reid, by contrast, rejects ethical\nmonism, maintaining that there is no such master principle, but only a\nvariety of moral principles that are self-evident and irreducible to\none another. The locution “the principle of duty,” in\nReid’s mouth, is probably best understood to be a shorthand way\nof referring to one or another of these principles which can govern\npractical deliberation.", "\nIn his chapter “Of the first principles of morals,” Reid\npresents the first principles of morality “without pretending to\na complete enumeration” (EAP V.i: 270). The constellation of\nprinciples that Reid presents is a hodgepodge. Some are metaethical\nprinciples that specify certain properties of moral principles, such\nas that they apply only to free actions, while others are normative\nprinciples that one might consult when deliberating. Among the\nnormative principles that Reid presents are these:", "\n\n\nWe ought to prefer a greater good, though more distant, to a less; and\na less evil to the greater.\n\n\nEvery man ought to consider himself as member of the common society of\nmankind, and of the subordinate societies to which he belongs, such as\nfamily, friends, neighborhood, and country, and do as much good as he\ncan, and as little hurt to the societies of which he is a part.\n\n\nIn every case, we ought to act that part toward another, which we\nwould judge to be right in him to act toward us, if we were in his\ncircumstance and he in ours. (EAP V.i)\n", "\nPrinciples such as these, Reid says, form a system of morality, but\nonly in a weak sense. They form a system only in the sense that we can\norganize them in such a way that facilitates “apprehension and\nmemory.” In this respect, a system of morals, according to Reid,\nis not like a system of geometry “where the subsequent parts\nderive their evidence from the preceding” but “resembles\nmore a system of botany … where the subsequent parts depend not\nfor their evidence upon the preceding” (EAP V.ii: 281). So,\nwhile Reid admits that the last principle stated above is the\n“most comprehensive,” he does not claim that it is\nfundamental in the sense that it grounds the other moral principles.\nRather, he holds that each of the principles of morality is\nself-evident, at least to those who have a sound understanding, a\nsatisfactory moral education, and are not in the grip of self-interest\nor passion. These principles are self-evident, in part, because they\nare not amenable to direct argument or proof, for any such argument\n“will either take for granted the thing to be proved” or\nbe “something not more evident” (EAP V.i: 361; for more\ndiscussion, see Cuneo 2004, 259 and Davis 2006, Ch. 6).", "\nThose familiar with the history of ethical intuitionism know that its\ncritics have found the view unsatisfactory because the intuitionists\nhad almost nothing informative to say about why, in a given situation,\na particular moral principle takes precedence, and how we could know\nthat it did (see McNaughton 1996). In hindsight, it is remarkable that\nReid shows little interest in this problem, stating that it is usually\nclear to a candid mind which moral principles take precedence and what\none should do (see EAP V.i; although see Roeser 2010a, 15–16).\nInstead, Reid is more concerned to argue that there must be\nfirst-principles of morality. In his argument for this claim, Reid\nappeals to a traditional regress-style argument according to which\nthere must be some fundamental moral principles which both ground and\njustify our moral deliberation on pain of our being unable to engage\nin such deliberation, which we clearly can (see EAP V.i).", "\nAt first glance, this can give the impression that moral judgments\nmust, in Reid’s view, derive their warrant from moral first\nprinciples, presumably by being inferred from them. Although Reid\nmight encourage this impression in places, in other places he clearly\nindicates that this is not how he views things. In his account of\nparticular moral judgments, for example, Reid insists that we\nordinarily form them immediately or non-inferentially. A moderately\nvirtuous agent “will rarely be at a loss to distinguish good\nfrom ill in his own conduct, without the labour of reasoning”\n(EAP V.ii: 280). If the first principles of morality were\nwarrant-conferring axioms, however, this presumably would not be the\ncase (see Cuneo 2014).", "\nSuppose, then, that in Reid’s view appeal to moral first\nprinciples rarely plays a role in the formation of particular moral\njudgments. It is natural to wonder about the role Reid envisions moral\nfirst principles to play in ordinary moral thought. On this matter,\nReid says less than one might like. A promising strategy of\ninterpretation, however, is to draw a parallel between the first\nprinciples of morality, on the one hand, and what Reid says about the\nfirst principles of common sense in the Inquiry and\nEssays on the Intellectual Powers, on the other.", "\nIn his discussion of the principles of common sense, Reid presents\nvarious first principles, including the claims that memory is reliable\nand that those things exist that we distinctly perceive. Although\nsometimes he seems to claim that our particular perceptual judgments\nare derived from them, a closer look at what Reid says makes it clear\nthat this is not his considered view. For, in Reid’s view,\nordinary perceptual judgments are formed non-inferentially and are not\nself-evident. What role, then, do these principles of common sense\nplay? Nicholas Wolterstorff (2001, Ch. IX and 2004) argues that Reid\nthinks of such principles as being similar to what Wittgenstein, in\nOn Certainty, called “framework propositions.”\nThey are propositions that ordinary people do not typically explicitly\nbelieve but rather take for granted in their everyday comings and\ngoings. Similarly, one might hold that, properly understood,\nReid’s view is that the moral first-principles are not\npropositions that ordinary agents who have received a decent moral\neducation ordinarily consciously believe at some time or other.\nRather, they are what these agents take for granted in their moral\ndeliberations; they form the horizon or background against which they\ndeliberate—although these agents would, presumably, assent to\nthem if they were explicitly presented (for an alternative but, in\nprinciple, complimentary account, see Davis 2006, Ch. 6).", "\nBe that as it may, Reid’s deep impulse for affirming the\nexistence of these principles is not so much to reply to traditional\nworries about stopping a regress of reasons as to make an anti-Humean\npoint. (Hume, after all, also accepts the regress argument; see EAP\nV.vii.) According to Reid’s construal of it, the aim of Humean\npractical reason is not to determine the ends that we should have, but\nmerely to ascertain how most effectively to satisfy our passions (EAP\nIII.iii.i: 153; cf. also EAP II.ii: 54). Reid, by contrast, takes it\nto be evident that we can form a conception of our good on the whole\nand regulate our actions in accordance with it. But if we can do this,\nReid contends, then Hume’s account of practical reason cannot be\ncorrect. We can reason not just about means but also ends. Moreover,\nif Reid is correct and it is the province of reason to form a\nconception of one’s good on the whole, then Hume’s more\nextravagant claims about reason also cannot be correct. For, if Reid\nis right, not only is it reason’s province to form a notion of\none’s good upon the whole, it is also its role to guide action\nin such a way that it is conducive to one’s own good. It cannot\nbe true, then, that it is not contrary to reason for an agent to\nprefer his lesser good to his greater, as Hume claimed." ], "section_title": "3. Moral Principles", "subsections": [ { "content": [ "\nSo far, then, we have a sense of what, according to Reid, the first\nprinciples of morality are and the roles that Reid wished them to\nplay. What should be added is that Reid thinks them to be objective in\na fairly strong sense. Or to put things somewhat more guardedly, if we\ninterpret Reid’s claims that motives do not exist to mean only\nthat they do not exist in space/time, then Reid thinks they are\nobjective in a fairly robust sense (for different interpretations, see\nDavid 1985, Nichols 2002, Yaffe 2004, and Van Cleve 2015, ch. 10).", "\nIn the first place, Reid believes that the fundamental moral\nprinciples cannot be the product of convention. His argument in this\ncase is directed against Hume. In Reid’s view, Hume defends a\nconventionalist account of justice, which rides on a quasi-genetic\naccount of the emergence of the norms of justice. According to\nHume’s story, we begin with a notion of our good on the whole.\nOut of a concern to secure our good on the whole, we create the rules\nof justice by convention. In response, Reid notes that to have the\nconcept of one’s good on the whole, one must also have the\nconcepts of ‘being a favor’ and ‘being an\ninjury.’ These concepts, however, are “early in the mind\nof man as any rational notion whatever” (EAP V.v: 309). Reid\ncontends that Hume would seem also to be committed to as much. Hume,\nafter all, believes gratitude and resentment to be\n“natural” sentiments that are concerned with favors and\ninjuries. Call those concepts that cluster around the notion of\njustice, such as ‘being wronged,’ ‘being what is\ndeserved,’ and ‘being that to which one is\nentitled,’ our concepts of primary justice. Reid argues\nthat Hume’s quasi-genetic story faces a problem, for a person\ncannot have the concepts ‘being a favor’ and ‘being\nan injury’ without first having the concepts of primary\njustice.", "\nConsider favors. Favors, says Reid, are naturally connected with the\nbenevolent affection of gratitude; they are what merit this response.\nBut to express gratitude toward someone who has performed a favor is\nto believe or presuppose that that agent has benefited you by going\nbeyond what is owed. Or consider being injured (as opposed to simply\nbeing harmed). Being injured, says Reid, is naturally connected with\nthe malevolent affection of resentment. To express resentment toward\nan agent who has injured you is, however, to believe or presuppose\nthat he has wronged you, given you less than you deserve. If this is\nright, we do not derive the primary concepts of justice from an\ninterest to secure our good on the whole. To the contrary, the reverse\nis true; we can arrive at a notion of our own good on the whole only\nif we possess the concepts of primary justice. But if so, we cannot\nhold that we somehow constructed our notions and the rules of justice\nfrom a concern to secure our good on the whole. Our notion of our good\non the whole presupposes them (see Cuneo 2015 and Powell and Yaffe\n2015).", "\nIn fact, Reid believes that reflection on our concepts of primary\njustice reveals more than this. It also reveals that these concepts\nare irreducible to other normative concepts and fundamental to moral\nthinking. Reid’s way of making this point is to note that Hume\nattempts to ground the rules of justice not just in our notion of our\ngood on the whole, but also in considerations of utility. Reid holds\nthat this is a mistake. To “have the conception of\njustice,” it is necessary that “one perceive its\nobligation distinct from its utility” (EAP V.v: 306).\nConsiderations of utility, Reid holds, are the wrong sort of reasons\nto ground accountability relations, which are among the objects of our\nconcepts of primary justice. In his book, The Second-Person\nStandpoint, Stephen Darwall puts the point like this: To see that\nsomething is required of another is to take up the\n“second-person standpoint” with regard to him. To occupy\nthis standpoint is to have the authority to hold that person\naccountable for not doing what is required of him. Failure to perform\nan act that increases utility, however, is not the right sort of thing\nfor which to hold someone accountable (see Darwall 2006, especially\nthe discussion of Reid in Ch. 8; see also Wolterstorff 2010).", "\nIn addition to rejecting moral constructivist accounts of justice,\nReid rejects what we today would call response-dependent accounts of\nmoral facts. Roughly put, response-dependent views, which Reid\nattributes to sentimentalists such as Hutcheson and Hume, maintain\nthat moral reality is determined by the sorts of affective reactions\nwe have to the world. It is because certain actions and events elicit\ncertain types of affective states in us that they have properties such\nas being wrong or being obligatory. Drawing upon\nwhat rationalists such as Balguy and Price had argued, Reid asks us to\nconsider fundamental moral principles, such as the claim that, in\nordinary conditions, an agent ought to honor his promise. Claims such\nas this, Reid says, are necessarily true. But if the\nresponse-dependent view were correct, it is difficult to see how that\ncould be so. After all, we can imagine being constituted in such a way\nthat we failed to disapprove of those who do not honor their promises.\nIf the response-dependent view were true, then in those counterfactual\ncircumstances honoring one’s promises would not be obligatory;\nfailing to honor them, accordingly, would not be wrong. But that is\nfalse, for basic moral principles do not exhibit this sort of\ncontingency. Even in those counterfactual conditions it would be wrong\nnot to honor one’s word. If so, sentimentalists views, Reid\nconcludes, are false (see EIP VI.vi: 494–95)." ], "subsection_title": "3.1 Reid’s defense of the objectivity of moral first principles" } ] }, { "main_content": [ "\nWe noted earlier that contemporary philosophers tend to think of\nmodern philosophers as being either rationalists or sentimentalists\nabout morality. We also noted that Reid does not fit comfortably in\neither category, as his views tend to blend together both rationalist\nand sentimentalist commitments. This becomes especially evident in\nReid’s discussion of the moral sense. (See Davis 2006 for a\ndiscussion of how Reid’s account of the moral sense is\ninfluenced by the legal practices of his day.)", "\nIt was Francis Hutcheson who first developed the claim that we are\nendowed with a moral sense. While Hutcheson’s position has been\nvariously interpreted, his considered position appears to run as\nfollows. Rationalists tell us that our moral judgments are the output\nof reason. But many of our ordinary, nonmoral judgments are not the\noutput of reason. Our perceptual judgments concerning the external\nworld, our judgments about our own pain and pleasure, and our\naesthetic judgments, for example, are not the products of reason.\nRather, they are the products of various “senses” or\n“determinations of our minds to receive Ideas independently of\nour Will” (ONC, 17). Moral judgments, Hutcheson claims, are no\ndifferent in this respect. They are also the product not of reason but\nof a sense, in this case, the moral sense. Although Hutcheson\nhimself describes this sense in different ways, it is probably best to\nthink of it as a faculty that has two basic functions.", "\nIn the first place, it is that faculty by which we form moral ideas or\nconcepts and in such a way that does not involve any sort of reasoning\nor calculation. Rather, the “author of Nature” has\ndesigned us in such a way that, in a certain range of circumstances,\nwhen an agent is aware of the behavior of himself or others, this\nawareness evokes in him states of approbation. These states of\napprobation, in turn, elicit states of love and esteem for the person\nwhose behavior of which he’s aware. States of approbation,\nHutcheson indicates, thus function as signs of an\nagent’s benevolence, indicating its presence. Love and esteem,\nby contrast, do not indicate benevolence but are rather appropriate\naffective responses to it. Second, these affective states move us to\nbenevolent action. The moral sense at once puts us in contact with\nmoral reality and motivates us to act (see Cuneo 2013; Kail 2007)." ], "section_title": "4. The Moral Sense", "subsections": [ { "content": [ "\nThose familiar with Reid’s writing on perception will\nimmediately notice rather striking similarities between\nHutcheson’s account of the moral sense and Reid’s account\nof external sense. To see this, consider a case of ordinary tactile\nperception, such as when one perceives that the table before one is\nhard by touching it. In cases such as these, how do we perceive the\ntable’s hardness? According to Reid, in such cases, it is\npressure sensations—which, Reid stresses, largely go unnoticed\nand unnamed—that immediately produce in us a “conception\nand belief” of the table that it is hard. As such, Reid says,\nthe best explanation of how we perceive things such as a table’s\nhardness is that the “Author of our Nature” has designed\nus in such a way that, when all goes well, feelings of a certain range\nfunction as signs or indicators of it. (God, Reid emphasizes, could\nhave easily fashioned us in such a way that the perceptual process\nworked differently. For all we reasonably believe, God could have\nconstructed us in such a way that signs of an entirely different sort,\nsuch as noises or smells of a certain range, indicate a table’s\nhardness.) Reid stresses that, according to this account of\nperception, pressure sensations are not ideas in the sense that Locke\nor Hume thought of them. For pressure sensations do not function as\nintermediaries of which we are aware that imagistically represent the\ntable’s hardness and from which we infer its existence.", "\nIn order to explain judgments of these sorts, then, both Hutcheson and\nReid appeal not to reason but to an indigenous sense with which we\ncome hardwired. Both thinkers maintain that (in the ordinary case)\ninference plays no role in the production of such\njudgments—feelings being such as to immediately evoke them.\nBoth, moreover, offer thoroughly teleological accounts of perception,\nwhich appeal to the plan of the “Author of our nature.”\nAnd, finally, both champion semiotic accounts of perceptual judgment\nformation. According to the relevant design plans, sensations or\nfeelings of various kinds play the role of being signs for or\nindicators of qualities of things in the world.", "\nAt various points, Reid himself highlights the similarities between\nthe two senses (see EAP III.iii.vi: 179–80 and PE, 144). Having\nnoted these similarities, however, Reid goes on to claim that there is\nalso an important disanalogy between the judgments produced by\nexternal sense, on the one hand, and the moral sense, on the other: In\nthe former case, when all goes well, feelings elicit judgments about\nthe external world. In the latter case, the order of explanation is\nreversed: “In the approbation of a good action … there is\nfeeling indeed, but there is also esteem of the agent; and both the\nfeeling and the esteem depend upon the judgment we form of his\nconduct,” not vice-versa (EAP V.vii: 349; for discussion, see\nBroadie 1998 and Cuneo 2006). By stressing that states of approbation\nare not mere feelings but include full-blooded moral judgments, Reid\ntakes himself to have corrected a deficiency in Hutcheson’s\nview. For while Hutcheson nowhere denies that the outputs of the moral\nsense include the acceptance of moral propositions neither does he\naffirm this. Rather, what Hutcheson tells us is that states of\napprobation are feelings of pleasure and that they yield\n“love” for the benevolent. But Hutcheson, Reid points out,\nsays next to nothing about this latter state, never specifying whether\nit includes moral propositional content. By explicitly specifying that\nthe outputs of the moral sense have moral propositional\ncontent—indeed, a wide range of such contents—Reid takes\nhimself to have identified more accurately the character of its\noutputs.", "\nLet us pull these strands of argument together. Both Hutcheson and\nReid, we’ve seen, maintain that we come equipped with a moral\nsense that bears certain resemblances to external sense. The Reidian\nmoral sense differs in two important respects, however, from the\nHutchesonian one. First, the outputs of the Reidian moral sense\ninclude not only moral conceptions, but also full-blooded moral\nbeliefs with moral propositional content. (Reid, incidentally,\nunderstood Hume to deny that moral judgments have moral propositional\ncontent; for his attack on this view, see EAP V.vii and Cuneo 2004).\nThese moral beliefs themselves concern not only general moral truths,\nsuch as the moral first principles, but also particular ones, such as\nthat this particular person’s behavior merits approbation.", "\nSecond, we have seen that Reid reverses the order of explanation\nbetween sentiment and moral judgment. In the paradigmatic case, moral\njudgments elicit moral sentiments, not vice-versa. Although Reid\nreverses Hutcheson’s order of explanation claim, he still thinks\nof a range of particular moral judgments as being cases of moral\nperception. His basic approach is to claim that, in moral perception,\nit is not sentiments that function as signs of moral properties.\nRather, it is the behavior and countenance of agents that play this\nrole. Roughly, the guiding idea is that moral properties of a certain\nrange attach to the mental states of agents such as their beliefs,\ndesires, and intentions. For example, the property being kind\ncan attach to an agent’s intention to perform a certain act.\nThese mental states and their properties manifest themselves in the\nbehavior and countenance of agents. Ordinary mature agents are so\nconstituted that, when all goes well, upon becoming aware of the\nbehavior and countenance of these agents, this awareness\nnon-inferentially evokes in us the conception and belief of those\nagents that they have properties such as being kind,\ndeceitful, faithful, and so forth. In this regard,\nmoral perception exhibits the same fundamental structure as our\nperception of what Reid calls visible figure, such as an\nobject’s length and height (see Cuneo 2003, 2006, Kroeker 2010,\nCopenhaver 2014). In both cases, features of our environment function\nas signs for a given quality, these signs being such as to\nnon-inferentially produce conception and belief. Here is how Reid\nhimself puts the point:", "\n\n\nIntelligence, design, and skill, are not objects of the external\nsenses, nor can we be conscious of them in any person but\nourselves….\n\n\nA man’s wisdom is known to us only by the signs of it in his\nconduct; his eloquence by the signs of it in his speech. In the same\nmanner we judge of his virtue, of his fortitude, and of all his\ntalents and qualities of mind.\n\n\nYet it is to be observed, that we judge of men’s talents with as\nlittle doubt or hesitation as we judge of the immediate objects of\nsense.\n\n\n… We perceive one man to be open, another cunning; one to be\nignorant, another very knowing; one to be slow of understanding,\nanother quick. Every man forms such judgments of those he converses\nwith; and the common affairs of life depend upon such judgments. We\ncan as little avoid them as we can avoid seeing what is before our\neyes.\n\n\nFrom this it appears, that it is no less part of the human\nconstitution, to judge of men’s characters, and of their\nintellectual powers, from the signs of them in their actions and\ndiscourse, than to judge of corporeal objects by our senses. (EIP\nVI.vi: 503–4)\n", "\nIt is Reid’s view, then, that we can apprehend both the external\nworld and moral reality. He also holds that the beliefs formed on the\nbasis of these apprehensions are generally in good epistemic order.\nSo, in the case of our perception of external objects, Reid rejects\nskepticism. Admittedly, Reid says, we may lack a complete explanation\nof how we become aware of external reality. But this, says Reid, is no\nreason to doubt that we can in fact apprehend it.", "\nIn fact, Reid claims, there are powerful reasons to reject skepticism\nabout external sense. For consider our indigenous or\n“original” epistemic faculties such as memory,\nintrospection, reasoning, and perception. The outputs of these\nfaculties include judgments of various sorts—judgments about\nwhat happened, what one is feeling, what to conclude given one’s\nevidence, and so forth. The practices of forming these judgments are\nsocially well-established over time. Indeed, they are so deeply\nentrenched that engaging in them is, for all practical purposes,\ninescapable; we cannot avoid forming memory judgments, introspective\njudgments, perceptual judgments, and so forth. Moreover, we have\nsophisticated methods of evaluating judgments made in these domains,\nincluding ways of checking their reliability and the appeal to experts\nof various sorts. Finally, many of the judgments made in these domains\nare not subject to systemic disagreement among competent participants.\nBy and large, our judgments about the external world, for example,\nconverge.", "\nShould we trust the deliverance of indigenous faculties of this sort?\nIn one of his better known dialectal maneuvers, Reid claims that we\nshould. For, Reid says, our situation is this. If we didn’t\ntrust any of our indigenous faculties, we would face wholesale\nskepticism. Our most basic processes of reasoning would be rationally\nundercut, for we could not trust their deliverances. If we trust only\nsome but not all of our original faculties, then Reid claims we are\nbeing arbitrarily partial. Given that these faculties exhibit similar\nfeatures, what reason could we have—at least at the outset of\ntheorizing—for trusting one but not the other? In a well-known\npassage, Reid puts the point like this:", "\nReason, says the sceptic, is the only judge of truth, and you ought to\nthrow off every opinion and every belief that is not grounded on\nreason. Why, Sir, should I believe the faculty of reason more than\nthat of perception; they came both out of the same shop, and were made\nby the same artist; and if he puts one piece of false ware into my\nhands, what should hinder him from putting another? (IHM VI.xx: 169)\n", "\nReid continues in this vein, noting that trusting our indigenous\nfaculties does not imply that we must suppose that they operate\nflawlessly:", "\nThere is no more reason to account our senses fallacious, than our\nreason, our memory, or any other faculty of judging which nature hath\ngiven us. They are all limited and imperfect…. We are liable to\nerror and wrong judgment in the use of them all; but as little in the\ninformations of sense as in the deductions of reasoning. (EIP II.xxii:\n251–52; for discussion, see Greco 2002 and 2004)\n" ], "subsection_title": "4.1 Reid’s view compared with Hutcheson’s" }, { "content": [ "\nIn Essays on the Active Powers, Reid extends this line of\nargument to the moral sense. The fact that we have no well-worked out\ntheory of how we form moral judgments does not itself rationally\nundercut the epistemic status of these judgments (see EAP V.ii:\n282–83). More importantly, the moral sense, Reid argues, is also\nindigenous. All normal human beings raised in a normal environment\nhave it. Moreover, its outputs include judgments of various\nsorts—judgments about what is wrong, right, approbation-worthy,\nand so forth. The practice of forming moral judgments is, furthermore,\nsocially well-established over time. In fact, it is so deeply\nentrenched that it is, for all practical purposes, inescapable; try as\nwe might, we cannot avoid forming moral judgments. We also have\nsophisticated methods of evaluating moral judgments, such as appeals\nto what we today would call reflective equilibrium (see EAP\nIII.iii.vi). Finally, many moral judgments—in particular, those\nthat concern the first principles—are not subject to systemic\ndisagreement among competent participants. By and large, in\nReid’s view, our judgments about these principles converge (see\nEAP III.iii.vi; for discussion, see Cuneo 2011b, 2011c and Levy 1999.\nDavis 2006 and 2010 explore Reid’s treatment of moral\ndisagreement).", "\nGiven all this, Reid contends that we should reject moral skepticism.\nAt the outset of inquiry, the deliverances of the moral faculty, like\nthe deliverances of our other indigenous cognitive faculties, deserve\nan innocent until proven guilty status. Unlike Ross after him, Reid\nseems to think that our beliefs about not only moral first principles\nbut also particular cases can count as instances of knowledge.", "\nTo this point, we have seen important respects in which Reid’s\naccount of the moral sense both articulates with and deviates from\nHutcheson’s. On the one hand, Reid is, like Hutcheson, concerned\nto distance his view from the rationalists, who come very close to\ncharacterizing moral knowledge as a species of ordinary theoretical\nknowledge such as that achieved in mathematics. On the other, Reid\nalso wants to correct certain deficiencies in the sentimentalist\nprogram, such as the tendency to drive a sharp wedge between reason\nand “sense” and to think of the deliverances of the moral\nsense as mere feelings. This allows Reid to defend the claim that the\nmoral sense is reliable in a perfectly straightforward sense.", "\nStill, while Reid wishes to emphasize that the moral sense issues in\nbona fide moral judgments, he also emphasizes that it issues in more\nthan mere moral judgments. Reid writes: “Our moral judgments are\nnot, like those we form in speculative matters, dry and unaffecting,\nbut from their nature, are necessarily accompanied with affections and\nfeelings …” (EAP III.iii.vii: 180). Reid calls the\ncomplex state that combines moral judgment, affection, and feeling\n“moral approbation.”", "\nMoral approbation, then, comprises three elements: moral judgment,\naffection, and feeling. Reid is clear that the moral judgments in\nquestion are not general ones that concern the first principles of\nmorals, but particular judgments that concern whether someone has\nbehaved well or badly or exemplifies a virtue or vice. The affections\nthat accompany them are, in turn, dispositions “to do good or\nhurt to others,” which have a de re structure since\nthey have “persons, and not things” [i.e., propositions]\nas their immediate object (EAP III.iii.iv: 107). Finally, Reid accepts\na minimalist account of the feelings that comprise moral approbation.\nFeelings such as pleasure and pain, in Reid’s view, have no\nintentional object; they are not about anything. Rather, they are, as\nit were, adverbial modifiers of mental states and events: one esteems\nanother pleasurably or disapproves of another painfully. By\ndistinguishing approbation from feeling, Reid clearly rejects the\nposition according to which (what we today would call) desires are to\nbe identified with feelings of one or another sort.", "\nIt is not difficult to discern the theoretical work that this account\nof moral approbation is supposed to do for Reid. Under a natural\nreading, in both the Treatise and the second\nEnquiry, Hume charged rational intuitionists with having no\naccount of why moral judgments, which are the output of reason, should\nhave such an intimate connection with motivation. Reid’s answer\nto this challenge is to “go nativist”: We are so\nconstituted that when we judge that, say, an action is unjust, we are\nmoved to action. That the moral sense should yield both judgments and\nmotivational states is built into its functional profile or design\nplan. By emphasizing that this is how things go in the moral realm,\nReid takes himself to employ a strategy he has used elsewhere in his\nelaboration of our perception of the external world.", "\nRecall in this regard Reid’s account of tactile perception. In\nthe case of tactile perception, Reid says that given certain\nexperiential inputs, such as the pressure sensations evoked upon\ntouching a table, we form judgments about the hardness of the table.\nThe pressure sensations function as signs of the table’s\nhardness, which immediately evoke the judgment in question. According\nto this account, there are no mental images or “ideas”\nfrom which we infer the hardness of the table. Likewise, in the moral\ncase, we are presented with various kinds of experiential inputs such\nas the behavior and countenance of agents. These experiential inputs\nfunction as signs, immediately evoking in us moral judgments of\nvarious sorts. When all goes well, these judgments, in turn, yield\naffection and feelings of various sorts. Once again, there are no\nideas from which we infer moral judgments and the process of judgment\nformation is itself noninferential. By emphasizing the similarities\nbetween these two cases, we have seen that Reid takes himself to\ndefend an account of moral perception. It is an account, in\nReid’s view, which blends together the most promising features\nof both the rationalist and sentimentalist traditions (see Cuneo\n2007a, forthcoming b). For it implies both that moral judgments\nexpress genuine moral propositional content and that these judgments\nbear an intimate connection with moral motivation." ], "subsection_title": "4.2 Reid’s defense of the reliability of the moral sense" } ] }, { "main_content": [ "\nReid’s view is a version of agency-centered ethical\nintuitionism. The view is agency-centered because Reid develops his\naccount of moral motives in light of his broadly agent causal account\nof agency and regulation account of autonomy, according to which our\nrational nature consists in our ability to regulate our conduct by\nappeal to the rational principles of action. This account of moral\nmotives, we have seen, borrows a great deal from the rationalists. The\nmoral first principles, says Reid, are self-evident necessary truths\nwhich are knowable to a person with a sound understanding, a decent\nmoral education, and not in the grip of distorting influences. Reid,\nhowever, was no ideologue, and freely borrowed from sentimentalists\nsuch as Hutcheson. In particular, he borrows from the sentimentalists\nthe conceptuality of the moral sense, which figures so importantly in\nhis work. The idea that the moral sense is at once an\ninformation-processing system whose deliverances are affective states\nthat move us to action, we’ve seen, resembles closely what\nfigures such as Hutcheson claim. Finally, we have also seen that, at\nvarious points, Reid’s thought coincides with Kant’s. This\nis especially evident when one considers Reid’s regulation\naccount of autonomy and his defense of what Darwall calls the\nsecond-person standpoint.", "\nRather few contemporary philosophers could accept all of Reid’s\ncentral claims—agent causation, teleological accounts of action,\nand occasionalism not being the dominant views of our day. Still, for\nthose who resonate with a broadly realist version of ethical\nnon-naturalism with emphases similar to Kant’s, Reid’s\nview is intriguing. Its resources remain to be mined." ], "section_title": "5. Conclusion", "subsections": [] } ]

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Thomas Reid and the Story of\nEpistemology, Cambridge: Cambridge University Press.", "–––, 2004. “Reid on Common sense,”\nin Cuneo and van Woudenberg 2004.", "–––, 2010. “Reid on Justice,” in\nRoeser (ed.) 2010.", "Yaffe, Gideon, 2004. Manifest Activity: Thomas Reid’s\nTheory of Action, Oxford: Oxford University Press.", "–––, 2007. “Promises, Social Acts, and\nReid’s First Argument for Moral Liberty,” Journal for\nthe History of Philosophy, 45: 267–89." ]

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[ "\n\nThomas Reid held a direct realist theory of memory. Like his direct\nrealism about perception, Reid developed his account as an alternative\nto the model of the mind that he called ‘the theory of\nideas.’ On such a theory, mental operations such as perception\nand memory have mental states—ideas or impressions—as\ntheir direct objects. These mental states are understood as\nrepresentations that encode information about their causes. The mind\nis directed towards and reads off from these representations,\ninformation about extra-mental items. By contrast, Reid holds that the\ndirect objects of memory and perception are extra-mental. In the case\nof perception, the mind is directed to present material objects and\nproperties; in the case of memory, the mind is directed towards past\nevents to which the person was agent or witness. In other words,\naccording to Reid, when we remember, we do not recall previous\nexperiences. In memory, the mind is directed neither towards an idea\nexperienced previously nor towards an idea of a previous\nexperience. Rather, we recall events, experienced\npreviously.", "\n\nReid is interested in the notion of memory not only for its own sake\nbut also because of its conceptual connection to the notion of personal\nidentity. Reid criticizes Locke’s theory of personal\nidentity for inferring a metaphysical hypothesis now called the Memory\nTheory from the conceptual connection between memory and personal\nidentity. On this theory, personal identity consists in\nmemory; sameness of memory is metaphysically necessary and sufficient\nfor sameness of persons. According to Reid, memory is neither necessary\nnor sufficient for personal identity, metaphysically speaking.\nIndeed, Reid holds that it is impossible to account for personal\nidentity in any terms other than itself. Personal identity is\nsimple and unanalyzable. Though memory is not the metaphysical ground\nof personal identity, according to Reid, it provides first-personal\nevidence of personal identity. I know that I was present at my\ngraduation because I remember being there. Memories do not\nmake one the same person over time. Rather, memories\nallow one to know one’s own past, immediately and directly." ]

[ { "content_title": "1. Criticizing the Storehouse Model of Memory", "sub_toc": [] }, { "content_title": "2. A Direct Realist Theory of Memory", "sub_toc": [] }, { "content_title": "3. Objecting to Locke on Personal Identity", "sub_toc": [] }, { "content_title": "4. Personal Identity as Simple and Unanalyzable", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Primary Works", "Secondary Works" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nReid traces the target of his criticisms back to the Ancients, whom he\ndepicts as holding that the mind is a sensorium—a repository of\npast ideas and impressions (Essays,\n 280).[1] \n On this\ntheory, perception, memory and imagination are causal processes\nbeginning with purely physiological events: impressions on the\nbrain. These physiological states are taken to have mental\ncorrelates—sensations or ideas of sense or sense\nimpressions—which are the objects of perception, memory and\nimagination. These ideas or impressions are representations in the\nsense that they preserve, or re-present information from their\nphysiological correlates. According to Reid, this view recognizes no\ndistinction between imagination and memory. Each consists in having a\npicture-like impression that remains after the object that\nimpressed upon the senses is gone. The only difference between the two\nis in the fidelity of the imagistic impression to its cause. Memory\nconsists in the preservation of images imprinted in the mind from\nprevious experiences, while imagination consists in constructing\nimages that lack a duplicate in experience.", "\n\nReid offers two criticisms of the ancient theory, as he understands\nit. First, the theory falls afoul of one of Reid’s own\nmethodological strictures, namely, that a theory must adhere to\nNewton’s regulae philosophandi, or rules of\nphilosophizing (Inquiry, 12). The first rule is to posit\nno merely theoretical causes and in Reid’s view the second rule\nforbids positing causes insufficient to explain the phenomenon in\nquestion. According to Reid, there is no observational evidence\nof the existence of impressions on the brain—they are merely\ntheoretical entities (Essays, 281). Furthermore, even if\nwe granted the otherwise theoretical existence of impressions, such\nentities would not be sufficient to explain memory. We might\nestablish a correlation between impressions and memories, but it would\nremain at best just that: a correlation, not a causal\nexplanation. Having learned Hume’s lessons about causation,\nReid denies any necessary connections between impressions and memories\nsufficient to regard the former as a cause of the latter. Reid\nalso considers whether resemblance could ground such a causal\nexplanation, but, having learned Berkeley’s lessons about\nresemblance, he denies that any mental states can resemble material\nstates such as impressions on the brain. Reid’s second\ncriticism is that even if we were to grant that impressions remain\nafter the objects that impressed upon the senses are gone, this would\nentail that we should continue to perceive objects rather than remember\nthem, since on the ancient theory, impressions are the immediate causes\nand objects of perception (Essays, 282).", "\n\nThough Reid identifies his target as having ancient origins, his\nprimary concern is with what he regards as its modern equivalent.\nThis modern theory was introduced by Locke and, according to Reid,\nextended to its inevitable idealist and skeptical conclusions by\nBerkeley and Hume. Reid excerpts passages from Locke’s\nEssay Concerning Human Understanding to illustrate the\nmisleading metaphors Locke inherits from the ancient\ntheory—metaphors of the mind as a storehouse and of ideas and\nimpressions as pictures.", "\n\nThe other way of Retention is the Power to revive again in our Minds\nthose Ideas, which after imprinting have disappeared, or have\nbeen as it were laid aside out of sight…This is Memory,\nwhich is as it were the Store-house of our Ideas…But\nour Ideas being nothing but actual Perceptions in the Mind,\nwhich cease to be any thing, when there is no perception of them, this\nlaying up of our Ideas in the Repository of the\nMemory, signifies no more but this, that the Mind has a Power, in many\ncases, to revive Perceptions, which it once had, with this additional\nPerception annexed to them, that it has had them before. And in\nthis Sense it is, that our Ideas are said to be in our\nMemories, when indeed, they are actually no where, but only there is an\nability in the Mind, when it will, to revive them again; and as it were\npaint them anew on it self, though some with more, some with less\ndifficulty; some more lively, and others more obscurely (Locke,\nEssay, Book II.x.1–2).", "\n\nAs this passage illustrates, Locke himself acknowledges that the\nnotion that the mind is a kind of repository or storehouse is\nmetaphorical. According to Locke’s own theory, ideas and\nimpressions cannot be stored. Locke is committed to the thesis\nthat ideas are momentary and non-continuous and to the thesis that\nidentity over time requires continuous existence. These two\ntheses jointly entail that numerically identical ideas cannot be stored\nover time. Nevertheless, Reid criticizes Locke for being unable\nto extricate himself from metaphor when Locke claims that in memory,\n“the mind, as it were, paints ideas anew on it self.”\nOn what model does the mind paint the idea anew? In order to use\na previous idea as its model, the mind must remember it. But then\nthe ability to paint ideas anew upon itself presupposes rather than\nexplains memory.", "\n\nLocke offers a non-metaphorical account of memory when he claims\nthat memory consists of two perceptions: a present perception and a\nbelief about that present perception, namely that one has enjoyed the\nperception before. Because Locke is committed to the thesis that\nnumerically identical ideas cannot be stored over time, the belief must\nbe the belief that one has previously enjoyed a perception\nqualitatively similar to the present perception, rather than\nnumerically identical with it. Reid criticizes this account as\ncircular, once more. A first-personal belief that one’s\npresent perception is qualitatively similar to a perception one had in\nthe past requires remembering having had that previous perception and\nrecalling its quality and character. As before, Locke’s\naccount presupposes rather than explains the phenomenon of memory\n(Essays, 285).", "\n\nReid criticizes Hume’s account of memory for duplicating\nLocke’s mistakes. He quotes from Hume’s Treatise\nof Human Nature:", "\n\nWe find by experience, that when any impression has been present\nwith the mind, it again makes its appearance there as an idea; and this\nit may do after two different ways: Either when in its new appearance\nit retains a considerable degree of its first vivacity, and is somewhat\nintermediate betwixt an impression and an idea; or when it entirely\nloses that vivacity, and is a perfect idea. The faculty by which\nwe repeat our impressions in the first manner, is call’d the\nMEMORY, and the other the IMAGINATION (Hume, Treatise,\n1.1.3.1).", "\n\nLike Locke, Hume holds that ideas have no continued existence.\nAnd so, Reid argues, Hume cannot claim that a numerically identical\nidea can reappear. In addition, Hume’s account faces the\nsame circularity objection as Locke’s. Hume accounts for\nmemory by appealing to an idea that is qualitatively similar to, but\nless forceful and vivacious than a previous idea. But the ability\nto judge qualitative similarity and degrees of force and vivacity\nbetween present ideas and past impressions presupposes memory.", "\n\nReid provides additional criticisms of Hume’s account of\nmemory. First, Reid interprets Hume’s account of memory as\ncommitting him to the position that we have the power to repeat ideas\n(though notice that Hume does not commit to this in the quoted\npassage). Reid argues that this position is inconsistent with\nHume’s claim that impressions are the efficient causes of\nideas. Reid’s second criticism is more insightful; he\nargues that differences in degrees of force and vivacity are\ninsufficient to sustain the distinctions between perception, memory and\nimagination. Reid interprets Hume as holding that these three\nfaculties do not differ in kind, but rather in the degree of force and\nvivacity of the ideas that are their objects. Ideas with the\ngreatest degree of force and vivacity are perceptions, those with a\nlesser degree are memories, and those with the least degree of force\nand vivacity are imaginings. Reid criticizes this taxonomy on\nphenomenological grounds. Some perceptions are less forceful and\nlively than some memories, as when lost in reminiscence, and some\nmemories are less forceful and lively than imaginings, as when lost in\nreverie. Furthermore, increasing the degree of force and vivacity\ndoes not transform a memory or an imagining into a perception.\nReid compares striking one’s head against the wall to lightly\ntouching it to the wall. The latter has much less force and\nvivacity than the former, yet lightly touching one’s head to the\nwall is neither a memory nor an imagining (Essays, 289).", "\n\nReid grants that perceptions, memories and imaginings often differ in\ndegree of force and vivacity, but, he argues, this difference is\ninsufficient to account for the special quality of presentness\nrepresented in perceptions, the special quality of pastness\nrepresented in memories, and the special quality of atemporality\nrepresented in imaginings (Inquiry, 197). While memories may\nbe faint, or weak, these features are not necessary to these states\nbeing memories, and so cannot be used to individuate them. In\naddition, a present idea—whatever its degree of force and\nvivacity—cannot ground judgments about events in the past\nbecause present ideas represent events as present.", "\n\nFor according to that theory, the immediate object of memory, as\nwell as every other operation of the understanding, is an idea present\nto the mind. And, from the present existence of this idea of\nmemory I am led to infer, by reasoning, that six months ago or six\nyears ago, there did exist an object similar to this one…But\nwhat is there in the idea that can lead me to this conclusion?\nWhat mark does it bear of the date of its archetype?\n(Essays, 476)", "\n\nPresent ideas contain no information, qualitatively or\nrepresentationally, that could serve as the basis of judgments about\npast events. As a result, no reflection on present ideas and\ntheir quality or character is sufficient for a representation of events\nin the past, as past." ], "section_title": "1. Criticizing the Storehouse Model of Memory", "subsections": [] }, { "main_content": [ "\n\nContemporary philosophers and cognitive scientists recognize that\nmemory is a diverse phenomenon and they draw some useful distinctions\namong varieties of\n memory.[2]\nFor example, Endel Tulving distinguishes\nbetween episodic memory, semantic memory and procedural memory.\nRemembering how to ride a bike is an example of procedural\nmemory. Remembering that Napoleon was defeated at Waterloo is an\nexample of a semantic memory. Remembering one’s tenth\nbirthday party is an example of an episodic memory.", "\n\nThe distinction most relevant to the issues Reid, Locke and Hume raise\nfor memory and personal identity is between semantic and episodic\nmemory. Henri Bergson and Bertrand Russell developed a similar\ndistinction, and Russell’s distinction between factual and personal\nmemory accords with that between semantic and episodic memory.\nSemantic memories are properly reported using a factive\ncomplement—a that-clause—after the verbs\n‘remember’ or ‘recall’, as in ‘Jane\nremembers that Napoleon was defeated at Waterloo’. In\nparticular, a semantic memory\ncannot be reported using the form ‘S\nremembers/recalls [x] f-ing’, as in ‘Jane\nrecalls her tenth birthday party,’ or ‘John remembers\nfalling off his bike.’ Only episodic memories may be\nproperly reported using this form. No one today can properly\nreport ‘I remember Napoleon being defeated at Waterloo,’\nthough many may properly report ‘I remember that\nNapoleon was defeated at Waterloo.’ On the other hand, an\nepisodic memory can be reported using the same form by which\nsemantic memories are reported because episodic memories may ground\nsemantic memories under certain circumstances. It is legitimate\nto state both ‘I recall my tenth birthday party,’ in\nreporting an episodic memory of that event and to state ‘I\nremember that I had a tenth birthday party’, in reporting a\nsemantic memory, whose justification would appeal to the previous\nepisodic memory.", "\n\nEpisodic memories are further distinguished from semantic memories\nby the Previous Awareness Condition on episodic memory. The\nPrevious Awareness Condition has been developed and examined by Sydney\nShoemaker (1970), among\n others.\nPut simply, one has an episodic memory of\nan event only if one was agent or witness to the event\nremembered. The Previous Awareness Condition is a necessary but\ninsufficient condition on episodic memory. If one has an\nexperience as of being lost in a store as a child, but one was not in\nfact lost in a store as a child, such an experience is not an episodic\nmemory. On the other hand, each of us has been agent or witness\nto many events of which we have no episodic memory. For example,\none may not remember one’s third birthday party and so lack an\nepisodic memory of an event to which one was surely witness.", "\n\nReid is most interested in episodic memory. Though Reid does\nnot use the contemporary terminology, his theory draws upon both the\ndistinction between episodic and semantic memory and the Previous\nAwareness Condition on episodic memory. As he puts the matter:", "\n\nThings remembered must be things formerly perceived or known.\nI remember the transit of Venus over the sun in the year 1769. I\nmust therefore have perceived it at the time it happened, otherwise I\ncould not now remember it. Our first acquaintance with any object\nof thought cannot be by remembrance. Memory can only produce a\ncontinuance or renewal of a former acquaintance with the things\nremembered (Essays, 255).", "\n\nThough Reid uses the term ‘acquaintance,’ the things\nretained through memory are things previously perceived or\nexperienced. The term ‘acquaintance’ has acquired a\ntechnical sense that it did not have in Reid’s day, so it is\nbetter to see Reid as holding that memory preserves contact with events\npreviously apprehended through perception and thereby known by\nacquaintance. Acquaintance presupposes apprehension, and prior\nepisodes of apprehension are necessary for retained acquaintance.", "\n\nAccording to Reid, episodic memory is not a current apprehension of a\npast event, nor is it a current apprehension of a past\nexperience. These theoretical options were ruled out by\nReid’s criticism of Locke and Hume. Rather, according to\nReid, memory is an act that preserves a past apprehension. Reid\ncharacterizes memory as exhibiting what we now call the Previous\nAwareness Condition. He holds that reports of episodic memory are\ntrue only if the person reporting satisfies the condition, and that\nexperiences that otherwise appear to be episodic memories, but\nwhich fail the condition, are not episodic memories (Essays,\n264).", "\n\nReid does not count what we term ‘semantic memories’ as\nmemories in the proper sense. He discounts them not because they fail to\nmeet the Previous Awareness Condition, but because he holds that\nsemantic memories are better classified as beliefs or knowledge rather\nthan memories. For example, he would hold that a person today who\nreports remembering that Napoleon was defeated at Waterloo\nexpresses a belief or knowledge rather than a memory. He holds\nthis because he requires a distinction between two sorts of beliefs\nthat would otherwise be obscured by the fact that each sort can be\nexpressed in the form of a semantic memory report. The distinction is\nbetween beliefs that play a role in preserving past apprehension\n(and which are constituents of episodic memory), and those\nthat do not play a role in preserving past apprehension (and which are\nnot, strictly speaking, memories). For example, Jane believes\nthat she dined with a friend last night. Jane has an episodic\nmemory of this event, and according to Reid, her belief ‘that I\ndined with a friend last night,’ plays a role in preserving\nJane’s past apprehension of dining with her friend. On the\nother hand, Jane’s belief that she had a third birthday party\ndoes not play a role in preserving her past apprehension of her third\nbirthday party; she has no episodic memory of her third birthday\nparty. The difference between these two sorts of belief is\nobscured by the fact that each may be expressed by using the factive\ncompliment: ‘Jane remembers that she dined with a friend\nlast night,’ and ‘Jane remembers that she had a\nthird birthday party.’", "\n\nAccording to Reid, a memory consists in a conception of a past event\nand a belief about that past event, that it happened to the person who\nis represented in that memory as agent or witness (Essays,\n228, 232, 254, 257). This conception-belief structure mirrors Reid’s\naccounts of perception and consciousness, each of which also consist\nin a conception and belief. Folescu (2018a) examines whether memorial\nconception differs from or is the same as the kind of conception\ningredient in perception, consciousness, and other intentional mental\nstates. The belief that is a constituent of memory, on Reid’s view, is\na belief of some past event, that it happened. In particular, it is a\nbelief that it happened to me, where the pronoun is indexed to the\nperson who is represented in the memory as agent or witness to the\nevent (Essays, 255, 262). The belief is about\nor of the event because the other constituent of\nmemory—the conception—supplies the event, which is the\nobject of the belief. On Reid’s view, the objects of memory are the\nevents presented in past apprehensions. Memory preserves past\napprehensions by relating us to the events originally presented in\nperception—memory preserves past apprehension through conception\nand belief. In particular, the objects of memory are not the past\napprehensions themselves but that which is presented in the past\napprehensions, namely, the original event (Inquiry,\n28). Folescu (2018b) examines a tension in Reid’s accounts of memory\nand perception. According to Reid, we remember events that were\napprehended in the past by perception. But Reid insists that\nperception is confined to the present. Because perception is confined\nto the present, we cannot perceive events, which have a duration. How,\nthen, can we remember what we cannot have perceived? ", "\n\nReid holds that memory is not a current apprehension of an event\nalready presented in a past apprehension. In other words, we do\nnot remember events by re-apprehending them. Rather, the\npast apprehension is itself preserved by the act of remembering the\nevent apprehended. Memory is an act of preservation through\nconception and belief. Such preservation does not itself\nconstitute an additional apprehension over and above the\napprehension preserved. Indeed, according to Reid, it is\nimpossible to currently apprehend any events in the past; apprehension\nis confined to perceiving present objects or being conscious of present\nmental operations (Essays, 23, 253). Reid does not deny\nthat memory is itself a current mental state, nor does he deny that\nmemory presupposes a past apprehension. He denies only that\nmemory is a current apprehension, and that the object of a memory is a\npast apprehension (Essays, 253). Memory preserves past\napprehension by conceiving of an event previously apprehended and\nbelieving, of this event, that it happened to me.", "\n\nReid holds that memory, like perception, is immediate. Neither\nthe conception nor the belief that are the ingredients of memory are\nformed on the basis of reasoning or testimony. Memory is an\noriginal faculty of our constitution governed by what Reid calls\n“the first principles of contingent truths.” In the\ncase of memory, the governing principle is that “those things did\nreally happen which I distinctly remember” (Essays,\n474). On Reid’s view, a normally functioning human does not\nand need not infer to a past event in episodic memory. In order\nto infer to a past event, one must have some prior, non-inferential\nrelation to the event if it is to be a memory rather than a belief or\nknowledge. But then this prior, non-inferential relation would be\nan episodic memory. In addition, if episodic memory involved an\ninference to the effect that the event happened to me, the inference\nwould be otiose because, as Reid claims, such a belief is already an\nimmediate, non-inferential component of episodic memory. In\nprinciple, one could infer from the conception and belief that are\ningredients in memory to a further belief that the event\nhappened. But if such a belief plays a role in preserving past\napprehension then it is superfluous—such a belief, subject to\nthe Previous Awareness Condition, is already embedded in episodic\nmemory. If the belief does not play a role in preserving past\napprehension then it is a semantic memory, which, according to Reid, is\namong the species of belief or knowledge rather memory.", "\n\nThe distinction between beliefs that are ingredients in episodic\nmemories and beliefs that are based on, but not ingredients in,\nepisodic memories allows Reid to account for cases in which a memorial\nexperience continues to represent an event as having happened, even\nwhen the person who seems to remember the event has what she regards as\nan overriding reason to believe that the event did not occur. The\nbelief that is an ingredient in the experience represents the event as\nhaving happened to the person who seems to remember it. Further, the\nbelief will continue to represent the event as having happened to the\nperson, even under conditions in which she forms a separate belief, not\nembedded in the memorial experience, to the effect that it did not\nhappen to her.", "\n\nThe distinction also allows Reid to satisfy a constraint on any\nadequate theory of memory; namely, that it explain why memory\nrepresents events as having the special quality of being in the\npast. If belief were not an ingredient in episodic memory, then\nthough we might believe that the events we remember are in the\npast, memory could not represent events as past. If\nbelief were not an ingredient in memory, then memory alone would relate\nus to an event previously apprehended. But the apprehension\npreserved is an apprehension of an event that was, at that time,\nrepresented in that apprehension as present. The pastness of the\nevent apprehended is not part of the content of the past\napprehension. But because a belief that the event happened to me\nis embedded in the memory itself, memory represents not merely past\nevents, but past events as having occurred. In other words, the\nbelief that is partly constitutive of episodic memory is tensed.", "\n\nOne might wonder whether Reid’s account of memory is subject to the\nsame criticisms he levels against Locke and Hume. Does Reid appeal to\nthe storehouse metaphor when he claims that memory is preserved past\napprehension? Reid criticizes Locke and Hume for begging the\nquestion. Yet by holding that memory is in part constituted by a\nbelief, does Reid not also assume the very phenomenon to be explained?\nReid can avoid the criticisms to which the theory of ideas is\nvulnerable by insisting that memory is not a current apprehension, but\nrather a preserved past apprehension. His theory of memory is a direct\nrealist theory because, according to Reid, memory is not directed\ntowards any present perceptions, ideas, or impressions—stored or\notherwise. Neither is memory directed towards any past perceptions,\nideas, or impressions—stored or otherwise. Memory is directed\ntowards the events presented in past apprehensions. Because\napprehensions, perceptions, ideas, and impressions are never the\nobjects of memory, they do not need to be stored for use by\nmemory. Likewise, the belief that is an ingredient in memory is not\nabout any present or past apprehensions. If it were, Reid’s theory\nwould be subject to the same circularity objection he presses against\nLocke and Hume.", "\n\nOn Reid’s theory of memory, an apprehension establishes a\ndirect relation to an event, which relation is preserved in memory by\nthe acts of conceiving the event and believing of the event conceived\nthat it happened to the person who remembers. It is a direct\nrealist theory of memory because it departs from the model on which\nmemory is a current apprehension of a past event or a current\napprehension of a past apprehension. On the direct realist view,\nmemory preserves past apprehension of an event through conception and\nbelief. Reid’s theory captures how memory, like perception,\nrepresents the world, rather than our experiences of the world." ], "section_title": "2. A Direct Realist Theory of Memory", "subsections": [] }, { "main_content": [ "\n\nReid, Locke and others are interested in the notion of episodic memory\nnot only for its own sake, but also because of its conceptual\nconnection to the notion of personal identity. If Joe remembers,\nepisodically, winning the World Series, then Joe must have existed at\nthe time of his winning the World Series. This is why the Previous\nAwareness Condition characterizes episodic but not semantic\nmemory. Unlike Joe’s memory that Napoleon was defeated at Waterloo,\nhis memory of winning the World Series logically entails Joe’s\nexistence at the time of the event remembered. In other words,\nepisodic memory is logically sufficient for personal identity: if\nS remembers at time tn\n(episodically) an event at time t1, then\nS existed at time t1. In addition, memory\nreports are often taken to be prima facie evidence for\nstatements about the past history of the person reporting.", "\n\nReid’s main criticism of Locke’s theory of personal identity is that\nLocke moves from these truisms concerning the conceptual and\nevidential relations among the notions of memory and personal identity\nto a hypothesis concerning the metaphysical relations among them\n(Essays, 277). In this, Reid follows Butler’s influential\ndissertation “Of Personal Identity,” appended to The\nAnalogy of Religion in 1736.", "\n\nReid interprets\nLocke as holding what is now called the Memory Theory of personal\nidentity (Essays, 277). On this theory, personal\nidentity consists in memory; sameness of episodic memory is\nmetaphysically necessary and sufficient for sameness of persons.\nIn other words, on the Memory Theory, what makes a person\nidentical with herself over time is her remembering or being able to\nremember the events to which she was witness or agent. If she\ncannot episodically remember an event, then she is not identical with\nany of the persons who was witness or agent to the event. In such\na case, she would bear the same relation to that event as any other\nperson for whom a memory of the event could rise at best to the level\nof a semantic memory. If she can episodically remember an event,\nthen her recollection or ability to recall that event makes her\nidentical with the person represented in that memory as agent or\nwitness to the event.", "\n\nBut there is a secondary, more subtle line of disagreement between\nReid and Locke. Much of Locke’s chapter Identity and\nDiversity is dedicated to establishing that the self is not a\nsubstance, material or immaterial. By contrast, Reid holds that\nthe self is a simple, unanalyzable immaterial substance with active\npowers. Reid argues that Locke cannot sustain both the thesis\nthat the self is not a substance and the thesis that self remains\nidentical over time. While Reid’s criticisms of the Memory\nTheory are more well known, his criticism of Locke’s insistence\nthat the self is not a substance reveals two very different accounts of\nthe metaphysics of identity. While Locke argues that the identity\nconditions for different kinds of things differ, so that the conditions\nunder which a mass of matter, and an animal, and a person are not the\nsame, Reid holds that identity is confined solely to substances that\nhave a continued, uninterrupted existence and which do not have\nparts. In other words, according to Reid, strictly speaking the\nonly real identity is personal identity (Essays,\n266–267). “The identity…we ascribe to bodies,\nwhether natural or artificial, is not perfect identity; it is rather\nsomething which, for the conveniency of speech, we call identity”\n(Essays, 266).", "\n\nReid begins his interpretation and criticism of Locke’s theory\nby noting that Locke defines the term ‘person’ as meaning\n“a thinking intelligent Being, that has reason and\nreflection…” (Locke Essay, Book\nII.xxvii.9). Reid is friendly to this characterization of the\nself. But, Reid notes, Locke appears to equivocate between the\nnotion of a person as a ‘thinking Being,’ and the notion of\na person as that which is preserved through consciousness and\nmemory. Reid paraphrases a passage from Locke’s Essay\nConcerning Human Understanding:", "\n\nMr LOCKE tells us however, “that personal identity, that is, the\nsameness of a rational being, consists in consciousness alone, as, as\nfar as this consciousness can be extended backwards to any past action\nor thought, so far reaches the identity of that person. So that\nwhatever hath the consciousness of present and past actions, is the\nsame person to whom they belong” (Essays\n275–276).", "\n\nThe passage in Locke differs from Reid’s paraphrase:", "\n\n…personal Identity, i.e. the sameness of a\nrational Being: And as far as this consciousness can be extended\nbackwards to any past Action or Thought, so far reaches the Identity of\nthat Person; it is the same self now it was then; and\n‘tis by the same self with this present one that now\nreflects on it, that that Action was done (Locke, Essay, Book\nII.xxvii.9).", "\n\nReid’s first criticism rests on his interpreting Locke’s\ndefinition as committing him to the position that a person is a subject\nof thought, which Reid regards as implying that a person is a thinking\nsubstance. At the same time, Locke appears to be committed to an\nanalysis of personal identity in terms of memory, or, as Locke would\nput it, consciousness of the past. Reid notes that Locke is aware\nof some of the consequences of the Memory Theory: if sameness of\nconsciousness or memory is necessary and sufficient for sameness of\nperson, then it is possible for there to be sameness of person without\nsameness of thinking Being. In other words, it is logically and\nmetaphysically possible for a person to be “transferred from one\nintelligent being to another,” or for “two or twenty\nintelligent beings to be the same person” (Essays,\n276). Locke’s response to these worries, as well as worries\nabout periods of interrupted consciousness, as in sleep, highlights\nReid’s criticism: “…[I]n all these\ncases…doubts are raised whether we are the same thinking thing;\ni.e. the same substance or no. Which however reasonable,\nor unreasonable, concerns not personal Identity at all.\nThe Question being what makes the same Person, and not whether\nit be the same Identical Substance…” (Locke,\nEssay, Book II.xxvii.10). Reid’s criticism is not\nthat cases of transfer or fission are incoherent, though he thinks they\nare. Rather, his criticism is that the possibility of sameness of\nperson without sameness of thinking Being that the Memory Theory allows is\ninconsistent with Locke’s characterization of a person as a\n‘thinking Being’. Given that Reid thinks that this\ninitial characterization is correct, he regards this as a\nreductio of the Memory Theory.", "\n\nReid’s second criticism is his most famous and is often\nreferred to as the case of the Brave Officer:", "\n\nSuppose a brave officer to have been flogged when a boy at school,\nfor robbing an orchard, to have taken a standard from the enemy in his\nfirst campaign, and to have been made a general in advanced life:\nSuppose also, which must be admitted to be possible, that when he took\nthe standard, he was conscious of his having been flogged at school,\nand that when made a general he was conscious of his taking the\nstandard, but had absolutely lost the consciousness of his\nflogging.", "\n\nThese things being supposed, it follows, from Mr LOCKE’s\ndoctrine, that he who was flogged at school is the same person who took\nthe standard, and that he who took the standard is the same person who\nwas made a general. When it follows, if there be any truth in\nlogic, that the general is the same person with him who was flogged at\nschool. But the general’s consciousness does not reach so\nfar back as his flogging, therefore, according to Mr LOCKE’s\ndoctrine, he is not the person who was flogged. Therefore the\ngeneral is, and at the same time is not the same person as him who was\nflogged at school (Essays, 276).", "\n\nAccording to the Memory Theory, personal identity consists in\nmemory; that is, sameness of memory is metaphysically necessary and\nsufficient for sameness of person. On this account, given that\nsameness of memory is sufficient for sameness of person, if a person\nat time tn remembers (episodically) an\nevent that occurred at time t1 then the person at\ntime tn is identical with the person who\nwas witness or agent to the event at time t1. If\nthe brave officer who has just taken the flag of the enemy remembers\nbeing beaten at school, then the brave officer is identical with the\nboy who was beaten. So too, if the general remembers taking the\nenemy’s flag, then the general is identical with the brave officer. If\nthe general is identical with the brave officer, and the brave officer\nis identical with the boy, then by the transitivity of identity, the\ngeneral is identical with the boy.", "\n\nHowever, on this account, given that sameness of memory is a necessary\ncondition for sameness of person, if a person at time\ntn does not remember (episodically) an\nevent that occurred at time t1, then the person at\ntime tn cannot be identical with any\nperson who was witness or agent to the event at time\nt1. If the general cannot remember being beaten at\nschool, he cannot be identical with the boy who was beaten. Thus, the\nMemory Theory is committed to mutually incompatible theses: that the\nGeneral is identical with the boy and that he is not.", "\n\nReid’s third criticism is terminological: he argues that Locke\nconfounds consciousness with memory—elsewhere Reid also argues\nthat Locke confounds consciousness with reflection (Essays,\n58). Consciousness and memory are distinct phenomena, according\nto Reid. The former is directed towards present mental acts and\noperations, while the latter is directed towards past events to which\none was agent or witness. If consciousness could extend to past\nevents, then memory would be redundant (Essays, 277).", "\n\nAccording to Reid, memory is neither necessary nor sufficient for\npersonal identity, metaphysically speaking, despite the conceptual and\nevidential relations memory bears to personal identity. It is not a\nnecessary condition because each us has been agent or witness to many\nevents that we do not now remember. “I may have other good\nevidence of things which befell me, and which I do not remember: I\nknow who bare me, and suckled me, but I do not remember these\nevents” (Essays, 264). It is not a sufficient\ncondition, for, as Butler showed, while having an episodic memory of\nan event entails that one existed at the time of the event remembered,\nit is not the recollection or the ability to recall that\nmakes one identical with the person who was witness or agent\nto the event. “It may here be observed…that it is not my\nremembering any action of mine that makes be to be the person who did\nit. This remembrance makes me know assuredly that I did it; but I\nmight have done it, though I did not remember it”\n(Essays, 265). Reid’s fourth criticism is that while memory\nis tied to personal identity conceptually and evidentially, such ties\ndo not entail a metaphysical connection that would license analyzing\nthe latter in terms of the former (Essays, 277).", "\n\nReid’s final criticism is that the Memory Theory is committed to the\nabsurdity that identity consists in something that has no continued\nexistence (Essays, 278). Reid and Locke agree that memory,\nconsciousness, thought, and other mental operations have no continued\nexistence. They are fleeting and non-continuous. But they also agree\nthat identity, and in particular personal identity, requires a\ncontinued existence over time. As Locke puts it, “one thing\ncannot have two beginnings of Existence, nor two things one\nbeginning” (Locke, Essay, Book II.xxvii.1). But these\ncommitments are jointly inconsistent with the thesis that personal\nidentity consists in memory.", "\n\nA theory of personal identity is intended to account for how a\nperson remains identical over time. When analyzed in terms of\nitems that are fleeting and non-continuous—ideas, memories,\nthoughts—identity is reduced to diversity; that is, it is\neliminated. By contrast, if one locates personal identity in that\nwhich thinks and remembers, and which has a continued, uninterrupted\nexistence, one purchases personal identity at the cost of admitting\nthat the self is a substance. Reid captures Locke on the horns of\na dilemma: either the self is a substance, in which case it remains\nidentical over time, or the self is not a substance, in which case\nthere is no personal identity. Reid holds that this dilemma\napplies with equal force against any reductionist account of personal\nidentity that employs the theory of ideas, for example Hume’s\nbundle theory of the self (Essays, 473–474)." ], "section_title": "3. Objecting to Locke on Personal Identity", "subsections": [] }, { "main_content": [ "\n\nThose familiar with the contemporary literature on personal identity,\nwith its emphasis on the necessary and sufficient conditions under\nwhich a person remains identical over time, may wonder: if Reid holds\nthat memory is not the criterion of identity, and if Reid’s substance\ndualism rules out bodily identity as a criterion of personal\nidentity, in what does personal identity consist? Reid’s\nanswer is that identity cannot be accounted for in any terms other\nthan itself. This is neither quietism nor epistemic humility on Reid’s\npart. Rather, Reid argues that the nature of personal\nidentity—its simplicity and indivisibility—rules out any\nreductive account that appeals to notions other than identity in\nexplaining how a person persists over time.", "\n\nReid holds that numerical identity is, strictly speaking,\nindefinable, but it can be contrasted with other relations, such as\ndiversity, similarity and dissimilarity (Essays, 263). It\nrequires a continued existence over time—a duration—and\nrequires that there be no two beginnings of existence. Because\nmental states are fleeting and non-continuous they cannot remain\nidentical over time. A mental state may be indistinguishable from\na previous mental state, but because mental states do not have a\ncontinued existence, no mental state at one time can be numerically\nidentical with another at a different time. As a result, persons\ncannot be identified with their thoughts, actions or feelings\n(Essays, 264). However, according to Reid, thoughts,\nactions, feelings and all other mental operations are had or performed\nby a subject that has a continued existence and that bears the same\nrelation to all them. The subject is an immaterial substance that\nthinks, acts and feels. According to Reid, this substantial self\nhas no parts—it is indivisible—which contributes to its\nresistance to reductive explanation. Reid appeals to\nLeibniz’s notion of a monad to describe the\nindivisibility of this immaterial, substantial self (Essays,\n264).", "\n\nThough memory is not the metaphysical ground of personal identity,\nit provides first-personal evidence of it. Reid notes that the\nevidence we use to make judgments about our own pasts is different from\nthe evidence we use to make judgments about other people and their\npasts (Essays 266). Memory justifies first-personal\nreports about one’s own witnessed past, while judgments of\nqualitative similarity justify third-personal statements about the\nidentities of other persons. I know that I was present at my\nwedding because I remember being there. I know that the man I\nlive with was at my wedding because he looks like the man I\nmarried.", "\n\nFirst-personal, memorial reports about one’s own past are\neither true or false: if the memorial experience is a genuine episodic\nmemory, then it is impossible for it to testify falsely concerning\none’s presence at the event remembered. This aspect of\nepisodic memory reports is often expressed by saying that they are\nimmune to error through misidentification. If the memorial\nexperience testifies falsely concerning one’s presence at the\nevent remembered, then it cannot be an episodic memory. For\nexample, if I have an experience as of having been lost in a shopping\nmall as a child, but I was never lost, I cannot be said to remember\nhaving been lost, strictly speaking. The upshot is that\nfirst-personal memorial reports, if they are episodic memory reports,\nprovide certainty concerning one’s presence at the event\nremembered. Because third-personal judgments about the pasts of\nother persons are based on judgments of qualitative similarity rather\nthan episodic memory, they are never certain; they are only ever more\nor less well justified (Essays 264–265).", "\n\nIt is important to notice that while Reid uses the term\n‘evidence,’ when describing the role that memory plays in\nfirst-personal knowledge of one’s own past, memory is not\nused by persons to justify judgments or beliefs about their\nown pasts. In other words, people do not remember events and then\nconclude from having remembered them, that it was\nthey who were witness to the events. Rather, memory\nitself represents one’s presence at the event remembered.\nAccording to Reid, a memory consists in a conception of an event and a\nbelief, about the event conceived, that it happened to me, where the\npronoun is indexed to the person who is represented in the memory as\nagent or witness. In other words, memory consists in part in a\njudgment that represents one’s presence at the event. Any\nfurther judgment, justified by memory, to the effect that I\nwas the person who was there would be superfluous—memory\nalready testifies to my having been there. This is why Reid calls\nthe evidence of memory immediate: first-personal statements\nabout one’s own past are memory statements, not statements made\non the basis of memory.", "\n\nReid’s picture is one on which each of us is immediately and\njustifiably aware of our own past because each of us remembers\nhaving been there. This is the moral of the story concerning the\nlogical relationship between the concept of memory and the concept of\npersonal identity. Memories do not make me the same\nperson as the person represented in my memories. Rather, memories\nallow me to know my own past, immediately and directly." ], "section_title": "4. Personal Identity as Simple and Unanalyzable", "subsections": [] } ]

[ "Essays on the\nIntellectual Powers of Man, Brookes, Derek R. (ed.), University Park, Pennsylvania: Pennsylvania\nState University Press, 2002.", "An Inquiry into the Human Mind on the Principles of Common Sense,\nBrookes, Derek R. (ed.), University Park, Pennsylvania: Pennsylvania State University\nPress, 1997.", "Bergson, H., 1911, Matter and Memory, London: Allen and\nUnwin.", "Butler, J., 1736, The Analogy of Religion, Natural and\nRevealed, to the Constitution and Course of Nature, London:\nJ. and P. Knapton, 2nd corrected edition.", "Copenhaver, R., 2006, “Thomas Reid’s Theory of\nMemory”, History of Philosophy Quarterly, 23(2):\n171–187.", "–––, 2017, “John Locke and Thomas\nReid,” in The Routledge Handbook of Philosophy of\nMemory, S. Bernecker and K. Michaelian (eds.), London:\nRoutledge.", "Folescu, M., 2018a, “Reid’s View of Memorial\nConception”, Journal of Scottish Philosophy, 16(3):\n211–226.", "–––, 2018b, “Remembering Events: A Reidean\nAccount of (Episodic) Memory”, Philosophy and\nPhenomenological Research, 97(2): 304–321.", "Hamilton, A., 2003, “‘Scottish Common Sense’\nabout Memory: A Defense of Thomas Reid’s Direct Knowledge\nAccount,” Australasian Journal of Philosophy, 81:\n229–245.", "Lesser, H., 1978, “Reid’s Criticism of Hume’s Theory of\nPersonal Identity,” Hume Studies, 4: 41–63.", "Loptson, P., 2004, “Locke, Reid, and Personal\nIdentity,” Philosophical Forum, 35(1):\n51–63.", "Locke, J., 1690, Essay Concerning Human Understanding,\nP.H. Nidditch (ed.), Oxford: Oxford University Press, 1975.", "Malcolm, N., 1977, Memory and Mind, Ithaca, N.Y.: Cornell\nUniversity Press.", "Martin, M.G.F., 2001, “Out of the Past: Episodic Recall as\nRetained Acquaintance,” in Time and Memory, C. Hoerl\nand T. McCormack (eds.), Oxford: Oxford University Press.", "Parfit, D., 1985, Reasons and Persons, Oxford: Clarendon\nPress.", "Robinson, D., 1978, “Personal Identity: Reid’s Answer to\nHume,” The Monist, 61: 326–339.", "Russell, B., 1921, The Analysis of Mind, London: Allen\nand Unwin.", "Shoemaker, S., 1997, “Self and Substance,”\nPhilosophical Perspectives, 11: 283–304.", "–––, 1970, “Persons and their\nPasts,” American Philosophical Quarterly, 7(4):\n269–285; reprinted in Shoemaker (1984), Identity, Cause and\nMind, Cambridge: Cambridge University Press, 19–48.", "–––, 1959, “Personal Identity and\nMemory,” The Journal of Philosophy, 56,\n868–902.", "Stewart, M.A., 2004, “Reid and Personal Identity: A Study in\nSources,” in Thomas Reid: Context, Influence and\nSignificance, J. Houston (ed.), Edinburgh: Dunedin Academic\nPress, pp. 9–28.", "Tulving, E., 1983, Elements of Episodic Memory, Oxford:\nOxford University Press.", "Van Woudenberg, R., 2004, “Reid on Memory and the Identity\nof Persons,” in The Cambridge Companion to Thomas Reid,\nT. Cuneo and R. Van Woudenberg (eds.), Cambridge: Cambridge University\nPress, pp. 204 –221.", "–––, 1999, “Thomas Reid on Memory,”\nJournal of the History of Philosophy, 37: 117–133.", "Ward, A., 2000, “Reid on Personal Identity: Some Comparisons\nwith Locke and Kant,” Reid Studies, 3:\n55–64.", "Yaffe, G., 2010, “Beyond the Brave Officer: Reid on the\nUnity of Mind, the Moral Sense, and Locke’s Theory of Personal\nIdentity,” in Reid on Ethics, S. Roeser (ed.),\nBasingstoke: Palgrave Macmillan." ]

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[ "\nIt is common today to take the concept religion as a taxon\nfor sets of social practices, a category-concept whose paradigmatic\nexamples are the so-called “world” religions of Judaism,\nChristianity, Islam, Hinduism, Buddhism, Confucianism, and\n Daoism.[1]\n Perhaps equally paradigmatic, though somewhat trickier to label, are\nforms of life that have not been given a name, either by practitioners\nor by observers, but are common to a geographical area or a group of\npeople—for example, the religion of China or that of ancient\nRome, the religion of the Yoruba or that of the Cherokee. In short,\nthe concept is today used for a genus of social formations that\nincludes several members, a type of which there are many tokens.", "\nThe concept religion did not originally refer to a social\ngenus, however. Its earliest references were not to social kinds and,\nover time, the extension of the concept has evolved in different\ndirections, to the point that it threatens incoherence. As Paul\nGriffiths notes, listening to the discussions about the concept\nreligion", "\nThis entry therefore provides a brief history of the how the semantic\nrange of religion has grown and shifted over the years, and\nthen considers two philosophical issues that arise for the contested\nconcept, issues that are likely to arise for other abstract concepts\nused to sort cultural types (such as “literature”,\n“democracy”, or “culture” itself). First, the\ndisparate variety of practices now said to fall within this category\nraises a question of whether one can understand this social taxon in\nterms of necessary and sufficient properties or whether instead one\nshould instead treat it as a family resemblance concept. Here, the\nquestion is whether the concept religion can be said to have\nan essence. Second, the recognition that the concept has shifted its\nmeanings, that it arose at a particular time and place but was unknown\nelsewhere, and that it has so often been used to denigrate certain\ncultures, raises the question whether the concept corresponds to any\nkind of entity in the world at all or whether, instead, it is simply a\nrhetorical device that should be retired. This entry therefore\nconsiders the rise of critical and skeptical analyses of the concept,\nincluding those that argue that the term refers to nothing." ]

[ { "content_title": "1. A History of the Concept", "sub_toc": [] }, { "content_title": "2. Two Kinds of Analysis of the Concept", "sub_toc": [ "2.1 Monothetic approaches", "2.2 Polythetic approaches" ] }, { "content_title": "3. Reflexivity, Reference, and Skepticism", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThe concept religion did not originally refer to a social\ngenus or cultural type. It was adapted from the Latin term\nreligio, a term roughly equivalent to\n“scrupulousness”. Religio also approximates\n“conscientiousness”, “devotedness”, or\n“felt obligation”, since religio was an effect of\ntaboos, promises, curses, or transgressions, even when these were\nunrelated to the gods. In western antiquity, and likely in many or\nmost cultures, there was a recognition that some people worshipped\ndifferent gods with commitments that were incompatible with each other\nand that these people constituted social groups that could be rivals.\nIn that context, one sometimes sees the use of nobis religio\nto mean “our way of worship”. Nevertheless,\nreligio had a range of senses and so Augustine could consider\nbut reject it as the right abstract term for “how one\nworships God” because the Latin term (like the Latin terms for\n“cult” and “service”) was used for the\nobservance of duties in both one’s divine and one’s human\nrelationships (Augustine City of God [1968: Book X, Chapter\n1, 251–253]). In the Middle Ages, as Christians developed\nmonastic orders in which one took vows to live under a specific rule,\nthey called such an order religio (and\nreligiones for the plural), though the term continued to be\nused, as it had been in antiquity, in adjective form to describe those\nwho were devout and in noun form to refer to worship (Biller 1985:\n358; Nongbri 2013: ch. 2).", "\nThe most significant shift in the history of the concept is when\npeople began to use religion as a genus of which Christian\nand non-Christian groups were species. One sees a clear example of\nthis use in the writings of Edward Herbert (1583–1648). As\nthe post-Reformation Christian community fractured into literal\nwarring camps, Herbert sought to remind the different protesting\ngroups of what they nevertheless had in common. Herbert identified\nfive “articles” or “elements” that he proposed\nwere found in every religion, which he called the Common Notions,\nnamely: the beliefs that", "\nIgnoring rituals and group membership, this proposal takes an\nidealized Protestant monotheism as the model of religion as such.\nHerbert was aware of peoples who worshipped something other than a\nsingle supreme deity. He noted that ancient Egyptians, for instance,\nworshipped multiple gods and people in other cultures worshipped\ncelestial bodies or forces in nature. Herbert might have argued that,\nlacking a belief in a supreme deity, these practices were not\nreligions at all but belonged instead in some other category such as\nsuperstition, heresy, or magic. But Herbert did include them, arguing\nthat they were religions because the multiple gods were actually\nservants to or even aspects of the one supreme deity, and those who\nworshiped natural forces worshipped the supreme deity “in His\nworks”.", "\nThe concept religion understood as a social genus was\nincreasingly put to use by to European Christians as they sought\nto categorize the variety of cultures they encountered as their\nempires moved into the Americas, South Asia, East Asia, Africa, and\nOceania. In this context, fed by reports from missionaries and\ncolonial administrators, the extension of the generic concept was\nexpanded. The most influential example is that of anthropologist\nEdward Burnett Tylor (1832–1917) who had a scholarly interest in\npre-Columbian Mexico. Like Herbert, Tylor sought to identify the\ncommon denominator of all religions, what Tylor called a\n“minimal definition” of religion, and he proposed that the\nkey characteristic was “belief in spiritual beings” (1871\n[1970: 8]). This generic definition included the forms of life\npredicated on belief in a supreme deity that Herbert had classified as\nreligion. But it could also now include—without Herbert’s\nprocrustean assumption that these practices were really directed to\none supreme being—the practices used by Hindus, ancient\nAthenians, and the Navajo to connect to the gods they revere, the\npractices used by Mahayana Buddhists to connect to Bodhisattvas, and\nthe practices used by Malagasy people to connect to the cult of the\ndead. The use of a unifying concept for such diverse practices is\ndeliberate on Tylor’s part as he sought to undermine assumptions\nthat human cultures poorly understood in Christian\nEurope—especially those despised ones, “painted black on\nthe missionary maps” (1871 [1970: 4])—were not on the very\nsame spectrum as the religion of his readers. This opposition to\ndividing European and non-European cultures into separate categories\nunderlies Tylor’s insistence that all human beings are\nequivalent in terms of their intelligence. He argued that so-called\n“primitive” peoples generate their religious ideas when\nthey wrestle with the same questions that all people do, such as the\nbiological question of what explains life, and they do so with the\nsame cognitive capacities. They may lack microscopes or telescopes,\nbut Tylor claims that they seek to answer these questions in ways that\nare “rational”, “consistent”, and\n“logical”. Tylor repeatedly calls the Americans, Africans,\nand Asians he studies “thinking men” and\n“philosophers”. Tylor was conscious that the definition he\nproposed was part of a shift: though it was still common to describe\nsome people as so primitive that they had no religion, Tylor complains\nthat those who speak this way are guilty of “the use of wide\nwords in narrow senses” because they are only willing to\ndescribe as religion practices that resemble their own expectations\n(1871 [1970: 3–4]).", "\nIn the twentieth century, one sees a third and last growth spurt in\nthe extension of the concept. Here the concept religion is\nenlarged to include not only practices that connect people to one or\nmore spirits, but also practices that connect people to\n“powers” or “forces” that lack minds, wills,\nand personalities. One sees this shift in the work of William James,\nfor example, when he writes,", "\n\n\nWere one asked to characterize the life of religion in the broadest\nand most general terms possible, one might say that it consists of the\nbelief that there is an unseen order, and our supreme good lies in\nharmoniously adjusting ourselves thereto. (1902 [1985: 51]; cf.\nProudfoot 2000)\n", "\nBy an “unseen order”, James presumably means a structure\nthat is non-empirical, though he is not clear about why the term would\nnot also include political, economic, or other invisible but\nhuman-created orders. The same problem plagues James’s\ndescription of “a MORE” operating in the universe that is\nsimilar to but outside oneself (1902 [1985: 400], capitalization in\nthe original). The anthropologist Clifford Geertz addresses this\nissue, also defining religion in terms of an\n“order” but specifying that he means practices tied to\nconceptions of “a general order of existence”,\nthat is, as he also says, something whose existence is\n“fundamental”, “all-pervading”, or\n“unconditioned” (1973: 98, emphasis added). The practices\nthat are distinctly religious for Geertz are those tied to a\nculture’s metaphysics or worldview, their conception of\n“the overall shape of reality” (1973: 104). Like James,\nthen, Geertz would include as religions not only the forms of life\nbased on the theistic and polytheistic (or, more broadly, animist or\nspiritualist) beliefs that Herbert and Tylor recognized, but also\nthose based on belief in the involuntary, spontaneous, or\n“natural” operations of the law of karma, the Dao in\nDaoism, the Principle in Neo-Confucianism, and the Logos in Stoicism.\nThis expansion also includes Theravada Buddhism because dependent\nco-origination (pratītyasamutpāda) is a conception\nof the general order of existence and it includes Zen Buddhism because\nBuddha-nature is said to pervade everything. This third expansion is\nwhy non-theistic forms of Buddhism, excluded by the Herbert’s\nand Tylor’s definitions but today widely considered religions,\ncan serve as “a litmus test” for definitions of the\nconcept (Turner 2011: xxiii; cf. Southwold 1978). In sum, then, one\ncan think of the growth of the social genus version of the concept\nreligion as analogous to three concentric circles—from\na theistic to a polytheistic and then to a cosmic (or\n“cosmographic” [Dubuisson 1998]) criterion. Given the\nnear-automatic way that Buddhism is taken as a religion today, the\ncosmic version now seems to be the dominant one.", "\nSome scholars resist this third expansion of the concept and retain a\nTylorean definition, and it is true that there is a marked difference\nbetween practices that do and practices that do not involve\ninteracting with person-like beings. In the former, anthropomorphic\ncases, practitioners can ask for help, make offerings, and pray with\nan understanding that they are heard. In the latter,\nnon-anthropomorphic cases, practitioners instead typically engage in\nactions that put themselves “in accord with” the order of\nthings. The anthropologist Robert Marett marks this difference between\nthe last two extensions of the concept religion by\ndistinguishing between “animism” and\n“animatism” (1909), the philosopher John Hick by\ndistinguishing between religious “personae” and religious\n“impersonae” (1989: ch. 14–15). This difference\nraises a philosophical question: on what grounds can one place the\npractices based on these two kinds of realities in the same category?\nThe many loa spirits, the creator Allah, and the\nall-pervading Dao are not available to the methods of the natural\nsciences, and so they are often called “supernatural”. If\nthat term works, then religions in all three concentric circles can be\nunderstood as sets of practices predicated on belief in the\nsupernatural. However, “supernatural” suggests a two-level\nview of reality that separates the empirically available natural world\nfrom some other realm metaphorically “above” or\n“behind” it. Many cultures lack or reject a distinction\nbetween natural and supernatural (Saler 1977, 2021). They believe that\ndisembodied persons or powers are not in some otherworldly realm but\nrather on the top of a certain mountain, in the depths of the forest,\nor “everywhere”. To avoid the assumption of a two-level\nview of reality, then, some scholars have replaced supernatural with\nother terms, such as “superhuman”. Hick uses the term\n“transcendent”:", "\n\n\nthe putative reality which transcends everything other than itself but\nis not transcended by anything other than itself. (1993: 164)\n", "\nIn order to include loa, Allah, and the Dao but to exclude\nnations and economies, Kevin Schilbrack (2013) proposes the neologism\n“superempirical” to refer to non-empirical things that are\nalso not the product of any empirical thing. Wouter Hanegraaff (1995),\nfollowing J. G. Platvoet (1982: 30) uses “meta-empirical”.\nWhether a common element can be identified that will coherently ground\na substantive definition of “religion” is not a settled\nquestion.", "\nDespite this murkiness, all three of these versions are\n“substantive” definitions of religion because\nthey determine membership in the category in terms of the presence of\na belief in a distinctive kind of reality. In the twentieth century,\nhowever, one sees the emergence of an importantly different approach:\na definition that drops the substantive element and instead defines\nthe concept religion in terms of a distinctive role that a\nform of life can play in one’s life—that is, a\n“functional” definition. One sees a functional approach in\nEmile Durkheim (1912), who defines religion as whatever\nsystem of practices unite a number of people into a single moral\ncommunity (whether or not those practices involve belief in any\nunusual realities). Durkheim’s definition turns on the social\nfunction of creating solidarity. One also sees a functional approach\nin Paul Tillich (1957), who defines religion as whatever\ndominant concern serves to organize a person’s values (whether\nor not that concern involve belief in any unusual realities).\nTillich’s definition turns on the axiological function of\nproviding orientation for a person’s life.", "\nSubstantive and functional approaches can produce non-overlapping\nextensions for the concept. Famously, a functional approach can hold\nthat even atheistic forms of capitalism, nationalism, and Marxism\nfunction as religions. The literature on these secular institutions as\nfunctionally religions is massive. As Trevor Ling says,", "\n\n\nthe bulk of literature supporting the view that Marxism is a religion\nis so great that it cannot easily be set aside. (1980: 152)\n", "\nOn capitalism as a religion, see, e.g., McCarraher (2019); on\nnationalism, see, e.g., Omer and Springs (2013: ch. 2). One\nfunctionalist might count white supremacy as a religion (Weed 2019;\nFinley et al. 2020) and another might count anti-racism as a religion\n(McWhorter 2021). Here, celebrities can reach a religious status and\nfandom can be one’s religious identity (e.g., Lofton 2011;\nLovric 2020). Without a supernatural, transcendent, or superempirical\nelement, these phenomena would not count as religious for Herbert,\nTylor, James, or Geertz. Conversely, interactions with supernatural\nbeings may be categorized on a functional approach as something other\nthan religion. For example, the Thai villager who wears an apotropaic\namulet and avoids the forest because of a belief that malevolent\nspirits live there, or the ancient Roman citizen who takes a bird to\nbe sacrificed in a temple before she goes on a journey are for\nDurkheim examples of magic rather than religion, and for Tillich\nquotidian rather than ultimate concerns.", "\nIt is sometimes assumed that to define religion as a social\ngenus is to treat it as something universal, as something that appears\nin every human culture. It is true that some scholars have treated\nreligion as pan-human. For example, when a scholar defines\nreligion functionally as the beliefs and practices that\ngenerate social cohesion or as the ones that provide orientation in\nlife, then religion names an inevitable feature of the human\ncondition. The universality of religion that one then finds is not a\ndiscovery but a product of one’s definition. However, a social\ngenus can be both present in more than one culture without being\npresent in all of them, and so one can define religion,\neither substantively or functionally, in ways that are not universal.\nAs common as beliefs in disembodied spirits or cosmological orders\nhave been in human history, for instance, there were people in the\npast and there are people in the present who have no views of an\nafterlife, supernatural beings, or explicit metaphysics." ], "section_title": "1. A History of the Concept", "subsections": [] }, { "main_content": [ "\nThe history of the concept religion above shows how its\nsenses have shifted over time. A concept used for scrupulous devotion\nwas retooled to refer to a particular type of social practice. But the\nquestion—what type?—is now convoluted. The cosmic version\nof the concept is broader than the polytheistic version, which is in\nturn broader than the theistic version, and the functional definitions\nshift the sense of the term into a completely different register. What\nis counted as religion by one definition is often not counted by\nothers. How might this disarray be understood? Does the concept have a\nstructure? This section distinguishes between two kinds of answer to\nthese questions. Most of the attempts to analyze the term have been\n“monothetic” in that they operate with the classical view\nthat every instance that is accurately described by a concept will\nshare a defining property that puts them in that category. The last\nseveral decades, however, have seen the emergence of\n“polythetic” approaches that abandon the classical view\nand treat religion, instead, as having a prototype structure.\nFor incisive explanations of the classical theory and the prototype\ntheory of concepts, see Laurence and Margolis (1999)." ], "section_title": "2. Two Kinds of Analysis of the Concept", "subsections": [ { "content": [ "\nMonothetic approaches use a single property (or a single set\nof properties) as the criterion that determines whether a concept\napplies. The key to a monothetic approach is that it proposes\nnecessary and sufficient conditions for membership in the given class.\nThat is, a monothetic approach claims that there is some\ncharacteristic, or set of them, found in every religion and that if a\nform of life has it, then that form of life is a religion. Most\ndefinitions of the concept religion have been of this type.\nFor example, as we saw above, Edward Tylor proposes belief in\nspiritual beings as his minimal definition of religion, and this\nis a substantive criterion that distinguishes religion from\nnon-religion in terms of belief in this particular kind of entity.\nSimilarly, Paul Tillich proposes ultimate concern as a\nfunctional criterion that distinguishes religion from non-religion in\nterms of what serves this particular role in one’s life. These\nare single criterion monothetic definitions.", "\nThere are also monothetic definitions that define religion in terms of\na single set of criteria. Herbert’s five Common Notions are an\nearly example. More recently, Clifford Geertz (1973: ch. 4) proposes a\ndefinition that he breaks down into five elements:", "\nOne can find each of these five elements separately, of course: not\nall symbols are religious symbols; historians (but not novelists)\ntypically consider their conceptions factual; and so on. For Geertz,\nhowever, any religious form of life will have all five. Aware of\nfunctional approaches like that of Tillich, Geertz is explicit that\nsymbols and rituals that lack reference to a metaphysical\nframework—that is, those without the substantive element he\nrequires as his (2)—would be secular and not religious, no\nmatter how intense or important one’s feelings about them are\n(1973: 98). Reference to a metaphysical entity or power is what marks\nthe other four elements as religious. Without it, Geertz writes,\n“the empirical differentia of religious activity or religious\nexperience would not exist” (1973: 98). As a third example,\nBruce Lincoln (2006: ch. 1) enumerates four elements that a religion\nwould have, namely:", "\nThis definition is monothetic since, for Lincoln, religions always\nhave these four features “at a minimum” (2006:\n 5).[4]\n To be sure, people constantly engage in practices that generate\nsocial groups that then have to be maintained and managed by rules or\nauthorities. However, when the practices, communities, and\ninstitutions lack the distinctive kind of discourse that claims\ntranscendent status for itself, they would not count for Lincoln as\nreligions.", "\nIt is worth noting that when a monothetic definition includes multiple\ncriteria, one does not have to choose between the substantive and\nfunctional strategies for defining religion, but can instead\ninclude both. If a monothetic definition include both strategies,\nthen, to count as a religion, a form of life would have to refer to a\ndistinctive substantive reality and also play a certain role in the\nparticipants’ lives. This double-sided approach avoids the\nresult of purely substantive definitions that might count as religion\na feckless set of beliefs (for instance, “something must have\ncreated the world”) unconnected from the believers’\ndesires and behavior, while also avoiding the result of purely\nfunctional definitions that might count as religion some universal\naspect of human existence (for instance, creating collective\neffervescence or ranking of one’s values). William James’s\ndefinition of religion (“the belief that there is an unseen\norder, and our supreme good lies in harmoniously adjusting ourselves\nthereto”) is double-sided in this way, combining a belief in the\nexistence of a distinctive referent with the spiritual disciplines\nwith which one seeks to embody that belief. Geertz’s definition\nof religion also required both substantive and functional aspects,\nwhich he labelled “worldview” and “ethos”\n(1973: ch. 5). To treat religion as “both/and” in this way\nis to refuse to abstract one aspect of a complex social reality but\ninstead recognizes, as Geertz puts it, both “the dispositional\nand conceptual aspects of religious life” (1973:\n 113).[5]", "\nThese “monothetic-set definitions” treat the concept of\nreligion as referring to a multifaceted or multidimensional complex.\nIt may seem avant garde today to see religion described as a\n“constellation”, “assemblage”,\n“network”, or “system”, but in fact to treat\nreligion as a complex is not new. Christian theologians traditionally\nanalyzed the anatomy of their way of life as simultaneously\nfides, fiducia, and fidelitas. Each of\nthese terms might be translated into English as “faith”,\nbut each actually corresponds to a different dimension of a social\npractice. Fides refers to a cognitive state, one in which a\nperson assents to a certain proposition and takes it as true. It could\nbe translated as “belief” or “intellectual\ncommitment”. Beliefs or intellectual commitments distinctive to\nparticipation in the group will be present whether or not a religious\nform of life has developed any authoritative doctrines. In contrast,\nfiducia refers to an affective state in which a person is\nmoved by a feeling or experience that is so positive that it bonds the\nrecipient to its source. It could be translated as “trust”\nor “emotional commitment”. Trust or emotional commitment\nwill be present whether or not a religious form of life teaches that\nparticipation in their practices aims at some particular experience of\nliberation, enlightenment, or salvation. And fidelitas refers\nto a conative state in which a person commits themselves to a path of\naction, a path that typically involves emulating certain role models\nand inculcating the dispositions that the group considers virtuous. It\ncould be translated as “loyalty” or\n“submission”. Loyalty or submission will be present\nwhether or not a religious form of life is theistic or teaches moral\nrules. By the time of Martin Luther, Christian catechisms organized\nthese aspects of religious life in terms of the “three\nC’s”: the creed one believed, the cult or worship one\noffered, and the code one followed. When Tillich (1957: ch. 2) argues\nthat religious faith is distorted when one treats it not as a complex\nbut instead as a function of the intellect alone, emotion alone, or\nthe will alone, he is speaking from within this tradition. These three\ndimensions of religious practices—symbolically, the head, the\nheart, and the hand—are not necessarily Christian. In fact,\nuntil one adds a delimiting criterion like those discussed above,\nthese dimensions are not even distinctively religious. Creed, cult,\nand code correspond to any pursuit of what a people considers true,\nbeautiful, and good, respectively, and they will be found in any\ncollective movement or cultural tradition. As Melford Spiro says, any\nhuman institution will involve a belief system, a value system, and an\naction system (Spiro 1966: 98).", "\nMany have complained that arguments about how religion should\nbe defined seem unresolvable. To a great extent, however, this is\nbecause these arguments have not simply been about a particular aspect\nof society but rather have served as proxy in a debate about the\nstructure of human subjectivity. There is deep agreement among the\nrival positions insofar as they presuppose the\ncognitive-affective-conative model of being human. However, what we\nmight call a “Cartesian” cohort argues that cognition is\nthe root of religious emotions and actions. This cohort includes the\n“intellectualists” whose influence stretches from Edward\nTylor and James Frazer to E. E. Evans-Pritchard, Robin Horton, Jack\nGoody, Melford Spiro, Stewart Guthrie, and J. Z. Smith, and it shapes\nmuch of the emerging field of cognitive science of religion (e.g.,\nBoyer\n 2001).[6]\n A “Humean” cohort disagrees, arguing that affect is what\ndrives human behavior and that cognition serves merely to justify the\nvalues one has already adopted. In theology and religious studies,\nthis feelings-centered approach is identified above all with the work\nof Friedrich Schleiermacher and Rudolf Otto, and with the tradition\ncalled phenomenology of religion, but it has had a place in\nanthropology of religion since Robert Marett (Tylor’s student),\nand it is alive and well in the work of moral intuitionists (e.g.,\nHaidt 2012) and affect theory (e.g., Schaefer 2015). A\n“Kantian” cohort treats beliefs and emotions regarding\nsupernatural realities as relatively unimportant and argues instead\nthat for religion the will is\n basic.[7]\n This approach treats a religion as at root a set of required actions\n(e.g., Vásquez 2011; C. Smith 2017). These different approaches\ndisagree about the essence of religion, but all three camps operate\nwithin a shared account of the human. Thus, when William James\ndescribes religion as", "\n\n\nthe feelings, acts, and experiences of individual [people] in their\nsolitude, so far as they apprehend themselves to stand in relation to\nwhatever they may consider the divine. (1902 [1985: 34])\n", "\nhe is foregrounding an affective view and playing down (though not\ndenying) the cognitive. When James’s Harvard colleague Alfred\nNorth Whitehead corrects him, saying that “[r]eligion is what a\nperson does with their solitariness” (1926: 3, emphasis\nadded), Whitehead stresses the conative, though Whitehead also insists\nthat feelings always play a role. These are primarily disagreements of\nemphasis that do not trouble this model of human subjectivity. There\nhave been some attempts to leave this three-part framework. For\nexample, some in the Humean camp have suggested that religion is\nessentially a particular feeling with zero cognition. But that\nromantic suggestion collapses under the inability to articulate how an\naffective state can be noncognitive but still identifiable as a\nparticular feeling (Proudfoot 1985).", "\nAlthough the three-sided model of the true, the beautiful, and the\ngood is a classic account of what any social group explicitly and\nimplicitly teaches, one aspect is still missing. To recognize the\nalways-presupposed material reality of the people who constitute the\nsocial group, even when this reality has not been conceptualized by\nthe group’s members, one should also include the contributions\nof their bodies, habits, physical culture, and social structures. To\ninclude this dimension mnemonically, one can add a “fourth\nC”, for community. Catherine Albanese (1981) may have been the\nfirst to propose the idea of adding this materialist dimension. Ninian\nSmart’s famous anatomy of religion (1996) has seven dimensions,\nnot four, but the two models are actually very similar. Smart calls\nthe affective dimension the “experiential and emotional”,\nand then divides the cognitive dimension into two (“doctrinal\nand philosophical” and “narrative and\nmythological”), the conative into two (“ethical and\nlegal” and “ritual”), and the communal into two\n(“social and institutional” and “material”).\nIn an attempt to dislodge the focus on human subjectivity found in the\nthree Cs, some have argued that the material dimension is the source\nof the others. They argue, in other words, that the cognitive,\naffective, and conative aspects of the members of a social group are\nnot the causes but rather the effects of the group’s structured\npractices (e.g., Asad 1993: ch. 1–4; Lopez 1998). Some argue\nthat to understand religion in terms of beliefs, or even in terms of\nany subjective states, reflects a Protestant bias and that scholars of\nreligion should therefore shift attention from hidden mental states to\nthe visible institutional structures that produce them. Although the\nstructure/agency debate is still live in the social sciences, it is\nunlikely that one can give a coherent account of religion in terms of\ninstitutions or disciplinary practices without reintroducing mental\nstates such as judgements, decisions, and dispositions (Schilbrack\n2021).", "\nWhether a monothetic approach focuses on one essential property or a\nset, and whether that essence is the substance or the function of the\nreligion, those using this approach ask a Yes/No question regarding a\nsingle criterion. This approach therefore typically produces\nrelatively clear lines between what is and is not religion. Given\nTylor’s monothetic definition, for instance, a form of life must\ninclude belief in spiritual beings to be a religion; a form of life\nlacking this property would not be a religion, even if it included\nbelief in a general order of existence that participants took as their\nultimate concern, and even if that form of life included rituals,\nethics, and scriptures. In a famous discussion, Melford Spiro (1966)\nworks with a Tylorean definition and argues exactly this: lacking a\nbelief in superhuman beings, Theravada Buddhism, for instance, is\nsomething other than a\n religion.[8]\n For Spiro, there is nothing pejorative about this classification.", "\n\n\nHaving combatted the notion that “we” have religion (which\nis “good”) and “they” have superstition (which\nis “bad”), why should we be dismayed if it be discovered\nthat that society x does not have religion as we have defined\nthe term? (1966: 88)\n" ], "subsection_title": "2.1 Monothetic approaches" }, { "content": [ "\nThat a concept always corresponds to something possessing a defining\nproperty is a very old idea. This assumption undergirds Plato’s\nEuthyphro and other dialogues in which Socrates pushes his\ninterlocutors to make that hidden, defining property explicit, and\nthis pursuit has provided a model for much not only of philosophy, but\nof the theorizing in all fields. The traditional assumption is that\nevery entity has some essence that makes it the thing it is, and every\ninstance that is accurately described by a concept of that entity will\nhave that essence. The recent argument that there is an alternative\nstructure—that a concept need not have necessary and sufficient\ncriteria for its application—has been called a “conceptual\nrevolution” (Needham 1975: 351), “one of the greatest and\nmost valuable discoveries that has been made of late years in the\nrepublic of letters” (Bambrough 1960–1: 207).", "\nIn discussions of the concept religion, this\nanti-essentialist approach is usually traced to Ludwig Wittgenstein\n(1953, posthumous). Wittgenstein argues that, in some cases, when one\nconsiders the variety of instances described with a given concept, one\nsees that among them there are multiple features that “crop up\nand disappear”, the result being “a complicated network of\nsimilarities overlapping and criss-crossing” (Wittgenstein 1953,\n§68). The instances falling under some concepts lack a single\ndefining property but instead have a family resemblance to each other\nin that each one resembles some of the others in different ways. All\npolythetic approaches reject the monothetic idea that a concept\nrequires necessary and sufficient criteria. But unappreciated is the\nfact that polythetic approaches come in different kinds, operating\nwith different logics. Here are three.", "\nThe most basic kind of polythetic approach holds that membership in a\ngiven class is not determined by the presence of a single crucial\ncharacteristic. Instead, the concept maps a cluster of characteristics\nand, to count as a member of that class, a particular case has to have\na certain number of them, no particular one of which is required. To\nillustrate, imagine that there are five characteristics typical of\nreligions (call this the “properties set”) and that, to be\na religion, a form of life has to have a minimum of three of them\n(call this the “threshold number”). Because this\nillustration limits the number of characteristics in the properties\nset, I will call this first kind a “bounded” polythetic\napproach. For example, the five religion-making characteristics could\nbe these:", "\nUnderstanding the concept religion in this polythetic way\nproduces a graded hierarchy of\n instances.[9]\n A form of life that has all five of these characteristics would be a\nprototypical example of a religion. Historically speaking,\nprototypical examples of the concept are likely to be instances to\nwhich the concept was first applied. Psychologically speaking, they\nare also likely to be the example that comes to mind first to those\nwho use the concept. For instance, robins and finches are prototypical\nexamples of a bird, and when one is prompted to name a bird, people\nare more likely to name a robin or a finch than an ostrich or a\npenguin. A form of life that has only four of these characteristics\nwould nevertheless still be a clear example of a\n religion.[10]\n If a form of life has only three, then it would be a\nborderline example. A form of life that has only two of these\ncharacteristics would not be included in the category, though such\ncases might be considered “quasi-religions” and they might\nbe the most interesting social forms to compare to religions (J. E.\nSmith 1994). A form of life that only had one of the five\ncharacteristics would be unremarkable. The forms of life that had\nthree, four, or five of these characteristics would not be an\nunrelated set but rather a “family” with multiple shared\nfeatures, but no one characteristic (not even belief in superempirical\nbeings or powers) possessed by all of them. On this polythetic\napproach, the concept religion has no essence, and a member\nof this family that only lacked one of the five\ncharacteristics—no matter which one—would still\nclearly be a\n religion.[11]\n As Benson Saler (1993) points out, one can use this non-essentialist\napproach not only for the concept religion but also for the\nelements within a religion (sacrifice, scripture, and so on) and to\nindividual religions (Christianity, Hinduism, and so on).", "\nSome have claimed that, lacking an essence, polythetic approaches to\nreligion make the concept so vague that it becomes useless\n(e.g., Fitzgerald 2000: 72–3; Martin 2009: 167). Given the\nfocused example of a “bounded” approach in the previous\nparagraph and the widespread adoption of polythetic approaches in the\nbiological sciences, this seems clearly false. However, it is true\nthat one must pay attention to the parameters at work in a polythetic\napproach. Using a properties set with only five elements produces a\nvery focused class, but the properties set is simply a list of\nsimilarities among at least two of the members of a class, and since\nthe class of religions might have hundreds of members, one could\neasily create a properties set that is much bigger. Not long after\nWittgenstein’s death, a “bounded” polythetic\napproach was applied to the concept religion by William\nAlston who identified nine religion-making\n characteristics.[12]\n Southwold (1978) has twelve; Rem Edwards (1972) has fourteen and\nleaves room for more. But there is no reason why one might not work\nwith a properties set for religion with dozens or even\nhundreds of shared properties. Half a century ago, Rodney Needham\n(1975: 361) mentions a computer program that sorted 1500 different\nbacterial strains according to 200 different properties. As J. Z.\nSmith (1982: ch. 1) argues, treating the concept religion in\nthis way can lead to surprising discoveries of patterns within the\nclass and the co-appearance of properties that can lead to explanatory\ntheories. The second key parameter for a polythetic approach is the\nthreshold number. Alston does not stipulate the number of\ncharacteristics a member of the class has to have, saying simply,\n“When enough of these characteristics are present to a\nsufficient degree, we have a religion” (1967: 142). Needham\n(1975) discusses the sensible idea that each member has a\nmajority of the properties, but this is not a requirement of\npolythetic approaches. The critics are right that as one increases the\nsize of the properties set and decreases the threshold number, the\nresulting category becomes more and more diffuse. This can produce a\nclass that is so sprawling that it is difficult to use for empirical\nstudy.", "\nScholars of religion who have used a polythetic approach have\ntypically worked with a “bounded” approach (that is, with\na properties set that is fixed), but this is not actually the view for\nwhich Wittgenstein himself argues. Wittgenstein’s goal is to\ndraw attention to the fact that the actual use of concepts is\ntypically not bound: “the extension of the concept is\nnot closed by a frontier” (Wittgenstein 1953, §67). We can\ncall this an “open” polythetic approach. To grasp the open\napproach, consider a group of people who have a concept they apply to\na certain range of instances. In time, a member of the group\nencounters something new that resembles the other instances enough in\nher eyes that she applies the concept to it. When the linguistic\ncommunity adopts this novel application, the extension of the concept\ngrows. If their use of the concept is “open”, however,\nthen, as the group adds a new member to the category named by a\nconcept, properties of that new member that had not been part of the\nearlier uses can be added to the properties set and thereby increase\nthe range of legitimate applications of the concept in the future. We\nmight say that a bounded polythetic approach produces concepts that\nare fuzzy, and an open polythetic approach produces concepts that are\nfuzzy and evolving. Timothy Williamson calls this “the\ndynamic quality of family resemblance concepts” (1994: 86). One\ncould symbolize the shift of properties over time this way:", "\nWittgenstein famously illustrated this open polythetic approach with\nthe concept game, and he also applied it to the concepts of\nlanguage and number (Wittgenstein 1953,\n§67). If we substitute our concept as Wittgenstein’s\nexample, however, his treatment fits religion just as\nwell:", "\n\n\nWhy do we call something a “religion”? Well, perhaps\nbecause it has a direct relationship with several things that have\nhitherto been called religion; and this can be said to give an\nindirect relationship to other things we call the same\nname. (Wittgenstein 1953, §67)\n", "\nGiven an open polythetic approach, a concept evolves in the light of\nthe precedents that speakers recognize, although, over time, what\npeople come to label with the concept can become very different from\nthe original use.", "\nIn the academic study of religions, discussions of monothetic and\npolythetic approaches have primarily been in service of developing a\ndefinition of the\n term.[13]\n How can alternate definitions of religion be assessed? If\none were to offer a lexical definition (that is, a description of what\nthe term means in common usage, as with a dictionary definition), then\nthe definition one offers could be shown to be wrong. In common usage,\nfor example, Buddhism typically is considered a religion and\ncapitalism typically is not. On this point, some believe erroneously\nthat one can correct a definition by pointing to some fact about the\nreferents of the term. One sees this assumption, for example, in those\nwho argue that the western discovery of Buddhism shows that theistic\ndefinitions of religion are wrong (e.g., Southwold 1978:\n367). One can correct a real or lexical definition in this way, but\nnot a stipulative definition, that is, a description of the meaning\nthat one assigns to the term. When one offers a stipulative\ndefinition, that definition cannot be wrong. Stipulative definitions\nare assessed not by whether they are true or false but rather by their\nusefulness, and that assessment will be purpose-relative (cf. Berger\n1967: 175). De Muckadell (2014) rejects stipulative definitions of\nreligion for this reason, arguing that one cannot critique\nthem and that they force scholars simply to “accept whatever\ndefinition is offered”. She gives the example of a problematic\nstipulative definition of religion as “ice-skating\nwhile singing” which, she argues, can only be rejected by using\na real definition of religion that shows the ice-skating\ndefinition to be false. However, even without knowing the real essence\nof religion, one can critique a stipulative definition, either for\nbeing less adequate or appropriate for a particular purpose (such as\nstudying forms of life across cultures) or, as with the ice-skating\nexample, for being so far from a lexical definition that it is\nadequate or appropriate for almost no purpose.", "\nPolythetic definitions are increasingly popular today as people seek\nto avoid the claim that an evolving social category has an ahistorical\n essence.[14]\n However, the difference between these two approaches is not that\nmonothetic definitions fasten on a single property whereas polythetic\ndefinitions recognize more. Monothetic definitions can be\nmultifactorial, as we have seen, and they can recognize just as many\nproperties that are “common” or even “typical”\nof religions, without being essential. The difference is also not that\nthe monothetic identification of the essence of religion\nreflects an ethnocentrism that polythetic approaches avoid. The\npolythetic identification of a prototypical religion is equally\nethnocentric. The difference between them, rather, is that a\nmonothetic definition sorts instances with a Yes/No mechanism and is\ntherefore digital, and a polythetic definition produces gradations and\nis therefore analog. It follows that a monothetic definition treats a\nset of instances that all possess the one defining property as\nequally religion, whereas a polythetic definition produces a\ngray area for instances that are more prototypical or less so. This\nmakes a monothetic definition superior for cases (for example, legal\ncases) in which one seeks a Yes/No answer. Even if an open polythetic\napproach accurately describes how a concept operates, therefore, one\nmight, for purposes of focus or clarity, prefer to work with a closed\npolythetic account that limits the properties set, or even with a\nmonothetic approach that limits the properties set to one. That is,\none might judge that it is valuable to treat the concept\nreligion as structurally fuzzy or temporally fluid, but\nnevertheless place boundaries on the forms of life one will\ncompare.", "\nThis strategy gives rise to a third kind of polythetic approach, one\nthat stipulates that one property (or one set of properties) is\nrequired. Call this an “anchored” polythetic definition.\nConsistently treating concepts as tools, Wittgenstein suggests this\n“anchored” idea when he writes that when we look at the\nhistory of a concept,", "\n\n\nwhat we see is something constantly fluctuating … [but we might\nnevertheless] set over against this fluctuation something more fixed,\njust as one paints a stationary picture of the constantly altering\nface of the landscape. (1974: 77)\n", "\nGiven a stipulated “anchor”, a concept will then possess a\nnecessary property, and this property reintroduces essentialism. Such\na definition nevertheless still reflects a polythetic approach because\nthe presence of the required property is not sufficient to make\nsomething a religion. To illustrate this strategy, one might stipulate\nthat the only forms of life one will consider a religion will\ninclude", "\n(thereby excluding nationalism and capitalism, for example), but the\npresence of this property does not suffice to count this form of life\nas a religion. Consider the properties set introduced above that also\nincludes", "\nIf the threshold number is still three, then to be a religion, a form\nof life would have to have three of these properties, one of which\nmust be\n (A).\n An anchored definition of religion like this would have the benefits\nof the other polythetic definitions. For example, it would not produce\na clear line between religion and nonreligion but would instead\narticulate gradations between different forms of life (or between\nversions of one form of life at different times) that are less or more\nprototypically religious. However, given its anchor, it would produce\na more focused range of\n cases.[15]\n In this way, the use of an anchor might both reflect the contemporary\ncosmological view of the concept religion and also address\nthe criticism that polythetic approaches make a concept too vague." ], "subsection_title": "2.2 Polythetic approaches" } ] }, { "main_content": [ "\nOver the past forty years or so, there has been a reflexive turn in\nthe social sciences and humanities as scholars have pulled the camera\nback, so to speak, to examine the constructed nature of the objects\npreviously taken for granted as unproblematically “there”.\nReflexive scholars have argued that the fact that what counts as\nreligion shifts according to one’s definition reflects an\narbitrariness in the use of the term. They argue that the fact that\nreligion is not a concept found in all cultures but rather a\ntool invented at a certain time and place, by certain people for their\nown purposes, and then imposed on others, reveals its political\ncharacter. The perception that religion is a politically\nmotivated conceptual invention has therefore led some to skepticism\nabout whether the concept picks out something real in the world. As\nwith instrumentalism in philosophy of science, then, reflection on\nreligion has raised doubts about the ontological status of\nthe referent of one’s technical term.", "\nA watershed text for the reflexive turn regarding the concept\nreligion is Jonathan Z. Smith’s Imagining\nReligion (1982). Smith engages simultaneously in comparing\nreligions and in analyzing the scholarly practice of comparison. A\ncentral theme of his essays is that the concept religion (and\nsubcategories such as world religions, Abrahamic\nfaiths, or nonliterate traditions) are not scientific\nterms but often reflect the unrecognized biases of those who use these\nconcepts to sort their world into those who are or are not “like\n us”.[16]\n Smith shows that, again and again, the concept religion was\nshaped by implicit Protestant assumptions, if not explicit Protestant\napologetics. In the short preface to that book, Smith famously\nsays,", "\n\n\n[T]here is no data for religion. Religion is solely\nthe creation of the scholar’s study. It is created for the\nscholar’s analytic purposes by his imaginative acts of\ncomparison and generalization. Religion has no independent existence\napart from the academy. (1982: xi, italics in original)\n", "\nThis dramatic statement has sometimes been taken as Smith’s\nassertion that the concept religion has no referent. However,\nin his actual practice of comparing societies, Smith is not a\nnonrealist about religion. In the first place, he did not\nthink that the constructed nature of religion was something\nparticular to this concept: any judgement that two things\nwere similar or different in some respect presupposed a process of\nselection, juxtaposition, and categorization by the observer. This is\nthe process of imagination in his book’s title. Second, Smith\ndid not think that the fact that concepts were human products\nundermined the possibility that they successfully corresponded to\nentities in the world: an invented concept for social structures can\nhelp one discover religion—not “invent”\nit—even in societies whose members did not know the\n concept.[17]\n His slogan is that one’s (conceptual) map is not the same as\nand should be tested and rectified by the (non-conceptual) territory\n(J. Z. Smith 1978). Lastly, Smith did not think that scholars should\ncease to use religion as a redescriptive or second-order\ncategory to study people in history who lacked a comparable concept.\nOn the contrary, he chastised scholars of religion for resting within\ntradition-specific studies, avoiding cross-cultural comparisons, and\nnot defending the coherence of the generic concept. He writes that\nscholars of religion should be", "\n\n\nprepared to insist, in some explicit and coherent fashion, on the\npriority of some generic category of religion. (1995: 412; cf. 1998:\n281–2)\n", "\nSmith himself repeatedly uses religion and related technical\nterms he invented, such as “locative religion”, to\nilluminate social structures that operate whether or not those so\ndescribed had named those structures themselves—social\nstructures that exist, as his 1982 subtitle says, from Babylon to\nJonestown.", "\nThe second most influential book in the reflexive turn in religious\nstudies is Talal Asad’s Genealogies of Religion (1993).\nAdopting Michel Foucault’s “genealogical” approach,\nAsad seeks to show that the concept religion operating in\ncontemporary anthropology has been shaped by assumptions that are\nChristian (insofar as one takes belief as a mental state\ncharacteristic of all religions) and modern (insofar as one treats\nreligion as essentially distinct from politics). Asad’s\nFoucauldian point is that though people may have all kinds of\nreligious beliefs, experiences, moods, or motivations, the mechanism\nthat inculcates them will be the disciplining techniques of some\nauthorizing power and for this reason one cannot treat religion as\nsimply inner states. Like Smith, then, Asad asks scholars to shift\ntheir attention to the concept religion and to recognize that\nassumptions baked into the concept have distorted our grasp of the\nhistorical realities. However, also like Smith, Asad does not draw a\nnonrealist\n conclusion.[18]\n For Asad, religion names a real thing that would operate in\nthe world even had the concept not been invented, namely, “a\ncoherent existential complex” (2001: 217). Asad’s critical\naim is not to undermine the idea that religion exists qua social\nreality but rather to undermine the idea that religion is essentially\nan interior state independent of social power. He points out that\nanthropologists like Clifford Geertz adopt a hermeneutic approach to\nculture that treats actions as if they are texts that say something,\nand this approach has reinforced the attention given to the meaning of\nreligious symbols, deracinated from their social and historical\ncontext. Asad seeks to balance this bias for the subjective with a\ndisciplinary approach that sees human subjectivity as also the product\nof social structures. Smith and Asad are therefore examples of\nscholars who critique the concept religion without denying\nthat it can still refer to something in the world, something that\nexists even before it is named. They are able, so to speak, to look at\none’s conceptual window without denying that the window provides\na perspective on things outside.", "\nOther critics have gone farther. They build upon the claims that the\nconcept religion is an invented category and that its modern\nsemantic expansion went hand in hand with European colonialism, and\nthey argue that people should cease treating religion as if\nit corresponds to something that exists outside the sphere of modern\nEuropean influence. It is common today to hear the slogan that there\nis no such “thing” as religion. In some cases, the point\nof rejecting thing-hood is to deny that religion names a\ncategory, all the instances of which focus on belief in the same kind\nof object—that is, the slogan is a rejection of substantive\ndefinitions of the concept (e.g., Possamai 2018: ch. 5). In this case,\nthe objection bolsters a functional definition and does not deny that\nreligion corresponds to a functionally distinct kind of form\nof life. Here, the “no such thing” claim reflects the\nunsettled question, mentioned above, about the grounds of substantive\ndefinitions of “religion”. In other cases, the point of\nthis objection is to deny that religion names a defining\ncharacteristic of any kind—that is, the slogan is a rejection of\nall monothetic definitions of the concept. Perhaps religion\n(or a religion, like Judaism) should always be referred to in the\nplural (“Judaisms”) rather than the singular. In this\ncase, the objection bolsters a polythetic definition and does not deny\nthat religion corresponds to a distinct family of forms of\nlife. Here, the “no such thing” claim rejects the\nassumption that religion has an essence. Despite their negativity,\nthese two objections to the concept are still realist in that they do\nnot deny that the phrase “a religion” can correspond to a\nform of life operating in the world.", "\nMore radically, one sees a denial of this realism, for example, in the\ncritique offered by Wilfred Cantwell Smith (1962). Smith’s\nthesis is that in many different cultures, people developed a concept\nfor the individuals they considered pious, but they did not develop a\nconcept for a generic social entity, a system of beliefs and practices\nrelated to superempirical realities. Before modernity, “there is\nno such entity [as religion and] … the use of a plural, or with\nan article, is false” (1962: 326, 194; cf. 144). Smith\nrecommends dropping religion. Not only did those so described\nlack the concept, but the use of the concept also treats\npeople’s behavior as if the phrase “a religion”\nnames something in addition to that behavior. A methodological\nindividualist, Smith denies that groups have any reality not explained\nby the individuals who constitute them. What one finds in history,\nthen, is religious people, and so the adjective is useful,\nbut there are no religious entities above and beyond those people, and\nso the noun reifies an abstraction. Smith contends that", "\n\n\n[n]either religion in general nor any one of the religions … is\nin itself an intelligible entity, a valid object of inquiry or of\nconcern either for the scholar or for the [person] of faith. (1962:\n12)\n", "\nMore radical still are the nonrealists who argue that the concepts\nreligion, religions, and religious are all\nchimerical. Often drawing on post-structuralist arguments, these\ncritics propose that the notion that religions exist is simply an\nillusion generated by the discourse about them (e.g., McCutcheon 1997;\n2018; Fitzgerald 2000; 2007; 2017; Dubuisson 1998; 2019). As Timothy\nFitzgerald writes, the concept religion", "\n\n\npicks out nothing and it clarifies nothing … the word has no\ngenuine analytical work to do and its continued use merely contributes\nto the general illusion that it has a genuine referent ….\n(2000: 17, 14; also 4)\n", "\nAdvocates of this position sometimes call their approach the\n“Critical Study of Religion” or simply “Critical\nReligion”, a name that signals their shift away from the\npre-critical assumption that religion names entities in the\nworld and to a focus on who invented the concept, the shifting\ncontrast terms it has had, and the uses to which it has been\n put.[19]\n Like the concept of witches or the concept of biological races (e.g.,\nNye 2020), religion is a fiction (Fitzgerald 2015) or a\nfabrication (McCutcheon 2018), a concept invented and deployed not to\nrespond to some reality in the world but rather to sort and control\npeople. The classification of something as “religion” is\nnot neutral but", "\n\n\na political activity, and one particularly related to the colonial and\nimperial situation of a foreign power rendering newly encountered\nsocieties digestible and manipulable in terms congenial to its own\nculture and agenda. (McCutcheon & Arnal 2012: 107)\n", "\nAs part of European colonial projects, the concept has been imposed on\npeople who lacked it and did not consider anything in their society\n“their religion”. In fact, the concept was for centuries\nthe central tool used to rank societies on a scale from primitive to\ncivilized. To avoid this “conceptual violence” or\n“epistemic imperialism” (Dubuisson 2019: 137), scholars\nneed to cease naturalizing this term invented in modern Europe and\ninstead historicize it, uncovering the conditions that gave rise to\nthe concept and the interests it serves. The study of religions\noutside Europe should end. As Timothy Fitzgerald writes, “The\ncategory ‘religion’ should be the object, not the tool, of\nanalysis” (2000: 106; also 2017: 125; cf. McCutcheon 2018:\n18).", "\nInspired by the post-structuralist critiques that religion\ndoes not apply to cultures that lack the concept, some historians have\nargued that the term should no longer be used to describe any\npremodern societies, even in Europe. For example, Brent Nongbri\n(2013), citing McCutcheon, argues that though it is common to speak of\nreligions existing in the past, human history until the concept\nemerged in modernity is more accurately understood as a time\n“before religion”. His aim is “to dispel the\ncommonly held idea that there is such a thing as ‘ancient\nreligion’” (2013: 8). Citing Nongbri, Carlin Barton and\nDaniel Boyarin (2016) argue that the Latin religio and the\nGreek thrēskeia do not correspond to the modern\nunderstanding of religion and those studying antiquity should\ncease translating them with that concept. There was no “Roman\nreligious reality”, they say (2016: 19). These historians\nsuggest that if a culture does not have the concept of X,\nthen the reality of X does not exist for that culture.\nBoyarin calls this position “nominalism”, arguing that\nreligion is", "\n\n\nnot in any possible way a “real” object, an object that is\nhistorical or ontological, before the term comes to be used. (2017:\n25)\n", "\nThese critics are right to draw attention to the fact that in the mind\nof most contemporary people, the concept religion does imply\nfeatures that did not exist in ancient societies, but the argument\nthat religion did not exist in antiquity involves a sleight of hand.\nNone of these historians argues that people in antiquity did not\nbelieve in gods or other spiritual beings, did not seek to interact\nwith them with sacrifices and other rituals, did not create temples or\nscriptures, and so on. If one uses Tylor’s definition of\nreligion as belief in spiritual beings or James’s\ndefinition of religion as adjusting one’s life to an\nunseen order—or any of the other definitions considered in\nthis entry—then religion did exist in antiquity.\nWhat these historians are pointing out is that ancient practices\nrelated to the gods permeated their cultures. As Nongbri puts\nit,", "\n\n\nTo be sure, ancient people had words to describe proper reverence of\nthe gods, but … [t]he very idea of “being\nreligious” requires a companion notion of what it would mean to\nbe “not religious” and this dichotomy was not part of the\nancient world; (2013: 4)\n", "\nthere was no “discrete sphere of religion existing prior to the\nmodern period” (2019: 1, typo corrected). And Barton and\nBoyarin:", "\n\n\nThe point is not … that there weren’t practices with\nrespect to “gods” (of whatever sort) but that these\npractices were not divided off into separate spheres …. (2016:\n4)\n", "\nSteve Mason also argues that religion did not exist in antiquity since\nreligion is “a voluntary sphere of activity, separate in\nprinciple” from politics, work, entertainment, and military\nservice (2019: 29). In short, what people later came to conceptualize\nas religion was in antiquity not a freestanding entity. The nominalist\nargument, in other words, adds to the definition of the concept\nreligion a distinctively modern feature (usually some version\nof “the separation of church and state”), and then argues\nthat the referent of this now-circumscribed concept did not exist in\nantiquity. Their argument is not that religion did not exist outside\nmodernity, but that modern religion did not exist outside\nmodernity.", "\nThese post-structuralist and nominalist arguments that deny that\nreligion is “out there” have a realist alternative.\nAccording to this alternative, there is a world independent of human\nconceptualization, and something can be real and it can even affect\none’s life, whether or not any human beings have identified it.\nThis is true of things whose existence does not depend on collective\nagreement, like biochemical signaling cascades or radioactive beta\nparticles, and it is equally true of things whose existence does\ndepend on collective agreement, like kinship structures, linguistic\nrules, and religious commitments. A realist about social structures\nholds that a person can be in a bilateral kinship system, can speak a\nUralic language, and can be a member of a religion—even if they\nlack these concepts.", "\nThis realist claim that social structures have existed without being\nconceptualized raises the question: if human beings had different ways\nof practicing religion since prehistoric times, why and when did\npeople “finally” create the taxon? Almost every scholar\ninvolved in the reflexive turn says that religion is a modern\n invention.[20]\n The critique of the concept religion then becomes part of\ntheir critique of modernity. Given the potent uses of\nreligion—to categorize certain cultures as godless and\ntherefore inferior or, later, to categorize certain cultures as\nsuperstitious and therefore backwards—the significance of the\ncritique of religion for postcolonial and decolonial\nscholarship is undeniable. Nevertheless, it is not plausible that\nmodern Europeans were the first to want a generic concept for\ndifferent ways of interacting with gods. It is easy to imagine that if\nthe way that a people worship their gods permeates their work, art,\nand politics, and they do not know of alternative ways, then it would\nnot be likely that they would have created a concept for it. There is\nlittle need for a generic concept that abstracts a particular aspect\nof one’s culture as one option out of many until one is in a\nsustained pluralistic situation. The actions that today are\ncategorized as religious practices—burial rites, the making of\nofferings, the imitation of divinized ancestors—may have existed\nfor tens of thousands of years without the practitioners experiencing\nthat diversity or caring to name it. Nevertheless, it is likely that a\ndesire to compare the rules by which different people live in relation\nto their gods would have emerged in many parts of the world long\nbefore modernity. One would expect to find people developing such\nsocial abstractions as cities and then empires emerged and their\ncultures came into contact with each other. From this realist\nperspective, it is no surprise that, according to the detailed and\nexample-filled argument of Barton and Boyarin (2016), the first use of\nreligion as a generic social category, distinct from the\nconcept of politics, for the ways that people interact with\ngods is not a product of the Renaissance, the Reformation, or modern\ncolonialism at all, but can be found in the writings of Josephus\n(37–c. 100 CE) and Tertullian (c. 155–c. 220\n CE).[21]\n From the realist perspective, it is no surprise to see the\ndevelopment of analogous terms in medieval China, centuries before\ninteraction with Europeans (Campany 2003, 2012, 2018) and in medieval\nIslam (Abbasi 2020, 2021). The emergence of social kinds does not wait\non language, and the development of language for social kinds is not\nonly a Western project. If this is right, then the development of a\nconcept for religion as a social genus is at least two thousand\nyears old, though the social reality so labeled would be much\nolder." ], "section_title": "3. Reflexivity, Reference, and Skepticism", "subsections": [] } ]

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Translated as\nReligion within the Limits of Reason Alone, Theodore M.\nGreene and Hoyt H. Hudson (trans.), La Salle, IL: The Open Court,\n1934.", "Laurence, Stephen and Eric Margolis, 1999, “Concepts and\nCognitive Science”, in Concepts: Core Readings, Eric\nMargolis and Stephen Laurence (eds), Cambridge: MIT Press,\n1–81.", "Lehrich, Christopher I., 2021, Jonathan Z. Smith on\nReligion, London: Routledge.", "Lincoln, Bruce, 2006, Holy Terrors: Thinking about Religion\nafter September 11. Second edition. Chicago: The University of\nChicago Press. ", "Ling, Trevor, 1980, Karl Marx and Religion: In Europe and\nIndia, London: Palgrave Macmillan.", "Lofton, Kathryn, 2011, Oprah: The Gospel of an Icon,\nBerkeley, CA: University of California Press.", "–––, 2012, “Religious History as Religious\nStudies”, Religion, 42(3): 383–394.\ndoi:10.1080/0048721X.2012.681878", "Lopez, Donald S., Jr., 1998, “Belief”, in Critical\nTerms for Religious Studies, Mark C. 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(ed.), 2019, Theorizing\n“Religion” in Antiquity, (Studies in Ancient Religion\nand Culture), Bristol, UK: Equinox Publishing.", "Saler, Benson, 1977, “Supernatural as a Western\nCategory”, Ethos, 5(1): 31–53.\ndoi:10.1525/eth.1977.5.1.02a00040", "–––, 1993, Conceptualizing Religion:\nImmanent Anthropologists, Transcendent Natives, and Unbounded\nCategories, Leiden: E. J. Brill.", "–––, 1999, “Family Resemblance and the\nDefinition of Religion”, Historical Reflections /\nRéflexions Historiques, 25(3): 391–404.", "–––, 2021, The Construction of the\nSupernatural in Euro-American Cultures: Something Nice about\nVampires, London: Bloomsbury.", "Schaefer, Donovan O., 2015, Religious Affects: Animals,\nEvolution, and Power, Durham, NC: Duke University Press.", "Schellenberg, J. 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Taylor (ed.), Chicago, IL: University of Chicago Press.", "Smith, Wilfred Cantwell, 1962, The Meaning and End of\nReligion, New York: Macmillan.", "Southwold, Martin, 1978, “Buddhism and the Definition of\nReligion”, Man, New Series 13(3): 362–379.\ndoi:10.2307/2801935", "Spiro, Melford, 1966, “Religion: Problems of Definition and\nExplanation”, in Anthropological Approaches to the Study of\nReligion, Michael Banton (ed.), London: Tavistock,\n85–126.", "Taves, Ann, 2009, Religious Experience Reconsidered: A\nBuilding-Block Approach to the Study of Religion and other Special\nThings., Princeton, NJ: Princeton University Press.", "Tillich, Paul, 1957, Dynamics of Faith, New York: Harper\nand Row.", "–––, 1963, Christianity and the Encounter of\nthe World Religions, New York: Columbia University Press.", "Turner, Bryan S., 2011, Religion and Modern Society:\nCitizenship, Secularization and the State, Cambridge: Cambridge\nUniversity Press. doi:10.1017/CBO9780511975660", "Tylor, Edward Burnett, 1871 [1970], Primitive Culture,\ntwo vols., London: John Murray, 1871; vol. 2 reprinted as Religion\nin Primitive Culture, Gloucester: Peter Smith, 1970.", "Vásquez, Manuel A., 2011, More than Belief: A\nMaterialist Theory of Religion, Oxford: Oxford University\nPress.", "Weed, Eric, 2019, The Religion of White Supremacy in the\nUnited States, Lanham, MD: Lexington.", "Whitehead, Alfred North, 1926, Religion in the Making,\nCambridge: Cambridge University Press.", "Williamson, Timothy, 1994, Vagueness, London:\nRoutledge.", "Wittgenstein, Ludwig, 1953 [2009], Philosophical\nInvestigations, G. E. M. Armstrong (trans.), Oxford: Basil\nBlackwell; reprinted: 4th edition, Malden: Blackwell,\n2009.", "–––, 1974, Philosophical Grammar,\nAnthony Kenny (trans.), Oxford: Blackwell." ]

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[ "\n\nContemporary epistemology of religion may conveniently be treated as a\ndebate over whether evidentialism applies to religious\nbeliefs, or whether we should instead adopt a more permissive\nepistemology. Here evidentialism is the initially plausible position\nthat a belief is justified only if “it is proportioned to the\nevidence”. For example, suppose a local weather forecaster has\nnoticed that over the two hundred years since records began a wetter\nthan average Winter is followed in 85% of cases by a hotter than\naverage Summer. Then, assuming for simplicity that the records are\nreliable, the forecaster is justified in believing with less than full\nconfidence that this Winter, which is wetter than average, will be\nfollowed by a hotter than average Summer. But evidentialism implies\nthat it would not be justified to have full belief, that is belief\nwith 100% confidence. Again, consider someone who has a hunch\nthat this Summer will be hotter than average but cannot justify that\nhunch further. Hunches are not considered evidence, so the belief is\nnot considered justified. If, however, the huncher can cite a good\ntrack record of hunches about the weather that have turned out correct\nthen the belief would be considered justified. For although hunches\nare not considered evidence, memories about past hunches are, as are\nthe observations that corroborated the past hunches.", " Evidentialism implies that full religious belief is justified only\nif there is conclusive evidence for it. It follows that if the\narguments for there being a God, including any arguments from\nreligious experience, are at best probable ones, no one would be\njustified in having a full belief that there is a God. And the same\nholds for other religious beliefs, such as the belief that God is not\njust good in a utilitarian fashion but loving, or the belief that\nthere is an afterlife. Likewise it would be unjustified to believe\neven with less than full confidence that, say, Krishna is divine or\nthat Mohammed is the last and most authoritative of the prophets,\nunless a good case can be made for these claims from the evidence.", " Evidentialism, then, sets rather high standards for justification,\nstandards that the majority do not, it would seem, meet when it comes\nto religious beliefs, where many rely on “faith”, which is\nmore like the forecaster’s hunch about the weather than the argument\nfrom past climate records. Many others take some body of scripture,\nsuch as the Bible or the Koran as of special authority, contrary to\nthe evidentialist treatment of these as just like any other\nbooks making various claims. Are these standards too high?", " This century has seen a turn in the debate, with emphasis on the\nimplications of disagreement, “How can sincere intelligent\npeople disagree? Should not we all suspend judgement?”" ]

[ { "content_title": "1. Simplifications", "sub_toc": [] }, { "content_title": "2. The Rejection of Enlightenment Evidentialism", "sub_toc": [] }, { "content_title": "3. Evidentialism Defended", "sub_toc": [] }, { "content_title": "4. Natural theology", "sub_toc": [] }, { "content_title": "5. The Relevance of Newman", "sub_toc": [] }, { "content_title": "6. Wittgensteinian Fideism", "sub_toc": [] }, { "content_title": "7. Reformed Epistemology", "sub_toc": [] }, { "content_title": "8. Religious Experience, Revelation and Tradition", "sub_toc": [] }, { "content_title": "9. Religious Disagreement", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Works Cited", "Other Important Works" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nEpistemology is confusing because there are several sorts of items to\nbe evaluated and several sorts of evaluation. Since the topic of this\narticle is the epistemology of religion not general epistemology it\nwill be assumed that what is being evaluated is something related to\nfaith, namely individual religious beliefs, and that the way of\nevaluating religious beliefs is as justified or unjustified.", "This entry, therefore, concentrates on questions such as, “Is\nit justified for Fatima to believe in God?”, “Is it\njustified for Richard to believe in the Trinity?”, or “Is\nit justified for Ramanujan to believe that Krishna is a human\nincarnation of the divine?” It ignores such questions as whether\nthese beliefs count as knowledge or whether these beliefs are\nscientific. It also ignores disputes between coherence theorists and\nfoundationalists and disputes over whether belief is\nvoluntary. Although these have some implications for the epistemology\nof religion they are primarily topics in general epistemology.", "Although the topic is religious belief the same questions can be\nasked about faith in the absence of belief, where the standards might\nbe more lax. For example John Schellenberg (2009) has argued that it is\nnot justified to believe in a personal God, not justified to have\nfaith in a personal God , not justified even to believe in something\nultimate but it is justified to have a religious attitude of faith in\nsomething ultimate. Finally, and more controversially, this entry\nconcentrates on Western epistemology of religion, which is not,\nhowever, the same as the epistemology of Western religion. Note,\nthough, that epistemological disputes between Hindu and Buddhist\nphilosophers over a thousand years ago are much the same as those here\nconsidered." ], "section_title": "1. Simplifications", "subsections": [] }, { "main_content": [ "\n\nMost contemporary epistemology of religion may be called post\nmodern in the sense of being a reaction to the Enlightenment, in\nparticular to the thesis of the hegemony of\nevidentialism. (Compare Vanhoozer 2003.) Hegemony is discussed below,\nbut first consider evidentialism. This is the initially plausible\nposition that a belief is justified only if “it is proportioned\nto the evidence”. (Beliefs proportioned to the evidence include,\nas a special case, the evidence itself.) Here several sorts of\nevidence are allowed. One consists of beliefs in that which is\n“evident to the senses”, that is, beliefs directly due to\nsense-experience. Another sort of evidence is that which is\n“self-evident”, that is, obvious once you think about\nit. Evidence may also include the beliefs directly due to memory and\nintrospection. Again moral convictions might count as evidence, even\nif not treated as “self-evident”. But in order to state\nthe sort of evidentialism characteristic of Enlightenment thought, it\nis stipulated that no beliefs asserting the content of religious or\nmystical experiences count as evidence. For example, if Fatima had an\nexperience that she would describe as of the presence of God she\nshould not treat God’s presence to her as a piece of evidence. That\ndoes not prevent the claim that someone has had a religious experience\nwith a certain content from counting as evidence. For example, the\nfact that Fatima had an experience as if of God’s presence would be a\npiece of evidence. Likewise the fact that various people report\nmiracles counts as evidence.", "\n\nEvidentialism implies that no full religious belief (i.e., a religious\nbelief held with full confidence) is justified unless there is\nconclusive evidence for it, or it is self-evident. The content of\nreligious experience has been stipulated not to count as\nevidence. Even if, as Descartes held, the existence of God is\nself-evident, beliefs such as Richard’s in the Trinity and\nRamanujan’s in the divinity of Krishna are not. So the only\navailable evidence for these beliefs would seem to be non-religious\npremises, from which the religious beliefs are inferred. Therefore,\nthe only way of deciding whether the religious beliefs are justified\nwould be to examine various arguments with the non-religious beliefs\nas premises and the religious beliefs as conclusions.", "\n\nAccording to evidentialism it follows that if the arguments for there\nbeing a God, including any arguments from religious experience, are at\nbest probable ones, and if, as most hold, God’s existence is not\nself-evident then no one would be justified in having full belief that\nthere is a God. And the same holds for other religious\nbeliefs. Likewise, it would not be justified to believe even partially\n(i.e., with less than full confidence) if there is not a balance of\nevidence for belief.", "\n\nIn fact it seems that many religious believers combine full belief\nwith “doubts” in the sense of some reasons for doubting,\nor they combine partial belief with what they take to be weighty\nreasons for disbelief. According to evidentialism this is not\njustified. Other believers consider that, on reflection, they have\nlittle reason for doubting but that they have almost no positive\nevidence for their religious beliefs. According to evidentialism this\ntoo is unjustified. This raises the question, how can we adjudicate\nbetween an epistemological thesis which might otherwise be believed\nand a religious belief which that thesis implies is unjustified? The\nEnlightenment assumed two related, hegemony theses, those of\nepistemology and of evidentialism. The hegemony of epistemology states\nthat (a) human beings can discover the correct epistemology in\nisolation from discovering actual human tendencies to form beliefs,\nand so (b) there is an overriding reason to use the correct\nepistemology (once discovered) to correct the above-mentioned\ntendencies. The hegemony of evidentialism adds to the hegemony of\nepistemology the further thesis that (c) evidentialism is the correct\nepistemology. If, according to evidentialism, full or even partial\nreligious beliefs are unjustified, then, given the hegemony of\nevidentialism there is an overriding reason to reject those beliefs.\nPerhaps the clearest exponent of this position is the comparatively\nrecent Clifford whose use of moral vocabulary conveys well the\noverriding character of the reasons epistemology is said to provide.\nHis position is summed up in the famous quotation: “It is wrong\nalways, everywhere, and for anyone, to believe anything upon\ninsufficient evidence” (Clifford 1879: 186).", "\n\nAt the other extreme from Clifford is the position of\nfideism, namely, that if an epistemological theory such as\nevidentialism conflicts with the holding of religious beliefs\nthen that is so much the worse for the epistemological theory.", "\n\nThe rejection of the hegemony of epistemology is quite compatible\nwith holding a hegemony thesis for a fragment of epistemology. Such a\nfragment might, for instance, contain the principle of\nself-referential consistency, relied upon by Plantinga (1983:\n60). This states that it is not justified to have a belief according\nto which that belief is itself not justified. Consider, for instance,\nthe extreme case of the person who believes that no belief is\njustified unless it can be proven from premises everyone agrees\nupon. ", "\n\nPostmodernism implies more than being post modern in the above sense.\nFor it is the rejection of the hegemony of even a fragment of\nepistemology. That might seem agreeable to fideists. Postmodernism\ntends, however, to trivialize fideism by obliterating any contrast\nbetween faith in divine revelation and trust in human capacities to\ndiscover the truth. (For a discussion of fideism and postmodernism see\nStiver 2003.) ", "\n\nMuch contemporary epistemology of religion seeks to avoid the extremes\nboth of the Enlightenment thesis of the hegemony of evidentialism and\nof fideism. It is thus post modern without necessarily being\npostmodernist. Call the injunction to avoid these extremes\nthe problematic of contemporary epistemology of religion." ], "section_title": "2. The Rejection of Enlightenment Evidentialism", "subsections": [] }, { "main_content": [ "\n\nOne response to the problematic is to separate evidentialism from the\nhegemony of epistemology. Evidentialism may then be defended by noting\nhow we implicitly rely upon evidentialist principles in many different\nareas of enquiry, or by noting which principles generalise various\nparticular examples of justified and unjustified\nreasoning. Such a defence of evidentialism is part of\nthe project of some contemporary philosophers who seek to attack\ntheism in favour of agnosticism and/or atheism. This defence may well\nbe implicit in Flew’s famous “The Presumption of Atheism”\n(1972). It is more explicit in Scriven’s\nPrimary Philosophy (1966, ch 4). Scriven and Flew are relying\non the Ockhamist principle that, in the absence of evidence for the\nexistence of things of kind X, belief in Xs is\nnot reasonable. This they can defend by means of examples in which\nnon-Ockhamist thinking is judged not to be justified. So even if the\nwhole of evidentialism is not defended, the Ockhamist fragment of it\nmay be.", "\n\nNot surprisingly the reliance of non-theist philosophers on\nevidentialism has been criticised. First there is an ad hominem.\nShalkowski (1989) has pointed out that these defenders of\nevidentialism tend in fact to be atheists not agnostics, yet a careful\nexamination, he says, of the examples used to support Ockham’s\nRazor show that either they are ones in which there is independent\nevidence for denying the existence of Xs or ones in which\nsuspense of judgement seems to be the appropriate response, not\ndenial. Another criticism is Plantinga’s claim that\nevidentialism is self-referentially inconsistent for there is no\nevidence for evidentialism (Plantinga 1983: 60). This might be met in\neither of two ways. First, it could be said that all that is being\ndefended is the Ockhamist fragment of evidentialism and that this is\nnot itself vulnerable to Ockham’s Razor. Or it could be argued\nthat deriving an epistemology from a wide range of examples is\nevidence for it. To be sure this is far from conclusive evidence. But\neven a less than full belief in an epistemological thesis which showed\ntheism to be unjustified would be damaging. This may be illustrated\nusing an example with artificial numerical precision: 80% confidence\nin an epistemology which showed that no degree of belief in theism\ngreater than 60% was justified is incompatible with a degree of belief\nin theism greater than 68%. The person in question could have a\ndegree of belief of in the conjunction of theism and the (80% likely)\nepistemology of no greater than 48% (80% of 60%) and a degree of\nbelief in the conjunction of theism and the denial of that\nepistemology of no greater than 20% (since that epistemology has a\nprobability of 80%).\n" ], "section_title": "3. Evidentialism Defended", "subsections": [] }, { "main_content": [ "\n\nTheistic philosophers may, of course, grant evidentialism and even\ngrant its hegemony, but defend theism by providing the case which\nevidentialists demand. Here the details of the arguments are not\nwithin the scope of an article on epistemology. What is of interest is\nthe kind of argument put forward. For a start there is the\nproject of demonstrating God’s existence, and this project is\nnot restricted to neo-Thomists. (See Craig 1979, Braine 1988, Miller\n1991.) To show the justifiability of full belief that there is a God\nit is sufficient (a) to have a deductively valid argument from\npremisses which are themselves justifiably held with full belief\nunless defeated by an objection and (b) to have considered and\ndefeated all available objections to either the premisses, the\nconclusion or any intermediate steps. Some of the premisses of these\narguments are said to be self-evident, that is, obvious once you think\nabout it. (E.g., the denial of the explanatory power of an infinite\ncausal regress, or the principle that the existence of any composite\nthing needs to be explained). And that raises a further\nepistemological problem. Does something’s being self-evident to you\njustify your full belief in it even if you know of those of equal or\ngreater intellectual ability to whom it is not self-evident?", "\n\nMany natural theologians have, however, abandoned the search for\ndemonstrative arguments, appealing instead to ones which are probable,\neither in the sense of having weight but being inconclusive or in the\nsense of having a mathematical probability assigned to them. Notable\nin this regard are Mitchell’s cumulative argument (Mitchell 1973) and\nSwinburne’s Bayesian reliance on probability (Swinburne 1979). In a\npopular exposition of his argument Swinburne appeals instead to an\ninference to the best explanation (Swinburne 1995; see also Forrest\n1996). While there are differences of approach, the common theme is\nthat there is evidence for theism but evidence of a probable rather\nthan a conclusive kind, justifying belief but not full belief." ], "section_title": "4. Natural theology", "subsections": [] }, { "main_content": [ "\n\nAlthough pre-dating the current debate, John Henry Newman’s\nrejection of Locke’s and Paley’s evidentialism is relevant\nto the problematic of contemporary epistemology of religion. First he\nquite clearly rejected the hegemony of epistemology. His procedure was\nto examine how in fact people made up their minds on non-religious\nissues and argue that by the same standards religious beliefs were\njustified. As a result he qualified evidentialism by insisting that\nan implicit and\ncumulative argument could lead to justified certainty. (See\nMitchell 1990.) ", "\n\nNewman’s position has two interpretations. One, which differs little\nfrom Swinburne’s probabilistic approach to natural theology, asserts\nthat the consilience of a number of independent pieces of probable\nreasoning can result in a probability so high as to be negligibly\ndifferent from certainty. If, to use an example Newman would not have\nliked, Aquinas’s five ways were independent and each had probability\n75% then taken together their probability is about 99.9%. One\ndifficulty with this interpretation is that even a highly probable\nargument differs from a demonstration in that the former is vulnerable\nto probabilistic counter-arguments. Thus a probabilistic version of\nthe Argument from Evil might subsequently reduce the probability from\n99.9% down to 75% again.", "\n\nThe other interpretation of Newman’s position is to say that\nevidentialism falsely presupposes that there are fine gradations on a\nscale from full belief through partial belief to partial disbelief to\nfull disbelief. Newman claims that human beings are not like that when\nit comes to those beliefs which form part of religious faith. In such\ncases the only available states are those of full belief and full\ndisbelief or, perhaps, full belief, and lack of full belief. Of course\nsomeone can believe that theism has a probability between 90% and 60%,\nsay, but that could be interpreted as believing that relative to the\nevidence theism has a probability between 90% and 60%, which, in turn,\nis a comment on the strength of the case for theism not the expression\nof a merely partial belief.", "\n\nIf Newman is right then evidentialism is slightly wrong. Instead of\nrequiring belief to be proportioned to the evidence, full belief is\njustified if the case for it holds “on the balance of\nprobabilities”. Hence a natural theology consisting of merely\nprobable arguments, such as Swinburne’s, can still show full\nreligious belief to be justified." ], "section_title": "5. The Relevance of Newman", "subsections": [] }, { "main_content": [ "\n\nAnother reaction to the problematic is Wittgensteinian fideism, the\nthesis that there are various different “language games”,\nand that while it is appropriate to ask questions about justification\nwithin a language game it is a mistake to ask about the justification\nof “playing” the game in question. In this way\nepistemology is relativised to language games, themselves related to\nforms of life, and the one used for assessing religious claims is less\nstringent than evidentialism. Here there seems to be both an autonomy\nthesis and an incommensurability thesis. The autonomy thesis tells us\nthat religious utterances are only to be judged as justified or\notherwise by the standards implicit in the religious form of life, and\nthis may be further restricted to Christianity or Hinduism, or any\nother religion (Malcolm 1992). The incommensurability thesis tells us\nthat religious utterances are unlike scientific or metaphysical claims\nand so we are confusing different uses of language if we judge\nreligious utterances by the standards of science or metaphysics\n(Phillips 1992). Stress on the autonomy thesis brings Wittgensteinian\nfideism close to the fideism of many religious conservatives, but\nstress on the incommensurability thesis brings it close to the extreme\nliberal position of Braithwaite (1955), namely that religion is about\nattitudes not facts, which would, of course, be rejected by religious\nconservatives.", "\n\nPerhaps the most obvious criticism of Wittgensteinian fideism is that\neven if the underlying theory of forms of life and language games is\ngranted, it is an historical fact, itself justified by the criteria of\nthe “game” of history, that the tradition to which the\nmajority of Jews, Christians and Muslims belong to is a form of life\nwith heavy metaphysical commitments, and in which such utterances as\n“There is a God” are intended as much like “There is\na star ten times more massive than the Sun” as like “There\nis hope”. So Wittgensteinian fideism is only appropriate for\nsuch religions as Zen Buddhism and for some, relatively recent,\nliberal strands of Judaism and Christianity which have rejected the\ntraditional metaphysical commitment (as in Cupitt 1984).", "\nThe Wittgensteinian position could be modified to allow a metaphysical\n“language game” with its own criteria for justification\netc, and in which natural theology should be pursued. Then the\nJudeo-Christian-Islamic “language game” would be part of\nthis larger, autonomous metaphysical “language game”. That\nmodified account would cohere with the historical fact of the\nmetaphysical commitment of that religious tradition. In that case,\nthough, it would seem that, not just the Judeo-Christian-Islamic\n“language game”, but all serious intellectual enquiry\nshould also be treated as parts of the one “game”, with\none set of rules. Thus Wittgensteinian fideism would have been\nqualified out of existence.", "\n\nEven if you reject Wittgensteinian fideism you might still take a lesson\nfrom it. For it must surely be granted that religious utterances are\nnot made in a purely intellectual way. Their entanglement with\ncommitment to a way of life and their emotional charge might help to\nexplain the fact, if it is one, that those who take religion\nseriously, whether believers or not, do not in fact have a continuous\nrange of degrees of confidence but operate instead with full belief or\nfull disbelief. For, normally, emotionally charged beliefs are either\nfull on or full off, and in abnormal cases tend to be divided rather\nthan partial. Thus, confronted with conflicting evidence about whether\nyour affection is reciprocated you are far less likely to suspend\njudgement than to oscillate between full belief and full\ndisbelief. Likewise it seems more normal to oscillate between full\nbelief in God in moments of crisis and full disbelief when things go\nwell than to suspend judgement at all times. This ties in with the\nNewmanian modification of evidentialism, mentioned above." ], "section_title": "6. Wittgensteinian Fideism", "subsections": [] }, { "main_content": [ "\n\nAn influential contemporary rejection of evidentialism is reformed\nepistemology, due to Wolterstorff (1976) and Plantinga (1983). As\nPlantinga develops it in his paper (1983), beliefs\nare warranted without Enlightenment-approved evidence\nprovided they are (a) grounded, and (b) defended against known\nobjections. Such beliefs may then themselves be used as evidence for\nother beliefs. But what grounding amounts to could be debated. Later,\nPlantinga proposed an account of warrant as proper functioning. This\naccount seems to entail that S’s belief that p\nis grounded in event E if (a) in the circumstances E\ncaused S to believe that p, and\n(b) S’s coming to believe that p was a case of\nproper functioning (Plantinga 1993b). It should be noted that the term\n“warrant” used elsewhere in philosophy as a synonym for\n“justified” (as in “warranted assertibility”)\nis used by Plantinga to mean that which has to be adjoined to a true\nbelief for it to be knowledge. (See Plantinga 1993a). Accordingly the\nmost pressing criticism of Plantinga’s later position is that it\nlargely ignores the question of justification, or reasonableness\nwhich, as Swinburne explicates it (Swinburne 2001) amounts to whether\nthe religious beliefs are probable relative to total evidence.", "\n\nWhile the details of grounding might be controversial it may be assumed\nthat reformed epistemologists assert that ordinary religious\nexperiences of awe, gratitude, contrition, etc., ground the beliefs\nimplied by the believer’s sincere reports of such experiences, provided\nthey can be said to cause those beliefs. Such grounded beliefs are\nwarranted provided they can be defended against known objections. They\ncan then be used as evidence for further religious beliefs. Thus if\nreligious experience grounds the belief that God has forgiven you for\ndoing what is wrong to other humans beings, then that is evidence for a\npersonal God who acts in a morally upright fashion. For, it can be\nargued, only such a God would find anything to forgive in the wrongs you\ndo to your fellow human beings.", "\n\nJerome Gellman (1992, 2017) draws our attention to the experience of\ngodlessness. This is occasioned by, but not inferred from, the evils\nthat surround us. If Reformed Epistemology is correct this would seem\nto ground atheism in the same way that the experience of forgiveness\ncan ground theism.", "\n\nOne difference between reformed epistemology and fideism is that the\nformer requires defence against known objections, whereas the latter\nmight dismiss such objections as either irrelevant or, worse,\nintellectual temptations. Included in the objections are not only\nthose such as the Argument from Evil that seek to rebut, but arguments\nfrom sociology and, more recently, cognitive science that seek to\nundermine by proposing a naturalistic cause for basic religious\nbeliefs. For instance, Justin Barrett (2004) posits a HADD\n(hyperactive/hypersensitive agency detection device), suggesting that\na sensitive agency detection device functions properly if the goal is\nsurvival but is hypersensitive if the goal is truth. This\nhypersensitivity then explains the human tendency towards supernatural\nbeliefs, undermining the proper basicality of those beliefs. Clark and\nBarrett (2011) suggest that this hypersensitivity could itself be part\nof the divine plan. An alternative, Bayesian, theistic response would\nbe that HADD exaggerates a properly basic probability for theism that\nis neither high nor too low prior to further evidence. This justifies\na part evidentialist, part reformed, program of assessing the\nall-things-considered probability resulting from the effect of\nevidence on this basic probability.", "\nA difference between reformed epistemology and Wittgensteinian fideism\nis that the former proposes a universal relaxation of the stringent\nconditions of evidentialism while the latter only proposes a\nrelaxation for some“language games”, including\nreligion.", "\n\nReformed epistemology could be correct and yet far less significant\nthan its proponents take it to be. That would occur if in fact rather\nfew religious beliefs are grounded in the sorts of ordinary religious\nexperiences most believers have. For it may well be that the beliefs\nare part of the cause of the experience rather than the other way round\n(Katz 1978)." ], "section_title": "7. Reformed Epistemology", "subsections": [] }, { "main_content": [ "\nReformed epistemology might be thought of as a modification of\nevidentialism in which the permissible kinds of evidence are expanded.\nNotable in this context is Alston’s work arguing that\ncertain kinds of religious experience can be assimilated to perception\n(Alston 1991).", "\n\nThe difference between reformed epistemology and Enlightenment-style\nevidentialism is also shown by a consideration of revelation and\ninspiration. An evidentialist will consider arguments from the premiss\nthat it is said such and such was revealed or the premiss that so and\nso claimed to be inspired by God, but a reformed epistemologist might\nallow as warranted those religious beliefs grounded in the event of\nrevelation or inspiration. Thus Mavrodes has argued that any belief\ndue to a genuine revelation is warranted, and has discussed several\nmodes of revelation (Mavrodes 1988). Zagzebski argues that this would\nhave the unacceptable consequence that warrant, and hence knowledge,\nbecomes totally inaccessible either to the person concerned\nor the community (Zagzebski 1993a: 204–205). For instance, Mavrodes\nwould probably not consider Ramanujan’s belief that Krishna is divine\nas warranted, but even if Mavrodes is correct Ramanujan would have no\naccess to this truth about the unwarranted character of his own\nbeliefs. A similar criticism could be made of beliefs grounded in\nreligious experience. In both cases, the question of whether a belief\nis genuinely grounded in religious experience or is genuinely grounded\nin inspiration is one that several religious traditions have paid\nattention to, with such theories as that of discernment of spirits\n(Murphy, 1990, ch 5).", "\n\nIn what might be called “counter-reformed epistemology”\nit could be allowed that a belief can be warranted if grounded in a\nreligious tradition. Such a belief would have to be caused in the right\nsort of way by the right sort of tradition. As in the previous cases we\nmight note that such grounding should be partially accessible to the\nbeliever. Rather little work has been done on this\nextension of reformed epistemology, but the social dimension of warrant\nhas been noted (Zagzebski 1993a).", "\n\nMore recently Plantinga (2000) has defended a rather different account of\ndivine inspiration, which he calls the Aquinas/Calvin model. This\nrelies upon the doctrine of ‘original sin’ claiming that\nmost humans suffer from a cognitive-affective disorder, but that as a\nresult of Redemption the Holy Spirit heals us so that we are able to\nfunction properly, and come to believe the Christian revelation in an\nimmediate, non-inferential manner. In this way the Aquinas/Calvin\nmodel supports the Christian metaphysics, which in turn supports the\nAquinas/Calvin model. Presumably it will be granted that the\nprobability, y, of the Aquinas/Calvin model given Christian\nmetaphysics is significantly less than 100%, because there are rival\nChristian models. As a consequence, the probability, z, of\nChristian metaphysics is less than x/(1−y)\nwhere x is the probability of Christian metaphysics given the\nfalsity of the Aquinas/Calvin model. Hence Plantinga’s proposal can\nsucceed only if either y is near 100% or x is not\ntoo small." ], "section_title": "8. Religious Experience, Revelation and Tradition", "subsections": [] }, { "main_content": [ "\n\nReligious disagreement is a long-standing problem in philosophy of\nreligion, but in this century there has been great interest in\ndisagreements between theists and atheists as well as the\ndisagreements between followers of various religions. (See Kelly 2005,\nChristensen 2007, Feldman 2007, Kraft 2007, Feldman and Warfield 2011,\nChristensen and Lackey 2013) The problem here is obvious: how can\nsincere intelligent people disagree? Should not both disputants\nsuspend judgement? To be sure, sometimes those who disagree with you\nare your intellectual inferiors in some respect. Consider, for\ninstance, someone who insisted that π was precisely 22/7. Those who\nknow of and can follow a proof that π is an irrational number may\njustifiably dismiss that person as a mathematical ignoramus. The case\nof interest, however, is that in which no such inferiority is on\npublic display. This is referred to as a situation of public\nepistemic parity. Richard Feldman criticizes the relativist\nsolution to the problem, namely that there is not always a unique\nreasonable doxastic attitude to a given proposition in a given\nepistemic situation. He also rejects unargued dismissal, and reaches\nthe conclusion that in situations of epistemic parity disputants\nshould suspend judgement. Many, however, agree with Peter van Inwagen\nwho, in his autobiographical ‘Quam Delicta’ (1994),\nimplies that it is justified for both parties in a dispute to appeal\nto what is privately available to them. Such private assertions of\nepistemic superiority are often expressed by saying that someone\n“just does not get the point”. Typically, not getting the\npoint requires a cognitive blind-spot. It is not that you know there\nis a point you cannot grasp, which reasonably requires some deference\nto those who claim to grasp it. You fail to see there is a point. A\nsomewhat different response to Feldman is that of Forrest (2019), who\nargues that when the cases for and against a thesis are of different\nkinds we may sometimes commit to the thesis, because\nnon-comparability is not the same as epistemic parity.", "\n\nOne obvious complication concerning religious disagreements is the\nappeal to divine inspiration, as a source of private epistemic\nsuperiority, as in Plantinga’s “Aquinas/Calvin” model\n(Plantinga 2000). It is hard to see, though, how this could apply to\ndisputes between two religions that both rely on the role of divine\ninspiration. Perhaps the only substitute for unargued dismissal is\nargued dismissal. " ], "section_title": "9. Religious Disagreement", "subsections": [] } ]

[ "Alston, William P., 1991, Perceiving God: The Epistemology of\nReligious Experience, Ithaca: Cornell University Press.", "Barrett, Justin L., 2004, Why would anyone believe in\nGod?, Lanham: AltaMira. ", "Braine, David, 1988, The Reality of Time and the Existence of\nGod: The Project of Proving God’s Existence, Oxford: Clarendon\nPress.", "Braithwaite, Richard B., 1955, An Empiricist’s View of the\nNature of Religious Belief, Cambridge: Cambridge University\nPress.", "Clark, Kelly James and Barrett, Justin L., 2011, ‘Reidian\nReligious Epistemology and the Cognitive Science of Religion’,\nJournal of the American Academy of Religion, 79:\n639–675.", "Clifford, William Kingdon, 1879, Lectures and Essays,\nF. Pollock (ed.), London: Macmillan.", "Christensen, David, 2007, ‘Epistemology of Disagreement:\nThe Good News’, Philosophical\nReview , 116: 187–217.", "Christensen, David and Jennifer Lackey (eds.), 2013, The\nEpistemology of Disagreement: New Essays, Oxford: Oxford\nUniversity Press.", "Craig, William Lane, 1979, The Kalam Cosmological\nArgument, London: Macmillan", "Cupitt, Don, 1984, The Sea of Faith, Cambridge:\nCambridge University Press.", "Feldman, Richard, 2007, ‘Reasonable Religious\nDisagreements,’ in L. Antony (ed.), Philosophers without\nGod: Meditations on Atheism and the Secular Life , Oxford: Oxford\nUniversity Press.", "Feldman, Richard and Ted Warfield (eds.),\n2011, Disagreement, Oxford: Oxford University Press.", "Flew, Antony, 1972, “The Presumption of\nAtheism,” Canadian Journal of Philosophy, 2:\n29–46", "Forrest, Peter, 1996, God without the Supernatural: A Defense\nof Scientific Theism, Ithaca: Cornell University Press", "–––, 2019, Intellectual, Humanist and\nReligious Commitment: Acts of Assent, London: Bloomsbury.", "Geivett, R.D., and B. Sweetman, 1992, Contemporary\nPerspectives on Religious Epistemology, Oxford: Oxford\nUniversity Press.", "Gellman, Jerome, 1992, “A New Look at the Problem of\nEvil”, Faith and Philosophy, 9: 210–216.", "–––, 2017, “A Surviving Version of the\nCommon-sense Problem of Evil: A Reply to Tweedt”, Faith and\nPhilosophy, 34: 82–92.", "Katz, Steven, 1978, “Language Epistemology and\nMysticism,” in Mysticism and Philosophical Analysis,\nS. Katz (ed.), Oxford: Oxford University Press.", "Kelly, Thomas, 2005, ‘The Epistemic Significance of\nDisagreement,’ in J. Hawthorne and T. Gendler Szabo\n(eds.) Oxford Studies in Epistemology (Volume 1), Oxford:\nOxford University Press: 167–196.", "Kraft, James, 2007, ‘Religious disagreement, externalism,\nand the epistemology of disagreement: listening to our\ngrandmothers,’ Religious Studies, 43: 417–432. ", "Malcolm, Norman, 1992, “The Groundlessness of\nBelief”, in Geivett and Sweetman 1992, 92–103; reprinted\nfrom Reason and Religion, Stuart C. Brown (ed.), \nIthaca: Cornell university Press, 1977.", "Mavrodes, George I., 1988, Revelation in Religious\nBelief, Philadelphia: Temple University Press.", "Miller, Barry, 1991, From Existence to God : A Contemporary\nPhilosophical Argument, London: Routledge.", "Mitchell, Basil, 1973, The Justification of Religious\nBelief, London: Macmillan.", "–––, 1990, ‘Newman as a Philosopher,’\nin Newman after a Hundred Years, I. Ker and A. G. Hill\n(eds.), Oxford: Clarendon Press.", "Murphy, Nancey, 1990, Theology in an Age of Scientific\nReasoning, Ithaca: Cornell University Press", "Phillips, D. Z., 1992, ‘Faith, Skepticism, and Religious\nUnderstanding’, in Geivett and Sweetman 1992, 81–91; reprinted\nfrom D. Z. Phillips, Faith and Philosophical Enquiry, London:\nRoutledge & Kegan Paul, 1970.", "Plantinga, Alvin, 1983, ‘Reason and Belief in God,’\nin Plantinga and Wolterstorff 1983, 16–93.", "–––, 1993a, Warrant: The Current Debate,\nOxford: The Clarendon Press.", "–––, 1993b, Warrant and Proper Function,\nOxford: Oxford University Press.", "–––, 2000, Warranted Christian Belief,\nOxford: Oxford University Press", "Plantinga, Alvin and Nicholas Wolterstorff (eds.), 1983, Faith\nand Rationality, Notre Dame: University of Notre Dame Press.", "Scriven, Michael, 1966, Primary Philosophy, New York:\nMcGraw Hill.", "Shalkowski, Scott, 1989, ‘Atheological\nApologetics,’ American Philosophical Quarterly, 26:\n1–17.", "Schellenberg, John, 2009, The will to imagine: a\njustification of skeptical religion, Ithaca: Cornell University\nPress.", "Stiver, Dan, 2003, ‘Theological Methodology,’ in Kevin\nVanhoozer (ed.), Cambridge Companion to Postmodern Theology,\nCambridge: Cambridge University Press, 170–185.", "Swinburne, Richard, 1979, The Existence of God, Oxford:\nClarendon Press.", "–––, 1996, Is There a God?, Oxford: Oxford\nUniversity Press.", "–––, 2001, Review of Warranted Christian\nBelief by Alvin Plantinga, Religious Studies, 37:\n203–214.", "Wolterstorff, Nicholas, 1976, Reason within the Bounds of\nReligion, Grand Rapids: Eerdmans.", "Vanhoozer, Kevin, 2003, ‘Theology and the condition of\npostmodernity:a report on knowledge (of God),’ in Kevin\nVanhoozer (ed.), Cambridge Companion to Postmodern Theology,\nCambridge: Cambridge University Press, 3–25.", "Van Inwagen, Peter, 1994, ‘Quam Dilecta,’ in God\nand the Philosophers , T. V. Morris (ed.), Oxford: Oxford\nUniversity Press, 31–40. ", "Zagzebski Linda, 1993a, ‘Religious Knowledge and the Virtues of\nthe Mind’, in Zagzebski (1993b).", "Audi, Robert and William J. Wainwright (eds.), 1986,\nRationality, Religious Belief, and Moral Commitment, Ithaca:\nCornell University Press.", "Geivett, Douglas R. and Brendan Sweetman (eds.), 1992,\nContemporary Perspectives on Religious Epistemology, Oxford:\nOxford University Press.", "Howard-Snyder, Daniel (ed.), 1996, The Evidential Argument from\nEvil, Bloomington: Indiana University Press.", "Plantinga, Alvin, 1998, “Religion and Epistemology”\nin E. Craig (ed.), Routledge Encyclopedia of Philosophy (Volume 8), London:\nRoutledge.", "Zagzebski, Linda (ed.), 1993b, Rational Faith: Catholic\nResponses to Reformed Epistemology, Notre Dame: University of\nNotre Dame." ]

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[ "\n\nFrom the beginning of the Abrahamic faiths and of Greek philosophy,\nreligion and morality have been closely intertwined. This is true\nwhether we go back within Greek philosophy or within Christianity and\nJudaism and Islam. The present entry will not try to step beyond these\nconfines, since there are other entries on Eastern thought (see, for \nexample, the entries on\n Ethics in Indian and Tibetan Buddhism\nand\n Chinese Ethics).\n The entry\nproceeds chronologically, giving greatest length to the contemporary\nperiod. It cannot, within the present compass, aspire to be\ncomprehensive. But it will be able to describe the main\noptions as they have occurred historically. The purpose of proceeding\nhistorically is to substantiate the claim that morality and religion\nhave been inseparable until very recently, and that our moral\nvocabulary is still deeply infused with this history. Since there are\nhistorically so many different ways to see the relation, a purely\nschematic or typological account is not likely to succeed as well.\nThe entry will not try to enter deeply into the ethical theories of\nthe individual philosophers mentioned, since this encyclopedia already\ncontains individual entries about them; it will focus on what they say\nabout the relation between morality and religion. ", "\n\nThe term ‘morality’ as used in this entry will not be\ndistinguished from ‘ethics.’ Philosophers have drawn\nvarious contrasts between the two at various times (Kant for example,\nand Hegel, and more recently R.M. Hare and Bernard Williams). But\netymologically, the term ‘moral’ comes from the\nLatin mos, which means custom or habit, and it is a\ntranslation of the Greek ethos, which means roughly the same\nthing, and is the origin of the term ‘ethics’. In\ncontemporary non-technical use, the two terms are more or less\ninterchangeable, though ‘ethics’ has slightly more flavor\nof theory, and has been associated with the prescribed practice of\nvarious professions (e.g., medical ethics, etc.). In any case, this\nentry will assume that morality is a set of customs and habits that\nshape how we think about how we should live or about what is a good\nhuman life. The term ‘religion’ is much disputed. Again,\nwe can learn from the etymology. The origin of the word is probably\nthe Latin\nreligare, to bind back. Not all uses of the term require\nreference to a divinity or divinities. But this entry will use the\nterm so that there is such a reference, and a religion is a system of\nbelief and practice that accepting a ‘binding’ relation to\nsuch a being or beings. This does not, however, give us a single\nessence of religion, since the conceptions of divinity are so various,\nand human relations with divinity are conceived so variously that no\nsuch essence is apparent even within Western thought. The ancient\nGreeks, for example, had many intermediate categories between full\ngods or goddesses and human beings. There were spirits (in Greek\ndaimones) and spiritual beings like Socrates's mysterious\nvoice (daimonion) (Apology, 31d1–4, 40a2–c3). There\nwere heroes who were offspring of one divine and one human\nparent. There were humans who were deified, like the kings of\nSparta. This is just within the culture of ancient Greece. If we\nincluded Eastern religions in the scope of the discussion, the hope\nfor finding a single essence of religion would recede\nfurther. Probably it is best to understand ‘religion’ as a term for a\ngroup of belief/practice amalgams with a family resemblance to each\nother, but no set of necessary and sufficient conditions tying them\ntogether (see Wittgenstein, Philosophical Investigations,\n65–7)." ]

[ { "content_title": "1. Ancient Greek Philosophy", "sub_toc": [] }, { "content_title": "2. The Hebrew Bible and the New Testament", "sub_toc": [] }, { "content_title": "3. The Middle Ages", "sub_toc": [] }, { "content_title": "4. Modern Philosophy", "sub_toc": [] }, { "content_title": "5. Contemporary Philosophy", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nWe can start with the Greeks, and this means starting with Homer, a\nbody of texts transmitted first orally and then written down in the\nseventh century BCE. So what does the relation between morality and\nreligion look like in Homer? The first thing to say is that the gods\nand goddesses of the Homeric poems behave remarkably like the noble\nhumans described in the same poems, even though the humans are mortal\nand the gods and goddesses immortal. Both groups are motivated by the\ndesire for honor and glory, and are accordingly jealous when they\nreceive less than they think they should while others receive more,\nand work ceaselessly to rectify this. The two groups are not however\nsymmetrical, because the noble humans have the same kind of client\nrelation to the divinities as subordinate humans do to them. There is\na complex pattern that we might call ‘an honor-loop’ (see\nMikalson,\nHonor Thy Gods). The divinities have their functions (in\nGreek, the word is the same as ‘honors’), such as Poseidon's\noversight of the sea, and humans seek their favor with ‘honor’, which\nwe might here translate as ‘worship’. This includes, for example,\nsanctuaries devoted to them, dedications, hymns, dances, libations,\nrituals, prayers, festivals and sacrifices. In all of these the gods\ntake pleasure, and in return they give ‘honor’ to mortals in the form\nof help or assistance, especially in the areas of their own\nexpertise. There is a clear analogy with purely human\nclient-relations, which are validated in the Homeric narrative, since\nthe poems were probably originally sung at the courts of the princes\nwho claimed descent from the heroes whose exploits make up the\nstory. The gods and goddesses are not, however, completely at\nliberty. They too are accountable to fate or justice, as in the scene\nin the Iliad, where Zeus wants to save Hector, but he cannot\nbecause ‘his doom has long been sealed’ (Iliad, 22:\n179).", "\nIt is sometimes said that the Presocratic philosophers come\nout of Homer by rejecting religion in favor of science. There\nis a grain of truth in this, for when Thales (who flourished around\n580) is reported as saying ‘Water is the origin (or principle) of all\nthings,’ this is different from saying, for example, that Tethys is\nmother of all the rivers, because it deletes the character of\nnarrative or story (Aristotle's Metaphysics, 983b20–8). When\nAnaximenes (around 545) talks of air as the primary element differing\nin respect of thinness and thickness, or Heraclitus explains all\nchange as a pattern in the turnings of fire igniting in measures and\ngoing out in measures, they are not giving stories with plot-lines\ninvolving quasi-human intentions and frustrations (DK 13, A 5, DK 22,\nB 30). But it is wrong to say that they have left religion\nbehind. Heraclitus puts this enigmatically by saying that the one and\nonly wisdom does and does not consent to be called Zeus (DK 22, B\n14). He is affirming the divinity of this wisdom, but denying the\nanthropomorphic character of much Greek religion. ‘To god all things\nare beautiful and good and just but humans suppose some things to be\njust and others unjust’ (DK 22, B 102). He ties this divine wisdom to\nthe laws of a city, ‘for all human laws are nourished by the one\ndivine law’ (DK 22, B 114), though he does not have confidence that\n‘the many’ are capable of making law. The sophists, to whom Socrates\nresponded, rejected this tie between human law and divine law and this\nwas in part because of their expertise in rhetoric, by which they\ntaught their students how to manipulate the deliberations of popular\nassemblies, and so change the laws to their own advantage. The most\nfamous case is Protagoras (c. 490–21), who stated in the first\nsentence of his book Truth that ‘A human being is the measure\nof all things, of what is that it is, and of what is not that it is\nnot’ (Plato's Theaetetus, 152a). Protagoras is not correctly\nseen here as skeptical about morality or religion. It is true that he\nclaimed he was not in a position to know either the manner in\nwhich the gods are or are not (another translation is ‘that they are\nor are not’) or what they are like in appearance (DK 80, B 4). But as\nPlato (c. 430–347) presents him, he told the story that all humans\nhave been given by the gods the gifts of shame and justice, so as to\nmake possible the founding of cities; this is why each human\nis the measure. Even Thrasymachus, in the first book of Plato's\nRepublic, thinks of justice as the same thing amongst gods\nand humans (Republic, 388c). His view of what this justice\nis, namely the interest of the stronger, is disputed by Plato. But the\nclaim that justice operates at both the divine and human levels is\ncommon ground.", "\nSocrates (c. 470–399) in one of the early dialogues debates the\nnature of the holy with Euthyphro, who is a religious\nprofessional. Euthyphro is taking his own father to court for murder,\nand though ordinary Greek morality would condemn such an action as\nimpiety, Euthyphro defends it on the basis that the gods behave in the\nsame sort of way, according to the traditional stories. Socrates makes\nit clear that he does not believe these stories, because they\nattribute immorality to the gods. This does not mean, however, that he\ndoes not believe in the gods. He was observant in his religious\npractices, and he objects to the charge of not believing in the city's\ngods that was one of the bases of the prosecution at his own trial. He\npoints to the spirit who gives him commands about what not to do\n(Apology, 31d), and we learn later that he found it\nsignificant that this voice never told him to stop conducting his\ntrial in the way that in fact led to his death (Ibid.,\n40a-c). Socrates interpreted this as an invitation from the gods to\ndie, thus refuting the charge that, by conducting his trial in the way\nhe did, he was guilty of theft – i.e., depriving the gods of his\nlife that properly belonged to them (Phaedo, 62b). His life\nin particular was a service to god, he thought, because his testing of\nthe wisdom of others was carrying out Apollo's charge given by the\noracle at Delphi, implicit in the startling pronouncement that he was\nthe wisest man in Greece (Apology, 21a-d).", "\n\nSocrates's problem with the traditional stories about the gods gives\nrise to what is sometimes called ‘the Euthyphro\ndilemma’. If we try to define the holy as what is loved by all\nthe gods (and goddesses), we will be faced with the question ‘Is\nthe holy holy because it is loved by the gods, or do they love it\nbecause it is holy?’ (Euthyphro, 10a). Socrates makes\nit clear that his view is the second (though he does not argue for\nthis conclusion in addressing this question, and he is probably\nrelying on the earlier premise, at\nEuthyphro, 7c10f, that we love things because of the\nproperties they have). (See Hare, Plato's Euthyphro, on this\npassage.) But his view is not an objection to tying morality and\nreligion together. He hints at the end of the dialogue\n(Euthyphro, 13de) that the right way to link them is to see\nthat when we do good we are serving the gods well. Plato probably does\nnot intend for us to construe the dialogues together as a single\nphilosophical system, and we must not erase the differences between\nthem. But it is significant that in the Theaetetus (176b),\nSocrates says again that our goal is to be as like the god as\npossible, and since the god is in no way and in no manner unjust, but\nas just as it is possible to be, nothing is more like the god than the\none among us who becomes correspondingly as just as possible. In\nseveral dialogues this thought is connected with a belief in the\nimmortality of the soul; we become like the god by paying attention to\nthe immortal and best part of ourselves (e.g., Symposium,\n210A-212B). The doctrine of the immortality of the soul is also tied\nto the doctrine of the Forms, whereby things with characteristics that\nwe experience in this life (e.g., beauty) are copies or imitations of\nthe Forms (e.g., The Beautiful-Itself) that we see without the\ndistraction of the body when our souls are separated at death. The\nForm of the Good, according to the Republic, is above all the\nother Forms and gives them their intelligibility (as, by analogy, the\nsun gives visibility), and is (in a pregnant phrase) ‘on the other\nside of being’ (Republic, 509b). Finally, in the\nLaws (716b), perhaps Plato's last work, the character called\n‘the Athenian’ says that the god can serve for us in the highest\ndegree as a measure of all things, and much more than any human can,\nwhatever some people say; so people who are going to be friends with\nsuch a god must, as far as their powers allow, be like the gods\nthemselves.", "\nThis train of thought sees the god or gods as like a magnet, drawing\nus to be like them by the power of their goodness or excellence. In\nPlato's Ion (533d), the divine is compared to a magnet to\nwhich is attached a chain of rings, through which the attraction is\npassed. This conception is also pervasive in Aristotle (384–22),\nPlato's student for twenty years. In the Nicomachean Ethics,\nfor example, the words ‘god’ and ‘divine’\noccur roughly twice as often as the words ‘happiness’ and\n‘happy’. This is significant, given that Aristotle's\nethical theory is (like Plato's) ‘eudaimonist’ (meaning\nthat our morality aims at our happiness). Mention of the divine is not\nmerely conventional for Aristotle, but does important philosophical\nwork. In the Eudemian Ethics (1249b5–22) he tells us\nthat the goal of our lives is service and contemplation of the god. He\nthinks that we become like what we contemplate, and so we become most\nlike the god by contemplating the god. Incidentally, this is why the\ngod does not contemplate us; for this would mean becoming less than\nthe god, which is impossible. As in Plato, the well-being of the city\ntakes precedence over the individual, and this, too, is justified\ntheologically. It is nobler and more divine to achieve an end for a\ncity than for an individual (NE 1094b9–10). Aristotle\ndraws a distinction between what we honor and what we merely commend\n(NE, 1101b10–35). There are six states for a human\nlife, on a normative scale from best to worst: divine (which exceeds\nthe merely human on the one extreme), virtuous (without wrongful\ndesire), strong-willed (able to overcome wrongful desire), weak-willed\n(unable to do so), vicious and bestial (which exceeds the merely human\non the other extreme, and which Aristotle says is mostly found among\nbarbarians) (NE, 1145a15–22). The highest form of\nhappiness, which he calls blessedness, is something we honor as we\nhonor gods, whereas virtue we merely commend. It would be as wrong to\ncommend blessedness as it would be to commend gods (NE,\n1096a10–1097a15). Sometimes Aristotle uses the phrase ‘God\nor understanding’ (in Greek, nous) (e.g.,\nPolitics, 1287a27–32). The activity of the god, he says in\nthe Metaphysics, is nous thinking itself\n(1074b34). The best human activity is the most god-like, namely\nthinking about the god and about things that do not\nchange. Aristotle's virtue ethics, then, needs to be understood\nagainst the background of these theological premises. He is thinking\nof the divine, to use Plato's metaphor, as magnetic, drawing us, by\nits attractive power, to live the best kind of life possible for\nus. This gives him a defense against the charge sometimes made\nagainst virtue theories that they simply embed the prevailing social\nconsensus into an account of human nature. Aristotle defines ethical\nvirtue as lying in a mean between excess and defect, and the mean is\ndetermined by the person of practical wisdom (actually the male,\nsince Aristotle is sexist on this point). He then gives a\nconventional account of the virtues such a person displays (such as\ncourage, literally manliness, which requires the right amount of fear\nand confidence, between cowardice and rashness). But the virtuous\nperson in each case acts ‘for the sake of the noble (or beautiful)’,\nand Aristotle continually associates the noble with the divine (e.g.,\nNE, 1115b12).", "\n\nThere are tensions in Aristotle's account of virtue and happiness. It\nis not clear whether the Nicomachean Ethics has a consistent\nview of the relation between the activity of contemplation and the\nother activities of a virtuous life (see Hare, God and\nMorality, chapter 1, and Sarah Broadie, Ethics with\nAristotle, chapter 7). But the connection of the highest human\nstate with the divine is pervasive in the text. One result of this\nconnection is the eudaimonism mentioned earlier. If the god does not\ncare about what is not divine (for this would be to become\nlike what is not divine), the highest and most god-like human\nalso does not care about other human beings except to the degree they\ncontribute to his own best state. This degree is not negligible, since\nhumans are social animals, and their well-being depends on the\nwell-being of the families and cities of which they are\nmembers. Aristotle is not preaching self-sufficiency in any sense that\nimplies we could be happy on our own, isolated from other human\nbeings. But our concern for the well-being of other people is always,\nfor him, contingent on our special relation to them. Within the\nhighest kind of friendship ‘a friend is another self’, he says, and\nwithin such friendship we care about friends for their own sake, but\nif the friend becomes divine and we do not, then the friendship is\nover (NE, 1159a7). We therefore do not want our friends to\nbecome gods, even though that would be the best thing for\nthem. Finally, Aristotle ties our happiness to our end (in Greek,\ntelos); for humans, as for all living things, the best state\nis its own activity in accordance with the natural function that is\nunique to each species. For humans the best state is happiness, and\nthe best activity within this state is contemplation (NE,\n1178b17–23).", "\n\nThe Epicureans and Stoics who followed Aristotle differed with each\nother and with him in many ways, but they agreed in tying morality and\nreligion together. For the Epicureans, the gods do not care about us,\nthough they are entertained by looking at our tragicomic lives (rather\nas we look at soap operas on television). We can be released from a\ngood deal of anxiety, the Epicureans thought, by realizing that the\ngods are not going to punish us. Our goal should be to be as like the\ngods as we can, enjoying ourselves without interruption, but for us\nthis means limiting our desires to what we can obtain without\nfrustration. They did not mean that our happiness is self-interested\nin any narrow sense, because they held that we can include others in\nour happiness by means of our sympathetic pleasures. The Stoics\nlikewise tied the best kind of human life, for them the life of the\nsage, to being like the divine. The sage follows nature in all his\ndesires and actions, and is thus the closest to the divine. One of the\nvirtues he will have is ‘apathy’ (in\nGreek apatheia), which does not mean listlessness, but\ndetachment from wanting anything other than what nature, or the god,\nis already providing. Like the Epicureans, the Stoics had an argument\nagainst any narrow self-interest, but this time based on their\nconception of right reason which is directed by the law common to all,\n‘which pervades everything and is the same as Zeus, lord of the\nordering of all that exists’ (Diogenes Laertius, Lives of\nthe Philosophers, VII 88. For the views of the Epicureans and\nStoics about morality and religion, see Julia Annas, The Morality\nof Happiness, chapters 5 and 7.)" ], "section_title": "1. Ancient Greek Philosophy", "subsections": [] }, { "main_content": [ "\n\nThe second line of thought to be traced in this entry starts with the\nHebrew Bible and continues with the Greek scriptures called by\nChristians ‘The New Testament’. Morality and religion are\nconnected in the Hebrew Bible primarily by the category of God's\ncommand. Such commands come already in the first chapter\nof Genesis. God created by command, for example ‘Let\nthere be light’ (Gen. 1:3). Then, after the creation of\nanimals, God gives the command, ‘Be fruitful and\nmultiply’, and repeats the command to the humans he creates in\nthe divine image (Gen. 1:22). In the second chapter God tells\nAdam that he is free to eat from any tree in the garden, but he must\nnot eat from the tree of the knowledge of good and evil. When Eve and\nAdam disobey and eat of that fruit, they are expelled from the\ngarden. There is a family of concepts here that is different from what\nwe met in Greek philosophy. God is setting up a kind of covenant by\nwhich humans will be blessed if they obey the commands God gives\nthem. Human disobedience is not explained in the text, except that the\nserpent says to Eve that they will not die if they eat the fruit, but\nwill be like God, knowing good and evil, and Eve sees the fruit as\ngood for food and pleasing to the eye and desirable for gaining\nwisdom. After they eat, Adam and Eve know that they are naked, and are\nashamed, and hide from God. There is a turning away from God and from\nobedience to God that characterizes this as a ‘fall into\nsin’. As the story goes on, and Cain kills Abel, evil spreads to\nall the people of the earth, and Genesis describes the basic\nstate as a corruption of the heart (6:9). This idea of a\nbasic orientation away from or towards God and God's commands becomes\nin the Patristic period of early Christianity the idea of a\nwill. There is no such idea in Plato or Aristotle, and no Greek word\nthat the English word ‘will’ properly translates.", "\n\nIn the Pentateuch, the story continues with Abraham, and God's command\nto leave his ancestral land and go to the land God promised to give\nhim and his offspring (Gen. 17:7–8). Then there is the\ncommand to Abraham to kill his son, a deed prevented at the last\nminute by the provision of a ram instead\n(Gen. 22:11–14). Abraham's great grandchildren end up\nin Egypt, because of famine, and the people of Israel suffer for\ngenerations under Pharaoh's yoke. Under Moses the people are finally\nliberated, and during their wanderings in the desert, Moses receives\nfrom God the Ten Commandments, in two tables or tablets\n(Exod. 20:1–17, 31:18). The first table concerns our\nobligations to God directly, to worship God alone and keep God's name\nholy, and keep the Sabbath. The second table concerns our obligations\nto other human beings, and all of the commands are negative (do not\nkill, commit adultery, steal, lie, or covet) except for the first,\nwhich tells us to honor our fathers and mothers. God's commands taken\ntogether give us the law (on some lists there are 613\nmitzvot, Hebrew for ‘commands’.) One more term belongs here,\nnamely ‘kingdom’. The Greeks had the notion of a kingdom, under a\nhuman king (though the Athenians were in the classical period\nsuspicious of such an arrangement). But they did not have the idea of\na kingdom of God, though there is something approaching this in some\nof the Stoics. This idea is explicable in terms of law, and is\nintroduced as such in Exodus in connection with the covenant\non Mt. Sinai. The kingdom is the realm in which the laws obtain.", "\n\nThis raises a question about the extent of this realm. The Ten\nCommandments are given in the context of a covenant with the people of\nIsrael, though there are references to God's intention to bless the\nwhole world through this covenant. The surrounding laws in the\nPentateuch include prescriptions and proscriptions about ritual purity\nand sacrifice and the use of the land that seem to apply to this\nparticular people in this particular place. But the covenant that God\nmakes with Noah after the flood is applicable to the whole human race,\nand universal scope is explicit in the Wisdom books, which make a\ncontinual connection between how we should live and how we were\ncreated as human beings. For example, in Proverbs 8 Wisdom\nraises her voice to all humankind, and says that she detests\nwickedness, which she goes on to describe in considerable detail. She\nsays that she was the artisan at God's side when God created the world\nand its inhabitants. Judaism distinguishes seven ‘Noahide’\nlaws given to Noah before the covenant with Abraham.", "\n\nIn the writings which Christians call ‘The New Testament’\nthe theme of God's commands is recapitulated. Jesus sums up the\ncommandments under two, the command to love God with all one's heart\nand soul and mind (see Deuteronomy 6:5), and the command to\nlove the neighbor as the self (see Leviticus 19:18). The\nfirst of these probably sums up the first ‘table’ of the\nTen Commandments to Moses, and the second sums up the second. The New\nTestament is unlike the Hebrew Bible, however, in presenting a\nnarrative about a man who is the perfect exemplification of obedience\nand who has a life without sin. New Testament scholars disagree about\nthe extent to which Jesus actually claimed to be God, but the\ntraditional interpretation is that he did make this claim; in any case\nthe Christian doctrine is that we can see in his life the clearest\npossible revelation in human terms both of what God is like and at the\nsame time of what our lives ought to be like. In the ‘Sermon on\nthe Mount’ (Matthew 5–7) Jesus issues a number of\nradical injunctions. He takes the commandments inside the heart; for\nexample, we are required not merely not to murder, but not to be\nangry, and not merely not to commit adultery, but not to lust\n(see Ezekiel 11:19, ‘I will give them a heart of flesh,\nthat they may walk in my statutes.’) We are told, if someone\nstrikes us on the right cheek, to turn to him also the left. Jesus\ntells us to love our enemies and those who hate and persecute us, and\nin this way he makes it clear that the love commandment is not based\non reciprocity (Matt 5:43–48; Luke\n6:27–36). Finally, when he is asked ‘Who is my\nneighbor?’, he tells the story (Luke 10) of a Samaritan\n(traditional enemies of the Jews) who met a wounded Jew he did not\nknow by the side of the road, was moved with compassion, and went out\nof his way to meet his needs; Jesus commends the Samaritan for being\n‘neighbor’ to the wounded traveler.", "\n\nThe theme of self-sacrifice is clearest in the part of the narrative\nthat deals with Jesus' death. This event is understood in many\ndifferent ways in the New Testament, but one central theme is that\nJesus died on our behalf, an innocent man on behalf of the\nguilty. Jesus describes the paradigm of loving our neighbors as the\nwillingness to die for them. This theme is connected with our\nrelationship to God, which we violate by disobedience, but which is\nrestored by God's forgiveness through redemption. In Paul's letters\nespecially we are given a three-fold temporal location for the\nrelation of morality to God's work on our behalf. We are forgiven for\nour past failures on the basis of Jesus' sacrifice\n(Rom. 3:21–26). We are reconciled now with God\nthrough God's adoption of us in Christ\n(Rom. 8:14–19). And we are given the hope\nof future progress in holiness by the work of the Holy Spirit\n(Rom. 5:3–5). All of this theology requires more\ndetailed analysis, but this is not the place for it.", "\n\nThere is a contrast between the two traditions I have so far\ndescribed, namely the Greek and the Judeo-Christian. The idea of God\nthat is central in Greek philosophy is the idea of God attracting us,\nlike a kind of magnet, so that we desire to become more like God,\nthough there is a minority account by Socrates of receiving divine\ncommands. In the Jewish and Christian scriptures, the notion of God\ncommanding us is central. It is tempting to simplify this contrast by\nsaying that the Greeks favor the good, in their account of\nthe relation of morality and religion, and the Judeo-Christian account\nfavors the right or obligation. It is true that the notion of\nobligation makes most sense against the background of command. But the\npicture is over-simple because the Greeks had room in their account\nfor the constraint of desire; thus the temperate or brave person in\nAristotle's picture has desires for food or sex or safety that have to\nbe disciplined by the love of the noble. On the other side, the\nJudeo-Christian account adds God's love to the notion of God's\ncommand, so that the covenant in which the commands are embedded is a\ncovenant by which God blesses us, and we are given a route towards our\nhighest good which is union with God." ], "section_title": "2. The Hebrew Bible And The New Testament", "subsections": [] }, { "main_content": [ "\n\nThe rest of the history to be described in this entry is a\ncross-fertilization of these two traditions or lines of thought. In\nthe patristic period, or the period of the early Fathers, it was\npredominantly Plato and the Stoics amongst the Greek philosophers\nwhose influence was felt. The Eastern and Western parts of the\nChristian church split during the period, and the Eastern church\nremained more comfortable than the Western with language about humans\nbeing deified (in Greek theosis). In the Western church,\nAugustine (354–430) emphasized the gap between the world we are\nin as resident aliens and our citizenship in the heavenly Jerusalem,\nand even in our next life the distance between ourselves and God. He\ndescribes in the\nConfessions the route by which his heart or will, together\nwith his understanding, moved from paganism through Neo-Platonism to\nChristianity. The Neo-Platonists (such as Plotinus, 205-270) taught a\nworld-system of emanation, whereby the One (like Plato's Form of the\nGood) flowed into Intellect (the realm of the Forms) and from there\ninto the World-Soul and individual souls, where it encountered the\nrealm of bodies, from where it returned to itself (‘the flight of the\nalone to the alone’). Augustine accepted that the Platonists taught,\nlike the beginning of the prologue of John, that the Word (in\nGreek, logos) is with God and is God, since the Intellect is\nthe mediating principle between the One and the Many (John\n1:1–5). Augustine held that Plato had asserted that the supreme good,\npossession of which alone gives us blessedness, is God, ‘and therefore\n(Plato) thought that to be a philosopher is to be a lover of God.’\n(De Civ. Dei VIII.8). But the Platonists did not teach, like\nthe end of John's prologue, that the Word is made flesh in\nJesus Christ, and so they did not have access to the way to salvation\nrevealed in Christ or God's grace to us through Christ's\ndeath. Nonetheless, it is surprising how far Augustine can go in\nrapprochement. The Forms, he says, are in the mind of God and God uses\nthem in the creation of the world. Human beings were created for union\nwith God, but they have the freedom to turn towards themselves instead\nof God. If they turn to God, they can receive divine illumination\nthrough a personal intuition of the eternal standards (the Forms). If\nthey turn towards themselves, they will lose the sense of the order of\ncreation, which the order of their own loves should reflect. Augustine\ngives primacy to the virtue of loving what ought to be loved,\nespecially God. In his homily on I John 4:8, he says, ‘Love\nand do what you will.’ But this is not a denial of the moral law. He\nheld that humans who truly love God will also act in accord with the\nother precepts of divine and moral law; though love not merely\nfulfills the cardinal virtues (wisdom, justice, courage and\ntemperance) but transforms them by supernatural grace.", "\n\nThe influence of Augustine in the subsequent history of ethics\nresulted from the fact that it was his synthesis of Christianity (the\nofficial religion of the Roman Empire after 325) and Greek philosophy\nthat survived the destruction of the Western Roman Empire, especially\nin the monasteries where the texts were still read. Boethius\n(c. 480–524) gave us the definition of the concept of\n‘person’ that has been fundamental to ethical theory. To\nunderstand this, we need to go back into the history of the\ndevelopment of the doctrine of the Trinity. The church had to explain\nhow the Father, the Son and the Holy Spirit could be distinct and yet\nnot three different gods. They used, in Latin, the\nterm persona, which means ‘role’ but which was\nalso used by the grammarians to distinguish what we call ‘first\nperson, second person and third person’ pronouns and\nverb-forms. The same human being can be first person ‘I’,\nsecond person ‘you’, and third person ‘he’ or\n‘she’, depending on the relations in which he or she\nstands. The doctrine of the Trinity comes to be understood in terms of\nthree persons, one God, with the persons standing in different\nrelations to each other. But then this term ‘person’ is\nalso used to understand the relation of the second person's divinity\nto his humanity. The church came to talk about one person with two\nnatures, the person standing under the natures. This had the merit of\nnot making either the humanity or the divinity less essential to who\nJesus was. Plato and Aristotle did not have any term that we can\ntranslate ‘person’ in the modern sense, as\nsomeone (as opposed to something) that stands under\nall his or her attributes. Boethius, however, defines\n‘person’ as ‘individual substance of rational\nnature,’ a key step in the introduction of our present\nconcept.", "\n\nIn the West knowledge of most of Aristotle's texts was lost, but not\nin the East. They were translated into Syriac, and Arabic, and\neventually (in Muslim Spain) into Latin, and re-entered Christian\nEurope in the twelfth century accompanied by translations of the great\nArabic commentaries. In the initial prophetic period of Islam (CE\n610–32) the Qur'an was given to Mohammad, who explained it and\nreinforced it through his own teachings and practices. The notion of\nGod's (Allah's) commands is again central, and our obedience to these\ncommands is the basis of our eventual resurrection. Disputes about\npolitical authority in the period after Mohammad's death led to the\nsplit between Sunnis and Shiites. Within Sunni Muslim ethical theory\nin the Middle Ages two major alternative ways developed of thinking\nabout the relation between morality and religion. The first, the\nMu'tazilite, was given its most developed statement by ‘Abd\nal-Jabbar from Basra (d. 1025). ‘Abd al-Jabbar defines a\nwrongful act as one that deserves blame, and holds that the right and\nwrong character of acts is known immediately to human reason,\nindependently of revelation. These standards that we learn from reason\napply also to God, so that we can use them to judge what God is and is\nnot commanding us to do. He also teaches that humans have freedom, in\nthe sense of a power to perform both an act and its opposite, though\nnot at the same time. (For Mu'tazilite ethical theory, see Sophia\nVasalou,\nMoral Agents and Their Deserts: The Character of Mu'tazilite\nEthics and George Hourani, Islamic Rationalism: The Ethics of\n‘Abd al-Jabbar.) The second alternative was taught by al-Ashari\n(d. 935), who started off as a Mu'tazilite, but came to reject their\nview. He insists that God is subject to none and to no standard that\ncan fix bounds for Him. Nothing can be wrong for God, who sets the\nstandard of right and wrong. This means that ‘if God declared lying to\nbe right, it would be right, and if He commanded it, none could\ngainsay Him’ (The Theology of al-Ash'ari, 169-70). With\nrespect to our freedom, he holds that God gives us only the power to\ndo the act (not its opposite) and this power is simultaneous to the\nact and does not precede it. A figure contemporary with al-Ashari, but\nin some ways intermediate between Mu'tazilites and Asharites, is\nal-Maturidi of Samarqand (d. 944). He holds that because humans have\nthe tendency in their nature towards ugly or harmful actions as well\nas beautiful or beneficial ones, God has to reveal to us by command\nwhat to pursue and what to avoid. He also teaches that God gives us\ntwo different kinds of power, both the power simultaneous with the act\n(which is simply to do the act) and the power preceding the act (to\nchoose either the act or its opposite). (For the work of al-Maturidi,\nsee Ulrich Rudolph, Al-Maturidi and Sunni Theology in\nSamarkand.)", "\n\nMedieval reflection within Judaism about morality and religion has, as\nits most significant figure, Maimonides (d. 1204) who was born in\nMuslim Spain, and was familiar with much of the Muslim discussion of\nthese questions. The Guide of the Perplexed was written for\nyoung men who had read Aristotle and were worried about the tension\nbetween the views of the philosopher and their faith. Maimonides\nteaches that we do indeed have some access just as human beings to the\nrightness and wrongness of acts; but what renders conforming to these\nstandards obligatory is that God reveals them in special\nrevelation. The laws are obligatory whether we understand the reasons\nfor them or not, but sometimes we do see how it is beneficial to obey,\nand Maimonides is remarkably fertile in providing such reasons.", "\n\nThe reentry of Aristotle into Europe caused a rebirth (a\n‘renaissance’), but it also gave rise to a crisis, because\nit threatened to undermine the harmony established from the time of\nAugustine between the authority of reason, as represented by Greek\nphilosophy, and the authority of faith, as represented by the\ndoctrines of the Christian church. There were especially three\n‘errors of Aristotle’ that seemed threatening: his\nteaching that the world was eternal, his apparent denial of personal\nimmortality, and his denial of God's active agency in the world. (See,\nfor example, Bonaventure,\nIn Hexaemeron, VI.5 and In II Sent., lib. II, d.1,\npars 1, a.1, q.2.) These three issues (‘the world, the soul, and God’)\nbecome in one form or another the focus of philosophical thought for\nthe next six centuries.", "\n\nThomas Aquinas (c. 1224–74) undertook the project of synthesis\nbetween Aristotle and Christianity, though his version of Christianity\nwas already deeply influenced by Augustine, and so by\nNeo-Platonism. Aquinas, like Aristotle, emphasized the ends\n(vegetative, animal and typically human) given to humans in the\nnatural order. He described both the cardinal virtues and the\ntheological virtues of faith, hope and love, but he did not feel the\ntension that current virtue ethicists sometimes feel between virtue\nand the following of rules or principles. The rules governing how we\nought to live are known, some of them by revelation, some of them by\nordinary natural experience and rational reflection. But Aquinas\nthought these rules consistent in the determination of our good, since\nGod only requires us to do what is consistent with our own\ngood. Aquinas's theory is eudaimonist; ‘And so the will\nnaturally tends towards its own last end, for every man naturally\nwills beatitude. And from this natural willing are caused all other\nwillings, since whatever a man wills, he wills on account of the\nend.’ (Summa Theologiae I, q.60. a.2) God's will is not\nexercised by arbitrary fiat; but what is good for some human being can\nbe understood as fitting for this kind of agent, in relation to the\npurpose this agent intends to accomplish, in the real environment of\nthe action, including other persons individually and collectively. The\nprinciples of natural moral law are the universal judgments made by\nright reasoning about the kinds of actions that are morally\nappropriate and inappropriate for human agents. They are thus, at\nleast in principle and at a highly general level, deducible from human\nnature. Aquinas held that reason, in knowing these principles, is\nparticipating in the eternal law, which is in the mind of God\n(Summa Theologiae I, q.91. a.2). Aquinas was not initially\nsuccessful in persuading the church to embrace Aristotle. In 1277 the\nBishop of Paris condemned 219 propositions (not all Thomist),\nincluding the thesis that a person virtuous in Aristotle's terms\n‘is sufficiently disposed for eternal happiness.’ But in\nthe Counter-Reformation, the synthesis which Aquinas achieved became\nauthoritative in Roman Catholic education.", "\n\nAquinas was a Dominican friar. The other major order of friars, the\nFranciscan, had its own school of philosophy, starting with\nBonaventure (c. 1217–74), who held that while we can learn from\nboth Plato and Aristotle, and both are also in error, the greater\nerror is Aristotle's. One other major figure from this tradition is\nJohn Duns Scotus (literally John from Duns, the Scot,\nc. 1266–1308), and there are three significant differences\nbetween him and Aquinas on the relation between morality and\nreligion. First, Scotus is not a eudaimonist. He takes a double\naccount of motivation from Anselm (1033–1109), who made the\ndistinction between two affections of the will, the affection for\nadvantage (an inclination towards one's own happiness and perfection)\nand the affection for justice (an inclination towards what is good in\nitself independent of advantage) (Anselm, De Concordia 3.11,\n281:7–10; De Casu Diaboli 12, 255:8–11). Original\nsin is a ranking of advantage over justice, which needs to be reversed\nby God's assistance before we can be pleasing to God. Scotus says that\nwe should be willing to sacrifice our own happiness for God if God\nwere to require this. Second, he does not think that the moral law is\nself-evident or necessary. He takes the first table to be necessary,\nsince it derives (except for the ‘every seventh day’\nprovision of the command about the Sabbath) from the necessary\nprinciple that God is to be loved. But the second table is contingent,\nthough fitting our nature, and God could prescribe different commands\neven for human beings (Ord. I, dist. 44). One of his examples\nis the proscription on theft, which applies only to beings with\nproperty, and so not necessarily to human beings (since they are not\nnecessarily propertied). God also gives dispensation from the\ncommands, according to Scotus, for example the command to Abraham to\nkill Isaac (Ord III, suppl. Dist. 37). Third, Scotus denied\nthe application of teleology to non-intentional nature, and thus\ndeparted from the Aristotelian and Thomist view. This does not mean\nthat we have no natural end or\ntelos, but that this end is related to the intention of God\nin the same way a human artisan intends his or her products to have a\ncertain purpose (see Hare 2006, chapter 2)." ], "section_title": "3. The Middle Ages", "subsections": [] }, { "main_content": [ "\n\nEurope experienced a second Renaissance when scholars fled\nConstantinople after its capture by the Muslims in 1453, and brought\nwith them Greek manuscripts that were previously inaccessible. In\nFlorence Marsilio Ficino (1433–99) identified Plato as the\nprimary ancient teacher of wisdom, and (like Bonaventure) cited\nAugustine as his guide in elevating Plato in this way. His choice of\nPlato was determined by the harmony he believed to exist between\nPlato's thought and the Christian faith, and he set about making Latin\ntranslations of all the Platonic texts so that this wisdom could be\navailable for his contemporaries who did not know Greek. He was also\nthe first Latin translator of Plotinus, the Neo-Platonist.", "\n\nMany of the central figures in the Reformation were humanists in the\nRenaissance sense (where there is no implication of atheism). But\nthere is also a fundamental similarity in the way the relation between\nmorality and religion is conceived between Scotus and the two\nReformers Martin Luther (1483–1546) and John Calvin\n(1509–64), though neither of them make the distinctions about\nnatural law that Scotus (the ‘subtle doctor’) does. Luther\nsays ‘What God wills is not right because he ought or was bound\nso to will; on the contrary, what takes place must be right, because\nhe so wills.’ (Bondage of the Will, Works,\npp. 195–6). Calvin says ‘God's will is so much the highest\nrule of righteousness that whatever he wills, by the very fact that he\nwills it, must be considered righteous’ (Institutes\n3. 23. 2). The historical connection between Scotus and the Reformers\ncan be traced through William of Ockham (d. 1349) and Gabriel Biel\n(1410–95). The Counter-Reformation in Roman Catholic Europe, on\nthe other hand, took the work of Aquinas as authoritative for\neducation. Francisco de Suarez (1548–1617) claimed that the\nprecepts of natural law can be distinguished into those (like\n‘Do good and avoid evil’) which are known immediately and\nintuitively by all normal human beings, those (like ‘Do no\ninjury to anyone’) which require experience and thought to know\nthem, but which are then self-evident, and those (like ‘Lying is\nalways immoral’) which are not self-evident but can be derived\nfrom the more basic precepts (De Legibus, 2. 7. 5). However,\nSuarez accepted Scotus's double account of motivation.", "\n\nThe next two centuries in European philosophy can be described in\nterms of two lines of development, rationalism and empiricism, both of\nwhich led, in different ways, to the possibility of a greater\ndetachment of ethics from theology. The history of rationalism from\nRené Descartes (1596–1650) to Gottfried Wilhelm Leibniz\n(1646–1716) is a history of re-establishing human knowledge on\nthe foundation of rational principles that could not be doubted, after\nmodern science started to shake the traditional foundations supported\nby the authority of Greek philosophy and the church. Descartes was not\nprimarily an ethicist, but he located the source of moral law\n(surprisingly for a rationalist) in God's will. The most important\nrationalist in ethics was Benedict de Spinoza (1623–77). He was\na Jew, but was condemned by his contemporary faith community as\nunorthodox. Like Descartes, he attempted to duplicate the methods of\ngeometry in philosophy. Substance, according to Spinoza, exists in\nitself and is conceived through itself (Ethics, I, def. 3);\nit is consequently one, infinite, and identical with God\n(Ethics, I, prop. 15). There is no such thing as natural law,\nsince all events in nature (‘God or Nature’) are equally\nnatural. Everything in the universe is necessary, and there is no free\nwill, except in as far as Spinoza is in favor of calling someone free\nwho is led by reason ( Ethics, I, prop. 32). Each human mind\nis a limited aspect of the divine intellect. On this view (which has\nits antecedent in Stoicism) the human task is to move towards the\ngreatest possible rational control of human life. Leibniz was, like\nDescartes, not primarily an ethicist. He said, however, that\n‘the highest perfection of any thinking being lies in careful\nand constant pursuit of true happiness’ (New Essays on Human\nUnderstanding, XXI, 51). The rationalists were not denying the\ncentrality of God in human moral life, but their emphasis was on the\naccess we have through the light of reason rather than through sacred\ntext or ecclesiastical authority.", "\n\nAfter Leibniz there was in Germany a long-running battle between the\nrationalists and the pietists, who tried to remain true to the goals\nof the Lutheran Reformation. Examples of the two schools are Christian\nWolff (1679–1754) and Christian August Crusius (1715–75),\nand we can understand Immanuel Kant (1724–1804), like his\nteacher Martin Knutzen (1713–51), as trying to mediate between\nthe two. Wolff was a very successful popularizer of the thought of\nLeibniz, but fuller in his ethical system. He took from Leibniz the\nprinciple that we will always select what pleases us most, and the\nprinciple that pleasure is the apprehension of perfection, so that the\namount of pleasure we feel is proportional to the amount of perfection\nwe intuit (New Essays on Human Understanding, XXI, 41). He\nthought we are obligated to do what will make us and our condition, or\nthat of others, more perfect, and this is the law of nature that would\nbe binding on us even if (per impossible) God did not\nexist. He saw no problem about the connection between virtue and\nhappiness, since both of them result directly from our perfection, and\nno problem about the connection between virtue and duty, since a duty\nis simply an act in accordance with law, which prescribes the pursuit\nof perfection. His views were offensive to the pietists, because he\nclaimed that Confucius already knew (by reason) all that mattered\nabout morality, even though he did not know anything about\nChrist. Crusius by contrast accepted Scotus's double theory of\nmotivation, and held that there are actions that we ought to do\nregardless of any ends we have, even the end of our own perfection and\nhappiness. It is plausible to see here the origin of Kant's\ncategorical imperative. But he also added a third motivation, what he\ncalled ‘the drive of conscience’ which is ‘the\nnatural drive to recognize a divine moral law’ (“A Guide\nto Rational Living,”\nMoral Philosophy from Montaigne to Kant, §132, 574). His idea\nwas that we have within us this separate capacity to recognize divine\ncommand and to be drawn towards it out of a sense of dependence on the\nGod who prescribes the command to us, and will punish us if we disobey\n(though our motive should not be to avoid punishment) (Ibid.,\n§135). ", "\n\nThe history of empiricism in Britain from Hobbes to Hume is also the\nhistory of the attempt to re-establish human knowledge, but not from\nabove (from indubitable principles of reason) but from below (from\nexperience and especially the experience of the senses). Thomas Hobbes\n(1588–1649) said that all reality is bodily (including God), and\nall events are motions in space. Willing, then, is a motion, and is\nmerely the last act of desire or aversion in any process of\ndeliberation. His view is that it is natural, and so reasonable, for\neach of us to aim solely at our own preservation or pleasure. In the\nstate of nature, humans are selfish, and their lives are\n‘solitary, poor, nasty, brutish, and short’, a war of all\nagainst all (Leviathan, Ch. 13). The first precept of the law\nof nature is then for each of us, pursuing our own interest, ‘to\nendeavor peace, as far as he has hope of attaining it; and when he\ncannot obtain it, that he may seek, and use, all helps, and advantages\nof war.’ (Ibid., Ch. 14). The second precept is that\neach of us should be willing to lay down our natural rights to\neverything to the extent that others are also willing, and Hobbes\nconcludes with the need to subordinate ourselves to a sovereign who\nalone will be able to secure peace. The second and longest portion\nof Leviathan is devoted to religion, where Hobbes argues for\nthe authority of Scripture (‘God's word’), which he thinks\nis needed for the authority of law. He argues for the authority in\nthe interpretation of Scripture to be given to that same\nearthly sovereign, and not to competing ecclesiastical authorities\n(whose competition had been seen to exacerbate the miseries of war\nboth in Britain and on the continent) (Ibid., Ch. 33).", "\n\nJohn Locke (1632–1704) followed Hobbes in deriving morality from\nour need to live together in peace given our natural discord, but he\ndenied that we are mechanically moved by our desires. He agreed with\nHobbes in saying that moral laws are God's imposition, but disagreed\nby making God's power and benevolence both necessary\nconditions for God's authority in this respect (Treatises,\nIV. XIII. 3). He also held that our reason can work out counsels or\nadvice about moral matters; but only God's imposition makes\nlaw (and hence obligation), and we only know about God's\nimposition from revelation (The Reasonableness of\nChristianity, 62–5). He therefore devoted considerable attention\nto justifying our belief in the reliability of revelation.", "\n\nThe deists (e.g., William Wollaston, 1659–1724) believed that\nhumans can reason from their experience of nature to the existence and\nsome of the attributes of God, that special revelation is accordingly\nunnecessary, that God does not intervene in human affairs (after\ncreation) and that the good life for humans finds adequate guidance in\nphilosophical ethics. Frances Hutcheson (1694–1746) was not a\ndeist, but does give a reading of the sort of guidance involved\nhere. He distinguished between objects that are naturally good, which\nexcite personal or selfish pleasure, and those that are morally good,\nwhich are advantageous to all persons affected. He took\nhimself to be giving a reading of moral goodness as agape,\nthe Greek word for the love of our neighbor that Jesus\nprescribes. This love is benevolence, Hutcheson said, and it is\nformulated in the principle ‘That Action is best, which procures\nthe greatest Happiness for the greatest Numbers’\n(Inquiry II, III, VIII). Because these definitions of natural\nand moral good produce a possible gap between the two, we need some\nway to believe that morality and happiness are coincident. Hutcheson\nthought that God has given us a moral sense for this purpose\n(Essay on the Nature and Conduct of the Passions, II). This\nmoral sense responds to examples of benevolence with approbation and a\nunique kind of pleasure, and benevolence is the only thing it responds\nto, as it were the only signal it picks up. It is, like Scotus's\naffection for justice, not confined to our perception of\nadvantage. The result of our having moral sense is that when intending\nthe good of others, we ‘undesignedly’ end up promoting our\nown greatest good as well because we end up gratifying ourselves along\nwith others. God shows benevolence by first making us\nbenevolent and then giving us this moral sense that gets joy from the\napprobation of our benevolence. To contemporary British opponents of\nmoral sense theory, this seemed too rosy or benign a picture; our joy\nin approving benevolence is not enough to make morality and happiness\ncoincident. We need also obligation and divine sanction.", "\n\nJoseph Butler (1692–1752, Bishop of Bristol and then of Durham)\nheld that God's goodness consists in benevolence, in wanting us to be\nhappy, and that we should want the same for each other. He made the\nimportant point that something can be good for an agent because it is\nwhat he wants without this meaning that the content of what\nhe wants has anything to do with himself (Fifteen Sermons,\n126–27).", "\n\nDavid Hume (1711–76) is the first figure in this narrative who\ncan properly be attached to the Enlightenment, though this term means\nvery different things in Scotland, in France and in Germany. Hume held\nthat reason cannot command or move the human will. Since morals\nclearly do have an influence on actions and affections, ‘it\nfollows that they cannot be derived from reason; and that because\nreason alone, as we have already proved, can never have any such\ninfluence’ (Treatise III.1). For Hume an action, or\nsentiment, or character, is virtuous or vicious ‘because its\nview causes a pleasure or uneasiness of a particular kind’\n(Ibid., III.2). The denial of motive power to reason is part\nof his general skepticism. He accepted from Locke the principle that\nour knowledge is restricted to sense impressions from experience and\nlogically necessary relations of ideas in advance of experience (in\nLatin, a priori). From this principle he derived more radical\nconclusions than Locke had done. For example, we cannot know about\ncausation or the soul. The only thing we can know about morals is that\nwe get pleasure from the thought of some things and pain from the\nthought of others. Since the idea of morality implies something\nuniversal, there must be some sentiment of sympathy or (he later says)\nhumanity, which is common to all human beings, and which\n‘recommends the same object to general approbation’\n(Enquiry Concerning the Principles of Morals,\nIX. I. 221). Hume thought we could get conventional moral conclusions\nfrom these moral sentiments, which nature has fortunately given us. He\nwas also skeptical about any attempt to derive conclusions containing\n‘ought’ from premises containing only ‘is’,\nthough scholars debate about the scope of the premises he is talking\nabout here. Probably he included premises about God's will or nature\nor action. This does not mean he was arguing against the existence of\nGod. He thought (like Calvin) that we cannot rely on rational proofs\nof God's existence, even though humans have what Calvin called a sense\nof the divine and Human called ‘true religion’. But Hume\nnever identified himself as an atheist, though he had opportunity in\nthe atheist circles he frequented in Paris, and his Dialogues on\nNatural Religion end with the sentiment that ‘to be a\nphilosophical skeptic is, in a man of letters, the first and most\nessential step towards being a sound, believing Christian’\n(Dialogues, part XII, penultimate paragraph). Some scholars\ntake this remark (like similar statements in Hobbes) as purely ironic,\nbut this goes beyond the evidence.", "\n\nThe Enlightenment in France had a more anti-clerical flavor (in part\nbecause of the history of Jansenism, unique to France), and for the\nfirst time in this narrative we meet genuine atheists, such as Baron\nd'Holbach (1723–89) who held not only that morality did not need\nreligion, but that religion, and especially Christianity, was its\nmajor impediment. François-Marie Voltaire (1694-1778) was,\nespecially towards the end of his life, opposed to Christianity, but\nnot to religion in general (Letters of Voltaire and Frederick the\nGreat, letter 156). He accepted from the English deists the idea\nthat what is true in Christian teachings is the core of human values\nthat are universally true in all religions, and (like the German\nrationalists) he admired Confucius. Jean-Jacques Rousseau (1712-78)\nsaid, famously, that mankind is born free, but everywhere he is in\nchains (The Social Contract, Ch. 1). This supposes a\ndisjunction between nature and contemporary society, and Rousseau held\nthat the life of primitive human beings was happy inasmuch as they\nknew how to live in accordance with their own innate needs; now we\nneed some kind of social contract to protect us from the corrupting\neffects of society upon the proper love of self. Nature is understood\nas the whole realm of being created by God, who guarantees its\ngoodness, unity, and order. Rousseau held that we do not need any\nintermediary between us and God, and we can attain salvation by\nreturning to nature in this high sense and by developing all our\nfaculties harmoniously. Our ultimate happiness is to feel ourselves at\none with the system that God created.", "\n\nImmanuel Kant (1724–1804) is the most important figure of the\nEnlightenment in Germany, but his project is different in many ways\nfrom those of his French contemporaries. He was brought up in a\npietist Lutheran family, and his system retains many features from,\nfor example, Crusius. But he was also indebted through Wolff to\nLeibniz. Moreover, he was ‘awoken from his dogmatic\nslumbers’ by reading Hume, though Kant is referring here to\nHume's attack on causation, not his ethical theory\n(Prolegomena, 4:260). Kant's mature project was to limit\nhuman knowledge ‘in order to make room for faith’\n(KrV, B xxx). He accepted from Hume that our knowledge is\nconfined within the limits of possible sense experience, but he did\nnot accept skeptical conclusions about causation or the soul. Reason\nis not confined, in his view, to the same limits as knowledge, and we\nare rationally required to hold beliefs about things as they are in\nthemselves, not merely things as they appear to us. In particular, we\nare required to believe in God, freedom and immortality. These are\nthree ‘postulates of practical reason’, required to make\nrational sense of the fact of moral obligation, the fact that we are\nunder the moral law (the ‘categorical imperative’) that\nrequires us to will the maxim of an action (the prescription of the\naction together with the reason for it) as a universal law (removing\nany self-preference) and to treat humanity in any person as always at\nthe same time an end and never merely as a means (Groundwork,\n4.421, 429). Kant thought that humans have to be able to believe that\nmorality in this demanding form is consistent in the long run with\nhappiness (both their own and that of the people they affect by their\nactions), if they are going to be able to persevere in the moral life\nwithout rational instability. He did not accept the three\ntraditional theoretical arguments for the existence of God\n(though he was sympathetic to a modest version of the teleological\nargument). But the practical argument was decisive for him,\nthough he held that it was possible to be morally good without being a\ntheist, despite such a position being rationally unstable.", "\n\nIn Religion within the Boundaries of Mere Reason he undertook\nthe project of using moral language in order to translate the four\nmain themes of Biblical revelation (accessible only to particular\npeople at particular times) into the revelation to Reason (accessible\nto all people at all times). This does not mean that he intended to\nreduce Biblical faith to morality, though some scholars have taken him\nthis way. The translated versions of Creation, Fall, Redemption and\nSecond Coming are as follows (see Hare 1996): Humans have an initial\npredisposition to the good, which is essential to them, but is\noverlaid with a propensity to evil, which is not essential to\nthem. Since they are born under ‘the Evil Maxim’ that\nsubordinates duty to happiness, they are unable by their own devices\nto reverse this ranking, and require ‘an effect of grace’\n(Religion, 6.53). Providence ushers in progress (though not\ncontinuous) towards an ‘ethical commonwealth’ in which we\ntogether make the moral law our own law, by appropriating it as\nauthoritative for our own lives (this is what Kant means by\n‘autonomy’) (Religion, 6.98–99;\nGroundwork, 4.433–34). ", "\n\nA whole succession of Kant's followers tried to ‘go\nbeyond’ Kant by showing that there was finally no need to make\nthe separation between our knowledge and the thing-in-itself beyond\nour knowledge. One key step in departing from the surviving influence\nin Kant of Lutheran pietism was taken by Johann Gottlieb Fichte\n(1762–1814), who identified (as Kant did not) the will of the\nindividual with the infinite Ego which is ordering the universe\nmorally. Georg Wilhelm Friedrich Hegel (1770–1831) accomplished\na somewhat similar end by proposing that we should make the truth of\nideas relative to their original historical context against the\nbackground of a history that is progressing towards a final stage of\n‘absolute knowledge’, in which Spirit (in\nGerman Geist, which means also ‘mind’)\nunderstands that reality is its own creation and there is no\n‘beyond’ for it to know. Hegel is giving a philosophical\naccount of the Biblical notion of all things returning to God,\n‘so that God may be all in all.’ (I Cor. 15:28)\nIn this world-history, Hegel located the Reformation as ‘the\nall-enlightening sun’ of the bright day that is our modern time\n(The Philosophy of History, 412). He thought that Geist moves\nimmanently through human history, and that the various stages of\nknowledge are also stages of freedom, each stage producing first its\nown internal contradiction, and then a radical transition into a new\nstage. The stage of absolute freedom will be one in which all members\nfreely by reason endorse the organic community and the concrete\ninstitutions in which they actually live (Phenomenology, BB,\nVI, B, III).", "\n\nOne of Hegel's opponents was Arthur Schopenhauer (1799–1860),\nthe philosopher of pessimism. Schopenhauer thought that Hegel had\nstrayed from the Kantian truth that there is a thing-in-itself beyond\nappearance, and that the Will is such a thing. He differed from Kant,\nhowever, in seeing the Will as the source of all our endless\nsuffering, a blind striving power without ultimate purpose or design\n(The World as Will and Representation, §56 p. 310 and\n§57 p. 311). It is, moreover, one universal Will that underlies\nthe wills of all separate individuals. The intellect and its ideas are\nsimply the Will's servant. On this view, there is no happiness for us,\nand our only consolation is a (quasi-Buddhist) release from the Will\nto the limited extent we can attain it, especially through aesthetic\nenjoyment.", "\n\nHegel's followers split into what are sometimes called ‘Right\nHegelians’ and ‘Left Hegelians’ (or ‘Young\nHegelians’). Right Hegelians promoted the generally positive\nview of the Prussian state that Hegel expressed in the Philosophy\nof Right. Left Hegelians rejected it, and with it the Protestant\nChristianity which they saw as its vehicle. In this way Hegel's\npeculiar way of promoting Christianity ended up causing its vehement\nrejection by thinkers who shared many of his social ideals. David\nFriedrich Strauss (1808–74) wrote The Life of Jesus\nCritically Examined, launching the historical-critical method of\nBiblical scholarship with the suggestion that much of the Biblical\naccount is myth or ‘unconscious invention’ that needs to\nbe separated out from the historical account. Ludwig Andreas Feuerbach\n(1804–72) wrote The Essence of Christianity in which he\npictured all religion as the means by which ‘man projects his\nbeing into objectivity, and then again makes himself an object to this\nprojected image of himself’ (The Essence of\nChristianity, 30). Feuerbach thought religion resulted from\nhumanity's alienation from itself, and philosophy needed to destroy\nthe religious illusion so that we could learn to love humankind and\nnot divert this love onto an imaginary object. Karl Marx\n(1818–83) followed Feuerbach in this diagnosis of religion, but\nhe was interested primarily in social and political relations rather\nthan psychology. He became suspicious of theory (for example Hegel's),\non the grounds that theory is itself a symptom of the power structures\nin the societies that produce it. “Theory,” Marx writes,\n“is realized in a people only in so far as it is a realization\nof the people's needs” (“Critique of Hegel's Philosophy of\nRight,” Early Writings, 252). And\n‘ideologies’ and ‘religion,’ he believes,\narise from “conditions that require [these] illusions”\n(Ibid., 244). Marx returned to Hegel's thoughts about work revealing\nto the worker his value through what the worker produces, but Marx\nargues that under capitalism the worker was alienated from this\nproduct because other people owned both the product and the means of\nproducing it. Marx urged that the only way to prevent this was to\ndestroy the institution of private property (“Economic and\nPhilosophic Manuscripts,” Early Writings, 348). Thus he\nbelieved, like Hegel, in progress through history towards freedom, but\nhe thought it would take Communist revolution to bring this about.", "\n\nA very different response to Hegel (and Kant) is found in the work of\nSøren Kierkegaard (1813–55), a religious thinker who\nstarted, like Hegel and Kant, from Lutheranism. Kierkegaard mocked\nHegel constantly for presuming to understand the whole system in which\nhuman history is embedded, while still being located in a particular\nsmall part of it. On the other hand, he used Hegelian categories of\nthought himself, especially in his idea of the aesthetic life, the\nethical life and the religious life as stages through which human\nbeings develop by means of first internal contradiction and then\nradical transition. Kierkegaard's relation with Kant was problematic\nas well. In Either/Or he caricatured Kant's ethical thought\n(as well as Hegel's) in the person of Judge William, who is stuck\nwithin the ethical life and has not been able to reach the life of\nfaith. On the other hand, his own description of the religious life is\nfull of echoes of Kant's Religion within the Boundaries of Mere\nReason. Kierkegaard wrote most of his work pseudonymously, taking\non the names of characters who lived the lives he describes. In the\naesthetic life the goal is to keep at bay the boredom that is\nconstantly threatening, and this requires enough distance from one's\nprojects that one is not stuck with them but can flit from engagement\nto engagement without pain (Either/Or, II. 77). This life\ndeconstructs, because it requires (in order to sustain interest) the\nvery commitment that it also rejects. The transition is accomplished\nby making a choice for one's life as a whole from a position that is\nnot attached to any particular project, a radical choice that requires\nadmitting the aesthetic life has been a failure. In this choice one\ndiscovers freedom, and thus the ethical life (Either/Or,\nII. 188). But this life too deconstructs, because it sets up the goal\nof living by a demand, the moral law, that is higher than we can live\nby our own human devices. Kierkegaard thought we have to realize that\nGod is (contrary to Fichte) ‘another’ (Sickness unto\nDeath xi 128), with whom we have to relate, and whose assistance\nis necessary even for the kind of repentance that is the transition\ninto the religious life. He also suggested that within the religious\nlife, there is a ‘repetition’ of the aesthetic life and\nthe ethical life, though in a transformed version.", "\n\nFriedrich Nietzsche (1844–1900) was the son of a Lutheran pastor\nin Prussia. He was trained as a classical philologist, and his first\nbook, The Birth of Tragedy, was an account of the origin and\ndeath of ancient Greek tragedy. Nietzsche was deeply influenced by\nSchopenhauer, especially his view of the will (which Nietzsche called\n‘the Will to Power’), and was first attracted and then\nrepelled by Wagner, who was also one of Schopenhauer's disciples. The\nbreaking point seems to have been\nWagner's Parsifal. Nietzsche by this time was opposed to\northodox Christianity and was promoting Ancient Greece instead, and he\nthought that Wagner was betraying his integrity by using an\n‘anti-Greek’ Christian story for the opera. Nietzsche saw\nclearly the intimate link between Christianity and the ethical\ntheories of his predecessors in Europe, especially Kant. In On the\nGenealogy of Morals, he says, ‘The advent of the Christian\nGod, as the maximum god attained so far, was therefore accompanied by\nthe maximum feeling of guilty indebtedness on earth. Presuming we have\ngradually entered upon the reverse course, there is no small\nprobability that with the irresistible decline of faith in the\nChristian God, there is now also a considerable decline in mankind's\nfeeling of guilt’ (On the Genealogy of Morals,\n90–1). This is the ‘death of God’ which Nietzsche\nannounced, and which he predicted would also be the end of Kantian\nethics (The Gay Science, §108, 125, 343). It is harder\nto know what Nietzsche was for, than what he was against. This is\npartly an inheritance from Schopenhauer, who thought any system of\nconstructive ethical thought a delusion. But Nietzsche clearly admired\nthe Ancient Greeks, and thought we would be better off with a\n‘master’ morality like theirs, rather than a\n‘slave’ morality like Christianity. ‘Mastery over\nhimself also necessarily gives him mastery over circumstances, over\nnature, and over all more short-willed and unreliable creatures’\n(Genealogy, 59-60). By this last clause, he meant mastery\nover other people, and the model of this mastery is the\n‘overman’ who is free of the resentment by the weak of the\nstrong that Nietzsche thought lay at the basis of Christian\nethics.", "\n\nTo return to Britain, Hume had a number of successors who accepted the\nview (which Hume took from Hutcheson) that our fundamental obligation\nis to work for the greatest happiness of the greatest number. Four are\nespecially significant. William Paley (1743–1805) thought he\ncould demonstrate that morality derived from the will of God and\nrequired promoting the happiness of all, that happiness was the sum of\npleasures, and that we need to believe that God is the final granter\nof happiness if we are to sustain motivation to do what we know we\nought to do (The Principles of Moral and Political\nPhilosophy, II. 4). Jeremy Bentham (1748–1832) rejected\nthis theological context. His grounds were radically empiricist, that\nthe only ‘real’ entities are publicly observable, and so\ndo not include God (or, for that matter, right or time or relations or\nqualities). He thought he could provide a scientific calculus of\npleasures, where the unit that stays constant is the minimum state of\nsensibility that can be distinguished from indifference. He thought we\ncould then separate different ‘dimensions’ in which these\nunits vary, such as intensity, duration, certainty, propinquity (how\nsoon the pleasures will come), fecundity (how many other pleasures\nthis pleasure will produce) and purity. Discarding the theological\ncontext made moral motivation problematic, for why should we expect\n(without God) more units of pleasure for ourselves by contributing to\nthe greater pleasure of others? Bentham's solution was to hope that\nlaw and social custom could provide individuals with adequate motives\nthrough the threat of social sanctions, and that what he called\n‘deontology’ (which is personal or private morality) could\nmobilize hidden or long-range interests that were already present but\nobscure.", "\n\nJohn Stuart Mill (1806–73) was raised on strict utilitarian\nprinciples by his father, a follower of Bentham. Unlike Bentham,\nhowever, Mill accepted that there are qualitative differences in\npleasures simply as pleasures, and he thought that the higher\npleasures were those of the intellect, the feelings and imagination,\nand the moral sentiments. He observed that those who have experienced\nboth these and the lower pleasures, tend to prefer the former. At the\nage of twenty he had a collapse and a prolonged period of\n‘melancholy’. He realized that his education had neglected\nthe culture or cultivation of\nfeelings, of which hope is a primary instance\n(Autobiography, 1. 84). In his Three Essays on\nReligion (published posthumously in 1874) he returned to the idea\nof hope, saying that ‘the indulgence of hope with regard to the\ngovernment of the universe and the destiny of man after death, while\nwe recognize as a clear truth that we have no ground for more than a\nhope, is legitimate and philosophically defensible’; without\nsuch hope, we are kept down by ‘the disastrous feeling of\n“not worth while”’ (Three Essays\n249–50). Mill did not believe, however, that God was omnipotent,\ngiven all the evil in the world, and he insisted, like Kant, that we\nhave to be God's co-workers, not merely passive recipients of God's\nassistance.", "\n\nHenry Sidgwick (1838–1900) in Methods of Ethics\ndistinguished three methods: Intuitionism (which is, roughly, the\ncommon sense morality that some things, like deliberate ingratitude to\na benefactor, are self-evidently wrong in themselves independently of\ntheir consequences), Egoistic Hedonism (the view that self-evidently\nan individual ought to aim at a maximum balance of happiness for\nherself, where this is understood as the greatest balance of pleasure\nover pain), and Utilitarianism or Universalistic Hedonism, (the view\nthat self-evidently she ought to aim at the maximum balance of\nhappiness for all sentient beings present and future, whatever the\ncost to herself). Of these three, he rejected the first, on the\ngrounds that no concrete ethical principles are self-evident, and that\nwhen they conflict (as they do) we have to take consequences into\naccount in order to decide how to act. But Sidgwick found the relation\nbetween the other two methods much more problematic. Each principle\nseparately seemed to him self-evident, but when taken together they\nseems to be mutually inconsistent. He considered two solutions,\npsychological and metaphysical. The psychological solution was to\nbring in the pleasures and pains of sympathy, so that if we do good to\nall we end up (because of these pleasures) making ourselves\nhappiest. Sidgwick rejected this on the basis that sympathy is\ninevitably limited in its range, and we feel it most towards those\nclosest to us, so that even if we include sympathetic pleasures and\npains under Egoism, it will tend to increase the divergence between\nEgoistic and Utilitarian conduct, rather than bring them closer\ntogether. The metaphysical solution was to bring in a god who desires\nthe greatest total good of all living things, and who will reward and\npunish in accordance with this desire. Sidgwick recognized this as a\nreturn to the utilitarianism of Paley (Compare Methods of\nEthics, II. 1, 2 and IV. 4, 5). He thought this solution was both\nnecessary and sufficient to remove the contradiction in ethics. But\nthis was only a reason to accept it, if in general it is reasonable to\naccept certain principles (such as the Uniformity of Nature) which are\nnot self-evident and which cannot be proved, but which bring order and\ncoherence into a central part of our thought. Sidgwick did not commit\nhimself to an answer to this, one way or the other." ], "section_title": "4. Modern Philosophy", "subsections": [] }, { "main_content": [ "\n\nIn the twentieth century professional philosophy in the West divided\nup into two streams, sometimes called ‘Analytic’ and\n‘Continental’, and there were periods during which the two\nschools lost contact with each other. Towards the end of the century,\nhowever, there were more philosophers who could speak the languages of\nboth traditions. The beginning of the analytic school is sometimes\nlocated with the rejection of a neo-Hegelian idealism by G.E. Moore\n(1873-1958). One way to characterize the two schools is that the\nContinental school continued to read and be influenced by Hegel, and\nthe Analytic school (with some exceptions) did not. Another way to\nmake the distinction is geographical; the analytic school is located\nprimarily in Britain, Scandinavia and N. America, and the continental\nschool in the rest of Europe, in Latin America and in certain schools\nin N. America.", "\n\nWe will start with some figures from the Continental school, and then\nmove to the analytic (which is this writer's own). Martin Heidegger\n(1889–1976) was initially trained as a theologian, and wrote his\ndissertation on what he took to be a work of Duns Scotus. He took an\nappointment under Edmund Husserl (1855–1938) at Freiburg, and\nwas then appointed to succeed him in his chair. Husserl's program of\n‘phenomenology’ was to recover a sense of certainty about\nthe world by studying in exhaustive detail the cognitive structure of\nappearance. Heidegger departed from Husserl in approaching Being\nthrough a focus on ‘Human Being’ (in\nGerman Dasein) concerned above all for its fate in an alien\nworld, or as ‘anxiety’ (Angst) towards death\n(see Being and Time I. 6). In this sense he is the first\nexistentialist, though he did not use the term. Heidegger emphasized\nthat we are ‘thrown’ into a world that is not\n‘home’, and we have a radical choice about what\npossibilities for ourselves we will make actual. Heidegger drew here\nfrom Kierkegaard, and he is also similar in describing the danger of\nfalling back into mere conventionality, what Heidegger calls\n‘the They’ (das Man). On the other hand he is\nunlike Kierkegaard in thinking of traditional Christianity as just one\nmore convention making authentic existence more difficult. In\nHeidegger, as in Nietzsche and Schopenhauer, it is hard to find a\npositive or constructive ethics. Heidegger's position is somewhat\ncompromised, moreover, by his initial embrace of the Nazi party. In\nhis later work he moved increasingly towards a kind of quasi-religious\nmysticism. His Romantic hatred of the modern world and his distrust of\nsystem-building led to the espousal of either silence or poetry as the\nbest way to be open to the ‘something’ (sometimes he says\n‘the earth’) which reveals itself only as\n‘self-secluding’ or hiding itself away from our various\nconceptualizations. He held the hope that through poetry, and in\nparticular the poetry of Hölderlin, we might be able to still\nsense something of the unknown god who appears ‘as the one who\nremains unknown,’ who is quite different from the object of\ntheology or piety, but who can bring us back to the Being we have long\nlost sight of (Poetry, Language, Thought, 222).", "\n\nJean-Paul Sartre (1905-80) did use the label\n‘existentialist’, and said that ‘Existentialism is\nnothing else than an attempt to draw all the consequences of a\ncoherent atheist position’ (Existentialism and Human\nEmotions, 51). He denied (like Scotus) that the moral law could\nbe deduced from human nature, but this was because (unlike Scotus) he\nthought that we give ourselves our own essences by the choices we\nmake. His slogan was, ‘Existence precedes essence’ (Ibid.,\n13). ‘Essence’ is here the defining property of a thing,\nand Sartre gave the example of a paper cutter, which is given its\ndefinition by the artisan who makes it. Sartre said that when people\nbelieved God made human beings, they could believe humans had a\nGod-given essence; but now that we do not believe this, we have\nrealized that humans give themselves their own essences (‘First\nof all, man exists, turns up, appears on the scene, and, only\nafterwards, defines himself.’ Ibid., 15). On this view there are\nno outside commands to appeal to for legitimation, and we are\ncondemned to our own freedom. Sartre thought of human beings as trying\nto be God (on a Hegelian account of what God is), even though there is\nno God. This is an inevitably fruitless undertaking, which he called\n‘anguish’. Moreover, we inevitably desire to choose not\njust for ourselves, but for the world. We want, like God, to create\nhumankind in our own image, ‘If I want to marry, to have\nchildren, even if this marriage depends solely on my own circumstances\nor passion or wish, I am involving all humanity in monogamy and not\nmerely myself. Therefore, I am responsible for myself and for everyone\nelse. I am creating a certain image of man of my own choosing. In\nchoosing myself, I choose man’ (Ibid., 18). To recognize that\nthis project does not make sense is required by honesty, and to hide\nthis from ourselves is ‘bad faith’. One form of bad faith\nis to pretend that there is a God who is giving us our tasks. Another\nis to pretend that there is a ‘human nature’ that is doing\nthe same thing. To live authentically is to realize both that we\ncreate these tasks for ourselves, and that they are futile.", "\n\nThe twentieth century also saw, within Roman Catholicism, forms of\nChristian Existentialism and new adaptations of the system of Thomas\nAquinas. Gabriel Marcel (1889–1973), like Heidegger, was\nconcerned with the nature of Being as it appears to human being, but\nhe tried to show that there are experiences of love, joy, hope and\nfaith which, as understood from within, give us reason to\nbelieve in an inexhaustible Presence, which is God. Jacques Maritain\n(1882–1973) developed a form of Thomism that retained the\nnatural law, but regarded ethical judgment as not purely cognitive but\nguided by pre-conceptual affective inclinations. He gave more place to\nhistory than traditional Thomism did, allowing for development in the\nhuman knowledge of natural law, and he defended democracy as the\nappropriate way for human persons to attain freedom and dignity. The\nnotion of the value of the person and the capacities given to persons\nby their creator was at the center of the ‘personalism’ of\nPope John Paul II's\nThe Acting Person (1979), influenced by Max Scheler\n(1874–1928).", "\n\nNatural law theory has been taken up and modified more recently by\nthree philosophers who write in a style closer to the analytic\ntradition, John Finnis, Alastair MacIntyre and Jean Porter. Finnis\nholds that our knowledge of the fundamental moral truths is\nself-evident, and so is not deduced from human nature. His Natural\nLaw and Natural Rights (1980) was a landmark in integrating the\nmodern vocabulary and grammar of rights into the tradition of Natural\nLaw. MacIntyre, who has been on a long journey back from Marxism to\nThomism, holds that we can know what kind of life we ought to live on\nthe basis of knowing our natural end, which he now identifies in\ntheological terms. In After Virtue (1981) he is still\ninfluenced by a Hegelian historicism, and holds that the only way to\nsettle rival knowledge claims is to see how successfully each can\naccount for the shape taken by its rivals. A different account of\nnatural law is found in Porter, who in Nature as Reason\n(2005) retains the view that our final motivation is our own happiness\nand perfection, but rejects the view that we can deduce absolute\naction-guiding moral principles from human nature. Another\ncontemporary school is virtue ethics, for example Philippa Foot in\nNatural Goodness (2001) and Rosalind Hursthouse in On\nVirtue Ethics (1999). They are not Roman Catholic but they are\nstrongly influenced by Aristotle and Aquinas. They emphasize the\nnotion of virtue which belongs to human nature just as bees have\nstings. Hursthouse ends her book by saying that we have to hold onto\nthe hope that we can live together, not at each other's\nexpense, a hope which she says used to be called belief in (God's)\nProvidence (On Virtue Ethics, 265). One final contribution to\nbe mentioned here is Linda Zagzebski's Divine Motivation\nTheory (2004) which proposes, as an alternative to divine command\ntheory, that we can understand all moral normatively in terms of the\nnotion of a good emotion, and that God's emotions are the best\nexemplar. We will return to the rebirth of divine command theory at\nthe end of this entry.", "\n\nMichel Foucault (1926–84) followed Nietzsche in aspiring to\nuncover the ‘genealogy’ of various contemporary forms of\nthought and practice (he was concerned, for example, with our\ntreatment of sexuality and mental illness), and how relations of power\nand domination have produced ‘discourses of truth’\n(“Truth and Power,” Power, 131). In his later\nwork he described four different aspects of the ‘practice of the\nself’: We select the desires, acts, and thoughts that we attend\nto morally, we recognize ourselves as morally bound by some particular\nground, e.g., divine commands, or rationality, or human nature, we\ntransform ourselves into ethical subjects by some set of techniques,\ne.g., meditation or mortification or consciousness-raising, and\nfinally, we propose a ‘telos’ or goal, the way of\nlife or mode of being that the subject is aiming at, e.g.,\nself-mastery, tranquility or purification. Foucault criticized\nChristian conventions that tend to take morality as a juristic and\noften universal code of laws, and to ignore the creative practice of\nself-making. Even if Christian and post-Christian moralists turn their\nattention to self-expression, he thought they tend to focus on the\nconfession of truth about oneself, a mode of expression which is\nhistorically linked to the church and the modern\npsycho-sciences. Foucault preferred stressing our freedom to form\nourselves as ethical subjects, and develop ‘a new form of\nright’ and a ‘non-disciplinary form of power’\n(“Disciplinary Power and Subjection,”\nPower, 242). He did not, however, tell us much more about\nwhat these new forms would be like.", "\n\nJürgen Habermas (1929-) proposed a ‘communicative\nethics’ that develops the Kantian element in Marxism (The\nTheory of Communicative Action, Vols. I and II). By analyzing the\nstructure of communication (using speech-act theory developed in\nanalytic philosophy) he lays out a procedure that will rationally\njustify norms, though he does not claim to know what norms a society\nwill adopt by using this procedure. The two ideas behind this\nprocedure are that norms are valid if they receive the consent of all\nthe affected parties in unconstrained practical communication, and if\nthe consequences of the general observance of the norms (in terms of\nhow each person's interests are affected) are acceptable to\nall. Habermas thinks he fulfills in this way Hegel's aim of\nreconciling the individual and society, because the communication\nprocess extends individuals beyond their private perspectives in the\nprocess of reaching agreement. Religious convictions need to be left\nbehind when entering the public square, on this scheme, because they\nare not communicable in the way the procedure requires. In recent work\nhe has modified this position, by recognizing that certain religious\nforms require their adherents to speak in an explicitly religious way\nwhen advancing their prescriptions for public life, and it is\ndiscriminatory to try to prevent their doing so.", "\n\nWithin contemporary Jewish ethics mention should be made of Martin\nBuber (1878–1965) and Emmanuel Levinas (1906–95). Buber's\nform of existentialism emphasized the I-You relationship, which exists\nnot only between human beings but (out of that) between human beings\nand God. When we reject I-You relationship, we return to I-It\nrelations, governed by our impositions of our own conceptualizations\non objects. Buber said these two relations are\nexhaustive. ‘There is no I as such but only the I of the basic\nword I-You and the I of the basic word I-It.’ (I and\nThou, 54). Levinas studied under Husserl, and knew Heidegger,\nwhose work he first embraced and then rejected. His focus, like\nBuber's, was on the ‘ethics of the Other’, and he held\nthat the face of the Other makes a demand on us even before we\nrecognize our freedom to accept it or reject it. To meet the Other is\nto have the idea of Infinity (Ethics and Infinity,\n90–1).", "\n\nWe are sometimes said to live now in a ‘post-modern’\nage. This term is problematic in various ways. As used within\narchitectural theory in the 1960's and 1970's it had a relatively\nclear sense. There was a recognizable style that either borrowed bits\nand pieces from styles of the past, or mocked the very idea (in\nmodernist architecture) of essential functionality. In philosophy, the\nterm is less clearly definable. It combines a distaste for\n‘meta-narratives’ and a rejection of any form of\nfoundationalism. The effect on philosophical thinking about the\nrelation between morality and religion is two-fold. On the one hand,\nthe modernist rejection of religion on the basis of a foundationalist\nempiricism is itself rejected. This makes the current climate more\nhospitable to religious language than it was for most of the twentieth\ncentury. But on the other hand, the distaste for over-arching theory\nmeans that religious meta-narratives are suspect to the same degree as\nany other, and the hospitality is more likely to be towards bits and\npieces of traditional theology than to any theological system as a\nwhole. Habermas uses the term ‘post-secular age’ to\ndescribe our current condition, in which the secularization hypothesis\n(that religion was destined to wither away under the impact of science\nand education) has apparently failed.", "\n\nMention should be made of some movements that are not philosophical in\na professional sense, but are important in understanding the relation\nbetween morality and religion. Liberation theology, of which a leading\nspokesman from Latin America is Gustavo Gutiérrez (1928-), has\nattempted to reconcile the Christian gospel with a commitment\n(influenced by Marxist categories) to revolution to relieve the\ncondition of the oppressed. The civil rights movement (drawing heavily\non Exodus), feminist ethics, animal liberation, environmental\nethics, and the gay rights and children's rights movements have shown\nspecial sensitivity to the moral status of some particular oppressed\nclass. The leadership of some of these movements has been religiously\ncommitted, while the leadership of others has not. At the same time,\nthe notion of human rights, or justified claims by every\nhuman being, has grown in global reach, partly through the various\ninstrumentalities of the United Nations. There has, however, been less\nconsensus on the question of how to justify human\nrights. There are theological justifications, deriving from the image\nof God in every human being, or the command to love the neighbor, or\nthe covenant between God and humanity (see Wolterstorff,\nJustice: Rights and Wrongs, chapter 16). Whether\nthere is a non-theological justification is not yet clear. Finally,\nthere has also been a burst of activity in professional ethics, such\nas medical ethics, engineering ethics, and business ethics. This has\nnot been associated with any one school of philosophy rather than\nanother. The connection of religion with these developments has been\nvariable. In some cases (e.g., medical ethics) the initial impetus for\nthe new sub-discipline was strongly influenced by theology, and in\nother cases not.", "\n\nThe origin of analytic philosophy can be associated with\nG.E. Moore. His Principia Ethica (1903) can be regarded as\nthe first major ethical document of the school. He was strongly\ninfluenced by Sidgwick at Cambridge, but rejected Sidgwick's negative\nviews about intuitionism. He thought that intrinsic goodness was a\nreal property of things, even though (like the number two) it does not\nexist in time and is not the object of sense experience. He explicitly\naligned himself here with Plato and against the class of empiricist\nphilosophers, ‘to which most Englishmen have belonged’\n(Principia Ethica, 162). His predecessors, Moore thought, had\nalmost all committed the error, which he called ‘the\nnaturalistic fallacy,’ of trying to define this value property\nby identifying it with a non-evaluative property. For example, they\nproposed that goodness is pleasure, or what produces pleasure. But\nwhatever non-evaluative property we try to say goodness is identical\nto, we will find that it remains an open question whether that\nproperty is in fact good. For example, it makes sense to ask whether\npleasure or the production of pleasure is good. This is true also if\nwe propose a supernatural property to identify with goodness, for\nexample the property of being commanded by God. It still makes sense\nto ask whether what God commands is good. This question cannot be the\nsame as the question ‘Is what God commands what God\ncommands?’ which is not still an open question. Moore thought\nthat if these questions are different, then the two properties,\ngoodness and being commanded by God, cannot be the same, and to say\n(by way of a definition) that they are the same is to commit the\nfallacy. Intrinsic goodness, Moore said, is a simple non-natural\nproperty (i.e., neither natural nor supernatural) and indefinable. He\nthought we had a special form of cognition that he called\n‘intuition,’ which gives us access to such properties. By\nthis he meant that the access was not based on inference or argument,\nbut was self-evident (though we could still get it wrong, just as we\ncan with sense-perception). He thought the way to determine what\nthings had positive value intrinsically was to consider what things\nwere such that, if they existed by themselves in isolation,\nwe would yet judge their existence to be good.", "\n\nAt Cambridge Moore was a colleague of Bertrand Russell\n(1872–1970) and Ludwig Wittgenstein (1889–1951). Russell\nwas not primarily a moral philosopher, but he expressed radically\ndifferent views at different times about ethics. In 1910 he agreed\nwith Moore that goodness (like roundness) is a quality that belongs to\nobjects independently of our opinions, and that when two people differ\nabout whether a thing is good, only one of them can be right. By 1922\nhe was holding an error theory (like that of John Mackie,\n1917–81) that although we mean by ‘good’ an\nobjective property in this way, there is in fact no such thing, and\nhence all our value judgments are strictly speaking false (“The\nElement of Ethics,” Philosophical Essays). Then by 1935\nhe had dropped also the claim about meaning, holding that value\njudgments are expressions of desire or wish, and not assertions at\nall. Wittgenstein's views on ethics are enigmatic and subject to\nwildly different interpretations. In the Tractatus (which is\nabout logic) he says at the end, ‘It is clear that ethics cannot\nbe put into words. Ethics is transcendental. (Ethics and aesthetics\nare one and the same.)’ (Tractatus, 6.421). Perhaps he\nmeans that the world we occupy is good or bad (and happy or unhappy)\nas a whole, and not piece-by-piece. Wittgenstein (like Nietzsche) was\nstrongly influenced by Schopenhauer's notion of will, and by his\ndisdain for ethical theories that purport to be able to tell one what\nto do and what not to do. The Tractatus was taken up by the\nLogical Positivists, though Wittgenstein himself was never a Logical\nPositivist. The Logical Positivists held a\n‘verificationist’ theory of meaning, that assertions can\nbe meaningful only if they can in principle be verified by sense\nexperience or if they are tautologies (for example, ‘All\nbachelors are unmarried men.’) This seems to leave ethical\nstatements (and statements about God) meaningless, and indeed that was\nthe deliberately provocative position taken by A.J. Ayer\n(1910–89). Ayer accepted Moore's arguments about the\nnaturalistic fallacy, and since Moore's talk of ‘non-natural\nproperties’ seemed to Ayer just nonsense, he was led to\nemphasize and analyze further the non-cognitive ingredient in\nevaluation which Moore had identified. Suppose I say to a cannibal,\n‘You acted wrongly in eating your prisoner.’ Ayer thought\nI am not stating anything more than if I had simply said,\n‘You ate your prisoner.’ I am, rather, evincing my moral\ndisapproval of it. It is as if I had said, ‘You ate your\nprisoner’ in a peculiar tone of horror, or written it with the\naddition of some special exclamation marks (Language, Truth and\nLogic, 107–8).", "\n\nThe emotivist theory of ethics had its most articulate treatment in\nEthics and Language by Charles Stevenson (1908–79). Stevenson\nwas a positivist, but also the heir of John Dewey (1859–1952) and the\nAmerican pragmatist tradition. Dewey had rejected the idea of fixed\nends for human beings, and stressed that moral deliberation occurs in\nthe context of competition within a person between different ends,\nnone of which can be assumed permanent. He criticized theories that\ntried to derive moral principles from self-certifying reason, or\nintuition, or cosmic forms, or divine commands, both because he\nthought there are no self-certifying faculties or self-evident norms,\nand because the alleged derivation disguises the actual function of\nthe principles as devices for social action. Stevenson applied this\nemphasis to the competition between people with different\nends, and stressed the role of moral language as a social instrument\nfor persuasion (Ethics and Language, Ch. 5). On his account,\nnormative judgments express attitudes and invite others to share these\nattitudes, but they are not strictly speaking true or false.", "\n\nWittgenstein did not publish any book after the Tractatus,\nbut he wrote and taught; and after his death Philosophical\nInvestigations was published in 1953. The later thought of\nWittgenstein bears a similar relation to the Tractatus as\nHeidegger bears to Husserl. In both cases the quest for a kind of\nscientific certainty was replaced by the recognition that science is\nitself just one language, and not in many cases prior by right. The\nlater Wittgenstein employed the notion of different ‘forms of\nlife’ in which different ‘language games’ including\nthose of religion are at home (Philosophical Investigation,\n§7, 19, 373). In Oxford there was a parallel though distinct\ndevelopment centering round the work of John Austin\n(1911–60). Austin did not suppose that ordinary language was\ninfallible, but he did think that it preserved a great deal of wisdom\nthat had passed the test of centuries of experience, and that\ntraditional philosophical discussion had ignored this primary\nmaterial. In How to do Things with Words (published\nposthumously) Austin labeled ‘the descriptive fallacy’ the\nmistake of thinking that all language is used to perform the act of\ndescribing or reporting, and he attributed the discovery of this\nfallacy to Kant (How to do Things with Words, 3).", "\n\nR.M. Hare (1919–2002) took up the diagnosis of this fallacy, and\nproposed a ‘universal prescriptivism’ which attributed\nthree characteristics to the language of morality. First, it is\nprescriptive, which is to say that moral judgments express the will in\na way analogous to commands. This preserves the emotivist insight that\nmoral judgment is different from assertion, but does not deny the role\nof rationality in such judgment. Second, moral judgment is\nuniversalizable. This is similar to the formula of Kant's categorical\nimperative that requires that we be able to will the maxims of our\nactions as universal laws. Third, moral judgment is overriding. This\nmeans that moral prescriptions legitimately take precedence over any\nother normative prescriptions. In Moral Thinking (1981) Hare\nclaimed to demonstrate that utilitarianism followed from these three\nfeatures of morality, though he excluded ideals (in the sense of\npreferences for how the world should be independently of the agent's\nconcurrent desires or experience) from the scope of this argument. God\nenters in two ways into this picture. First, Hare proposed a figure he\ncalls ‘the archangel’ who is the model for fully critical\n(as opposed to intuitive) moral thinking, having full access to all\nthe relevant information and complete impartiality between the\naffected parties. Hare acknowledge that since archangels (e.g.,\nLucifer) are not reliably impartial in this way, it is really God who\nis the model. Second, we have to be able to believe (as Kant argued)\nthat the universe sustains morality in the sense that it is worthwhile\ntrying to be morally good. Hare thought that this requires something\nlike a belief (he called it a ‘blik’) in the operation of\nProvidence (“The Simple Believer,” Essays on Religion\nand Education, appendix, 37–9).", "\n\nThe most important opponent of utilitarianism in the twentieth century\nwas John Rawls (1921–2005). In his Theory of Justice\n(1971) he gave, like Hare, an account of ethics heavily indebted to\nKant. But he insisted that utilitarianism does not capture the Kantian\ninsight that each person is an end in himself or herself, because it\n‘does not take seriously the distinction between persons’\n(Theory of Justice, 22). He constructed the thought\nexperiment of the ‘Original Position’ in which individuals\nimagine themselves not knowing what role in society they are going to\nplay or what endowments of talent or material wealth they possess, and\nagree together on what principles of justice they will accept. Rawls\nthought it important that substantive conceptions of the good life\nwere left behind in moving to the Original Position, because he was\nattempting to provide an account of justice that people with competing\nvisions of the good could agree to in a pluralist society. Like early\nHabermas he included religions under this\nprohibition. In Political Liberalism (1993) he conceded that\nthe procedure of the Original Position is itself ideologically\nconstrained, and he moved to the idea of an overlapping consensus:\nKantians can accept the idea of justice as fairness (which the\nprocedure describes) because it realizes autonomy, utilitarians\nbecause it promotes overall utility, Christians because it is part of\ndivine law, etc. But even here Rawls wanted to insist that adherents\nof the competing visions of the good leave their particular\nconceptions behind in public discourse and justify the\npolicies they endorse on grounds that are publicly accessible. He\ndescribed this as the citizen's duty of civility (Political\nLiberalism, iv).", "\n\nThe section of this entry on the continental school discussed briefly\nthe topic of postmodernism. Within analytic philosophy the term is\nless prevalent. But both schools live in the same increasingly global\ncultural context. In this context we can reflect on the two main\ndisqualifiers of the project of relating morality intimately to\nreligion that seemed to emerge in the nineteenth and twentieth\ncenturies. The first disqualifier was the prestige of natural science,\nand the attempt to make it foundational for all human knowledge. The\nvarious empiricist, verificationist, and reductionist forms of\nfoundationalism have not yet succeeded, and even within modern\nphilosophy there has been a continuous resistance to them. This is not\nto say they will not succeed in the future (for example we may\ndiscover a foundation for ethics in the theory of evolution), but the\nconfidence in their future success has waned. Moreover, the\nsecularization hypothesis seems to have been false, as mentioned\nearlier. Certainly parts of Western Europe are less attached to\ntraditional institutional forms of religion. But taking the world as a\nwhole, religion seems to be increasing in influence rather than\ndeclining as the world's educational standards improve. The second\nmain disqualifier was the liberal idea (present in the narrative of\nthis entry from the time of the religious wars in Europe) that we need\na moral discourse based on reason and not religion in order to avoid\nthe hatred and bloodshed that religion seems to bring with it. Here\nthe response to Rawls has been telling. It seems false that we can\nrespect persons and at the same time tell them to leave their\nfundamental commitments behind in public discourse, and it seems false\nalso that some purely rational but still action-guiding component can\nbe separated off from these competing substantive conceptions of the\ngood (see Wolterstorff, “An Engagement with Rorty”.) It is\ntrue that religious commitment can produce the deliberate targeting of\ncivilians in a skyscraper. But the history of the twentieth century\nsuggests that non-religious totalitarian regimes have at least as much\nblood on their hands. Perhaps the truth is, as Kant saw, that people\nunder the Evil Maxim will use any available ideology for their\npurposes. Progress towards civility is more likely if Muslims,\nChristians, Jews, (and Buddhists and Hindus) are encouraged to enter\n‘the public square’ with their commitments\nexplicit, and see how much common ethical ground there in fact\nis. This writer has done some of this discussion, and found the common\nground surprisingly extensive, though sometime common language\ndisguises significant differences. Progress seems more likely in this\nway than by trying to construct a neutral philosophical ground that\nvery few people actually accept.", "\n\nOne recent development in analytic ethical theory has been a revival\nof divine command theory parallel to the revival of natural law theory\nthat I have already described. A pioneer in this revival was Philip\nQuinn's Divine Command and Moral Requirements (1978). He\ndefended the theory against the usual objections (one, deriving from\nPlato's Euthyprho, that it makes morality arbitrary, and the\nsecond, deriving from a misunderstanding of Kant, that it is\ninconsistent with human autonomy), and proposed that we understand the\nrelation between God and moral rightness causally, rather than\nanalyzing the terms of moral obligation as meaning\n‘commanded by God’. Though we could stipulate such a\ndefinition, it would make it obscure how theists and non-theists could\nhave genuine moral discussion, as they certainly seem to do. Robert\nM. Adams, in a series of articles and then in Finite and Infinite\nGoods (1999), first separates off the good (which he analyzes\nPlatonically in terms of imitating the ultimate good, which is God)\nand the right. He then defends a divine command theory of the right by\narguing that obligation is always obligation to someone, and\nGod is the most appropriate person, given human limitations. John\nHare, In\nGod and Morality (2007) and Divine Command (2015),\ndefends a version of the theory that derives from God's sovereignty\nand defends the theory against the objection that obedience to divine\ncommand itself requires justification. He also compares Christian,\nJewish and Muslim accounts of divine command. Thomas L. Carson's\nValue and the Good Life (2000) argues that normative theory\nneeds to be based on an account of rationality, and then proposes that\na divine-preference account of rationality is superior to all the\navailable alternatives. An objection to divine command theory is\nmounted by Mark Murphy's An Essay on Divine Authority (2002)\nand God and Moral Law (2012) on the grounds that divine\ncommand only has authority over those persons that have submitted\nthemselves to divine authority, but moral obligation has authority\nmore broadly. William Wainwright's Religion and Morality\ndefends the claim that divine command theory provides a more\nconvincing account of moral obligation than any virtue-based theory,\nincluding Zagzebski's divine motivation theory, discussed\nearlier. Finally, C. Stephen Evans, in Kierkegaard's Ethics of\nLove: Divine Commands and Moral Obligations (2004) and\nGod and Moral Obligation(2013) articulates both in\nKierkegaard and in its own right a divine command theory that is\nargued to be superior to all the main alternative non-theist accounts\nof the nature and basis of moral obligation.", "\n\nTo conclude this entry, the revival of interest in divine command\ntheory, when combined with the revival of natural law theory I already\ndiscussed, shows evidence that the attempt to connect morality closely\nto religion is undergoing a robust recovery within professional\nphilosophy." ], "section_title": "5. Contemporary Philosophy", "subsections": [] } ]

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L., 2000, Value and the Good Life, Notre Dame:\nNotre Dame Press.", "Coplestone, F., 1985, A History of Philosophy, Garden\nCity, NY: Image Books.", "Crusius, Christian August, “A Guide to Rational\nLiving,” Moral Philosophy from Montaigne to Kant,\nVol. 2, J.B. Schneewind (ed.), Cambridge: Cambridge University Press,\n1990.", "Evans, C. S., 2004, Kierkegaard's Ethics of Love: Divine\nCommand and Moral Obligations, Oxford: Oxford University\nPress.", "–––, 2013, God and Moral Obligation,\nOxford: Oxford University Press.", "Feuerbach, L., The Essence of Christianity, George Eliot\n(trans.), Buffalo, NY: Prometheus Books, 1989.", "Finnis, J., 1980, Natural Law and Natural Rights, Oxford:\nOxford University Press.", "Foot, Philippa, Natural Goodness, Oxford: Clarendon\nPress, 2001.", "Foucault, Michel, 1988, “Disciplinary Power and\nSubjection,” Power, Steven Lukes (ed.), New York: New\nYork University Press.", "–––, 1988, “Truth and\nPower,” Power, Steven Lukes (ed.), New York: New York\nUniversity Press.", "Habermas, J., 2010, An Awareness of What s Missing: Faith and\nReason in a Post-Secular Age, trans. Ciaran Cronin, Malden, MA:\nPolity Press.", "Hare, J., 2006, God and Morality A Philosophical History,\nOxford: Blackwell.", "–––, 1996, The Moral Gap, Oxford:\nClarendon Press.", "–––, 1985, Plato's Euthyphro, Bryn Mawr\nCommentaries, Bryn Mawr.", "–––, 2015, Divine Command, Oxford:\nClarendon Press.", "Hare, R. M., 1981, Moral Thinking, Oxford: Clarendon\nPress.", "–––, 1992, “The Simple\nBeliever,” Essays on Religion and Education, Oxford:\nClarendon Press.", "Hegel, G. W. F., Phenomenology of Spirit, A. V. Miller\n(trans.), Oxford: Oxford University Press, 1979.", "–––, The Philosophy of History,\nC. J. Friedrich (ed.), New York: Dover Publications, 1956.", "Heidegger, M., 1927, Being and Time, John Macquarrie and\nEdward Robinson (trans.), New York: Harper and Row, 1962.", "–––, Poetry, Language, Thought, Albert\nHofstadter (trans.), New York: Harper & Row, 1971.", "Hobbes, Thomas, Leviathan, Richard Tuck (ed.), Cambridge:\nCambridge University Press, [1991] 1996.", "Hourani, George, Islamic Rationalism: The Ethics of\n‘Abd al-Jabbar, Oxford: Clarendon Press, 1971.", "Hume, David, Dialogues Concerning Natural Religion, New\nYork: Bobbs-Merrill, 1947.", "–––, Enquiry Concerning the Principles of\nMorals, L. A. Selby-Biggie (ed.), Oxford: Clarendon Press,\n1975.", "–––, A Treatise of Human Nature,\nL. A. Selby-Bigges (ed.), Oxford: Clarendon Press, 1978.", "Hursthouse, Rosalind, 1999, On Virtue Ethics, Oxford: Oxford\nUniversity Press.", "Hutcheson, F., Essay on the Nature and Conduct of the Passions\nwith Illustrations on the Moral Sense, A. 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Wood\nand George di Giovanni (eds.), Cambridge: Cambridge University Press,\n1996.", "Kierkegaard, S., Samlede Voerker, A. B. Drachmann,\nJ. L. Heiberg and H. O. Lange (eds.), Copenhagen: Gyldendal,\n1901–06.", "Leibniz, G. W., New Essays on Human Understanding, Peter\nRemnant and Jonathan Bennett (eds. and trans.), Cambridge: Cambridge\nUniversity Press, 1996.", "Levinas, E., 1969, Totality and Infinity, trans. Alphonso\nLingis, Pittsburgh: Duquesne University Press.", "–––, 1985, Ethics and Infinity,\ntrans. Richard A. Cohen, Pittsburgh: Duquesne University Press.", "Locke, John, The Reasonableness of Christianity,\nI. T. Ramsey (ed.), Stanford: Stanford University Press, 1958.", "–––, Two Treatises on Government\nand A Letter Concerning Toleration, Ian Shapiro (ed.), New\nHaven: Yale University Press, 2003.", "Luther, Martin, The Bondage of the Will, in Martin\nLuther: Selections from his Writings, John Dillenberger (ed.),\nGarden City: Doubleday, 1961.", "MacIntyre, A., 1988, Whose Justice, Which Rationality,\nLondon: Duckworth.", "Maimonides, The Guide of the Perplexed, trans. Schlomo\nPines, Chicago: University of Chicago Press, 1963.", "Marx, Karl, “Critique of Hegel's Philosophy of Right,”\nEarly Writings, Rodney Livingstone and Gregor Benton\n(trans.), London: Penguin Books, [1975] 1992.", "–––, “Economic and Philosophic\nManuscripts,”\nEarly Writings, Rodney Livingstone and Gregor Benton\n(trans.), London: Penguin Books, [1975] 1992.", "Mikalson, J., 1991, Honor Thy Gods, Chapel Hill: The\nUniversity of North Carolina Press.", "Mill, J. S., Autobiography, Jack Stillinger (ed.),\nBoston: Houghton Mifflin Co., 1969.", "–––, 1874, Three Essays on Religion,\nLondon: Henry Holt.", "Moore, G. E., 1903, Principia Ethica, Cambridge:\nCambridge University Press.", "Mouw, R., 1990, The God Who Commands, Notre Dame: Notre\nDame Press.", "Murphy, M., 2002, An Essay on Divine Authority, Ithaca:\nCornell University Press.", "–––, 2011, God and Moral Law: On\nthe Theistic Explanation of Morality, Oxford: Oxford University\nPress.", "Nietzsche, Friedrich, The Gay Science, Walter Kaufman (trans.),\nNew York: Vintage Books, 1974.", "–––, On the Genealogy of Morals, Walter\nKaufman (trans.), New York: Vintage Books, 1967.", "Paley, W., 1830, The Principles of Moral and Political\nPhilosophy, Cambridge: Hillard and Brown.", "Plato, Collected Dialogues, Edith Hamilton and Huntington\nCairns (eds.), Princeton: Princeton University Press, 1963.", "–––, Republic, Robin Waterfield\n(trans.), Oxford: Oxford University Press, 1993.", "Porter, J., 1999, Natural and Divine Law, Grand Rapids,\nMI: Eerdmans.", "–––, 2005, Nature as Reason, Grand\nRapids, MI: Eerdmans.", "Quinn, P., 1978, Divine Commands and Moral Requirements,\nOxford: Oxford University Press.", "Rawls, J., 1993, Political Liberalism, New York: Columbia\nUniversity Press.", "–––, 1971, A Theory of Justice,\nCambridge, MA: Harvard University Press.", "Rousseau, J.-J., The Social Contract and other Later Political\nWritings, Victor Gourevitch (ed.), Cambridge: Cambridge\nUniversity Press, 1997.", "Rudolph, Ulrich, Al-Maturidi and Sunni Theology in\nSamarkand, Leiden: Brill, 2014.", "Russell, B., 1910, “The Elements of Ethics,”\nPhilosophical Essays, New York: Longmans, Green.", "Sartre, J.-P., 1957, Existentialism and Human Emotions,\nSecaucus: Citadel Press.", "Schneewind, J., 1998, The Invention of Autonomy,\nCambridge: Cambridge University Press. ", "Schopenhauer, A., The World as Will and Representation,\nE. F. J. Payne (trans.), New York: Dover Publications, 1966.", "Scotus, D., A Treatise on God as First Principle, Allan\nB. Wolter (ed. and trans.), Chicago: Franciscan Herald Press,\n1966.", "–––, Duns Scotus on the Will and\nMorality, Allan B. Wolter (ed. and trans.), Washington DC: The\nCatholic University of America Press, 1986.", "Sidgwick, H., Methods of Ethics, 7th edn,\nIndianapolis: Hackett, 1981.", "Spinoza, B., Ethics, G. H. R. Parkinson (trans.), Oxford:\nOxford University Press, 2000.", "Stevenson, C., [1944] 1962, Ethics and Language, New\nHaven: Yale University Press.", "Suarez, Francisco, De Legibus, in Selections from\nThree Works of Francisco Suarez, S. J., 2 vols., Oxford:\nClarendon Press; and London: H. 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[ "\nPhilosophy of religion is the philosophical examination of the themes\nand concepts involved in religious traditions as well as the broader\nphilosophical task of reflecting on matters of religious significance\nincluding the nature of religion itself, alternative concepts of God\nor ultimate reality, and the religious significance of general\nfeatures of the cosmos (e.g., the laws of nature, the emergence of\nconsciousness) and of historical events (e.g., the 1755 Lisbon\nEarthquake, the Holocaust). Philosophy of religion also includes the\ninvestigation and assessment of worldviews (such as secular\nnaturalism) that are alternatives to religious worldviews. Philosophy\nof religion involves all the main areas of philosophy: metaphysics,\nepistemology, value theory (including moral theory and applied\nethics), philosophy of language, science, history, politics, art, and\nso on. Section 1 offers an overview of the field and its significance,\nwith subsequent sections covering developments in the field since the\nmid-twentieth century. These sections address philosophy of religion\nas practiced primarily (but not exclusively) in departments of\nphilosophy and religious studies that are in the broadly analytic\ntradition. The entry concludes with highlighting the increasing\nbreadth of the field, as more traditions outside the Abrahamic faiths\n(Judaism, Christianity, and Islam) have become the focus of important\nphilosophical work." ]

[ { "content_title": "1. The Field and its Significance", "sub_toc": [] }, { "content_title": "2. The Meaning of Religious Beliefs", "sub_toc": [ "2.1 Positivism", "2.2 Wittgensteinian Philosophy of Religion" ] }, { "content_title": "3. Religious Epistemology", "sub_toc": [ "3.1 Evidentialism, Reformed Epistemology, and Volitional Epistemology", "3.2 The Epistemology of Disagreement" ] }, { "content_title": "4. Religion and Science", "sub_toc": [] }, { "content_title": "5. Philosophical Reflection on Theism and Its Alternatives", "sub_toc": [ "5.1 Philosophical Reflection on Divine Attributes", "5.2 God’s Existence" ] }, { "content_title": "6. Religious Pluralism", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nIdeally, a guide to the nature and history of philosophy of religion\nwould begin with an analysis or definition of religion. Unfortunately,\nthere is no current consensus on a precise identification of the\nnecessary and sufficient conditions of what counts as a religion. We\ntherefore currently lack a decisive criterion that would enable clear\nrulings whether some movements should count as religions (e.g.,\nScientology or Cargo cults of the Pacific islands). But while\nconsensus in precise details is elusive, the following general\ndepiction of what counts as a religion may be helpful:", "\n\n\nA religion involves a communal, transmittable body of teachings and\nprescribed practices about an ultimate, sacred reality or state of\nbeing that calls for reverence or awe, a body which guides its\npractitioners into what it describes as a saving, illuminating or\nemancipatory relationship to this reality through a personally\ntransformative life of prayer, ritualized meditation, and/or moral\npractices like repentance and personal regeneration. [This is a\nslightly modified definition of the one for “Religion” in\nthe Dictionary of Philosophy of Religion, Taliaferro &\nMarty 2010: 196–197; 2018, 240.]\n", "\nThis definition does not involve some obvious shortcomings such as\nonly counting a tradition as religious if it involves belief in God or\ngods, as some recognized religions such as Buddhism (in its main\nforms) does not involve a belief in God or gods. Although\ncontroversial, the definition provides some reason for thinking\nScientology and the Cargo cults are proto-religious insofar as these\nmovements do not have a robust communal, transmittable body of\nteachings and meet the other conditions for being a religion. (So,\nwhile both examples are not decisively ruled out as religions, it is\nperhaps understandable that in Germany, Scientology is labeled a\n“sect”, whereas in France it is classified as “a\ncult”.) For a discussion of other definitions of religion, see\nTaliaferro 2009, chapter one, and for a recent, different analysis,\nsee Graham Oppy 2018, chapter three. The topic of defining religion is\nre-engaged below in the\n section 4, “Religion and Science”.\n But rather than devoting more space to definitions at the outset, a\npragmatic policy will be adopted: for the purpose of this entry, it\nwill be assumed that those traditions that are widely recognized today\nas religions are, indeed, religions. It will be assumed, then, that\nreligions include (at least) Hinduism, Buddhism, Daoism, Confucianism,\nJudaism, Christianity, Islam, and those traditions that are like them.\nThis way of delimiting a domain is sometimes described as employing a\ndefinition by examples (an ostensive definition) or making an appeal\nto a family resemblance between things. It will also be assumed that\nGreco-Roman views of gods, rituals, the afterlife, the soul, are\nbroadly “religious” or “religiously\nsignificant”. Given the pragmatic, open-ended use of the term\n“religion” the hope is to avoid beginning our inquiry with\na procrustean bed.", "\nGiven the above, broad perspective of what counts as religion, the\nroots of what we call philosophy of religion stretch back to\nthe earliest forms of philosophy. From the outset, philosophers in\nAsia, the Near and Middle East, North Africa, and Europe reflected on\nthe gods or God, duties to the divine, the origin and nature of the\ncosmos, an afterlife, the nature of happiness and obligations, whether\nthere are sacred duties to family or rulers, and so on. As with each\nof what would come to be considered sub-fields of philosophy today\n(like philosophy of science, philosophy of art), philosophers in the\nAncient world addressed religiously significant themes (just as they\ntook up reflections on what we call science and art) in the course of\ntheir overall practice of philosophy. While from time to time in the\nMedieval era, some Jewish, Christian, and Islamic philosophers sought\nto demarcate philosophy from theology or religion, the evident role of\nphilosophy of religion as a distinct field of philosophy does not seem\napparent until the mid-twentieth century. A case can be made, however,\nthat there is some hint of the emergence of philosophy of religion in\nthe seventeenth century philosophical movement Cambridge Platonism.\nRalph Cudworth (1617–1688), Henry More (1614–1687), and\nother members of this movement were the first philosophers to practice\nphilosophy in English; they introduced in English many of the terms\nthat are frequently employed in philosophy of religion today,\nincluding the term “philosophy of religion”, as well as\n“theism”, “consciousness”,and\n“materialism”. The Cambridge Platonists provided the first\nEnglish versions of the cosmological, ontological, and teleological\narguments, reflections on the relationship of faith and reason, and\nthe case for tolerating different religions. While the Cambridge\nPlatonists might have been the first explicit philosophers of\nreligion, for the most part, their contemporaries and successors\naddressed religion as part of their overall work. There is reason,\ntherefore, to believe that philosophy of religion only gradually\nemerged as a distinct sub-field of philosophy in the mid-twentieth\ncentury. (For an earlier date, see James Collins’ stress on\nHume, Kant and Hegel in The Emergence of Philosophy of\nReligion, 1967.)", "\nToday, philosophy of religion is one of the most vibrant areas of\nphilosophy. Articles in philosophy of religion appear in virtually all\nthe main philosophical journals, while some journals (such as the\nInternational Journal for Philosophy of Religion,\nReligious Studies, Sophia, Faith and\nPhilosophy, and others) are dedicated especially to philosophy of\nreligion. Philosophy of religion is in evidence at institutional\nmeetings of philosophers (such as the meetings of the American\nPhilosophical Association and of the Royal Society of Philosophy).\nThere are societies dedicated to the field such as the Society for\nPhilosophy of Religion (USA) and the British Society for Philosophy of\nReligion and the field is supported by multiple centers such as the\nCenter for Philosophy of Religion at the University of Notre Dame, the\nRutgers Center for Philosophy of Religion, the Centre for the\nPhilosophy of Religion at Glasgow University, The John Hick Centre for\nPhilosophy of Religion at the University of Birmingham, and other\nsites (such as the University of Roehampton and Nottingham\nUniversity). Oxford University Press published in 2009 The History\nof Western Philosophy of Religion in five volumes involving over\n100 contributors (Oppy & Trakakis 2009), and the Wiley\nBlackwell Encyclopedia of Philosophy of Religion in five volumes,\nwith over 350 contributors from around the world, is scheduled for\npublication by 2021. What accounts for this vibrancy? Consider four\npossible reasons.", "\nFirst: The religious nature of the world population. Most social\nresearch on religion supports the view that the majority of the\nworld’s population is either part of a religion or influenced by\nreligion (see the Pew Research Center online). To engage in philosophy\nof religion is therefore to engage in a subject that affects actual\npeople, rather than only tangentially touching on matters of present\nsocial concern. Perhaps one of the reasons why philosophy of religion\nis often the first topic in textbook introductions to philosophy is\nthat this is one way to propose to readers that philosophical study\ncan impact what large numbers of people actually think about life and\nvalue. The role of philosophy of religion in engaging real life\nbeliefs (and doubts) about religion is perhaps also evidenced by the\ncurrent popularity of books for and against theism in the UK and\nUSA.", "\nOne other aspect of religious populations that may motivate philosophy\nof religion is that philosophy is a tool that may be used when persons\ncompare different religious traditions. Philosophy of religion can\nplay an important role in helping persons understand and evaluate\ndifferent religious traditions and their alternatives.", "\nSecond: Philosophy of religion as a field may be popular because of\nthe overlapping interests found in both religious and philosophical\ntraditions. Both religious and philosophical thinking raise many of\nthe same, fascinating questions and possibilities about the nature of\nreality, the limits of reason, the meaning of life, and so on. Are\nthere good reasons for believing in God? What is good and evil? What\nis the nature and scope of human knowledge? In Hinduism; A\nContemporary Philosophical Investigation (2018), Shyam\nRanganathan argues that in Asian thought philosophy and religion are\nalmost inseparable such that interest in the one supports an interest\nin the other.", "\nThird, studying the history of philosophy provides ample reasons to\nhave some expertise in philosophy of religion. In the West, the\nmajority of ancient, medieval, and modern philosophers philosophically\nreflected on matters of religious significance. Among these modern\nphilosophers, it would be impossible to comprehensively engage their\nwork without looking at their philosophical work on religious beliefs:\nRené Descartes (1596–1650), Thomas Hobbes\n(1588–1679), Anne Conway (1631–1679), Baruch Spinoza\n(1632–1677), Margaret Cavendish (1623–1673), Gottfried\nLeibniz (1646–1716), John Locke (1632–1704), George\nBerkeley (1685–1753), David Hume (1711–1776), Immanuel\nKant (1724–1804), and G.W.F. Hegel (1770–1831) (the list\nis partial). And in the twentieth century, one should make note of the\nimportant philosophical work by Continental philosophers on matters of\nreligious significance: Martin Heidegger (1889–1976), Jean-Paul\nSartre (1905–1980), Simone de Beauvoir (1908–1986), Albert\nCamus (1913–1960), Gabriel Marcel (1889–1973), Franz\nRosenzweig (1886–1929), Martin Buber (1878–1956), Emmanuel\nLevinas (1906–1995), Simone Weil (1909–1943) and, more\nrecently Jacques Derrida (1930–2004), Michel Foucault\n(1926–1984), and Luce Irigary (1930–). Evidence of\nphilosophers taking religious matters seriously can also be found in\ncases of when thinkers who would not (normally) be classified as\nphilosophers of religion have addressed religion, including A.N.\nWhitehead (1861–1947), Bertrand Russell (1872–1970), G.E.\nMoore (1873–1958), John Rawls (1921–2002), Bernard\nWilliams (1929–2003), Hilary Putnam (1926–2016), Derek\nParfit (1942–2017), Thomas Nagel (1937–), Jürgen\nHabermas (1929–), and others.", "\nIn Chinese and Indian philosophy there is an even greater challenge\nthan in the West to distinguish important philosophical and religious\nsources of philosophy of religion. It would be difficult to classify\nNagarjuna (150–250 CE) or Adi Shankara (788–820 CE) as\nexclusively philosophical or religious thinkers. Their work seems as\nequally important philosophically as it is religiously (see\nRanganathan 2018).", "\nFourth, a comprehensive study of theology or religious studies also\nprovides good reasons to have expertise in philosophy of religion. As\njust observed, Asian philosophy and religious thought are intertwined\nand so the questions engaged in philosophy of religion seem relevant:\nwhat is space and time? Are there many things or one reality? Might\nour empirically observable world be an illusion? Could the world be\ngoverned by Karma? Is reincarnation possible? In terms of the West,\nthere is reason to think that even the sacred texts of the Abrahamic\nfaith involve strong philosophical elements: In Judaism, Job is\nperhaps the most explicitly philosophical text in the Hebrew Bible.\nThe wisdom tradition of each Abrahamic faith may reflect broader\nphilosophical ways of thinking; the Christian New Testament seems to\ninclude or address Platonic themes (the Logos, the soul and body\nrelationship). Much of Islamic thought includes critical reflection on\nPlato, Aristotle, Plotinus, as well as independent philosophical\nwork.", "\nLet us now turn to the way philosophers have approached the meaning of\nreligious beliefs." ], "section_title": "1. The Field and its Significance", "subsections": [] }, { "main_content": [ "\nPrior to the twentieth century, a substantial amount of philosophical\nreflection on matters of religious significance (but not all) has been\nrealist. That is, it has often been held that religious beliefs are\ntrue or false. Xenophanes and other pre-Socratic thinkers, Socrates,\nPlato, Aristotle, the Epicureans, the Stoics, Philo, Plotinus differed\non their beliefs (or speculation) about the divine, and they and their\ncontemporaries differed about skepticism, but they held (for example)\nthat there either was a divine reality or not. Medieval and modern\nJewish, Christian, and Islamic philosophers differed in terms of their\nassessment of faith and reason. They also faced important\nphilosophical questions about the authority of revelation claims in\nthe Hebrew Bible, the Christian Bible, and the Qur’an. In Asian\nphilosophy of religion, some religions do not include revelation\nclaims, as in Buddhism and Confucianism, but Hindu tradition\nconfronted philosophers with assessing the Vedas and Upanishads. But\nfor the most part, philosophers in the West and East thought there\nwere truths about whether there is a God, the soul, an afterlife, that\nwhich is sacred (whether these are known or understood by any human\nbeing or not). Realism of some kind is so pervasive that the great\nhistorian of philosophy Richard Popkin (1923–2005) once defined\nphilosophy as “the attempt the give an account of what is true\nand what is important” (Popkin 1999: 1). Important philosophers\nin the West such as Immanuel Kant (1724–1804) and Friedrich\nNietzsche (1844–1900), among others, challenged classical\nrealist views of truth and metaphysics (ontology or the theory of what\nis), but the twentieth century saw two, especially powerful movements\nthat challenged realism: logical positivism and philosophy of religion\ninspired by Wittgenstein.", "\nPrior to addressing these two movements, let us take note of some of\nthe nuances in philosophical reflection on the realist treatment of\nreligious language. Many theistic philosophers (and their critics)\ncontend that language about God may be used univocally, analogically\nor equivocally. A term is used univocally about God and humans when it\nhas the same sense. Arguably, the term “to know” is used\nunivocally of God in the claims “God knows you” and\n“You know London”, even though how God knows you and how\nyou know London differ radically. In terms of the later difference,\nphilosophers sometimes distinguish between what is attributed\nto some thing and the mode in which some state (such as\nknowledge) is realized. Terms are used analogously when there is some\nsimilarity between what is being attributed, e.g., when it is said\nthat “two human persons love each other” and “God\nloves the world”, the term “love” may be used\nanalogically when there is some similarity between these loves). Terms\nare used equivocally when the meaning is different as in the statement\n“Adam knew Eve” (which in the King James’ Bible\nmeant Adam and Eve had intercourse) and “God knows the\nworld” (while some of the Homeric gods did have intercourse with\nhumans, this was not part of theistic worldviews). Theological work\nthat stresses our ability to form a positive concept of the divine has\nbeen called the via positiva or catophatic theology.\nOn the other hand, those who stress the unknowability of God embrace\nwhat is called the via negativa or apophatic\ntheology. Maimonides (1135–1204) was a great proponent of\nthe via negativa, favoring the view that we know God\nprincipally through what God is not (God is not material, not evil,\nnot ignorant, and so on).", "\nWhile some (but not all) philosophers of religion in the Continental\ntradition have aligned themselves with apophatic theology such as\nLevinas (who was non-theistic) and Jean-Luc Marion (1946–), a\nsubstantial amount (but not all) of analytically oriented philosophy\nof religion have tended to adopt the via positiva One of the\nchallenges of apophatic theology is that it seems to make the\nphilosophy of God remote from religious practices such as prayer,\nworship, trust in God’s power and goodness, pilgrimages, and\nreligious ethics. According to Karen Armstrong, some of the greatest\ntheologians in the Abrahamic faiths held that God", "\n\n\nwas not good, divine, powerful, or intelligent in any way that we\ncould understand. We could not even say that God\n“existed”, because our concept of existence is too\nlimited. Some of the sages preferred to say that God was\n“Nothing” because God was not another being… To\nthese theologians some of our modern ideas about God would have seemed\nidolatrous. (Armstrong 2009: x)\n", "\nA prima facie challenge to this position is that it is hard\nto believe that religious practitioners could pray or worship or trust\nin a being which was altogether inscrutable or a being that we cannot\nin any way understand. For a realist, via positiva\nphilosophy of God that seeks to appreciate the force of apophatic\ntheology, see Mikael Stenmark’s “Competing conceptions of\nGod: the personal God versus the God beyond being” (2015).", "\nLet us now turn to two prominent philosophical movements that\nchallenged a realist philosophy of God." ], "section_title": "2. The Meaning of Religious Beliefs", "subsections": [ { "content": [ "\n“Positivism” is a term introduced by Auguste Comte\n(1798–1857), a French philosopher who championed the natural and\nsocial sciences over against theology and the philosophical practice\nof metaphysics. The term “positivism” was used later\n(sometimes amplified to Logical Positivism by A.J. Ayer) by a\ngroup of philosophers who met in Austria called the Vienna Circle from\n1922 to 1938. This group, which included Moritz Schlick and Max\nPlanck, advanced an empirical account of meaning, according to which\nfor a proposition to be meaningful it needed either to be a conceptual\nor formal statement in mathematics or about analytic definitions\n(“triangles have three angles”) or about matters that can\nbe empirically verified or falsified. Ostensibly factual claims that\ndo not make any difference in terms of our actual (or possible)\nempirical experience are void of meaning. A British philosopher, who\nvisited the Vienna Circle, A.J. Ayer popularized this criterion of\nmeaning in his 1936 book, Language, Truth, and Logic. In it,\nAyer argued that religious claims as well as their denial were without\ncognitive content. By his lights, theism, and also atheism and\nagnosticism, were nonsense, because they were about the reality (or\nunreality or unknowability) of that which made no difference to our\nempirical experience. How might one empirically confirm or disconfirm\nthat there is an incorporeal, invisible God or that Krishna is an\navatar of Vishnu? Famously, Antony Flew employed this strategy in his\nlikening the God of theism to a belief that there is an undetectable,\ninvisible gardener who could not be heard or smelled or otherwise\nempirically discovered (Flew 1955). In addition to rejecting\ntraditional religious beliefs as meaningless, Ayer and other logical\npositivists rejected the meaningfulness of moral statements. By their\nlights, moral or ethical statements were expressions of persons’\nfeelings, not about values that have a reality independent of\npersons’ feelings.", "\nThe logical positivist critique of religion is not dead. It can be\nseen at work in Herman Philipse’s God in the Age of Science;\nA Critique of Religious Reasons (2012). Still, the criterion of\nmeaning advanced by logical positivism faced a series of objections\n(for details see Copleston 1960 and Taliaferro 2005b).", "\nConsider five objections that were instrumental in the retreat of\nlogical positivism from its position of dominance.", "\nFirst, it was charged that logical positivism itself is self-refuting.\nIs the statement of its standard of meaning (propositions are\nmeaningful if and only if they are about the relations of ideas or\nabout matters that are subject to empirical verification or\nfalsification) itself about the relations of ideas or about matters\nthat are subject to empirical verification or falsification? Arguably\nnot. At best, the positivist criterion of meaning is a recommendation\nabout what to count as meaningful.", "\nSecond, it was argued that there are meaningful statements about the\nworld that are not subject to direct or indirect empirical\nconfirmation or disconfirmation. Plausible candidates include\nstatements about the origin of the cosmos or, closer to home, the\nmental states of other persons or of nonhuman animals (for discussion,\nsee Van Cleve 1999 and Taliaferro 1994).", "\nThird, limiting human experience to what is narrowly understood to be\nempirical seemed to many philosophers to be arbitrary or capricious.\nC. D. Broad and others defended a wider understanding of experience to\nallow for the meaningfulness of moral experience: arguably, one can\nexperience the wrongness of an act as when an innocent person feels\nherself to be violated.", "\nFourth, Ayer’s rejection of the meaningfulness of ethics seemed\nto cut against his epistemology or normative account of beliefs, for\nhe construed empirical knowledge in terms of having the right to\ncertain beliefs. If it is meaningful to refer to the right to beliefs,\nwhy is it not meaningful to refer to moral rights such as the right\nnot to be tortured? And if we are countenancing a broader concept of\nwhat may be experienced, in the tradition of phenomenology (which\ninvolves the analysis of appearances) why rule out, as a matter of\nprinciple, the experience of the divine or the sacred?", "\nFifth, and probably most importantly in terms of the history of ideas,\nthe seminal philosopher of science Carl Hempel (1905–1997)\ncontended that the project of logical positivism was too limited\n(Hempel 1950). It was insensitive to the broader task of scientific\ninquiry which is properly conducted not on the tactical scale of\nscrutinizing particular claims about empirical experience but in terms\nof a coherent, overall theory or view of the world. According to\nHempel, we should be concerned with empirical inquiry but see this as\ndefined by an overall theoretical understanding of reality and the\nlaws of nature. This was not ipso facto a position that\nfavored the meaningfulness of religious belief, but Hempel’s\ncriticism of positivism removed their barrier for overall metaphysical\naccounts of reality, be these accounts theistic, pantheistic (roughly,\nGod is everything), naturalistic, and so on. Moreover, the positivist\ncritique of what they called metaphysics was attacked as confused as\nsome metaphysics was implied in their claims about empirical\nexperience; see the aptly titled classic The Metaphysics of\nLogical Positivism (1954) by Gustav Bergmann\n(1906–1987).", "\nLet us now turn to Wittgenstein (1889–1951) and the philosophy\nof religion his work inspired." ], "subsection_title": "2.1 Positivism" }, { "content": [ "\nWittgenstein’s early work was interpreted by some members of the\nVienna Circle as friendly to their empiricism, but they were surprised\nwhen he visited the Circle and, rather than Wittgenstein discussing\nhis Tractatus, he read them poetry by Rabindranath Tagore\n(1861–1941), a Bengal mystic (see Taliaferro 2005b: chapter\neight). In any case, Wittgenstein’s later work, which was not\nfriendly to their empiricism, was especially influential in post-World\nWar II philosophy and theology and will be the focus here.", "\nIn the Philosophical Investigations (published posthumously\nin 1953) and in many other works (including the publication of notes\ntaken by his students on his lectures), Wittgenstein opposed what he\ncalled the picture theory of meaning. On this view, statements are\ntrue or false depending upon whether reality matches the picture\nexpressed by the statements. Wittgenstein came to see this view of\nmeaning as deeply problematic. The meaning of language is, rather, to\nbe found not in referential fidelity but in its use in what\nWittgenstein referred to as forms of life. As this position\nwas applied to religious matters, D.Z. Phillips (1966, 1976),\nB.R. Tilghman (1994), and, more recently, Howard Wettstein (2012),\nsought to displace traditional metaphysical debate and arguments over\ntheism and its alternatives and to focus instead on the way language\nabout God, the soul, prayer, resurrection, the afterlife, and so on,\nfunctions in the life of religious practitioners. For example,\nPhillips contended that the practice of prayer is best not viewed as\nhumans seeking to influence an all powerful, invisible person, but to\nachieve solidarity with other persons in light of the fragility of\nlife. Phillips thereby sees himself as following Wittgenstein’s\nlead by focusing, not on which picture of reality seems most faithful,\nbut on the non-theoretical ways in which religion is practiced.", "\n\n\nTo ask whether God exists is not to ask a theoretical question. If it\nis to mean anything at all, it is to wonder about praising and\npraying; it is to wonder whether there is anything in all that. This\nis why philosophy cannot answer the question “Does God\nexist?” with either an affirmative or a negative reply …\n“There is a God”, though it appears to be in the\nindicative mood, is an expression of faith. (Phillips 1976: 181)\n", "\nAt least two reasons bolstered this philosophy of religion inspired by\nWittgenstein. First, it seemed as though this methodology was more\nfaithful to the practice of philosophy of religion being truly\nabout the actual practice of religious persons themselves.\nSecond, while there has been a revival of philosophical arguments for\nand against theism and alternative concepts of God (as will be noted\nin\n section 5),\n significant numbers of philosophers from the mid-twentieth century\nonward have concluded that all the traditional arguments and\ncounter-arguments about the metaphysical claims of religion are\nindecisive. If that is the case, the Wittgenstein-inspired new\nphilosophy of religion had the advantage of shifting ground to what\nmight be a more promising area of agreement.", "\nWhile this non-realist approach to religion has its defenders today,\nespecially in work by Howard Wettstein, many philosophers have\ncontended that traditional and contemporary religious life rests on\nmaking claims about what is truly the case in a realist context. It is\nhard to imagine why persons would pray to God if they, literally,\nthought there is no God (of any kind).", "\nInterestingly, perhaps inheriting the Wittgenstein stress on practice,\nsome philosophers working on religion today place greater stress on\nthe meaning of religion in life, rather than seeing religious belief\nas primarily a matter of assessing an hypothesis (see Cottingham\n2014)." ], "subsection_title": "2.2 Wittgensteinian Philosophy of Religion" } ] }, { "main_content": [ "\nAccording to the prestigious Cambridge Dictionary of\nPhilosophy, religious epistemology is “a branch of\nphilosophy that investigates the epistemic status of propositional\nattitudes about religious claims” (Audi 2015: 925). Virtually\nall the extant and current methodologies in epistemology have been\nemployed in assessing religious claims. Some of these methods have\nbeen more rationalistic in the sense that they have involved reasoning\nfrom ostensibly self-evident truths (e.g., a principle of sufficient\nreason), while others have been more experiential (e.g., empiricism,\nphenomenology, the stress on passion and subjectivity, the stress on\npractice as found in pragmatism). Also, some have sought to be\nahistorical (not dependent upon historical revelation claims), while\nothers are profoundly historical (e.g., grounded on revelation either\nknown by faith alone or justified evidentially by an appeal to\nmiracles and/or religious experience.", "\nOver the past twenty years, there has been a growing literature on the\nnature of religious faith. Among many philosophers in the analytical\ntradition, faith has often been treated as the propositional attitude\nbelief, e.g., believing that there is or is not a God, and much work\ndevoted to examining when such belief is backed up by evidence and, if\nso, how much and what kinds of evidence. There has been a famous\ndebate over “the ethics of belief”, determining what kinds\nof belief should not be entertained or countenanced when the evidence\nis deemed insufficient, and when matters of religious faith may be\njustified on pragmatic grounds (e.g., as a wager or venture). Faith\nhas also been philosophically treated as trust, a form of hope, an\nallegiance to an ideal, commitment, and faithful action with or\nwithout belief (for a survey see Abraham & Aquino 2017; for a\nrecent defense of religious faith without belief, see Schellenberg\n2017).", "\nThe following examines first what is known as evidentialism and\nreformed epistemology and then a form of what is called volitional\nepistemology of religion." ], "section_title": "3. Religious Epistemology", "subsections": [ { "content": [ "\nEvidentialism is the view that for a person to be justified in some\nbelief, that person must have some awareness of the evidence for the\nbelief. This is usually articulated as a person’s belief being\njustified given the total evidence available to the person. On this\nview, the belief in question must not be undermined (or defeated) by\nother, evident beliefs held by the person. Moreover, evidentialists\noften contend that the degree of confidence in a belief should be\nproportional to the evidence. Evidentialism has been defended by\nrepresentatives of all the different viewpoints in philosophy of\nreligion: theism, atheism, advocates of non-theistic models of God,\nagnostics. Evidentialists have differed in terms of their accounts of\nevidence (what weight might be given to phenomenology?) and the\nrelationship between evident beliefs (must beliefs either be\nfoundational or basic or entailed by such foundational beliefs?)\nProbably the most well known evidentialist in the field of philosophy\nof religion who advocates for theism is Richard Swinburne\n(1934–).", "\nSwinburne was (and is) the leading advocate of theistic natural\ntheology since the early 1970s. Swinburne has applied his considerable\nanalytical skills in arguing for the coherence and cogency of theism,\nand the analysis and defense of specific Christian teachings about the\ntrinity, incarnation, the resurrection of Christ, revelation, and\nmore. Swinburne’s projects in the evidentialist tradition in\nphilosophy of religion are in the great tradition of British\nphilosophy of religion from the Cambridge Platonists in the\nseventeenth century through Joseph Butler (1692–1752) and\nWilliam Paley (1743–1805) to twentieth century British\nphilosophers such as A.E. Taylor (1869–1945), F. R. Tennant\n(1866–1957), William Temple (1881–1944), H.D. Lewis\n(1910–1992), and A.C. Ewing (1899–1973). The positive\nphilosophical case for theism has been met by work by many powerful\nphilosophers, most recently Ronald Hepburn (1927–2008), J.L.\nMackie (1917–1981), Antony Flew (1923–2010), Richard Gale\n(1932–2015), William Rowe (1931–2015), Michael Martin\n(1932–2015), Graham Oppy (1960–), J.L. Schellenberg\n(1959–), and Paul Draper (1957–). (See The Routledge\nCompanion to Theism [Taliaferro, Harrison, & Goetz 2012] for\nan overview of such work.)", "\nThere have been at least two interesting, recent developments in the\nphilosophy of religion in the framework of evidentialism. One has been\nadvanced by John Schellenberg who argues that if the God of\nChristianity exists, God’s reality would be far more evident\nthan it is. Arguably, in the Christian understanding of values, an\nevident relationship with God is part of the highest human good, and\nif God were loving, God would bring about such a good. Because there\nis evidence that God does not make Godself available to earnest\nseekers of such a relationship, this is evidence that such a God does\nnot exist. According to this line of reasoning, the absence of\nevidence of the God of Christianity is evidence of absence (see\nSchellenberg 2007 and Howard-Snyder & Moser 2001). The argument\napplies beyond Christian values and theism, and to any concept of God\nin which God is powerful and good and such that a relationship with\nsuch a good God would be fulfilling and good for creatures. It would\nnot work with a concept of God (as we find, for example, in the work\nof Aristotle) in which God is not lovingly and providentially engaged\nin the world. This line of reasoning is often referred to in terms of\nthe hiddenness of God.", "\nAnother interesting development has been advanced by Sandra Menssen\nand Thomas Sullivan. In philosophical reflection about God the\ntendency has been to give priority to what may be called bare theism\n(assessing the plausibility of there being the God of theism) rather\nthan a more specific concept of God. This priority makes sense insofar\nas the plausibility of a general thesis (there are mammals on the\nsavanna) will be greater than a more specific thesis (there are 12,796\ngiraffes on the savanna). But Menssen and Sullivan argue that\npracticing philosophy of religion from a more particular, especially\nChristian, context, provides a richer “data base” for\nreflection.", "\n\n\nThe all–too–common insistence among philosophers that\nproper procedure requires establishing the likelihood of God’s\nexistence prior to testing revelatory claims cuts off a huge part of\nthe data base relevant to arguing for theism… For it is\ndifficult to establish God’s existence as likely unless some\naccount can be given of the evils of the world, and the account\nChristianity has to offer is unimaginably richer than any\nnon-religious account. The Christian account, accessed through\nscripture, is a story of love: of God’s love for us and of what\nGod has prepared for those who love him… It is a story of the\nsalvific value of suffering: our sufferings are caught up with\nChrist’s, and are included in the sufferings adequate for the\nworld’s redemption, sufferings Christ has willed to make his\nown. (Menssen & Sullivan 2017: 37–38)\n", "\nIn terms of the order of inquiry, it may be helpful at times, to\nconsider more specific philosophical positions—for example, it\nmay seem at first glance that materialism is hopeless until one\nengages the resources of some specific materialist account that\ninvolves functionalism—but, arguably, this does not alone offset\nthe logical primacy of the more general thesis (whether this is bare\ntheism or bare materialism). Perhaps the import of the\nMenssen-Sullivan proposal is that philosophers of religion need to\nenhance their critical assessment of general positions along with\ntaking seriously more specific accounts about the data on hand (e.g.,\nwhen it comes to theism, assessing the problem of evil in terms of\npossible theological positions on redemption as presented in\nostensible revelations).", "\nEvidentialism has been challenged on many grounds. Some argue that it\nis too stringent; we have many evident beliefs that we would be at a\nloss to successfully justify. Instead of evidentialism, some\nphilosophers adopt a form of reliabilism, according to which a person\nmay be justified in a belief so long as the belief is produced by a\nreliable means, whether or not the person is aware of evidence that\njustifies the belief. Two movements in philosophy of religion develop\npositions that are not in line with the traditional evidential\ntradition: reformed epistemology and volitional epistemology.", "\nReformed epistemology has been championed by Alvin Plantinga\n(1932–) and Nicholas Wolterstorff (1932–), among others.\nReformed epistemology is “Reformed” insofar as it draws on\nthe Reformer John Calvin (1509–1564) who claimed that persons\nare created with a sense of God (sensus divinitatis). While\nthis sense of God may not be apparent due to sin, it can reliably\nprompt persons to believe in God and support a life of Christian\nfaith. While this prompting may play an evidential role in terms of\nthe experience or ostensible perception of God, it can also warrant\nChristian belief in the absence of evidence or argument (see K. Clark\n& VanArragon 2011; M. Bergmann 2017; and Plantinga & Bergmann\n2016). In the language Plantinga introduced, belief in God may be as\nproperly basic as our ordinary beliefs about other persons and the\nworld. The framework of Reformed epistemology is conditional as it\nadvances the thesis that if there is a God and if God has indeed\ncreated us with a sensus divinitatis that reliably leads us\nto believe (truly) that God exists, then such belief is warranted.\nThere is a sense in which Reformed epistemology is more of a defensive\nstrategy (offering grounds for thinking that religious belief, if\ntrue, is warranted) rather than providing a positive reason why\npersons who do not have (or believe they have) a sensus\ndivinitatis should embrace Christian faith. Plantinga has argued\nthat at least one alternative to Christian faith, secular naturalism,\nis deeply problematic, if not self-refuting, but this position (if\ncogent) has been advanced more as a reason not to be a naturalist than\nas a reason for being a theist. (For a stronger version of the\nargument that theism better accounts for the normativity of reason\nthan alternatives, see Angus Menuge’s Agents Under\nFire, 2004.)", "\nReformed epistemology is not ipso facto fideism. Fideism\nexplicitly endorses the legitimacy of faith without the support, not\njust of (propositional) evidence, but also of reason (MacSwain 2013).\nBy contrast, Reformed epistemology offers a metaphysical and\nepistemological account of warrant according to which belief in God\ncan be warranted even if it is not supported by evidence and it offers\nan account of properly basic belief according to which basic belief in\nGod is on an epistemic par with our ordinary basic beliefs about the\nworld and other minds which seem to be paradigmatically rational.\nNonetheless, while Reformed epistemology is not necessarily fideistic,\nit shares with fideism the idea that a person may have a justified\nreligious belief in the absence of evidence.", "\nConsider now what is called volitional epistemology in the philosophy\nof religion. Paul Moser has systematically argued for a profoundly\ndifferent framework in which he contends that if the God of\nChristianity exists, this God would not be evident to inquirers who\n(for example) are curious about whether God exists. By Moser’s\nlights, the God of Christianity would only become evident in a process\nthat would involve the moral and spiritual transformation of persons\n(Moser 2017). This process might involve persons receiving (accepting)\nthe revelation of Jesus Christ as redeemer and sanctifier who calls\npersons to a radical life of loving compassion, even the loving of our\nenemies. By willfully subjecting oneself to the commanding love of\nGod, a person in this filial relationship with God through Christ may\nexperience a change of character (from self-centeredness to serving\nothers) in which the person’s character (or very being) may come\nto serve as evidence of the truths of faith." ], "subsection_title": "3.1 Evidentialism, Reformed Epistemology, and Volitional Epistemology" }, { "content": [ "\nThe terrain covered so far in this entry indicates considerable\ndisagreement over epistemic justification and religious belief. If the\nexperts disagree about such matters, what should non-experts think and\ndo? Or, putting the question to the so-called experts, if you (as a\ntrained inquirer) disagree about the above matters with those whom you\nregard as equally intelligent and sensitive to evidence, should that\nfact alone bring you to modify or even abandon the confidence you hold\nconcerning your own beliefs?", "\nSome philosophers propose that in the case of disagreements among\nepistemic peers, one should seek some kind of account of the\ndisagreement. For example, is there any reason to think that the\nevidence available to you and your peers differs or is conceived of\ndifferently. Perhaps there are ways of explaining, for example, why\nBuddhists may claim not to observe themselves as substantial selves\nexisting over time whereas a non-Buddhist might claim that\nself-observation provides grounds for believing that persons are\nsubstantial, enduring agents (David Lund 2005). The non-Buddhist might\nneed another reason to prefer her framework over the Buddhist one, but\nshe would at least (perhaps) have found a way of accounting for why\nequally reasonable persons would come to different conclusions in the\nface of ostensibly identical evidence.", "\nAssessing the significance of disagreement over religious belief is\nvery different from assessing the significance of disagreement in\ndomains where there are clearer, shared understandings of methodology\nand evidence. For example, if two equally proficient detectives\nexamine the same evidence that Smith murdered Jones, their\ndisagreement should (other things being equal) lead us to modify\nconfidence that Smith is guilty, for the detectives may be presumed to\nuse the same evidence and methods of investigation. But in assessing\nthe disagreements among philosophers over (for example) the coherence\nand plausibility of theism, philosophers today often rely on different\nmethodologies (phenomenology, empiricism, conceptual or linguistic\nanalysis, structural theory, post-structuralism, psychoanalysis, and\nso on). But what if a person accepts a given religion as reasonable\nand yet acknowledges that equally reasonable, mature, responsible\ninquirers adopt a different religion incompatible with her own and\nthey all share a similar philosophical methodology? This\nsituation is not an abstract thought experiment. In Christian-Muslim\ndialogue, philosophers often share a common philosophical inheritance\nfrom Plato, Aristotle, Plotinus, and a broad range of shared views\nabout the perfection of God/Allah.", "\nOne option would be to adopt an epistemological pluralism, according\nto which persons can be equally well justified in affirming\nincompatible beliefs. This option would seem to provide some grounds\nfor epistemic humility (Audi 2011; Ward 2002, 2014, 2017). In an\nappropriately titled essay, “Why religious pluralism is not evil\nand is in some respects quite good”, (2018) Robert McKim\npresents reasons why, from a philosophical point of view, it may be\ngood to encourage (and not merely acknowledge) ostensibly equally\nreasonable worldviews. For an overview of the current state of play in\nphilosophy of religion on the topic of religious disagreement, see\n“Disagreement and the Epistemology of Theology” (King\n& Kelly 2017). ", "\nAt the end of this section, two observations are also worth noting\nabout epistemic disagreements. First, our beliefs and our confidence\nin the truth of our beliefs may not be under our voluntary control.\nPerhaps you form a belief of the truth of Buddhism based on what you\ntake to be compelling evidence. Even if you are convinced that equally\nintelligent persons do not reach a similar conclusion, that alone may\nnot empower you to deny what seems to you to be compelling. Second, if\nthe disagreement between experts gives you reason to abandon a\nposition, then the very principle you are relying on (one should\nabandon a belief that X if experts disagree about X)\nwould be undermined, for experts disagree about what one should do\nwhen experts disagree. For overviews and explorations of relevant\nphilosophical work in a pluralistic setting, see New Models of\nReligious Understanding (2018) edited by Fiona Ellis and\nRenewing Philosophy of Religion (2017) edited by Paul Draper\nand J.L. Schellenberg." ], "subsection_title": "3.2 The Epistemology of Disagreement" } ] }, { "main_content": [ "\nThe relationship between religion and science has been an important\ntopic in twentieth century philosophy of religion and it seems highly\nimportant today. ", "\nThis section begins by considering the National Academy of Sciences\nand Institute of Medicine (now the National Academy of Medicine)\nstatement on the relationship between science and religion:", "\n\n\nScience and religion are based on different aspects of human\nexperience. In science, explanations must be based on evidence drawn\nfrom examining the natural world. Scientifically based observations or\nexperiments that conflict with an explanation eventually must lead to\nmodification or even abandonment of that explanation. Religious faith,\nin contrast, does not depend only on empirical evidence, is not\nnecessarily modified in the face of conflicting evidence, and\ntypically involves supernatural forces or entities. Because they are\nnot a part of nature, supernatural entities cannot be investigated by\nscience. In this sense, science and religion are separate and address\naspects of human understanding in different ways. Attempts to pit\nscience and religion against each other create controversy where none\nneeds to exist. (NASIM 2008: 12)\n", "\nThis view of science and religion seems promising on many fronts. If\nthe above statement on science and religion is accepted, then it seems\nto insure there is minimal conflict between two dynamic domains of\nwhat the Academies refer to as “human experience”. The\nNational Academies do seem to be correct in implying that the key\nelements of many religions do not admit of direct scientific\ninvestigations nor rest “only on empirical evidence”.\nNeither God nor Allah nor Brahman (the divine as conceived of in\nJudaism, Christianity, Islam, and Hinduism) is a physical or material\nobject or process. It seems, then, that the divine or the sacred and\nmany other elements in world religions (meditation, prayer, sin and\nforgiveness, deliverance from craving) can only be indirectly\ninvestigated scientifically. So, a neurologist can produce detailed\nstudies of the brains of monks and nuns when they pray and meditate,\nand there can be comparative studies of the health of those who\npractice a religion and those who do not, but it is very hard to\nconceive of how to scientifically measure God or Allah or Brahman or\nthe Dao, heaven, and so on. Despite the initial plausibility of the\nAcademies stance, however, it may be problematic.", "\nFirst, a minor (and controversial) critical point in response to the\nAcademies: The statement makes use of the terms “supernatural\nforces or entities” that “are not part of nature”.\nThe term “supernatural” is not the standard term used to\nrefer only to God or the divine, probably (in part) because in English the\nterm “supernatural” refers not just to God or the divine,\nbut also to poltergeists, ghosts, devils, witches, mediums, oracles,\nand so on. The later are a panoply of what is commonly thought of as\npreposterous superstition. (The similarity of the terms\nsupernatural and superstitious may not be an\naccident.) The standard philosophical term to reference God in the\nEnglish language, from the seventeenth century onward, is\ntheism (from the Greek theos for god/God). So,\nrather than the statement refer to “supernatural forces or\nentities”, a more charitable phrase might refer to how many\nworld religions are theistic or involve some sacred reality that is\nnot directly, empirically measurable. ", "\nMoving beyond this minor point about terminology, religious beliefs\nhave traditionally and today been thought of as subject to\nevidence. Evidence for religious beliefs have included appeal to the\ncontingency of the cosmos and principles of explanation, the\nostensibly purposive nature of the cosmos, the emergence of\nconsciousness, and so on. Evidence against religious belief have\nincluded appeal to the evident, quantity of evil in the cosmos, the\nsuccess of the natural sciences, and so on. ", "\nOne reason, however, for supporting the Academies notion that religion\nand science do not overlap is the fact that in modern science there\nhas been a bracketing of reference to minds and the mental. That is,\nthe sciences have been concerned with a mind-independent physical\nworld, whereas in religion this is chiefly a domain concerned with\nmind (feelings, emotions, thoughts, ideas, and so on), created minds\nand (in the case of some religions) the mind of God. The science of\nKepler, Copernicus, Galileo, and Newton was carried out with an\nexplicit study of the world without appeal to anything involving what\ntoday would be referred to as the psychological, the mind or the\nmental. So, Newton’s laws of motion about the attraction and\nrepulsion of material objects make no mention of how love or desire or\nemotional need might be required to explain the motion of two material\nbodies to embrace romantically. The bracketing of mind from the\nphysical sciences was not a sign of early scientists having any doubts\nabout the existence, power and importance of minds. That is, from\nKepler through Newton and on to the early twentieth century,\nscientists themselves did not doubt the causal significance of minds;\nthey simply did not include minds (their own or the minds of others)\namong the data of what they were studying. But interestingly, each of\nthe early modern scientists believed that what they were studying was\nin some fashion made possible by the whole of the natural world\n(terrestrial and celestial) being created and sustained in existence\nby a Divine Mind, an all good, necessarily existing Creator. They had\nan overall or comprehensive worldview according to which science\nitself was reasonable and made sense. Scientists have to have a kind\nof faith or trust in their methods and that the cosmos is so ordered\nthat their methods are effective and reliable. The earliest modern\nscientists thought such faith (in what Einstein refers to as\n“the rationality and intelligibility of the world” (Cain\n2015: 42, quoting a 1929 statement in Einstein 1954 [1973: 262]) was\nreasonable because of their belief in the existence of God (Cain\n2015).", "\nWhether there is sufficient evidence for or against some religious\nconception of the cosmos will be addressed in\n section 4.\n Let us contrast briefly, however, two very different views on whether\ncontemporary science has undermined religious belief.", "\nAccording to Steven Pinker, science has shown the beliefs of many\nreligions to be false.", "\n\n\nTo begin with, the findings of science entail that the belief systems\nof all the world’s traditional religions and\ncultures—their theories of the origins of life, humans, and\nsocieties—are factually mistaken. We know, but our ancestors did\nnot, that humans belong to a single species of African primate that\ndeveloped agriculture, government, and writing late in its history. We\nknow that our species is a tiny twig of a genealogical tree that\nembraces all living things and that emerged from prebiotic chemicals\nalmost four billion years ago.… We know that the laws governing\nthe physical world (including accidents, disease, and other\nmisfortunes) have no goals that pertain to human well-being. There is\nno such thing as fate, providence, karma, spells, curses, augury,\ndivine retribution, or answered prayer—though the discrepancy\nbetween the laws of probability and the workings of cognition may\nexplain why people think there is. (Pinker 2013)\n", "\nFollowing up on Pinker, it should be noted that it would not be\nscientifically acceptable today to appeal to miracles or to direct\nacts of God. Any supposed miracle would (to many, if not all\nscientists) be a kind of defeat and to welcome an unacceptable\nmystery. This is why some philosophers of science propose that the\nsciences are methodologically atheistic. That is, while\nscience itself does not pass judgment on whether God exists (even\nthough some philosophers of science do), appealing to God’s\nexistence forms no part of their scientific theories and\ninvestigations.", "\nThere is some reason to think that Pinker’s case may be\noverstated, however, and that it would be more fair to characterize\nthe sciences as methodologically agnostic (simply not taking\na view on the matter of whether or not God exists) rather than\natheistic (taking a position on the matter). First, Pinker’s\nexamples of what science has shown to be wrong, seem unsubstantial. As\nMichael Ruse points out:", "\n\n\nThe arguments that are given for suggesting that science necessitates\natheism are not convincing. There is no question that many of the\nclaims of religion are no longer tenable in light of modern science.\nAdam and Eve, Noah’s Flood, the sun stopping for Joshua, Jonah\nand the whale, and much more. But more sophisticated Christians know\nthat already. The thing is that these things are not all there is to\nreligions, and many would say that they are far from the central\nclaims of religion—God existing and being creator and having a\nspecial place for humans and so forth. (Ruse 2014: 74–75)\n", "\nRuse goes on to note that religions address important concerns that go\nbeyond what is approachable only from the standpoint of the natural\nsciences.", "\n\n\nWhy is there something rather than nothing? What is the purpose of it\nall? And (somewhat more controversially) what are the basic\nfoundations of morality and what is sentience? Science takes the world\nas given Science sees no ultimate purpose to reality… I would\nsay that as science does not speak to these issues, I see no reason\nwhy the religious person should not offer answers. They cannot be\nscientific answers. They must be religious answers—answers that\nwill involve a God or gods. There is something rather than nothing\nbecause a good God created them from love out of nothing. The purpose\nof it all is to find eternal bliss with the Creator. Morality is a\nfunction of God’s will; it is doing what He wants us to do.\nSentience is that by which we realize that we are made in God’s\nimage. We humans are not just any old kind of organism. This does not\nmean that the religious answers are beyond criticism, but they must be\nanswered on philosophical or theological grounds and not simply\nbecause they are not scientific. (2014: 76)\n", "\nThe debate over religion and science is ongoing (for promising work,\nsee Stenmark 2001, 2004)." ], "section_title": "4. Religion and Science", "subsections": [] }, { "main_content": [ "\nFor much of the history of philosophy of religion, there has been\nstress on the assessment of theism. Non-theistic concepts of the\ndivine have increasingly become part of philosophy of religion (see,\nfor example, Buckareff & Nagasawa 2016; Diller & Kasher 2013;\nand Harrison 2006, 2012, 2015).\n Section 6\n makes special note of this broadening of horizons. Theism still has\nsome claim for special attention given the large world population that\nis aligned with theistic traditions (the Abrahamic faiths and theistic\nHinduism) and the enormity of attention given to the defense and\ncritique of theism in philosophy of religion historically and\ntoday." ], "section_title": "5. Philosophical Reflection on Theism and Its Alternatives", "subsections": [ { "content": [ "\nSpeculation about divine attributes in theistic tradition has often\nbeen carried out in accord with what is currently referred to as\nperfect being theology, according to which God is understood\nto be maximally excellent or unsurpassable in greatness. This\ntradition was (famously) developed by Anselm of Canterbury\n(1033/4–1109). For a contemporary work offering an historic\noverview of Anselmian theism, see Yujin Nagasawa’s Maximal\nGod; A New Defense of Perfect Being Theism (2017). Divine\nattributes in this tradition have been identified by philosophers as\nthose attributes that are the greatest compossible set of great-making\nproperties; properties are compossible when they can be instantiated\nby the same being. Traditionally, the divine attributes have been\nidentified as omnipotence, omniscience, perfect goodness, worthiness\nof worship, necessary of non-contingent existence, and eternality\n(existing outside of time or atemporally). Each of these attributes\nhas been subject to nuanced different analysis, as noted below. God\nhas also been traditionally conceived to be incorporeal or immaterial,\nimmutable, impassable, omnipresent. And unlike Judaism and Islam,\nChristian theists conceive of God as triune (the Godhead is not\nhomogenous but consists of three Persons, Father, Son, and Holy\nSpirit) and incarnate as Jesus of Nazareth (fully God and fully\nhuman).", "\nOne of the tools philosophers use in their investigation into divine\nattributes involve thought experiments. In thought experiments,\nhypothetical cases are described—cases that may or may not\nrepresent the way things are. In these descriptions, terms normally\nused in one context are employed in expanded settings. Thus, in\nthinking of God as omniscient, one might begin with a\nnon-controversial case of a person knowing that a proposition is true,\ntaking note of what it means for someone to possess that knowledge and\nof the ways in which the knowledge is secured. A theistic thought\nexperiment would seek to extend our understanding of knowledge as we\nthink of it in our own case, working toward the conception of a\nmaximum or supreme intellectual excellence befitting the religious\nbelievers’ understanding of God. Various degrees of refinement\nwould then be in order, as one speculates not only about the extent of\na maximum set of propositions known but also about how these might be\nknown. That is, in attributing omniscience to God, would one thereby\nclaim God knows all truths in a way that is analogous to the way we\ncome to know truths about the world? Too close an analogy would\nproduce a peculiar picture of God relying upon, for example,\ninduction, sensory evidence, or the testimony of others. One move in\nthe philosophy of God has been to assert that the claim “God\nknows something” employs the word “knows” univocally\nwhen read as picking out the thesis that God knows something,\nwhile it uses the term in only a remotely analogical sense if read as\nidentifying how God knows (Swinburne 1977).", "\nUsing thought experiments often employs an appearance principle. One\nversion of an appearance principle is that a person has a reason for\nbelieving that some state of affairs (SOA) is possible if she can\nconceive, describe or imagine the SOA obtaining and she knows of no\nindependent reasons for believing the SOA is impossible. As stated the\nprinciple is advanced as simply offering a reason for believing the\nSOA to be possible, and it thus may be seen a advancing a prima\nfacie reason. But it might be seen as a secundum facie\nreason insofar as the person carefully scrutinizes the SOA and its\npossible defeaters (see Taliaferro & Knuths 2017). Some\nphilosophers are skeptical of appealing to thought experiments (see\nVan Inwagen 1998; for a defense see Taliaferro 2002, Kwan 2013, and\nSwinburne 1979; for general treatments see Sorensen 1992 and Gendler\n& Hawthorne 2002).", "\nImagine there is a God who knows the future free action of human\nbeings. If God does know you will freely do some act X, then it\nis true that you will indeed do X. But if you are free, would\nyou not be free to avoid doing X? Given that it is foreknown\nyou will do X, it appears you would not be free to refrain from\nthe act. ", "\nInitially this paradox seems easy to dispel. If God knows about your\nfree action, then God knows that you will freely do something and that\nyou could have refrained from it. God’s foreknowing the act does\nnot make it necessary. Does not the paradox only arise because the\nproposition, “Necessarily, if God knows X, then\nX” is confused with “If God knows X, then\nnecessarily X?” After all, it is necessarily the case\nthat if someone knows you are reading this entry right now, then it is\ntrue that you are reading this entry, but your reading this entry may\nstill be seen as a contingent, not necessary state of affairs. But the\nproblem is not so easily diffused, however, because God’s\nknowledge, unlike human knowledge, is infallible, and if God\ninfallibly knows that some state of affairs obtains then it cannot be\nthat the state of affairs does not obtain. Think of what is sometimes\ncalled the necessity of the past. Once a state of affairs has\nobtained, it is unalterably or necessarily the case that it did\noccur. If the future is known precisely and comprehensively,\nisn’t the future like the past, necessarily or unalterably the\ncase? If the problem is put in first-person terms and one imagines God\nforeknows you will freely turn to a different entry in this\nEncyclopedia (moreover, God knows with unsurpassable precision when\nyou will do so, which entry you will select and what you will think\nabout it), then an easy resolution of the paradox seems elusive. To\nhighlight the nature of this problem, imagine God tells you what you\nwill freely do in the next hour. Under such conditions, is it still\nintelligible to believe you have the ability to do otherwise if it is\nknown by God as well as yourself what you will indeed elect to do?\nSelf-foreknowledge, then, produces an additional related problem\nbecause the psychology of choice seems to require prior ignorance\nabout what will be choose.", "\nVarious replies to the freedom-foreknowledge debate have been given.\nSome adopt compatibilism, affirming the compatibility of free will and\ndeterminism, and conclude that foreknowledge is no more threatening to\nfreedom than determinism. While some prominent philosophical theists\nin the past have taken this route (most dramatically Jonathan Edwards\n(1703–1758)), this seems to be the minority position in\nphilosophy of religion today (exceptions include Paul Helm, John\nFischer, and Lynne Baker). A second position adheres to the\nlibertarian outlook, which insists that freedom involves a radical,\nindeterminist exercise of power, and concludes that God cannot know\nfuture free action. What prevents such philosophers from denying that\nGod is omniscient is that they contend there are no truths about\nfuture free actions, or that while there are truths about the future,\nGod either cannot know those truths (Swinburne) or freely decides not\nto know them in order to preserve free choice (John Lucas). On the\nfirst view, prior to someone’s doing a free action, there is no\nfact of the matter that he or she will do a given act. This is in\nkeeping with a traditional, but controversial, interpretation of\nAristotle’s philosophy of time and truth. Aristotle may have\nthought it was neither true nor false prior to a given sea battle\nwhether a given side would win it. Some theists, such as Richard\nSwinburne, adopt this line today, holding that the future cannot be\nknown. If it cannot be known for metaphysical reasons, then\nomniscience can be analyzed as knowing all that it is possible to\nknow. That God cannot know future free action is no more of a\nmark against God’s being omniscient than God’s inability\nto make square circles is a mark against God’s being omnipotent.\nOther philosophers deny the original paradox. They insist that\nGod’s foreknowledge is compatible with libertarian freedom and\nseek to resolve the quandary by claiming that God is not bound in time\n(God does not so much foreknow the future as God knows what for us is\nthe future from an eternal viewpoint) and by arguing that the unique\nvantage point of an omniscient God prevents any impingement on\nfreedom. God can simply know the future without this having to be\ngrounded on an established, determinate future. But this only works if\nthere is no necessity of eternity analogous to the necessity of the\npast. Why think that we have any more control over God’s\ntimeless belief than over God’s past belief? If not, then there\nis an exactly parallel dilemma of timeless knowledge. For outstanding\ncurrent analysis of freedom and foreknowledge, see the work of Linda\nZagzebski.", "\nCould there be a being that is outside time? In the great monotheistic\ntraditions, God is thought of as without any kind of beginning or end.\nGod will never, indeed, can never, cease to be. Some philosophical\ntheists hold that God’s temporality is very much like ours in\nthe sense that there is a before, during, and an after for God, or a\npast, present, and future for God. This view is sometimes referred to\nas the thesis that God is everlasting. Those adopting a more radical\nstance claim that God is independent of temporality, arguing either\nthat God is not in time at all, or that God is\n“simultaneously” at or in all times. This is sometimes\ncalled the view that God is eternal as opposed to everlasting.", "\nWhy adopt the more radical stance? One reason, already noted, is that\nif God is not temporally bound, there may be a resolution to the\nearlier problem of reconciling freedom and foreknowledge. As St.\nAugustine of Hippo put it: ", "\n\n\nso that of those things which emerge in time, the future, indeed, are\nnot yet, and the present are now, and the past no longer are; but all\nof these are by Him comprehended in His stable and eternal presence.\n(The City of God, XI.21) \n", "\nIf God is outside time, there may also be a secure foundation\nexplaining God’s immutability (changelessness),\nincorruptibility, and immortality. Furthermore, there may be an\nopportunity to use God’s standing outside of time to launch an\nargument that God is the creator of time.", "\nThose affirming God to be unbounded by temporal sequences face several\npuzzles which I note without trying to settle. If God is somehow at or\nin all times, is God simultaneously at or in each? If so, there is the\nfollowing problem. If God is simultaneous with the event of Rome\nburning in 410 CE, and also simultaneous with your reading this entry,\nthen it seems that Rome must be burning at the same time you are\nreading this entry. (This problem was advanced by Nelson Pike (1970);\nStump and Kretzmann 1981 have replied that the simultaneity involved\nin God’s eternal knowledge is not transitive). A different\nproblem arises with respect to eternity and omniscience. If God is\noutside of time, can God know what time it is now? Arguably, there is\na fact of the matter that it is now, say, midnight on 1 July 2018. A\nGod outside of time might know that at midnight on 1 July 2018 certain\nthings occur, but could God know when it is now that time?\nThe problem is that the more emphasis one places on the claim that\nGod’s supreme existence is independent of time, the more one\nseems to jeopardize taking seriously time as it is known. Finally,\nwhile the great monotheistic traditions provide a portrait of the\nDivine as supremely different from the creation, there is also an\ninsistence on God’s proximity or immanence. For some theists,\ndescribing God as a person or person-like (God loves, acts, knows) is\nnot to equivocate. But it is not clear that an eternal God could be\npersonal. For recent work on God’s relation to time, see work by\nKatherine Rogers (2007, 2008). ", "\nAll known world religions address the nature of good and evil and\ncommend ways of achieving human well-being, whether this be thought of\nin terms of salvation, liberation, deliverance, enlightenment,\ntranquility, or an egoless state of Nirvana. Notwithstanding important\ndifferences, there is a substantial overlap between many of these\nconceptions of the good as witnessed by the commending of the Golden\nRule (“Do unto others as you would have them do unto you”)\nin many religions. Some religions construe the Divine as in some\nrespect beyond our human notions of good and evil. In some forms of\nHinduism, for example, Brahman has been extolled as possessing a sort\nof moral transcendence, and some Christian theologians and\nphilosophers have likewise insisted that God is only a moral agent in\na highly qualified sense, if at all (Davies 1993). To call God good\nis, for them, very different from calling a human being good.", "\nHere are only some of the ways in which philosophers have articulated\nwhat it means to call God good. In treating the matter, there has been\na tendency either to explain God’s goodness in terms of\nstandards that are not God’s creation and thus, in some measure,\nindependent of God’s will, or in terms of God’s will and\nthe standards God has created. The latter view has been termed\ntheistic voluntarism. A common version of theistic\nvoluntarism is the claim that for something to be good or right simply\nmeans that God approves of permits it and for something to be bad or\nwrong means that God disapproves or forbids it.", "\nTheistic voluntarists face several difficulties: moral language seems\nintelligible without having to be explained in terms of the Divine\nwill. Indeed, many people make what they take to be objective moral\njudgments without making any reference to God. If they are using moral\nlanguage intelligibly, how could it be that the very meaning of such\nmoral language should be analyzed in terms of Divine volitions? New\nwork in the philosophy of language may be of use to theistic\nvoluntarists. According to a causal theory of reference,\n“water” necessarily designates H2O. It is not a\ncontingent fact that water is H2O notwithstanding the fact\nthat many people can use the term “water” without knowing\nits composition. Similarly, could it not be the case that\n“good” may refer to that which is willed by God even\nthough many people are not aware of (or even deny) the existence of\nGod? Another difficulty for voluntarism lies in accounting for the\napparent meaningful content of claims like “God is good”.\nIt appears that in calling God or in particular God’s will\n“good” the religious believer is saying more than\n“God wills what God wills”. If so, must not the very\nnotion of goodness have some meaning independent of God’s will?\nAlso at issue is the worry that if voluntarism is accepted, the theist\nhas threatened the normative objectivity of moral judgments. Could God\nmake it the case that moral judgments were turned upside down? For\nexample, could God make cruelty good? Arguably, the moral universe is\nnot so malleable. In reply, some voluntarists have sought to\nunderstand the stability of the moral laws in light of God’s\nimmutably fixed, necessary nature.", "\nBy understanding God’s goodness in terms of God’s being\n(as opposed to God’s will alone), one comes close to the\nnon-voluntarist stand. Aquinas and others hold that God is essentially\ngood in virtue of God’s very being. All such positions are\nnon-voluntarist in so far as they do not claim that what it means for\nsomething to be good is that God wills it to be so. The goodness of\nGod may be articulated in various ways, either by arguing that\nGod’s perfection requires God being good as an agent or by\narguing that God’s goodness can be articulated in terms of other\nDivine attributes such as those outlined above. For example, because\nknowledge is in itself good, omniscience is a supreme good. God has\nalso been considered good in so far as God has created and conserves\nin existence a good cosmos. Debates over the problem of evil (if God\nis indeed omnipotent and perfectly good, why is there evil?) have\npoignancy precisely because one side challenges this chief judgment\nabout God’s goodness. (The debate over the problem of evil is\ntaken up in\n section 5.2.4.)", "\nThe choice between voluntarism and seeing God’s very being as\ngood is rarely strict. Some theists who oppose a full-scale\nvoluntarism allow for partial voluntarist elements. According to one\nsuch moderate stance, while God cannot make cruelty good, God can make\nsome actions morally required or morally forbidden which\notherwise would be morally neutral. Arguments for this have been based\non the thesis that the cosmos and all its contents are God’s\ncreation. According to some theories of property, an agent making\nsomething good gains entitlements over the property. The crucial moves\nin arguments that the cosmos and its contents belong to their Creator\nhave been to guard against the idea that human parents would then\n“own” their children (they do not, because parents are not\nradical creators like God), and the idea that Divine ownership would\npermit anything, thus construing human duties owed to God as the\nduties of a slave to a master (a view to which not all theists have\nobjected). Theories spelling out why and how the cosmos belongs to God\nhave been prominent in all three monotheistic traditions. Plato\ndefended the notion, as did Aquinas and Locke (see Brody 1974 for a\ndefense).", "\nA new development in theorizing about God’s goodness has been\nadvanced in Zagzebski 2004. Zagzebski contends that being an exemplary\nvirtuous person consists in having good motives. Motives have an\ninternal, affective or emotive structure. An emotion is “an\naffective perception of the world” (2004: xvi) that\n“initiates and directs action” (2004: 1). The ultimate\ngrounding of what makes human motives good is that they are in accord\nwith the motives of God. Zagzebski’s theory is perhaps the most\nambitious virtue theory in print, offering an account of human virtues\nin light of theism. Not all theists resonate with her bold claim that\nGod is a person who has emotions, but many allow that (at least in\nsome analogical sense) God may be see as personal and having affective\nstates.", "\nOne other effort worth noting to link judgments of good and evil with\njudgments about God relies upon the ideal observer theory of ethics.\nAccording to this theory, moral judgments can be analyzed in terms of\nhow an ideal observer would judge matters. To say an act is right\nentails a commitment to holding that if there were an ideal observer,\nit would approve of the act; to claim an act is wrong entails the\nthesis that if there were an ideal observer, it would disapprove of\nit. The theory can be found in works by Hume, Adam Smith, R.M. Hare,\nand R. Firth (see Firth 1952 [1970]). The ideal observer is variously\ndescribed, but typically is thought of as an impartial omniscient\nregarding non-moral facts (facts that can be grasped without already\nknowing the moral status or implications of the fact—for\ninstance, “He did something bad” is a moral fact;\n“He hit Smith” is not), and as omnipercipient\n(Firth’s term for adopting a position of universal affective\nappreciation of the points of view of all involved parties). The\ntheory receives some support from the fact that most moral disputes\ncan be analyzed in terms of different parties challenging each other\nto be impartial, to get their empirical facts straight, and to be more\nsensitive—for example, by realizing what it feels like to be\ndisadvantaged. The theory has formidable critics and defenders. If\ntrue, it does not follow that there is an ideal observer, but if it is\ntrue and moral judgments are coherent, then the idea of an ideal\nobserver is coherent. Given certain conceptions of God in the three\ngreat monotheistic traditions, God fits the ideal observer description\n(and more besides, of course). This need not be unwelcome to atheists.\nShould an ideal observer theory be cogent, a theist would have some\nreason for claiming that atheists committed to normative, ethical\njudgments are also committed to the idea of a God or a God-like being.\n(For a defense of a theistic form of the ideal observer theory, see\nTaliaferro 2005a; for criticism see Anderson 2005. For further work on\nGod, goodness, and morality, see Evans 2013 and Hare 2015. For\ninteresting work on the notion of religious authority, see Zagzebski\n2012.)", "\nIt should be noted that in addition to attention to the classical\ndivine attributes discussed in this section, there has also been\nphilosophical work on divine simplicity, immutability, impassibility,\nomnipresence, God’s freedom, divine necessity, sovereignty,\nGod’s relationship with abstract objects, Christian teachings\nabout the Trinity, the incarnation, atonement, the sacraments, and\nmore." ], "subsection_title": "5.1 Philosophical Reflection on Divine Attributes" }, { "content": [ "\nIn some introductory philosophy textbooks and anthologies, the\narguments for God’s existence are presented as ostensible proofs\nwhich are then shown to be fallible. For example, an argument from the\napparent order and purposive nature of the cosmos will be criticized\non the grounds that, at best, the argument would establish there is a\npurposive, designing intelligence at work in the cosmos. This falls\nfar short of establishing that there is a God who is omnipotent,\nomniscient, benevolent, and so on. But two comments need to be made:\nFirst, that “meager” conclusion alone would be enough to\ndisturb a scientific naturalist who wishes to rule out all such\ntranscendent intelligence. Second, few philosophers today advance a\nsingle argument as a proof. Customarily, a design argument might be\nadvanced alongside an argument from religious experience, and the\nother arguments to be considered below. True to Hempel’s advice\n(cited earlier) about comprehensive inquiry, it is increasingly common\nto see philosophies—scientific naturalism or\ntheism—advanced with cumulative arguments, a whole range of\nconsiderations, and not with a supposed knock-down, single proof.", "\nThis section surveys some of the main theistic arguments.", "\nThere is a host of arguments under this title; version of the argument\nworks, then it can be deployed using only the concept of God as\nmaximally excellent and some modal principles of inference, that is,\nprinciples concerning possibility and necessity. The argument need not\nresist all empirical support, however, as shall be indicated. The\nfocus of the argument is the thesis that, if there is a God, then\nGod’s existence is necessary. In other words, God’s\nexistence is not contingent—God is not the sort of being that\njust happens to exist or not exist. That necessary existence is built\ninto the concept of God can be supported by appealing to the way God\nis conceived in Jewish, Christian, and Islamic traditions. This would\ninvolve some a posteriori, empirical research into the way\nGod is thought of in these traditions. Alternatively, a defender of\nthe ontological argument might hope to convince others that the\nconcept of God is the concept of a being that exists necessarily by\nbeginning with the idea of a maximally perfect being. If there were a\nmaximally perfect being, what would it be like? It has been argued\nthat among its array of great-making qualities (omniscience and\nomnipotence) would be necessary existence. Once fully articulated, it\ncan be argued that a maximally perfect being which existed necessarily\ncould be called “God”. For an interesting, recent\ntreatment of the relationship between the concept of there being a\nnecessarily existing being and there being a God, see Necessary\nExistence by Alexander Pruss and Joshua Rasmussen (2018: chapters\none to three).", "\nThe ontological argument goes back to St. Anselm (1033/34–1109),\nbut this section shall explore a current version relying heavily on\nthe principle that if something is possibly necessarily the case, then\nit is necessarily the case (or, to put it redundantly, it is\nnecessarily necessary). The principle can be illustrated in the case\nof propositions. That six is the smallest perfect number (that number\nwhich is equal to the sum of its divisors including one but not\nincluding itself) does not seem to be the sort of thing that might\njust happen to be true. Rather, either it is necessarily true or\nnecessarily false. If the latter, it is not possible, if the former,\nit is possible. If one knows that it is possible that six is the\nsmallest perfect number, then one has good reason to believe that.\nDoes one have reason to think it is possible that God exists\nnecessarily? Defenders of the argument answer in the affirmative and\ninfer that God exists. There have been hundreds of objections and\nreplies to this argument. Perhaps the most ambitious objection is that\nthe same sort of reasoning can be used to argue that God cannot exist;\nfor if it is possible that God not exist and necessary existence is\npart of the meaning of “God”, then it follows that God\ncannot exist.", "\nClassical, alternative versions of the ontological argument are\npropounded by Anselm, Spinoza, and Descartes, with current versions by\nAlvin Plantinga, Charles Hartshorne, Norman Malcolm, and C. Dore;\nclassical critics include Gaunilo and Kant, and current critics are\nmany, including William Rowe, J. Barnes, G. Oppy, and J. L. Mackie.\nThe latest book-length treatments of the ontological argument are two\ndefenses: Rethinking the Ontological Argument by Daniel\nDombrowski (2006) and Yujin Nagasawa’s Maximal God; A New\nDefence of Perfect Being Theism (2017). Not every advocate of\nperfect being theology embraces the ontological argument. Famously\nThomas Aquinas did not accept the ontological argument. Alvin\nPlantinga, who is one of the philosophers responsible for the revival\nof interest in the ontological argument, contends that while he,\npersonally, takes the argument to be sound (because he believes that\nthe conclusion that God exists necessarily is true, which entails that\nthe premise, that it is possible that God exists necessarily is true)\nhe does not think the argument has sufficient force to convince an\natheist (Plantinga 1974: 216–217).", "\nArguments in this vein are more firmly planted in empirical, a\nposteriori reflection than the ontological argument, but some\nversions employ a priori reasons as well. There are various\nversions. Some argue that the cosmos had an initial cause outside it,\na First Cause in time. Others argue that the cosmos has a necessary,\nsustaining cause from instant to instant, whether or not the cosmos\nhad a temporal origin. The two versions are not mutually exclusive,\nfor it is possible both that the cosmos had a First Cause and that it\nhas a continuous, sustaining cause.", "\nThe cosmological argument relies on the intelligibility of the notion\nof there being at least one powerful being which is self-existing or\nwhose origin and continued being does not depend on any other being.\nThis could be either the all-out necessity of supreme pre-eminence\nacross all possible worlds used in versions of the ontological\nargument, or a more local, limited notion of a being that is uncaused\nin the actual world. If successful, the argument would provide reason\nfor thinking there is at least one such being of extraordinary power\nresponsible for the existence of the cosmos. At best, it may not\njustify a full picture of the God of religion (a First Cause would be\npowerful, but not necessarily omnipotent), but it would nonetheless\nchallenge naturalistic alternatives and provide some reason theism.\n(The later point is analogous to the idea that evidence that there was\nsome life on another planet would not establish that such life is\nintelligent, but it increases—perhaps only slightly—the\nhypothesis that there is intelligent life on another planet.)", "\nBoth versions of the argument ask us to consider the cosmos in its\npresent state. Is the world as we know it something that necessarily\nexists? At least with respect to ourselves, the planet, the solar\nsystem and the galaxy, it appears not. With respect to these items in\nthe cosmos, it makes sense to ask why they exist rather than not. In\nrelation to scientific accounts of the natural world, such enquiries\ninto causes make abundant sense and are perhaps even essential\npresuppositions of the natural sciences. Some proponents of the\nargument contend that we know a priori that if something\nexists there is a reason for its existence. So, why does the cosmos\nexist? Arguably, if explanations of the contingent existence of the\ncosmos (or states of the cosmos) are only in terms of other contingent\nthings (earlier states of the cosmos, say), then a full cosmic\nexplanation will never be attained. However, if there is at least one\nnecessarily (non-contingent) being causally responsible for the\ncosmos, the cosmos does have an explanation. At this point the two\nversions of the argument divide.", "\nArguments to a First Cause in time contend that a continuous temporal\nregress from one contingent existence to another would never account\nfor the existence of the cosmos, and they conclude that it is more\nreasonable to accept there was a First Cause than to accept either a\nregress or the claim that the cosmos just came into being from\nnothing. Arguments to a sustaining cause of the cosmos claim that\nexplanations of why something exists now cannot be adequate without\nassuming a present, contemporaneous sustaining cause. The arguments\nhave been based on the denial of all actual infinities or on the\nacceptance of some infinities (for instance, the coherence of\nsupposing there to be infinitely many stars) combined with the\nrejection of an infinite regress of explanations solely involving\ncontingent states of affairs. The latter has been described as a\nvicious regress as opposed to one that is benign. There are plausible\nexamples of vicious infinite regresses that do not generate\nexplanations: for instance, imagine that Tom explains his possession\nof a book by reporting that he got it from A who got it from\nB, and so on to infinity. This would not explain how Tom got\nthe book. Alternatively, imagine a mirror with light reflected in it.\nWould the presence of light be successfully explained if one claimed\nthat the light was a reflection of light from another mirror, and the\nlight in that mirror came from yet another mirror, and so on to\ninfinity? Consider a final case. You come across a word you do not\nunderstand; let it be “ongggt”. You ask its meaning and\nare given another word which is unintelligible to you, and so on,\nforming an infinite regress. Would you ever know the meaning of the\nfirst term? The force of these cases is to show how similar they are\nto the regress of contingent explanations.", "\nVersions of the argument that reject all actual infinities face the\nembarrassment of explaining what is to be made of the First Cause,\nespecially since it might have some features that are actually\ninfinite. In reply, Craig and others have contended that they have no\nobjection to potential infinities (although the First Cause will never\ncease to be, it will never become an actual infinity). They further\naccept that prior to the creation, the First Cause was not in time, a\nposition relying on the theory that time is relational rather than\nabsolute. The current scientific popularity of the relational view may\noffer support to defenders of the argument.", "\nIt has been objected that both versions of the cosmological argument\nset out an inflated picture of what explanations are reasonable. Why\nshould the cosmos as a whole need an explanation? If everything in the\ncosmos can be explained, albeit through infinite, regressive accounts,\nwhat is left to explain? One may reply either by denying that infinite\nregresses actually do satisfactorily explain, or by charging that the\nfailure to seek an explanation for the whole is arbitrary. The\nquestion, “Why is there a cosmos?” seems a perfectly\nintelligible one. If there are accounts for things in the cosmos, why\nnot for the whole? The argument is not built on the fallacy of\ntreating every whole as having all the properties of its parts. But if\neverything in the cosmos is contingent, it seems just as reasonable to\nbelieve that the whole cosmos is contingent as it is to believe that\nif everything in the cosmos were invisible, the cosmos as a whole\nwould be invisible.", "\nAnother objection is that rather than explaining the contingent\ncosmos, the cosmological argument introduces a mysterious entity of\nwhich we can make very little philosophical or scientific sense. How\ncan positing at least one First Cause provide a better account of the\ncosmos than simply concluding that the cosmos lacks an ultimate\naccount? In the end, the theist seems bound to admit that why the\nFirst Cause created at all was a contingent matter. If, on the\ncontrary, the theist has to claim that the First Cause had to do what\nit did, would not the cosmos be necessary rather than contingent?", "\nSome theists come close to concluding that it was indeed essential\nthat God created the cosmos. If God is supremely good, there had to be\nsome overflowing of goodness in the form of a cosmos (see Stump &\nKretzmann 1981, on the ideas of Dionysius the Areopagite; see Rowe\n2004 for arguments that God is not free). But theists typically\nreserve some role for the freedom of God and thus seek to retain the\nidea that the cosmos is contingent. Defenders of the cosmological\nargument still contend that its account of the cosmos has a\ncomprehensive simplicity lacking in alternative views. God’s\nchoices may be contingent, but not God’s existence and the\nDivine choice of creating the cosmos can be understood to be\nprofoundly simple in its supreme, overriding endeavor, namely to\ncreate something good. Swinburne has argued that accounting for\nnatural laws in terms of God’s will provides for a simple,\noverarching framework within which to comprehend the order and\npurposive character of the cosmos (see also Foster 2004).", "\nDefenders of the cosmological argument include Swinburne, Richard\nTaylor, Hugo Meynell, Timothy O’Connor, Bruce Reichenbach,\nRobert Koons, Alexander Pruss, and William Rowe; prominent opponents\ninclude Antony Flew, Michael Martin, Howard Sobel, Graham Oppy,\nNicholas Everitt, and J. L Mackie. While Rowe had defended the\ncosmological argument, his reservations about the principle of\nsufficient reason prevents his accepting the argument as fully\nsatisfying.", "\nThese arguments focus on characteristics of the cosmos that seem to\nreflect the design or intentionality of God or, more modestly, of one\nor more powerful, intelligent God-like, purposive forces. Part of the\nargument may be formulated as providing evidence that the cosmos is\nthe sort of reality that would be produced by an intelligent being,\nand then arguing that positing this source is more reasonable than\nagnosticism or denying it. As in the case of the cosmological\nargument, the defender of the teleological argument may want to claim\nit only provides some reason for thinking there is a God. It\nmay be that some kind of cumulative case for theism would require\nconstruing various arguments as mutually reinforcing. If successful in\narguing for an intelligent, trans-cosmos cause, the teleological\nargument may provide some reason for thinking that the First Cause of\nthe cosmological argument (if it is successful) is purposive, while\nthe ontological argument (if it has some probative force) may provides\nsome reason for thinking that it makes sense to posit a being that has\nDivine attributes and necessarily exists. Behind all of them an\nargument from religious experience (to be addressed below) may provide\nsome reasons to seek further support for a religious conception of the\ncosmos and to question the adequacy of naturalism.", "\nOne version of the teleological argument will depend on the\nintelligibility of purposive explanation. In our own human case it\nappears that intentional, purposive explanations are legitimate and\ncan truly account for the nature and occurrence of events. In thinking\nabout an explanation for the ultimate character of the cosmos, is it\nmore likely for the cosmos to be accounted for in terms of a powerful,\nintelligent agent or in terms of a naturalistic scheme of final laws\nwith no intelligence behind them? Theists employing the teleological\nargument draw attention to the order and stability of the cosmos, the\nemergence of vegetative and animal life, the existence of\nconsciousness, morality, rational agents and the like, in an effort to\nidentify what might plausibly be seen as purposive explicable features\nof the cosmos. Naturalistic explanations, whether in biology or\nphysics, are then cast as being comparatively local in application\nwhen held up against the broader schema of a theistic metaphysics.\nDarwinian accounts of biological evolution will not necessarily assist\nus in thinking through why there are either any such laws or any\norganisms to begin with. Arguments supporting and opposing the\nteleological argument will then resemble arguments about the\ncosmological argument, with the negative side contending that there is\nno need to move beyond a naturalistic account, and the positive side\naiming to establish that failing to go beyond naturalism is\nunreasonable.", "\nIn assessing the teleological argument, consider the objection from\nuniqueness. The cosmos is utterly unique. There is no access to\nmultiple universes, some of which are known to be designed and some\nare known not to be. Without being able o compare the cosmos to\nalternative sets of cosmic worlds, the argument fails. Replies to this\nobjection have contended that were we to insist that inferences in\nunique cases are out of order, then this would rule out otherwise\nrespectable scientific accounts of the origin of the cosmos. Besides,\nwhile it is not possible to compare the layout of different cosmic\nhistories, it is in principle possible to envisage worlds that seem\nchaotic, random, or based on laws that cripple the emergence of life.\nNow we can envisage an intelligent being creating such worlds, but,\nthrough considering their features, we can articulate some marks of\npurposive design to help judge whether the cosmos is more reasonably\nbelieved to be designed rather than not designed. Some critics appeal\nto the possibility that the cosmos has an infinite history to bolster\nand re-introduce the uniqueness objection. Given infinite time and\nchance, it seems likely that something like our world will come into\nexistence, with all its appearance of design. If so, why should we\ntake it to be so shocking that our world has its apparent design, and\nwhy should explaining the world require positing one or more\nintelligent designers? Replies repeat the earlier move of insisting\nthat if the objection were to be decisive, then many seemingly\nrespectable accounts would also have to fall by the wayside. It is\noften conceded that the teleological argument does not demonstrate\nthat one or more designers are required; it seeks rather to establish\nthat positing such purposive intelligence is reasonable and preferable\nto naturalism. Recent defenders of the argument include George\nSchlesinger, Robin Collins, and Richard Swinburne. It is rejected by\nJ. L. Mackie, Michael Martin, Nicholas Everitt, and many others.", "\nOne feature of the teleological argument currently receiving increased\nattention focuses on epistemology. It has been argued by Richard\nTaylor (1963), Alvin Plantinga (2011 and in Beilby 2002), and others\nthat if we reasonably rely on our cognitive faculties, it is\nreasonable to believe that these are not brought about by naturalistic\nforces—forces that are entirely driven by chance or are the\noutcome of processes not formed by an overriding intelligence. An\nillustration may help to understand the argument. Imagine Tom coming\nacross what appears to be a sign reporting some information about his\ncurrent altitude (some rocks in a configuration giving him his current\nlocation and precise height above sea-level in meters). If he had\nreason to believe that this “sign” was totally the result\nof chance configurations, would he be reasonable to trust it? Some\ntheists argue that it would not be reasonable, and that trusting our\ncognitive faculties requires us to accept that they were formed by an\noverarching, good, creative agent. This rekindles Descartes’\npoint about relying on the goodness of God to ensure that our\ncognitive faculties are in good working order. Objections to this\nargument center on naturalistic explanations, especially those\nfriendly to evolution. In evolutionary epistemology, one tries to\naccount for the reliability of cognitive faculties in terms of trial\nand error leading to survival. A rejoinder by theists is that survival\nalone is not necessarily linked to true beliefs. It could, in\nprinciple, be false beliefs that enhance survival. In fact, some\natheists think that believing in God has been crucial to\npeople’s survival, though the belief is radically false.\nEvolutionary epistemologists reply that the lack of a\nnecessary link between beliefs that promote survival and\ntruth and the fact that some false beliefs or unreliable belief\nproducing mechanisms promote survival nor falls far short of\nundermining evolutionary epistemology. See Martin (1990), Mackie\n(1983), and Tooley (see Tooley’s chapters 2, 4, and 6 in\nPlantinga & Tooley 2008), among others, object to the epistemic\nteleological argument.", "\nAnother recent development in teleological argumentation has involved\nan argument from fine-tuning.", "\nFine tuning arguments contend that life would not exist were it not\nfor the fact that multiple physical parameters (e.g., the cosmological\nconstant and the ratio of the mass of the neutron to the mass of the\nproton) have numerical values that fall within a range of values known\nto be life-permitting that is very narrow compared to the range of\nvalues that are compatible with current physical theory and are known\nto be life-prohibiting. For example, even minor changes to the nuclear\nweak force would not have allowed for stars, nor would stars have\nendured if the ratio of electromagnetism to gravity had been much\ndifferent. John Leslie observes: ", "\n\n\nAlterations by less than one part in a billion to the expansion speed\nearly in the Big Bang would have led to runaway expansion, everything\nquickly becoming so dilute that no stars could have formed, or else to\ngravitational collapse inside under a second. (Leslie 2007: 76) \n", "\nRobin Collins and others have argued that theism better accounts for\nthe fine tuning than naturalism (see Collins 2009; for criticism of\nthe argument, see Craig & Smith 1993). For a collection of\narticles covering both sides of the debate and both biological and\ncosmological design arguments, see Manson 2003.", "\nA more sustained objection against virtually all versions of the\nteleological argument takes issue with the assumption that the cosmos\nis good or that it is the sort of thing that would be brought about by\nan intelligent, completely benevolent being. This leads us directly to\nthe next central concern of the philosophy of God. ", "\nIf there is a God who is omnipotent, omniscient, and completely good,\nwhy is there evil? The problem of evil is the most widely considered\nobjection to theism in both Western and Eastern philosophy. There are\ntwo general versions of the problem: the deductive or logical version,\nwhich asserts that the existence of any evil at all (regardless of its\nrole in producing good) is incompatible with God’s existence;\nand the probabilistic version, which asserts that given the quantity\nand severity of evil that actually exists, it is unlikely that God\nexists. The deductive problem is currently less commonly debated\nbecause many (but not all) philosophers acknowledge that a thoroughly\ngood being might allow or inflict some harm under certain morally\ncompelling conditions (such as causing a child pain when removing a\nsplinter). More intense debate concerns the likelihood (or even\npossibility) that there is a completely good God given the vast amount\nof evil in the cosmos. Such evidential arguments from evil may be\ndeductive or inductive arguments but they include some attempt to show\nthat some known fact about evil bears a negative evidence relation to\ntheism (e.g., it lowers its probability or renders it improbable)\nwhether or not it is logically incompatible with theism. Consider\nhuman and animal suffering caused by death, predation, birth defects,\nravaging diseases, virtually unchecked human wickedness, torture,\nrape, oppression, and “natural disasters”. Consider how\noften those who suffer are innocent. Why should there be so much\ngratuitous, apparently pointless evil?", "\nIn the face of the problem of evil, some philosophers and theologians\ndeny that God is all-powerful and all-knowing. John Stuart Mill took\nthis line, and panentheist theologians today also question the\ntraditional treatments of Divine power. According to panentheism, God\nis immanent in the world, suffering with the oppressed and working to\nbring good out of evil, although in spite of God’s efforts, evil\nwill invariably mar the created order. Another response is to think of\nGod as being very different from a moral agent. Brian Davies and\nothers have contended that what it means for God to be good is\ndifferent from what it means for an agent to be morally good (Davies\n2006). See also Mark Murphy’s 2017 book God’s Own\nEthics; Norms of Divine Agency and the Argument from Evil. A\ndifferent, more substantial strategy is to deny the existence of evil,\nbut it is difficult to reconcile traditional monotheism with moral\nskepticism. Also, insofar as we believe there to be a God worthy of\nworship and a fitting object of human love, the appeal to moral\nskepticism will carry little weight. The idea that evil is a privation\nor twisting of the good may have some currency in thinking through the\nproblem of evil, but it is difficult to see how it alone could go very\nfar to vindicate belief in God’s goodness. Searing pain and\nendless suffering seem altogether real even if they are analyzed as\nbeing philosophically parasitic on something valuable. The three great\nmonotheistic, Abrahamic traditions, with their ample insistence on the\nreality of evil, offer little reason to try to defuse the problem of\nevil by this route. Indeed, classical Judaism, Christianity, and Islam\nare so committed to the existence of evil that a reason to reject evil\nwould be a reason to reject these religious traditions. What would be\nthe point of the Judaic teaching about the Exodus (God liberating the\npeople of Israel from slavery), or the Christian teaching about the\nincarnation (Christ revealing God as love and releasing a Divine power\nthat will, in the end, conquer death), or the Islamic teaching of\nMohammed (the holy prophet of Allah, whom is all-just and\nall-merciful) if slavery, hate, death, and injustice did not\nexist?", "\nIn part, the magnitude of the difficulty one takes the problem of evil\nto pose for theism will depend upon one’s commitments in other\nareas of philosophy, especially ethics, epistemology, and metaphysics.\nIf in ethics you hold that there should be no preventable suffering\nfor any reason, regardless of the cause or consequence, then the\nproblem of evil will conflict with your acceptance of traditional\ntheism. Moreover, if you hold that any solution to the problem of evil\nshould be evident to all persons, then again traditional theism is in\njeopardy, for clearly the “solution” is not evident to\nall. Debate has largely centered on the legitimacy of adopting some\nmiddle position: a theory of values that would preserve a clear\nassessment of the profound evil in the cosmos as well as some\nunderstanding of how this might be compatible with the existence of an\nall powerful, completely good Creator. Could there be reasons why God\nwould permit cosmic ills? If we do not know what those reasons might\nbe, are we in a position to conclude that there are none or that there\ncould not be any? Exploring different possibilities will be shaped by\none’s metaphysics. For example, if you do not believe there is\nfree will, then you will not be moved by any appeal to the positive\nvalue of free will and its role in bringing about good as offsetting\nits role in bringing about evil.", "\nTheistic responses to the problem of evil distinguish between a\ndefense and a theodicy. A defense seeks to establish that rational\nbelief that God exists is still possible (when the defense is employed\nagainst the logical version of the problem of evil) and that the\nexistence of evil does not make it improbable that God exists (when\nused against the probabilistic version). Some have adopted the defense\nstrategy while arguing that we are in a position to have rational\nbelief in the existence of evil and in a completely good God who hates\nthis evil, even though we may be unable to see how these two beliefs\nare compatible. A theodicy is more ambitious and is typically part of\na broader project, arguing that it is reasonable to believe that God\nexists on the basis of the good as well as the evident evil of the\ncosmos. In a theodicy, the project is not to account for each and\nevery evil, but to provide an overarching framework within which to\nunderstand at least roughly how the evil that occurs is part of some\noverall good—for instance, the overcoming of evil is itself a\ngreat good. In practice, a defense and a theodicy often appeal to\nsimilar factors, the first and foremost being what many call the\nGreater Good Defense.", "\nIn the Greater Good Defense, it is contended that evil can be\nunderstood as either a necessary accompaniment to bringing about\ngreater goods or an integral part of these goods. Thus, in a version\noften called the Free Will Defense, it is proposed that free creatures\nwho are able to care for each other and whose welfare depends on each\nother’s freely chosen action constitute a good. For this good to\nbe realized, it is argued, there must be the bona fide\npossibility of persons harming each other. The free will defense is\nsometimes used narrowly only to cover evil that occurs as a result,\ndirect or indirect, of human action. But it has been speculatively\nextended by those proposing a defense rather than a theodicy to cover\nother evils which might be brought about by supernatural agents other\nthan God. According to the Greater Good case, evil provides an\nopportunity to realize great values, such as the virtues of courage\nand the pursuit of justice. Reichenbach (1982), Tennant (1930),\nSwinburne (1979), and van Inwagen (2006) have also underscored the\ngood of a stable world of natural laws in which animals and humans\nlearn about the cosmos and develop autonomously, independent of the\ncertainty that God exists. Some atheists accord value to the good of\nliving in a world without God, and these views have been used by\ntheists to back up the claim that God might have had reason to create\na cosmos in which Divine existence is not overwhelmingly obvious to\nus. If God’s existence were overwhelmingly obvious, then\nmotivations to virtue might be clouded by self-interest and by the\nbare fear of offending an omnipotent being. Further, there may even be\nsome good to acting virtuously even if circumstances guarantee a\ntragic outcome. John Hick (1966 [1977]) so argued and has developed\nwhat he construes to be an Irenaean approach to the problem of evil\n(named after St. Irenaeus of the second century). On this approach, it\nis deemed good that humanity develops the life of virtue gradually,\nevolving to a life of grace, maturity, and love. This contrasts with a\ntheodicy associated with St. Augustine, according to which God made\nus perfect and then allowed us to fall into perdition, only to be\nredeemed later by Christ. Hick thinks the Augustinian model fails\nwhereas the Irenaean one is credible.", "\nSome have based an argument from the problem of evil on the charge\nthat this is not the best possible world. If there were a supreme,\nmaximally excellent God, surely God would bring about the best\npossible creation. Because this is not the best possible creation,\nthere is no supreme, maximally excellent God. Following Adams (1987),\nmany now reply that the whole notion of a best possible world, like\nthe highest possible number, is incoherent. For any world that can be\nimagined with such and such happiness, goodness, virtue and so on, a\nhigher one can be imagined. If the notion of a best possible world is\nincoherent, would this count against belief that there could be a\nsupreme, maximally excellent being? It has been argued on the contrary\nthat Divine excellences admit of upper limits or maxima that are not\nquantifiable in a serial fashion (for example, Divine omnipotence\ninvolves being able to do anything logically or metaphysically\npossible, but does not require actually doing the greatest number of\nacts or a series of acts of which there can be no more).", "\nThose concerned with the problem of evil clash over the question of\nhow one assesses the likelihood of Divine existence. Someone who\nreports seeing no point to the existence of evil or no justification\nfor God to allow it seems to imply that if there were a point they\nwould see it. Note the difference between seeing no point and not\nseeing a point. In the cosmic case, is it clear that if there were a\nreason justifying the existence of evil, we would see it? William Rowe\nthinks some plausible understanding of God’s justificatory\nreason for allowing the evil should be detectable, but that there are\ncases of evil that are altogether gratuitous. Defenders like William\nHasker (1989) and Stephen Wykstra (1984) reply that these cases are\nnot decisive counter-examples to the claim that there is a good God.\nThese philosophers hold that we can recognize evil and grasp our duty\nto do all in our power to prevent or alleviate it. But we should not\ntake our failure to see what reason God might have for allowing evil\nto count as grounds for thinking that there is no reason. This later\nmove has led to a position commonly called skeptical theism.\nMichael Bergmann, Michael Rea, William Alston and others have argued\nthat we have good reason to be skeptical about whether we can assess\nwhether ostensibly gratuitous evils may or may not be permitted by an\nall-good God (Bergmann 2012a and 2012b, 2001; Bergmann & Rea 2005;\nfor criticism see Almeida & Oppy 2003; Draper 2014, 2013,\n1996). Overall, it needs to be noted that from the alleged fact that\nwe would be unlikely to see a reason for God to allow some evil if\nthere were one, it only follows that our failure to see such a reason\nis not strong evidence against theism.", "\nFor an interesting practical application of the traditional problem of\nevil to the topic of the ethics of procreation, see Marsh 2015. It has\nbeen argued that if one does believe that the world is not good, then\nthat can provide a prima facie reason against procreation.\nWhy should one bring children into a world that is not good? Another\ninteresting, recent development in the philosophy of religion\nliterature has been the engagement of philosophers with ostensible\nevils that God commands in the Bible (see Bergmann, Murray, & Rea\n2010). For a fascinating engagement with the problem of evil that\nemploys Biblical narratives, see Eleonore Stumps’ Wandering\nin Darkness (2010). The treatment of the problem of evil has also\nextended to important reflection on the suffering of non-human animals\n(see S. Clark 1987, 1995, 2017; Murray 2008; Meister 2018). Problems\nraised by evil and suffering are multifarious and are being addressed\nby contemporary philosophers across the religious and non-religious\nspectrums. See, for example, The History of Evil edited by\nMeister and Taliaferro, in six volumes with over 130 contributors from\nvirtually all religious and secular points of view, and the recent\nThe Cambridge Companion to the Problem of Evil edited by\nMeister and Moser (2017).", "\nSome portraits of an afterlife seem to have little bearing on our\nresponse to the magnitude of evil here and now. Does it help to\nunderstand why God allows evil if all victims will receive happiness\nlater? But it is difficult to treat the possibility of an afterlife as\nentirely irrelevant. Is death the annihilation of persons or an event\ninvolving a transfiguration to a higher state? If you do not think\nthat it matters whether persons continue to exist after death, then\nsuch speculation is of little consequence. But suppose that the\nafterlife is understood as being morally intertwined with this life,\nwith opportunity for moral and spiritual reformation, transfiguration\nof the wicked, rejuvenation and occasions for new life, perhaps even\nreconciliation and communion between oppressors seeking forgiveness\nand their victims. Then these considerations might help to defend\nagainst arguments based on the existence of evil. Insofar as one\ncannot rule out the possibility of an afterlife morally tied to our\nlife, one cannot rule out the possibility that God brings some good\nout of cosmic ills. ", "\nThe most recent work on the afterlife in philosophy of religion has\nfocused on the compatibility of an individual afterlife with some\nforms of physicalism. Arguably, a dualist treatment of human persons\nis more promising. If you are not metaphysically identical with your\nbody, then perhaps the annihilation of your body is not the\nannihilation of you. Today, a range of philosophers have argued that\neven if physicalism is true, an afterlife is still possible (Peter van\nInwagen, Lynne Baker, Trenton Merricks, Kevin Corcoran). The import of\nthis work for the problem of evil is that the possible redemptive\nvalue of an afterlife should not be ruled out (without argument) if\none assumes physicalism to be true. (For an extraordinary, rich\nresource on the relevant literature, see The Oxford Handbook of\nEschatology, edited by J. Walls, 2007.)", "\nPerhaps the justification most widely offered for religious belief\nconcerns the occurrence of religious experience or the cumulative\nweight of testimony of those claiming to have had religious\nexperiences. Putting the latter case in theistic terms, the argument\nappeals to the fact that many people have testified that they have\nfelt God’s presence. Does such testimony provide evidence that\nGod exists? That it is evidence has been argued by Jerome Gellman,\nKeith Yandell, William Alston, Caroline Davis, Gary Gutting, Kai-Man\nKwan, Richard Swinburne, Charles Taliaferro, and others. That it is\nnot (or that its evidential force is trivial) is argued by Michael\nMartin, J. L. Mackie, Kai Nielson, Matthew Bagger, John Schellenberg,\nWilliam Rowe, Graham Oppy, and others. In an effort to stimulate\nfurther investigation, consider the following sketch of some of the\nmoves and countermoves in the debate. ", "\nObjection: Religious experience cannot be experience\nof God for perceptual experience is only sensory and if God is\nnon-physical, God cannot be sensed.", "\nReply: The thesis that perceptual experience is only\nsensory can be challenged. Yandell marks out some experiences (as when\none has “a feeling” someone is present but without having\nany accompanying sensations) that might provide grounds for\nquestioning a narrow sensory notion of perceptual experience.", "\nObjection: Testimony to have experienced God is only\ntestimony that one thinks one has experienced God; it is only\ntestimony of a conviction, not evidence.", "\nReply: The literature on religious experience\ntestifies to the existence of experience of some Divine being on the\nbasis of which the subject comes to think the experience is of God. If\nread charitably, the testimony is not testimony to a conviction, but\nto experiences that form the grounds for the conviction. (See Bagger\n1999 for a vigorous articulation of this objection, and note the reply\nby Kai-man Kwam 2003).", "\nObjection: Because religious experience is unique,\nhow could one ever determine whether it is reliable? We simply lack\nthe ability to examine the object of religious experience in order to\ntest whether the reported experiences are indeed reliable.", "\nReply: As we learned from Descartes, all our\nexperiences of external objects face a problem of uniqueness. It is\npossible in principle that all our senses are mistaken and we do not\nhave the public, embodied life we think we lead. We cannot step out of\nour own subjectivity to vindicate our ordinary perceptual beliefs any\nmore than in the religious case. (See the debate between William\nAlston [2004] and Evan Fales [2004]).", "\nObjection: Reports of religious experience differ\nradically and the testimony of one religious party neutralizes the\ntestimony of others. The testimony of Hindus cancels out the testimony\nof Christians. The testimony of atheists to experience God’s\nabsence cancels out the testimony of “believers”.", "\nReply: Several replies might be offered here.\nTestimony to experience the absence of God might be better understood\nas testimony not to experience God. Failing to experience God might be\njustification for believing that there is no God only to the extent\nthat we have reason to believe that if God exists God would be\nexperienced by all. Theists might even appeal to the claim by many\natheists that it can be virtuous to live ethically with atheist\nbeliefs. Perhaps if there is a God, God does not think this is\naltogether bad, and actually desires religious belief to be fashioned\nunder conditions of trust and faith rather than knowledge. The\ndiversity of religious experiences has caused some defenders of the\nargument from religious experience to mute their conclusion. Thus,\nGutting (1982) contends that the argument is not strong enough to\nfully vindicate a specific religious tradition, but that it is strong\nenough to overturn an anti-religious naturalism. Other defenders use\ntheir specific tradition to deal with ostensibly competing claims\nbased on different sorts of religious experiences. Theists have\nproposed that more impersonal experiences of the Divine represent only\none aspect of God. God is a person or is person-like, but God can also\nbe experienced, for example, as sheer luminous unity. Hindus have\nclaimed the experience of God as personal is only one stage in the\noverall journey of the soul to truth, the highest truth being that\nBrahman transcends personhood. (For a discussion of these objections\nand replies and references, see Taliaferro 1998.)", "\nHow one settles the argument will depend on one’s overall\nconvictions in many areas of philosophy. The holistic, interwoven\nnature of both theistic and atheistic arguments can be readily\nillustrated. If you diminish the implications of religious experience\nand have a high standard regarding the burden of proof for any sort of\nreligious outlook, then it is highly likely that the classical\narguments for God’s existence will not be persuasive. Moreover,\nif one thinks that theism can be shown to be intellectually confused\nfrom the start, then theistic arguments from religious experience will\ncarry little weight. Testimony to have experienced God will have no\nmore weight than testimony to have experienced a round square, and\nnon-religious explanations of religious experience—like those of\nFreud (a result of wish-fulfillment), Marx (a reflection of the\neconomic base), or Durkheim (a product of social forces)—will\nincrease their appeal. If, on the other hand, you think the theistic\npicture is coherent and that the testimony of religious experience\nprovides some evidence for theism, then your assessment of the\nclassical theistic arguments might be more favorable, for they would\nserve to corroborate and further support what you already have some\nreason to believe. From such a vantage point, appeal to\nwish-fulfillment, economics, and social forces might have a role, but\nthe role is to explain why some parties do not have experiences of God\nand to counter the charge that failure to have such experiences\nprovides evidence that there is no religious reality. (For an\nexcellent collection of recent work on explaining the emergence and\ncontinuation of religious experience, see Schloss & Murray (eds.)\n2009.)", "\nThere is not space to cover the many other arguments for and against\nthe existence of God, but several additional arguments are briefly\nnoted. The argument from miracles starts from specific extraordinary\nevents, arguing that they provide reasons for believing there to be a\nsupernatural agent or, more modestly, reasons for skepticism about the\nsufficiency of a naturalistic world view. The argument has attracted\nmuch philosophical attention, especially since David Hume’s\nrejection of miracles. The debate has turned mainly on how one defines\na miracle, understands the laws of nature, and specifies the\nprinciples of evidence that govern the explanation of highly unusual\nhistorical occurrences. There is considerable debate over whether\nHume’s case against miracles simply begs the question against\n“believers”. Detailed exposition is impossible in this\nshort entry. Taliaferro has argued elsewhere that Hume’s case\nagainst the rationality of belief in miracles is best seen as part of\nhis overall case for a form of naturalism (Taliaferro 2005b).", "\nThere are various arguments that are advanced to motivate religious\nbelief. One of the most interesting and popular is a wager argument\noften associated with Pascal (1623–1662). It is designed to\noffer practical reasons to cultivate a belief in God. Imagine that you\nare unsure whether there is or is not a God. You have it within your\npower to live on either assumption and perhaps, through various\npractices, to get yourself to believe one or the other. There would be\ngood consequences of believing in God even if your belief were false,\nand if the belief were true you would receive even greater good. There\nwould also be good consequences of believing that there is no God, but\nin this case the consequences would not alter if you were correct. If,\nhowever, you believe that there is no God and you are wrong, then you\nwould risk losing the many goods which follow from the belief that God\nexists and from actual Divine existence. On this basis, it may seem\nreasonable to believe there is a God.", "\nIn different forms the argument may be given a rough edge (for\nexample, imagine that if you do not believe in God and there is a God,\nhell is waiting). It may be put as an appeal to individual\nself-interest (you will be better off) or more generally (believers\nwhose lives are bound together can realize some of the goods\ncomprising a mature religious life). Objectors worry about whether one\never is able to bring choices down to just such a narrow\nselection—for example, to choose either theism or naturalism.\nSome think the argument is too thoroughly egotistic and thus offensive\nto religion. Many of these objections have generated some plausible\nreplies (Rescher 1985). (For a thoroughgoing exploration of the\nrelevant arguments, see the collection of essays edited by Jeffrey\nJordan (1994).)", "\nRecent work on Pascalian wagering has a bearing on work on the nature\nof faith (is it voluntary or involuntary?), its value (when, if ever,\nis it a virtue?), and relation to evidence (insofar as faith involves\nbelief, is it possible to have faith without evidence?). For an\noverview and promising analysis, see Chappell (1996), Swinburne\n(1979), and Schellenberg (2005). A promising feature of such new work\nis that it is often accompanied by a rich understanding of revelation\nthat is not limited to a sacred scripture, but sees a revelatory role\nin scripture plus the history of its interpretation, the use of\ncreeds, icons, and so on (see the work of William Abraham [1998]).", "\nA burgeoning question in recent years is whether the cognitive science\nof religion (CSR) has significance for the truth or rationality of\nreligious commitment. According to CSR, belief in supernatural agents\nappears to be cognitively natural (Barrett 2004, Kelemen 2004, Dennett\n2006, De Cruz, H., & De Smedt, J. 2010) and easy to spread (Boyer\n2001). The naturalness of religion thesis has led some, including\nAlvin Plantinga it seems (2011: 60), to imply that we have scientific\nevidence for Calvin’s sensus divinitatis. But others\nhave argued that CSR can intensify the problem of divine hiddenness,\nsince diverse religious concepts are cognitively natural and early\nhumans seem to have lacked anything like a theistic concept (Marsh\n2013). There are many other questions being investigated about CSR,\nsuch as whether it provides a debunking challenge to religion (Murray\n& Schloss 2009), whether it poses a cultural challenge for\nreligious outlooks like Schellenberg’s Ultimism (Marsh 2014),\nand whether it challenges human dignity (Audi 2013). Needless to say,\nat the present time, there is nothing like a clear consensus on\nwhether CSR should be seen as worrisome, welcome, or neither, by\nreligious believers.", "\nFor some further work on the framework of assessing the evidence for\nand against theism (and other religious and secular worldviews) see C.\nS. Evans 2010, Chandler and Harrison 2012. In the last twenty years\nthere has been increasing attention given to the aesthetic dimension\nof arguments for and against religiously significant conceptions of\nultimate reality and of the meaning of life (see Brown 2004; Wynn\n2013; Hedley 2016; Mawson 2016; Taliaferro & Evans 2010,\n2013)." ], "subsection_title": "5.2 God’s Existence" } ] }, { "main_content": [ "\nIn the midst of the new work on religious traditions, there has been a\nsteady, growing representation of non-monotheistic traditions. An\nearly proponent of this expanded format was Ninian Smart\n(1927–2001), who, through many publications, scholarly as well\nas popular, secured philosophies of Hinduism and Buddhism as\ncomponents in the standard canon of English-speaking philosophy of\nreligion. ", "\nSmart championed the thesis that there are genuine differences between\nreligious traditions. He therefore resisted seeing some core\nexperience as capturing the essential identity of being religious.\nUnder Smart’s tutelage, there has been considerable growth in\ncross-cultural philosophy of religion. Wilfred Cantwell Smith\n(1916–2000) also did a great deal to improve the representation\nof non-Western religions and reflection. See, for example, the\nRoutledge series Investigating Philosophy of Religion with\nRoutledge with volumes already published or forthcoming on Buddhism\n(Burton 2017), Hinduism (Ranganathan 2018), Daoism, and Confucianism.\nThe five volume Encyclopedia of Philosophy of Religion\n(mentioned earlier) to be published by Wiley Blackwell (projected for\n2021) will have ample contributions on the widest spectrum of\nphilosophical treatments of diverse religions to date.", "\nThe explanation of philosophy of religion has involved fresh\ntranslations of philosophical and religious texts from India, China,\nSoutheast Asia, and Africa. Exceptional figures from non-Western\ntraditions have an increased role in cross-cultural philosophy of\nreligion and religious dialogue. The late Bimal Krishna Matilal\n(1935–1991) made salient contributions to enrich Western\nexposure to Indian philosophy of religion (see Matilal 1882). Among the\nmid-twentieth-century Asian philosophers, two who stand out for\nspecial note are T.R.V. Murti (1955) and S.N. Dasgupta\n(1922–1955). Both brought high philosophical standards along\nwith the essential philology to educate Western thinkers. As evidence\nof non-Western productivity in the Anglophone world, see Arvind Sharma\n1990 and 1995. There are now extensive treatments of pantheism and\nstudent-friendly guides to diverse religious conceptions of the\ncosmos. ", "\nThe expanded interest in religious pluralism has led to extensive\nreflection on the compatibility and possible synthesis of religions.\nJohn Hick is the preeminent synthesizer of religious traditions. Hick\n(1973 a and b)) advanced a complex\npicture of the afterlife involving components from diverse traditions.\nOver many publications and many years, Hick has moved from a broadly\nbased theistic view of God to what Hick calls “the Real”,\na noumenal sacred reality. Hick claims that different religions\nprovide us with a glimpse or partial access to the Real. In an\ninfluential article, “The New Map of the Universe of\nFaiths” (1973a), Hick raised the possibility that many of the\ngreat world religions are revelatory of the Real. ", "\n\n\nSeen in [an] historical context these movements of faith—the\nJudaic-Christian, the Buddhist, the Hindu, the Muslim—are not\nessentially rivals. They began at different times and in different\nplaces, and each expanded outwards into the surrounding world of\nprimitive natural religion until most of the world was drawn up into\none or the other of the great revealed faiths. And once this global\npattern had become established it has ever since remained fairly\nstable… Then in Persia the great prophet Zoroaster appeared;\nChina produced Lao-tzu and then the Buddha lived, the Mahavira, the\nfounder of the Jain religion and, probably about the end of this\nperiod, the writing of the Bhagavad Gita; and Greece produced\nPythagoras and then, ending this golden age, Socrates and Plato. Then\nafter the gap of some three hundred years came Jesus of Nazareth and\nthe emergence of Christianity; and after another gap the prophet\nMohammed and the rise of Islam. The suggestion that we must\nconsider is that these were all movements of the divine\nrevelation. (Hick 1989: 136; emphasis added)\n", "\nHick sees these traditions, and others as well, as different meeting\npoints in which a person might be in relation to the same reality or\nthe Real: ", "\n\n\nThe great world faiths embody different perceptions and conceptions\nof, and correspondingly different responses to, the Real from within\nthe major variant ways of being human; and that within each of them\nthe transformation of human existence from self-centeredness to\nReality-centeredness is taking place. (1989: 240) \n", "\nHick uses Kant to develop his central thesis. ", "\n\n\nKant distinguishes between noumenon and phenomenon, or between a\nDing an sich [the thing itself] and the thing as it appears\nto human consciousness…. In this strand of Kant’s\nthought—not the only strand, but the one which I am seeking to\npress into service in the epistemology of religion—the noumenal\nworld exists independently of our perception of it and the phenomenal\nworld is that same world as it appears to our human\nconsciousness…. I want to say that the noumenal Real is\nexperienced and thought by different human mentalities, forming and\nformed by different religious traditions, as the range of gods and\nabsolutes which the phenomenology of religion reports. (1989:\n241–242)\n", "\nOne advantage of Hick’s position is that it undermines a\nrationale for religious conflict. If successful, this approach would\noffer a way to accommodate diverse communities and undermine what has\nbeen a source of grave conflict in the past. ", "\nHick’s work since the early 1980s provided an impetus for not\ntaking what appears to be religious conflict as outright\ncontradictions. He advanced a philosophy of religion that paid careful\nattention to the historical and social context. By doing so, Hick\nthought that apparently conflicting descriptions of the sacred could\nbe reconciled as representing different perspectives on the same\nreality, the Real (see Hick 2004, 2006).", "\nThe response to Hick’s proposal has been mixed. Some contend\nthat the very concept of “the Real” is incoherent or not\nreligiously adequate. Indeed, articulating the nature of the Real is\nno easy task. Hick writes that the Real ", "\n\n\ncannot be said to be one thing or many, person or thing, substance or\nprocess, good or bad, purposive or non-purposive. None of the concrete\ndescriptions that apply within the realm of human experience can apply\nliterally to the unexperienceable ground of that realm…. We\ncannot even speak of this as a thing or an entity. (1989: 246). \n", "\nIt has been argued that Hick has secured not the equal acceptability\nof diverse religions but rather their unacceptability. In their\nclassical forms, Judaism, Islam, and Christianity diverge. If, say,\nthe Incarnation of God in Christ did not occur, isn’t\nChristianity false? In reply, Hick has sought to interpret specific\nclaims about the Incarnation in ways that do not commit Christians to\nthe “literal truth” of God becoming enfleshed. The\n“truth” of the Incarnation has been interpreted in such\nterms as these: in Jesus Christ (or in the narratives about Christ)\nGod is disclosed. Or: Jesus Christ was so united with God’s will\nthat his actions were and are the functional display of God’s\ncharacter. Perhaps as a result of Hick’s challenge,\nphilosophical work on the incarnation and other beliefs and practice\nspecific to religious traditions have received renewed attention (see,\nfor example, Taliaferro and Meister 2009). Hick has been a leading,\nwidely appreciated force in the expansion of philosophy of religion in\nthe late twentieth century. ", "\nIn addition to the expansion of philosophy of religion to take into\naccount a wider set of religions, the field has also seen an expansion\nin terms of methodology. Philosophers of religion have re-discovered\nmedieval philosophy—the new translations and commentaries of\nmedieval Christian, Jewish, and Islamic texts have blossomed. There is\nnow a self-conscious, deliberate effort to combine work on the\nconcepts in religious belief alongside a critical understanding of\ntheir social and political roots (the work of Foucault has been\ninfluential on this point), feminist philosophy of religion has been\nespecially important in re-thinking what may be called the ethics of\nmethodology and, as this is in some respects the most current debate\nin the field, it is a fitting point to end this entry by highlighting\nthe work of Pamela Sue Anderson (1955–2017) and others.", "\nAnderson (1997 and 2012) seeks to question respects in which gender\nenters into traditional conceptions of God and in their moral and\npolitical repercussions. She also advances a concept of method which\ndelimits justice and human flourishing. A mark of legitimation of\nphilosophy should be the extent to which it contributes to human\nwelfare. In a sense, this is a venerable thesis in some ancient,\nspecifically Platonic philosophy that envisaged the goal and method of\nphilosophy in terms of virtue and the good. Feminist philosophy today\nis not exclusively a critical undertaking, critiquing\n“patriarchy”. For a constructive, subtle treatment of\nreligious contemplation and practice, see Coakley 2002. Another key\nmovement that is developing has come to be called Continental\nPhilosophy of Religion. A major advocate of this new turn is John\nCaputo. This movement approaches the themes of this entry (the concept\nof God, pluralism, religious experience, metaphysics and epistemology)\nin light of Heidegger, Derrida, and other continental philosophers.\n(For a good representation of this movement, see Caputo 2001 and\nCrocket, Putt, & Robins 2014.)" ], "section_title": "6. Religious Pluralism", "subsections": [] } ]

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The Morality of\nProcreation and Parenting, Sarah Hannan, Samantha Brennan, and\nRichard Vernon (eds.), Oxford: Oxford University Press, 65–86.\ndoi:10.1093/acprof:oso/9780199378111.003.0003", "Martin, Michael, 1990, Atheism: A Philosophical Analysis,\nPhiladelphia, PA: Temple University Press.", "Mawson, T.J., 2016, God and the Meanings of Life: What God\nCould and Couldn’t Do to Make Our Lives More Meaningful,\nLondon: Bloomsbury Academic.", "McKim, Robert, 2018, “Why Religious Pluralism is Not Evil\nand is in Some Respects Quite Good” in The History of Evil\nfrom the Mid-Twentieth Century to Today, (The History of Evil,\n6), Jerome Gellman (ed.), London: Routledge, chapter 12.", "Meister, Chad (ed.), 2010, The Oxford Handbook of Religious\nDiversity, Oxford: Oxford University Press.\ndoi:10.1093/oxfordhb/9780195340136.001.0001", "–––, 2018, Evil: A Guide for the\nPerplexed, second edition, London: Bloomsbury.", "Meister, Chad and Paul Moser (eds.), 2017, The Cambridge\nCompanion to the Problem of Evil, Cambridge: Cambridge University\nPress. doi:10.1017/9781107295278", "Meister, Chad and Charles Taliaferro (series editors), 2018,\nHistory of Evil, London: Routledge, 6 volumes\n\n\n\nAngier, Tom P.S. (ed.), The History of Evil in Antiquity: 2000\nBCE – 450 CE, (History of Evil, 1)\n\nMurray, Michael, 2008, Nature Red in tooth and claw,\nOxford: Oxford University Press.\n\nPinsent, Andrew (ed.), The History of Evil in the Medieval\nAge: 450–1450 CE, (History of Evil, 2)\n\nRobinson, Daniel (ed.), The History of Evil in the Early\nModern Age: 1450–1700 CE, (History of Evil, 3)\n\nHedley, Douglas (ed.), The History of Evil in the Eighteenth\nand Nineteenth Centuries: 1700–1900 CE, (History of Evil,\n4)\n\nHarrison, Victoria S. (ed.), The History of Evil in the Early\nTwentieth Century: 1900–1950 CE, (History of Evil, 5)\n\nGellman, Jerome (ed.), The History of Evil from the\nMid-Twentieth Century to Today: 1950–2018, (History of\nEvil, 6)\n", "Angier, Tom P.S. (ed.), The History of Evil in Antiquity: 2000\nBCE – 450 CE, (History of Evil, 1)", "Murray, Michael, 2008, Nature Red in tooth and claw,\nOxford: Oxford University Press.", "Pinsent, Andrew (ed.), The History of Evil in the Medieval\nAge: 450–1450 CE, (History of Evil, 2)", "Robinson, Daniel (ed.), The History of Evil in the Early\nModern Age: 1450–1700 CE, (History of Evil, 3)", "Hedley, Douglas (ed.), The History of Evil in the Eighteenth\nand Nineteenth Centuries: 1700–1900 CE, (History of Evil,\n4)", "Harrison, Victoria S. (ed.), The History of Evil in the Early\nTwentieth Century: 1900–1950 CE, (History of Evil, 5)", "Gellman, Jerome (ed.), The History of Evil from the\nMid-Twentieth Century to Today: 1950–2018, (History of\nEvil, 6)", "Menssen, Sandra and Thomas Sullivan, 2007, The Agnostic\nInquirer: Revelation form a Philosophical Perspective, Grand\nRapids: Eerdmans.", "–––, 2017, “Revelation and\nScripture”, in Abraham and Aquino 2017.\ndoi:10.1093/oxfordhb/9780199662241.013.22", "Matilal, B. K., 1982, Logical and Ethical Issues of Religious\nBelief, Calcutta: University of Calcutta Press.", "Menuge, Angus J.L., 2004, Agents under Fire: Materialism and\nthe Rationality of Science, Lanham, MD: Rowman and\nLittlefield.", "Meynell, Hugo A., 1982, The Intelligible Universe: A\nCosmological Argument, London: Macmillan.", "Mitchell, Basil (ed.), 1971, The Philosophy of Religion,\n(Oxford Readings in Philosophy), Oxford: Oxford University Press.", "–––, 1973, The Justification of Religious\nBelief, London: Macmillan.", "–––, 1994, Faith and Criticism, Oxford:\nOxford University Press.\ndoi:10.1093/acprof:oso/9780198267584.001.0001", "Moreland, James Porter, 2008, Consciousness and the Existence\nof God: A Theistic Argument, (Routledge Studies in the Philosophy\nof Religion, 4), London: Routledge.", "Morris, Thomas V., 1986, The Logic of God Incarnate,\nIthaca, NY: Cornell University Press.", "–––, 1987a, Anselmian Explorations: Essays\nin Philosophical Theology, Notre Dame, IN: University of Notre\nDame Press.", "––– (ed.), 1987b, The Concept of God,\n(Oxford Readings in Philosophy), Oxford: Oxford University Press.", "–––, 1991, Our Idea of God: An Introduction\nto Philosophical Theology, Downers Grove, IL: InterVarsity\nPress.", "Moser, Paul K., 2008, The Elusive God: Reorienting Religious\nEpistemology, Cambridge: Cambridge University Press.\ndoi:10.1017/CBO9780511499012", "–––, 2010, The Evidence for God: Religious\nKnowledge Reexamined, Cambridge: Cambridge University Press.\ndoi:10.1017/CBO9780511817731", "–––, 2017, The God Relationship: The Ethics\nfor Inquiry about the Divine, Cambridge: Cambridge University\nPress. doi:10.1017/9781108164009", "Murphy, Mark C., 2017, God’s Own Ethics: Norms of Divine\nAgency and the Argument from Evil, Oxford: Oxford University\nPress. doi:10.1093/oso/9780198796916.001.0001", "Murray, Michael J., 2008, Nature Red in Tooth and Claw: Theism\nand the Problem of Animal Suffering, Oxford: Oxford University\nPress. doi:10.1093/acprof:oso/9780199237272.001.0001", "Murti, T.R.V., 1955, Central Philosophy of Buddhism: A Study\nof the Mādhyamika System, London: George Allen and\nUnwin.", "Nagasawa, Yujin, 2017, Maximal God: A New Defence of Perfect\nBeing Theism, Oxford: Oxford University Press.\ndoi:10.1093/oso/9780198758686.001.0001", "[NASIM] National Academy of Sciences and Institute of Medicine,\n2008, Science, Evolution, and Creationism, third edition,\nWashington, DC: National Academies Press. doi:10.17226/11876\n [NASIM 2008 quote in this entry is also available online at the National Academy of Sciences]", "Nielsen, Kai, 1996, Naturalism Without Foundations,\nBuffalo, NY: Prometheus Press.", "O’Connor, Timothy, 2008, Theism and Ultimate\nExplanation: The Necessary Shape of Contingency, Oxford:\nBlackwell. doi:10.1002/9781444345490", "Oppy, Graham, 1995, Ontological Arguments and Belief in\nGod, Cambridge: Cambridge University Press.\ndoi:10.1017/CBO9780511663840", "–––, 2006, Arguing About Gods,\nCambridge: Cambridge University Press.\ndoi:10.1017/CBO9780511498978", "–––, 2018, Naturalism and Religion; A\nContemporary Philosophical Investigation, (Investigating\nPhilosophy of Religion), London: Routledge.", "Oppy, Graham Robert and Nick Trakakis (eds.), 2009, The\nHistory of Western Philosophy of Religion, 5 volumes, New York:\nOxford University Press. ", "Padgett, Alan G., 1992, God, Eternity and the Nature of\nTime, New York: St. Martin’s Press.", "Penelhum, Terence, 1983, God and Skepticism: A Study in\nSkepticism and Fideism, Dordrecht: Springer Netherlands.\ndoi:10.1007/978-94-009-7083-0", "–––, 1989, Faith, New York: Macmillan.\n", "Peterson, Michael L., William Hasker, Bruce Reichenbach, and David\nBasinger (eds.), 1991, Reason and Religious Belief: An\nIntroduction to the Philosophy of Religion, first edition, New\nYork: Oxford University Press. Fifth edition, 2012.", "––– (eds.), 1996, Philosophy of Religion:\nSelected Readings, first edition, New York: Oxford University\nPress. Fifth edition, 2014.", "Peterson, Michael L. and Raymond J. VanArragon (eds.), 2004,\nContemporary Debates in Philosophy of Religion, (Contemporary\nDebates in Philosophy), Malden, MA: Blackwell.", "Philipse, Herman, 2012, God in the Age of Science? A Critique\nof Religious Reason, Oxford: Oxford University Press.\ndoi:10.1093/acprof:oso/9780199697533.001.0001", "Phillips, D.Z., 1966, the Concept of Prayer, New York:\nSchocken Books.", "–––, 1976, Religion Without\nExplanation, Oxford: Blackwell. ", "–––, 2001. “Theism Without Theodicy,”\nin S. Davis (ed.), Encountering Evil: Live Options in Theodicy,\nLouisville: Westminster John Knox Press.", "–––, 2004, The Problem of Evil and the\nProblem of God, London: SCM Press. ", "Pike, Nelson, 1970 [2002], God and Timelessness, New\nYork: Schocken Books; reprinted Eugene, OR: Wipf and Stock Publishers,\n2002.", "Pinker, Steven, 2013, “Science Is Not Your Enemy”,\nThe New Republic, August 7. URL =\n <https://newrepublic.com/article/114127/science-not-enemy-humanities>", "Plantinga, Alvin, 1967, God and Other Minds: A Study of the\nRational Justification of Belief in God, Ithaca, NY: Cornell\nUniversity Press.", "–––, 1974, The Nature of Necessity,\nOxford: Oxford University Press. doi:10.1093/0198244142.001.0001", "–––, 1980, Does God Have a Nature?\nMilwaukee, WI: Marquette University Press.", "–––, 1993, Warrant: the Current Debate,\nOxford: Oxford University Press. doi:10.1093/0195078624.001.0001", "–––, 1993, Warrant and Proper Function,\nOxford: Oxford University Press. doi:10.1093/0195078640.001.0001", "–––, 2000, Warranted Christian Belief,\nOxford: Oxford University Press. doi:10.1093/0195131932.001.0001", "–––, 2011, Where the Conflict Really Lies:\nScience, Religion, and Naturalism, New York: Oxford University\nPress. doi:10.1093/acprof:oso/9780199812097.001.0001", "Plantinga, Alvin and Michael Bergmann, 2016, “Religion and\nEpistemology”, in Routledge Encyclopedia of Philosophy,\nTim Crane (ed.), London: Routledge.\ndoi:10.4324/9780415249126-K080-2", "Alvin Plantinga and Michael Tooley, 2008, Knowledge of\nGod, Oxford: Wiley Blackwell.", "Popkin, Richard H., 1999, The Pimlico History of\nPhilosophy, London: Pimlico.", "Proudfoot, Wayne, 1976, God and the Self: Three Types of\nPhilosophy of Religion, Lewisburg, PA: Bucknell University\nPress.", "–––, 1985, Religious Experience,\nBerkeley, CA: University of California Press.", "Pruss, Alexander R. and Joshua L. Rasmussen, 2018, Necessary\nExistence, Oxford: Oxford University Press.\ndoi:10.1093/oso/9780198746898.001.0001", "Putnam, Hilary, 1983, Realism and Reason: Philosophical\nPapers, Volume 3, Cambridge: Cambridge University Press.", "Ranganathan, Shyam, 2018, Hinduism: A Contemporary\nPhilosophical Investigation, (Investigating Philosophy of\nReligion), London: Routledge.", "Re Manning, Russell (ed.), 2013, The Oxford Handbook of\nNatural Theology, Oxford: Oxford University Press.\ndoi:10.1093/oxfordhb/9780199556939.001.0001", "Reichenbach, Bruce R., 1972, The Cosmological Argument: A\nReassessment, Springfield, IL: Thomas Press.", "–––, 1982, Evil and a Good God, New\nYork: Fordham University Press.", "Rescher, Nicholas, 1985, Pascal’s Wager: A Study of\nPractical Reasoning in Philosophical Theology, Notre Dame, IN:\nUniversity of Notre Dame Press.", "Rhees, Rush, 1969, Without Answers, New York: Schocken\nBooks.", "Rogers, Katherin A., 2007, “Anselmian Eternalism: The\nPresence of a Timeless God”, Faith and Philosophy,\n24(1): 3–27. doi:10.5840/faithphil200724134", "–––, 2008, Anselm on Freedom, Oxford:\nOxford University Press.\ndoi:10.1093/acprof:oso/9780199231676.001.0001", "Rowe, William L., 1975, The Cosmological Argument,\nPrinceton: Princeton University Press.", "–––, 1978 [1993], Philosophy of Religion: An\nIntroduction, Belmont: Wadsworth. Second Edition, 1993.", "–––, 2004, Can God Be Free?, Oxford:\nOxford University Press.", "Rundle, Bede, 2004, Why There Is Something Rather than\nNothing, Oxford: Oxford University Press.\ndoi:10.1093/0199270503.001.0001", "Ruse, Michael, 2014, “Atheism and Science”, in The\nCustomization of Science: The Impact of Religious and Political\nWorldviews on Contemporary Science Steve Fuller, Mikael Stenmark,\nUlf Zackariasson (eds), New York: Palgrave, 73–88.\ndoi:10.1057/9781137379610_5", "Schellenberg, J.L., 2005, Prolegomena to Philosophy of\nReligion, Ithaca, NY: Cornell University Press.", "–––, 2007, The Wisdom to Doubt: A\nJustification of Religious Skepticism, Ithaca, NY: Cornell\nUniversity Press.", "–––, 2009, The Will To Imagine: A\nJustification of Skeptical Religion, Ithaca, NY: Cornell\nUniversity Press.", "–––, 2013, Evolutionary Religion,\nOxford: Oxford University Press.\ndoi:10.1093/acprof:oso/9780199673766.001.0001", "–––, 2017, “Religion Without God (And\nWithout Turning East: A New Western Alternative to Traditional\nTheistic Faith”, World and Word, 37(2): 118–127.\n [Schellenberg 2017 available online]", "Schlesinger, George N., 1977, Religion and Scientific\nMethod, Dordrecht: Reidel. doi:10.1007/978-94-010-1235-5", "–––, 1988, New Perspectives on Old-Time\nReligion, New York: Oxford University Press.", "Schloss, Jeffrey and Michael J. Murray (eds.), 2009, The\nBelieving Primate: Scientific, Philosophical, and Theological\nReflections on the Origin of Religion, Oxford ; New York:\nOxford University Press. doi:10.1093/acprof:oso/9780199557028.001.0001\n", "Sessions, William Lad, 1994, The Concept of Faith: A\nPhilosophical Investigation, Ithaca, NY: Cornell University\nPress.", "Sharma, Arvind, 1990, A Hindu Perspective on the Philosophy of\nReligion, New York: St. Martin’s Press.", "–––, 1995, Philosophy of Religion and\nAdvaita Vedanta: A Comparative Study in Religion and Reason,\nUniversity Park, PA: The Pennsylvania State University Press.", "Smart, J.J.C. and J.J. Haldane, 1996, Atheism and Theism,\nOxford: Blackwell. Second edition 2003. doi:10.1002/9780470756225", "Smart, Ninian, 1962 [1986], “Religion as a\nDiscipline?”, Higher Education Quarterly, 17(1):\n48–53; reprinted in his Concept and Empathy: Essays in the\nStudy of Religion, Donald Wiebe (ed.), New York: New York\nUniversity Press, 1986. doi:10.1111/j.1468-2273.1962.tb00978.x", "Sobel, Jordan Howard, 2003, Logic and Theism: Arguments For\nand Against Beliefs in God, Cambridge: Cambridge University\nPress. doi:10.1017/CBO9780511497988", "Sorensen, Roy A., 1992, Thought Experiments, Oxford:\nOxford University Press. doi:10.1093/019512913X.001.0001", "Soskice, Janet Martin, 1985, Metaphor and Religious\nLanguage, Oxford: Clarendon Press.", "Stenmark, Mikael, 2001, Scientism: Science, Ethics, and\nReligion, Aldershot, UK: Ashgate.", "–––, 2004, How to Relate Science and\nReligion: A Multidimensional Model, Grand Rapids, MI:\nEerdmans.", "–––, 2015, “Competing Conceptions of God:\nThe Personal God versus the God beyond Being”, Religious\nStudies, 51(2): 205–220. doi:10.1017/S0034412514000304", "Stiver, Dan R., 1996, The Philosophy of Religious Language:\nSign, Symbol, and Story, Cambridge, MA: Blackwell\nPublishers.", "Stump, Eleonore, 2010, Wandering in Darkness: Narrative and\nthe Problem of Suffering, Oxford: Oxford University Press.\ndoi:10.1093/acprof:oso/9780199277421.001.0001", "Stump, Eleonore and Norman Kretzmann, 1981,\n“Eternity”, The Journal of Philosophy, 78(8):\n429–458; reprinted in Morris 1987b: pp. 219–52.\ndoi:10.2307/2026047", "Swinburne, Richard, 1977, The Coherence of Theism,\nOxford: Clarendon Press. doi:10.1093/0198240708.001.0001", "–––, 1979, The Existence of God,\nOxford: Clarendon Press.\ndoi:10.1093/acprof:oso/9780199271672.001.0001", "–––, 1981, Faith and Reason, Oxford:\nClarendon Press. doi:10.1093/0198247257.001.0001", "–––, 1986, The Evolution of the Soul,\nOxford: Clarendon Press. doi:10.1093/0198236980.001.0001", "–––, 1994, The Christian God, Oxford:\nClarendon Press.", "–––, 1996, Is There a God?, Oxford:\nOxford University Press.\ndoi:10.1093/acprof:oso/9780198235446.001.0001", "–––, 1998, Providence and the Problem of\nEvil, Oxford: Oxford University Press.\ndoi:10.1093/0198237987.001.0001", "Taliaferro, Charles, 1994, Consciousness and the Mind of\nGod, Cambridge: Cambridge University Press.\ndoi:10.1017/CBO9780511520693", "–––, 1998, Contemporary Philosophy of\nReligion, Oxford: Blackwell.", "–––, 2001, “Sensibility and Possibilia: A\nDefense of Thought Experiments”, Philosophia Christi,\n3(2): 403–421.", "–––, 2002, “Philosophy of Religion”,\nin The Blackwell Companion to Philosophy, Nicholas Bunnin and\nE. P. Tsui-James (eds.), second edition, Oxford: Blackwell,\n453–489. doi:10.1002/9780470996362.ch17", "–––, 2005a, “A God’s Eye Point of\nView: The Divine Ethic”, in Harris and Insole 2005:\n76–84.", "–––, 2005b, Evidence and Faith: Philosophy\nof Religion Since the Seventeenth Century, Cambridge: Cambridge\nUniversity Press. doi:10.1017/CBO9780511610370", "–––, 2009, Philosophy of Religion: A\nBeginner’s Guide, Oxford: Oneworld. ", "Taliaferro, Charles and Jil Evans (eds.), 2011, Turning Images\nin Philosophy, Science, and Religion: A New Book of Nature,\nOxford; New York: Oxford University Press.\ndoi:10.1093/acprof:oso/9780199563340.001.0001", "–––, 2013, The Image in Mind: Theism,\nNaturalism, and the Imagination, London: Continuum.", "Taliaferro, Charles and Chad Meister (eds.), 2009, The\nCambridge Companion to Christian Philosophical Theology,\nCambridge: Cambridge University Press.\ndoi:10.1017/CCOL9780521514330", "Taliaferro, Charles, Paul Draper, and Philip L. Quinn, 2010, A\nCompanion to Philosophy of Religion, second edition, (Blackwell\nCompanions to Philosophy, 9), Hoboken, NJ: Wiley-Blackwell.", "Taliaferro, Charles, Victoria S. Harrison, and Stewart Goetz,\n2012, The Routledge Companion to Theism, London:\nRoutledge.", "Taliaferro, Charles and Elliot Knuths, 2017, “Thought\nExperiments in Philosophy of Religion: The Virtues of Phenomenological\nRealism and Values”, Open Theology, 3(1):\n167–173. doi:10.1515/opth-2017-0013", "Taliaferro, Charles and Elsa J. Marty (eds.), 2010 [2018], A\nDictionary of Philosophy of Religion, New York: Continuum. Second\nedition 2018.", "Taylor, Richard, 1963, Metaphysics, Englewood Cliffs, NJ:\nPrentice-Hall.", "Tennant, F.R., 1930, Philosophical Theology (Volume II), Cambridge:\nCambridge University Press.", "Tilghman, Benjamin R., 1994, An Introduction to the Philosophy\nof Religion, Oxford: Blackwell.", "Timpe, Kevin, 2014, Free Will in Philosophical Theology,\nLondon: Bloomsbury.", "Tracy, Thomas F. (ed.), 1994, The God Who Acts: Philosophical\nand Theological Explorations, University Park, PA: Pennsylvania\nState University Press.", "Trigg, Roger, 1989, Reality at Risk, London:\nHarvester.", "–––, 1993, Rationality and Science: Can\nScience Explain Everything?, Oxford: Blackwell.", "Van Cleve, James, 1999, Problems from Kant, Oxford:\nOxford University Press. ", "van Inwagen, Peter, 1983, An Essay on Free Will, Oxford:\nClarendon Press. ", "–––, 1995, God, Knowledge and Mystery:\nEssays in Philosophical Theology, Ithaca, NY: Cornell University\nPress. ", "–––, 1998, “Modal Epistemology”,\nPhilosophical Studies, 92(1/2): 67–84.\ndoi:10.1023/A:1017159501073", "–––, 2006, The Problem of Evil, Oxford:\nOxford University Press.\ndoi:10.1093/acprof:oso/9780199245604.001.0001", "–––, 2017, Thinking about Free Will,\nCambridge: Cambridge University Press. doi:10.1017/9781316711101", "Wainwright, William J., 1981, Mysticism: A Study of Its\nNature, Cognitive Value, and Moral Implications, Madison, WI:\nUniversity of Wisconsin Press.", "–––, 1988, Philosophy of Religion, (The\nWadsworth Basic Issues in Philosophy Series), first edition, Belmont,\nCA: Wadsworth Publishing. Second edition, 1998.", "––– (ed.), 1996, God, Philosophy, and\nAcademic Culture, Atlanta: Scholars Press", "Walls, Jerry L. (ed.), 2007, The Oxford Handbook of\nEschatology, Oxford: Oxford University Press.\ndoi:10.1093/oxfordhb/9780195170498.001.0001", "Ward, Keith, 1974, The Concept of God, Hoboken: Basil\nBlackwell.", "–––, 2002, God, a Guide for the\nPerplexed, London: Oneworld.", "–––, 2014, The Evidence for God: The Case\nfor the Existence of the Spiritual Dimension, London: Darton,\nLongman & Todd.", "–––, 2017, The Christian Idea of God: A\nPhilosophical Foundation for Faith, Cambridge: Cambridge\nUniversity Press. doi:10.1017/9781108297431", "Westphal, Merold, 1984, God, Guilt, and Death: An Existential\nPhenomenology of Religion, Bloomington, IN: Indiana University\nPress.", "Wettstein, Howard, 2012, The Significance of Religious\nExperience, Oxford: Oxford University Press\ndoi:10.1093/acprof:oso/9780199841363.001.0001", "Whitehead, Alfred North, 1929 [1978], Process and Reality: An\nEssay in Cosmology, Cambridge: Cambridge University Press.\nCorrected edition, David Ray Griffin and Donald W. Sherburne (eds),\nNew York: Free Press, 1978. Gifford lectures delivered in the\nUniversity of Edinburgh during the session 1927–28. ", "Wierenga, Edward R., 1989, The Nature of God: An Inquiry into\nDivine Attributes, Ithaca, NY: Cornell University Press.", "Wisdom, J., 1945, “Gods”, Proceedings of the\nAristotelian Society, 45: 185–206.\ndoi:10.1093/aristotelian/45.1.185", "Wittgenstein, Ludwig, 1953, Philosophical Investigations\n(Philosophische Untersuchungen), G.E.M. Anscombe (trans.),\nOxford: Blackwell.", "Wolterstorff, Nicholas, 1976, Reason within the Bounds of\nReligion, Grand Rapids, MI: Eerdmans.", "–––, 1982, “God Everlasting”, in\nContemporary Philosophy of Religion, Steven M. Cahn and David\nShatz (eds.), New York: Oxford University Press.", "Wykstra, Stephen J., 1984, “The Humean Obstacle to\nEvidential Arguments from Suffering: On Avoiding the Evils of\n‘Appearance’”, International Journal for\nPhilosophy of Religion, 16(2): 73–93.\ndoi:10.1007/BF00136567", "Wynn, Mark R., 2013, Renewing the Senses: A Study of the\nPhilosophy and Theology of the Spiritual Life, Oxford: Oxford\nUniversity Press. doi:10.1093/acprof:oso/9780199669981.001.0001", "Yandell, Keith E., 1993, The Epistemology of Religious\nExperience, Cambridge: Cambridge University Press.", "Zagzebski, Linda Trinkaus, 1991, The Dilemma of Freedom and\nForeknowledge, New York: Oxford University Press.\ndoi:10.1093/acprof:oso/9780195107630.001.0001", "–––, 2004, Divine Motivation Theory,\nCambridge: Cambridge University Press.\ndoi:10.1017/CBO9780511606823", "–––, 2008, “Omnisubjectivity”, in\nOxford Studies in Philosophy of Religion, Jonathan L. Kvanvig\n(ed.), Oxford: Oxford University Press, volume 1, 231–247.", "–––, 2012, Epistemic Authority: A Theory of\nTrust, Authority, and Autonomy in Belief, New York: Oxford\nUniversity Press. doi:10.1093/acprof:oso/9780199936472.001.0001" ]

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[ "\nThe relationship between religion and science is the subject of\ncontinued debate in philosophy and theology. To what extent are\nreligion and science compatible? Are religious beliefs sometimes\nconducive to science, or do they inevitably pose obstacles to\nscientific inquiry? The interdisciplinary field of “science and\nreligion”, also called “theology and science”, aims\nto answer these and other questions. It studies historical and\ncontemporary interactions between these fields, and provides\nphilosophical analyses of how they interrelate.", "\nThis entry provides an overview of the topics and discussions in\nscience and religion. Section 1 outlines the scope of both fields, and\nhow they are related. Section 2 looks at the relationship between\nscience and religion in five religious traditions, Christianity,\nIslam, Hinduism, Buddhism, and Judaism. Section 3 discusses\ncontemporary topics of scientific inquiry in which science and\nreligion intersect, focusing on divine action, creation, and human\norigins." ]

[ { "content_title": "1. Science, religion, and how they interrelate", "sub_toc": [ "1.1 A brief history", "1.2 What is science, and what is religion?", "1.3 Taxonomies of the interaction between science and religion", "1.4 The scientific study of religion" ] }, { "content_title": "2. Science and religion in various religions", "sub_toc": [ "2.1 Christianity", "2.2 Islam", "2.3 Hinduism", "2.4 Buddhism", "2.5 Judaism" ] }, { "content_title": "3. Central topics in the debate", "sub_toc": [ "3.1 Divine action and creation", "3.2 Human origins" ] }, { "content_title": "Bibliography", "sub_toc": [ "Works cited", "Other important works" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Science, religion, and how they interrelate", "subsections": [ { "content": [ "\nSince the 1960s, scholars in theology, philosophy, history, and the\nsciences have studied the relationship between science and religion.\nScience and religion is a recognized field of study with dedicated\njournals (e.g., Zygon: Journal of Religion and Science),\nacademic chairs (e.g., the Andreas Idreos Professor of Science and\nReligion at Oxford University), scholarly societies (e.g., the Science\nand Religion Forum), and recurring conferences (e.g., the European\nSociety for the Study of Science and Theology’s biennial\nmeetings). Most of its authors are theologians (e.g., John Haught,\nSarah Coakley), philosophers with an interest in science (e.g., Nancey\nMurphy), or (former) scientists with long-standing interests in\nreligion, some of whom are also ordained clergy (e.g., the physicist\nJohn Polkinghorne, the molecular biophysicist Alister McGrath, and the\natmospheric scientist Katharine Hayhoe). Recently, authors in science\nand religion also have degrees in that interdisciplinary field (e.g.,\nSarah Lane Ritchie).", "\nThe systematic study of science and religion started in the 1960s,\nwith authors such as Ian Barbour (1966) and Thomas F. Torrance (1969)\nwho challenged the prevailing view that science and religion were\neither at war or indifferent to each other. Barbour’s Issues\nin Science and Religion (1966) set out several enduring themes of\nthe field, including a comparison of methodology and theory in both\nfields. Zygon, the first specialist journal on science and\nreligion, was also founded in 1966. While the early study of science\nand religion focused on methodological issues, authors from the late\n1980s to the 2000s developed contextual approaches, including detailed\nhistorical examinations of the relationship between science and\nreligion (e.g., Brooke 1991). Peter Harrison (1998) challenged the\nwarfare model by arguing that Protestant theological conceptions of\nnature and humanity helped to give rise to science in the seventeenth\ncentury. Peter Bowler (2001, 2009) drew attention to a broad movement\nof liberal Christians and evolutionists in the nineteenth and\ntwentieth centuries who aimed to reconcile evolutionary theory with\nreligious belief. In the 1990s, the Vatican Observatory (Castel\nGandolfo, Italy) and the Center for Theology and the Natural Sciences\n(Berkeley, California) co-sponsored a series of conferences on divine\naction and how it can be understood in the light of various\ncontemporary sciences. This resulted in six edited volumes (see\nRussell, Murphy, & Stoeger 2008 for a book-length summary of the\nfindings of this project). ", "\nThe field has presently diversified so much that contemporary\ndiscussions on religion and science tend to focus on specific\ndisciplines and questions. Rather than ask if religion and science\n(broadly speaking) are compatible, productive questions focus on\nspecific topics. For example, Buddhist modernists (see\n section 2.4)\n have argued that Buddhist theories about the self (the no-self) and\nBuddhist practices, such as mindfulness meditation, are compatible and\nare corroborated by neuroscience.", "\nIn the contemporary public sphere, a prominent interaction between\nscience and religion concerns evolutionary theory and\ncreationism/Intelligent Design. The legal battles (e.g., the\nKitzmiller versus Dover trial in 2005) and lobbying surrounding the\nteaching of evolution and creationism in American schools suggest\nthere’s a conflict between religion and science. However, even\nif one were to focus on the reception of evolutionary theory, the\nrelationship between religion and science is complex. For instance, in\nthe United Kingdom, scientists, clergy, and popular writers (the\nso-called Modernists), sought to reconcile science and religion during\nthe late nineteenth and early twentieth century, whereas the US saw the\nrise of a fundamentalist opposition to evolutionary thinking,\nexemplified by the Scopes trial in 1925 (Bowler 2001, 2009).", "\nAnother prominent offshoot of the discussion on science and religion\nis the New Atheist movement, with authors such as Richard Dawkins, Sam\nHarris, Daniel Dennett, and Christopher Hitchens. They argue that\npublic life, including government, education, and policy should be\nguided by rational argument and scientific evidence, and that any form\nof supernaturalism (especially religion, but also, e.g., astrology)\nhas no place in public life. They treat religious claims, such as the\nexistence of God, as testable scientific hypotheses (see, e.g.,\nDawkins 2006).", "\nIn recent decades, the leaders of some Christian churches have issued\nconciliatory public statements on evolutionary theory. Pope John Paul\nII (1996) affirmed evolutionary theory in his message to the\nPontifical Academy of Sciences, but rejected it for the human soul,\nwhich he saw as the result of a separate, special creation. The Church\nof England publicly endorsed evolutionary theory (e.g., C. M. Brown\n2008), including an apology to Charles Darwin for its initial\nrejection of his theory.", "\nThis entry will focus on the relationship between religious and\nscientific ideas as rather abstract philosophical positions, rather\nthan as practices. However, this relationship has a large practical\nimpact on the lives of religious people and scientists (including\nthose who are both scientists and religious believers). A rich\nsociological literature indicates the complexity of these\ninteractions, among others, how religious scientists conceive of this\nrelationship (for recent reviews, see Ecklund 2010, 2021; Ecklund\n& Scheitle 2007; Gross & Simmons 2009).", "\nFor the past fifty years, the discussion on science and religion has\nde facto been on Western science and Christianity: to what\nextent can the findings of Western sciences be reconciled with\nChristian beliefs? The field of science and religion has only recently\nturned to an examination of non-Christian traditions, providing a\nricher picture of interaction." ], "subsection_title": "1.1 A brief history" }, { "content": [ "\nIn order to understand the scope of science and religion and their\ninteractions, we must at least get a rough sense of what science and\nreligion are. After all, “science” and\n“religion” are not eternally unchanging terms with\nunambiguous meanings. Indeed, they are terms that were coined\nrecently, with meanings that vary across contexts. Before the\nnineteenth century, the term “religion” was rarely used.\nFor a medieval author such as Aquinas, the term religio meant\npiety or worship, and was not applied to religious systems\noutside of what he considered orthodoxy (Harrison 2015). The term\n“religion” obtained its considerably broader current\nmeaning through the works of early anthropologists, such as E.B. Tylor\n(1871), who systematically used the term for religions across the\nworld. As a result, “religion” became a comparative\nconcept, referring to traits that could be compared and scientifically\nstudied, such as rituals, dietary restrictions, and belief systems\n(Jonathan Smith 1998).", "\nThe term “science” as it is currently used also became\ncommon in the nineteenth century. Prior to this, what we call\n“science” fell under the terminology of “natural\nphilosophy” or, if the experimental part was emphasized,\n“experimental philosophy”. William Whewell (1834)\nstandardized the term “scientist” to refer to\npractitioners of diverse natural philosophies. Philosophers of science\nhave attempted to demarcate science from other knowledge-seeking\nendeavors, in particular religion. For instance, Karl Popper (1959)\nclaimed that scientific hypotheses (unlike religious and philosophical\nones) are in principle falsifiable. Many authors (e.g., Taylor 1996)\naffirm a disparity between science and religion, even if the meanings\nof both terms are historically contingent. They disagree, however, on\nhow to precisely (and across times and cultures) demarcate the two\ndomains.", "\nOne way to distinguish between science and religion is the claim that\nscience concerns the natural world, whereas religion concerns the\nsupernatural world and its relationship to the natural. Scientific\nexplanations do not appeal to supernatural entities such as gods or\nangels (fallen or not), or to non-natural forces (such as miracles,\nkarma, or qi). For example, neuroscientists typically explain\nour thoughts in terms of brain states, not by reference to an\nimmaterial soul or spirit, and legal scholars do not invoke karmic\nload when discussing why people commit crimes.", "\nNaturalists draw a distinction between methodological\nnaturalism, an epistemological principle that limits scientific\ninquiry to natural entities and laws, and ontological or\nphilosophical naturalism, a metaphysical principle that rejects\nthe supernatural (Forrest 2000). Since methodological naturalism is\nconcerned with the practice of science (in particular, with the kinds\nof entities and processes that are invoked), it does not make any\nstatements about whether or not supernatural entities exist. They\nmight exist, but lie outside of the scope of scientific investigation.\nSome authors (e.g., Rosenberg 2014) hold that taking the results of\nscience seriously entails negative answers to such persistent\nquestions into the existence of free will or moral knowledge. However,\nthese stronger conclusions are controversial.", "\nThe view that science can be demarcated from religion in its\nmethodological naturalism is more commonly accepted. For instance, in\nthe Kitzmiller versus Dover trial, the philosopher of science Robert\nPennock was called to testify by the plaintiffs on whether Intelligent\nDesign was a form of creationism, and therefore religion. If it were,\nthe Dover school board policy would violate the Establishment Clause\nof the First Amendment to the United States Constitution. Building on\nearlier work (e.g., Pennock 1998), Pennock argued that Intelligent\nDesign, in its appeal to supernatural mechanisms, was not\nmethodologically naturalistic, and that methodological naturalism is\nan essential component of science. ", "\nMethodological naturalism is a recent development in the history of\nscience, though we can see precursors of it in medieval authors such\nas Aquinas who attempted to draw a theological distinction\nbetween miracles, such as the working of relics, and unusual natural\nphenomena, such as magnetism and the tides (see Perry & Ritchie\n2018). Natural and experimental philosophers such as Isaac Newton,\nJohannes Kepler, Robert Hooke, and Robert Boyle regularly appealed to\nsupernatural agents in their natural philosophy (which we now call\n“science”). Still, overall there was a tendency to favor\nnaturalistic explanations in natural philosophy. The X-club was a\nlobby group for the professionalization of science founded in 1864 by\nThomas Huxley and friends. While the X-club may have been in part\nmotivated by the desire to remove competition by amateur-clergymen\nscientists in the field of science, and thus to open up the field to\nfull-time professionals, its explicit aim was to promote a science\nthat would be free from religious dogma (Garwood 2008, Barton 2018).\nThis preference for naturalistic causes may have been encouraged by\npast successes of naturalistic explanations, leading authors such as\nPaul Draper (2005) to argue that the success of methodological\nnaturalism could be evidence for ontological naturalism. " ], "subsection_title": "1.2 What is science, and what is religion?" }, { "content": [ "\nSeveral typologies probe the interaction between science and religion.\nFor example, Mikael Stenmark (2004) distinguishes between three views:\nthe independence view (no overlap between science and religion), the\ncontact view (some overlap between the fields), and a union of the\ndomains of science and religion; within these views he recognizes\nfurther subdivisions, e.g., contact can be in the form of conflict or\nharmony. The most influential taxonomy of the relationship between\nscience and religion remains Barbour’s (2000): conflict,\nindependence, dialogue, and integration. Subsequent authors, as well\nas Barbour himself, have refined and amended this taxonomy. However,\nothers (e.g., Cantor & Kenny 2001) have argued that this taxonomy\nis not useful to understand past interactions between both fields.\nNevertheless, because of its enduring influence, it is still\nworthwhile to discuss it in detail.", "\nThe conflict model holds that science and religion are in\nperpetual and principal conflict. It relies heavily on two historical\nnarratives: the trial of Galileo (see Dawes 2016) and the reception of\nDarwinism (see Bowler 2001). Contrary to common conception, the\nconflict model did not originate in two seminal publications,\nnamely John Draper’s (1874) History of the Conflict between\nReligion and Science and Andrew Dickson White’s (1896)\ntwo-volume opus A History of the Warfare of Science with Theology\nin Christendom. Rather, as James Ungureanu (2019) argues, the\nproject of these early architects of the conflict thesis needs to be\ncontextualized in a liberal Protestant tradition of attempting to\nseparate religion from theology, and thus salvage religion. Their work\nwas later appropriated by skeptics and atheists who used their\narguments about the incompatibility of traditional theological views\nwith science to argue for secularization, something Draper and White\ndid not envisage.", "\nThe vast majority of authors in the science and religion field is\ncritical of the conflict model and believes it is based on a shallow\nand partisan reading of the historical record. While the conflict\nmodel is at present a minority position, some have used philosophical\nargumentation (e.g., Philipse 2012) or have carefully re-examined\nhistorical evidence such as the Galileo trial (e.g., Dawes 2016) to\nargue for this model. Alvin Plantinga (2011) has argued that the\nconflict is not between science and religion, but between science and\nnaturalism. In his Evolutionary Argument Against Naturalism (first\nformulated in 1993), Plantinga argues that naturalism is epistemically\nself-defeating: if both naturalism and evolution are true, then\nit’s unlikely we would have reliable cognitive faculties.", "\nThe independence model holds that science and religion\nexplore separate domains that ask distinct questions. Stephen Jay\nGould developed an influential independence model with his NOMA\nprinciple (“Non-Overlapping Magisteria”):", "\n\n\nThe lack of conflict between science and religion arises from a lack\nof overlap between their respective domains of professional expertise.\n(2001: 739)\n", "\nHe identified science’s areas of expertise as empirical\nquestions about the constitution of the universe, and religion’s\ndomain of expertise as ethical values and spiritual meaning. NOMA is\nboth descriptive and normative: religious leaders should refrain from\nmaking factual claims about, for instance, evolutionary theory, just\nas scientists should not claim insight on moral matters. Gould held\nthat there might be interactions at the borders of each magisterium,\nsuch as our responsibility toward other living things. One obvious\nproblem with the independence model is that if religion were barred\nfrom making any statement of fact, it would be difficult to justify\nits claims of value and ethics. For example, one could not argue that\none should love one’s neighbor because it pleases the creator\n(Worrall 2004). Moreover, religions do seem to make empirical claims,\nfor example, that Jesus appeared after his death or that the early\nHebrews passed through the parted waters of the Red Sea.", "\nThe dialogue model proposes a mutualistic relationship\nbetween religion and science. Unlike independence, it assumes a common\nground between both fields, perhaps in their presuppositions, methods,\nand concepts. For example, the Christian doctrine of creation may have\nencouraged science by assuming that creation (being the product of a\ndesigner) is both intelligible and orderly, so one can expect there\nare laws that can be discovered. Creation, as a product of God’s\nfree actions, is also contingent, so the laws of nature cannot be\nlearned through a priori thinking which prompts the need for\nempirical investigation. According to Barbour (2000), both scientific\nand theological inquiry are theory-dependent, or at least\nmodel-dependent. For example, the doctrine of the Trinity colors how\nChristian theologians interpret the first chapters of Genesis. Next\nto this, both rely on metaphors and models. Both fields remain\nseparate but they talk to each other, using common methods, concepts,\nand presuppositions. Wentzel van Huyssteen (1998) has argued for a\ndialogue position, proposing that science and religion can be in a\ngraceful duet, based on their epistemological overlaps. The Partially\nOverlapping Magisteria (POMA) model defended by Alister McGrath (e.g.,\nMcGrath and Collicutt McGrath 2007) is also worth mentioning.\nAccording to McGrath, science and religion each draw on several\ndifferent methodologies and approaches. These methods and approaches\nare different ways of knowing that have been shaped through historical\nfactors. It is beneficial for scientists and theologians to be in\ndialogue with each other.", "\nThe integration model is more extensive in its unification of\nscience and theology. Barbour (2000) identifies three forms of\nintegration. First, natural theology, which formulates arguments for\nthe existence and attributes of God. It uses interpretations of\nresults from the natural sciences as premises in its arguments. For\ninstance, the supposition that the universe has a temporal origin\nfeatures in contemporary cosmological arguments for the existence of\nGod. Likewise, the fact that the cosmological constants and laws of\nnature are life-permitting (whereas many other combinations of\nconstants and laws would not permit life) is used in contemporary\nfine-tuning arguments (see the entry to\n fine-tuning arguments).\n Second, theology of nature starts not from science but from a\nreligious framework, and examines how this can enrich or even revise\nfindings of the sciences. For example, McGrath (2016) developed a\nChristian theology of nature, examining how nature and scientific\nfindings can be interpreted through a Christian lens. Thirdly, Barbour\nbelieved that Whitehead’s process philosophy was a promising way\nto integrate science and religion.", "\nWhile integration seems attractive (especially to theologians), it is\ndifficult to do justice to both the scientific and religious aspects\nof a given domain, especially given their complexities. For example,\nPierre Teilhard de Chardin (1971), who was both knowledgeable in\npaleoanthropology and theology, ended up with an unconventional view\nof evolution as teleological (which put him at odds with the\nscientific establishment) and with an unorthodox theology (which\ndenied original sin and led to a series of condemnations by the Roman\nCatholic Church). Theological heterodoxy, by itself, is no reason to\ndoubt a model. However, it shows obstacles for the integration model\nto become a live option in the broader community of theologians and\nphilosophers who want to remain affiliate to a specific religious\ncommunity without transgressing its boundaries. Moreover, integration\nseems skewed towards theism: Barbour described arguments based on\nscientific results that support (but do not demonstrate) theism, but\nfailed to discuss arguments based on scientific results that support\n(but do not demonstrate) the denial of theism. Hybrid positions like\nMcGrath’s POMA indicate some difficulty for Barbour’s\ntaxonomy: the scope of conflict, independence, dialogue, and\nintegration is not clearly defined and they are not mutually\nexclusive. For example, if conflict is defined broadly then it is\ncompatible with integration. Take the case of Frederick Tennant\n(1902), who sought to explain sin as the result of evolutionary\npressures on human ancestors. This view led him to reject the Fall as\na historical event, as it was not compatible with evolutionary\nbiology. His view has conflict (as he saw Christian doctrine in\nconflict with evolutionary biology) but also integration (he sought to\nintegrate the theological concept of sin in an evolutionary picture).\nIt is clear that many positions defined by authors in the religion and\nscience literature do not clearly fall within one of Barbour’s\nfour domains." ], "subsection_title": "1.3 Taxonomies of the interaction between science and religion" }, { "content": [ "\nScience and religion are closely interconnected in the scientific\nstudy of religion, which can be traced back to seventeenth-century\nnatural histories of religion. Natural historians attempted to provide\nnaturalistic explanations for human behavior and culture, including\nreligion and morality. For example, Bernard Le Bovier de\nFontenelle’s De l’Origine des Fables (1724)\noffered a causal account of belief in the supernatural. People often\nassert supernatural explanations when they lack an understanding of\nthe natural causes underlying extraordinary events: “To the\nextent that one is more ignorant, or one has less experience, one sees\nmore miracles” (1724 [1824: 295], my\ntranslation). Hume’s Natural History of Religion (1757)\nis perhaps the best-known philosophical example of a natural\nhistorical explanation of religious belief. It traces the origins of\npolytheism—which Hume thought was the earliest form of religious\nbelief—to ignorance about natural causes combined with fear and\napprehension about the environment. By deifying aspects of the\nenvironment, early humans tried to persuade or bribe the gods, thereby\ngaining a sense of control.", "\nIn the nineteenth and early twentieth centuries, authors from newly\nemerging scientific disciplines, such as anthropology, sociology, and\npsychology examined the purported naturalistic roots of religious\nbeliefs. They did so with a broad brush, trying to explain what\nunifies diverse religious beliefs across cultures. Auguste Comte\n(1841) proposed that all societies, in their attempts to make sense of\nthe world, go through the same stages of development: the theological\n(religious) stage is the earliest phase, where religious explanations\npredominate, followed by the metaphysical stage (a non-intervening\nGod), and culminating in the positive or scientific stage, marked by\nscientific explanations and empirical observations.", "\nIn anthropology, this positivist idea influenced cultural\nevolutionism, a theoretical framework that sought to explain cultural\nchange using universal patterns. The underlying supposition was that\nall cultures evolve and progress along the same trajectory. Cultures\nwith differing religious views were explained as being in different\nstages of their development. For example, Tylor (1871) regarded\nanimism as the earliest form of religious belief. James Frazer’s\nGolden Bough (1890) is somewhat unusual within this\nliterature, as he saw commonalities between magic, religion, and\nscience. Though he proposed a linear progression, he also argued that\na proto-scientific mindset gave rise to magical practices, including\nthe discovery of regularities in nature. Cultural evolutionist models\ndealt poorly with religious diversity and with the complex\nrelationships between science and religion across cultures. Many\nauthors proposed that religion was just a stage in human development,\nwhich would eventually be superseded. For example, social theorists\nsuch as Karl Marx and Max Weber proposed versions of the\nsecularization thesis, the view that religion would decline in the\nface of modern technology, science, and culture.", "\nFunctionalism was another theoretical framework that sought to explain\nreligion. Functionalists did not consider religion to be a stage in\nhuman cultural development that would eventually be overcome. They saw\nit as a set of social institutions that served important functions in\nthe societies they were part of. For example, the sociologist\nÉmile Durkheim (1912 [1915]) argued that religious beliefs are\nsocial glue that helps to keep societies together.", "\nSigmund Freud and other early psychologists aimed to explain religion\nas the result of cognitive dispositions. For example, Freud (1927) saw\nreligious belief as an illusion, a childlike yearning for a fatherly\nfigure. He also considered “oceanic feeling” (a feeling of\nlimitlessness and of being connected with the world, a concept he\nderived from the French author Romain Rolland) as one of the origins\nof religious belief. He thought this feeling was a remnant of an\ninfant’s experience of the self, prior to being weaned off the\nbreast. William James (1902) was interested in the psychological roots\nand the phenomenology of religious experiences, which he believed were\nthe ultimate source of all institutional religions.", "\nFrom the 1920s onward, the scientific study of religion became less\nconcerned with grand unifying narratives, and focused more on\nparticular religious traditions and beliefs. Anthropologists such as\nEdward Evans-Pritchard (1937) and Bronisław Malinowski (1925) no\nlonger relied exclusively on second-hand reports (usually of poor\nquality and from distorted sources), but engaged in serious fieldwork.\nTheir ethnographies indicated that cultural evolutionism was a\ndefective theoretical framework and that religious beliefs were more\ndiverse than was previously assumed. They argued that religious\nbeliefs were not the result of ignorance of naturalistic mechanisms.\nFor instance, Evans-Pritchard (1937) noted that the Azande were well\naware that houses could collapse because termites ate away at their\nfoundations, but they still appealed to witchcraft to explain why a\nparticular house collapsed at a particular time. More recently,\nCristine Legare et al. (2012) found that people in various cultures\nstraightforwardly combine supernatural and natural explanations, for\ninstance, South Africans are aware AIDS is caused by the HIV virus,\nbut some also believe that the viral infection is ultimately caused by\na witch.", "\nPsychologists and sociologists of religion also began to doubt that\nreligious beliefs were rooted in irrationality, psychopathology, and\nother atypical psychological states, as James (1902) and other early\npsychologists had assumed. In the US, in the late 1930s through the\n1960s, psychologists developed a renewed interest for religion, fueled\nby the observation that religion refused to decline and seemed to\nundergo a substantial revival, thus casting doubt on the\nsecularization thesis (see Stark 1999 for an overview). Psychologists\nof religion have made increasingly fine-grained distinctions between\ntypes of religiosity, including extrinsic religiosity (being religious\nas means to an end, for instance, getting the benefits of being a\nmember of a social group) and intrinsic religiosity (people who adhere\nto religions for the sake of their teachings) (Allport & Ross\n1967). Psychologists and sociologists now commonly study religiosity\nas an independent variable, with an impact on, for instance, health,\ncriminality, sexuality, socio-economic profile, and social\nnetworks.", "\nA recent development in the scientific study of religion is the\ncognitive science of religion (CSR). This is a multidisciplinary\nfield, with authors from, among others, developmental psychology,\nanthropology, philosophy, and cognitive psychology (see C. White 2021\nfor a comprehensive overview). It differs from other scientific\napproaches to religion in its presupposition that religion is not a\npurely cultural phenomenon. Rather, authors in CSR hold that religion\nis the result of ordinary, early developed, and universal human\ncognitive processes (e.g., Barrett 2004, Boyer 2002). Some authors\nregard religion as the byproduct of cognitive processes that are not\nevolved for religion. For example, according to Paul Bloom (2007),\nreligion emerges as a byproduct of our intuitive distinction between\nminds and bodies: we can think of minds as continuing, even after the\nbody dies (e.g., by attributing desires to a dead family member),\nwhich makes belief in an afterlife and in disembodied spirits natural\nand spontaneous. Another family of hypotheses regards religion as a\nbiological or cultural adaptive response that helps humans solve\ncooperative problems (e.g., Bering 2011; Purzycki & Sosis 2022):\nthrough their belief in big, powerful gods that can punish, humans\nbehave more cooperatively, which allowed human group sizes to expand\nbeyond small hunter-gatherer communities. Groups with belief in big\ngods thus out-competed groups without such beliefs for resources\nduring the Neolithic, which would explain the current success of\nbelief in such gods (Norenzayan 2013). However, the question of which\ncame first—big god beliefs or large-scale societies—is a\ncontinued matter of debate." ], "subsection_title": "1.4 The scientific study of religion" } ] }, { "main_content": [ "\nAs noted, most studies on the relationship between science and\nreligion have focused on science and Christianity, with only a small\nnumber of publications devoted to other religious traditions (e.g.,\nBrooke & Numbers 2011; Lopez 2008). Since science makes universal\nclaims, it is easy to assume that its encounter with other religious\ntraditions would be similar to its interactions with Christianity.\nHowever, given different creedal tenets (e.g., in Hindu traditions God\nis usually not entirely distinct from creation, unlike in Christianity\nand Judaism), and because science has had distinct historical\ntrajectories in other cultures, one can expect disanalogies in the\nrelationship between science and religion in different religious\ntraditions. To give a sense of this diversity, this section provides a\nbird’s eye view of science and religion in five major world\nreligions: Christianity, Islam, Hinduism, Buddhism, and Judaism." ], "section_title": "2. Science and religion in various religions", "subsections": [ { "content": [ "\nChristianity is an Abrahamic monotheistic religion, currently the\nreligion with the most adherents. It developed in the first century CE\nout of Judaism. Christians adhere to asserted revelations described in\na series of canonical texts, which include the Old Testament, which\ncomprises texts inherited from Judaism, and the New Testament, which\ncontains the Gospels of Matthew, Mark, Luke, and John (narratives on\nthe life and teachings of Jesus), as well as events and teachings of\nthe early Christian churches (e.g., Acts of the Apostles, letters by\nPaul), and Revelation, a prophetic book on the end times.", "\nGiven the prominence of revealed texts in Christianity, a useful\nstarting point to examine the relationship between Christianity and\nscience is the two books metaphor (see Tanzella-Nitti 2005 for an\noverview): God revealed Godself through the “Book of\nNature”, with its orderly laws, and the “Book of\nScripture”, with its historical narratives and accounts of\nmiracles. Augustine (354–430) argued that the book of nature was\nthe more accessible of the two, since scripture requires literacy\nwhereas illiterates and literates alike could read the book of nature.\nMaximus Confessor (c. 580–662), in his Ambigua (see\nLouth 1996 for a collection of and critical introduction to these\ntexts) compared scripture and natural law to two clothes that\nenvelop the Incarnated Logos: Jesus’ humanity is revealed by\nnature, whereas his divinity is revealed by the scriptures. During the\nMiddle Ages, authors such as Hugh of St. Victor (ca. 1096–1141)\nand Bonaventure (1221–1274) began to realize that the book of\nnature was not at all straightforward to read. Given that original sin\nmarred our reason and perception, what conclusions could humans\nlegitimately draw about ultimate reality? Bonaventure used the\nmetaphor of the books to the extent that “liber\nnaturae” was a synonym for creation, the natural world. He\nargued that sin has clouded human reason so much that the book of\nnature has become unreadable, and that scripture is needed as an aid\nas it contains teachings about the world.", "\nChristian authors in the field of science and religion continue to\ndebate how these two books interrelate. Concordism is the attempt to\ninterpret scripture in the light of modern science. It is a\nhermeneutical approach to Bible interpretation, where one expects that\nthe Bible foretells scientific theories, such as the Big Bang theory\nor evolutionary theory. However, as Denis Lamoureux (2008: chapter 5)\nargues, many scientific-sounding statements in the Bible are false:\nthe mustard seed is not the smallest seed, male reproductive seeds do\nnot contain miniature persons, there is no firmament, and the earth is\nneither flat nor immovable. Thus, any plausible form of integrating\nthe book of nature and scripture will require more nuance and\nsophistication. Theologians such as John Wesley (1703–1791) have\nproposed the addition of other sources of knowledge to scripture and\nscience: the Wesleyan quadrilateral (a term not coined by Wesley\nhimself) is the dynamic interaction of scripture, experience\n(including the empirical findings of the sciences), tradition, and\nreason (Outler 1985).", "\nSeveral Christian authors have attempted to integrate science and\nreligion (e.g., Haught 1995, Lamoureux 2008, Murphy 1995), making\nintegration a highly popular view on the relationship between science\nand religion. These authors tend to interpret findings from the\nsciences, such as evolutionary theory or chaos theory, in a\ntheological light, using established theological models such as\nclassical theism or the doctrine of creation. John Haught (1995)\nargues that the theological view of kenosis (self-emptying of God in\ncreation) anticipates scientific findings such as evolutionary theory:\na self-emptying God (i.e., who limits Godself), who creates a distinct\nand autonomous world, makes a world with internal self-coherence, with\na self-organizing universe as the result.", "\nThe dominant epistemological outlook in Christian science and religion\nhas been critical realism, a position that applies both to theology\n(theological realism) and to science (scientific realism). Barbour\n(1966) introduced this view into the science and religion literature;\nit has been further developed by theologians such as Arthur Peacocke\n(1984) and Wentzel van Huyssteen (1999). Critical realism aims to\noffer a middle way between naïve realism (the world is as we\nperceive it) and instrumentalism (our perceptions and concepts are\npurely instrumental). It encourages critical reflection on perception\nand the world, hence “critical”. Critical realism has\ndistinct flavors in the works of different authors, for instance, van\nHuyssteen (1998, 1999) develops a weak form of critical realism set\nwithin a postfoundationalist notion of rationality, where theological\nviews are shaped by social, cultural, and evolved biological factors.\nMurphy (1995: 329–330) outlines doctrinal and scientific\nrequirements for approaches in science and religion: ideally, an\nintegrated approach should be broadly in line with Christian doctrine,\nespecially core tenets such as the doctrine of creation, while at the\nsame time it should be in line with empirical observations without\nundercutting scientific practices.", "\nSeveral historians (e.g., Hooykaas 1972) have argued that Christianity\nwas instrumental to the development of Western science. Peter Harrison\n(2007) maintains that the doctrine of original sin played a crucial\nrole in this, arguing there was a widespread belief in the early\nmodern period that Adam, prior to the Fall, had superior senses,\nintellect, and understanding. As a result of the Fall, human senses\nbecame duller, our ability to make correct inferences was diminished,\nand nature itself became less intelligible. Postlapsarian humans\n(i.e., humans after the Fall) are no longer able to exclusively rely\non their a priori reasoning to understand nature. They must\nsupplement their reasoning and senses with observation through\nspecialized instruments, such as microscopes and telescopes. As the\nexperimental philosopher Robert Hooke wrote in the introduction to his\nMicrographia:", "\n\n\nevery man, both from a deriv’d corruption, innate and born with\nhim, and from his breeding and converse with men, is very subject to\nslip into all sorts of errors … These being the dangers in the\nprocess of humane Reason, the remedies of them all can only proceed\nfrom the real, the mechanical, the experimental Philosophy\n[experiment-based science]. (1665, cited in Harrison 2007: 5)\n", "\nAnother theological development that may have facilitated the rise of\nscience was the Condemnation of Paris (1277), which forbade teaching\nand reading natural philosophical views that were considered\nheretical, such as Aristotle’s physical treatises. As a result,\nthe Condemnation opened up intellectual space to think beyond ancient\nGreek natural philosophy. For example, medieval philosophers such as\nJohn Buridan (fl. 14th c) held the Aristotelian belief that there\ncould be no vacuum in nature, but once the idea of a vacuum became\nplausible, natural philosophers such as Evangelista Torricelli\n(1608–1647) and Blaise Pascal (1623–1662) could experiment\nwith air pressure and vacua (see Grant 1996, for discussion).", "\nSome authors claim that Christianity was unique and instrumental in\ncatalyzing the scientific revolution. For example, according to the\nsociologist of religion Rodney Stark (2004), the scientific revolution\nwas in fact a slow, gradual development from medieval Christian\ntheology. Claims such as Stark’s, however, fail to recognize the\nlegitimate contributions of Islamic and Greek scholars to the\ndevelopment of modern science, and fail to do justice to the\nimportance of practical technological innovations in map-making and\nstar-charting in the emergence of modern science. In spite of these\npositive readings of the relationship between science and religion in\nChristianity, there are sources of enduring tension. For example,\nthere is still vocal opposition to the theory of evolution among\nChristian fundamentalists. In the public sphere, the conflict view\nbetween Christianity and science prevails, in stark contrast to the\nscholarly literature. This is due to an important extent to the\noutsize influence of a vocal conservative Christian minority in the\nAmerican public debate, which sidelines more moderate voices (Evans\n2016)." ], "subsection_title": "2.1 Christianity" }, { "content": [ "\nIslam is a monotheistic religion that emerged in the seventh century,\nfollowing a series of purported revelations to the prophet\nMuḥammad. The term “Islam” also denotes\ngeo-political structures, such as caliphates and empires, which were\nfounded by Muslim rulers from the seventh century onward, including\nthe Umayyad, Abbasid, and Ottoman caliphates. Additionally, it refers\nto a culture which flourished within this political and religious\ncontext, with its own philosophical and scientific traditions (Dhanani\n2002). The defining characteristic of Islam is belief in one God\n(Allāh), who communicates through prophets, including Adam,\nAbraham, and Muḥammad. Allāh‎’s revelations to\nMuḥammad are recorded in the Qurʾān, the central\nreligious text for Islam. Next to the Qurʾān, an important\nsource of jurisprudence and theology is the ḥadīth, an oral\ncorpus of attested sayings, actions, and tacit approvals of the\nprophet Muḥammad. The two major branches of Islam, Sunni and\nShia, are based on a dispute over the succession of Muḥammad. As\nthe second largest religion in the world, Islam shows a wide variety\nof beliefs. Core creedal views include the oneness of God\n(tawḥīd), the view that there is only one\nundivided God who created and sustains the universe, prophetic\nrevelation (in particular to Muḥammad), and an afterlife. Beyond\nthis, Muslims disagree on a number of doctrinal issues.", "\nThe relationship between Islam and science is complex. Today,\npredominantly Muslim countries, such as the United Arabic Emirates,\nenjoy high urbanization and technological development, but they still\nunderperform in common metrics of scientific research, such as\npublications in leading journals and number of citations per\nscientist, compared to other regions outside of the west such as India\nand China (see Edis 2007). Some Muslims hold a number of\npseudoscientific ideas, some of which it shares with Christianity such\nas Old Earth creationism, whereas others are specific to Islam such as\nthe recreation of human bodies from the tailbone on the day of\nresurrection, and the superiority of prayer in treating lower-back\npain instead of conventional methods (Guessoum 2011: 4–5).", "\nThis contemporary lack of scientific prominence is remarkable given\nthat the Islamic world far exceeded European cultures in the range and\nquality of its scientific knowledge between approximately the ninth\nand the fifteenth century, excelling in domains such as mathematics\n(algebra and geometry, trigonometry in particular), astronomy\n(seriously considering, but not adopting, heliocentrism), optics, and\nmedicine. These domains of knowledge are commonly referred to as\n“Arabic science”, to distinguish them from the pursuits of\nscience that arose in the west (Huff 2003). “Arabic\nscience” is an imperfect term, as many of the practitioners were\nnot speakers of Arabic, hence the term “science in the Islamic\nworld” is more accurate. Many scientists in the Islamic world\nwere polymaths, for example, Ibn Sīnā (Avicenna,\n980–1037) is commonly regarded as one of the most significant\ninnovators, not only in philosophy, but also in medicine and\nastronomy. His Canon of Medicine, a medical encyclopedia, was\na standard textbook in universities across Europe for many centuries\nafter his death. Al-Fārābī (ca. 872–ca. 950), a\npolitical philosopher from Damascus, also investigated music theory,\nscience, and mathematics. Omar Khayyám (1048–1131)\nachieved lasting fame in disparate domains such as poetry, astronomy,\ngeography, and mineralogy. The Andalusian Ibn Rušd (Averroes,\n1126–1198) wrote on medicine, physics, astronomy, psychology,\njurisprudence, music, and geography, next to developing a Greek-inspired\nphilosophical theology.", "\nA major impetus for science in the Islamic world was the patronage of\nthe Abbasid caliphate (758–1258), centered in Baghdad. Early\nAbbasid rulers, such as Harun al-Rashid (ruled 786–809) and his\nsuccessor Abū Jaʿfar Abdullāh al-Ma’mūn\n(ruled 813–833), were significant patrons of science. The former\nfounded the Bayt al-Hikma (House of Wisdom), which\ncommissioned translations of major works by Aristotle, Galen, and many\nPersian and Indian scholars into Arabic. It was cosmopolitan in its\noutlook, employing astronomers, mathematicians, and physicians from\nabroad, including Indian mathematicians and Nestorian (Christian)\nastronomers. Throughout the Islamic world, public libraries attached\nto mosques provided access to a vast compendium of knowledge, which\nspread Islam, Greek philosophy, and science. The use of a common\nlanguage (Arabic), as well as common religious and political\ninstitutions and flourishing trade relations encouraged the spread of\nscientific ideas throughout the Islamic world. Some of this\ntransmission was informal, e.g., correspondence between like-minded\npeople (see Dhanani 2002), some formal, e.g., in hospitals where\nstudents learned about medicine in a practical, master-apprentice\nsetting, and in astronomical observatories and academies. The decline\nand fall of the Abbasid caliphate dealt a blow to science in the Islamic world, but it\nremains unclear why it ultimately stagnated, and why it did not\nexperience something analogous to the scientific revolution in Western\nEurope. Note, the decline of science in the Islamic world should not\nbe generalized to other fields, such as philosophy and philosophical\ntheology, which continued to flourish after the Abbasid caliphate\nfell.", "\nSome liberal Muslim authors, such as Fatima Mernissi (1992), argue\nthat the rise of conservative forms of Islamic philosophical theology\nstifled more scientifically-minded natural philosophy. In the ninth to\nthe twelfth century, the Mu’tazila (a philosophical theological\nschool) helped the growth of science in the Islamic world thanks to\ntheir embrace of Greek natural philosophy. But eventually, the\nMu’tazila and their intellectual descendants lost their\ninfluence to more conservative brands of theology.\nAl-Ghazālī’s influential eleventh-century work,\nThe Incoherence of the Philosophers (Tahāfut\nal-falāsifa), was a scathing and sophisticated critique of\nGreek-inspired Muslim philosophy, arguing that their metaphysical assumptions\ncould not be demonstrated. This book vindicated more orthodox Muslim\nreligious views. As Muslim intellectual life became more orthodox, it\nbecame less open to non-Muslim philosophical ideas, which led to the\ndecline of science in the Islamic world, according to this view.", "\nThe problem with this narrative is that orthodox worries about\nnon-Islamic knowledge were already present before Al-Ghazālī\nand continued long after his death (Edis 2007: chapter 2). The study\nof law (fiqh) was more stifling for science in the Islamic\nworld than developments in theology. The eleventh century saw changes\nin Islamic law that discouraged heterodox thought: lack of orthodoxy\ncould now be regarded as apostasy from Islam (zandaqa) which\nis punishable by death, whereas before, a Muslim could only apostatize\nby an explicit declaration (Griffel 2009: 105). (Al-Ghazālī\nhimself only regarded the violation of three core doctrines as\nzandaqa, namely statements that challenged monotheism, the\nprophecy of Muḥammad, and resurrection after death.) Given that\nheterodox thoughts could be interpreted as apostasy, this created a\nstifling climate for science. In the second half of the nineteenth\ncentury, as science and technology became firmly entrenched in Western\nsociety, Muslim empires were languishing or colonized. Scientific\nideas, such as evolutionary theory, became equated with European\ncolonialism, and thus met with distrust. The enduring association\nbetween western culture, colonialism, and science led to a more\nprominent conflict view of the relationship between science and\nreligion in Muslim countries.", "\nIn spite of this negative association between science and Western\nmodernity, there is an emerging literature on science and religion by\nMuslim scholars (mostly scientists). The physicist Nidhal Guessoum\n(2011) holds that science and religion are not only compatible, but in\nharmony. He rejects the idea of treating the Qurʾān as a\nscientific encyclopedia, something other Muslim authors in the debate\non science and religion tend to do. Moreover, he adheres to the\nno-possible-conflict principle, outlined by Ibn Rušd: there\ncan be no conflict between God’s word (properly understood) and\nGod’s work (properly understood). If an apparent conflict\narises, the Qurʾān may not have been interpreted\ncorrectly.", "\nWhile the Qurʾān asserts a creation in six days (like the\nHebrew Bible), “day” is often interpreted as a very long\nspan of time, rather than a 24-hour period. As a result, Old Earth\ncreationism is more influential in Islam than Young Earth creationism.\nAdnan Oktar’s Atlas of Creation (published in 2007\nunder the pseudonym Harun Yahya), a glossy coffee table book that\ndraws heavily on Christian Old Earth creationism, has been distributed\nworldwide (Hameed 2008). Since the Qurʾān explicitly\nmentions the special creation of Adam out of clay, most Muslims refuse\nto accept that humans evolved from hominin ancestors. Nevertheless,\nMuslim scientists such as Guessoum (2011) and Rana Dajani (2015) have\nadvocated acceptance of evolution." ], "subsection_title": "2.2 Islam" }, { "content": [ "\nHinduism is the world’s third largest religion, though the term\n“Hinduism” is an awkward catch-all phrase that denotes\ndiverse religious and philosophical traditions that emerged on the\nIndian subcontinent between 500 BCE and 300 CE. The vast majority of\nHindus live in India; most others live in Nepal, Sri Lanka, and\nSoutheast Asia, with a significant diaspora in western countries such\nas the United States (Hackett 2015\n [Other Internet Resources]).\n In contrast to the Abrahamic monotheistic religions, Hinduism does not\nalways draw a sharp distinction between God and creation. (While there\nare pantheistic and panentheistic views in Christianity, Judaism, and\nIslam, these are minority positions.) Many Hindus believe in a\npersonal God, and identify this God as immanent in creation. This view\nhas ramifications for the science and religion debate, in that there\nis no sharp ontological distinction between creator and creature\n(Subbarayappa 2011). Religious traditions originating on the Indian\nsubcontinent, including Hinduism, Jainism, Buddhism, and Sikhism, are\nreferred to as dharmic religions. Philosophical points of view are\nreferred to as darśana. ", "\nOne factor that unites the different strands of Hinduism is the\nimportance of foundational texts composed between ca. 1600 and 700\nBCE. These include the Vedas, which contain hymns and prescriptions\nfor performing rituals, Brāhmaṇa, accompanying liturgical\ntexts, and Upaniṣad, metaphysical treatises. The Vedas discuss\ngods who personify and embody natural phenomena such as fire (Agni)\nand wind (Vāyu). More gods appear in the following centuries\n(e.g., Gaṇeśa and Sati-Parvati in the 4th century). Note\nthat there are both polytheistic and monotheistic strands in Hinduism,\nso it is not the case that individual believers worship or recognize\nall of these gods. Ancient Vedic rituals encouraged knowledge of\ndiverse sciences, including astronomy, linguistics, and mathematics.\nAstronomical knowledge was required to determine the timing of rituals\nand the construction of sacrificial altars. Linguistics developed out\nof a need to formalize grammatical rules for classical Sanskrit, which\nwas used in rituals. Large public offerings also required the\nconstruction of elaborate altars, which posed geometrical problems and\nthus led to advances in geometry. Classic Vedic texts also frequently\nused very large numbers, for instance, to denote the age of humanity\nand the Earth, which required a system to represent numbers\nparsimoniously, giving rise to a 10-base positional system and a\nsymbolic representation for zero as a placeholder, which would later\nbe imported in other mathematical traditions (Joseph 1991 [2000]). In\nthis way, ancient Indian dharma encouraged the emergence of the\nsciences.", "\nAround the sixth–fifth century BCE, the northern part of the\nIndian subcontinent experienced an extensive urbanization. In this\ncontext, medicine (āyurveda) became standardized. This\nperiod also gave rise to a wide range of heterodox philosophical\nschools, including Buddhism, Jainism, and Cārvāka. The\nlatter defended a form of metaphysical naturalism, denying the\nexistence of gods or karma. The relationship between science and\nreligion on the Indian subcontinent is complex, in part because the\ndharmic religions and philosophical schools are so diverse. For\nexample, Cārvāka proponents had a strong suspicion of\ninferential beliefs, and rejected Vedic revelation and supernaturalism\nin general, instead favoring direct observation as a source of\nknowledge.", "\nNatural theology also flourished in the pre-colonial period,\nespecially in the Advaita Vedānta, a darśana that\nidentifies the self, ātman, with ultimate reality,\nBrahman. Advaita Vedāntin philosopher Adi Śaṅkara\n(fl. first half eighth century) was an author who regarded Brahman as\nthe only reality, both the material and the efficient cause of the\ncosmos. Śaṅkara formulated design and cosmological\narguments, drawing on analogies between the world and artifacts: in\nordinary life, we never see non-intelligent agents produce purposive\ndesign, yet the universe is suitable for human life, just like benches\nand pleasure gardens are designed for us. Given that the universe is\nso complex that even an intelligent craftsman cannot comprehend it,\nhow could it have been created by non-intelligent natural forces?\nŚaṅkara concluded that it must have been designed by an\nintelligent creator (C.M. Brown 2008: 108).", "\nFrom 1757 to 1947, India was under British colonial rule. This had a\nprofound influence on its culture as Hindus came into contact with\nWestern science and technology. For local intellectuals, the contact\nwith Western science presented a challenge: how to assimilate these\nideas with Hinduism? Mahendrahal Sircar (1833–1904) was one of\nthe first authors to examine evolutionary theory and its implications\nfor Hindu religious beliefs. Sircar was an evolutionary theist, who\nbelieved that God used evolution to create current life forms.\nEvolutionary theism was not a new hypothesis in Hinduism, but the many\nlines of empirical evidence Darwin provided for evolution gave it a\nfresh impetus. While Sircar accepted organic evolution through common\ndescent, he questioned the mechanism of natural selection as it was\nnot teleological, which went against his evolutionary theism. This was\na widespread problem for the acceptance of evolutionary theory, one\nthat Christian evolutionary theists also wrestled with (Bowler 2009).\nHe also argued against the British colonists’ beliefs that\nHindus were incapable of scientific thought, and encouraged fellow\nHindus to engage in science, which he hoped would help regenerate the\nIndian nation (C.M. Brown 2012: chapter 6).", "\nThe assimilation of Western culture prompted various revivalist\nmovements that sought to reaffirm the cultural value of Hinduism. They\nput forward the idea of a Vedic science, where all scientific findings\nare already prefigured in the Vedas and other ancient texts\n(e.g., Vivekananda 1904). This idea is still popular within\ncontemporary Hinduism, and is quite similar to ideas held by\ncontemporary Muslims, who refer to the Qurʾān as a harbinger\nof scientific theories.", "\nResponses to evolutionary theory were as diverse as Christian views on\nthis subject, ranging from creationism (denial of evolutionary theory\nbased on a perceived incompatibility with Vedic texts) to acceptance\n(see C.M. Brown 2012 for a thorough overview). Authors such as\nDayananda Saraswati (1930–2015) rejected evolutionary theory. By\ncontrast, Vivekananda (1863–1902), a proponent of the monistic\nAdvaita Vedānta enthusiastically endorsed evolutionary theory and\nargued that it is already prefigured in ancient Vedic texts. His\nintegrative view claimed that Hinduism and science are in harmony:\nHinduism is scientific in spirit, as is evident from its long history\nof scientific discovery (Vivekananda 1904). Sri Aurobindo Ghose, a\nyogi and Indian nationalist who was educated in the West, formulated a\nsynthesis of evolutionary thought and Hinduism. He interpreted the\nclassic avatara doctrine, according to which God incarnates\ninto the world repeatedly throughout time, in evolutionary terms. God\nthus appears first as an animal, later as a dwarf, then as a violent\nman (Rama), and then as Buddha, and as Kṛṣṇa. He\nproposed a metaphysical picture where both spiritual evolution\n(reincarnation and avatars) and physical evolution are ultimately a\nmanifestation of God (Brahman). This view of reality as\nconsisting of matter (prakṛti) and consciousness\n(puruṣa) goes back to sāṃkhya, one\nof the orthodox Hindu darśana, but Aurobindo made\nexplicit reference to the divine, calling the process during which the\nsupreme Consciousness dwells in matter involution (Aurobindo,\n1914–18 [2005], see C.M. Brown 2007 for discussion).", "\nDuring the twentieth century, Indian scientists began to gain\nprominence, including C.V. Raman (1888–1970), a Nobel Prize\nwinner in physics, and Satyendra Nath Bose (1894–1974), a\ntheoretical physicist who described the behavior of photons\nstatistically, and who gave his name to bosons. However, these authors\nwere silent on the relationship between their scientific work and\ntheir religious beliefs. By contrast, the mathematician Srinivasa\nRamanujan (1887–1920) was open about his religious beliefs and\ntheir influence on his mathematical work. He claimed that the goddess\nNamagiri helped him to intuit solutions to mathematical problems.\nLikewise, Jagadish Chandra Bose (1858–1937), a theoretical\nphysicist, biologist, biophysicist, botanist, and archaeologist who\nworked on radio waves, saw the Hindu idea of unity reflected in the\nstudy of nature. He started the Bose institute in Kolkata in 1917, the\nearliest interdisciplinary scientific institute in India (Subbarayappa\n2011)." ], "subsection_title": "2.3 Hinduism" }, { "content": [ "\nBuddhism, like the other religious traditions surveyed in this entry,\nencompasses many views and practices. The principal forms of Buddhism\nthat exist today are Theravāda and Mahāyāna.\n(Vajrayāna, the tantric tradition of Buddhism, is also sometimes\nseen as a distinct form.) Theravāda is the dominant form of\nBuddhism of Sri Lanka and Southeast Asia. It traditionally refers to\nmonastic and textual lineages associated with the study of the Pāli\nBuddhist Canon. Mahāyāna refers to a movement that likely\nbegan roughly four centuries after the Buddha’s death; it became\nthe dominant form of Buddhism in East and Central Asia. It includes\nChan or Zen, and also tantric Buddhism, which today is found mostly in\nTibet, though East Asian forms also exist.", "\nBuddhism originated in the historical figure of the Buddha\n(historically, Gautama Buddha or Siddhārtha Gautama, ca.\n5th–4th century BCE). His teaching\ncentered on ethics as well as metaphysics, incapsulated in the Four\nNoble Truths (on suffering and its origin in human desires), and the\nNoble Eightfold Path (right view, right aspiration, right speech,\nright action, right livelihood, right effort, right mindfulness, right\nconcentration) to end suffering and to break the cycle of rebirths,\nculminating in reaching Nirvana. Substantive metaphysical teachings\ninclude belief in karma, the no-self, and the cycle of rebirth.", "\nAs a response to colonialist attitudes, modern Buddhists since the\nnineteenth century have often presented Buddhism as harmonious with\nscience (Lopez 2008). The argument is roughly that since Buddhism\ndoesn’t require belief in metaphysically substantive entities\nsuch as God, the soul, or the self (unlike, for example,\nChristianity), Buddhism should be easily compatible with the factual\nclaims that scientists make. (Note, however, that historically most\nBuddhist have believed in various forms of divine abode and\ndivinities.) We could thus expect the dialogue and integration view to\nprevail in Buddhism. An exemplar for integration is the fourteenth\nDalai Lama, who is known for his numerous efforts to lead dialogue\nbetween religious people and scientists. He has extensively written on\nthe relationship between Buddhism and various scientific disciplines\nsuch as neuroscience and cosmology (e.g., Dalai Lama 2005, see also\nthe Science and Philosophy in the Indian Buddhist Classics\nseries, a four-volume series conceived and compiled by the Dalai Lama,\ne.g., Jinpa 2017). Donald Lopez Jr (2008) identifies compatibility as\nan enduring claim in the debate on science and Buddhism, in spite of\nthe fact that what is meant by these concepts has shifted markedly\nover time. As David McMahan (2009) argues, Buddhism underwent profound\nshifts in response to modernity in the west as well as globally. In\nthis modern context, Buddhists have often asserted the compatibility\nof Buddhism with science, favorably contrasting their religion to\nChristianity in that respect.", "\nThe full picture of the relationship between Buddhism and religion is\nmore nuanced than one of wholesale acceptance of scientific claims. I\nwill here focus on East Asia, primarily Japan and China, and the\nreception of evolutionary theory in the early twentieth century to\ngive a sense of this more complex picture. The earliest translations\nof evolutionary thought in Japan and China were not drawn from\nDarwin’s Origin of Species or Descent of Man,\nbut from works by authors who worked in Darwin’s wake, such as\nErnst Haeckel and Thomas Huxley. For example, the earliest translated\nwritings on evolutionary theory in China was a compilation by Yan Fu\nentitled On Natural Evolution (Tianyan lun), which\nincorporated excerpts by Herbert Spencer and Thomas Huxley. This work\ndrew a close distinction between social Darwinism and biological\nevolution (Ritzinger 2013). Chinese and Japanese Buddhists received\nthese ideas in the context of western colonialism and imperialism.\nEast Asian intellectuals saw how western colonial powers competed with\neach other for influence on their territory, and discerned parallels\nbetween this and the Darwinian struggle for existence. As a result,\nsome intellectuals such as the Japanese political adviser and academic\nKatō Hiroyuki (1836–1916) drew on Darwinian thought and\npopularized notions such as “survival of the fittest” to\njustify the foreign policies of the Meiji government (Burenina 2020).\nIt is in this context that we can situate Buddhist responses to\nevolutionary theory.", "\nBuddhists do not distinguish between human beings as possessing a soul\nand other animals as soulless. As we are all part of the cycle of\nrebirth, we have all been in previous lives various other beings,\nincluding birds, insects, and fish. The problem of the specificity of\nthe human soul does not even arise because of the no-self doctrine.\nNevertheless, as Justin Ritzinger (2013) points out, Chinese Buddhists\nin the 1920s and 1930s who were confronted with early evolutionary\ntheory did not accept Darwin’s theory wholesale. In their view,\nthe central element of Darwinism—the struggle for\nexistence—was incompatible with Buddhism, with its emphasis on\ncompassion with other creatures. They rejected social Darwinism (which\nsought to engineer societies along Darwinian principles) because it\nwas incompatible with Buddhist ethics and metaphysics. Struggling to\nsurvive and to propagate was clinging onto worldly things. Taixu\n(1890–1947), a Chinese Reformer and Buddhist modernist, instead\nchose to appropriate Pyotr Kropotkin’s evolutionary views,\nspecifically on mutual aid and altruism. The Russian anarchist \nargued that cooperation was central to evolutionary change, a view\nthat is currently also more mainstream. However, Kropotkin’s\nview did not go far enough in Taixu’s opinion because mutual aid\nstill requires a self. Only when one recognizes the no-self doctrine\ncould one dedicate oneself entirely to helping others, as bodhisattvas\ndo (Ritzinger 2013).", "\nSimilar dynamics can be seen in the reception of evolutionary theory\namong Japanese Buddhists. Evolutionary theory was introduced in Japan\nduring the early Meji period (1868–1912) when Japan opened\nitself to foreign trade and ideas. Foreign experts, such as the\nAmerican zoologist Edward S. Morse (1838–1925) shared their\nknowledge of the sciences with Japanese scholars. The latter were\ninterested in the social ramifications of Darwinism, particularly\nbecause they had access to translated versions of Spencer’s and\nHuxley’s work before they could read Darwin’s. Japanese\nBuddhists of the Nichiren tradition accepted many elements of\nevolutionary theory, but they rejected other elements, notably the\nstruggle for existence, and randomness and chance, as this contradicts\nthe role of karma in one’s circumstances at birth.", "\nAmong the advocates of the modern Nishiren Buddhist movement is Honda\nNisshō (1867–1931). Honda emphasized the importance of\nretrogressions (in addition to progress, which was the main element in\nevolution that western authors such as Haeckel and Spencer\nconsidered). He strongly argued against social Darwinism, the\napplication of evolutionary principles in social engineering, on\nreligious grounds. He argued that we can accept humans are descended\nfrom apes without having to posit a pessimistic view of human nature\nthat sees us as engaged in a struggle for survival with fellow human\nbeings. Like Chinese Buddhists, Honda thought Kropotkin’s thesis\nof mutual aid was more compatible with Buddhism, but he was suspicious\nof Kropotkin’s anarchism (Burenina 2020). His work, like that of\nother East Asian Buddhists indicates that historically, Buddhists are\nnot passive recipients of western science but creative interpreters.\nIn some cases, their religious reasons for rejecting some metaphysical\nassumptions in evolutionary theory led them to anticipate recent\ndevelopments in biology, such as the recognition of cooperation as an\nevolutionary principle." ], "subsection_title": "2.4 Buddhism" }, { "content": [ "\nJudaism is one of the three major Abrahamic monotheistic traditions,\nencompassing a range of beliefs and practices that express a covenant\nbetween God and the people of Israel. Central to both Jewish practice\nand beliefs is the study of texts, including the written Torah (the\nTanakh, sometimes called “Hebrew Bible”), and the\n“Oral Law” of Rabbinic Judaism, compiled in such works\nlike the Talmud. There is also a corpus of esoteric, mystical\ninterpretations of biblical texts, the Kabbalah, which has influenced\nJewish works on the relationship between science and religion. The\nKabbalah also had an influence on Renaissance and early modern\nChristian authors such as Pico Della Mirandola, whose work helped to\nshape the scientific revolution (see the entry on\n Giovanni Pico della Mirandola).\n The theologian Maimonides (Rabbi Moshe ben-Maimon, 1138–1204,\naka Rambam) had an enduring influence on Jewish thought up until\ntoday, also in the science and religion literature.", "\nMost contemporary strains of Judaism are Rabbinic, rather than\nbiblical, and this has profound implications for the relationship\nbetween religion and science. While both Jews and Evangelical\nChristians emphasize the reading of sacred texts, the Rabbinic\ntraditions (unlike, for example, the Evangelical Christian tradition)\nholds that reading and interpreting texts is far from straightforward.\nScripture should not be read in a simple literal fashion. This opens\nup more space for accepting scientific theories (e.g., Big Bang\ncosmology) that seem at odds with a simple literal reading of the\nTorah (e.g., the six-day creation in Genesis) (Mitelman 2011\n [Other Internet Resources]).\n Moreover, most non-Orthodox Jews in the US identify as politically\nliberal, so openness to science may also be an identity marker given\nthat politically liberal people in the US have positive attitudes\ntoward science (Pew Forum, 2021\n [Other Internet Resources]).", "\nJewish thinkers have made substantive theoretical contributions to the\nrelationship between science and religion, which differ in interesting\nrespects from those seen in the literature written by Christian\nauthors. To give just a few examples, Hermann Cohen (1842–1918),\na prominent neo-Kantian German Jewish philosopher, thought of the\nrelationship between Judaism and science in the light of the advances\nin scientific disciplines and the increased participation of Jewish\nscholars in the sciences. He argued that science, ethics, and Judaism\nshould all be conceived of as distinct but complementary sciences.\nCohen believed that his Jewish religious community was facing an\nepistemic crisis. All references to God had become suspect due to an\nadherence to naturalism, at first epistemological, but fast becoming\nontological. Cohen saw the concept of a transcendent God as\nfoundational to both Jewish practice and belief, so he thought\nadherence to wholesale naturalism threatened both Jewish orthodoxy and\northopraxy. As Teri Merrick (2020) argues, Cohen suspected this was in\npart due to epistemic oppression and self-censuring (though Cohen did\nnot frame it in these terms). Because Jewish scientists wanted to\nretain credibility in the Christian majority culture, they underplayed\nand neglected the rich Jewish intellectual legacy in their practice.\nIn response to this intellectual crisis, Cohen proposed to reframe\nJewish thought and philosophy so that it would be recognized as both\ncontinuous with the tradition and essentially contributing to ethical\nand scientific advances. In this way, he reframed this tradition,\narticulating a broadly Kantian philosophy of science to combat a\nperceived conflict between Judaism and science (see the entry on\n Hermann Cohen\n for an in-depth discussion).", "\nJewish religious scholars have examined how science might influence\nreligious beliefs, and vice versa. Rather than a unified response we\nsee a spectrum of philosophical views, especially since the nineteenth\nand early twentieth century. As Shai Cherry (2003) surveys, Jewish\nscholars in the early twentieth century accepted biological evolution\nbut were hesitant about Darwinian natural selection as the mechanism.\nThe Latvian-born Israeli rabbi Abraham Isaac Kook (1865–1935)\nthought that religion and science are largely separate domains (a view\nsomewhat similar to Gould’s NOMA), though he believed that there\nwas a possible flow from religion to science. For example, Kook\nchallenged the lack of directionality in Darwinian evolutionary\ntheory. Using readings of the Kabbalah (and Halakhah, Jewish law), he\nproposed that biological evolution fits in a larger picture of cosmic\nevolution towards perfection.", "\nBy contrast, the American rabbi Morcedai Kaplan (1881–1983)\nthought information flow between science and religion could go in both\ndirections, a view reminiscent to Barbour’s dialogue position.\nHe repeatedly argued against scientism (the encroachment of science on\ntoo many aspects of human life, including ethics and religion), but he\nbelieved nevertheless we ought to apply scientific methods to\nreligion. He saw reality as an unfolding process without a\npre-ordained goal: it was progressive, but not teleologically\ndetermined. Kaplan emphasized the importance of morality (and\nidentified God as the source of this process), and conceptualized\nhumanity as not merely a passive recipient of evolutionary change, but\nan active participant, prefiguring work in evolutionary biology on the\nimportance of agency in evolution (e.g., Okasha 2018). Thus,\nKaplan’s reception of scientific theories, especially evolution,\nled him to formulate an early Jewish process theology.", "\nReform Judaism endorses an explicit anti-conflict view on the\nrelationship between science and religion. For example, the Pittsburgh\nPlatform of 1885, the first document of the Reform rabbinate, has a\nstatement that explicitly says that science and Judaism are not in\nconflict: ", "\n\n\nWe hold that the modern discoveries of scientific researches in the\ndomain of nature and history are not antagonistic to the doctrines of\nJudaism. \n", "\nThis Platform had an enduring influence on Reform Judaism over the\nnext decades. Secular Jewish scientists such as Albert Einstein,\nRichard Feynman, Douglas Daniel Kahneman, and Stephen J. Gould have\nalso reflected on the relationship between science and broader issues\nof existential significance, and have exerted considerable influence\non the science and religion debate." ], "subsection_title": "2.5 Judaism" } ] }, { "main_content": [ "\nCurrent work in the field of science and religion encompasses a wealth\nof topics, including free will, ethics, human nature, and\nconsciousness. Contemporary natural theologians discuss fine-tuning,\nin particular design arguments based on it (e.g., R. Collins 2009),\nthe interpretation of multiverse cosmology, and the significance of\nthe Big Bang (see entries on\n fine-tuning arguments and\n natural theology and natural religion).\n For instance, authors such as Hud Hudson (2013)\nhave explored the idea that God has actualized the best of all\npossible multiverses. Here follows an overview of two topics that\ncontinue to generate substantial interest and debate: divine action\n(and the closely related topic of creation) and human origins. The\nfocus will be on Christian work in science and religion, due to its\nprevalence in the literature." ], "section_title": "3. Central topics in the debate", "subsections": [ { "content": [ "\nBefore scientists developed their views on cosmology and origins of\nthe world, Western cultures already had a doctrine of creation, based\non biblical texts (e.g., the first three chapters of Genesis and the\nbook of Revelation) and the writings of church fathers such as\nAugustine. This doctrine of creation has the following interrelated\nfeatures: first, God created the world ex nihilo, i.e., out\nof nothing. Differently put, God did not need any pre-existing\nmaterials to make the world, unlike, e.g., the Demiurge (from Greek\nphilosophy), who created the world from chaotic, pre-existing matter.\nSecond, God is distinct from the world; the world is not equal to or\npart of God (contra pantheism or panentheism) or a (necessary)\nemanation of God’s being (contra Neoplatonism). Rather, God\ncreated the world freely. This introduces an asymmetry between creator\nand creature: the world is radically contingent upon God’s\ncreative act and is also sustained by God, whereas God does not need\ncreation (Jaeger 2012b: 3). Third, the doctrine of creation holds that\ncreation is essentially good (this is repeatedly affirmed in Genesis\n1). The world does contain evil, but God does not directly cause this\nevil to exist. Moreover, God does not merely passively sustain\ncreation, but rather plays an active role in it, using special divine\nactions (e.g., miracles and revelations) to care for creatures.\nFourth, God made provisions for the end of the world, and will create\na new heaven and earth, in this way eradicating evil.", "\nViews on divine action are related to the doctrine of creation.\nTheologians commonly draw a distinction between general and special\ndivine action, but within the field of science and religion there is\nno universally accepted definition of these two concepts. One way to\ndistinguish them (Wildman 2008: 140) is to regard general divine\naction as the creation and sustenance of reality, and special divine\naction as the collection of specific providential acts, such as\nmiracles and revelations to prophets. Drawing this distinction allows\nfor creatures to be autonomous and indicates that God does not\nmicromanage every detail of creation. Still, the distinction is not\nalways clear-cut, as some phenomena are difficult to classify as\neither general or special divine action. For example, the Roman\nCatholic Eucharist (in which bread and wine become the body and blood\nof Jesus) or some healing miracles outside of scripture seem mundane\nenough to be part of general housekeeping (general divine action), but\nstill seem to involve some form of special intervention on God’s\npart. Alston (1989) makes a related distinction between direct and\nindirect divine acts. God brings about direct acts without the use of\nnatural causes, whereas indirect acts are achieved through natural\ncauses. Using this distinction, there are four possible kinds of\nactions that God could do: God could not act in the world at all, God\ncould act only directly, God could act only indirectly, or God could\nact both directly and indirectly.", "\nIn the science and religion literature, there are two central\nquestions on creation and divine action. To what extent are the\nChristian doctrine of creation and traditional views of divine action\ncompatible with science? How can these concepts be understood within a\nscientific context, e.g., what does it mean for God to create and act?\nNote that the doctrine of creation says nothing about the age of the\nEarth, nor does it specify a mode of creation. This allows for a wide\nrange of possible views within science and religion, of which Young\nEarth creationism is but one that is consistent with scripture.\nIndeed, some scientific theories, such as the Big Bang theory, first\nproposed by the Belgian Roman Catholic priest and astronomer Georges\nLemaître (1927), look congenial to the doctrine of creation. The\ntheory is not in contradiction, and could be integrated into\ncreatio ex nihilo as it specifies that the universe\noriginated from an extremely hot and dense state around 13.8 billion\nyears ago (Craig 2003), although some philosophers have argued against\nthe interpretation that the universe has a temporal beginning (e.g.,\nPitts 2008).", "\nThe net result of scientific findings since the seventeenth century\nhas been that God was increasingly pushed into the margins. This\nencroachment of science on the territory of religion happened in two\nways: first, scientific findings—in particular from geology and\nevolutionary theory—challenged and replaced biblical accounts of\ncreation. Although the doctrine of creation does not contain details\nof the mode and timing of creation, the Bible was regarded as\nauthoritative, and that authority got eroded by the sciences. Second,\nthe emerging concept of scientific laws in seventeenth- and\neighteenth-century physics seemed to leave no room for special divine\naction. These two challenges will be discussed below, along with\nproposed solutions in the contemporary science and religion\nliterature.", "\nChristian authors have traditionally used the Bible as a source of\nhistorical information. Biblical exegesis of the creation narratives,\nespecially Genesis 1 and 2 (and some other scattered passages, such as\nin the Book of Job), remains fraught with difficulties. Are these\ntexts to be interpreted in a historical, metaphorical, or poetic\nfashion, and what are we to make of the fact that the order of\ncreation differs between these accounts (Harris 2013)? The Anglican\narchbishop James Ussher (1581–1656) used the Bible to date the\nbeginning of creation at 4004 BCE. Although such literalist\ninterpretations of the biblical creation narratives were not uncommon,\nand are still used by Young Earth creationists today, theologians\nbefore Ussher already offered alternative, non-literalist readings of\nthe biblical materials (e.g., Augustine De Genesi ad\nlitteram, 416). From the seventeenth century onward, the\nChristian doctrine of creation came under pressure from geology, with\nfindings suggesting that the Earth was significantly older than 4004\nBCE. From the eighteenth century on, natural philosophers, such as\nBenoît de Maillet, Lamarck, Chambers, and Darwin, proposed\ntransmutationist (what would now be called evolutionary) theories,\nwhich seem incompatible with scriptural interpretations of the special\ncreation of species. Following the publication of Darwin’s\nOrigin of Species (1859), there has been an ongoing\ndiscussion on how to reinterpret the doctrine of creation in the light\nof evolutionary theory (see Bowler 2009 for an overview).", "\nTed Peters and Martinez Hewlett (2003) have outlined a divine action\nspectrum to clarify the distinct positions about creation and divine\naction in the contemporary science and religion literature that\nfocuses on Christians, agnostics, and atheists. They discern two\ndimensions in this spectrum: the degree of divine action in the\nnatural world, and the form of causal explanations that relate divine\naction to natural processes. At one extreme are creationists. Like\nother theists, they believe God has created the world and its\nfundamental laws, and that God occasionally performs special divine\nactions (miracles) that intervene in the fabric of those laws.\nCreationists deny any role of natural selection in the origin of\nspecies. Within creationism, there are Old and Young Earth\ncreationism, with the former accepting geology and rejecting\nevolutionary biology, and the latter rejecting both. Next to\ncreationism is Intelligent Design, which affirms divine intervention\nin natural processes. Intelligent Design creationists (e.g., Dembski\n1998) believe there is evidence of intelligent design in\norganisms’ irreducible complexity; on the basis of this they\ninfer design and purposiveness (see Kojonen 2016). Like other\ncreationists, they deny a significant role for natural selection in\nshaping organic complexity and they affirm an interventionist account\nof divine action. For political reasons they do not label their\nintelligent designer as God, as they hope to circumvent the\nconstitutional separation of church and state in the US which\nprohibits teaching religious doctrines in public schools (Forrest\n& Gross 2004). Theistic evolutionists hold a non-interventionist\napproach to divine action: God creates indirectly, through the laws of\nnature (e.g., through natural selection). For example, the theologian\nJohn Haught (2000) regards divine providence as self-giving love, and\nnatural selection and other natural processes as manifestations of\nthis love, as they foster creaturely autonomy and independence. While\ntheistic evolutionists allow for special divine action, particularly\nthe miracle of the Incarnation in Christ (e.g., Deane-Drummond 2009),\ndeists such as Michael Corey (1994) think there is only general divine\naction: God has laid out the laws of nature and lets it run like\nclockwork without further interference. Deism is still a long distance\nfrom ontological materialism, the view that the material world is all\nthere is. Ontological materialists tend to hold that the universe is\nintelligible, with laws that scientists can discover, but there is no\nlawgiver and no creator.", "\nViews on divine action were influenced by developments in physics and\ntheir philosophical interpretation. In the seventeenth century,\nnatural philosophers, such as Robert Boyle and John Wilkins, developed\na mechanistic view of the world as governed by orderly and lawlike\nprocesses. Laws, understood as immutable and stable, created\ndifficulties for the concept of special divine action (Pannenberg\n2002). How could God act in a world that was determined by laws?", "\nOne way to regard miracles and other forms of special divine action is\nto see them as actions that somehow suspend or ignore the laws of\nnature. David Hume (1748: 181), for instance, defined a miracle as\n“a transgression of a law of nature by a particular volition of\nthe deity, or by the interposal of some invisible agent”, and,\nmore recently, Richard Swinburne (1968: 320) defines a miracle as\n“a violation of a law of Nature by a god”. This concept of\ndivine action is commonly labeled interventionist. Interventionism\nregards the world as causally deterministic, so God has to create room\nfor special divine actions. By contrast, non-interventionist forms of\ndivine action require a world that is, at some level,\nnon-deterministic, so that God can act without having to suspend or\nignore the laws of nature.", "\nIn the seventeenth century, the explanation of the workings of nature\nin terms of elegant physical laws suggested the ingenuity of a divine\ndesigner. The design argument reached its peak during the seventeenth\nand early eighteenth century (McGrath 2011). For example, Samuel\nClarke (1705: part XI, cited in Schliesser 2012: 451) proposed an\na posteriori argument from design by appealing to Newtonian\nscience, calling attention to the ", "\n\n\nexquisite regularity of all the planets’ motions without\nepicycles, stations, retrogradations, or any other deviation or\nconfusion whatsoever. \n", "\nA late proponent of this view of nature as a perfect smooth machine is\nWilliam Paley’s Natural Theology (1802).", "\nAnother conclusion that the new laws-based physics suggested was that\nthe universe was able to run smoothly without requiring an intervening\nGod. The increasingly deterministic understanding of the universe,\nruled by deterministic causal laws as, for example, outlined by\nPierre-Simon Laplace (1749–1827), seemed to leave no room for\nspecial divine action, which is a key element of the traditional\nChristian doctrine of creation. Newton resisted interpretations like\nthese in an addendum to the Principia in 1713: the\nplanets’ motions could be explained by laws of gravity, but the\npositions of their orbits, and the positions of the stars—far\nenough apart so as not to influence each other\ngravitationally—required a divine explanation (Schliesser 2012).\nAlston (1989) argued, contra authors such as Polkinghorne (1998), that\nmechanistic, pre-twentieth century physics is compatible with divine\naction and divine free will. Assuming a completely deterministic world\nand divine omniscience, God could set up initial conditions and the\nlaws of nature in such a way as to bring God’s plans about. In\nsuch a mechanistic world, every event is an indirect divine act.", "\nAdvances in twentieth-century physics, including the theories of\ngeneral and special relativity, chaos theory, and quantum theory,\noverturned the mechanical clockwork view of creation. In the latter\nhalf of the twentieth century, chaos theory and quantum physics have\nbeen explored as possible avenues to reinterpret divine action. John\nPolkinghorne (1998) proposed that chaos theory not only presents\nepistemological limits to what we can know about the world, but that\nit also provides the world with an “ontological openness”\nin which God can operate without violating the laws of nature. One\ndifficulty with this model is that it moves from our knowledge of the\nworld to assumptions about how the world is: does chaos theory mean\nthat outcomes are genuinely undetermined, or that we as limited\nknowers cannot predict them? Robert Russell (2006) proposed that God\nacts in quantum events. This would allow God to directly act in nature\nwithout having to contravene the laws of nature. His is therefore a\nnon-interventionist model: since, under the Copenhagen interpretation\nof quantum mechanics, there are no natural efficient causes at the\nquantum level, God is not reduced to a natural cause. Murphy (1995)\noutlined a similar bottom-up model where God acts in the space\nprovided by quantum indeterminacy. These attempts to locate\nGod’s actions either in chaos theory or quantum mechanics, which\nLydia Jaeger (2012a) has termed “physicalism-plus-God”,\nhave met with sharp criticism (e.g., Saunders 2002; Jaeger 2012a,b).\nAfter all, it is not even clear whether quantum theory would allow for\nfree human action, let alone divine action, which we do not know much\nabout (Jaeger 2012a). Next to this, William Carroll (2008), building\non Thomistic philosophy, argues that authors such as Polkinghorne and\nMurphy are making a category mistake: God is not a cause in the way\ncreatures are causes, competing with natural causes, and God does not\nneed indeterminacy in order to act in the world. Rather, as primary\ncause God supports and grounds secondary causes. While this\nneo-Thomistic proposal is compatible with determinism (indeed, on this\nview, the precise details of physics do not matter much), it blurs the\ndistinction between general and special divine action. Moreover, the\nIncarnation suggests that the idea of God as a cause among natural\ncauses is not an alien idea in theology, and that God incarnate as\nJesus at least sometimes acts as a natural cause (Sollereder\n2015).", "\nThere has been a debate on the question to what extent randomness is a\ngenuine feature of creation, and how divine action and chance\ninterrelate. Chance and stochasticity are important features of\nevolutionary theory (the non-random retention of random variations).\nIn a famous thought experiment, Gould (1989) imagined that we could\nrewind the tape of life back to the time of the Burgess Shale (508\nmillion years ago); the chance that a rerun of the tape of life would\nend up with anything like the present-day life forms is vanishingly\nsmall. However, Simon Conway Morris (2003) has insisted species very\nsimilar to the ones we know now, including humans, would evolve under\na broad range of conditions.", "\nUnder a theist interpretation, randomness could either be a merely\napparent aspect of creation, or a genuine feature. Plantinga suggests\nthat randomness is a physicalist interpretation of the evidence. God\nmay have guided every mutation along the evolutionary process. In this\nway, God could", "\n\n\nguide the course of evolutionary history by causing the right\nmutations to arise at the right time and preserving the forms of life\nthat lead to the results he intends. (2011: 121)\n", "\nBy contrast, other authors see stochasticity as a genuine design\nfeature, and not just as a physicalist gloss. Their challenge is to\nexplain how divine providence is compatible with genuine randomness.\n(Under a deistic view, one could simply say that God started the\nuniverse up and did not interfere with how it went, but that option is\nnot open to the theist, and most authors in the field of science and\nreligion are not deists.) The neo-Thomist Elizabeth Johnson (1996)\nargues that divine providence and true randomness are compatible: God\ngives creatures true causal powers, thus making creation more\nexcellent than if they lacked such powers. Random occurrences are also\nsecondary causes. Chance is a form of divine creativity that creates\nnovelty, variety, and freedom. One implication of this view is that\nGod may be a risk taker—although, if God has a providential plan\nfor possible outcomes, there is unpredictability but not risk. Johnson\nuses metaphors of risk taking that, on the whole, leave the creator in\na position of control. Creation, then, is akin to jazz improvisation.\nWhy would God take risks? There are several solutions to this\nquestion. The free will theodicy says that a creation that exhibits\nstochasticity can be truly free and autonomous:", "\n\n\nAuthentic love requires freedom, not manipulation. Such freedom is\nbest supplied by the open contingency of evolution, and not by strings\nof divine direction attached to every living creature. (Miller 1999\n[2007: 289])\n", "\nThe “only way theodicy” goes a step further, arguing that\na combination of laws and chance is not only the best way, but the\nonly way for God to achieve God’s creative plans (see, e.g.,\nSouthgate 2008 for a defense)." ], "subsection_title": "3.1 Divine action and creation" } ] } ]

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Connecting Evolution, Brain, Cognition and Culture,\nAbingdon & New York: Routledge.", "Wildman, Wesley, 2008, “The Divine Action Project,\n1988–2003”, in Scientific Perspectives on Divine\nAction: Twenty Years of Challenge and Progress, Robert Russell,\nNancey Murphy, and William Stoeger (eds.), Berkeley, CA: Vatican\nObservatory Publications; Center for Theology and the Natural\nSciences, pp. 133–176.", "Worrall, John, 2004, “Science Discredits Religion”, in\nContemporary Debates in Philosophy of Religion, Michael L.\nPeterson and Raymond J. VanArragon (eds.), Malden, MA: Blackwell, pp.\n59–72.", "Clayton, Philip and Zachary Simpson (eds.), 2006, The Oxford\nHandbook of Religion and Science, Oxford/New York: Oxford\nUniversity Press. doi:10.1093/oxfordhb/9780199543656.001.0001", "Dixon, Thomas, G. N. Cantor, and Stephen Pumfrey (eds.), 2010,\nScience and Religion: New Historical Perspectives,\nCambridge/New York: Cambridge University Press.", "Fehige, Yiftach (ed.), 2016, Science and Religion: East and\nWest, London: Routledge. doi:10.4324/9781315659831", "Harrison, Peter (ed.), 2010, The Cambridge Companion to\nScience and Religion, Cambridge: Cambridge University Press.\ndoi:10.1017/CCOL9780521885386", "McGrath, Alister, 2020, Science and Religion: A New\nIntroduction, third edition, Hoboken, NJ: Wiley-Blackwell.", "Stump, J. B. and Alan G. Padgett (eds.), 2012, The Blackwell\nCompanion to Science and Christianity, Chichester, UK: John Wiley\n& Sons. doi:10.1002/9781118241455" ]

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[ "\nThe notion of collective responsibility, like that of\npersonal responsibility and shared responsibility,\nrefers in most contexts to both the causal responsibility of\nmoral agents for harm in the world and the blameworthiness that we\nascribe to them for having caused such harm. Hence, it is, like its\ntwo more purely individualistic counterparts, almost always a notion\nof moral, rather than purely causal, responsibility.\nBut, unlike its two more purely individualistic counterparts, it does\nnot associate either causal responsibility or blameworthiness with\ndiscrete individuals or locate the source of moral responsibility in\nthe free will of individual moral agents. Instead, it associates both\ncausal responsibility and blameworthiness with groups and\nlocates the source of moral responsibility in the collective actions\ntaken by these groups understood as collectives.", "\nSince this notion of collective responsibility makes groups, as\ndistinct from their individual members, out to be moral agents, it has\nundergone a great deal of scrutiny in recent years by methodological\nand normative individualists alike. Methodological individualists\nchallenge the very possibility of associating moral agency with\ngroups, as distinct from their individual members, and normative\nindividualists argue that collective responsibility violates\nprinciples of both individual responsibility and fairness. In response\nto these challenges, proponents of collective responsibility set out\nto show that collective responsibility, as well as group intentions,\ncollective action, and group blameworthiness, are metaphysically\npossible and can be ascribed to agents fairly in at least some, if not\nall, cases.", "\nWhile the vast majority of those now writing on collective\nresponsibility in philosophical circles continue to debate the\npossibility of collective responsibility, a growing number of scholars\nhave in recent years placed three further—and very\nimportant—concerns at the center of our attention. The first has\nto do with whether groups have to meet the same stringent conditions\nof moral responsibility that individuals do. (Intentionality becomes a\nprimary site of controversy here.) The second has to do with the\nadvantages and disadvantages of holding particular kinds of groups,\ne.g., nation states, races, and ethnic groups, morally responsible in\npractice. The third has to do with what moral implications follow for\ngroup members from the moral responsibility of their group for harm.\n(Do they, too, become morally responsible for the harms and, if so,\nhow is the blame to be distributed?)", "\nThe backward looking notion of collective responsibility cited above\nis what most philosophers have in mind when they talk about collective\nresponsibility. But during the past several years there has been a\ngrowing interest in what has come to be known as forward looking\ncollective responsibility or forward looking collective moral\nresponsibility. Forward looking collective responsibility, unlike\nits backward looking counterpart, does not focus on whether a\nparticular collective agent caused harm in the sense relevant to moral\nblameworthiness. Nor does it involve itself with blame in general.\nInstead, it focuses on what, if anything, the agent can be expected to\ndo with respect to remedying the harm and preventing its reoccurrence.\nHence, it is sometimes referred to as remedial responsibility\nand incorporated into larger controversies about the scope of our\nduties to respond." ]

[ { "content_title": "1. Collective Responsibility: the Controversies", "sub_toc": [] }, { "content_title": "2. Making Sense of Collective Responsibility: Actions, Intentions, and Group Solidarity", "sub_toc": [] }, { "content_title": "3. Collective Responsibility and the Structure of Groups", "sub_toc": [] }, { "content_title": "4. Can Collective Responsibility be Distributed?", "sub_toc": [] }, { "content_title": "5. Alternative Approaches to Collective Responsibility", "sub_toc": [] }, { "content_title": "6. Collective Responsibility and the Question of Consequences", "sub_toc": [] }, { "content_title": "7. Forward Looking Collective Responsibility", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nBoth notions of collective responsibility are controversial. The\ntraditional, backward looking, notion does not sit well with those who\nare skeptical about the ability of collective entities to\nwill and to act as collective entities. The forward\nlooking notion is less controversial than its backward looking\ncounterpart is with respect to its metaphysical foundations. But it\ndoes raise questions about how—on the basis of what norms and\nprinciples—we can ascribe such responsibility in practice.", "\nThree kinds of controversies surround the traditional notion of\ncollective responsibility.", "\nThe first of these controversies concerns whether or not collective\nresponsibility makes sense as a form of moral responsibility. Not\nsurprisingly, the primary focus of attention here has been with both\nthe moral agency of groups in general and the possibility of group\nintentions in particular. How, participants in this controversy have\nasked, can we understand the notion of collective responsibility as a\nmatter of moral—and not just causal—responsibility? Is it\npossible for groups, as distinct from their members, to cause harm in\nthe sense required by moral responsibility? to act as collectives? to\nhave intentions? Is it possible for groups, as distinct from their\nmembers, to be morally blameworthy for bringing about harm? to be\nguilty as moral agents?", "\nThe second controversy, interestingly enough, is not really about the\nmoral responsibility of groups at all, even though it is couched in\nthe language of collective moral responsibility. Instead, it is about\nthe moral responsibility of individuals who belong to groups that are\nthemselves thought to be morally responsible for particular cases of\nharm. How, participants in this controversy have asked, can we\ndistribute collective responsibility across individual members of such\na group? Does it makes sense to distribute collective responsibility\nin general? Is it appropriate to hold individual group members morally\nresponsible for harm that other group members caused? that the group\nitself caused? that the group as a whole failed to prevent? If so,\nunder what conditions and with respect to what particular kinds of\ngroups? Random collections of individuals? Interest-based groups?\nCorporate entities? ", "\nThe third controversy is primarily normative and concerns the value of\nascribing collective responsibility in practice. In some cases, the\nconcern is with the general practice of collective responsibility and\nits consequences for our ability to sustain the values of\nindividualism, freedom, and justice. In other cases, the concern is\nwith the ascriptions of collective responsibility in particular\ncontexts, e.g., in the contexts of war tribunals, reparations for\nslavery, terrorism, and rape, and with whether such ascriptions are\nproductive and/or fair to those being blamed. What would happen,\ncritics ask, if we were to replace individual responsibility with\ncollective responsibility? Would we be letting individuals off the\nhook? Would we be eroding the practice of personal responsibility in\ngeneral?", "\nThe controversies surrounding forward looking collective\nresponsibility have to do with both the role of agent causation in\nascribing responsibility for remedying harm in the world and the norms\nand principles that may—or may not—be appropriate to\ninvoke in this context. Does responsibility for remedying harm come\ndown to who caused the harm? If not, what other criteria should we\nemploy? Should we turn to those who are most capable of preventing the\nharm and hold them—and the community of which they are a\npart—responsible for remedial action? (Is forward looking\ncollective responsibility primarily an exercise in pragmatism?) Do\nconsiderations of fairness have any place in our ascriptions of such\nresponsibility and, if so, what kinds of fairness are relevant? What\nhappens in cases where there is no collective entity capable of taking\nremedial action? Do we have a moral obligation to bring such a\ncollective entity about and, if so, on what basis?" ], "section_title": "1. Collective Responsibility: the Controversies", "subsections": [] }, { "main_content": [ "\nAlmost all of those now writing about collective responsibility agree\nthat collective responsibility would make sense if it were merely an\naggregative phenomenon. But they disagree markedly about whether\ncollective responsibility makes sense as a non-distributive\nphenomenon, i.e., as a phenomenon that transcends the contributions of\nparticular group members. In this context, as in many others, skeptics\nset the agenda. Two claims become crucial. The first is that groups,\nunlike individuals, cannot form intentions and hence cannot be\nunderstood to act or to cause harm qua groups. The second is\nthat groups, as distinct from their individual members, cannot be\nunderstood as morally blameworthy in the sense required by moral\nresponsibility.", "\nBoth claims come out of classical methodological individualism of the\nsort articulated by Max Weber (Weber 1914) and H. D. Lewis (Lewis\n1948) in their respective rejections of collective responsibility. In\nEconomy and Society Vol. I, Weber (Weber 1914) argues that\ncollective responsibility makes no sense both because we cannot\nisolate genuinely collective actions, as distinct from identical\nactions of many persons, and because groups, unlike the individuals\nwho belong to them, cannot think as groups or formulate intentions of\nthe kind normally thought to be necessary to actions. H. D. Lewis\nfollows suit in his own arguments and couples his methodological\nindividualism with a sense of moral outrage at the idea of blaming\nindividuals for the actions of others. Lewis writes:", "\nValue belongs to the individual and it is the individual who is the\nsole bearer of moral responsibility. No one is morally guilty except\nin relation to some conduct which he himself considered to be wrong\n… Collective responsibility is … barbarous. (Lewis 1948,\npp. 3–6)\n", "\nContemporary critics of collective responsibility do not generally go\nas far as Lewis does here in equating collective responsibility with\nbarbarism. But they do generally share their predecessors’\nskepticism about the possibility of both group intentions and\ngenuinely collective actions. (See below.) Likewise, they, too, worry\nabout the fairness of ascribing collective responsibility to\nindividuals who do not themselves directly cause harm or who do not\nbring about harm purposefully. Stephen Sverdlik writes:", "\nIt would be unfair, whether we are considering a result produced by\nmore than one person’s action or by a single person, to blame a\nperson for a result that he or she did not intend to produce.\n(Sverdlik 1987, p. 68)\n", "\nBoth of these claims—that genuinely collective actions are not\npossible and that it would be unfair to consider agents morally\nblameworthy for harm that they did not bring about\npurposively—rest on two normative assumptions that are key to\nthe critic’s position. Both concern the importance of\nintentions. The first is that actions—whether they are\nindividual or collective—necessarily begin with intentions.\n(Otherwise, they are not actions but instead kinds of behavior.) The\nsecond is that moral blameworthiness has its source in and requires\nthe existence of bad intentions—or at least moral\nfaultiness—on the part of those being held responsible.", "\nThe first assumption, namely, that all actions begin with intentions,\nis very useful to critics because it enables them to write group\nintentions into the definition of collective action itself and hence\nrender group intentions a necessary condition of collective\nresponsibility. J. Angelo Corlett’s definition of a collective\naction is typical here. According to Corlett,", "\n[a] collective (intentional) action is an action the subject of which\nis a collective intentional agent. A collective behavior is a\ndoing or behavior that is the result of a collective, though not the\nresult of its intentions. A collective action is caused by\nthe beliefs and desires (wants) of the collective itself, whether or\nnot such beliefs and desires can be accounted for or explained in\nindividualistic terms (Corlett 2001, p. 575).\n", "\nThe second assumption, namely, that moral blameworthiness of all kinds\nis grounded in the bad intentions of moral agents who cause harm, is\nalso very useful to critics of collective responsibility, since it\nenables them to stipulate that collective responsibility requires, not\njust group intentions, but the ability of groups to have bad\nintentions or at least to be morally faulty. How, critics ask, can\ngroups, as distinct from their individual members, be understood to\nhave bad intentions? to be morally faulty? to have a moral character,\nfaulty or not? How, in other words, can they be understood as\nappropriate bearers of moral blameworthiness, guilt, or shame?", "\nA majority of critics here concentrate on showing either that actions\nare associated exclusively with individuals, not groups, or that\ngroups, which do not have minds of their own, cannot make choices or\nhold beliefs in the sense required by the formulation of intentions.\nH. D Lewis concentrates on making both points in his 1948 critique of\ncollective responsibility. So, too, does J. W. N. Watkins (1957).\nLater methodological individualists such as Alvin Goldman (1970),\nStephen Sverdlik (1987), J. Angelo Corlett (Corlett 2001), and Jan\nNarveson (2002), unlike their predecessors, are generally willing to\nacknowledge the sensibility of collective responsibility in a limited\nnumber of cases. But, they, too, draw attention to the host of\ndifficulties that arise for collective responsibility as a moral\nconstruct once we acknowledge the simple fact that collectives do not\nhave full blown mental lives.", "\nCritics of collective responsibility pay somewhat less attention to\nthe nature of collective moral blameworthiness than they do to the\nnature of collective actions. But they do sometimes worry about the\nappropriateness of associating moral blameworthiness with groups, as\ndistinct from group members. R. S. Downie, among others, places what\nturns out to be a very traditional notion of moral responsibility at\nthe center of his attention and argues that", "\n[c]ollectives do not have moral faults, since they don’t make\nmoral choices, and hence they cannot properly be ascribed moral\nresponsibility. … For there to be moral responsibility there\nmust be blameworthiness involving a morally faulty decision, and this\ncan only occur at the individual level (Downie 1969, p. 67).\n", "\nJan Narveson goes as far in this context as to argue that the bearers\nof moral blameworthiness have to be individuals because only\nindividuals can have moral agency. “Nothing else,”\nNarveson writes, “can literally be the bearer of full\nresponsibility” (Narveson 2002, p. 179). The word\n“literally” here turns out to be significant for those\nwriting on collective responsibility. For, it contrasts with the sense\nshared by Narveson and others that we might in the end be able to make\nsense of collective responsibility in metaphorical terms by treating\nindividual moral agency, including both agent causation and moral\nblameworthiness, as a metaphor for group agency of the sort relevant\nto moral responsibility traditionally understood.", "\nDefenders of collective responsibility rely on a variety of\nphilosophical strategies to debunk the above claims and to justify\nboth the possibility of collective responsibility in some, if not all,\ncases, and the coherence of collective responsibility as an\nintellectual construct. One of these strategies has been simply to\npoint out both that we blame groups all the time in practice and that\nwe do so in a way that is difficult to analyze with the precepts of\nmethodological individualism. David Cooper, among others, uses this\nstrategy to great effect in his own defense of collective\nresponsibility. According to Cooper, “[t]here is an obvious\npoint to be recognized and that obvious point is that responsibility\nis ascribed to collectives, as well as to individual persons. Blaming\nattitudes are held towards collective as well as towards\nindividuals,” (Cooper 1968, p. 258.)", "\nDeborah Tollefsen (Tollefsen, 2003) zeros in on the fact that we\nexpress various reactive attitudes to groups, e.g., anger, resentment,\nand moral indignation. How, she asks, can we make sense of these\nattitudes? She argues that we cannot do so by simply positing that our\nemotions are misfiring here or that our attitudes are really directed\nat group members rather than at groups themselves. Instead, we have to\nrecognize that, within our practices of moral responsibility (a\nlà Strawson), groups have the ability of moral address and\nexhibit moral competence.", "\nBut of course our practices of moral responsibility, as well as the\nreactive attitudes that ground them, may not be justified. Cooper\nhimself acknowledges that both our use of language here and our\nblaming attitudes may be misguided. Hence, they find it necessary to\nshow, not just that we ascribe blame to collectives in practice, but\nthat the collective blame that we ascribe cannot be analyzed in terms\nof individual blame. Cooper himself takes on this project by exploring\nparticular cases of blame, e.g., those associated with sports clubs\nand nations, that, he argues, can only attach to groups. According to\nCooper, when we look at how such collectives act, we see that whether\nwe regard statements about collectives as propositional functions or\nnot, we cannot deduce from them statements about particular\nindividuals. “This is so,” he argues, “because the\nexistence of a collective is compatible with varying membership. No\ndeterminate set of individuals is necessary for the existence of the\ncollective” (Cooper 1968, p. 260).", "\nIn a similar vein, Peter French focuses on that class of predicates\nthat, he contends, can only be true of collectives. According to\nFrench,", "\n[t]here is a class of predicates that just cannot be true of\nindividuals, that can only be true of collectives. Examples of such\npredicates abound … and include ‘disbanded’ (most\nuses of), ‘lost the football game’, ‘elected a\npresident’, and ‘passed an amendment’. …\nMethodological individualism would be at a loss in this context.\n(French 1998, p. 37)\n", "\nA majority of those who defend the possibility of group actions in\nthis context rely on linguistic analyses. But there are also those\nwho, like Larry May, turn instead to social theory and to the\nexistentialist tradition. May himself uses the relational theory of\nJean-Paul Sartre to argue that groups can legitimately be ascribed\nactions in cases where individuals are related to one another and act\nin ways together that would not be possible if they acted alone. May\nsets down two relationally-based conditions under which we can\nlegitimately say of an action that it is collective rather than\nindividual—which for May means, not trans-individual, but\nrelational. The first condition is that the individuals in question be\nrelated to each other so as to enable each to act in ways that they\ncould not manage on their own. The second is that some individuals be\nauthorized to represent their own actions as the actions of the group\nas a whole (May 1987, p. 55).", "\nWhat about group intentions? Not surprisingly, group intentions\npresent an even greater challenge than group actions do. For,\nintentions are mental states and hence not the kinds of things that\nare normally thought to be shareable. Are they shareable?", "\nAccording to Brook Sadler and others, the question is inherently\npuzzling. For, “if intentions are mental states, states which\nplay a fundamental role in an agent’s practical deliberation and\nvolition, the prospect of a shared intention introduces the specter of\nshared mental states and hence shared minds”—which is\nsomething that philosophers have traditionally hoped to leave behind.\n(Sadler 2006, p.115.)", "\nIndeed, the possibility that collective responsibility requires, not\nonly collective actions and intentions, but a collective mind, has\nproven to be one of the greatest challenges to those who want to\nsustain a notion of collective responsibility. For while groups can\nlegitimately be said to have beliefs and other states characteristic\nof a mind in particular cases, e.g., when the group is organized\naround such beliefs, they do not seem to have minds in any sense other\nthan their ability to build on the minds of individual members. As\nDavid Sosa argues, “groups might be said to have a mind or a\nwill but only in a derivative sense: the persons that are members of\nthe group have minds, and the group’s mind (in whatever sense it\nhas one, its beliefs and desires) is some sort of construct from those\nminds” (Sosa 2007, p. 215).", "\nNot surprisingly, the matter of consciousness becomes key here.\nMatthew Baddorf (2017) argues straightforwardly that for something to\nhave a mind, it must be phenomenologically conscious and, and\naccording to Baddorf, collectives lack consciousness. Baddorf is\nwilling to go as far as to conclude here that lacking such\nconsciousness, collectives are inappropriate sites of accountability\nand responsibility. But not everyone is willing to go so far.", "\nIndeed, there are an increasing number of scholars in the field who\nwonder whether we really need to talk about a collective mind (or\nconsciousness)—or even a unified self—in order to sustain\na notion of collective moral responsibility. Michael Bratman appears\nto have developed a coherent view of collective intentions that does\nnot require us to go that far. According to Bratman, we can talk about\ncollective intentions as intentions that are shared among group\nmembers.", "\n[w]e intend to do J if and only if: (1)(a) I intend that we J\nand (b) you intend that we J and (2) I intend that we J in accordance\nwith and because of (1)(a), (1)(b) and meshing sub-plans of (1)(a),\n(1)(b), and you intend likewise. (3):(1) and (2) are common knowledge\nbetween us. (Bratman 1999:121)\n", "\nIn Shared Agency: A Planning Theory of Acting Together\n(Bratman 2014), Bratman associates these shared intentions with a\npattern of ordinary intentions and beliefs that coordinates multiple\nindividuals’ activity in a fashion analogous to the way in which\nan individual’s intention coordinates her activity through time.\nHere, again, Bratman presents shared intentions as a matter of\n“meshing subplans.” According to Bratman, to say that we\nhave a “shared intention to J,” where J is a joint\nactivity, is to say that “[w]e each have intentions that we J,\nand we each intend that we J by way of each of our intentions that we\nJ and by way of subplans that mesh.” (Bratman 2014, p. 103)", "\nTwo things are important to underscore here. First of all, Bratman is\nnot concerned to account for a collective mind. Instead, he is\nconcerned to account for collective intentions. Second, while he\nsuggests in Shared Agency: A Planning Theory of Acting\nTogether that we can think of shared activity as the activity of\na group agent, he makes clear that he is not positing a group subject\nof the kind necessary to the ascription of moral blameworthiness to\nthe group itself qua moral agent.", "\nBoth points together suggest that while Bratman’s theory\nprovides us with a very helpful way of understanding both collective\nintentions and coordinated activities of various kinds, as well as a\nbasis for grasping the nature of shared deliberation and shared\nreasoning, it does not attach those collective intentions to the kind\nof collective moral agent that is required of moral responsibility.\nNor does it establish the kind of moral agent in question.", "\nBratman was not himself interested in establishing this kind of moral\nagent in his theory of collective intentions. But, if we want to talk\nabout collective moral responsibility, we will have to do so.\nMoreover, we will have to do so regardless of our stance on the\npossibility of a collective mind or a collective consciousness. (In\nother words, we will have to do so regardless of what other conditions\nof collective moral responsibility we posit and whether we think that\nthese conditions can be met.) For, responsibility of all kinds\nrequires the location of agents and moral responsibility requires that\nthese agents be appropriate sites of blameworthiness.", "\nHow, if at all, might we talk about the kind of collective moral agent\nand/or unified collective moral subject required by collective moral\nresponsibility? Interestingly enough, defenders of collective\nresponsibility frequently turn back here to the works of Durkheim\n(1895) and Simmel (1971), as well as to that of Sartre (1960), for\ninspiration, although they themselves proceed analytically. Margaret\nGilbert, who grounds several of her arguments in Durkheim’s\ntheory of social facts, develops what she calls a\n“plural-subject account” of shared intentions to justify\nthe coherence of collective responsibility (Gilbert 1989, 2000, 2006\nand 2013) (Gilbert and Priest 2020). She does so in large part by\nzeroing in on joint commitments. According to Gilbert, group\nintentions exist when two or more persons constitute the plural\nsubject of an intention to carry out a particular action, or, in other\nwords, when “they are jointly committed to intending as a body\nto do A” (Gilbert 2000, p. 22).", "\nDavid Velleman goes on to stress the unified nature of this plural\nsubject. A “truly plural subject”, he writes, involves\n“two or more subjects who combine in such a way as to make one\nsubject” (Velleman 1997). Both Gilbert and Velleman make clear\nthat a unified moral subject is required of a collective moral\nresponsibility.", "\nWhile Gilbert and Velleman provide us with a compelling view of a\nplural subject, two questions remain. Does their plural subject\nconstitute a unified moral subject of the kind that can be morally\nblameworthy for bringing about harm? If so, is the kind of moral\nblameworthiness associated with such a unified moral subject the same\nin the case of a collective as it is in the case of individual moral\nagents? We address these questions in Section 5.", "\nSuffice it to point out here both that (as Gilbert herself recognizes)\nsuch a unified moral subject is necessary to collective moral\nresponsibility and that the location of a plural subject is not the\nonly way of making sense of a collective moral agent. Raimo Tuomela\n(1989, 2005, 2006 and 2013) chooses a somewhat different strategy in\nhis defense of collective responsibility. He puts forward what he\ncalls “we intentions.” Like Gilbert, he constructs a\ncollective subject on the basis of joint commitments and then applies\nit to the notion of collective responsibility. But he does not, like\nGilbert, stress the pluralistic nature of this subject. Instead, he\nargues that collective intentional agency supervenes on\nindividual intentional agency in ways that allow us to talk about both\ncollective intentions and collective actions. According to Tuomela,\nactions by collectives supervene on the actions of the\noperative members of the collective in such a way that the properties\nof particular collectives, such as their intentions, beliefs, and\ndesires, are “embodied in” and “determined by”\nthe perspectives of the properties of individual members or\nrepresentatives of the collective in question (Tuomela 1989, p.\n494).", "\nInterestingly enough, Tuomela’s attempt here to save collective\nresponsibility by positing such a representative subject recalls the\nefforts of Thomas Hobbes to create a collective subject in the guise\nof his Leviathan (1651). Hobbes, in an effort both to explain\nsovereignty in general and to justify the legitimacy of the English\nmonarchy in particular, posited a higher authority in the\ncommunity—the Leviathan—whose own will, as well as\nactions, came to be those of its/his subjects as a result of their\nhaving transferred their own agency to it/him as part of the only kind\nof social contract that from Hobbes’s perspective made\ncollective life possible. Hobbes’s collective subject not only\nrepresented group members but captured their very being as members of\nhis Leviathan.", "\nContemporary defenders of collective responsibility sometimes recall\nHobbes’s Leviathan in their own attempt to develop a collective\nsubject (see for example: Copp 1980). But they do not, in light of\nHobbes’s own authoritarianism, go as far as to accept\nHobbes’s argument that a Leviathan is necessary to capture the\ncollective will. Nor do they generally toy with the possibility of\nreintroducing the seemingly more benevolent general will of Rousseau\n(1762) as a way of substantiating group intentions. Instead, they look\nfor an alternative, less authoritarian, way of substantiating group\nintentions—representational or not—or else argue that\ngroup intentions of the sort associated with traditional Kantian\nnotions of moral agency are not after all necessary to collective\nmoral responsibility.", "\nLarry May offers one of the most interesting arguments of the latter\nsort in his own defense of collective moral agency (May 1987, 2006 and\n2010). May rejects many of the above accounts of group intentions as\ntoo closely tied to Kantian notions of moral agency. But he does not\ndo away with group intentions as a necessary condition of collective\nresponsibility. Nor does he accept a fully collectivist methodology.\nInstead, he reformulates group intentions within a theory of what he\ncalls interdependence and, in doing so, develops a general outlook on\ncollective responsibility that not only combines individualism and\ncollectivism but places both relationships and social structures at\nthe center of our attention. The challenge here becomes to describe\nwhat such group intentions actually look like.", "\nMay relies in this context once again on the work of Sartre to develop\nhis account of group intentions and posits what he calls a\n“pre-reflective intention”, i.e., “an intention\nwhich is not yet reflected upon by each of the members of the\ngroup” (May 1987 p. 64). May makes clear here that group\nintentions of this sort arise out of the relationships between\nparticular members of a group rather than from any one group member.\nHence, while they are not trans-individual or collective in any sense\nthat stands totally above individuals, they can be treated “as\nif they are collective” (May 1987, p. 64) Moreover, these\nintentions are, May makes clear, not individual intentions\nbut group-based. “Since each member of the group comes\nto have the same intention, either reflectively or\npre-reflectively”, it is “different from their individual\nintentions.” Indeed, “the sameness of intention is\ncollective in the sense that it is caused by the group structure, that\nis, it is group-based” (May 1987, p. 65). The question for May,\nas for the others, is whether the “sameness of intention”\nis sufficient for talking about a collective moral agent worthy of\nblame.", "\nWhile many of those defending the possibility of collective moral\nresponsibility do not explore the conditions of collective moral\nblameworthiness, List and Pettit (2011), in an important work on the\nsubject, extend inquiry about collective moral agency into the realm\nof ethical, political, and legal accountability. List and Pettit argue\nthat groups can meet the requirements of moral agency by virtue of the\nfact that they “have representational states, motivational\nstates, and a capacity to process them and act on their basis.”\n(List and Pettit 2011, p. 21) Likewise, they argue that groups can\nhave obligations, entitlements, and power relations that have hitherto\ngone unnoticed and that require our moral attention.", "\nList and Pettit devote a great deal of their own attention to how we\nmight use our recognition of these obligations, entitlements, and\npower relations to re-work various institutions in contemporary\nsociety. But they do not neglect the question of collective moral\nblameworthiness. Nor do they simply assume that such blameworthiness\nfollows automatically from group moral agency. Instead they make clear\nthat in order for a group to be morally blameworthy, its actions must\nbe associated with a “grave matter”; the group must have\n“full knowledge of guilt”; and there must have been\n“full consent of the will” (List and Pettit 2011, 155).\nList and Pettit think that these conditions can be met by at least\nsome groups. Are they right?", "\nWhile they provide convincing evidence that at least some groups can\nmeet the first two conditions, we need, once again, to be worried\nabout the third, i.e., that which pertains to the willfulness or\ncontrol of a collective agent. In their own words, “the question\nraised by the third condition is whether a group agent is in control\nover the actions it takes so that we might expect its normative\njudgment, for example, to be capable of impacting on its\nbehavior” (List and Pettit, 2011, 159). How can a group, above\nits individual members, exert this level of control?", "\nList and Pettit do not answer this question. Instead, they point out\n(correctly) that the question is not more serious for groups than it\nis for individuals.", "\nThis notion of control needs analysis in any full theory of agency,\nbut since the issue arises with individual agency as much as it does\nwith group agency, we need not provide that analysis here. The\nchallenge for us is not to explain what an agent’s control is,\nbut rather to show that there is no special reason why such control,\nwhatever it involves, shouldn’t be instantiated in a group agent\nas much as in an individual. (List and Pettit, 2011, 159)\n", "\nBut if we are going to justify the possibility of group moral\nblameworthiness, we cannot be satisfied with simply knowing that the\nmatter of control is no more serious for groups than it is for\nindividuals. Instead, we have to know what group control entails in\nthis context and whether it is possible. In other words, we have to\ndevelop the kind of explanation of group control that List and Pettit\nconcede is important, as well as an account of the “whatever\nsuch control involves” that they cite.", "\nThere have been several interesting efforts in recent years to\narticulate and justify such a notion of group control. Kendy Hess, in\n“The Free Will of Corporations and Other Collectives”\n(Hess, 2014) argues that collectives possess free will to the extent\nthat they act from their own “actional springs” and from\ntheir own “reasons-responsive mechanisms”. Hess argues\nthat when collectives do so, they both act freely and are morally\nresponsible for what they do.", "\nKenneth Silver (2022) follows through on the reasons-responsive\napproach to group free will and moral responsibility. According to\nSilver, while it is difficult to establish a group mind or mental\nstate in this context, to do so is not necessary. Instead, we need\nonly establish that groups are sensitive to their reasons and can be\nmotivated to act by them. In Section 5, I address whether such a\nnotion of group control is sufficient to sustain ascriptions of moral\nblameworthiness.", "\nWhile List and Pettit do not provide us with their own notion of group\ncontrol (leaving the question of group moral blameworthiness still up\nin the air), they do make two related points of importance. The first\nis that control in this context does not need to reside in the group\nor in individuals. Instead, it can reside simultaneously in\nboth places, albeit in different forms: “programming\ncauses” vs. “implementing causes” (List and Pettit,\n2011, p. 162).", "\nThe second is that we need to think, not only about whether groups are\nmorally responsible for harm, but about whether we should\nhold them morally responsible for harm and, if so, under what\nconditions. List and Pettit do not take a wholly consequentialist\napproach to the latter matter themselves. But they do underscore the\npositive consequences that can follow from our holding groups\nmorally responsible in particular cases, consequences that range from\nour “recognition... of the true contours of the moral and\npolitical world we inhabit” (List and Pettit 2011, p. 185) to\nthe persuasion of group members to give up harmful behaviors to the\nsocialization of group members to act more responsibly in the future.\nWe discuss these and other consequences more fully in Section 6." ], "section_title": "2. Making Sense of Collective Responsibility: Actions, Intentions, and Group Solidarity", "subsections": [] }, { "main_content": [ "\nWhile Gilbert, May, List, Pettit, and others who concentrate on\nredeeming collective responsibility as an intellectual construct do so\nby defending the coherence of collective actions and group intentions,\nthey do not go as far as to assert that all kinds of groups are\ncapable of acting and intending collectively. Nor do they go as far as\nto assert that all kinds of groups can be understood as collectively\nresponsible for bringing about harm. Instead, they assert that only\nparticular kinds of groups are capable of acting and intending\ncollectively and that only particular kinds of groups are capable of\nbeing collectively responsible for harm. What kinds of groups are\nthese?", "\nThe most common approach taken to distinguishing between appropriate\nand inappropriate sites of collective responsibility has been to focus\non nations, corporations, and other groups that have well-ordered\ndecision-making procedures in place, since, it is argued, these groups\nare, by virtue of their well-ordered decision-making procedures, able\nto demonstrate two things that are often assumed to be necessary to\ncollective responsibility. The first is a set of group actions that\nhave an identifiable moral agent, e.g., a governing board or a\nrepresentative body, behind them capable of carrying out a group\naction. The second is a set of decisions that are made\nself-consciously on a rational basis—or at least\npurposively—by the group that take the form of group intentions\nor group choices.", "\nPeter French considers groups that are so organized to be especially\nappropriate sites of collective responsibility because of three\nsalient features that they all share. The first is a series of\norganizational mechanisms through which courses of concerted action\ncan be, though not necessarily are, chosen on a rational basis. The\nsecond is a set of enforced standards of conduct for individuals that\nare more stringent than those usually thought to apply in the larger\ncommunity of individuals, standards that enable us to talk about both\ngroup conduct and group discipline. The third is a configuration of\n“defined roles by which individuals can exercise certain powers\n” (French 1984, pp. 13–14) All three of these features,\naccording to French, signal the existence of purposeful and controlled\nactions that are capable of rendering groups collectively responsible\nfor harm.", "\nA second approach to the location of appropriate sites of collective\nresponsibility has been to use groups such as ethnic communities,\nclubs, and social movements as paradigmatic cases of appropriate\ncollective responsibility on the grounds that these groups have\nmembers who share interests or needs in common. Two assumptions\nprevail here. The first is that groups whose members share interests\nor needs in common show signs of group solidarity, which Joel Feinberg\ndefines in this context as a matter of individuals taking a strong\ninterest in each others’ interests (Feinberg 1968). The second\nis that groups that show signs of group solidarity understood in this\nway are capable of acting and intending in the sense relevant to\ncollective responsibility, since while they are made up of\nindividuals, they pursue projects together.", "\nNot surprisingly, group solidarity is generally thought to exist\nprimarily in either cases where group members identify themselves as\ngroup members and assert their shared interests and needs or in cases\nwhere group members exhibit collective consciousness to the extent\nthat they are inclined to take pride or feel shame in group actions\nwithout prompting. But, according to at least some of those who make\nuse of the concept of group solidarity here, e.g. Larry May (1987) and\nHoward McGary (1986), group solidarity does not require group\nself-consciousness. Indeed, according to both May and McGary, group\nsolidarity can be understood as present in what McGary calls\n“loosely structured groups”, such as privileged racial\ngroups whose members provide support or benefits to other members\nqua group members, even though they may not, in\nMcGary’s words, “see themselves as interested in one\nanother’s interests” (McGary 1986, p. 158). In these\ngroups, McGary contends, mutual benefits, as well as practices that\nmay, unbeknownst to those who participate in them, maintain forms of\noppression such as racism and sexism, signal group solidarity of the\nsort relevant to collective responsibility.", "\nA third approach here is to pick up on shared attitudes among\ngroup members as something that renders the group itself an\nappropriate site of collective responsibility. The attitudes taken to\nbe relevant here are generally those that both produce serious harm in\nsociety and that require acceptance by many individuals in a community\ntogether in order to be effective, e.g., attitudes such as racism,\nsexism, and anti-Semitism. May (1987), McGary (1986), Marilyn Friedman\n(Friedman and May 1985) and others cite these attitudes as enough to\nrender groups such as “men” and “white\nAmericans” collectively responsible for the oppression of women\nand black Americans in some, but not all, cases. Other defenders of\ncollective responsibility, e.g., Peter French, refrain from going this\nfar on the grounds that the groups in question are not organized\nenough to be capable of sustaining a sense of moral agency that is\ngenuinely collective (French 1984).", "\nAll three of the above approaches take us in different directions.\nHence, they are sometimes thought to be competing. But they all rest\non a general distinction between aggregate and conglomerate\ncollectivities. An aggregate collectivity, Peter French writes, is\n“merely a collection of people” (French 1984, p. 5). It is\nnot, from the perspective of most of those now writing on collective\nresponsibility, an appropriate site of collective responsibility. A\nconglomerate collectivity, on the other hand, is an\n“organization of individuals such that its identity is not\nexhausted by the conjunction of the identities of the persons in the\norganization” (French 1984, p. 13). It is, from the perspective\nof most of those now writing on collective responsibility, an\nappropriate site of collective responsibility, since, unlike an\naggregate collectivity, it supplies us with a moral agent capable of\npurposeful action.", "\nWhile most of those who defend collective responsibility as a moral\nconstruct adhere to this distinction in general, they do not all agree\non what counts as an aggregate collectivity in practice. Indeed, there\nis considerable disagreement among those now writing about collective\nresponsibility (including some who take the above three approaches)\nabout two particular kinds of groups that appear to some to be\naggregative groups. One of these kinds of groups is the mob. The other\nis what Virginia Held calls a “random collection of\nindividuals.” Neither of these kinds of groups has a\ndecision-making procedure in place. Nor do their members show much\nsolidarity. Hence, they are usually rejected as candidates for\ncollective responsibility by many of those who otherwise find the\nnotion of collective responsibility to be very useful. But there are\nthose who put forward both groups as appropriate sites of collective\nresponsibility.", "\nVirginia Held (Held 1970) argues that members of an unorganized group\nmay be said to be responsible for not taking an action that could have\nprevented harm in cases where they could have done something to\nprevent the harm together but chose not to do so. Her particular\nexamples are those of victims of violence who are beaten or killed in\nfull sight of strangers assembled around them, strangers who are\nthemselves neither related to the victim nor there together as part of\nany group-based project. According to Held, while none of these\nindividuals may have been able to prevent the violence on their own,\nthey could have prevented it if they had organized themselves into a\ngroup, i.e., cooperated with at least some of the others. Hence, they\ncan as a group be blamed for the victims’ suffering and/or\ndeath.", "\nHeld acknowledges here that holding a random collection of individuals\nresponsible for harm is more difficult than holding an organized group\nresponsible for it, since the latter, unlike the former, has a method\nfor deciding how to act, whether it is a voting procedure or a set of\nhierarchical authority relations. But, she argues, we can still hold\nthe former group, i.e., that which she calls a random collection of\nindividuals, responsible for the violence done to victims, since, if\nthey had tried, they could have come up with such decision-making\nprocedures themselves. “In the foregoing examples,” she\nwrites, “we can say that the random collection of individuals\nwas morally responsible for failing to transform itself into an\norganized group capable of taking action rather than inaction”\nwith respect to the prevention of harm. (Held 1970, p. 479.)", "\nMobs are often thought to be the last groups that we should be tying\nto hold collectively responsible. For, they completely lack\ndecision-making procedures, their members are seemingly not related,\nand they are often chaotic and irrational. But, Larry May (1987),\nRaimo Tuomela (1989), and others argue, we can nevertheless hold mobs\ncollectively responsible if at least some of their members contribute\ndirectly to harm and others either facilitate these contributions or\nfail to prevent them. For, in these cases, all mob members are\n“implicated” in mob action, even if not all of them\nproduced specific harms or organized together to do so. Tuomela (1989,\n2005, 2006), much like Le Bon (1896) before him, argues that both\ncrowds and rioters are appropriate sites of collective responsibility\nby virtue of the fact that they perform their acts as members of a\ngroup, even if they do not think of themselves as doing so.", "\nCrowds and rioters … are without much or any structure (and\ndivisions of tasks and activities) … with respect to the goals\nand interests of the group. … But they can be said to act in\nvirtue of their members’ actions. … Thus in a riot the\nmembers of the collective typically perform their destructive actions\nas members of a collective without acting on its behalf.\n(Tuomela 1989, p. 476.)\n", "\nInterestingly enough, in both of these cases—mobs and what Held\ncalls random collections of individuals—the groups in question\nmay not be as unrelated as Held and others suggest they are. Indeed,\nit may be precisely because these groups are made up of individuals\nwho become related to each other in the process of\nproducing harm together (even though they were initially strangers)\nthat they are now potentially appropriate sites of collective\nresponsibility. Stanley Bates suggests as much in his own arguments\nthat Held has presented us with a group that is neither as random nor\nas disconnected as the term “random” normally suggests,\nbut that is “related” to the extent that group whose\nmembers share a particular challenge and are capable of communicating\nwith one another (Bates 1971).", "\nTwo aspects of the debate about random collections have resurfaced in\nrecent years in two related debates about collective moral\nresponsibility. The first is the importance of group inaction\nwhen it comes to some cases of collective moral responsibility. The\nsecond is the ability of disorganized groups to constitute the kind of\nmoral agents that can be held morally responsible for not acting.", "\nThe matter of omissions turns out to be particularly challenging for\nthose who want to hold disorganized groups morally responsible for\nanything, since, as Joseph Metz (2021) points out, it is hard to see\nhow an individual contributes anything to a collective omission to\nprevent harm if she could not have made a difference to that\nharm’s coming about (or at least not on her own). But, Metz\nargues, we can scale things up to a model of group capability and\npoint to the ability of a group of individuals who did nothing to,\nsay, prevent global warming, and use that ability to say that they\ncould have acted together to prevent the harm.", "\nMetz may well be right here. But the ability of a collective to\nprevent harm is only one condition of its collective responsibility in\ncases where the collective did not act. Also necessary is that the\ncollective have been morally expected to act.", "\nWhere do these moral expectations come from? The most commonly cited\nsource of them is a collective obligation on the\ncollective’s part to prevent harm. David Copp (2020) underscores\nthe controversial nature of such an obligation and rightfully insists\nthat it be justified in general.", "\nNot surprisingly, a collective obligation to prevent harm is not all\nthat difficult to justify in the case of organized\ncollectives (whether we are talking about actions or omissions), since\nin these cases we can reference group identity, inter- and intra-\ngroup relationships, moral commitments, and promises, as well as\nexpediency. In Group Duties, Stephanie Collins (2019)\nexplores the various ways in which we might justify collective\nobligations in these cases; she also draws out the implications of\nthem for individual group members.", "\nIn “How Much Can We Ask of Collective Agents?”, Collins\n(2020) goes on to explore the scope of collective obligations and\ndefends them against claims of over-demandedness.", "\nIn cases of yet-to-be-formed collectives, collective obligations are\nmore difficult to justify, since the contours of the collective are by\nnature fuzzy and there is no clear collective moral agent to be\npinpointed. But there have been efforts to justify collective\nobligations in these cases nevertheless. Interestingly enough, they\nhave generally focussed on group capacity. In Violetta\nIgneski’s words (Igneski, 2020), “[W]hen there is evidence\nthat a group of individuals has the capacity to prevent harm or a\nwrong and the individual members are aware (or should be aware) of\nthis, they have a duty, as a group, to prevent the harm or\nwrong” (p. 447).", "\nAs we shall see in Section 7, things may not be quite so simple. For,\neven if a group has the capacity to act if organized, there are other\nfactors that need to be taken into consideration before we can posit a\ncollective obligation and make a subsequent claim of collective\nresponsibility. One of these considerations is whether the prevention\nof the particular case of harm in question ranks high on the list of\nthe many cases of harm prevention that require the group’s\nattention in a situation where choices have to be made. Another is\nwhether, given other demands on the group, including the well being of\nthe group itself, it would be fair to expect the group to pursue this\nparticular project (and hence take it on as a collective\nobligation).", "\nMoreover, even in cases where we agree that the group should\ntake on the project as a collective obligation, we still face a\nfurther challenge, namely, that the groups we are talking about here\nare not (at this point) organized to the point where they can act.\nHence, even if we can expect them to act and they would be\nable to do so if they were organized, they are not at this point able\nto d oso. How, we have to ask, can we transform a disorganized\ncollective into one that is organized enough to be associated with a\ncollective obligation (and hence collective responsibility)? What\nmight motivate such a transformation? Igneski (2020) gestures to the\nplace of individual moral agents with duties of their own as a\nstarting point for getting the requisite collective organized. We\ndiscuss this possibility more fully in Section 7, where the\ntransformation in question becomes key to the coherence and\nworkability of forward looking collective responsibility.", "\nSuffice it to underscore two things here. First of all, when it comes\nto traditional, backward looking, collective responsibility, we need,\nat the very least, to be able to locate a group that is capable of\nbeing construed as a collective moral agent, that could have been\nexpected to prevent the harm in question (by virtue of, say, having a\ncollective obligation to do so), and that was capable of acting in the\nways required. Second, it is much easier for a collective that is\norganized to meet these conditions than a collective that is not.\nThird, in order for a collective that is not organized to meet these\nconditions, it may have to rely on individual members to organize it,\nindividual members who are motivated in some way to do so qua\nindividual moral agents.", "\nIn almost all of the above discussions of collective moral\nresponsibility, the groups being held morally responsible for harm are\nmade up of those individuals who either caused the harm themselves or\nrefrained from preventing it at the time it occurred. But in recent\nyears, a number of efforts have been made to hold groups morally\nresponsible for actions performed by earlier generations. The case of\nslavery tends to take center stage here and is often accompanied by\narguments for reparations. While such efforts have generally taken\nplace in the legal arena, they have not been excluded entirely from\ncontemporary philosophical discussions of collective responsibility.\nIndeed, in recent years, a variety of philosophers have set out to\nascribe moral responsibility to groups whose present members were not\neven alive when the bad actions in question were carried out, even\nthough, as Janna Thompson points out, “not being born when an\ninjustice took place seems to be a very good reason for denying any\nresponsibility” (Thompson 2006, p. 155).", "\nHow can we possibly hope to hold groups morally responsible for the\nbad actions of previous generations? Farid Abdel-Nour (Abdel-Nour,\n2003) argues that community solidarity is sufficient to render at\nleast some kinds of groups morally responsible for the harms brought\nabout by earlier generations, especially if there is a high level of\ncross-generational identification and pride in one’s\nancestors’ deeds.", "\nNot surprisingly, these kinds of arguments run into trouble when\nquestions of agency arise. For, while the existence of solidarity and\nidentification may allow us to talk about a group over time and even\nlabel its actions morally wrong,they do not allow us to posit the kind\nof agency that is required of moral responsibility as traditionally\nunderstood. For, as Michael Bratman shows in his own work on\ncollective responsibility, the latter requires, not only that\nindividuals share intentions but that they interact. (See\nespecially Bratman 2000).", "\nWhile most of those writing on collective responsibility seem to agree\nwith Bratman here on the necessity of interaction, not all do. Linda\nRadzik (Radzik 2001) claims that we need only show that existing group\nmembers benefit from a past injustice to hold them responsible for it.\nLarry May makes similar claims throughout his work, including in his\narguments that men are collectively responsible for rape and whites in\nthe U.S. are collectively responsible for racism (May and Strikwerda\n1994).", "\nWhat place does benefiting from harm have in the ascription of\ncollective responsibility? As Janna Thompson (2002, 2006) points out,\nto benefit from a harm is not the same thing as to cause it. Hence\nbenefit—as when men benefit from sexism and whites from\nracism—does not appear to be an appropriate source of collective\nresponsibility for the past actions of others. But it might be an\nappropriate source of collective responsibility for the\nprolongation of the harm and/or its consequences into the\nfuture. In other words, it might be an appropriate source of\ncollective responsibility for present and future, if not for past,\ninjustices—including injustices that began with earlier\nwrongs.", "\nMoreover, while groups of persons might not be good candidates for\nmoral responsibility for past injustices, particular kinds of\ncollective entities—e.g., states, corporations, and organized\nreligions—might be. For, the latter have decision-making bodies,\nexecutive processes, and belief systems that extend over time. Surely,\npositing such a collective entity would be very helpful in the case of\nreparations for slavery in the U.S. and elsewhere. As Maeve McKeown\n(2021) argues in her study of collective responsibility and\nreparations, backward looking reparations for racial abuses\ncan—and should—be justified on the basis of state\nliability over time. Janna Thompson (2006) argues therefore that they\ncan be understood as legitimate sites of moral\nresponsibility—although it is not clear that they have the kinds\nof agency that we normally associate with moral responsibility.", "\nHow, if they are not moral agents, can Thompson or anyone else speak\nof groups such as states, corporations and organized religions, as\nmorally responsible? Thompson feels comfortable speaking of these\ngroups as morally responsible for harm on the grounds that they are\nlike moral agents. According to Thompson, “whether they\ncount as real moral persons or only act as if they were, it seems that\nwe are, at least sometimes, justified in judging these collectives\naccording to the standards that we apply to moral persons”\n(Thompson, 2006, p. 158).", "\nBut it is not clear that likeness is strong enough to sustain\nthe nature of these groups as moral agents of the kind that we\nnormally associate with moral responsibility. For “acting like a\nmoral agent” is not the same thing as being a moral agent. (And\nif one really is a moral agent then there is no need to go to the\nlengths of specifying likeness.)", "\nWe suggest below that the unlikelihood that groups are really moral\nagents does not mean that the latter cannot be held morally\nresponsible for harm. But it does mean that we have to re-think the\nkinds of moral responsibility that we associate with groups in such a\nway that moral agents of the Kantian kind are not necessary." ], "section_title": "3. Collective Responsibility and the Structure of Groups", "subsections": [] }, { "main_content": [ "\nCollective responsibility refers to the responsibility of a\ncollective entity, e.g., a corporation, a nation state, or a club, for\nharm in the world. Shared responsibility refers to the\nresponsibility of group members for such harm in cases where they\nacted together to bring the harm about. Collective responsibility is\nassociated with a single, unified, moral agent. Shared responsibility\nis associated with individual moral agents who contribute to harm as\nmembers of a group either directly through their own actions or\nindirectly through their membership in the group.", "\nContemporary moral and political philosophers are generally careful to\ndistinguish between collective responsibility, on the one hand, and\nshared and individual responsibility, on the other. But they do not\nleave individual moral agents behind altogether. Indeed, after\nanalyzing collective responsibility as part of group morality, they\nfrequently place individual moral agents back at the center of their\nattention in an effort to discern what collective responsibility means\non the level of individual moral actors. Is it possible, they ask, for\nindividual members of a group to be collectively responsible for\ngroup-based harms in cases where they did not directly cause it? In\ncases where they did not do anything to stop it? If so, under what\nconditions?", "\nWhile those who answer these questions tend to focus on the\ntransferability of collective responsibility and its relationship to\nindividual moral agency in general, they do not ignore concrete\nhistorical examples in which the moral responsibility of particular\ngroups of individuals for harm is in question. Indeed, almost all of\nthose who write about collective responsibility and the question of\ndistribution place such concrete historical examples of harm at the\ncenter of their analyses of collective responsibility in an effort,\nnot just to understand collective responsibility as an abstract\nconstruct, but to discern whether or not particular groups of\nindividuals in history can be held morally responsible for harms that\ntheir groups caused, whether those groups are ethnic groups\n(“Germans”), nations (“America”) or racial\ngroups (“Whites”).", "\nBoth Karl Jaspers (1961) and Hannah Arendt (1987), as well H. D. Lewis\n(1948), were clearly concerned in their writings on collective\nresponsibility about whether or not the German people can legitimately\nbe held collectively responsible for World War II Nazi crimes. So,\ntoo, were Sanford Levinson (1974), Richard Wasserstrom (1971) and\nothers who produced their own arguments about collective\nresponsibility in light of the Nuremberg trials. The My Lai killings\nof the Viet Nam War, along with the Kitty Genovese murder and\ncorporate scandals of all kinds, influenced much of the philosophical\nwork done on collective responsibility during the 1970s and 80s,\nincluding that of Peter French, Larry May, and Virginia Held, and\nwhile it is only recently that group-based oppression such as racism\nand sexism have come to be of interest to those writing on collective\nresponsibility, they now figure importantly in the writings of Larry\nMay (1987 and 1992), Howard McGary (1986), Marilyn Friedman (Friedman\nand May 1980), Anthony Appiah (1987), Derrick Darby and Nyla\nBranscombe (2012 and 2014), and Eva Boodman (2022).", "\nIn all of these discussions, the question is whether the whole\ncommunity—or large parts of it—can be held responsible for\nthe harms produced by particular group members in cases where not all\ngroup members caused the harm directly. Is it appropriate to hold all\nGermans responsible for the deaths of extermination camp victims\nduring WWII? all Americans for the atrocities of the Viet Nam War? Can\nwe legitimately blame all men for the gender-based oppression and\nsexual violence that women experience in all societies? Can we blame\nall whites for the racist treatment of blacks in the U.S.? What about\nmembers of these groups who go out of their way to stop the harm? Are\nthey excused from blame because they tried to reform their communities\nor are they, too, responsible for the harm in question by virtue of\ntheir group membership?", "\nWhile the arguments made in this context tend to be tied to particular\ncases of group-based harm, they are for the most part designed either\nto establish general criteria for distributing collective\nresponsibility among group members or to demonstrate that collective\nresponsibility cannot in the end be distributed at all. The latter\narguments frequently proceed as follows: While collective entities\ngenerally act through their individual members, their actions do not\ncoincide with their members’ actions. Nor is their\nmoral agency merely the moral agency of their members or the moral\nagency of group representatives. Instead, such agency is—if it\nis to be genuinely collective moral agency—an agency\nthat is attached to the collective itself and hence not the kind of\nthing that can be distributed across group members or, for that\nmatter, attached to anything other than a collective itself. In other\nwords, such agency is the kind of thing that necessarily has\ncollectives, and not individuals, as its subject matter.", "\nPeter French makes such an argument himself in Individual and\nCollective Responsibility (1998). But he cautions that the\nnon-distributional character of collective responsibility does not\nmean that individual members of the group that is collectively\nresponsible for harm are themselves blameless. Indeed, he claims, many\nof these group members will be morally responsible for all sorts of\nharms that their group causes.", "\n[I]t should be noted that from ‘Collectivity A is\nblameworthy for event n, and A is composed of\nx, y, and z,’ it would be\npresumptuous to conclude that x, y, and z\ndo not warrant any blame for n, or that x,\ny, r z is not himself blameworthy in the\ncase of n. My point is that such judgments assessed on\nmembers of the collectivity do not follow necessarily from judgments\nof collective blame (French 1998, p. 25).\n", "\nThe above claim clearly makes sense if we are talking about keeping\ncollective responsibility in tact qua collective\nresponsibility in our efforts to ascribe it in practice. But we might\nwant to loosen things up here a bit and suggest that collective\nresponsibility is the basis upon which we ascribe\nresponsibility to individual group members for harm that the group\nitself caused. In other words, we might want to suggest that\nindividual group members can take collective responsibility into\nthemselves as persons, in which case collective responsibility changes\nform and becomes something closer to personal responsibility, albeit\npersonal responsibility that exists only because one’s\ncollective is responsible for harm. In many cases, this is what those\nin philosophical circles who are concerned with the question of how to\ndistribute collective responsibility seem to have in mind. How do they\nattempt to distribute collective responsibility?", "\nIn The Question of German Guilt, Karl Jaspers (1961)\ndistinguishes between moral guilt that is based on what one does and\nmoral guilt that is based on who one is. He argues that the latter,\nwhich he calls “metaphysical guilt”, can be distributed to\nall members of a community who stand by while their fellows produce\nharm, e.g., murder Jews. In this context, to be morally blameworthy\nfor harm is largely a matter of belonging to an “evil”\ncommunity without asserting one’s own moral powers over the\ncommunity to cleanse it of such evil. According to Jaspers,\n“[t]here exists a solidarity among men as human beings that\nmakes each as responsible for every wrong and every injustice in the\nworld, especially for crimes committed in his presence or with his\nknowledge. If I fail to do whatever I can do to prevent them, I too am\nguilty” (Jaspers 1961, p. 36).", "\nJaspers has several contemporary followers, including Larry May and\nJuha Raikka (Raikka 1997), who choose to express Jaspers’ notion\nof metaphysical guilt as “moral taint”, a notion that\nemphasizes, among other things, the extent to which, in Anthony\nAppiah’s terms, we are “dirtied” by association with\nour community’s harmful actions. Appiah himself is very\nreluctant to apply the language of moral taint in general and does so\nonly in particular cases where there are strong causal connections\nbetween individuals and harm. May, on the other hand, finds moral\ntaint in many places and goes as far as to tout the utilitarian\nvirtues of distributing collective responsibility widely. According to\nMay, “seeing one’s own moral status as interrelated to\nthat of one’s fellow group members will negate the tendency to\nignore the most serious moral evils: those which can only be thwarted\nby the collective efforts of the community” (May 1987, p.\n253).", "\nMethodological and normative individualists tend to reject the notion\nof metaphysical guilt on two related grounds. The first is that it\nsevers the link between responsibility and control, especially in\ncases where the group membership being invoked is one that individuals\ncannot possibly choose, e.g., membership in racial, ethnic or national\ncommunities (For a very interesting assessment of this claim, see:\nRadzik 2001). The second is that the metaphysical notion of guilt\nviolates the liberal ethic of what Rawls calls the “separateness\nof persons”. According to Rawls, in ascribing responsibility we\nhave to consider persons separately and focus on their own actions so\nas not to violate principles of justice, principles of justice that\nfor Rawls themselves begin with the value of discrete individuals\n(Rawls 1971).", "\nWhile not all liberal individualists agree with Rawls’\nparticular claims here, they do agree with Rawls that, at the very\nleast, individual group members have to be faulty in some way in order\nto be held collectively responsible for harm. Joel Feinberg’s\ntheory of group liability is often taken as a starting point of\ndiscussion in this context. According to Feinberg, in distributing\ncollective responsibility, we need to focus on two kinds of cases:\ncases in which all members of a collective share the same fault or\ncases in which all members of a collective contribute to harm but at\ndifferent levels. In both kinds of cases, Feinberg stresses, there\ndoes not need be a direct link between the individual being held\nresponsible and the harm, but there does need to be the sharing of\nfaultiness.", "\nVarious faults can exist in the absence of any causal linkage to harm,\nwhere that absence is only a lucky accident reflecting no credit on\nthe person who is at fault. Where every member of a group shares the\nsame fault, but only one member’s fault leads to any harm, and\nthat not because it was more of a fault than that of others, but only\nbecause of independent fortuities, many will be inclined to ascribe\ncollective liability to the whole group (Feinberg 1968, p. 687).\n", "\nFeinberg himself is willing to ascribe collective responsibility to\ngroup members for such harm in some cases, although, he makes clear,\nin doing so we need to shift our attention away from strict liability\nto a softer kind of social blame on grounds of fairness. He concerns\nhimself with three kinds of cases in particular, namely, those in\nwhich large numbers of individuals are independently at fault; those\nin which the harm is caused by a joint undertaking of numerous persons\nacting cooperatively, and those in which the harm is ascribed to a\nparticular feature of the common culture which is self-consciously\naccepted by or participated in by members of the group. Feinberg is\nwilling to accept the possibility of ascribing collective\nresponsibility in all three kinds of cases. But he cautions that we\nneed to proceed on a situation-by-situation basis, since to ascribe\ncollective responsibility in cases such as these requires not only\nthat we locate genuinely shared faults but assess various\nincommensurable dimensions of individual contributions, including\ndegrees of initiative, importance of assigned task, levels of\nauthority, etc.", "\nGregory Mellema (2006) provides a very useful way of assessing\ndifferent levels of individual contribution by distinguishing between\nsix different ways in which individuals can be complicit in\nwrong-doing. According to Mellema, individuals can induce or command\nothers to produce harm. They can counsel others to produce harm. They\ncan give consent to the production of harm by others. They can praise\nthese others when they produce the harm. They can fail to stop them\nfrom producing it.", "\nA second way of tackling the distribution question in this context\nthat does not seem to violate the principle of individual freedom is\nto look, not just at the particular role that individuals played in\ntheir community’s production of harm, but at how much freedom\nthe individuals had to distance themselves from the community that has\ndone wrong. Here we might want to use voluntariness of membership as a\ncriterion of responsibility. Jan Narveson (2002) does so himself in\nhis generally skeptical work on collective responsibility. Narveson\nargues that in thinking about the responsibility of individuals for\ngroup harms we need to be careful to distinguish between four\ndifferent kinds of groups, namely: those that are fully voluntary;\nthose that are involuntary in entrance but voluntary in exit; those\nthat are voluntary in entrance but involuntary in exit; and those that\nare voluntary in neither respect. As Narveson makes clear,\nresponsibility is diminished, if not eradicated, as we go down this\nlist.", "\nNarveson clearly takes an individualistic perspective here. Hence, he\nis able to address the questions of individual freedom and personal\nresponsibility with relative ease. Not surprisingly, things get\nsomewhat more complicated when we start to think about individuals,\nnot only as participating in groups, but as taking their identity from\ngroups. Karen Kovach (2006) contends that in some cases, individuals\nalign themselves with their groups—Kovach is concerned with\nethnic groups in particular—to the extent that they see the\ngroup’s agency as an extension of their own. In these cases,\nKovach contends, we can distribute collective moral responsibility to\nall members of the group because of what she calls “moral\nalignment”.", "\n“Moral alignment” cannot of course be a simple matter of\nidentification if it is to sustain collective moral responsibility.\nFor, identification does not implicate an individual in either the\nintentions or the actions of the group with which she identifies.\nHence, Kovach finds it necessary to insist that if individuals are to\nbe held collectively responsible for group harms that they be\nunderstood as having “acted out the view of themselves as group\nmembers” or as having “performed” the group\nidentity.", "\nWhile such an insistence goes far in showing how collective\nresponsibility might be distributed to all members of a group for harm\nthat the group produced in particular cases, e.g., in cases such as\ngenocide or ethnic cleansing where ethnic identity is everything, it\nis not clear that the responsibility in question is the kind that we\nnormally associate with moral responsibility. For, while “acting\nout” or “performing” a group identity may contribute\nto harm in cases such as these, it is not the same thing as\ndoing something that contributes to that harm. In other\nwords, it does not signal moral agency—unless one asserts\none’s identity knowing that it will lead to harming others, in\nwhich case it is the act of assertion, not identification, that is\ndoing the work here.", "\nInterestingly enough, one of the major points of agreement among those\nnow writing about collective responsibility is that responsibility\ncannot be distributed to those group members who openly resist or\nfight against their communities’ bad actions or policies. See\nhere, for example, the arguments of Joel Feinberg (1968), Peter French\n(1998), Howard McGary (1986), J. R. Lucas (1993), and Michele\nMoody-Adams (1994). While the above writers, who find collective\nresponsibility to be a compelling moral construct in general, differ\nin particular respects, they all agree that it would be wrong to\nascribe responsibility to dissenters or, in other words, that if one\ntries to fight harm one should not be held responsible for it. McGary\nmakes his own claim here in terms of what he calls the\n“dissociation condition”, according to which a person is\nexempt from collective responsibility in cases where one’s\ncommunity caused harm if he or she dissociates him or herself from the\naction of the community by opposing its bad actions or policies\n(McGary 1986).", "\nBut there are some who do call for the distribution of collective\nresponsibility to individuals even in cases where these individuals\nactively opposed their community’s wrong doings. Juha Raikka,\nfor example, claims that the only way that opposition can exonerate\nthose who, say, live in a society that systematically pollutes the\nenvironment or depletes resources, is if they are able, by dissenting,\nto avoid supporting the system that does these things (a condition\nthat, Raikka acknowledges, is very hard to meet). According to\nRaikka,", "\n[o]pposing an evil practice cleans one’s hands only on the\ncondition that it does not require supporting another evil practice.\n… In the end, even those who oppose evil practices may be\nblameworthy for those practices. A single member of a group may have\nacted as he or she, all things considered, ought to have acted, but\nstill share responsibility for the group’s evil practices.\n(Raikka 1997, p.104.)\n", "\nRaikka claims in this context that dissenters can be morally\nblameworthy even if they cannot control the system that implicates\nthem in evil. Hence, he finds it necessary to do two things that not\nonly place him squarely in the camp of Karl Jaspers and other\nadvocates of metaphysical guilt but that are very telling with respect\nto contemporary philosophical debates about collective responsibility\nin general. The first is to subtract from the set of conventionally\ninvoked criteria of collective responsibility a criterion that the\nmajority of those now writing about collective responsibility take\nvery seriously, namely, the ability of individuals to control those\nthings (whether actions or harms) for which they are being blamed. The\nsecond is to detach moral blameworthiness from the will of discrete\nindividuals (where traditional, Kantian notions of agency place it)\nand to locate its source in the greater community of which the\nindividuals deemed guilty are ostensibly a part.", "\nBoth of these moves force us to acknowledge that, in the end, the\nvarious differences that exist among contemporary philosophers with\nrespect to the coherence and applicability of collective\nresponsibility as a construct have their source, not just in competing\ntheories of intentions and actions, but also in competing notions of\nmoral blameworthiness. While neither defenders nor critics of\ncollective responsibility generally take on the nature of the moral\nblameworthiness that they put at the center of our attention, they do\nmake clear that for some of them the traditional, Kantian standards of\nmoral blameworthiness still prevail and that for others the\nappropriate standards of moral blameworthiness take us beyond the\nwills of discrete individuals to the structure of guilty\ncommunities." ], "section_title": "4. Can Collective Responsibility be Distributed?", "subsections": [] }, { "main_content": [ "\nMoral Responsibility has traditionally been understood to entail\nmoral—and not just social or legal—blameworthiness and\nmoral blameworthiness has, during the modern period, been understood\nto be an aspect of an individual’s own moral agency rather than\na judgment that we ourselves make on the basis of our own social and\nlegal standards. Hence, those who search for the conditions of moral\nresponsibility generally insist that an agent has herself\ncaused—freely willed—that for which she is being held\nmorally responsible. Marion Smiley (1992) argues that this has not\nalways been the case but is rather a modern development.", "\nNot surprisingly, the kind of free will that is required of the modern\nnotion of moral responsibility—contra-causal freedom—is\ndifficult if not impossible to locate in practice. So, too, is the\n“softer” notion of free will preferred by\ncompatibilitists. Hence, when contemporary philosophers turn their\nattention to the conditions of moral responsibility in practice, they\nfrequently zero in on what they take to be one of free will’s\nkey components—intentionality—and ask: Under what\nconditions can we say that an agent intended X?", "\nSmiley (1992) argues that having an intention is neither equivalent to\nfree will nor sufficient to ground the modern notion of moral\nresponsibility (as distinct from its Aristotelian counterpart).\nSuffice it to point out here that contemporary philosophers who write\nabout collective responsibility place intentionality at the center of\ntheir attention and because they have accepted (consciously or\nunconsciously) the modern notion of moral responsibility, they\nassociate it with a unified moral self that is capable of controlling\noutcomes.", "\nBut, as we have seen in Section 2, such a unified moral self might not\nbe possible in the case of collective entities. Where, then, does that\nleave us? Critics of collective responsibility assume that if such a\nunified moral self is not possible in the case of collective entities,\ncollective moral responsibility does not make sense. But such an\nassumption may be premature and in the end not warranted. For, if we\nwere to develop an alternative notion of collective moral\nresponsibility, i.e., one that does not attempt to mimic its (modern)\nindividualist counterpart, we might not have to insist on such a\nunified moral self. What might such an alternative notion of\ncollective moral responsibility look like?", "\nThree things suggest that we have a lot more creative freedom in this\ncontext than we now realize. First of all, contrary to the assumptions\nof many contemporary philosophers, the modern notion of moral\nresponsibility is not moral responsibility per se. Instead,\nit is a distinctly Kantian notion of moral responsibility that has at\nleast a trio of respectable counterparts, namely, the Aristotelian,\nChristian, and pragmatist notions of moral responsibility (Smiley\n1992).", "\nSecond, while many contemporary moral philosophers may in the end\nprefer the Kantian notion, we cannot dismiss these others simply\nbecause they do not live up to Kantian standards. Nor, for that\nmatter, can we designate these other notions of moral responsibility\nas non-moral or as “merely sociological” simply because\nthey do not conform to what Kantians see as “the moral\nrealm”. Instead, we have to make room for the above notions of\nmoral responsibility—and perhaps others still—in our\ndiscussions of collective responsibility.", "\nThird, given its association with discrete individuals, the Kantian\nunderstanding of moral responsibility would seem to be especially out\nof place when it comes to collective responsibility. For, moral\nresponsibility as Kantians understood it is not something that we just\nhappen to associate with individual moral agents. Nor is its\nnotion of moral blameworthiness just incidentally applied to\nindividuals. Instead, moral responsibility as put forward by Kantians\nis by nature associated with individual moral agents. So,\ntoo, is the notion of moral blameworthiness that grounds it. Indeed,\nthe latter is best defined as individual moral\nblameworthiness.", "\nAll three points should be liberating for those who want to re-think\ncollective responsibility in ways that render it both possible and\nappropriate to groups. The first suggests that there are other notions\nof moral responsibility available to us. The second makes clear that\nthese other notions of moral responsibility cannot be dismissed simply\nbecause they do not conform to the Kantian notion of morality. The\nthird points to the need to move beyond what is by definition a notion\nof individual moral blameworthiness and to figure out how\ngroups might be understood as morally blameworthy qua\ngroups.", "\nWhat might it mean for groups to be morally blameworthy? What kind of\ncausation would be required to sustain a notion of group moral\nblameworthiness? How might we put these two things—group moral\nblameworthiness and causation—together in this context to\nconstitute an alternative way of thinking about collective\nresponsibility that is both possible and appropriate to groups?", "\nIn recent years, a small group of moral philosophers has begun to ask\nthese questions and in doing so has provided us with intriguing\nalternatives to the traditional understanding of moral responsibility.\nIn his own re-thinking of collective responsibility, Kenneth Shockley\n(2007 and 2016) sets out to replace the Kantian notion of moral\nblameworthiness with a looser notion of “being at fault”\nthat allows us to talk about a particular collective as\n“deserving of some kind of punishment apart from that meted out\nto its members for their role in harm” (p. 452). Such punishment\nmight mean “eradicating the groups themselves or dismantling\npart of them. Likewise, it might take the form of reducing the\nstrength of bonds between individual members or …\nde-institutionalizing group norms” (p. 452).", "\nNeta Crawford (2007, 2013 and 2014), who also distances herself from\nthe Kantian notion of moral blameworthiness, points to the importance\nof recognizing that collectives, as distinct from their members, can\ndo morally bad things—in some cases through the actions of their\nmembers—by virtue of the particular kind of group that they are\nand how they are organized. Crawford’s particular concern here\nis with military groups whose soldiers end up killing innocents as a\nresult of either their rules of engagement or the kinds of weapons\nthat they use. What sense does it make to say that such military\ngroups, as distinct from their members, are morally blameworthy for\nthe deaths of these innocents?", "\nCrawford argues that while it makes no sense to consider a military\ngroup morally guilty in the sense of having a tainted soul, it does\nmake sense to consider that it is in at least some respects a morally\nbad organization that deserves punishment. Not surprisingly, such\npunishment has to be appropriate to organizations, as distinct from\nindividuals, if it is going to ground collective moral responsibility.\nHence, Crawford chooses to view punishment here as a matter of forcing\na collective to apologize, make amends, and change.", "\nThe “change” here frequently amounts to either eradicating\nparts of the group in question or changing those aspects of the group\nthat lead it to produce harm. In the case of a morally blameworthy\nmilitary group, it means “reducing the likelihood of systematic\natrocities and avoidable accidents by reviewing and revising the\nchoice of weapons and rules of engagement … and apologizing and\nmaking amends when systematic atrocity occurs” (Crawford 2007,\np. 212).", "\nIn other cases, the punishment associated with a morally blameworthy\ncollective may amount to eradicating the group altogether or to\nforcing it to give up important aspects of itself. The Nazi\nregime—or any other regime whose purpose is to destroy a race of\npersons—would presumably fall into the first camp. A government\nor business club that excludes persons of color and/or women as part\nof its raison d’etre would presumably fall into the second.", "\nWhat kind of causation or agency is required by moral blameworthiness\nof this kind? Since we are not talking about a Kantian notion of moral\nblameworthiness, we do not have to go as far as to insist on free will\nor focus all of our attention on the possibility of a unified moral\nself. Nor as such do we have to make sense of a group’s having\nfreely willed something bad. But, unless we want to ground moral\nblameworthiness in pure utility, we do have to assume, at the very\nleast, that the collective in question has produced the\nharm.", "\nNot surprisingly, not just any kind of production will do here. At the\nvery least, the collective has to play what Shockley (2007) calls an\n“eliminable role” in the production of harm—even if\nthat role is primarily one of providing the conditions under which\nmembers of the collective carry out the harmful actions. In other\nwords, the collective has to be necessary to the harm’s\nproduction by virtue of what Shockley calls its “coordinating\ncontrol” over members.", "\nHow can we understand such control? In the case of corporations, we\ncan focus on the way in which the norms of the collective determine or\nshape particular paths of behavior, as well as on how incentive\nstructures and patterns of discipline lead individuals to act in\nharmful ways. Shockley finds many of these things at work in the case\nof Enron. According to him, “[t]he norms operative within the\nmembership of Enron controlled for the climate of secrecy and\ndoubt” (Shockley 2007, p. 449).", "\nShockley assumes here that the collective is morally responsible for\nharm because it exerts “coordinating control” over what\nhappens in the group. But he does not excuse individual members from\nmoral blameworthiness in the process. Nor, for that matter, does he\nallow for the possibility that individual members may together bring\nabout harm without having acted in a morally blameworthy fashion\nthemselves. Indeed, he insists on individual members having acted as\nsuch if collective moral responsibility is to be coherent. In cases\nwhere collectives are morally responsible for harm, “the\ncollective serves as an enabling condition of individual blameworthy\nagents to perform harmful acts” (Shockley 2007, p. 442).", "\nShockley is wise to point out that the moral responsibility of a\ncollective does not preclude the moral responsibility of its members.\nBut he may go too far in including the moral blameworthiness of\nindividual members in collective moral responsibility itself. For,\nthere are—even according to Shockley’s own criteria of\ncoordinating control—cases of collective moral responsibility in\nwhich individuals either do nothing wrong but together bring about\nharm within a collective or do harmful things but are excused from\nmoral blameworthiness by virtue of their inability to do otherwise.\nMobs are a case of the first kind. Neta Crawford’s soldiers are\na case of the second.", "\nMoreover, as argued in Smiley 2010, if we are truly concerned about\ncollective moral responsibility, rather than about the moral\nresponsibility of individuals who belong to collectives, we do not\nhave to insist that individual members have performed actions that\nrender them morally blameworthy. Instead, we have to insist only that\nthe collective, by virtue of its very nature as the particular kind of\ncollective that it is, has led individual members to produce harm that\nthey could not have produced themselves. For, it is the moral\nblameworthiness of the collective itself, rather than that of its\nmembers, that constitutes collective moral responsibility.", "\nWhile associating collectives with moral blameworthiness is difficult,\nit is not, as we have seen, impossible. Indeed, by both reimagining\nmoral blameworthiness in the context of groups and developing\nalternative notions of collective agency that allow us to locate such\nmoral blameworthiness, we can move toward a coherent and empirically\nfeasible practice of collective moral responsibility. Two recent\nefforts to defend collective moral responsibility appear to be\nparticularly promising in this context. The first involves\nappropriating P. F. Strawson’s reactive attitudes model of moral\nblameworthiness for the purpose of showing how a collective might be\nconstrued as morally blameworthy qua collective. Gunnar\nBjornsson and Kendy Hess (2017) pick up on Strawson’s approach\nin their own work on collective moral responsibility and ask whether\ncorporations and other collective entities can have the requisite\nreactive attitudes to be held morally responsible for bringing about\nharm. They answer in the affirmative and argue that collective\nentities can have the capacities associated with guilt and\nindignation, as well as the relevant epistemic and motivational\ncapacities to be blamed.", "\nThe second effort zeros in on the motivational capacities of groups\nassociated with reason-giving. Here the argument is that while\ncollectives may not have the kind of free will associated with\nindividual moral agents, they do have the capacity to formulate\nreasons and act on them. Silver (2022) argues that it is this capacity\nto respond to one’s reasons and to be motivated by them that\nrenders collectives self-directed in a way that lends credence to our\nascriptions of collective moral responsibility to them.", "\nPresumably, not all groups which are appropriate sites of moral\nresponsibility should be blamed. How, if at all, can groups\nwhich are appropriate sites of collective moral responsibility, in\ngeneral, avoid blame in particular cases? While, as Andrés\nGarcia (2021) argues, collective moral responsibility is not itself\ninherently unfair in ways that early critics such as H. D. Lewis\n(1948) claimed, it can be unfair in particular cases. In some of these\ncases, its unfairness will be a matter of a group’s not having\nmade a sufficient contribution to the harm for which it is being\nblamed. In other cases, it will be a matter of the group’s not\nhaving known what was going on. In these latter cases, we confront the\npossibility that the group can make a plea of ignorance to avoid blame\nin the way that individuals do. A plea that as Smiley (2016) points\nout, needs to be assessed with various standards of fairness in\nmind.", "\nNot surprisingly, the possibility of group-based ignorance is itself\ncontroversial. Anne Schwenkenbecher (2021) articulates several\ndifferent kinds of group-based ignorance and goes on to argue for\ncollective epistemic obligations. Säde Hormio (2018) explores how\ngroup-based ignorance is structured, as well as maintained, within\norganizations and provides us with a framework for distinguishing\nbetween acceptable and unacceptable excuses in the context of\ngroup-based blame. While such efforts face the same kinds of\nchallenges faced by all efforts that treat groups as moral agents,\nthey signal the possibility of yet another alternative approach to\ncollective moral responsibility (and a very promising one at that) by\ntreating collective moral responsibility as at least shaped, if not\ndesignated by worldly practices such as excuse-giving," ], "section_title": "5. Alternative Approaches to Collective Responsibility", "subsections": [] }, { "main_content": [ "\nWhen is it appropriate to hold a group responsible for harm? When is\nit appropriate to refrain from holding a group responsible? As things\nnow stand, we generally assume that to hold a group—or, for that\nmatter, an individual—responsible for harm is simply to\nestablish that he, she, or it is responsible for the harm, and as such\nwe do not generally find the above question especially challenging.\nIndeed, we often assume that we can answer it by simply reiterating\nthe conditions of collective responsibility itself.", "\nBut to hold an agent responsible for harm is not simply to establish\nthat he, she, or it is responsible for the harm. Instead, it is to\nmake the agents’ responsibility known both to them and to the\nrest of the community or, in other words, to publicize their\nresponsibility as part of a social or legal practice of accountability\nin particular contexts with particular purposes in mind.", "\nThe differences between these two things—the act of\nholding an agent responsible for harm and the agent’s\nbeing responsible for it—are worth underscoring.\nWhile X’s being responsible for harm is a\nmatter of what X has done, our holding of X\nresponsible is a matter of what we do with our knowledge of\nX’s behavior. The former is ostensibly a moral fact\nabout X. The latter is an act that we ourselves perform as\npart of a social or legal practice of accountability.", "\nWhen are we justified in performing such an act of accountability?\nSince holding agents responsible for harm sheds a negative light on\nthem and frequently results in calls for compensation and/or\npunishment, we generally insist on taking fairness seriously\nin this context and, in our efforts to take fairness seriously, we\ngenerally require accuracy with respect to the facts of\nresponsibility. Indeed, we often combine these two conditions and say\nthat it would not be fair to hold an agent responsible for harm if he,\nshe, or it was not really responsible for it.", "\nBut fairness is not always just a matter of factual accuracy when it\ncomes to holding groups responsible. Instead, it can be—and\noften is—a matter of making sure that we do not in our holding\nof agents responsible discriminate between equally responsible agents.\nIn other words, it can be—and often is—a matter of\ntreating like cases in the same fashion so as not to be\ndiscriminatory. Hence the emphasis that we now see being placed by\npost-war tribunals on making sure that if collective responsibility is\nascribed to particular groups it is ascribed to all groups according\nto general rules.", "\nAs it turns out, we do not always treat like cases in a similar\nfashion. Nor, for that matter, do we always place fairness above all\nelse. Indeed, we sometimes choose to discriminate between cases that\nappear to be the same. Moreover, we do so in some cases on\nself-consciously consequentialist grounds that we find to be\njustified.", "\nIn many of these cases, we are concerned with whether or not we can\nbring about positive consequences in the world by holding particular\ngroups responsible. (Would these groups behave better if we did? Would\nothers follow suit? Would harm be prevented?) In other cases, we are\nconcerned with consequences of a decidedly more negative sort. (Would\nholding particular groups responsible for harm lead to greater\nanimosity among groups? create resentment in the community? stand in\nthe way of peace?)", "\nInterestingly enough, those who are concerned about responsibility in\nphilosophical circles are frequently hesitant to enter into a full\nblown consequentialist debate about when we should hold particular\nagents responsible in practice. (We suggest why this may be so below.)\nBut they do often make clear that they have particular consequences in\nmind when, in an off-handed fashion, they assess collective\nresponsibility in practice. In the case of individual responsibility,\nthese consequences tend to be positive and include the reinforcement\nof norms associated with moral agency. In the case of collective\nresponsibility, they tend to be both positive and negative.", "\nWhile defenders of collective responsibility do not always distinguish\nbetween the consequences of holding particular groups responsible in\npractice and the value of collective responsibility per se,\nthey do make clear that we can do important things in the world by\nholding particular groups responsible for harm. Among other things, we\ncan raise consciousness among groups about what they are doing. We can\nget them to stop harming others. We can reinforce social norms that\nprevent such harm from occurring in the future. And we can make clear\nto the world that those being harmed are worth taking seriously.", "\nList and Pettit (2011), as we saw in Section 2, make clear that\nholding groups responsible for particular kinds of harm not only\n“lets us discern the true contours of the moral and political\nworld we inhabit” (List and Pettit 2011, p. 185), but provides\nincentives for change among group members (p. 168), and conditions\nthem to behave better in the future (p. 157). Likewise, it can provide\nthe basis for institutional reform in cases where collective acts were\nhitherto invisible.", "\nWhat about the negative consequences that might follow from holding\nparticular groups responsible for harm? Not surprisingly, the most\ncommonly cited of these consequences are those associated with the\nfreeing of individuals from personal responsibility in both private\nand public life. In some cases, the negative consequences thought to\nfollow from collective responsibility are a matter of moral degeneracy\nand/or the avoidance of just punishment. In other cases, they are a\nmatter of the erosion of liberal ideals and/or threats to democratic\ngovernance.", "\nNot surprisingly, these arguments have been taken in a variety of\ndirections over the years. Garrett Hardin’s early work focused\non the squashing of individual initiatives associated with collective\nresponsibility (Hardin 1968). So, too, did the works of many others\nduring the Cold War. Contemporary liberals tend to be less vehement\nthan Hardin with respect to the ways in which collective\nresponsibility undermines individual moral agency. But they, too,\nworry that individuals will not take responsibility for harm that\ntheir group is being held responsible for as well. Moreover, there is\nsome historical evidence for their concerns.", "\nRichard McKeon, in an essay that rarely finds its way into\ncontemporary work on collective responsibility, provides us with\nimportant insights into the ways in which the replacement of\ncollective responsibility with personal responsibility in the West was\npolitically, as well as morally, crucial to the development of\nliberalism. According to McKeon, the replacement of collective\nresponsibility with personal responsibility meant not only that\nindividuals could exercise moral agency as individuals but that the\nstate would no longer be as necessary as it once was, since\nindividuals could now take responsibility for governing themselves\n(McKeon 1957).", "\nBut, of course, we cannot, on an a priori basis, treat personal and\ncollective responsibility as mutually exclusive. For, there is always\nthe possibility of bringing them together and doing so in ways that\nenhance both. Robert Goodin (Goodin 1998) suggests what such an\nintegrated system of responsibility might look like in the context of\na welfare state. List and Pettit underscore how individual and\ncollective responsibility might co-exist on a more general level.\n(List and Pettit 2011, pp. 121–122)", "\nOne of the most interesting critiques of the practice of collective\nresponsibility put forward by a contemporary philosopher is that of\nMark Reiff (2008). Reiff concedes that holding particular groups\nresponsible for harm can do good things in the world, e.g., deter\nthese groups from performing harmful actions in the future, aid us in\nbringing about social order more generally, and provide communities\nwith a basis for justice. But he makes clear that holding groups\nresponsible for harm can also lead to both the escalation of violence\nand the watering down of moral strictures. Indeed, he claims,\n“some of the most heinous crimes in human\nhistory—including the Nazi’s Final Solution and genocide\nin Rwanda—have been facilitated if not motivated by a belief in\ncollective responsibility” (Reiff 2008, p. 234).", "\nReiff’s primary focus when discussing collective responsibility\nand violence is on what can go wrong when we hold groups responsible\nfor harm over time in contexts where each side in a conflict defines\nthe other as collectively responsible for historical wrongs. According\nto Reiff, in such cases, we are bound to encounter endless cycles of\nretaliation, as well as the presentation of murderous acts as acts of\npunishment. Moreover, we are bound to encounter these kinds of things\nnot because the actors in question lack a sense of morality but\nbecause of the particular kind of moral righteousness that claims of\ncollective responsibility allow those who want to retaliate against\ntheir enemies in the name of a higher morality.", "\nSince Reiff’s focus here is on moral righteousness, we might\nexpect him to view the practice of holding groups responsible as\nbolstering morality (albeit morality of a peculiar and skewed kind).\nBut he does not do so. Instead, he argues just the opposite, namely,\nthat claims of collective responsibility can—and often\ndo—undermine both the importance of morality in general and the\neffectiveness of punishment in particular. Here his focus is primarily\non what happens when we internalize claims of collective\nresponsibility.", "\nReiff argues that when we internalize claims of collective\nresponsibility, we may come to feel more responsibility—or\nresponsibility for more things—than we used to feel. But we are\nless likely to follow the dictates of morality. For, while the range\nof our responsibility has been expanded, the ties between\nresponsibility and morality have been weakened. Indeed, these ties may\nin some cases be totally severed. How might this happen?", "\nReiff does not claim, as those before him did, that the practice of\ncollective responsibility allows individuals to avoid personal\nresponsibility and hence reduces both their moral agency and their\nculpability for harm. Nor does he, as his predecessors did, understand\nthe problem in question as a matter of too little personal\nresponsibility in general. Instead, he understands the problem as a\nmatter of individuals feeling responsible for harm even when they have\ndone nothing wrong. (Presumably, the moral dictates that Reiff is\nconcerned with here are those associated with an individual’s\nown actions.) According to Reiff,", "\n[the] problem is not that people are less likely to feel\nresponsibility for their own misconduct if they feel that others will\nbe held collectively responsible for harm. … The problem is\nthat collective responsibility encourages people to feel responsible\nand subject to punishment even when they have behaved correctly.\nHence, punishment is no longer an incentive. (Reiff 2008, p. 241)\n", "\nIn the end, he concludes, “[e]mbracing collective responsibility\nundermines the very concept of responsibility itself, for it\nencourages people to disregard rather than obey the structures of\nmorality” (Reiff 2008, p. 242).", "\nInterestingly enough, most of those who offer consequentialist\ncritiques of collective responsibility—and again they are almost\nalways concerned with the practice of holding groups responsible for\nharm rather than with the facts of responsibility per\nse—do so on a surprisingly general level. In other words,\nthey do not provide us with a set of criteria for thinking about the\nvalue of holding groups morally responsible in particular situations.\nBut they could do so very productively on the basis of the more\ngeneral arguments that Reiff and others provide. Moreover, they could\ndo so without violating their own agent-based approaches to moral\nresponsibility. For, as we have suggested above, being morally\nresponsible and holding others morally responsible are not the same\nthing. Nor do they have the same relationship to consequences. While\nconsequences may be irrelevant to moral responsibility itself, they\nmay be absolutely key to our choice to hold—or not to\nhold—agents morally responsible in practice." ], "section_title": "6. Collective Responsibility and the Question of Consequences", "subsections": [] }, { "main_content": [ "\nWhile the majority of those now writing on collective responsibility\ncontinue to focus on the kind of responsibility explored above, i.e.,\nbackward looking collective responsibility, a small but growing number\nof philosophers have chosen to focus instead on forward looking\ncollective responsibility. Two things appear to explain such a shift\nin focus. The first is the recognition that collective entities such\nas states, corporations, and movements may now be the only agents\ncapable of preventing particular kinds of suffering in the world. The\nsecond is the publication of David Miller’s National\nResponsibility and Global Justice (Miller 2007), Iris\nYoung’s Responsibility for Justice (Young 2011), and\nPeter French and Howard Weinstein’s edited collection\nForward Looking Collective Responsibility (French and\nWeinstein 2014).", "\nWhat is forward looking responsibility? Forward looking\nresponsibility, like its backward looking counterpart, refers to a\ncollective agent’s responsibility for a particular state of\naffairs in the world. But, unlike its backward looking counterpart, it\ndoes not make responsibility out to be a matter of having caused an\nexisting (morally problematic) state of affairs. Instead, it makes\nresponsibility out to be a matter of being morally charged\nwith—responsible for—bringing about a state of affairs\nwhich we as a community consider to be better. Hence, when we ascribe\nforward looking responsibility to a collective agent, we do not tell a\ncausal story about the agent. Instead, we specify what the agent\nshould be doing in the world.", "\nNot surprisingly, we often end up pointing to the particular tasks\nthat we think the agent should be carrying out and refer to these\ntasks as the agent’s responsibilities. But we need to\nbe careful here. For forward looking responsibility is not simply a\nmatter of carrying out tasks. Instead, it is a matter of being morally\ncharged with bringing about a state of affairs that is, by virtue of\nthe ascription of forward looking responsibility itself, now part of\nthe agent’s moral business. Hence, in discussions of forward\nlooking responsibility, we do not simply say of an agent that the\nagent has responsibilities X, Y, and Z. Instead, we say that the agent\nis responsible for making sure that a particularly desirable state of\naffairs X, Y, or Z comes into existence.", "\nSince forward looking responsibility requires that an agent bring\nabout a particular state of affairs, it has a lot in common with\nbeing morally obliged to do something. But the emphasis is\ndifferent. So, too, is the level of flexibility associated with moral\nagency. In cases where we use the language of moral obligation, we\nsignal that the agent has to perform a particular act. In cases where\nwe use the language of responsibility, we allow the agent to use its\nown judgment in deciding how to bring about the desired state of\naffairs. Likewise, we charge it with exercising its judgment\nwisely.", "\nWhat is morally salient about forward looking collective\nresponsibility? Backward looking collective responsibility, as we have\nseen, is morally salient because of its association with\nblameworthiness. Forward looking responsibility is not completely\nremoved from considerations of blame—we sometimes blame those\nwho fail to take their responsibilities seriously—but it is not\nmorally salient because blame sometimes enters the picture. Instead,\nit is morally salient because we think that such responsibility may,\nif taken seriously by those who are being held responsible, help to\nbring about a desirable (or better) state of affairs in the world.", "\nThe requirements associated with forward looking collective\nresponsibility are not as steep as those associated with its backward\nlooking counterpart. Nor are they as metaphysical. For, unlike its\nbackward looking counterpart, forward looking collective\nresponsibility is not designed to capture an agent’s will.\nInstead, it is designed to distribute moral labor. Hence, while\nforward looking collective responsibility only works with purposeful\nagents, it does not require either a “collective mind” or\nthat an agent be able to form “we intentions”. Instead, it\nrequires only that the agent be able to do something in the\nworld and take responsibility for making things happen.", "\nWhile forward looking collective responsibility is thus not saddled\nwith controversial metaphysical conditions in the way that its\nbackward looking counterpart is, it is not without its own\ncontroversies. In some cases, these controversies are about what kinds\nof groups are capable of forward looking collective responsibility.\nBill Wringe (Wringe 2014) and Felix Pinket (Pinket 2014) cover these\ncontroversies nicely. In other cases, they are about how—on\nwhat normative basis—we can ascribe forward collective looking\nresponsibility in practice. What principles should we invoke to do so?\nHow should we order these principles?", "\nInterestingly enough, not everyone thinks that such principles are\nnecessary. Indeed, a few key figures in the field still assume that\nforward looking (remedial) responsibility is grounded in causal\nresponsibility for the harm now deemed in need of a remedy. David\nLyons (Lyons 2004) feels comfortable assuming that because the U.S.\nwas causally responsibility for poverty and racism in the past, it now\nhas a responsibility for doing everything that it can to create\nopportunities for the poor and minorities. David Schmidtz (Schmidtz\n1998), who, in contrast to Lyons, takes the poor to be causally\nresponsible for many of their own problems, also moves directly from\ncausal to remedial responsibility. So, too, does Iris Young (Young\n2011).", "\nBut, again, we need to be careful. For, forward looking (remedial)\nresponsibility is not ascribed for the purpose of gauging moral agency\nper se. Instead, it is ascribed for the purpose of ensuring the\nsuccess of a particular, morally justifiable, project, e.g.,\nalleviating poverty, hunger, or racism. Hence, when it comes to\nforward looking responsibility, we need to think about who is in the\nbest position to do something about the harm, and when we do, as\nRobert Goodin (1998) points out, we may—and probably\nwill—discover in some cases that the agent who caused the harm\nis not the agent who is now able to remedy it in practice.", "\nNone of this suggests that we should abandon judgments of causal\nresponsibility altogether when ascribing forward looking\nresponsibility. Indeed, as we suggest shortly, such judgments may\nbecome relevant to matters of fairness in ascribing remedial\nresponsibility. But it does suggest that we cannot move directly from\ncausal to remedial responsibility, i.e., ground the latter exclusively\nin the former. Likewise, it does suggest that we need intermediary\nconsiderations. Carol Rovane (Rovane 2014), Tracy Isaacs (Isaacs 2011;\nIsaacs 2014), Ludger Jansen (Jansen 2014), Derrick Darby and Nyla\nBranscombe (Darby and Branscombe, 2014) and Marion Smiley (Smiley\n2014) all make this clear from their own theoretical perspectives.", "\nHow, then, are we to ascribe forward looking collective responsibility\nin practice? At the very least, we need to make room for various kinds\nof practical judgments, including those that draw attention to who is\nbest able to remedy the harm in question and at what cost. But such\npractical judgments, which are very important, are not the only\nnon-causal matters that we need to take into consideration when\nascribing forward looking responsibility. Indeed, as recent debates\nconcerning our responsibility for remedying health care problems at\nhome, starvation abroad, and environmental disasters everywhere\nattest, judgments about the relative value of our projects in the\nworld are also crucial. So, too, are judgments about fairness and\nobligation.", "\nNot surprisingly, we incorporate judgments about relative value\nprimarily in cases where we cannot pursue all of our\nprojects—eradicating hunger, bringing up healthy children,\ncreating jobs, reversing global warming—at once or even at\nall. But we make these judgments in other kinds of cases as well,\nincluding those in which a supposed cause of harm, say, capitalism, is\nalso the cause of something that we value. In these cases, we may\nthink that our choice to focus on a particular state of affairs is\nuncontroversial. But it is in fact steeped in our own priorities.", "\nTake, for example, Young’s ascriptions of responsibility for\nalleviating poverty, hunger, and violence around the world cited\nabove. Young may be correct that capitalism (or at least unregulated\ncapitalism) is causally responsible for these problems. (There would\nof course be other agents to consider as well.) But if she is going to\ngo on to ascribe remedial responsibility to those who benefit from\ncapitalism—which is what she is concerned to do—then she\nhas to take into consideration that capitalism (or at least regulated\ncapitalism) may also be causally responsible for things in the world\nthat we value, e.g., significant improvements in health care,\neducation, and food production, as well as the separation of economic\nfrom political power.", "\nMoreover, she has to take these things into consideration because of\nthe very nature of remedial responsibility itself as organized and\ndistributed across cases. Remedial responsibility, as we have seen, is\nattached to a particular project. (Who, we ask, is responsible for\ncarrying out this project?) But it cannot be formulated in isolation.\nInstead, it has to be formulated with an eye to our other projects.\nFor, we are limited with respect to both moral energy and resources.\nHence, we have to prioritize our projects as well as to coordinate our\nascriptions of remedial responsibility across them. Likewise, we have\nto be aware of the priorities that others, e.g., Young, incorporate\ninto their own ascriptions of remedial responsibility.", "\nAll of this is to suggest that if we want to ascribe remedial\nresponsibility in a justifiable fashion— in a way that avoids\narbitrariness and bias— we will have to argue openly about the\nrelative value of our projects and proceed with an overview in mind.\nWhat projects, we will have to ask, are most valuable to us and how do\nthey rank in importance with respect to other projects? Whose needs\nand interests are being taken into consideration by these projects?\nHow might we ensure that everyone’s needs and interests are\ntaken into consideration? What is the relative cost of the projects in\nquestion and how does cost itself rank in importance here?", "\nRobert Goodin defends this kind of pragmatic approach to forward\nlooking collective responsibility in his arguments for why the U.S.\nshould be held responsible for providing the poor with welfare\nbenefits. In distancing himself from the practice of blame, he\nwrites:", "\nIt is forward-looking, task oriented, collective responsibility that I\nam championing.… There are good reasons for pursuing certain\nsorts of goals through some sort of coordinated, collective apparatus\nlike the state.…Responsibilities get collectivized simply\nbecause that is the only realistic way (or anyway, much the most\neffective way) of discharging them. (Goodin 1998, p. 50)\n", "\nThe pragmatic approach to forward looking collective responsibility\ngestured to here is very valuable (and sound). But we cannot treat it\nin isolation from other approaches. In other words, we cannot simply\nreplace causal responsibility with capacity for remedying\na problem as a basis for ascribing forward looking\nresponsibility. Instead, we have to incorporate other values and\nprinciples into our ascriptions of responsibility. What might they be?\nAs things now stand, the value of fairness is frequently invoked, if\nnot thoroughly explored, in this context. So, too, are the values of\ncitizenship and collective obligation, as well as the principle of a\nsocial contract.", "\nAdmittedly, those who invoke the value of fairness in ascribing\nforward looking responsibility do not always have the same thing in\nmind by the term. Alexander Brown [2009] incorporates judgments about\nwho caused harm into his arguments about who can fairly be held\nresponsible for remedying such harm and, in doing so, treats fairness\nas a response to causal agency. Brown’s concern is with the\nbehavioral lapses of the poor in a welfare state.", "\nIf a person is causally responsible for becoming an addict, then he\ncannot fairly expect our assistance in getting him off of\ndrugs.…The government can only be expected to do so much.\n(Brown 2009, p. 151)\n", "\nMichael Walzer also considers fairness to be very important to\nascriptions of forward looking collective responsibility in a welfare\nstate. But he does not consider fairness in this context to rest on\nconsiderations of who caused harm. Instead, he considers it to rest on\nthe norms of communal membership. According to Walzer, a fair\ndistribution of responsibilities in a welfare state will always come\ndown to what we owe each other as members of a community—which,\nfrom his perspective, translates into all of those things that will\nmake communal membership possible among those in the community, e.g.,\nfinancial security, health care, education, peace, and security,\nregardless of whether members caused harm to themselves. (Walzer\n2008)", "\nChristian Neuhauser, who underscores the importance of distributive\njustice in the organization of forward looking collective\nresponsibility, concurs on the importance of fairness to the\nascription of remedial responsibility. But he takes things in a\nsomewhat different direction from both Brown and Walzer by treating\nfairness as a matter of doing one’s fair share.\nMoreover, Neuhauser places fairness in the context of various\ncollective action scenarios. Hence, he is naturally led to talk about\nfairness as a motivating force. “The motivation of\nagents to embrace a forward looking responsibility also depends on\nwhether other actors contribute their fair share”. (Neuhauser\n2014, p. 246)", "\nWhile the value of fairness is commonly invoked by those concerned to\nlocate criteria for ascribing (or organizing or distributing) forward\nlooking collective responsibility in practice, it is not the only\nvalue or principle in play. Indeed, many of those in the field\ncontinue to look to collective obligations as a basis for remedial\nresponsibility. In some cases, the collective obligations in question\nare thought to be built into the collective itself. (Miller 2007) In\nother cases, they are thought to derive from various other norms of\nmoral and political life.", "\nIn her discussion of forward looking collective responsibility and the\nprospects of war, Neta Crawford locates the source of these\nobligations in the sphere of citizenship. According to Crawford,\n“ordinary citizens have a collective moral and political\nresponsibility to participate in decisions about wars that are\nundertaken by their governments and they have a responsibility to\nprotest unjust wars or immoral conduct during wars.” (Crawford,\n2014, p. 141) Moreover, they have such responsibility, according to\nCrawford, by virtue of their identity as citizens in a democratic\ncommunity. Bill Wringe takes such an analysis to the global level\n(Wringe 2014), as do many others in the field of global justice,\nincluding David Miller (2007).", "\nDerrick Darby and Nyla Branscombe, in their work on responsibility for\novercoming social, political, and economic inequality, choose to look,\nnot to the identities of democratic citizens, but to the kinds of\nsocial, political, and economic institutions that democratic citizens\nwould choose within a Rawlsian social contract, as a basis for\nascribing remedial responsibility. In doing so, they manage not only\nto bring both shared interests and rational choice together, but, in\ndoing so, to make clear what is unique about forward looking\nresponsibility.", "\nThe shift to a forward looking account of political responsibility\nrequires placing greater emphasis on the interest that we all share in\nsustaining the major social institutions that so profoundly shape our\nlife prospects.…Hence, we should take political responsibility\nfor inequality given our vital interest in sustaining the system of\ncooperation and institutions that give rise to both permissible and\nimpermissible inequalities. (Darby and Branscombe 2014, p. 133)\n", "\nTracy Isaacs, who develops a full-blown account of collective\nobligations and their relationship to collective responsibility\n[Isaacs 2011 and 2014], points to many of the norms cited above and\nemphasizes the centrality of identity. But, interestingly enough, she\ndoes not steer clear of causal responsibility in doing so. Instead,\nshe offers a sophisticated view of how causal responsibility helps\nshape our criteria for ascribing remedial responsibility fairly.", "\nAgents who are causally implicated and who benefit do indeed bear a\nheavier burden of obligation for alleviating harmful circumstances.\nWhere collective obligation is concerned, these connections to the\nharm or wrong doing make some collective agents more obligated than\nothers…and play a role in determining the identity of the\ncollective agent who has the collective obligation. (Isaacs 2014, p.\n41)\n", "\nAll of these arguments underscore the cluster of values and principles\nthat go into ascribing forward looking collective responsibility in\npractice. Isaac’s work in particular provides a way of bringing\ncausal responsibility back into play without either blurring the\ndistinction between backward and forward looking responsibility or\ntreating the latter as a natural extension of the former. How, if at\nall, should we prioritize all of these values, principles, and causal\njudgments, in ascribing remedial responsibility? It has been suggested\n(Smiley 2014) that instead of treating one of them as primary and the\nothers as secondary we bring all of them together into a pluralistic\nnormative account of forward looking collective responsibility. ", "\nIn doing so, we would undoubtedly make the project of forward looking\ncollective responsibility out to be more complicated than it now\nappears to be in the hands of those who choose one value to place at\nthe center of our attention in this context. But we would also make it\nmore sensitive to the various ethical demands that we rightly place on\neach other in holding each other responsible for harm in the\nworld.", "\nWhat about the practical constraints associated with forward looking\ncollective responsibility? Two such constraints (or possible\nconstraints) have come to the fore in recent years. The first has to\ndo with structured injustice. The second has to do with how we can (or\ncannot) move forward in cases where our collective is not yet\norganized, i.e., in cases where the kind of collective required for\nremedial action, namely one that is capable of acting, still has to be\ncreated or at least organized.", "\nIris Young introduces the matter of structural injustice in her\narguments for why we should now be focussing on forward looking rather\nthan backward looking, collective responsibility. According to Young,\nwe should be focussing on forward looking collective responsibility\nbecause the source of much injustice in the world is located in\nsocial, economic, and political structures, and only forward looking\ncollective responsibility can deal with confronting these structures\nhead-on. Robert Goodin and Christian Barry (2021) argue persuasively\nagainst the sharp distinction that Young relies on here between\nindividualized responsibility for past structural injustice and\ncollective responsibility for preventing structural injustice in the\nfuture. Moreover, Young herself relies on backward looking causal\nhistories of various collectives that bring about harm to sustain her\nnotion of forward looking collective responsibility. Nevertheless, her\ninsistence on viewing both backward and forward looking collective\nresponsibility through the lens of structural injustice sets a very\nimportant precedent for future theorizing in the field.", "\nThe second practical challenge to the practice of forward looking\ncollective responsibility pertains to the dilemma that we face when\ntrying to hold disorganized collectives responsible for preventing\nharm in the future that they could, if they were organized, prevent.\nThe problem is that they are not now organized and hence cannot act as\na collective. A transformation is necessary. But we cannot expect a\ndisorganized group (say, a mob or a group of persons who are not in\nany way institutionally connected) to instigate such a transformation.\nFor such a group is by definition not organized enough to act as a\ncollective.", "\nWhat, then, are we to do? How can we transform a disorganized group\ninto one that is organized enough to take on a collective obligation\nto prevent harm? A promising solution here might be to revisit the\nplace of individual moral agents in ascribing forward looking\ncollective responsibility in cases where a group is not yet organized\nenough to be ascribed such responsibility. In particular, we might\nwant to ask how, if at all, individual moral agents might be motivated\nand even obligated to create the kind of organized collective that is\nneeded here.", "\nNot surprisingly, the value of self-interest comes to the fore here,\nespecially with the recognition that moral agents may have\nintergenerational interests moving forward. But we need not rely on\nself-interest. Nor need we forgo the possibility that existing moral\nsystems of a non-utilitarian kind can provide the necessary moral\nmotivation. Indeed, we may even be able to argue that individual moral\nagents in a not-yet-organized collective (that, if organized, could\nprevent harm) have a moral duty to create (together) the kind of\ncollective capable of performing the required actions.", "\nFrank Hindriks takes on this challenge in “The Duty to Join\nForces: When Individuals Lack Control” (Hindriks, 2019) and\nelsewhere (Blomberg and Hindriks, 2020). Hindriks argues very\npersuasively that we can create the required organized collective if\nwe can substantiate a duty on the part of the individual moral agents\nto join forces: to approach others, to convince them to contribute to\nthe joint efforts, and to become part of a collective action. This\nduty is initially associated with individual moral agents. But,\nHindriks claims, since it focuses on mobilizing others rather than on\npreventing harm per se, it is “irreducibly\ncollective” (Hindriks, p. 204). ", "\nWhether or not the duty expressed here is “irreducibly\ncollective” (as distinct from being a fusion of individual and\ncollective responsibility) it does appear to be a very promising\nsolution to one of the thorniest problems associated with forward\nlooking collective responsibility, namely, how to bring organized\ncollectives about in cases where their existence is crucial to the\nprevention of harm.", "\nSuffice it here to underscore three more general points suggested by\nefforts such as Hindriks’. The first is that reliance on\nindividual moral duties and other kinds of individually based\nincentives to create new (or newly recognized) collective entities\ndoes not undermine the integrity of forward looking collective\nresponsibility, but instead makes the latter possible. The second is\nthat the creation (or recognition) of these new collective entities is\nabsolutely crucial in cases where we are faced, in Stephen\nGardiner’s words (Gardiner, 2017), with “paradigmatically\nglobal, intergenerational and ecological problems such as climate\nchange” (Gardiner, 2017, p. 22) that require an expanded\ncommunity of both concern and action. The third is that when we step\nback and ask how these expanded communities of concern and action can\nbe created, we confront the importance of thinking about individual\nand collective responsibility, not as mutually exclusive, but, at\nleast in some cases, as mutually supportive in both theory and\npractice." ], "section_title": "7. Forward Looking Collective Responsibility", "subsections": [] } ]

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[ " ‘In present-day political and moral philosophy the idea that\nall persons are in some way moral equals has become dogma’\n(Steinhoff ed. 2015, xi). Yet in the collection of essays from whose\nIntroduction this quotation comes and that seeks to explain and\njustify this foundational ‘dogma’, ‘children’\ndoes not figure in its index and are barely discussed if at\nall. Whilst children are thought of as human beings and thus having a\nmoral status such that it would be wrong to treat them in certain\nways, it is also thought reasonable that there are things children may\nnot do that adults may. In short, children are humans but not persons\nmorally equal to adults. This is nowhere clearer than when considering\nwhat in law children are permitted or entitled to do as well as\nprevented from doing. In most jurisdictions, for instance, children\nare not allowed to vote, to marry, to buy alcohol, to have sex, or to\nengage in paid employment. Then there are things that should not be\ndone to children because they are children, such as conscription into\nmilitary service. Why should that be the case?", "\nOne very obvious way in which this issue of what distinguishes\nchildren from adults can be addressed is by asking the following\nquestions, Do children have rights? If so, do they have all the rights\nthat adults have and do they have rights that adults do not have? If\nthey do not have rights how do we ensure that they are treated in the\nmorally right way? Most jurisdictions accord children legal rights.\nMost countries—though not the United States of\nAmerica—have ratified the United Nations Convention on the\nRights of the Child which was first adopted in 1989. The Convention\naccords to children a wide range of rights including, most centrally,\nthe ‘inherent right to life’ (Article 6), and the right of\na child “who is capable of forming his or her own views …\nto express these views freely in all matters affecting the\nchild” (Article 12) (United Nations 1989).", "\nHowever, it is normal to distinguish between ‘positive’\nrights, those that are recognised in law, and ‘moral’\nrights, those that are recognised by some moral theory. That children\nhave ‘positive’ rights does not then settle the question\nof whether they do or should have moral rights. Nevertheless, there\nare at least good political reasons why one might think that the UNCRC\nprovides an exemplary statement—in the language of positive\nrights—of how children should be treated and regarded. The idea\nof children as rights holders has been subject to different kinds of\nphilosophical criticism. There has also been philosophical\nconsideration of what kinds of rights children have if they do have\nany rights at all. The various debates shed invaluable light on both\nthe nature and value of rights, and on the moral status of\nchildren.", "\nThe question of how the putative rights of children stand in relation\nto the rights of those adults who, arguably, have rights over children\nbroaches the issues of parental rights and responsibilities which is\nnot discussed here. (See the entry on\n procreation and parenthood.)" ]

[ { "content_title": "1. Children and Rights", "sub_toc": [] }, { "content_title": "2. Critics of Children’s Rights", "sub_toc": [] }, { "content_title": "3. Liberationism", "sub_toc": [] }, { "content_title": "4. Arbitrariness", "sub_toc": [] }, { "content_title": "5. Children’s Rights and Adult Rights", "sub_toc": [] }, { "content_title": "6. The Child’s Right to Grow Up", "sub_toc": [] }, { "content_title": "7. Best Interests", "sub_toc": [] }, { "content_title": "8. Children and the Reproduction of Values", "sub_toc": [] }, { "content_title": "9. The Right to be Heard", "sub_toc": [] }, { "content_title": "10. Summary", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "References Cited", "Other Important Work" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nIn the background of any consideration of children and rights are two\nmatters: what counts as a child, and what is to be understood as\ncapacity. The latter arises inasmuch as the question of whether\nchildren have rights and, if so, which ones normally turns on whether\nthey have the relevant capacity.", "\nWhat counts as a child and how we should understand\n‘childhood’ are interesting philosophical questions. They\nare considered at length in Part I of Archard (2015). (See also the\nentry on\n childhood.)\n We may usefully distinguish a concept from a conception of the child\nas follows: ‘to have a concept of “childhood” is to\nrecognise that children differ interestingly from adults; to have a\nconception of childhood is to have a view of what those interesting\ndifferences are’ (Archard 2015, 32). Having made this distinction we should recognise that conceptions of childhood vary across time and\ncultures. Moreover, conceptions of childhood may beg normative\nquestions of why children have a different moral status to adults. In\nwhat follows a child is understood simply as a human being at a\ncertain chronological stage of development. For instance, Article 1 of\nthe United Nations Convention defines a child as any human being below\nthe age of eighteen years ‘unless,’ it adds, ‘under\nthe law applicable to the child, majority is attained earlier’\n(United Nations 1989; Archard and Tobin 2019).", "\nThe concept of capacity is relevant to questions both of which theory\nof rights is correct as well as to which rights children might have.\nOther terms such as ‘competence’ and ‘ability’\nare often used as if they were equivalent to ‘capacity’.\nHowever, it is important to be clear how ‘capacity’ is\nused (Cowden 2012). Here it is used as a dispositional concept.\nSomeone has the capacity to do X if they could do X given the\nopportunity and in the appropriate circumstances. It is to be\ndistinguished from an occurrent ability or competence to do X. Thus, a\nmature rational adult has the capacity to make autonomous choices, but\nmay be temporarily unable to choose autonomously because, for\ninstance, on this occasion their mind is disturbed, or their will is\noverborne. The notion of a child’s capacity should not be\nunderstood as meaning that they have it inasmuch as they would be able\nas an adult to do certain things. Nevertheless, the distinct claim –\nthat allowing a child at some age to exercise a given right would\nencourage the acquisition of the qualifying capacity that is otherwise\nlacked – should be acknowledged and given due weight.", "\nOn the question of whether children have rights and which ones, some\nthink it obvious that children do have rights and believe that the\nonly interesting question is whether children possess all and only\nthose rights which adults possess. Others are sceptical believing that\ngiven the nature both of rights and of children it is wrong to think\nof children as right-holders.", "\nFully and properly to address this issue it is necessary first to be\nclearer about the language of rights and to distinguish several\ndifferent questions. First, we can inquire as to what it is for\nsomeone to have a right, or, put another way, we can ask what being a\nright-holder consists in.We\ncan ask a second question, namely what must be true for there to be\nrights. That is, we can try to specify what have been called the\n‘existence conditions for rights’ (Sumner 1987,\n10–11). Third, we can ask what the different kinds of rights\nare. Finally, we can ask what the moral significance of having a right\nis, or what weight rights have. With regard to any acknowledged right\nwe can identify it by means of its content (what is it a right to?)\nand its scope (who has it and against whom do they have it?), as well\nas its weight relative to other rights and to other moral\nconsiderations. Not all of these questions are relevant when we want\nto focus on the particular issue of whether or not children have\nrights, and, if so, which ones. However, the first question raised\nabove is especially salient. In response, there are two competing\ntheories whose respective virtues and vices have been extensively\ndebated. In one camp is the will or choice theory (Hart 1973; Sumner\n1987; Steiner 1994); in the opposing camp is the welfare or interest\ntheory (MacCormick 1982; Raz 1984; Kramer 1998). The first theory sees\na right as the protected exercise of choice. In particular to have a\nright is to have the power to enforce or waive the duty of which the\nright is the correlative. The second theory sees a right as the\nprotection of an interest of sufficient importance to impose on others\ncertain duties whose discharge allows the right-holder to enjoy the\ninterest in question. It is natural to think that each theory is more\nappropriate for certain kinds of rights. The will theory fits rights\nactively to do things (to speak, to associate with others) whereas the\ninterest theory fits rights passively to enjoy or not to suffer things\n(to receive health care, not to be tortured). However, the distinction\nbetween the theories of what it is to have a right is not, and does\nnot coincide with the distinction between different kinds of rights,\neven if there are important relations between the two\ndistinctions.", "\nIn this present context one alleged defect of the will theory is its\nexclusion of some humans from the category of right-holders. This is\nbecause whilst all humans, and perhaps many classes of non-humans such\nas animals, have interests that ought to be protected, not all humans\nhave the capacity to exercise choice. Children—along with the\nseverely mentally disabled and the comatose—cannot thus, on the\nwill theory, be the holders of rights. For at least one prominent\ndefender of the interest theory, the fact that children evidently do\nhave rights is sufficient to display the falsity of the will theory,\nthus making children a ‘test-case’ for the latter\n(MacCormick 1982). Of course, someone who is convinced of the\ncorrectness of the will theory might readily concede that the theory\nentails the denial of rights to children but see no reason to abandon\nthe theory. For her, the entailment is not, ‘Children have\nrights. Therefore, the will theory is false’. It is, ‘The\nwill theory is true. Therefore, children cannot have\nrights’.", "\nThe following seven\nstatements set out the arguments for the conclusions of the two\ncompeting theories of rights. 1 – 4 sets out the argument for\nthe negative conclusion of the will theory, and 5 – 7 set out the\nargument for the positive conclusion of the interest theory:", "\n(6) states an important view held by many that for each and every\nright there is a correlative duty. To say that I have a right to\nsomething is to say that someone else has a duty to me in respect of\nthat thing. There may of course be some kinds of duties which do not\ncorrelate with any rights. Indeed, some critics of children’s\nrights will concede that adults have duties to protect important\ninterests of children but deny that these interests correlate with\nrights held by children. (7) is thus true only insofar as the duties\nadults have in respect of children are such that they do correlate\nwith rights held by children.", "\n(3) is obviously a contestable, and contested, claim. But insofar as\nchildren cannot exercise choice and are required to do so on the will\ntheory if they are to have rights, then it follows that they cannot\nhave rights.", "\nThe upshot of setting the two theories out in this fashion is as\nfollows: either children have rights, in which case the will theory\ncannot be true; or they do not, in which case that theory could be\ntrue.", "\nHowever, a will theorist who did not want to deny that children have\nrights might resist affirming (2). This could be done by accepting\nthat children are themselves incapable of exercising choice but\nallowing that children might have representatives or proxies, such as\nmost obviously their parents or guardians, who could exercise the\nchoices on behalf of the children. The representatives would choose\nfor the children as the children would choose if they were capable of\nchoosing for themselves. This proxy exercise of choice would take\nplace only during the period when the children were incapable of\nexercising choice and in acknowledgment of the fact that the children\nwill eventually be capable of exercising their own choices. The will\ntheory’s most prominent defender (Hart 1973, 184 n.86) makes\njust such a modification of the will theory in respect of\nchildren.", "\nNow such a modification must meet a number of challenges. First, how\nshould the representatives be selected? Should those empowered to act\nas representatives be those who are most likely to choose as the\nchildren would choose if capable, or are there are other independent\ngrounds on which they are selected—such as, most obviously, that\nthey are the child’s parents? Second, if we think of such\nrepresentation as a trust whose beneficiaries are children and whose\ntrustees are the adults choosing for children, are the terms of the\ntrust sufficiently clear and determinate? Is it, for instance,\nperspicuous and evident what a child would choose if capable of\nchoosing? Note that the criterion is not what is in the best interests\nof the child for, consistent with the will theory, we must appeal to\nchoices rather than interests. It is sometimes difficult to say what\nsome adult who cannot currently choose—because she is, for\ninstance, temporarily comatose—would choose if able. It is\nimpossibly hard in the case of someone, a child, who is for the period\nof childhood simply incapable of making any choices. Third, how is the\ntrust to be enforced and by whom? The representative may be presumed\nto have a duty to choose as the child would choose if able. If rights\nare correlative with duties then someone other than the representative\nand the child must be in a position to enforce or waive this duty.\nCould this be the state or its representative?", "\nIf the will theory can meet these formidable challenges, it can accord\nrights to children who are not then a straightforward\n‘test-case’ for determining which theory of rights is\ncorrect. Moreover, the will theorist can make two further points.\nFirst, she might accept (6)—that rights and duties are\ncorrelative—but deny or at least significantly modify\n(5)—that adults have duties to protect the important interests\nof children. She could say that the duties that are rightly specified\nunder (5) are not the duties that correlate with rights. This is just\nto say, as all rights theorists will repeatedly say, that rights do\nnot exhaust the moral domain. What we are obligated to do because\nothers have rights against us is not everything we must morally do.\n(6) asserts that for each and every right there is a correlate duty.\nIt is not the eminently disputable claim that for each and every duty\nthere is a correlate right. So, we should, as adults, ensure that the\ninterests of children are protected and promoted. It would not follow\nthat in consequence they have rights against us.", "\nSecond a will theorist might accept (5) and (6) as they stand but say\nthat the rights which correlate with these duties are possessed not by\nthe children but by adults who are in the best position to protect the\nchildren. Thus, even if the duties adults have in respect of children\ndo correlate with rights it does not follow that the rights in\nquestion are held by those whose interests they protect. Indeed, it\nmight be argued that it does not matter whether the rights are\npossessed by those whose interests they protect. Hillel Steiner thus\nasks rhetorically, Does it really matter whether the rights that\ncorrelate with adult duties to children are held by the children or by\nthose who would act as best they could for the children? (Steiner\n1998, 261).", "\nThis review of the will and interest theories has simply examined the\nissue of whether the denial of children’s rights can be thought\nof as a test case for the probity of the will theory. There may of\ncourse be other considerations that tell against the will theory and\nin favour of the interest theory; or the converse." ], "section_title": "1. Children and Rights", "subsections": [] }, { "main_content": [ "\nGrant that on either account of what it is to have a right children\ncould, in principle, be the holders of rights. Ought children to have\nrights? And, if so, what rights should they have? Note that the rights\ncan be moral or legal. Children do have rights in law (under the UN\nConvention most notably). These need not be accepted as moral rights.\nHowever, someone could believe that the best way, on balance, to\nprotect the interests of children is by continuing to accord them the\nlegal rights they have under something like the Convention. Someone\nmight also believe that children should have legal rights but not\nthose they are currently accorded. Conversely, if children do have\nmoral rights, these need not be enshrined in law, although there would\nevidently be a strong presumption that they should. In the first\ninstance, the question is whether children should have moral rights.\nIf they should, then there would be a good case for thinking that\nthese should be legally protected rights.", "\nThose who claim that children should have all the rights that adults\npresently have are called ‘liberationists’ (to be\ndiscussed in the next section) and include Holt, Farson and Cohen\n(Farson 1974; Holt 1975; Cohen 1980). We can distinguish real from\nrhetorical liberationists. The latter are those who see the demand for\nequal rights for children as a means both of drawing attention to the\ndiscrimination that children suffer by comparison with adults in their\ntreatment and for improving their condition. A rhetorical\nliberationist does not actually believe that children should be the\nequals of adults. Rather, he thinks that claiming as much is the best\nway of advancing their interests. A real liberationist does view\nchildren as the equals of adults. Then there are those who think that\nchildren should have some but not all of the rights which adults have.\nFinally, there are those who think that children should not have any\nrights. Or, put less brusquely, they are sceptical, for theoretical\nand political reasons, about attributing rights to children. Their\ncase is made in three ways. The first is to assert what liberationists\ndeny, namely that children are not qualified, as adults are, to have\nrights. The second is to argue that the ascription of rights to\nchildren is inappropriate because it displays a misunderstanding of\nwhat childhood is, what children are like, or what relationships\nchildren stand in to adults. The third is to argue that,\nnotwithstanding their lack of rights, children can be assured of\nadequate moral protection by other means.", "\nWith respect to the first claim, the question of qualification is the question of whether children have the requisite capacity for\nrights. On the will theory of rights the relevant capacity qualifying\nchildren for possession of rights is that of the ability to choose.\nBut there is a more general issue of capacity that is in dispute\nwhatever theory of rights is defended and that follows from attention\nto the fact that rights have a content. Each right is a right to do,\nto be, or to have something. Arguably, only those rights can be\npossessed whose content can be appropriately attributed to their\nowners. A right to free speech cannot properly be possessed by an\nentity incapable of speech. One conventional way to think of rights in\nterms of their content is to distinguish between freedom rights\n(rights to choose, such as to vote, practise a religion, and to\nassociate) and welfare rights (rights that protect important interests\nsuch as health).", "\nChildren in general lack certain cognitive abilities—to acquire\nand to process information in an ordered fashion, to form consistent\nand stable beliefs, to appreciate the significance of options and\ntheir consequences. They also lack certain volitional\nabilities—to form, retain and act in the light of consistent\ndesires, and to make independent choices. Children are not unique amongst\nhumans in this respect. Those adults who are seriously mentally\nimpaired are also disqualified in this sense, which is of course just\nto say that these adults are childlike. Children are unique in the\nfollowing regard. Not all humans are seriously mentally impaired, but\nall humans were once children. Thus every one of us was, during our\nearly years, not qualified to be a holder of rights even if now we are\nso qualified.", "\nIt is worth distinguishing – as Schapiro (1999, 2003) does\n– between two ways in which a child is, relative to an adult,\nincapable. Schapiro argues that childhood is a ‘normative\npredicament’ wherein the child is in a state of nature, lacking\nany independent will whereby she might authoritatively and in her own\nvoice order her desires. She is an ‘instinctual wanton’.\nOn her account, the capacities a child lacks are not those of making\ngood choices, but those of making any choices as such.", "\nA child’s incapacity, in the senses indicated above, would seem\nto disqualify them from having liberty rights. Someone incapable of\nchoosing cannot have a right whose content is a fundamental choice.\nIf, as some maintain, all human rights are best interpreted as\nprotecting human agency and its preconditions, then it would follow\nthat those incapable of agency, such as young children, should not be\naccorded human rights (Griffin 2002). On the other hand, it could be\nmaintained that, whilst children lack agency, they certainly have\nfundamental interests meriting protection and thus at least have\nwelfare rights (Brighouse 2002). Moreover, it can be important to\nrecognise that children become beings capable of making choices and\nthat rights may be attributed in recognition of this gradual\ndevelopment (Brennan 2002).", "\nThe second claim that may be made in denying rights to children is\nthat the ascription of rights to children is inappropriate because it\ndisplays a misunderstanding of what childhood is, of what children are\nlike, or of what relationships children do or ought to stand in to\nadults. This claim comes in various forms.", "\nOn one view we should start our thinking about what morally we owe\nto children by specifying our obligations as adults to them\n(O’Neill 1988). There certainly exist what are called perfect\nobligations. These are obligations that are either owed to all\nchildren or to some specified set of children. They are perfect in\nthat it is completely specified whom they are owed to and what is owed\nto them. We all are obliged not to maltreat any child, and parents\nhave a particular duty to care for their children. But then there are\nimperfect obligations which are those of caring for children to whom\nwe do not, as parents for instance, have specific obligations. All\nadults owe these, but they are not owed to all children (how could\nthey possibly be?) nor is it specified what precisely is owed to\nthem. The obligations are imperfect because which children we should\ncare for is not specified nor is it specified precisely what is owed\nto them. Both are left to individual discretion, depending in part on\ncircumstances. ", "\nPerhaps then we can agree that we are all under a duty to prevent the\nabuse of children. But clearly we cannot, as individuals, each act to\nstop every child being abused. Moreover what we ought to do—for\ninstance, by reporting suspected cases of abuse—will depend on\nthe circumstances, and also on what is in place by way of particular\ninstitutions and laws to deal with child abuse.", "\nCrucially whilst perfect obligations correlate with rights, imperfect\nobligations do not. This means that anyone who starts and finishes\nthinking about what morally is owed to children in terms of their\nrights is unable to capture what imperfect obligations express. Yet\nthis is to miss much of what is most important about the way in which,\nmorally, we should as adults stand in relation to children. For the\nfulfilment of these imperfect duties of care and concern is what\ncentrally protects and promotes the lives of children as children.\nThinking ethically about children’s lives in terms of their\nputative rights is to misperceive what is of central importance and\nvalue in these lives.", "\nOne possible response to O’Neill’s argument is as follows\n(Coady 1992). She does not deny that perfect obligations correlate\nwith rights. Thus, to the extent that we do have perfect obligations\nto children, they do have corresponding rights. Yet O’Neill\ndenies that imperfect obligations correlate with rights. But why\nshould we think that? The imperfect obligations are fundamental ones.\nThey are not supererogatory, that is beyond duty. Adults must show\nconsideration and kindness to children in general. So why cannot\nchildren claim such kindness and consideration from adults as their\nright? O’Neill does say that when imperfect obligations are\ninstitutionalised—when, for instance there are laws and\ninstitutions specifying who should act and how to detect and prevent\nchild abuse—there are created positive special obligations to\nwhich correspond positive rights. But she adds that the obligations\nof, say, the social worker exceed the positive obligations associated\nwith her job. However this is true of all our obligations, whether\nperfect or imperfect. A parent can have positive, that is legally\nrecognised and sanctioned, duties to her child. Yet her perfect\nobligations to her children are not exhaustively specified by what the\nlaw requires of her.", "\nO’Neill’s argument does not rely on any specification of\nthe content of the obligations that might be owed by adults to\nchildren. Rather it is about the structure of our moral reasoning in\nrespect of children, and the priority—false in the\nargument’s view—that is given to rights. As an argument it\nthus bears some comparison with a view that expresses general\nscepticism about rights in the context of adult-child relations and\nwhich emphasises the particular character of the family (Schrag 1980;\nSchoeman 1980). This view draws attention to the quality and nature of\nthe relationships within a family. These are marked by an especial\nintimacy and by deep, unconditional love between its members. One can\ngrant that many families do not conform to this ideal and yet\nacknowledge that when the family does conform to the ideal it is a\ndistinctive, and distinctively valuable, form of human\nassociation.", "\nWhat arguably follows from this ideal of the family is the\ninappropriateness of asserting or claiming rights. For to do so would\nbe to subvert and ultimately destroy what constitutes the family as\nthe distinctive form of human association it is. Appeal is being made\nhere to a familiar and oft-drawn distinction between two ways in which\nindividuals engaged in a common enterprise or bound together in some\nenduring association can be assured of their beneficent, or at least\nminimally good, treatment of one another. One way is by the\nrecognition—in law or custom or shared morality—of rights\nthat all individuals can claim, or by rules of justice—similarly\nand generally recognised—which provide an assurance of fair\ntreatment. Another way is by reliance on the dispositions or attitudes\nthat the individuals bound together have—spontaneously and\nnaturally—towards one another. Thus, for instance, if each is\nmotivated by general benevolence in respect of all then no one has any\nneed to claim or assert what is due to him as of right or rule. In the\ncase of the family, it is argued, neither justice nor benevolence\nsuffices but love does. Of course children may have rights against\nthose who are not family members (a right, for instance, that their\nschool teachers provide them with information and skills). Some rights\nare held against particular individuals. Others, including the most\nimportant ones, are held against everyone, including parents and other\nfamily members", "\nA further and quite distinct allegation is that not only is there no\nneed for any such claims, but that allowing them to be made will\nerode, and in due course destroy, the dispositions and attitudes that\nrendered the need for rights and rules of justices unnecessary in the\nfirst place. This further claim is an influential one in the general\ncritique communitarianism makes, within political philosophy, of what\nis characterised as a rights-based and individualistic liberalism\n(see, for instance, Sandel 1982, 32–5). In the context of the\nfamily the claim is that granting its members rights will subvert and\nbring about the end of the love between them that made rights\nsuperfluous in the first place.", "\nThe arguments considered thus far have appealed to the role that\nrights generally do and should play in our moral lives. A further\nargument considers what would actually follow from granting rights to\nchildren (Purdy 1992). The argument is that we need as adults to have\nacquired certain traits of character if we are to be able to pursue\nour goals and lead a valuable life. To acquire these traits it is\nessential that we not be allowed as children to make our own choices.\nGranting children the liberty to exercise rights is destructive of the\npreconditions for the possibility of having fulfilling adult lives.\nThe central, and empirical, premise in this argument is that children\ndo not spontaneously and naturally grow into adults. They need to be\nnurtured, supported, and, more particularly, subjected to control and\ndiscipline. Without that context giving children the rights that\nadults have is bad for the children. It is also bad for the adults\nthey will turn into and for the society we share as adults and\nchildren.", "\nThe defence of the view that children should not, as the liberationist\nasserts, have all the rights that adults have has rested on the claims\nthat, first, children lack the capacities that qualify adults for the\npossession of rights, and, second, that talk of children’s\nrights does not capture the truth about their lives or about the\nfamily or encourages a destructive permissiveness that has poor\nconsequences for adults and their society. The third step in defence\nof the denial of rights to children is to provide reassurance that\nsuch a denial is not bad for children.", "\nOne can thus maintain that rights do not exhaust the moral domain.\nThere are things we ought to do which do not correspond to the\nobligations we have as the correlates of rights. As adults we should\nprotect and promote the welfare of children. It need not follow that\nthey have rights against us.", "\nTo those who insist that children should, like other historically disadvantaged and discriminated groups, be emancipated by according them rights the reply\n(O’Neill 1988, 459– 463) is that such talk about rights\ntalk misses what is distinctively different about children as a group.\nThis is that childhood is not a permanently maintained status\nassociated with oppression or discrimination. It is rather a stage of\nhuman development which all go through. Moreover the adults who deny\nthat children do have rights may nevertheless also believe that it is\ntheir duty to ensure that the children for whom they have care do pass\nfrom childhood into adulthood." ], "section_title": "2. Critics of Children’s Rights", "subsections": [] }, { "main_content": [ "\nThe first claim in the defence of the denial of rights to children is\nthat children are disqualified by virtue of their incapacity to have\nrights. Liberationists dispute this. Liberationists can allow that the\nkey to the appropriateness of giving or not giving rights to children\nturns on capacity (Cohen 1980, ix). They will argue, however, that\nchildren are not disqualified from having rights by virtue of their\nlack of a capacity that adults do have. Note that on this view\nchildren are entitled to both welfare and freedom rights whereas those\nwho concede that children lack the latter in virtue of a certain\nincapacity can still insist that they ought to have welfare rights\nwhere such an incapacity is not relevant. There are two respects in\nwhich this liberationist case might be modified or qualified. The\nfirst is in its scope. The liberationist might claim that all children\nare qualified to have rights, or she might claim only that some\nchildren are so qualified. The latter is the more plausible position\nin view of the fact that the very young infant is evidently\nincapacitated. Indeed some liberationists seem to recognise as much\neven whilst they insist that every child should have rights (Farson\n1974, 31, 172, and 185). If the scope of the liberationist claim is\nthus limited it does not amount to the view that no line dividing\nhuman rights holders from humans who lack rights should be drawn.\nRather it is the view that such a line has been drawn in the wrong\nplace.", "\nA second possible qualification of the liberationist view is that\ngiving rights to children will play an important part in their\nacquiring the qualifying capacity. It is not thus argued that children\nare capable now and are illegitimately denied their rights. It is\nrather that they will only—or at least will more readily or will\nat an earlier stage—acquire that capacity if given their rights.\nThe denial of rights to children is, on this account, one significant\nelement in a culture that serves artificially to maintain children in\ntheir childlike state of dependence, vulnerability, and immaturity.\nAgain the qualification can concede that children of a very young age\nare not capable enough to have rights, and will not acquire that\ncapacity even if given rights. Yet it insists that the denial of\nrights to children of a certain age on account of their alleged\nincapacity is simply self-confirming. They cannot have rights because\nthey are incapable but they are incapable only because they do not\nhave these rights.", "\nOne plausible version of the claim refers to the facts of experience.\nChildren, or at least children of a certain age, may not differ\nmarkedly from adults in respect of their cognitive and volitional\ncapacities. They may be as capable as older humans of making their own\nminds up about what to do and be as independent in their resolution to\nact on their choices. But they may simply not have had as much\nexperience of the world as their adult counterparts. Being thus\nnaïve and inexperienced in the ways of the world they will not be\nas able, that is as qualified, as older (and wiser) humans are to make\nsensible choices. Grant that such a lack of experience can be\nattributed to a lack of opportunities to exercise choice. If such a\nlack of opportunity is in turn attributable not simply to not having\nbeen around for as long but to a denial of the freedom to make their\nown choices, then there is a powerful case for liberty rights being\nextended, even if cautiously, to these young people.", "\nThere are different ways in which the liberationist claim about\ncapacity—whether qualified or not—can be made. One is by\ndefending a ‘thin’ definition of capacity. For example it\nmay be said that children can make choices if what this means is\nexpressing preferences. Of course the response is that the ability to\nchoose, thus minimally defined, is indeed possessed by children (even\nfairly young children), but it is not a capacity sufficient to qualify\nfor rights ownership. What is needed for that is more than simply the\nability to express or communicate a desire; what is needed is an\nability to understand and appreciate the significance of the options\nfacing one together with independence of choice. After all, the animal\nwho moves from one feeding bowl to another may be said thereby to\n‘choose’ the food in the latter bowl. But the animal does\nnot have a general capacity of choice sufficient to qualify it as a\nholder of liberty rights." ], "section_title": "3. Liberationism", "subsections": [] }, { "main_content": [ "\nLiberationists might move in the other direction and argue that the\ncapacity which purportedly qualifies adults to have rights is in fact\nnot a capacity that most, or perhaps any, adults possess. Thus, it\nwill be said that no adult fully understands the nature of the choices\nshe faces, nor is she consistent in her beliefs and desires, nor is\nshe really independent of the influences of her environment and peers.\nWhether the liberationist urges a ‘thin’ definition of\ncapacity—which the child satisfies as much as the adult—or\nargues that on a ‘thick’ definition of capacity neither\nadult nor child qualifies as capable, the point is the same. This is\nthat the alleged differences between children and adults in respect of\na qualifying capacity are not sufficient to warrant the ascription of\nrights to the latter and their denial to the former.", "\nOne way, then, to charge that age is an arbitrary means of\ndistinguishing those qualified and those not qualified to have rights\nis that there is, in fact, no real division of capacities (Cohen 1980,\n48). We should note that this claim can be supported by an\n‘argument from marginal cases’, one that has been most\ninfluentially used in the case of animal rights. The argument in that\ncontext is that for whatever capacity is argued to distinguish the\nmoral status of humans from animals there will be marginal cases\n– some humans will fail to possess it (Singer 1975, 265). In the\npresent context, the argument would be that some older children\ndisplay those abilities that supposedly distinguish children in\ngeneral from adults (and some adults do not display those abilities\nthat older children have). Whatever the merits of an argument from\nmarginal cases the importance of being able to show that some children\nclose to but below the age threshold (such as adolescents) do or do\nnot merit the same treatment as other children is clear.", "\nAnother way to make the charge of arbitrariness turns on the idea that\ndividing lines as such—‘any’ lines—are\narbitrary. Thus, either it will be said that this age is the wrong\ndividing point or that using any age is wrong. The first objection\n– ‘wrong age’- may concede that there is a better\nage to be used, just as the second objection – ‘age is\nwrong’ – may concede that there is a way, better than using age,\nto mark the division. The initial and obvious reply to the second\nobjection is that age as such is not the issue but rather the reliable\ncorrelation of age with the acquisition of those capacities that\nqualify a person for the attribution of rights. Some liberationists\nmay thus not dispute that there should be a threshold age—one\nbeyond which adult rights are acquired—but think that the\nconventional or orthodox threshold is fixed too late. Liberationists\nmay also simply deny that there should be any threshold on the grounds\nthat there just is no difference between children and adults in\nrespect of their respective capacities for any threshold age to mark.\nThis version of the arbitrariness claim concedes that if age functions\nas a threshold it does so only inasmuch as it reliably correlates with\nthe acquisition of capacities which are necessary qualifications for\nthe possession of rights. In sum, the arbitrariness claim amounts\neither to the denial that the acquisition of the specified capacities\ndoes correlate with the threshold in question or to the denial that\nthere is any age at which the capacities are acquired.", "\nSetting aside this version of the arbitrariness claim, what remains of\nthe charge that ‘[a]ny line which uses age to distinguish people\nwith rights from people without can be shown to be arbitrary’?\nThere are two ideas. The first is that although the threshold of age\ndoes serve to mark a difference within the class of human beings it is\nbeing human which is important. Or, relatedly, what is being\ndistributed, namely rights, is so important that all humans should\nhave them. It is being human which should make the difference not\nbeing of a certain age. Rights are too important to be denied to some\nhumans on account of their (lesser) age and given to others on account\nof their (greater) age.", "\nThe reply is simple. Being human does matter and it is precisely\nbecause they are human beings, albeit young ones, that children are\nentitled to be treated in ways that non-humans may not. However, it is\nrights that are being distributed and to that end a threshold age does\nmark a significant point. Although having rights is better than not\nhaving them, those who lack rights do not lack any moral status\nwhatever. Children are acknowledged to be humans meriting moral regard\nand yet to be young humans meriting a certain and age specific\nregard.", "\nSome will still insist that a threshold age does not mark a\nsignificant enough difference. A 40-year-old differs greatly from a\n4-year-old. Someone who is 18 years and 1 month does not differ\ngreatly from someone who is 17 years and 11 months. It is\nunderstandable that the 40-year-old should have rights whereas the\n4-year-old should not. But this is not the case for the latter\npairing. This is a version of the marginal cases argument about the\nextent to which real differences between classes are displayed by the\nmembers of each class at the edge of these classes. The reply will be\nthat the criticism concedes a difference between being too young to\nhave rights and being old enough to have them. These differences are\nnot arbitrary. Moreover, a threshold has to be fixed. The fact that\nthere may not be significant—or significant\nenough—differences between the members of the two classes being\ndistinguished at the edges of each class is the price one pays for\nhaving to operate with a threshold.", "\nBut is this price one that must be paid? The complaint is that age\ndoes not always reliably correlate with competence. Thus, using age\nmay risk unfairly penalising some who are in fact competent just as it\nmay risk unfairly rewarding some who are in fact incompetent.\nMoreover, the penalties and rewards in question—lacking or\npossessing rights—are far too important to run such risks. Why\nthen should one not take each individual on her own and determine\nwhether or not she is qualified to have rights?", "\nThe problems with the suggested use of a test are various. First,\nthere is the sheer administrative scale of its employment in such a\ncase as human rights. Second, there is the problem of agreeing on a\ndeterminate procedure for testing. How exactly are we to examine\nsomeone in respect of their competence to possess rights? Third, there\nis the problem of fairness. Any test must not unfairly disqualify some\ngroup of putative rights-holders by, for instance, having a bias in\nthe testing procedure which, in effect, discriminates against that\ngroup. Fourth, the administration of any official test—and\nespecially one whose passing yields such important goods—is\nsubject to the risks of corruption or of misuse for the\nself-interested ends of those administering it. Again, this cannot be\ntrue of the use of age as a threshold. To summarise, these problems\nattaching to the use of a test are large and insuperable.", "\nThe counter-response to consider is that the burdens of any such test\nshould be borne by the state inasmuch as there is a considerable risk\nof egregious wrong – the denial of rights – that is run by\ncontinuing only to use an age-based proxy for the existence of the\nrelevant capacity (Godwin 2011, 286).", "\nThe charges of arbitrariness can be argued to be false or overstated.\nChildren do differ from adults in respect of their competence to\npossess rights. A threshold of age may be the appropriate way to\nregister that difference. One should, thus, acquire rights only on\nreaching a certain age. However, two riders to this summary are\nappropriate.", "\nFirst, different rights may be acquired at different ages. After all,\nit is plausible to think that the capacities needed for, and\nqualifying a person to possess, different rights are themselves\ndifferent. More particularly, different rights would seem to require\ndifferent degrees of competence. Liberty rights entitle their\npossessors to make choices, and the matters in respect of which\nchoices are made differ in their complexity, importance, and\nconsequential impact. Those who are allowed to choose require greater\nor lesser amounts of maturity, independence, and deliberative\nproficiency in order to be able to make these different kinds of\nchoice. The decisions to marry, consume alcohol, serve in the armed\nforces, undertake paid labour, vote, buy goods in a shop, travel\nunaccompanied, and open a bank account seem to presuppose different\nlevels of understanding and autonomy. Assuming that these levels are\nprogressively acquired at different ages, it makes sense to accord the\ncorresponding rights not all at once but in stages.", "\nSecond, there should be an ordered but consistent acquisition of\nrights. If children are assumed to display the competence required for\none kind of right, they should not be refused another kind of right\nwhich presupposes the same or even a lesser degree of ability. It\nwould not make sense, for instance, to deny a young person the right\nto refuse medical treatment but allow them to choose to die in the\narmed services of their state.", "\nThe liberationist may make one last move. They may concede that\nchildren do lack the capacities that are a prerequisite for the\npossession of rights. However, they can suggest that children should\nbe permitted ‘to borrow the capacities of others to secure\nwhatever it is we are entitled to’ (Cohen 1980, 56). Child\nagents would advise their clients with a view to ensuring that the\nchild’s right is properly exercised. However, to the various\nproblems with the use of proxies or representatives, which have\nalready been rehearsed in Section 1, we may add this question, Is the\nchild still free to act or not on the advice given? If the child is\nnot so free, then the role of the adviser is a strictly paternalist\none, supplanting the child’s choice as to what is best for\nherself with her own choice. If on the other hand the child is free to\nreject the adviser’s advice, then the child is free to do what\nshe wants anyway and the role of adviser is otiose and beside the\npoint. One only needs to ‘borrow’ what one does not have.\nNot using what could be borrowed leaves one with the lack—and\nits consequences—that made the borrowing necessary. On the other\nhand, if a child can distinguish good from bad advice, then the\nborrowing is unnecessary. The child can give as good advice to herself\nas would be given to her by an adviser. But then no adviser is needed\nand this is precisely what Cohen denies." ], "section_title": "4. Arbitrariness", "subsections": [] }, { "main_content": [ "\nThose who deny that children do have rights can, as O’Neill\nargues, believe that the interests of children are nevertheless\nadequately protected through adults’ discharging relevant\nobligations. Yet, for some, the value of rights is not adequately\ncaptured in this manner. Joel Feinberg, for instance, believes that\nthe value of a right lies in those who possess it being able to claim\nfrom others what is specified as its content (Feinberg 1970).", "\nIf having rights does have a distinctive and special value in this\nkind of way, then it matters greatly that children can have at least\nsome rights. What might these be? As indicated at the outset, children\nare humans. They have at least the right to life that all humans have.\nNevertheless, children are not thought to have all the rights that\nadult humans do. Central amongst these rights is that of\nself-determination, that is, the right to make choices in respect of\none’s own life. This right is the basis of derivative rights to\nmarry, have sex, choose one’s work, purse a course of education,\nand so on.", "\nMost who believe that adults have rights which children do not have\nmake the cut between liberty and welfare rights. Feinberg\ndistinguishes between rights that belong only to adults (A-rights),\nrights that are common to both adults and children (A-C-rights), and\nrights that children alone possess (C-rights) (Feinberg 1980). Thus, a\ncommon position is that the A-rights include, centrally, the liberty\nrights, and that the A-C-rights include, centrally, the welfare\nrights. To repeat, liberty rights are rights of choice (how and\nwhether to vote, what to say publicly, whether to practise a religion\nand which one, which if any association to join, and so on), whereas\nwelfare rights protect important interests (such as health, bodily\nintegrity, and privacy).", "\nWhat might be included in the C-rights? Feinberg distinguishes between\ntwo sub-classes of C-rights. There are, first, those rights which\nchildren possess in virtue of their condition of childishness.\nAlthough Feinberg does not further divide this first sub-class of\nC-rights, this can be done. There are the rights children have to\nreceive those goods they are incapable of securing for themselves and\nare incapable of so doing because of their dependence upon adults.\nThese goods might include food and shelter. There are, second, the\nrights to be protected against harms which befall children because of\ntheir childlike vulnerability and whose harmfulness is a function of a\nfact that they befall children. These harms might include abuse and\nneglect. Note that some adults might be argued to merit the same\ndegree of rights-based protection on account of their childlike\nvulnerability and dependence.", "\nFinally, there are goods that children should arguably receive just\nbecause they are children. Those who have written on children’s\ngoods do so for two reasons: first, to answer the question of what, as\na matter of justice, is owed to children; and, second, to answer the\nquestion of whether, and why if so, childhood is itself intrinsically\nvaluable (Gheaus 2015; Macleod 2010). Note that goods may be valuable\nto both children and adults, but of especial value to the former; or\nonly of value to children. Candidate goods include play and\ninnocence.", "\nHowever, the most central, and contentious, example is a child’s\nright to be loved. This is not an A-C-right but it is arguably a\nC-right, and indeed is cited by many as a C-right (MacCormick 1976,\n305). Various declarations of children’s rights include such a\nright and a respectable case can be made to meet the various\nobjections normally raised against its attribution (Liao 2015).", "\nIt is standard to classify the rights listed in the UNCRC under the\nthree P’s: those of protection (for example, against abuse), of\nprovision (for example, of education), and of participation (for\nexample, to speak and to associate freely). Protection rights will be\naccorded to children but not to adults inasmuch the condition or state\nof childhood calls forth and requires this protection. Children, along\nwith adults, have provision rights but the content of these will\ndiffer between them because of the form that children’s needs\nand circumstances take. Thus, grant that both children and adults have\na welfare right to health care. In the case of children, but not that\nof adults’, paediatric care and treatment is appropriate. But\nthat fact is no different in its significance from the fact that\namongst different adults the proper form of health care should vary in\nline with their various disabilities, diseases, and circumstances." ], "section_title": "5. Children’s Rights and Adult Rights", "subsections": [] }, { "main_content": [ "\nThe second sub-class of C-rights are those which Feinberg\ncharacterises as ‘rights-in-trust’ and which he thinks can\nbe subsumed under the single title of a ‘right to an open\nfuture’. These are the rights given to the child in the person\nof the adult she will become. They are the rights whose protection\nensures that, as an adult, she will be in a position to exercise her\nA- and A-C-rights to the maximal or at least to a very significant\ndegree. They keep her future open. Such rights impose limits on the\nrights of parents and also impose duties on the part of the state to\nprotect these rights.", "\nA couple of things are worth noting about these rights-in-trust.\nFirst, Feinberg refers to these C-rights as ‘anticipatory\nautonomy rights’, which might suggest that they are only\nA-rights-in-trust. But he also speaks of rights-in-trust of class C as\nprotecting those future interests a child will have as an adult. This\nimplies that they are also anticipatory welfare rights (Feinberg 1980,\n126–7). Hence this sub-class of C-rights ensures that the adult\ncan later exercise both her A-rights (liberty) and her A-C-rights\n(welfare).", "\nSecond, there is the question of how open a child’s future\nshould be. Some interpret the demand for an education for an\n‘open future’ as requiring individuals to acquire\n‘to the greatest possible extent’ the capacity to choose\nbetween ‘the widest possible variety of ways of life’\n(Arneson and Shapiro 1996, 388). Arneson and Shapiro have pointed out several\nobjections to such a ‘maximising’ interpretation. It may\nnot be possible to quantify in a determinate fashion the number of\noptions open to a future adult. Furthermore, some fulfilling life\nchoices are only available at the expense of denying the child a\nnumber of otherwise possible choices. For instance, a child\nintensively trained to realise his considerable innate musical\nabilities may be unable to pursue careers that would have been open to\nhim in the absence of such a dedicated education. The following\nfurther criticisms can be added. Requiring that a child be brought up\nto be able eventually to choose between as many options as possible\nmay impose unreasonable burdens on parents. It also seems implausible\nto think that a child suffers if she is denied one or even several\npossible insignificant further options beyond some threshold number of\nchoices. Is it really harmful to a child that she does not learn to\nplay all of the orchestral instruments and is thereby denied the\nopportunity to pursue a solo career in those she does not? Finally,\nsome future options are surely morally base or in some other respect\nwithout value (Mills 2003).", "\nFeinberg does sometimes talk only of the harms of closing off\nsignificant life choices. Yet he does also on occasion employ the\nlanguage of maximisation. ‘[Education] should send [the child]\nout into the adult world with as many open opportunities as possible,\nthus maximising his chances for self-fulfilment’. (1980, 135;\nsee also 151). However, it seems much more plausible to suggest that a\nchild should have enough autonomy to be able to make reasonable life\nchoices. The preconditions of autonomy are both internal (a capacity\nto think for oneself, to acquire and appreciate relevant information,\nand a volitional ability to act independently) and external (the\nprovision of a range of feasible and valuable options). In respect of\nboth conditions, it is perfectly possible to have a good sense of what\ncounts as adequate autonomy, even if there is no clear bright line\nmarking the point of sufficiency.", "\nClosely related to Feinberg’s idea of\n‘rights-in-trust’ is Eekelaar’s idea of a\nchild’s ‘developmental’ rights (Eekelaar 1986).\nThese are the rights of a child to develop her potential so that she\nenters adulthood without disadvantage. Whereas Feinberg attributes the\nrights to the child’s adult-self, the child holding them only in\n‘anticipatory’ form, Eekelaar attributes the rights to the\nadult’s child-self. Arguably, this makes no difference, since\nthe child and the adult are one and the same person. Although this is\na metaphysically contentious claim (Parfit 1984), grant that child and\nadult are merely distinct temporal stages of a single individual.\nWhether each temporal stage of the person has the same interest in the\nchild developing into an adult is a further issue which will be\nconsidered shortly.", "\nHowever, child and adult do stand in an asymmetrical relationship to\none another in a way that does not seem to be true of the different\ntemporal stages of the same adult. After all, adult Smith can now\nexercise her liberty rights in such a fashion that at a later time she\nis not able to exercise them and her welfare rights to the same degree\nas she can now. Smith can, for instance, choose now to enter into a\nslavery contract or to engage in a dangerous sport that risks death or\nserious disability. A child, on the other hand, is denied the right to\nmake choices that will fetter the adult exercise of her rights.", "\nThis can be justified by distinct thoughts. First, a child, unlike an\nadult, simply lacks the ability to make considered choices and should\nnot have liberty rights. An adult can make unwise choices but is\npresumed to possess a general minimal capacity to make choices, which\nthe child lacks. Second, what is done or not done in childhood can\naffect or shape the whole of one’s later life and in a way that\nis largely irreversible. By contrast, an adult is in a better position\nto change the course of her life. Third, a child may be thought to\nhave the formal deliberative abilities to make choices (knowing what is\nto be decided) but simply lack the life experiences to appreciate and\nproperly understand those choices.", "\nFourth, in the specific case of an adolescent – who is legally a\nchild but on the edge of and at the beginning of adulthood –\nthey may be judged as autonomous but nevertheless at a ‘life\nstage’ which merits paternalistic denial of choices\n(Franklin-Hall 2013).", "\nNow consider the case of a child who will not develop into an adult,\nsay someone who is suffering from a terminal disease that will prevent\nher living beyond the age of majority. Such a child lacks\ndevelopmental rights. Or rather, she has them, but her circumstances\ndo not allow for their protection. However, she does still have\nwelfare and protection rights whose correlate duties can be\ndischarged. The child has an interest in not suffering harm and in\nenjoying a certain standard of life even if she never lives beyond her\nchildhood.", "\nWhen, for instance, we provide a child with health care or protect her\nfrom abuse we not only thereby serve her immediate interests as a\nchild, but we also ensure that she will grow into a mentally and\nphysically healthy adult. At its simplest, a child’s welfare\nright not to be killed is a precondition of the very possibility of\nthere being a future adult with any rights at all. Even the education\nof a child can be represented as not merely of instrumental worth to\nthe future adult but of value to the child here and now. A child has\nan interest now in learning things and does so independently of what\nthis might later mean for her future adult self. (Coady 1992, 51).", "\nThe child with the terminal illness will not develop into an adult.\nCan we say of anybody that she has an interest, as a child, in\ndeveloping into an adult, an interest that is frustrated by her\nterminal condition? Or is there an interest in only being a child and\nnever becoming an adult? Grant that the child-Q and the adult-Q are\ntwo stages of one and the same individual. Could we speak of a\nconflict between the present interest of child-Q in staying a child\nand the future interest of adult-Q in child-Q developing into her\nlater adult self? The latter interest seems perfectly straightforward.\nHowever, it is at least controversial whether everybody does have an\ninterest in growing up. Earlier cited work on the putative goods of\nchildhood can be used to argue that childhood as such has a value that\nadulthood does not, with the further questions arising of whether the\nformer value exceeds the latter and of whether they can be compared at\nall (Gheaus 2015; Hannan 2018). It has also been argued that it would\nbe better for human beings never to have been born (Benatar 2008).\nEven if this is not a general truth, it may be true of some humans\nthat not growing into adulthood and ceasing to exist is better than\nbecoming an adult. This might be true, for instance, of somebody\nfacing the prospect of a life of unrelieved, extreme pain and misery.\nCould there be an interest—even without such a prospect—in\nbeing forever a child?", "\nSuch an interest cannot be physically satisfied in this world. It\nis satisfied in the fictional world of Peter Pan; but the author of\nthat fantasy, J.M. Barrie, clearly deprecates his eponymous\nhero’s infantile desire to escape the realities of the world\n(Barrie 1995). If we only mean, by the imagined interest, remaining\nchildish it is hard to see how any individual in our world could, if\nrational, have such an interest. It is one thing to be a child forever\nin a child’s world as Peter Pan is. It is quite another to\nremain a child in our adult world. Childhood is something best\nappreciated by the child. It is also something that needs to be left\nbehind. In the words of Paul, ‘When I was a child, I spoke as a\nchild, I understood as a child, I thought as a child: but when I\nbecame a man I put away these childish things’ (I Corinthians\n13:11)." ], "section_title": "6. The Child’s Right to Grow Up", "subsections": [] }, { "main_content": [ "\nIf children are not thought to have the A-rights, and, chiefly, do not\nhave the liberty rights to choose for themselves how to conduct their\nlives, nevertheless they are not morally abandoned to their own\ndevices. In the first place, it is a standard principle of child\nwelfare law and policy that the ‘best interests’ of a\nchild should be promoted. Article 3.1 of the United Nations Convention\non the Rights of the Child states that ‘In all actions\nconcerning children, whether undertaken by public or private social\nwelfare institutions, courts of law, administrative authorities or\nlegislative bodies, the best interests of the child shall be a primary\nconsideration’ (United Nations 1989).", "\nSecond, Article 12.1 of the Convention asserts that, ‘States\nParties shall assure to the child who is capable of forming his or her\nown views the right to express those views freely in all matters\naffecting the child, the views of the child being given due weight in\naccordance with the age and maturity of the child’ (United\nNations 1989).", "\nSection 9 discusses the right to be heard. This section discusses the\nbest interest principle, henceforward the BIP. The discussion is brief\nfor the following reason: Article 3 does not accord to children a\nright to have their best interests protected and promoted. Indeed, it\ndoes not use the word ‘right’. The Article does impose on\nStates parties an obligation to ensure that all relevant organizations\nand legislative bodies make the best interests of children a relevant\nconsideration. However, the BIP sits oddly besides the other\nenumerated rights.", "\nMoreover, the BIP has been subject to numerous criticisms (Kopelman\n1997; Parker 1994) and claims of ambiguity, chief amongst which are\nthe following. First, the weight given to best interests can be\nvariously specified, a choice between ‘primary’ or\n‘paramount’ being a significant one which preoccupied\nthose drafting the Convention. (Alston 1994 12). Second, there is an\nimportant difference between its use in respect of ‘a’\n(that is some particular) child and of ‘children’ (as a\nclass of humans). Third, it is implausible to view the BIP as\nrequiring that one must act ‘so as to promote maximally the\ngood’ of the child (Buchanan and Brock 1989, 10). Construed in\nliterally maximising terms (rather than merely what is good enough),\nthe BIP is unfeasibly demanding of agencies charged with the care of\nchildren. Fourth, the BIP does not, as it stands, take account of the\ninterests of others. We cannot be required to promote the best\ninterests of a child over and above, and without regard to, the\ninterests of any relevant adult.", "\nFifth, the interpretation of ‘best interests’ is unclear:\nit could be specified as what a child would choose for herself under\nspecified hypothetical circumstances; or what is, as a matter of fact,\nbest for the child, an account which is distinct from and independent\nof the child’s desires, actual or hypothetical. If it is the\nlatter then, some argue, we cannot with certainty determine what is\nbest for a child. We cannot in practice make complete and accurate\nassessments of what will be the outcome of each and every policy\noption that we might adopt in respect of a child (Mnookin 1979). The\nBIP is indeterminate even where there are only two possible decisions\nto be made (Elster 1989, 134–139). Such indeterminacy is\ncompounded and complicated by the fact of moral pluralism (Rawls 1993,\nxvi-xvii), whereby individuals subscribe to different conceptions of\nwhat makes life valuable. If we cannot agree how to rank as better or\nworse different kinds of life, we will not be able to agree what is\nbetter or best for the growing child. The fact of extensive\ndisagreement about what is best for children, or for a child, is often\nset in the context of broader cultural disagreements about morality in\ngeneral. It is said that the BIP is subverted, or at least rendered\ndeeply problematic, by the existence of these deep and pervasive\ncultural disagreements (Alston (ed.) 1994).", "\nIf we understand the BIP in terms of a child’s hypothetical\nchoices, the most striking and influential thought is that we should\nchoose what is best for the child as the child would choose for\nherself if the child were adult. For instance, John Rawls thinks the\nfollowing formulation defines the acceptable paternalism of a\nguardian’s treatment of his child: ‘We must choose for\nothers as we have reason to believe they would choose for themselves\nif they were at the age of reason and deciding rationally’\n(Rawls 1999, 183). This apparently simple formulation is in fact\nsusceptible of at least two quite different interpretations, each of\nwhich brings with it its own problems. In each case, we are seeking to\nspecify the adult person who chooses for the child.", "\nWe might, first, mean that we should choose for this child as the\nadult the child will become would choose. However, this does not\ndetermine a unique choice for, crucially, the nature of the adult that\nthe child will become precisely depends on the choices that are made\nfor it whilst a child. We can conceive of each of the different adult\nselves the child might develop into approving, respectively, of the\ndifferent choices made for its childhood self—choices which were\nresponsible for the development of these different selves. Or, second,\nthe adult person who chooses for the child is an adult analogue of the\nchild. This is not the child’s future adult self, which as we\nhave seen is indeterminate, but this child made into an adult version\nof itself. That is, we do not imagine this child developing in the\nfuture into its adult self. Rather we imagine a mature or grown-up\nversion of this child now making choices. This interpretation however\nwill still not work. The adult version of the child is one with\nchildish beliefs and desires filtered out. But, in the first place, it\nis not clear what remains of the child in any choice situation\nrendered hypothetical in this fashion. For the child just is someone\nwho has these childish beliefs and desires. What is it to be a child\nif not to think and want as a child does? Second, it is entirely\nindeterminate what should replace these beliefs and desires.", "\nHowever, in the case of children, by contrast with adults, we cannot\ncash out the various hypothetical conditionals. We do not know what a\nchild would choose if possessed of adult rational powers of choice,\nbecause what makes a child a child just is its lack of such powers\n(its ignorance, inconstant wants, inconsistent beliefs, and limited\npowers of ratiocination). At the same time, we cannot ask how an adult\nwould choose if in the child’s situation just because an adult\nwould not be in that situation, or would not be in a child’s\nsituation. We must, it seems, choose for a child because a child\ncannot choose for itself, and we must choose what is best for a child\nnot what some imagined adult version of the child would choose for\nitself.", "\nTo repeat, the BIP, despite its importance, is not a child’s\nright. Moreover, as well as being beset by these various problems, it\nis also arguably in tension with some of the other rights a child has.\nIn particular, the obligation to do what is best for the child stands\nagainst an obligation to give serious consideration to a child’s\nown view of what is in their interests. This requirement is discussed\nin Section 9." ], "section_title": "7. Best Interests", "subsections": [] }, { "main_content": [ "\nThe putative possession by a child of a right to an ‘open\nfuture’ together with the imperative to promote any\nchild’s best interests raises the question of what, if anything,\nis wrong with the transmission to a child of values. These most\nobviously may be those values by which the child’s parent lives\nand which may also help to define the identity of a community. Article\n2 of the UNCRC accords the child a right to non-discrimination on\nvarious grounds including ‘national, ethnic or social\norigin’; and Article 30 recognises that a child belonging to an\n‘ethnic, religious or linguistic’ minority ‘shall\nnot be denied the right, in community with other members of his or her\ngroup, to enjoy his or her own culture, to profess and practise his or\nher own religion, or to use his or her own language’.", "\nYet, for many liberals, there is a tension between the recognition of\nsuch rights and the requirement that a child not be inducted into a\ncommunity in such a manner that his or her future adult choices are\nconstrained. The main way in which this is set out is by means of an\nemphasis upon a liberal ideal of an autonomous life, one in which an\nindividual is able both to form his or her own conception of the good\nlife to lead and is not prevented – by external social\ncircumstances or the actions of others – from being able to lead\nthe preferred life. Often the target that is juxtaposed to such a\nliberal ideal is the values of religious minorities. The Supreme Court\njudgment that prompted Joel Feinberg’s defence of a\nchild’s right to an ‘open future’, and which has\nbeen extensively discussed, is Wisconsin v. Yoder (1972). This\nexempted the Amish community from the requirement to keep their\nchildren in school to the age others are so required in the interests\nof maintaining that community’s identity. Arneson and Shapiro in\nresponse contrast ‘religious traditionalist’ and\n‘secular worldly’ ways of life, seeing an education for\nthe latter as the best preparation for an open future (Arneson and\nShapiro 1996).", "\nThe problem with this approach is that the preferential treatment\n– in the way that children are schooled – is both\ndiscriminatory and may violate the central precept of liberal\nneutrality, the requirement that the state not, in its law and\npolicies, favour any conception of the good (see the entry on\nPerfectionism in Moral and Political Philosophy). Moreover, some\nliberals will argue that the character traits and dispositions of\nautonomy, for instance steadfastness of character, are best taught by\nbeing raised in adherence to a particular way of life, such as one of\nreligious faith (Callan, 2002; Burtt 1996).", "\nLiberals may escape the charge of violating the principle of\nneutrality by arguing that a liberal society requires that its\ncitizens be motivated by a sense of justice and an ability to\nparticipate effectively within democratic institutions. This\nrequirement is satisfied only if children are brought up in certain\nvalues and are able, when adults, to make maximally autonomous\nchoices. In this manner the promotion of autonomy and an open future\ncan be seen as an indirect consequence of a necessary education in\nthose civic capacities that are the necessary precondition of stable\nand sustainable liberal institutions.", "\nThe tension that is broached by a child’s right to an open\nfuture is given a clear and provocative reading in Matthew\nClayton’s book (Clayton 2006). He argues that parents may not\n‘enrol their children into comprehensive doctrines’, in\nother words, bring them up to believe in general truths about the best\nway to lead a life, whatever the provenance of those truths. Thus, his\nview is broader than a critique of a religious education. But at the\nsame time, it would indict the vast majority of conscientious parents\nseeking to bring up their children as they see best.", "\nHis defence of this view relies on a claimed analogy between the\nexercises of political and of parental power. The former is only\nlegitimate on liberal grounds in the absence of any appeal to the\ncorrectness of some comprehensive doctrine. Clayton thinks that the\nsimilarities between the two exercises of power are sufficiently\nstrong and robust for parental conduct to be constrained by the same\nliberal principle of legitimacy.", "\nIn response it may be argued that the two domains of power are not\nanalogous. It may also be suggested that there is a morally relevant\ndifference between parents setting out to enrol their children in a\ncomprehensive doctrine and children coming to share such a doctrine\nbecause of sharing their life with their parents (Archard 2002).\nIndeed, if the institution of the family as an essentially intimate\nand private community of adults and children can be defended and if,\nfurther, adults have a protected right to lead their lives by the\nlight of their preferred conception of the good, then such unintended\nenrolment is inevitable. Others will argue that it is not possible to\nteach children that sense of justice which liberals see as critical to\nthe sustainability of a fair society without embedding it in a\ncomprehensive doctrine (Franklin-Hall 2019).", "\nIt is of course a further question of whether certain communal\nvalues violate liberal values other than autonomy – such as\nequality. For example, it would be wrong to rear boys and girls in\ngendered stereotypes that perpetuate inequality and\ndiscrimination." ], "section_title": "8. Children and the Reproduction of Values", "subsections": [] }, { "main_content": [ "\nThe right to be heard is a valuable right. What makes it valuable is\nboth that there is a point to making one’s views known and,\nfurther, that making one’s views known makes a difference. It\nmatters to me that I can speak out on political questions. It matters\nalso, and probably more, if what I say leads to the changes I favour.\nCorrelatively, it is true both that I do not want to be silenced and\nthat I do not want the statement of my views to be ineffectual. As a\nfurther general point there will always be some issues on which it is\nmore important that I be allowed to speak and that what I say about\nthese issues carries weight in determining outcomes. Those are the\nissues that matter to me, and the more they matter the more important\nit is that I have the freedom to speak about them and be heard. On one\naccount, since children’s views should not be\n‘authoritative’, that is, determinative of what is done,\nthey have only a ‘consultative’ role (Brighouse 2003).\nThey may influence an outcome by, most obviously, providing those who\ndo make the decisions affecting a child’s interests with a\nclearer picture of what in fact is in those interests. On another\naccount, encouraging and according a weight to the expression of\nchildren’s views—even where this is unlikely to affect\noutcomes in line with the views’ content—is valuable just\nbecause the child is capable of expressing a view and deserves to be\nlistened to (Archard and Skivenes 2009).", "\nHow is it with the child’s right to be heard? It will be\nimportant for the child to be listened to. But it is also important\nthat the child is heard in the sense that her views are given due\nconsideration and may influence what is done. Note that the\nchild’s right to be heard on matters affecting its own interests\nis a substitute for the liberty right to make one’s own choices.\nThe right to be heard is only a right to have the opportunity to\ninfluence the person who will otherwise choose for the child. The\npower to make those choices resides with the adult guardian or\nrepresentative of the child. All the child retains is the right to try\nto motivate that adult to choose as the child herself would choose if\nshe was allowed to.", "\nArticle 12.1 of the United Nations Convention on the Rights of the\nChild not only accords the child the right freely to express its views\non matters affecting the child. It also, and crucially, gives the\nchild an assurance that these views will be given ‘due weight in\naccordance with the age and maturity of the child’. Great\nemphasis is now placed on what are termed a child’s\n‘participation rights’ as opposed to his or her\n‘protection rights’. The latter, as the name suggests,\nprotect the child from violent, abusive, cruel or exploitative\ntreatment. ‘Participation rights by contrast, give children\nsome entitlement to be the agents of their own lives. Article 12.1\nprovides a crucial underpinning justification for such rights. There\nare problems in understanding how practically to implement such rights\n(Ang, et al. 2006). There are also theoretical issues in making precise\nsense of what a right such as that enshrined in Article 12.1 might\nmean. Its complexities lie in understanding the difference between an\nadult’s power of choice and a child’s views on critical\npersonal matters, in the different ways we might consider a\nchild’s views, in how to weight those views and how their\nweighting makes a practical difference in coming to a decision\n(Archard and Uniacke 2020).", "\nThe celebrated British legal judgement in the Gillick case (Gillick\n[1986]) provides a useful contrast to Article 12. This judgement has\nbeen extensively discussed, and it has also been highly influential in\nmatters relating to the consent of children to medical treatment.", "\nThe Gillick judgement arose from the dissatisfaction of a mother with\nthe failure of her local health authority to withdraw an advisory\ncircular to the area’s doctors. This advised doctors that they\ncould counsel and inform young girls under the age of 16 about sexual\nmatters as well as provide them with contraception, and that they\ncould do this without the consent of the child’s parents. The\nmother, Victoria Gillick, went to court to have the circular declared\nunlawful. The final judgement by the British House of Lords was that\nthe circular was not unlawful. A key issue, relevant to the present\ndiscussion, concerned the proper relationship between the\nchild’s right to decide for itself and the parent’s right\nto decide for the child.", "\nIn deciding in favour of the health authority one of the Law Lords,\nLord Scarman, made a statement crucial to his finding and one that has\nsubsequently been much cited. It is worth reproducing:", "\n\nThe underlying principle of the law … is that\nparental right yields to the child’s right to make his own\ndecisions when he reaches a sufficient understanding and intelligence\nto be capable of making up his own mind on the matter requiring\ndecision. (Gilick [1986], 186)\n\n\nI would hold that as a matter of law the parental right to determine\nwhether or not their minor child below the age of 16 will have medical\ntreatment terminates if and when the child achieves a sufficient\nunderstanding and intelligence to enable him to understand fully what\nis proposed. (Gillick [1986], 188–9)\n", "\nVarious questions arise. First, what does it mean for a child to get\nto a particular point in their development? On what could be called\nthe threshold interpretation, once a child has achieved a certain\nlevel of competence, her views as to what shall happen to her have a\ndeterminate weight, either amounting to a liberty right of choice (on\na strong version) or (on a weak version) being counted in the balance\nagainst her parents’ views and the state’s judgement of\nher best interests. On what could be called the proportionality\ninterpretation, the child’s views progressively increase in\nweight as she gains a greater competence to choose for herself. They\nincrease up to the acquisition of a full liberty right of choice.", "\nSecond, on either the threshold or the proportionality account we need\na measure of that ability that marks the threshold or is simply\nprogressively acquired. How much intelligence and understanding, for\ninstance, is sufficient? In the first place, this measure must be\ntaken independently of any judgement of what is in the child’s\nbest interest. That a child would choose what is taken to be in her\nbest interests is at most evidence that she does have sufficient\nintelligence and understanding of the relevant issue. Her making such\na choice is not a necessary condition of her having the requisite\nability. Similarly, the making by a child of a poor choice is not\nconclusive evidence of her general incapacity to choose for herself.\nWise adults can occasionally make stupid decisions just as fools\nsometimes get it right.", "\nIn the Gillick judgement, Scarman required of the child that she\nmanifest an understanding of the ‘nature’ of the\ncontraceptive advice offered and ‘also have a sufficient\nmaturity to understand what is involved’ (Gillick [1986], 189).\nWe can distinguish here a number of possible elements. There is,\nfirst, knowledge of certain facts. One child, for instance, knows that\na contraceptive acts to prevent conception that might otherwise result\nfrom sexual intercourse. Another child, by contrast, could simply be\nignorant of or unable to comprehend the facts of reproduction. There\nis, second, an understanding of what follows for the child from an act\nor its omission. Thus, failure to use a contraceptive could lead a\nyoung person who had sexual intercourse to become pregnant. These two\nunderstandings together constitute knowledge of the\n‘nature’ of the act. Finally, there is what arguably comes\nwith ‘maturity’ which is the ability to appreciate the\nsignificance both of an act or its omission and of the relevant\nconsequences. It is one thing to know what it is to become pregnant,\nand another to understand what that means. This latter understanding\ninvolves realising that pregnancy brings in its wake physical changes,\nthat any resultant birth leaves a young person with a child to care\nfor, and so on. Scarman even insisted that the child would need to\nhave an appreciation of the ‘moral and family’ questions\ninvolved.", "\nThird, it is important in measuring a child’s competence against\nthat in respect of which he or she is expressing a view to distinguish\nbetween the complexity and the seriousness of the matter. A simple\nchoice—for instance that between only two options such as\nwhether to have a life-saving operation—may nevertheless be\nportentous, having enormous and far-reaching consequences. It may thus\nrequire much greater appreciation of what is involved than a more\ncomplex decision, one that ranges over many possibilities. Yet the\nlatter kind of choice—consider choosing a five-course meal from\na very large menu—is far less serious in its consequences. In\nshort, the difficulty or complexity of a choice should not be confused\nwith its importance or significance for the child.", "\nFourth, the English courts at least have detected a fundamental\nasymmetry between refusing and choosing to have treatment. A competent\nadult has a right both to choose to have treatment and to refuse it.\nShould this not also be the case with a competent child? A 15-year-old\nwho wants to have a particular operation against her parents’\nwishes and even contrary to the best judgement of her doctors may be\njudged competent and thus have her wishes respected. However, the\nEnglish courts in a series of judgements after Gillick have argued\nthat matters are somehow different when it is a case of a child\nrefusing an operation.", "\nOf course, there is no inconsistency if a refusal requires a greater\ndegree of understanding and appreciation of the issues than a positive\nacceptance. But where the choice is a simple disjunction, it is hard\nto see how this can be the case. Are not the issues at stake the same\nfor both disjuncts? If the courts believe that an obligation to act in\nthe best interests of the child trumps one to respect the wishes of a\ncompetent child, it needs to be shown why this obligation does not\nhave force in all circumstances. Why would a court not deny treatment\nto a child it does not believe in her best interests when it judges\nher competent to choose? If a child is competent then she is in all\nsignificant and relevant respects the equal of an adult and should be\nable both to choose and to refuse treatment.", "\nThree final comments on the child’s right to choose are in\norder. First, what is deemed to be in the child’s best interests\nis evidence for, but not finally determinative of, a judgement as to\nthe competence of the child. Nevertheless, balancing a child’s\nright to be heard against a child’s right to have its best\ninterests promoted is difficult. Second, it is arguably enough to show\na child’s competence that a child understands the nature of the\nact. After all, no more is needed for an adult’s consent to be\ninformed. In the law of contract adults need only to know what they\nare signing up to. They do not need a full appreciation of the\ncontract’s significance and of its import for their future\nlives. Third, Gillick competence as specified is very demanding.\nIndeed, there are many adults who, in making their choices, fail to\ndisplay the maturity and ‘understanding of what is\ninvolved’ that is dictated as necessary for the child. Why then\nshould a child have to display a competence that many adults lack both\nin general and in particular cases?" ], "section_title": "9. The Right to be Heard", "subsections": [] }, { "main_content": [ "\nOne important, indeed central, manner of understanding the moral\nstatus of the child is by questioning whether or not children have\nrights. It is normally thought that according to the\n‘will’ theory of rights children cannot have rights,\nwhereas according to the ‘interest’ theory they can. It\nis, however, at least possible on the ‘will’ theory that\nchildren could have rights, albeit ones that are exercised by trustees\nor representatives.", "\nChild ‘liberationists’ claim that children have all the\nrights that adults do. Others deny this, either believing that\nchildren have no rights or believing that children have only some of\nthe rights which adults possess. Those who believe children have no\nrights deny that children are qualified as adults are to have rights.\nThey further argue that the ascription of rights to children manifests\na misunderstanding of what children are like and of the nature of\nfamily relationships. Those who deny children all or some of the\nrights possessed by adults nevertheless believe that children, as\nhumans, have a certain moral status that ought to be protected.", "\nThose who say that drawing a line between adults and children in\nrespect of their possession of rights is arbitrary may mean different\nthings. To deny that different capacities are progressively acquired\nat different ages is implausible. To insist that drawing a line as\nsuch is wrong ignores the point of doing so, and recourse to the\nalternative of a competency test is not appropriate or practicable. On\nthe standard view, children have welfare but not liberty rights,\nwhereas adults have both. Adults also have the right that their\nchildhood selves shall grow up to be adults of a certain sort.\nChildren do not have an interest in remaining in childhood.", "\nThe best-interest principle with all its problems of interpretation\nsits oddly alongside the rights that are accorded to the child,\nespecially that of a right to be heard in matters affecting its\ninterests. This right in turn is a substitute not a complement to the\nright of choosing for oneself, and the Gillick competence which\nqualifies a child to exercise its rights of decision-making is\narguably stringently defined." ], "section_title": "10. Summary", "subsections": [] } ]

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Uniacke, 2020, ‘The Child’s Right\nto a Voice,’ Res Publica 4: 1–16.", "Arneson, R.J. and I, Shapiro, 1996, ‘Democratic Autonomy and\nReligious Freedom: A Critique of Wisconsin v. Yoder’, in I.\nShapiro and R. Hardin (eds.), NOMOS 38: Political Order, New\nYork: New York University Press, pp. 365–411.", "Barrie, J.M.,1995, Peter Pan and Other Plays, edited with\nan Introduction by Peter Hollindale, Oxford: Oxford University\nPress.", "Beckman, L., 2001, ‘Rights, Rights-Talk, and\nChildren’, The Journal of Value Inquiry, 35:\n509–515.", "Benatar, D., 2008, Better Never to Have Been: The Harm of\nComing into Existence, Oxford: Oxford University Press.", "Brennan, S., 2002, ‘Children’s Choices or\nChildren’s Interests: Which do their Rights Protect?’ in\nD. Archard and C. Macleod (eds.), The Moral and Political Status\nof Children: New Essays, Oxford: Oxford University Press, pp.\n53–69.", "Brighouse, H., 2002, ‘What Rights (if any) do Children\nHave?’ in D. Archard and C. 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Parental Rights,\nParental Authority and State Power, Totowa, NJ: Littlefield,\nAdams, and Co., pp. 237–253.", "Singer, P., 1975, Animal Liberation, New York: New York\nReview.", "Steiner, H., 1994, An Essay on Rights, Oxford:\nBlackwell.", "–––, 1998, ‘Working Rights’, in M.H.\nKramer, N. Simmonds and H. Steiner, A Debate Over Rights:\nPhilosophical Enquiries, Oxford: Clarendon Press, pp.\n235–301.", "Steinhoff, U. (ed.), 2015, Do All Persons Have Equal Moral\nWorth? On “Basic Equality” and Equal Respect and\nConcern, Oxford: Oxford University Press.", "Sumner, L.W., 1987, The Moral Foundation of Rights,\nOxford: Clarendon Press.", "United Nations, 1989, The Convention on the Rights of the\nChild, reprinted in P. Alston, S. Parker and J. Seymour (eds.),\nChildren, Rights and the Law, Oxford: Oxford University\nPress, pp. 245–264; and in L. LeBlanc, The Convention on the\nRights of the Child. 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[ { "href": "../advance-directives/", "text": "advance directives" }, { "href": "../autonomy-moral/", "text": "autonomy: in moral and political philosophy" }, { "href": "../childhood/", "text": "childhood, the philosophy of" }, { "href": "../feminism-family/", "text": "feminist philosophy, topics: perspectives on reproduction and the family" }, { "href": "../parenthood/", "text": "parenthood and procreation" }, { "href": "../rights/", "text": "rights" } ]

[ "\nRussell remains famous as a logician, a metaphysician, and as a\nphilosopher of mathematics, but in his own day he was also notorious\nfor his social and political opinions. He wrote an immense amount\nabout practical ethics—women’s rights, marriage and morals, war\nand peace, and the vexed question of whether socialists should smoke\ngood cigars. (They should.) And unlike present-day practical ethicists\n(with a few notable exceptions such as Peter Singer) he was widely\nread by the non-philosophical public. (See for instance Phillips 2013,\nwhich details Russell’s successes as a popular moralist in the 1950s.)\nBut though Russell was famous as a moralist and famous as a\nphilosopher, he does not have much of a reputation as a moral\nphilosopher in the more technical sense of the term. Until very\nrecently, his contributions to what is nowadays known as ethical\ntheory—meta-ethics (the nature and justification, if any,\nof moral judgments) and normative ethics (what makes right acts right\netc)—were either unknown, disregarded or dismissed as\nunoriginal. Key texts on the history of twentieth century\nethics—Warnock’s Ethics Since 1900 (1978), Urmson’s\nThe Emotivist Theory of Ethics (1968), Milller’s\nContemporary Metaethics: an Introduction (2013) and\nSchroeder’s Non-Cognitivism in Ethics (2010)—say\nnothing, or next to nothing, about Russell, at least in his capacity\nas a moral philosopher. It is only very recently—in the last\nfifteen years or so—that ethical theorists have begun to pay\nattention to him. (See Pigden 2003, 2007 and Potter 2006, though\nL.W. Aiken 1963 anticipated Potter and Pigden by about forty years.)\nPerhaps Russell would not have repined, since he professed himself\ndissatisfied with what he had said “on the\nphilosophical basis of ethics” (RoE:\n165/Papers 11: 310). But since he took an equally dim view of\nwhat he had read on that topic, the fact that he did not\nthink much of his own contributions does not mean that he thought them\nany worse than anybody else’s. In my view, they are often rather\nbetter and deserve to be disinterred. But “disinterred” is\nthe word since some of his most original contributions were left\nunpublished in his own lifetime and what he did publish was\noften buried in publications ostensibly devoted to less theoretical\ntopics. Thus Russell’s brilliant little paper “Is There an\nAbsolute Good”, which anticipates Mackie’s “The Refutation\nof Morals” by over twenty years, was delivered in 1922 at a\nmeeting of the Apostles (an exclusive, prestigious but secret\nCambridge discussion group of which Moore, Russell, and Ramsey were\nall members) and was not published until 1988. And Russell’s version\nof emotivism (which anticipates Ayer’s Language, Truth and\nLogic (1936) by one year, and Stevenson’s “The Emotive\nMeaning of Ethical Terms” (1937) by two) appeared towards the\nend of a popular book, Religion and Science (1935), whose\nprincipal purpose was not to discuss the nature of moral judgments,\nbut to do down religion in the name of science. However, Russell’s\ndissatisfaction with his writings on ethical theory did not extend to\nhis writings on social and political topics.", "\nHis perplexity, however, was theoretical rather than practical. He was\npretty clear about what we ought to do (work for world\ngovernment, for example), but “perplexed” about what he\nmeant when he said that we ought to do it.", "\nOne point to stress, before we go on. Russell took a pride in his\nwillingness to change his mind. Obstinacy in the face of\ncounter-arguments was not, in his opinion, a virtue in a\nscientifically-minded philosopher. Unfortunately he overdid the\nopen-mindedness, abandoning good theories for worse ones in the face\nof weak counter-arguments and sometimes forgetting some of his own\nbest insights (a forgivable fault in given the fountain of good ideas\nthat seemed to be continually erupting in his head). Russell’s mental\ndevelopment, therefore, is not always a stirring tale of intellectual\nprogress. His first thoughts are often better than his second thoughts\nand his second thoughts better than his third thoughts. Thus the\nemotivism that was his dominant view in the latter part of his life is\nvulnerable to objections that he himself had raised in an earlier\nincarnation, as was the error theory that he briefly espoused in 1922.\nNobody should be surprised, therefore, if I sometimes deploy an\nearlier Russell to criticize one of his later selves. Whitehead is\nreported to have said that Russell was a Platonic dialogue in himself,\nand in this temporally extended debate quite often it is one of the\nyounger Russells who wins the argument." ]

[ { "content_title": "1. The Open Question Argument and its Aftermath: Moore’s Influence on Russell", "sub_toc": [] }, { "content_title": "2. Desire, Motivation and the Open Question Argument: Did Russell Influence Moore?", "sub_toc": [ "2.1. The Open Question Argument versus the Barren Tautology Argument", "2.2. Wrestling With Desire: the Young Russell’s Adventures in Meta-Ethics", "2.3. Why the Open Question Argument?" ] }, { "content_title": "3. Sidgwick’s Problem and the Rejection of Idealism", "sub_toc": [] }, { "content_title": "4. Russell versus Moore: Two Kinds of Consequentialism", "sub_toc": [] }, { "content_title": "5. Politics, Consequentialism and the Need for Skepticism", "sub_toc": [] }, { "content_title": "6. Consequentialism, Emotivism and Moral Reform", "sub_toc": [] }, { "content_title": "7. Russell’s Ideal: the Influence of Spinoza", "sub_toc": [] }, { "content_title": "8. Objections to Emotivism and Relativism", "sub_toc": [ "8.1 The Vicious Circle Problem", "8.2 The Problem of the Disappearing Dispute", "8.3 “Ought” and the Open Question Argument", "8.4 The Problem of Validity", "8.5 Geach’s Problem", "8.6 Commitment and Inconsistency", "8.7 Russell’s Feelings and the Duck Argument", "8.8 Objections Concluded" ] }, { "content_title": "9. Objections to Objectivism", "sub_toc": [ "9.1 Persecution, Punishment and the Subjectivity of Value", "9.2 Russell and the Argument from Relativity", "9.3 Russell and Explanatory Impotence", "9.4 Emotivism or the Error Theory?" ] }, { "content_title": "10. Russell’s Error-Theoretic Wobble: There Is No Absolute Good", "sub_toc": [] }, { "content_title": "11. Russell’s Humean Wobble: Human Society in Ethics and Politics", "sub_toc": [] }, { "content_title": "12. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Primary Literature", "Secondary Literature" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nRussell’s destiny as an ethical thinker was dominated by one\nbook—G.E. Moore’s Principia Ethica (1903). Before 1903,\nRussell devoted some of the energy that he could spare from German\nSocial Democracy, the foundations of mathematics and the philosophy of\nLeibniz to working out a meta-ethic of his own. After 1903, he became\nan enthusiastic but critical convert to the doctrines of Principia\nEthica (though there is some evidence that the conversion process\nmay have begun as early as 1897). Moore is famous for the claim, which\nhe professes to prove by means of what has come to be known as the\nOpen Question Argument, that there is a “non-natural”\nproperty of goodness, not identical with or reducible to any\nother property or assemblage of properties, and that what we ought to\ndo is to maximize the good and minimize the bad. Russell subscribed to\nthis thesis—with certain important reservations—until\n1913. Thereafter he continued to believe that if judgments about\ngood and bad are to be objectively true, non-natural properties\nof goodness and badness are required to make them true. It is just\nthat he ceased to believe that there are any such properties. Does\nthis mean that judgments about good and evil are all false?\nNot necessarily (though Russell did subscribe to that view for a brief\nperiod during 1922). An alternative theory is that moral judgments are\nneither true nor false, since their role is not to\nstate facts or to describe the way the world is, but to express\nemotions, desires or even commands. This (despite some waverings) was\nRussell’s dominant view for the rest of his life, though it took him\ntwenty-two years to develop a well worked-out version of the theory.\nHe tended to call it subjectivism or “the subjectivity of moral\nvalues” though it is nowadays known as non-cognitivism,\nexpressivism or emotivism. He came to think that, despite their\nindicative appearance, moral judgments—at least judgments about\nwhat is good or bad in itself—are really in the optative mood.\n(A sentence is in the optative mood if it expresses a wish or a\ndesire.) What “X is good” means is “Would\nthat everyone desired X!”. It therefore expresses, but\ndoes not describe, the speaker’s state of mind, specifically his or\nher desires, and as such can be neither truth nor false, anymore than\n“Oh to be in England now that April’s here!”. If I say\n“Oh to be in England now that April’s here!”, you can\ninfer that I desire to be in England now that April’s here (since\nabsent an intention to mislead, it is not the sort of thing I would\nsay unless I desired to be in England and thought\nthat April was here). But I am not stating that I desire to\nbe in England, since I am not stating anything at all (except perhaps\nthat April is here). (See RoE: 131–144/Religion and\nScience: ch. 9.) Although this was Russell’s dominant view from\n1913 until his death, he did not care for it very much.", "\n\n\nI cannot see how to refute the arguments for the subjectivity of\nethical values, but I find myself incapable of believing that all that\nis wrong with wanton cruelty is that I don’t like it. (RoE:\n165/Papers 11: 310–11)\n", "\nIt is not entirely clear what Russell took these overwhelming\narguments to be. But one of them seems to have proceeded from a\nMoorean premise. Russell took Moore to have refuted\nnaturalism, the view that although there are moral truths,\nnothing metaphysically out of the ordinary is required to\nmake them true. Conversely Russell took Moore to have proved\nthat if there were to be moral truths about which things were\ngood or bad as ends rather than means, the truths in question would\nrequire spooky non-natural properties of goodness, badness\netc—quite unlike the “natural” properties posited by\nscience and commonsense—to make them true. In the\nsupposed absence of such properties, he was driven to the conclusion\nthat moral judgments (at least judgments about goodness and badness)\nwere either all false or neither true nor\nfalse. Thus Russell remained a renegade Moorean even after he had\nceased to believe in the Moorean good. But if Moore was a decisive\ninfluence on Russell, it seems that Russell was an important influence\non Moore. For Moore may have been driven to invent his most famous\nargument for a non-natural property of goodness—the\nOpen Question Argument—by the need to deal with a naturalistic\ntheory of Russell’s." ], "section_title": "1. The Open Question Argument and its Aftermath: Moore’s Influence on Russell", "subsections": [] }, { "main_content": [], "section_title": "2. Desire, Motivation and the Open Question Argument: Did Russell Influence Moore?", "subsections": [ { "content": [ "\n“I certainly have been more influenced by [Russell] than any\nother single philosopher” wrote Moore in his intellectual\nautobiography (Schilpp (ed.) 1942: 16). But Moore’s\n“Autobiography” suggests (without actually saying so) that\nthis influence was mostly metaphysical. I shall argue that Russell had\na considerable influence on Moore’s ethical doctrines and\nthat some of Moore’s key ideas were developed in the course of ongoing\ndebates with Russell.", "\nMoore’s Principia Ethica took a long time to finish. He had a\npretty good draft in 1898, but he did not publish it until 1903. Why\nthe long delay? One reason, I suspect, was that he had to deal with a\nproblem posed (perhaps unwittingly) by Russell.", "\nIt is not generally recognized that Principia Ethica contains\ntwo distinct arguments against the “Naturalistic\nFallacy”, the supposed intellectual error of identifying\ngoodness with some other property (usually, though not necessarily, a\nnaturalistic property). The first, which is derived from\nSidgwick, and has a long philosophical pedigree, goes something like\nthis:", "\nTo put the point another way:", "\nFollowing Russell, I call this the Barren Tautology Argument\nor BTA (RoE: 100/Papers 4: 572). The idea is that\n“good” cannot be synonymous with any naturalistic\n“X”, if “X things are good” is\nsupposed to be a reason for action rather than a “barren\ntautology”. So for example, if “good” just\nmeans “pleasant” then “Pleasant things are\ngood” is a barren tautology (equivalent to “Pleasant\nthings are pleasant” or “Good things are good”) and\ncannot provide us with a reason for the pursuit of pleasure. Only if\n“goodness” and “pleasure” are not\nsynonymous, can “Pleasant things are good” provide an\nintellectual incentive for the pursuit of pleasant things. This\nargument crops up at PE: §11 (though variants of it\nrecur throughout the first four chapters (PE: §§14,\n24 & 26):", "\n\n\nWhen A says “Good means pleasant” and B says\n“Good means desired,” they may merely wish to assert that\nmost people have used the word for what is pleasant and for what is\ndesired respectively. [But I do not think] that any exponent of\nnaturalistic Ethics would be willing to allow that this was all he\nmeant. They are all so anxious to persuade us that what they call the\ngood is what we really ought to do. “Do, pray, act so, because\nthe word ‘good’ is generally used to denote actions of\nthis nature”: such, on this view, would be the substance of\ntheir teaching … But how perfectly absurd is the reason they\nwould give for it! “You are to do this, because most people use\na certain word to denote conduct such as this.” “You are\nto say the thing which is not, because most people call it\nlying.” That is an argument just as good! …. When they\nsay “Pleasure is good,” we cannot believe that they merely\nmean “Pleasure is pleasure” and nothing more than\nthat.\n", "\nHowever Moore did not invent this argument. A.N. Prior, in his\nLogic and the Basis of Ethics (1949: ch. IX), traces it back\nto Cudworth in the 17th Century, though it doubtful whether\nMoore was aware of this. (He does not seem to have been particularly\nwell read.) But it certainly occurs in Sidgwick, which is presumably\nwhere Moore got it from. The Barren Tautology Argument is to be\ndistinguished from the Open Question Argument proper (the OQA), which\nMoore did invent, at least in its modern form. This occurs at\nPE: §13, a section that does not appear in the 1898\ndraft. It can be stated thus:", "\nFrom (1.4) and (1.5) it follows that", "\nIf “good” were synonymous with some naturalistic\npredicate “X”, then this would be obvious on\nreflection to every competent speaker. Hence there would be\nsome question of the form “Are X things\ngood?” which would not appear to be open to competent\nspeakers, since an understanding of the words involved would suffice\nfor an affirmative answer. Given (1.4), there is no such question;\nhence “good” is not synonymous with any naturalistic\npredicate “X”.", "\nFrom (1.6) and (1.7) it follows that", "\nThis argument is wheeled on to discredit a particular naturalistic\nanalysis of “good”—“one of the more plausible,\nbecause one of the more complicated of such\ndefinitions”—that “ good mean[s] … that which\nwe desire to desire”. Where did Moore get this definition? He\ndoes not say, crediting it, in effect, to Mr Nobody. But in fact the\ninventor of this plausible but fallacious definition was none other\nthan the Hon. Bertrand Russell." ], "subsection_title": "2.1. The Open Question Argument versus the Barren Tautology Argument" }, { "content": [ "\nThe desire-to-desire theory is the last in a sequence of three\nattempts to provide a foundation for ethics by defining\n“good” in terms of desire. In the first, “X\nis good” means “X will satisfy my desires”;\nin the second, it means “I want X for its own\nsake”; and in the third it means “X is what I\ndesire to desire” (RoE: chs. 7, 9 &\n10/Papers 1: nos. 36, 39 & 15).", "\n“Ethical Axioms” (1894) was the last piece that Russell\nwrote for Sidgwick’s course on ethics (RoE:\n53–56/Papers 1: 226–228). Russell takes it as a\ndatum that “we do make moral judgments” and that “we\nregard these, like judgments as to what is, as liable to truth and\nfalsehood”. We are “precluded from skepticism”\n(presumably the view that moral judgments are all false) “by the\nmere fact we will and act”. (This is not a very convincing\nargument since I can desire something—and hence\nact—without thinking it good, as non-human animals presumably\ndo. The precondition of action is desire, not desire tricked\nout in the vocabulary of good and evil.) Hence “some basis must\nbe found for ethical judgments”, but “it is sufficiently\nobvious that such a basis cannot be sought in any proposition about\nwhat is or has been”. Thus Russell has set himself a rather\ndifficult problem, since it is not at all clear that there\ncan be any true propositions that are not, in some sense,\npropositions about what is, has been or will be. Perhaps what he has\nin mind is a set of self-evident axioms about what ought to be or what\nwe ought to do which do not admit of any further analysis. But he\nrejects this option because “the Kantian maxim” (whatever\nthat is) is purely formal and because no “material\nprecept” “has obtained the universal consent of\nmoralists”. (It seems that a maxim cannot count as self-evident\nunless it is evident to every qualified self.) Russell also rejects\nthe view that moral judgments are “merely statements of a\npsychological state” (as, for example, that the speaker desires\nthis or that) on the grounds that in that case “they could not\nerr (except by the speaker’s mistaking his own feelings)”. He\nseems to think that it is a conceptual truth that moral judgments are\nliable to error. Finally he plumps for the view that “we may\ndefine the good as that which satisfies desire” (that is, that\nwhat is good for each person is what will satisfy that person’s\ndesires). This allows for the possibility of error, for though we\nusually know what we want, we can be wrong about whether we will like\nit when we get it. Russell hastens to explain that this definition is\nnot as sordid as it sounds. “Our duty will consist in\nself-realization, but self-realization may of course be best attained\nby what is commonly called self-sacrifice.”", "\nIt is nice to know that no sordid or selfish consequences flow from\ndefining the goodness in terms of the satisfaction of desire, but it\nis not at all clear that Russell has solved the problem that he had\nset himself. For propositions about what will satisfy desire are\npropositions about what will satisfy desire—that is,\npropositions about what will be. Underlying Russell’s\nargument is his evident desire to forge a conceptual connection\nbetween moral belief and action. The theory must (help) explain the\nfact that we often do what we believe to be our duty and\nusually pursue and promote what we believe to be good. This,\nnot the thesis that we are necessarily motivated by our moral\nbeliefs, is the premise of Hume’s famous Motivation Argument at\nTreatise, 3.1.1:", "\n\n\nAnd this is confirmed by common experience, which informs us that men\nare often governed by their duties, and are deterred from\nsome actions by the opinion of injustice, and impelled to\nothers by that of obligation [my italics].\n", "\n(See D.D. Raphael (ed.) 1991 The British Moralists\n[henceforward BM: §489].) Russell appears to have\nthought that a theory that left “good” and\n“ought” undefined would not meet this constraint. But if\n“good” means what procures satisfaction, then we\nhave the beginnings of such an explanation. For we usually desire that\nour desires be satisfied, and hence we have a reason to pursue and\npromote the good.", "\nThis theory soon ceased to satisfy, and Russell reverted to the\nproblem in “Are All Desires Equally Moral?”, a paper he\ncomposed in about 1896 (RoE: 68–70/Papers 1:\n242–44). “The Good, for me, at any moment”, he\ndeclares, “is what I want” not what will satisfy my wants,\nsince we desire the objects that will satisfy desire and not,\n“except derivatively”, that those desires should be\nsatisfied. (This last point is distinctly dubious. Isn’t Reid’s desire\nfor our good-on-the-whole in part a second order desire that at least\nsome of our first-order desires should be satisfied? [See\nThomas Reid, 1788, Essays on the Active Powers of Man,\nexcerpted in BM: §§ 861–865.] And did not\nRussell himself believe that this desire was not only real but often\nunduly predominant in civilized persons, so much so that most of what\nwe do is done for the sake of something else not because we have a\nspontaneous, first-order desire to do it? See for instance his 1894\npaper “Cleopatra or Maggie Tulliver” [RoE:\n57–67, Papers 1: 92–98] though the theme is\nrepeated in subsequent writings such as The Principles of Social\nReconstruction, first published in 1916.) Thus “X is\ngood”, means “I want X”, a particularly crude\nkind of subjectivism that goes back to Hobbes (“whatsoever is\nthe object of any man’s appetite or desire; that is it which he for\nhis part calleth good”, BM: §25). This\ntheory maintains the link between moral belief and action (naturally\nwe pursue and promote the things that we want!) though it a) reduces\nmoral judgments to “statements of a psychological state”\nand b) violates the requirement that statements about what ought to be\nshould have nothing to do with what is, since, on this theory, my\nmoral judgments reduce to statements about what is going on\ninside my head. The theory as stated is a little too crude\nfor Russell however, since it precludes the possibility of moral\nerror. After all, it is difficult to be wrong about what we want. The\ntheory has the further unhappy consequence that we cannot desire what\nwe believe to be bad, let alone what is bad, since from the\nvery fact that I desire something, it follows that for me, at least,\nit is good. All desires are equally moral since they are all desires\nfor the good.", "\nRussell tries to sidestep these problems by distinguishing between\n“primary desires, for ends, and secondary\ndesires, for means”. The good for each person is what he desires\nfor its own sake and generally speaking he cannot be mistaken about\nthis. But he can be mistaken about whether a given\nobject is the means to what he ultimately desires.\nFurthermore, if he is mistaken, his secondary desires may be\nimmoral. As Russell realizes, this leads to the “Socratic maxim\nthat no man sins wittingly” since nobody can desire what he\nbelieves to be bad. But an agent can both desire the bad and have bad\ndesires, since his secondary desires may be inimical to his ultimate\nends. Unfortunately this amendment cannot save the theory. According\nto Russell’s theory, in some cases at any rate\n“X is good”, means “I want X for its\nown sake”, and such judgments are relatively immune from error.\nFurthermore, people do seem to desire what they believe to be bad (the\n“Socratic maxim” is not known as the “Socratic\nParadox” for nothing!) and we commonly think that desires for\nends, as well as desires for means, can be bad. Finally, the theory,\neven in its amended form, reduces moral judgments to statements of a\npsychological state. Thus the theory violates Russell’s theoretical\nconstraints and is inconsistent with the way we usually talk.", "\nWhat about the desire-to-desire theory? If “X is\ngood” means “I desire to desire X” then there\nis a conceptual connection, though, as Lewis notes, an\n“iffy” one, between moral belief and action (Lewis 1989:\n116/72). I will pursue and promote what I believe to be good in so far\nas I desire what I desire to desire. Moral judgments “like\njudgments as to what is, [are] liable to truth and falsehood”,\nthough not very liable to falsehood, since it is difficult,\nbut not impossible, to be mistaken about what we desire to desire. (I\nmight be persuaded, especially under moral pressure, that I desire to\ndesire something when in fact I do not.) But it is possible both to\ndesire the bad (to desire what I desire not to desire) and to\nhave bad desires (to have desires which I desire to desire not to\ndesire). Self-conscious depravity is thus a real possibility and the\nSocratic paradox is dismissed. For like an unhappy junkie, I can act\non desires which I desire not to desire. But it is not possible to\ndesire to desire the bad since what we desire to desire is\nautomatically good. Furthermore, moral judgments are reduced to\nstatements of a psychological state, so much so that ethics becomes a\nbranch of empirical psychology. The axioms of ethics, in so far as\nthere are such things, are concerned with what is, since our desires,\nincluding our second-order desires are original existents.", "\nThus Russell was trying in the 1890s to devise a theory that would\nmeet six constraints:", "\nThe last condition, which amounts to the denial of naturalism, goes\nback to a paper that Russell wrote for Sidgwick in 1893, “The\nRelation of What Ought to be to What Is, Has Been or Will Be”\n(RoE: 37–40/Papers 1: 213–214). Russell\nobserves that “from the point of view of formal logic” it\nis impossible to derive an Ought from an Is. This leads him to the\nconclusion that “some one or more propositions ethical in form\nmust be regarded as axiomatic unless [and this is a big\n‘unless’] such propositions are materially equivalent to\nsome assertion about what is, has been or will be”. By\n“materially equivalent” he seems to mean “mean the\nsame as”. Thus morality might not hang from the skyhook of\nintuited axioms if moral judgments meant the same as natural judgments\nof some kind. But he goes on to argue against this possibility, that\nis, to argue that what Moore was to call naturalism is false.\nNor is it odd that he should have anticipated Moore, since Sidgwick,\nwho was their teacher, anticipated them both.", "\nHowever this provides Russell with a sextet of constraints that cannot\nbe jointly met. For example, it is hard to see how conditions (2.1)\nand (2.3) can be realized without analyzing “good” or\n“ought” in terms of desire or some such psychological\nstate. Yet to do so violates conditions (2.5) and (2.6). Thus it comes\nas no surprise that the theories which Russell managed to come up with\nall fail to meet his constraints. The first (“X is\ngood” means “X will satisfy my desires”)\nmeets conditions (2.1) (since what we want may not satisfy us once we\nget it). It also meets condition (2.4) (just about) since it is\npossible to want things that will not, in fact, satisfy us. But it\ndoesn’t meet (2.5), since “X is good” reduces to a\nstatement about a future psychological state; and a\nfortiori it fails to meet condition (2.6). The second theory\n(“X is good” means “I want X for its\nown sake”) fares far worse. It meets condition (2.1) but not\n(2.2), (2.3) but not (2.4), and fails (2.5) and (2.6) altogether. As\nfor the third (“X is good” means “X is\nwhat I desire to desire”), it meets (2.1), struggles to meet\n(2.2), meets (2.3) and (2.4) but fails both (2.5) and (2.6).", "\nInterestingly if Russell abandoned (2.1) and (2.2) and adopted a\nnon-cognitive theory he would have been able to arrive at a theory\nwhich would have satisfied the last four constraints. Take Russell’s\nown brand of emotivism (“X is good” means\n“Would that everyone desired X!”), which he did not\ndevelop until 1935 (RoE: 131–144/Religion and\nScience, ch. IX). This meets condition (2.3), since if I say that\nX is good, and if am sincere in my ethical pronouncements, then\nI desire that everyone (including myself) should desire\nX—a second order desire that is usually (but not always)\naccompanied by a first-order desire for X itself. Thus if I\n“believe” (note the scare quotes!) that X is good,\nI am likely to pursue or promote it. The theory meets condition (2.4)\ntoo, since I can desire things, from chocolate to crack, that I desire\nnobody (including myself) to desire. It meets condition (2.5) as well,\nsince good-judgments, so far from being statements of a psychological\nstate, are not statements at all but optatives. For much the same\nreason it meets condition (2.6): “X is good”, is\nnot equivalent to a proposition about what is, has been or will be,\nbecause it is not equivalent to any proposition whatsoever. But of\ncourse the standard objection to non-cognitivist theories is precisely\nthat they violate conditions (2.1) and (2.2). They treat utterances\nwhich are commonly regarded as true or false as lacking in truth-value\n(at least with respect to their primary meanings) and they immunize\nmoral judgments from error by depriving them of the possibility of\nfalsehood.", "\nNow I don’t say that Russell’s six constraints are correct (they can’t\nbe since they are inconsistent), nor that Russell’s meta-ethical\ntheories are right (which at most one of them can be since they, too,\nare inconsistent). But I do say that the constraints are\nplausible and that it is a desideratum in a meta-ethical\ntheory that it meet as many as possible. Russell demonstrates his\nphilosophical acumen by making the attempt.", "\nIn 1897, Russell decided in effect, to sacrifice conditions (2.5)\n(2.6), and perhaps (2.2) to conditions (2.1), (2.3) and (2.4). In that\nyear he read a paper to the Cambridge Apostles “Is Ethics a\nBranch of Empirical Psychology” in which he defined goodness as\nthat which we desire to desire. (RoE:\n71–78/Papers I: 100–104). Moral judgments (at\nleast judgments about goodness) reduce to “statements of a\npsychological state” since to say something is good is to say\nthat “we” desire to desire it, a statement well within the\nfrontiers of psychology (whether “we” refers to the\ncommunity at large or to the speaker whoever he or she may be). And of\ncourse, if judgments about goodness reduce to “statements of a\npsychological state”, they clearly reduce to statements about\n“what is, has been or will be”, since whether\n“we” desire to desire something is determined by whatever\nis the case in “our” minds. Are moral judgments\nliable to error? Only in so far as we can be mistaken about what we\ndesire to desire, which is, perhaps, not very far. On the plus side,\nmoral judgments will be true or false, and will have a conceptual\nconnection (albeit an iffy one) to our actions and passions. Assuming\nthat (at least sometimes) I actually desire what I desire to desire,\nthe fact that (for me) X is good means that (at least\nsometimes) I will have a desire to pursue or promote X.\nFinally, it is perfectly possible to have bad or even evil desires,\nnamely the desires I desire not to desire, thus solving a\nproblem with Russell’s previous attempts at a desire-based ethic (see\nRoE: ch. 9/Papers I: ch. 39). Thus the answer\nRussell provides to his own question (“Is Ethics a Branch of\nEmpirical Psychology?”) is a clear, but reluctant,\nyes." ], "subsection_title": "2.2. Wrestling With Desire: the Young Russell’s Adventures in Meta-Ethics" }, { "content": [ "\nNow why should this theory pose a problem for Moore? Because the\ntime-honored Barren Tautology argument does not work against it.\nRemember, the conclusion of the Barren Tautology Argument is this:", "\nBy substitution this gives us:", "\nBut the point of defining goodness in terms of what we desire to\ndesire is not to give us a reason to pursue or promote what\nwe desire to desire—rather, it is supposed to explain\nwhy something’s being good gives us a reason (or at least, a\nmotive), to pursue or promote it. Russell is not advocating\nthe pursuit of what we desire to desire: he is trying to provide an\nanalysis of “good” which helps to make sense of the fact\nthat we tend to pursue and promote (what we believe to be) good\nthings. (We do it because to be good just is to be something\nwhich we desire to desire, and hence something which, sometimes at any\nrate, we will actually desire.) In other words, (i′)\n“Things which we desire to desire are good” is\nmeant to be a barren tautology—barren in terms of\npractical consequences, that is, though, hopefully, philosophically\nilluminating. It does not provide (and is not intended to\nprovide) a reason for action. But in that case, the antecedent of\n(1.3″)—that the belief that “Things which we desire\nto desire are good”, provides a reason for action—is\nfalse, so far as Russell’s analysis is concerned. Thus even if the\nconditional (1.3″) is true, it does not support the\nconsequent—that “good” does not mean “what we\ndesire to desire”. The Barren Tautology Argument is therefore\nimpotent against the desire-to-desire theory.", "\nNor is this all. The Barren Tautology Argument fails against other\ntheories whose aim is to explicate the appeal of goodness rather than\nto advocate the pursuit of some alleged good thing. For instance, if\n“good” means “what we are ideally inclined to\napprove of”, then “What we are ideally inclined to approve\nof is good” will be a barren tautology. But since people like\nHume, who propound such definitions, don’t intend them to be anything\nelse, they are not compelled to the conclusion that such definitions\nare false. Thus if naturalism was to be defeated (which was\nclearly Moore’s project) a new argument had to be invented.\nAnd it is significant, I think, that Moore did not publish\nPrincipia Ethica until he had invented just such an\nargument.", "\nThe Open Question Argument proper does not terminate in a conditional\nbut a categorical. It starts with the assumption that “Are\nX things good?” is a significant or open question for any\nnaturalistic or metaphysical predicate “X”. It is\nnot a tautology, barren or otherwise, that what we desire to\ndesire is good, and the proof of this is that competent speakers\ncan sensibly wonder whether or not it is true. Indeed, according to\nMoore, “any one can easily convince himself by inspection”\nthat the predicate “good” “is positively different\nfrom the notion of ‘desiring to desire’”. If we\ngrant Moore’s first implicit assumption—that if two expressions\nare synonymous this is evident on reflection to every competent\nspeaker—we can derive the consequence that “good”\ndoes not mean “what we desire to desire”. And if\nwe grant his second implicit assumption—that if two predicates\nor property words have distinct meanings they name distinct\nproperties—then we can derive the conclusion that he really\nwants, namely that goodness is not identical with what we\ndesire to desire. And by parity or reasoning we can do the same for\nany naturalistic property whatsoever.", "\nNow Moore’s twin assumptions have subsequently fallen upon hard times.\nThe first leads straight to the Paradox of Analysis (see Langford\n1942), whilst the second would exclude synthetic identities such as\nwater is H2O. But if they were correct,\nthe OQA would indeed dispose of the desire-to-desire theory along with\nkindred theories such as Hume’s. It is notable that David Lewis, who\nrevived Russell’s theory in 1989 (without realizing it was Russell’s),\nexplicitly affirms what Moore implicitly denies—that there can\nbe unobvious analytic truths; that is, truths not\nevident to every competent speaker (see Lewis 1989 and Pigden 2007).\nBut if Moore were correct and there were no such things, then\nnaturalistic analyses of the moral concepts such as Russell’s would be\nin big trouble. The BTA only works against some naturalistic\nanalyses of “good”, namely those that define\n“good” in terms of some property that the theorist wishes\nto promote. The OQA, if it works at all, works against them all. It\nseems very likely that what prompted Moore to invent his philosophical\nweapon of mass destruction was the desire-to-desire theory of Bertrand\nRussell.", "\nThen why didn’t Moore say so—or at least, why didn’t he\nattribute the desire-to-desire definition to its original inventor?\nBecause Russell propounded his definition at a meeting of the\nApostles, a supposedly secret society. The rather priggish Moore took\nthe code of secrecy very seriously and used to fuss about discussing\nthe doings of the Apostles by postcard in case they were read in\ntransit. (The slightly less priggish Russell had to reassure him that\nonly college porters were likely to read them and only initiates would\nunderstand.) To have attributed the desire-to-desire theory to an\nApostolic paper of Russell’s would have broken the code of silence (a\ncode designed to promote the unfettered exchange of honest\nopinion).", "\nThere is an irony in this episode. The last page of the paper,\n“Is Ethics a Branch of Empirical Psychology?” is marked\nwith a query in Russell’s hand “Shall we spell {Good/good}\nwith”, to which Moore replies “Good =\ngood”—which looks like a succinct formulation of his\nfamous no-definition definition of “good” (“If I am\nasked ‘How is good to be defined?’ my answer is that it\ncannot be defined and that is all I have to say about it.”\nPE: 58). If I am right, Russell’s desire-to-desire theory\nposed a problem for Moore which it took him five years to solve. But,\ngiven the annotation, it seems that the debate on Russell’s paper\nbegan a process of conversion that led Russell himself to accept the\ndoctrines of Moore’s Principia Ethica." ], "subsection_title": "2.3. Why the Open Question Argument?" } ] }, { "main_content": [ "\n“We called him ‘old Sidg’ and regarded him as merely\nout of date” (My Philosophical Development: 30). So\nsaid Russell of his teacher, the great Victorian moral philosopher,\nHenry Sidgwick (though he later thought that he and his contemporaries\n“did not give [Sidgwick] nearly as much respect as he\ndeserved”). But though Russell may have regarded Sidgwick as an\nold fogey, he set the agenda for a lot of Russell’s work on ethics in\nthe 1890s. For Russell was much exercised by a problem that also\nbothered Sidgwick: the Dualism of Practical Reason. (See Sidgwick\n1907: 496–516; see also Schulz 2004: ch. 4, in which it becomes\nabundantly clear how very preoccupied Sidgwick was with this problem.)\nAccording to Sidgwick, it is rational to do what is morally right (by\nmaximizing pleasurable consciousness on the part of all sentient\nbeings) and rational to do what is prudentially right (by maximizing\npleasurable consciousness on the part of oneself), but, when the two\ncome into conflict, the one does not seem to be any more rational than\nthe other. If God exists, then He can ensure that it will pay in the\nlong term to promote the public interest, by rewarding the righteous\nin the life to come. What is morally right will coincide with what is\nprudentially right, and that, consequently, is what Practical Reason\nwill command. But if, as Sidgwick was reluctantly inclined to think,\nthere is no God, what is morally right and what is prudentially right\nwill sometimes come apart, and Practical Reason will speak with a\ndivided voice. If it does not always pay to be good, then it is not\nclear that is more rational to be good than to be bad, a conclusion\nthat Sidgwick found deeply disturbing. The rather priggish young\nRussell was bothered by the problem too (a solution, he said, would be\n“a real solid addition to my happiness”) because, like\nSidgwick, he did not believe in God. But as a fashionable young\nphilosopher of the 1890s he did believe in something that he thought\nwould do nearly as well, namely, the Absolute. For at this time,\nRussell, like most of his philosophical contemporaries in the\nEnglish-speaking world, was a neo-Hegelian or Absolute Idealist.\nThough we may seem to be living in a material world and to be\nmaterial boys and girls, this is an Appearance only. Reality, the\nAbsolute, is basically mental, a sort of timeless and harmonious group\nmind of which our separate selves are (perhaps delusory) aspects. As\nBradley put it,", "\n\n\nthe Absolute is one system, and … its contents are nothing but\nsentient experience. It will hence be a single and all-inclusive\nexperience, which embraces every partial diversity in concord. For it\ncannot be less than appearance, and hence no feeling or thought, of\nany kind, can fall outside its limits. (1930 [1893]: 129)\n", "\n(We stress that it is hard to present this doctrine concisely without\ngross caricature.) But there was a crucial difference between\nMcTaggart and Bradley, the two leading idealists of Russell’s day.\nMcTaggart believed in personal immortality and claimed the harmony\nthat already exists timelessly (so to speak) “must some day\nbecome explicit” (McTaggart 1996 [1893]: 210–211). Bradley\ndid not.", "\nAt first Russell was an adherent of McTaggart. This afforded him a\nneat solution to Sidgwick’s problem. The happy day when the harmony\nbecomes explicit can be promoted or retarded by human action. If I\nbenefit myself at your expense not only am I doing down a self with\nwhom I am, in Reality, intimately linked—I am putting off the\nday when the harmony that Really Is becomes apparent. And since this\nharmony will be supremely pleasurable I am harming myself into the\nbargain. Hence morality and self-interest coincide and Practical\nReason is reunited with itself (Russell, 1893, “On the\nFoundations of Ethics”, RoE:\n37–40/Papers 1: 206–211). This illustrates the\npoint made by a number of unkind critics, that in the late\n19th century Absolute Idealism functioned as a sort of\nmethadone program for high-minded Victorian intellectuals, providing\nthem with moral uplift as they struggled to get off the hard stuff of\nofficial Christianity. (See Stove 1991: chs. 5 & 6; Allard 2003\nand, in more restrained language, Griffin 2003b: pp. 85–88.)\nBefore long however, Russell moved over to Bradley’s camp and ceased\nto believe that the timelessly existing harmony would become manifest\nin time. Nevertheless, since we are all aspects of the Absolute, a\nsort of timeless super-self, there is essentially the same objection\nto indulging my desires at your expense as there is to indulging one\nof my own passions at the expense of others which are inconsistent\nwith it. I am hurting, if not myself, at least a larger whole of which\nwe are both parts (Russell, 1894, “Cleopatra or Maggie\nTulliver”, RoE: 57–67/Papers I:\n92–8). But before long even this solution ceased to satisfy. In\na paper not published until 1957, “Seems Madam? Nay It\nIs”, Russell argued (as he put it to Moore) that “for all\npurposes that are not purely intellectual, the world of\nAppearance is the real world”. In particular, the hypothesis\nthat there is a timeless and harmonious Reality provides no\nconsolation for our present pains since it is a Reality that we never\nget to experience. If “the world of daily life remains wholly\nunaffected by [Reality], and goes on its way just as if there were no\nworld of Reality at all”, and if this world of Reality is a\nworld that we not only do not but cannot experience\n(since experience is necessarily temporal), how can its alleged\nexistence afford us any consolation for what seems to be (and\ntherefore is) evil in the world of Appearance? (Russell,\n1897, “Seems, Madam? Nay, It Is”, RoE:\n79–86/Papers 1: 105–111/Why I am Not a\nChristian: 75–82).", "\nNow this argument has an interesting corollary which Russell does not\nexplicitly draw. It may be that in Reality the pains I inflict on you\naffect me—or at least a larger mind-like thing in which we both\nparticipate—but if I never experience those effects,\nhow can this give me a motive to do or forbear if my interests\nconflict with yours? How can the fact that you and I are in Reality\none (or at least part of one) give me a reason to look out for you, if\nthis oneness is something I never experience? If Absolute Idealism can\nprovide no consolation for life’s disasters—which is what\nRussell is explicitly arguing—then it seems that it cannot\nsupply me with a reason not to visit those disasters on you, if doing\nso is likely to benefit me. It may be that I suffer in a metaphysical\nsort of way when I profit at your expence, but if this suffering is\nsomething I never feel (since I am effectively confined to\nthe world of Appearance) why should this bother me? Thus the Dualism\nof Practical Reason reasserts itself. Sometimes what is morally right\nis at odds with what is prudentially right and when it is, there seems\nno reason to prefer the one to the other.", "\nWhether Russell realized this is not entirely clear. What is clear is\nthat “Seems, Madam? Nay, It Is” marks the beginning of the\nend for Russell’s Absolute Idealism. Once he realized that", "\n\n\nfor all purposes that are not purely intellectual [including\nperhaps the purpose of providing moral uplift] the world of Appearance\nis the real world,\n", "\nRussell came to feel that the world of Reality was no use for purely\nintellectual purposes either and soon resolved to do without it. A big\n“R” Reality, that could neither console us for life’s\ntroubles nor reconcile Duty and Interest, was a big “R”\nReality that might as well not exist. The methadone of Absolute\nIdealism having failed, Russell was forced to accept appearances at\nface value.", "\nBut what about the problem of the Dualism of Practical Reason? In\nlater life, Russell ceased to worry about it perhaps because he\nrealized that it is a problem that cannot be resolved. The Cosmos of\nDuty really is a Chaos (as Sidgwick rather colorfully put it). Duty\nand Interest can come into conflict, and when they do, there\nis no decisive reason for preferring the one to the other. All you can\ndo is to try to instill moral and altruistic motivations, which is\nwhat Russell tried to do with his children. But when they asked\nwhy they should care about other people (as his daughter Kate\ndefiantly did) his response was rather lame.", "\n\n\nKate:\n“I don’t want to! Why should I?”\nRussell:\n“Because more people will be happier if you do than if you\ndon’t.”\nKate:\n“So what? I don’t care about other people.”\nRussell:\n“You should.”\nKate:\n“But why?”\nRussell:\n“Because more people will be happier if you do than if you\ndon’t.” (RoE: 16; Tait 1975: 185)\n\n", "\nThis isn’t much of an answer, but since the Cosmos of Duty really is a\nChaos, it was perhaps the best that Russell could do." ], "section_title": "3. Sidgwick’s Problem and the Rejection of Idealism", "subsections": [] }, { "main_content": [ "\nAlthough Russell became a convert to the doctrines of Principia\nEthica, he disagreed with Moore on two important points. Russell,\nlike Moore was what is nowadays known as a consequentialist. He\nbelieved that the rightness or otherwise of an act is “in some\nway, dependent on consequences”. But for the young Moore, it is\n“demonstrably certain” (!) that “I am morally bound\nto perform this action” is identical [that is\nsynonymous] with the assertion “This action will produce the\ngreatest amount of possible good in the Universe” (PE:\nch. 5, §89). Thus it is analytic that the right thing to\ndo is the action that will, actually produce the best\nconsequences. But in Russell’s view this claim is neither analytic nor\ntrue. Moore’s own Open Question Argument can be deployed to prove that\nit is not analytic, and a little critical reflection reveals that it\nis not true.", "\n\n\nIt is held [by Moore] that what we ought to do is that action, among\nall that are possible, which will produce the best results on the\nwhole; and this is regarded as constituting a definition of\nought. I hold that this is not a definition, but a\nsignificant proposition, and in fact a false one. (RoE:\n101/Papers 4: 573)\n", "\nIt is a “significant” or non-analytic proposition because\na competent speaker can believe that X is the act that will\nproduce the best consequences without believing that she ought to do\nit. If the two propositions “X is the act available to me\nthat will produce the best consequences” and “I ought to\ndo X” were really synonymous, then a competent\nspeaker could not believe the one whilst remaining in doubt about the\nother. Since this is perfectly possible (as is shown by the fact that\n“Ought I to do what will have the best results?” is an\nobstinately open question for competent speakers of English) the two\nclaims are not synonymous. (W.D. Ross developed a similar line of\nargument in The Right and the Good (1930) but it was Russell\nwho convinced Moore that he was wrong. See Moore 1942: 558).", "\nBut the fact that these claims are not synonymous does not show that\nit is false that I ought to do that act which will, in\nfact, produce the best consequences. The latter claim could be\nsynthetic (or, as Russell would have it, “significant”)\nbut true. Why does Russell think it false? Russell raises the ad\nhominem objection that Moore’s thesis is flatly inconsistent with\nthe moral conservatism that he goes on to embrace. According to Moore,\nalthough “there are cases where [an established moral] rule\nshould be broken”, since “in some cases the neglect of an\nestablished moral rule will be the best course of action\npossible”, nevertheless, “we can never know what those\ncases are, and ought, therefore, never to break it”\n(PE: §99). “The individual, therefore, can be\nconfidently recommended always to conform to rules which are\ngenerally useful and generally practiced.” But if we ought to\nperform the best action possible, what this implies is that there are\nsome cases (though we can never know which) where we ought to do what\nit is not the case that we ought to do. Moore could avoid this\ncontradiction by adopting the view that what we ought to do is that\naction which we have reason to believe will produce the best\nconsequences. As Russell himself put it, Moore’s moral conservatism\n“implies that we ought to do what we have reason to\nthink will have the best results, rather than what really\nwill have the best results” [my italics]—since,\nin any given instance, we may have reason to think that the\nconventionally right act will have the best consequences even though\nwe know that this won’t always be the case.", "\nBut Russell did not reject Moore’s brand of consequentialism because\nit was inconsistent with his moral conservatism, since he\nalso rejected Moore’s moral conservatism. As he informed\nMoore by letter, he regarded his views on Practical Ethics as\n“unduly Conservative and anti-reforming”. However, anybody\nwho thinks that there are some actions which we ought to do\neven though, as a matter of fact they won’t have the best consequences\nmust, reject Moore’s view. And it is precisely because he believes\nthis that Russell rejects Moore’s brand of consequentialism.\n“Some people”, says Russell, “whom I refrain from\nnaming, might with advantage to the world have been strangled in\ninfancy; but we cannot blame the good women who brought them up for\nhaving omitted this precaution.” So if Stalin’s mother (say) did\nthe right thing in not strangling him at birth, then it\nfollows that the right thing to do is not always the act with the best\nactual consequences. Russell admits that his view is not without\nparadox, since if it sometimes right to do what is actually\ndisastrous, it follows that it can sometimes be “a pity [that] a\nman did his duty”, a thesis which Moore regards as “a\ncontradiction in terms”. But paradoxical as this may seem, it is\nonly a contradiction on the assumption that “the right\naction” simply means “the action with the best\nactual consequences”, an assumption which Moore’s own Open\nQuestion Argument proves to be false. Moore’s view, by contrast, is\ncontradictory however “right” and “ought” are\nto be defined, since it implies that we sometimes ought to perform\nacts which (since they are not optimific) it is not the case that we\nought to perform.", "\nRussell’s criticisms can be summed up as follows:", "\nMoore accepted argument A (see his “Reply to My Critics”:\n558), and in his later book Ethics (1912) he treats\nconsequentialism as a synthetic thesis.", "\n\n\nIt is, I think, quite plain that the meaning of the two words\n[“expedience” and “duty”] is not the\nsame; for if it were, then it would be a mere tautology to say that it\nis always our duty to do what will have the best possible\nconsequences. Our theory does not, therefore, do away with the\ndistinction between the meaning of the two words\n“duty” and “expediency”; it only implies that\nboth will always apply to the same actions. (Ethics: 89)\n", "\nHe also seems to have accepted Russell’s ad hominem argument\nB—that, given the fairly obvious fact that doing the done thing\ndoes not always produce the best results, his actualist brand of\nconsequentialism is inconsistent with his moral conservatism. However,\nhe did not resolve the problem by modifying thesis (1) as Russell, in\neffect, recommended—instead he resolved it by dropping thesis\n(3). In Principia, moral conservatism had been\n“confidently recommended” to the conscientious\n“individual”. By the time Moore came to write\nEthics in 1912 it had simply disappeared, leaving the puzzled\n“individual” bereft of practical guidance. What ought the\nindividual to do, when, as is usually the case, she cannot determine,\nwhich of the available acts will have the best total consequences?\nMoore does not say, thereby sacrificing helpfulness to theoretical\nconsistency." ], "section_title": "4. Russell versus Moore: Two Kinds of Consequentialism", "subsections": [] }, { "main_content": [ "\nDry and abstract as these disputes may seem, they are not devoid of\npractical import. A common complaint against consequentialism is that\nit encourages the consequentialist to do evil that good may come. If\nthe goods to be achieved or the evils to be averted are sufficiently\nlarge, it may be not only permissible but obligatory to\ntorture prisoners, execute hostages or to massacre civilians—so\nlong as there is no other, less costly, way to achieve the goods or\navert the evils. This is not only objectionable in itself—it\nencourages ruthless types to commit horrors in the here and now for\nthe sake of some imagined utopia, whilst pretending to themselves and\nothers that they are actuated by the highest motives. Because in\nprinciple consequentialism licenses doing evil that good may\ncome, in practice it encourages fanatics to do evil even when\nthe good to come is highly unlikely. In his “Newly Discovered\nMaxims of la Rochefoucauld”, Russell remarks that “the\npurpose of morality is to allow people to inflict suffering without\ncompunction” (Fact and Fiction: 184). And\nconsequentialist moralities have enabled some of their devotees to\ninflict a great deal of suffering, not only without compunction, but\noften with an insufferable air of moral smugness.", "\nBy adopting expected utility as the criterion of right action\nRussell goes some way towards meeting these objections. In practice\nwhen people propose to perpetrate horrors for the sake of some greater\ngood, the horrors are usually certain and the greater good is highly\nspeculative. In weighing up the options, the good to be achieved by\nsome tough course of action must be multiplied by the probability of\nachieving it, which is always a fraction of one, and often a rather\nsmall fraction at that. So although doing evil that good may come is\nnot excluded in principle, the expected utility theorist is\nfar less likely to do it in practice—at least if he or she is\nintellectually honest. The classless society (let us suppose) would be\na very good thing, but I am probably not justified in shooting the\nhostages to bring it about. For I can be certain that if I shoot them,\nthe hostages will be dead, whereas the probability that shooting them\nwill bring about the classless society is very low. Moreover there is\nlikely to be an as-good-or-better chance that I can bring about the\nclassless society without shooting the hostages. Thus even if\nthe classless society would be supremely good, the expected utility\ntheorist will not be justified in shooting the hostages to bring it\nabout. The expected utility theorist may be obliged to do evil that\ngood may come, but only if the good is large, highly likely given the\nevil, and most unlikely without the evil. These conditions\nare seldom met.", "\nThus Russell could use the criterion of expected utility\nagainst warmongers and enthusiasts for revolutionary violence who\nemployed utilitarian patterns of reasoning to inflict suffering\nwithout compunction. It was (for example) one of his chief weapons in\nhis polemics against the Bolsheviks during the 1920s. As he wrote in a\nreview of Bukharin’s Historical Materialism,", "\n\n\nwe do not know enough about the laws of social phenomena to be able to\npredict the future with any certainty, even in its broadest outlines\n… For this reason, it is unwise to adopt any policy involving\ngreat immediate suffering for the sake of even a great gain in the\ndistant future, because the gain may never be realized (RoE:\n203/Papers 9: 371).\n", "\nThus despite the desirability of socialism (in Russell’s eyes at any\nrate) the Bolshevik program had to be rejected for utilitarian or\nconsequentialist reasons. (See also The Practice and Theory\nof Bolshevism, particularly Part II. ch.iv.) The Bolshevik\n“habit of militant certainty about doubtful matters”\n(Practice and Theory: xi) was not only irrational, but\ndangerous, since it led to pointless suffering. Hence\n“The Need for Political Skepticism”, the title of one of\nRussell’s essays, and a major theme in his moral and political writing\n(Sceptical Essays: ch. 11). Dogmatism leads to cruelty since\nit encourages people to overestimate the likelihood that their\nobjectives will be realized and hence to exaggerate the expected\nutility of persecuting policies. Scepticism (or\n“fallibilism” as we would nowadays tend to say) is the\nantidote. Hence the maxim that Russell puts into the mouth of la\nRochefoucauld: “It does not matter what you believe, so long as\nyou don’t altogether believe it” (Fact and Fiction:\n185)." ], "section_title": "5. Politics, Consequentialism and the Need for Skepticism", "subsections": [] }, { "main_content": [ "\nThe criterion of expected utility had another advantage for Russell.\nIt allowed him to recommend a less “conservative and\nanti-reforming” version of Moore’s principle that “the\nindividual can be confidently recommended … to conform to rules\nwhich are generally useful and generally practiced.” Russell was\nan act-consequentialist rather than a rule-consequentialist. An act is\nright if the expected consequences of performing it are as good or\nbetter than any other. It is not right because it conforms to some\nrule, even a rule that it is generally useful to obey. Nevertheless,\nrules are necessary because we do not have world enough and time to\ncalculate the consequences of every act.", "\n\n\nI think that, speaking philosophically, all acts ought to be judged by\ntheir effects; but as this is difficult and uncertain and takes time,\nit is desirable, in practice, that some kinds of acts should be\ncondemned and others praised without waiting to investigate\nconsequences. I should say, therefore, with the utilitarians, that the\nright act, in any given circumstances, is that which, on the data,\nwill probably produce the greatest balance of good over evil of all\nthe acts that are possible; but that the performance of such acts may\nbe promoted by the existence of a moral code. (RoE:\n216/Power: 168)\n", "\nThus Russell believed that it is generally right to obey\n“generally useful” rules, though these are “rules of\nthumb” and there may be circumstances in which it is right (that\nis obligatory) to break them.", "\n\n\nEven the best moral rules, however, will have some\nexceptions, since no class of actions always has bad [or\ngood!] results. (RoE: 137/Religion and Science:\n227–8)\n", "\nBut though Russell thought it is generally right to obey generally\nuseful rules, he also thought that many of the rules that are\n“generally practiced” are not “generally\nuseful”. Sometimes they derive from bygone superstitions and\nsometimes they foster the interests of the powerful at other peoples\nexpense.", "\n\n\nPrimitive ethics …select certain modes of behavior for censure\n[or praise] for reasons which are lost in anthropological obscurity.\n(Education and the Social Order: 23)\n", "\nHowever,", "\n\n\none of the purposes—usually in large part unconscious—of a\ntraditional morality is to make the existing social system work. It\nachieves this purpose, when it is successful, both more cheaply and\nmore effectively than a police force does … The most obvious\nexample … is the inculcation of obedience. It is (or rather\nwas) the duty of children to submit to parents, wives to husbands,\nservants to masters, subjects to princes, and (in religious matters)\nlaymen to priests. (RoE: 207/Power: 157)\n", "\nThus Russell was inclined to agree with Plato’s Thrasymachus, at least\nto the extent that what passes for justice is often\n[to] the advantage of the stronger [that is the ruling caste, class or\ngender]. Russell was opposed both to power-moralities (codes designed\nto bolster the interests of exploitative elites) and to the senseless\nand often pernicious remnants of defunct superstitions.", "\n\n\nAn ethic not derived from superstition must decide first upon the kind\nof social effects which it desires to achieve and the social effects\nwhich it desires to avoid. It must then decide, as far as knowledge\npermits, what acts will promote the desired consequences: these acts\nit will praise, while those acts having a contrary tendency it will\ncondemn. (Education and the Social Order: 73)\n", "\nIt was Russell’s mission as a practical moralist, a social reformer\nand a popular sage to promote a humane and non-superstitious ethic.\nThis was partly a matter of preaching and partly a matter of argument:\npreaching as regards ends and argument as regards means.", "\nIn the latter, and more preachy, part of his career, it was Russell’s\ndominant view that judgments about what things are good or bad as ends\ndo not have a truth-value. To say that it is a good thing “that\nthe individual, like Leibniz’s monads should mirror the world”\n(Education and the Social Order: 10) is to say something like\n“Would that everyone desired that the individual, like one of\nLeibniz’s monads, should mirror the world!” Since this is\nneither true nor false, it cannot be rationally argued for. The best\nwe can do is to remove objections and present the end in a favorable\nlight. Russell was perfectly clear about this.", "\n\n\nWhy [should the individual mirror the world]? I cannot say why, except\nthat knowledge and comprehensiveness appear to me glorious attributes\nin virtue of which I prefer Newton to an oyster. The man who holds\nconcentrated within his own mind, as within a camera obscura,\nthe depths of space, the evolution of the sun and its planets, the\ngeological ages of the earth, and the brief history of humanity,\nappears to me to be doing what is distinctively human and what adds\nmost to the diversified spectacle of nature.\n", "\nThis is eloquent stuff (and too me, at least, convincing) but it\nhardly constitutes an argument. And this Russell freely admitted.", "\n\n\nUltimate values are not matters as to which argument is possible. If a\nman maintains that misery is desirable and that it would be a good\nthing if everybody always had a violent toothache, we may disagree\nwith him, and we may laugh at him if we catch him going to the\ndentist, but we cannot prove that he is mistaken as we could if he\nsaid that iron is lighter than water … As to ultimate values,\nmen may agree or disagree, they may fight with guns or with ballot\npapers but they cannot reason logically. (Education and the Social\nOrder: 136)\n", "\nThis is rather disconcerting, especially if we replace the comic\nexamples that Russell employs in Education and the Social\nOrder (he imagines a prophet “who advance[s] the theory\nthat happiness should be confined to those whose first names begin\nwith Z”) with the real-life moral elitists and chauvinists that\nhe discusses in other works of the 1930s and 1940s. Nietzsche and the\nNazis really did believe that the sufferings of some people were not\nsignificant evils (herd-men in the case of Nietzsche, Jews, Slavs and\nGypsies in the case of the Nazis) and it was Russell’s thesis that no\nrational argument could be advanced against them.", "\n\n\nLet us consider two theories as to the good. One says, like\nChristianity, Kant, and democracy: whatever the good may be, any one\nman’s enjoyment of it has the same value as any other man’s. The other\nsays: there is a certain sub-class of mankind—white men,\nGermans, gentiles, or what not—whose good or evil alone counts\nin an estimation of ends; other men are only to be considered as means\n… When [irrelevant] arguments are swept away, there remains, so\nfar as I can see, nothing to be said except for each party to express\nmoral disapproval of the other. Those who reject this conclusion\nadvance no argument against it except that it is unpleasant.\n(“Reply to Criticisms” RoE: 146–147/Papers\n11: 48–49)\n", "\nBut unpleasant as this conclusion may be, it does not imply that those\nwith a humane and egalitarian conception of the good should give up\npreaching on its behalf. On the contrary, such preaching becomes\nimperative, especially for those with rhetorical gifts. Which is why\nRussell devoted so much time and effort to this activity.", "\n\n\nAccording to me, the person who judges that A is good is\nwishing others to feel certain desires. He will therefore, if not\nhindered by other activities, try to rouse these desires in other\npeople if he thinks he knows how to do so. This is the purpose of\npreaching, and it was my purpose in the various books in which I have\nexpressed ethical opinions. The art of presenting one’s desires\npersuasively is totally different from that of logical demonstration,\nbut it is equally legitimate. (“Reply to Criticisms”\nRoE: 149/Papers 11: 51)\n", "\nPersuasion as regards ends may be a non-rational process, but that\ndoes not mean that it is irrational, let alone wrong, to\nengage in it.", "\nWhen it comes to means however, rational argument becomes a genuine\npossibility. It might seem otherwise since judgments about what is\nright or what ought to be done—which for Russell are essentially\nconcerned with means—would appear to be as incapable of truth as\njudgments about what is good and bad. In Russell’s view, “the\nright act, in any given circumstances, is that which, on the\ndata, will probably produce the greatest balance of good over\nevil” and the right rule or policy is likewise\nthe one that can be expected to produce the best effects. That is,\n“X is right” is assertible (roughly, a\nsensible thing to say) when X can be expected to lead to the\nbest results. But if “Y is good”, is really in the\noptative mood, amounting to the exclamation “Would that everyone\ndesired Y!”, then “X is right” would\nappear to be optative too, since it comes down to something like\n“X leads to more of what [would that everyone\ndesired!]”. Here, the clause in square brackets, which is\nobviously in the optative mood, infects the entire sentence with its\noptative character. “X leads to more of what [would that\neveryone desired!]”, in so far as it can be made sense of, does\nnot seem to be the kind of thing that could be true or false.", "\nHowever, Russell believed that judgments about what is right or what\nought to be done can be given an analysis which gives them a\nsort of ersatz objectivity and hence the possibility of truth. If\nDmitri has a reasonably determinate conception of the good, that is, a\ncoherent set of opinions about which things are good and which bad,\nthen although Dmitri’s opinions themselves are neither true\nnor false—since, despite appearances they are not really\nopinions at all but optative expressions of Dmitri’s desires—it\ncan nevertheless be true or false that X is good in Dmitri’s\nopinion, that is, good-according-to-Dmitri. “Oh to be in\nEngland, now that April’s here!” is neither true nor false, but\nif I say it sincerely, it will in fact be true that I desire to be in\nEngland. Similarly, if Dmitri says that “Bungy-jumping is\ngood” what he says won’t be true, since really it is in the\noptative mood, but if he says it sincerely, it will be true that\nBungy-jumping is good-in-Dmitri’s-opinion, or\ngood-according-to-Dmitri. Thus although there are no facts of the\nmatter about which things are good or bad, there are facts of\nthe matter about which things are believed by this or that\nperson to be good or bad. Furthermore—and this is the crucial\npoint—there are facts of the matter about whether a given action\nor a given policy is likely to promote what somebody-or-other\nbelieves to be good. Since Hitler believed that victory over\nBritain would be good, there was a fact of the matter about whether\nbombing London as opposed to bombing the RAF’s airfields would be\nlikely bring about the states of affairs that he desired. As it turned\nout, the policy he pursued did not produce results that were\nbest-according-to-Hitler. Hence if Hitler had adopted a\nconsequentialist reading of “ought”, and had indexed it to\nhis own requirements, “I ought to bomb London” (as said by\nHitler) would have been false. And its truth or its falsehood\nwould have been a factually arguable question.", "\nNow, suppose we define the right act with respect to\nB, not as “that which, on the data, will probably produce\nthe greatest balance of good over evil” but as “that\nwhich, on the data, will probably produce the greatest balance of what\nB believes to be good over what B believes to be\nevil”. The right rule of policy with respect to B will\ncorrespondingly be defined as the rule or policy that will probably,\nin the appropriate circumstances, produce the greatest balance of what\nB believes to be good over what B believes to be\nevil. Then, so long as B has a reasonably coherent set of\nideals, the claim that a given act or policy is right or wrong with\nrespect to B will usually have a determinate truth-value.\nClaims of the form “X is right wrt to B”\nwill be either true or false, so long as the person (or group of\npersons) designated by B has a clear and consistent set of\nvalues. There will thus be a fact of the matter about whether X\nis right wrt to B which can be the subject of rational enquiry.\nAnd if “B” stands in for us (whoever\n“we” may be) and if we share a reasonably\ncoherent set of ideals, then there will be a fact of the matter about\nwhether X is right or wrong with respect to our ideals. Thus if\nthere is agreement with respect to ideals and if we adopt a\nconsequentialist conception of rightness, indexed, not to what\nis good, but to what we believe to be good, then we\ncan have a rational debate—maybe even a scientific\nenquiry—about the rights and wrongs of actions, rules or\npolicies, or at least about their rightness or wrongness with respect\nto us.", "\n\n\nThe framing of moral rules, so long as the ultimate Good is supposed\nknown, [Russell should have said ‘supposed agreed’] is a\nmatter for science. For example: should capital punishment be\ninflicted for theft, or only for murder, or not at all? Jeremy\nBentham, who considered pleasure to be the Good, devoted himself to\nworking out what criminal code would most promote pleasure, and\nconcluded that it ought to be much less severe than that prevailing in\nhis day. All this, except the proposition that pleasure is the Good,\ncomes within the sphere of science. (RoE:\n137–138/Religion and Science: 228–229)\n", "\nOnce the ends have been agreed, we can have a rational debate about\nthe code most likely to promote those ends. In some cases, such\nquestions can be resolved by scientific enquiry, or at any rate by\nstatistics. But (with one or two exceptions) rational argument is only\nreally possible when we take the ends as read and confine our\nattention to the means.", "\nWe are now in a position to understand Russell’s general strategy as a\npolemicist for moral reform and its relation to his emotivist\nmeta-ethic." ], "section_title": "6. Consequentialism, Emotivism and Moral Reform", "subsections": [] }, { "main_content": [ "\nBefore going on to discuss Russell’s meta-ethic in more detail, it is\nworth pausing for a moment to consider his ideal. For although Russell\nclaimed to make his “practical moral judgments” on a\n“roughly hedonistic basis” (RoE:\n165–6/Papers 11: 311), he was far from being an out-and\nout hedonist. He was, as we have seen, a utilitarian of sorts, who\nbelieved that the right thing to do is the action that, on the\navailable evidence, seems likely to produce the best balance of good\nover evil consequences. Since we cannot perform the requisite\ncalculations in every case, we need codes of conduct, though these\nshould be taken with a pinch of salt and reassessed from time to time\nin the light of new information. This is sensible and humane, but\nperhaps a little pedestrian. However Russell’s conception of the\ngood—the end to be promoted—is a bit more interesting. To\nbegin with, although he valued human happiness, he did not see this in\ncrudely hedonistic terms. However pleasurable the life of a pig may\nbe, Russell would not have preferred the life of a pig to that of a\nhuman being. Russell also valued passion and a life which\nallowed for spontaneous (but “creative”) impulses. These\nviews distinguish him from the classical utilitarians who he otherwise\nadmired. However, the really distinctive features of Russell’s ethic\nwere derived from Spinoza (1632–1677), who remained a\nphilosophical hero even though Russell rejected most of his\nmetaphysics as set out (rather confusingly) in his Ethics of\n1677. There was something about Spinoza’s attitude to life that\nRussell regarded as profoundly right. Kenneth Blackwell calls this\n“the ethic of impersonal self-enlargement” (Blackwell\n1985: 17). According to this ideal, the best life is lived in\nawareness of the Other. This includes other selves (since Russell\nconsidered a purely selfish life unfulfilling, and a life without\nhistory—which involves knowledge of other\nselves—drab) but also the wholly other—the\nnon-human universe of large impersonal forces, the wind, the sea, the\nmountains and the stars and even (if they exist) the entities of\nmathematics. He felt that the self is enlarged by the contemplation of\nthe not-self and that the person whose concerns are limited to their\nown states of mind has confined themself within a spiritual prison. By\nthe same token, a philosophy that reduces reality to an emanation\neither of the self or of the collective reduces the self by denying it\naccess to the Other. All this may sound unduly elevated, but in\npractice what this means is that the good person takes an interest in\nother people (including people who may not be connected with them) and\nin the world at large. Russell sometimes talks about contemplation in\nthis connection, but this should not be understood as a purely passive\nprocess. The contemplative person does not just sit and stare (though\nRussell was not averse to this kind of contemplation) but actively\nseeks to know the Other through science, history and other forms of\nenquiry. Thus Russell’s distaste for idealism and for anti-realist and\ninstrumentalist philosophies of science is connected with his ideal of\nimpersonal self-enlargement. Of course Russell does not attempt to\nderive an Is (such as the claim that idealism or pragmatism\nis false) from an Ought (such as the claim that we\nought to enlarge the Self through contemplation of the Other,\nsomething that would be difficult if either of these philosophies were\ncorrect). But he does suggest that there is something morally suspect,\nas well as wrong-headed, about attempts to reduce the vast forces of\nnature to human experience or to useful predictive devices enabling\nhuman beings to achieve their puny ends. For Russell the good life is\na life that looks outward, which is one reason for his dislike of\nphilosophies that diminish what is outside ourselves into something\nnot worth looking at. (See RoE: 223–235 and, more\ngenerally, The Conquest of Happiness, 1930.)" ], "section_title": "7. Russell’s Ideal: the Influence of Spinoza", "subsections": [] }, { "main_content": [ "\nA we have seen, Russell’s meta-ethic was closely connected to his\nprogram of moral reform. The idea was to advocate a set of humane and\negalitarian ends, using non-rational methods of persuasion, and then\nto argue on the basis of psychology, social science, history and\ncommon sense that that these ends would be best achieved if, on the\nwhole, people obeyed a reformed moral code. Judgments that this or\nthat is good or bad were to be construed as disguised optatives\n(“Would that everyone desired X!” and “Would\nthat everyone desired not Y!” respectively).\n“Ought” and “right” were to be given a\nconsequentialist reading and indexed to the ends that Russell hoped\nhis audience could be persuaded to share. Thus Russell combined an\nemotivist analysis of “good” and “bad” with a\nconsequentialist/relativist reading of “ought” and\n“right”. But was he right to do so?", "\nAlthough Russell and Santayana were toying with emotivism in the\n1910s, it was not until the 1930s that the theory really hit the\nphilosophical headlines. Since then it has taken a beating, and\nalthough it still finds favor with the semi-philosophical public, it\nis no longer widely believed by professional philosophers. Relativism\nlikewise is generally regarded as a down-list option, though, as with\nemotivism, there are one or two distinguished philosophers who are\nprepared to stick up for it. Does Russell’s meta-ethic stand up\nagainst the objections that have laid emotivism and relativism\nlow?" ], "section_title": "8. Objections to Emotivism and Relativism", "subsections": [ { "content": [ "\nAccording to Stevenson and Ayer the function of moral judgments is to\nexpress approval and disapproval. But to approve of X is to\nthink or feel that X is good or right: to disapprove is to\nthink or feel that it is bad or wrong. Thus the emotivist analysis of\nthe moral terms is viciously circular. (Russell himself had developed\na similar line of argument against theories which identify rightness\nwith a tendency to arouse approval in his “The Elements of\nEthics” (1912).)", "\nThis objection leaves Russell untouched. To approve of X may be\nto think or feel that X is good, but for Russell to think\nX good is not to approve of it, but to desire that everyone\nshould desire X. Implausible as this may be, there is no\ncircle, vicious or otherwise." ], "subsection_title": "8.1 The Vicious Circle Problem" }, { "content": [ "\nIf judgments about what is good or bad in itself merely express\napproval and disapproval, then “X is good” said by\nme and “X is bad” said by you do not contradict\none another. After all, I am merely expressing my feelings whilst you\nare expressing yours, and there is nothing remotely inconsistent about\nthe supposition that X arouses approval in me and disapproval\nin you. But plainly when I call X good and you call it bad we\nare contradicting one other. Hence emotivism, which seems to\nimply otherwise, is false.", "\nAgain, Russell’s brand of emotivism is immune to this objection.\nAccording to Russell, “X is good” and\n“X is bad” are really in the optative mood despite\ntheir indicative appearances. As such, they express desires or wishes,\nand desires and wishes can, in a sense, be inconsistent with one\nother, namely when they are not (in Russell’s phrase)\n“compossible”, that is, when they cannot both be realized.\n“Would that I had all the ice-cream!” said by me and\n“Would that I had all the ice-cream!” said by you\nexpress contradictory desires since we cannot both have all the\nice-cream. As such, the two optatives contradict each other, not\nbecause they describe incompatible facts but because\nthey prescribe incompatible states of affairs.\nSimilarly “X is good” said by me and\n“X is bad” said by you express contradictory\ndesires and hence contradict each other. For “X is\ngood” means “Would that everybody desired X!”\nand “X is bad” means “Would that everybody\ndesired that not-X!”, and the desires expressed by these\ntwo optatives are not compossible, or at least, are only compossible\non the condition that we all have inconsistent desires (both for\nX and for not-X).", "\nBut the situation is a little different when we come to judgments\nabout what is right or what ought to be done. As we\nhave seen, Russell is inclined to give such judgments a\nconsequentialist reading and then to index them to some presumed set\nof projects. It is therefore true with respect to, say,\nRussell and myself that we ought to abolish the Death Penalty, since\nabolishing the Death Penalty is conducive to the ends that we happen\nto favor. But it is equally true with respect to some hardcore\nretributivist that we ought not to abolish the Death penalty,\nsince it is not conducive to the eye-for-an-eye ends that\nshe considers good. And this seems to be a problem. For when\nRussell and I say we ought to abolish the Death Penalty and\nthe retributivist says we that we ought not, it seems that we\nare contradicting each other. Yet if the two “oughts” are\nindexed to different visions of the good, it seems they are quite\ncompatible. What Russell and I are saying is that abolishing the Death\nPenalty can be rationally expected to maximize the things we\nconsider good and to minimize the things that we consider\nevil. What the retributivist is saying (if she is a consequentialist)\nis that not abolishing the Death Penalty can be rationally\nexpected to maximize the things she considers good (which\ninclude retributive punishment) and to minimize the things\nshe considers evil (such as murderers not getting their just\ndeserts). And these claims can both be true. Hence Russell’s theory\nbrings about a spurious appearance of semantic harmony where in fact\nthere is conflict and contradiction. His theory suggests that the\nfriends and foes of the Death Penalty are not contradicting\neach other, when in fact it is evident that they are. Genuine\ndisagreement would only be possible between those who agreed about the\nends but disagreed about the means. Thus if (in 1940) Hitler claimed\nthat the Luftwaffe ought to bomb London rather than the RAF airfields\nwhilst Goering claimed that the Luftwaffe ought to bomb the RAF\nairfields rather than bombing London, the two would be in\ncontradiction since their ends were presumably the same. But their\nviews would be quite compatible with those of a pacifist who claimed\nthat nobody ought ever to bomb anything!", "\nRussell himself had raised much the same objection against relativist\ndefinitions of “good” and “bad” in 1912:", "\n\n\nIf in asserting that A is good, X meant merely to assert\nthat A had a certain relation to himself such as pleasing his\ntaste in some way [or being conducive his ends] and Y, in\nsaying that A is not good, meant merely to deny that A\nhad a like relation to himself; then there would be no subject of\ndebate between them. (Philosophical Essays:\n20–21/Papers 6: 222)\n", "\nBut, as Russell plainly believes, there is a subject of\ndebate between them, which means that relativistic readings of\n“good” and “bad” must (at least sometimes) be\nwrong. A similar problem afflicts his own subsequent analyses of\n“ought” and “right”. Since their\n“oughts” are indexed to different ends, it seems that when\nthe Nazi says “We ought to bomb London” and the pacifist\nsays “Nobody ever ought to bomb anything” they are not\ncontradicting one another, though it is as clear as daylight that they\nare.", "\nRussell might reply that his suggestion is not intended as an\naccount of what “right”, “wrong” and\n“ought” actually mean, but as proposal\nabout what they ought to mean. His theory is not intended as\na description of our current semantic slum, but as a scheme\nfor linguistic reform. It may be that at present we\ntake those whose “oughts” are indexed to different ends to\nbe contradicting one other but Russell is hoping to change all that.\nGiven current usage, when Hitler says “We ought to bomb\nLondon” and the pacifist says “Nobody ever ought to bomb\nanything”, the two claims contradict each other, but once\nRussell’s reform is has been implemented this disagreeable dispute\nwill be smoothed into non-existence.", "\nThe problem with this is that Russell’s “proposal” is not\na very attractive one. One of the things we want to do with\nmoral language is express our disagreements. Russell’s new-fangled\n“ought” would be unable fulfill one of the most important\nlinguistic functions of the old-fashioned “ought”, namely\nto express that fact that people with different ends disagree (as we\nwould now put it) on what ought to be done. In depriving\npeople with different ends of the means to contradict each other\nRussell would be doing them a disservice. Moreover, Russell would be\nleft with a peculiarly ramshackle meta-ethic. He would have a\ndescriptive account of what “good” and “bad”\ndo mean and a prescriptive suggestion about the\nabout what “right”, “wrong” and\n“ought” ought to mean. There is no actual\ninconsistency in this but it does seem to be a bit anomalous. If the\nname of the game is to analyze the moral concepts, then it\nseems Russell’s analysis of “right” and\n“ought” is wrong. But if the name of the game is to\nreform the moral concepts, then why not subject\n“good” and “bad” to the same treatment, giving\nthem the kind objectivity that Russell would evidently have preferred\nthem to have?" ], "subsection_title": "8.2 The Problem of the Disappearing Dispute" }, { "content": [ "\nAnother problem is that the later Russell’s account of\n“ought”-judgments runs foul of Moore’s Open Question\nArgument (as his earlier self could have told him). To say that\nA ought to do X (with respect to B) is to say\nthat on the available evidence A’s doing X would be most\nlikely to maximize what some contextually specified person or group\nB takes to be good and to minimize what B takes to\nbe evil. But, construed as an account of what we actually mean, this\nis obviously incorrect. As Russell himself had nearly put it thirty\nyears earlier:", "\n\n\nIt is held that what we ought to do is that action, among all that are\npossible, which [is likely on the available evidence] to produce the\nbest results on the whole [according to some contextually specified\nstandard of goodness]; and this is regarded as constituting a\ndefinition of ought. I hold that this is not a definition,\nbut a significant proposition … It might be proved, in the\ncourse of moral exhortation, that such and such an action [is likely\non the available evidence to] have the best results [according to some\ncontextually specified standard of goodness]; and yet the person\nexhorted might inquire why he should perform the action. The exhorter\nwould have to reply: “Because you ought to do what [is likely\nto] have the best results [according to some contextually specified\nstandard of goodness].” And this reply distinctly adds\nsomething. The same arguments by which good was shown to be\nindefinable can be repeated here, mutatis mutandis, to show\nthe indefinability of ought. (RoE: 101/Papers 4:\n573, somewhat modified)\n", "\nThus Russell is making exactly the same mistake that he accused Moore\nof making in 1904!\n (See above, §4).", "\nAgain Russell might reply that he is not attempting to describe how we\nactually use “ought” but making a suggestion\nabout “ought” should be used. But if we are to ring out\nthe old “ought” and ring in the new, we need to be assured\nthat this would be a good idea. And that requires something rather\nmore solid in the way of a cost/benefit analysis than Russell manages\nto supply." ], "subsection_title": "8.3 “Ought” and the Open Question Argument" }, { "content": [ "\nIt is a common complaint against emotivism that it precludes the\npossibility of moral arguments that are valid in a non-trivial sense.\nAn argument is formally valid if and only if, no matter how the\nnon-logical vocabulary is interpreted, the premises cannot be true and\nthe conclusion false. But if the premises of a moral argument are not\ntruth-apt—if they are semantically incapable of truth\nor falsity—then all moral arguments, no matter how obviously\n“illogical” they may appear, will be trivially valid,\nsince the premises cannot be true! We can avoid this absurdity by\nmaking explicit what the standard definition of validity\npresupposes—that an argument cannot be a candidate for\nvalidity unless the premises and the conclusions are both truth-apt.\nBut if we do that, moral arguments cease to be candidates for\nvalidity, no matter how logically impeccable they may appear to be.\nStevenson (1944: 154–159) accepts this conclusion as a\nconsequence of his theory, but to the rest of us it seems a very large\ndead rat to swallow.", "\nRussell is immune to this argument as regards “ought”,\n“right” and “wrong” since in his view\nought-judgments are susceptible to truth and falsity. “It is\nwrong (wrt to B) to kill the innocent” is a truth-apt\nexpression. Hence the argument “It is wrong (wrt to B) to\nkill the innocent; to bomb the village would be to kill the innocent:\ntherefore it is wrong (wrt to B) to bomb the village”, is\na candidate for validity, and is in fact, valid. To argue from the\nsame premises that it would be right (wrt B) to bomb\nthe village would be obviously fallacious.", "\nBut what about this argument?", "\nTherefore", "\nIsn’t it obviously valid? And wouldn’t it be obviously\ninvalid to conclude from the same premises that contemplating\nMichelangelo’s David would be bad? Yet if arguments involving\n“good” are not even candidates for validity, it appears\nthat the two arguments are on a par!", "\nThis is a telling objection against some forms of emotivism\nwhich portray moral judgments as mere expressions of raw feeling,\nanalogous to cries of ecstasy or groans of pain. But Russell is better\nplaced to meet this difficulty, since in his view judgments about what\nis ultimately good and bad are disguised optatives, designed to\nexpress desires or wishes of a certain kind. And it is possible to\nconstruct a rudimentary concept of logical consequence (and hence of\nvalidity) that applies to arguments in the optative mood. Sentences in\nthe optative have fulfillment conditions just as sentences in the\nindicative have truth-conditions. To understand an optative sentence\nis a) to understand that it is in the optative and b) to\nunderstand what the world would have to be like to satisfy the desires\nor the wishes expressed. Just as indicative validity can be defined in\nterms of truth, optative validity can be defined in terms of\nfulfillment. (It would be nice to talk of “satisfaction”\nrather than “fulfillment” here, but the word\n“satisfaction” has been preempted to stand for a different\nbut related notion.) An optative sentence Q is the logical\nconsequence of a set of optative sentences P and a (possibly\nempty) set of factual sentences C, if and only if, however the\nnon-logical vocabulary is interpreted, the desires expressed in\nP cannot be fulfilled under the circumstances described in\nC unless the desire expressed by Q is fulfilled too. An\noptative argument is valid if the conclusion is an optative\nconsequence of the premises; invalid otherwise. Hence there can be\nvalid (and invalid!) arguments about goodness as well as logical\nrelations between the relevant sentences. Thus our argument\nbecomes:", "\nThis is not perhaps a very plausible reconstruction of the original\nargument, but it is logically valid in the sense defined. For\nthe wish expressed at premise 1′) cannot be fulfilled under the\nfactual conditions specified at premise 2′) without fulfilling\nthe wish expressed at the conclusion 3′)." ], "subsection_title": "8.4 The Problem of Validity" }, { "content": [ "\nBut there is another broadly logical objection to emotivism that is\nmuch more difficult for Russell to meet. The objection was first\nmooted by W.D. Ross (1939) but it was reinvented and refined by P.T.\nGeach (1960, 1965), who modestly attributes it to Frege. Consider the\nfollowing obviously valid argument:", "\nTherefore", "\nIn this argument, the sentence “It is always good to contemplate\nbeautiful works of art”, occurs twice. In (1) it occurs by\nitself as an assertion; in (2) it occurs unasserted as part of a\nlarger sentence. We know what the sentence is supposed to mean at its\nfirst occurrence—despite its indicative appearance it is really\nin the optative mood and expresses a wish: “Would that everyone\nalways desired to desire to contemplate beautiful works of\nart!”. But what about its second occurrence where it\nappears as the antecedent to a conditional? Is it expressing that wish\nthere? Surely not. For someone can subscribe to the conditional (2)\nwhilst rejecting the relevant wish. For example, we can imagine\nsomebody reasoning like this:", "\nTherefore", "\nThe person who accepts this argument clearly does not wish\nthat everyone should always desire to contemplate beautiful works of\nart. But she subscribes to premise (2) nonetheless. Thus the sentence\n“it is always good to contemplate beautiful works of art”,\ncannot generally be construed as an optative when it occurs in an\nembedded context (that is when it occurs as a sub-sentence within a\nlarger, more complex sentence). This is already a very damaging\nobjection to Russell’s theory of how “good” functions,\nsince it shows that the theory is radically incomplete. Russell can\nonly account for a very restricted class of cases, namely those in\nwhich sentences of the form “X is good” are used by\nthemselves to make an assertion, not the numerous cases in which such\nsentences occur, unasserted, as components of larger sentences. (It\nis, so to speak, a theory of the semantic atoms that cannot account\nfor their role within semantic molecules.) But there is worse to come.\nSuppose Russell added one or more epicycles to his theory to explain\nhow “X is good” manages to be meaningful in\nunasserted contexts. The revised theory would have to distinguish\nbetween different uses of “good”, giving one account for\nasserted contexts and a different account (or set of accounts) for the\nunasserted contexts. Thus “X is good” would\nsometimes be a disguised optative and sometimes something else. (Never\nmind what—it does not really matter.) Now, consider the\nfollowing argument schema:", "\nTherefore", "\nIn this argument “X is good” would have one meaning\nin premise (i)—in which it would be an optative—and\nanother in premise (ii)—in which it would be a creature of some\nother semantic kind. (I have emphasized the point by putting the first\noccurrence in italics and the second in bold.) But an argument is only\nvalid if the words involved retain the same meanings throughout the\ninference. If not, we have an instance of the fallacy of equivocation.\nSo it looks as if any attempt to deal with Geach’s first\nproblem by explaining how “good” works in unasserted\ncontexts would have the unintended side-effect of converting obviously\nvalid arguments such as the above into instances of equivocation. Not\nonly is the theory radically incomplete—if it were\ncompleted, it would reduce a huge number of obviously valid arguments\nto invalidity by construing them as equivocal.", "\nThis is, perhaps, the leading problem for non-cognitivist or\nexpressivist theories of value and a vast amount of ink has been spilt\ntrying to solve it. (See, for instance, A. Miller, 2013,\nContemporary Metaethics: an Introduction, 2nd edn:\n6, 37–9, 53–67, 68, 70–1, 73, 79n23, 89–102,\n118, 127–32 & 245 and Schroeder, 2010, Non-Cognitivism\nin Ethics: chs. 3, 4 & 7.) It would take me too far afield to\ndiscuss the matter in detail. Suffice to say that Russell’s theory\nfaces ship-wreck unless this problem can be solved and, in my opinion,\nthe problem is insoluble." ], "subsection_title": "8.5 Geach’s Problem" }, { "content": [ "\n\n\nI am accused of inconsistency, perhaps justly, because, although I\nhold ultimate ethical valuations to be subjective, I nevertheless\nallow myself emphatic opinions on ethical questions.\n", "\nThus wrote Russell in reply to critics who thought that his emotivism\nprecluded him from being so relentlessly preachy. There was, they\nthought, some kind of pragmatic inconsistency between vehement moral\nopinions (frequently voiced) and meta-ethical emotivism (RoE:\n145–150/Papers 11: 48–52). Russell makes short\nwork of this. In his view the function of the words “good”\nand “bad” is to express certain kinds of desires. Since he\nhad the relevant desires there was no inconsistency in his\nusing “good” and “bad” to express the desires\nthat they were designed to express. There is nothing inconsistent\nabout using a piece of verbal machinery to do what you think it is\ndesigned to do.", "\n\n\nI am quite at a loss to understand why any one should be surprised at\nmy expressing vehement ethical judgments. By my own theory, I am, in\ndoing so, expressing vehement desires as to the desires of mankind; I\nfeel such desires, so why not express them?\n", "\nNor (as he might have added) is there any inconsistency between\nRussell’s meta-ethical emotivism and his moral and political activism.\nTo think, for example, that nuclear war would be bad is to desire that\neveryone not desire it, a desire that presumably springs from a\nfirst-order desire that there should be no such thing. In trying to\navert nuclear war, therefore, Russell was acting on a desire that for\nhim had a high priority. Which looks like an eminently rational thing\nto do." ], "subsection_title": "8.6 Commitment and Inconsistency" }, { "content": [ "\nBut in defending himself against the charge of inconsistency, Russell\nmakes a crucial concession.", "\n\n\nBut what are “good” desires? Are they anything more than\ndesires that you share? Certainly there seems to be something\nmore … In opposing the proposal [to introduce bull-fighting\ninto America], I should feel, not only that I was expressing\nmy desires, but that my desires in the matter are right,\nwhatever that may mean.\n", "\nWhat exactly is it that Russell feels? That those who think\nbull-fighting is good (and therefore desire it) are making some kind\nof mistake and conversely that those think that bull-fighting\nis bad (and are therefore opposed to it) are in some sense getting\nit right. Thus the “something more” that Russell\ncould not help feeling was that his views about the badness of\nbullfighting were true and the views of the imaginary\nbull-fighting aficionados false. But how can that be if\n“bull-fighting is bad,” really is in the optative? For a\nsentence to be true or false it must be semantically capable of truth\nand falsity or, as the current jargon has it, truth-apt. Thus\nin admitting that he could not help feeling that he would be right\n(that is, correct) to oppose bull-fighting in America, Russell, was\nadmitting to feelings which suggest that his meta-ethic is false.\nMoreover the very fact that he had these feelings provides\nevidence for his theory’s falsehood. Consider “Oh to be in\nEngland, now that April’s here!”, a sentence that is clearly in\nthe optative (except for the bit about April’s being here). It is hard\nto see how anybody who understood this sentence could coherently feel\nor think it to be true or false. Its optative character is obvious (to\nthose who understand English) and the fact that it is in the optative\nexcludes the possibility of truth and falsehood. Since Russell\nwas inclined to feel that “Bull-fighting is bad”\nis true, and since this is not an incoherent thing to feel or think,\nthis strongly suggests that “bull-fighting is bad”, unlike\n“Oh to be in England!”, is not in the optative mood.", "\nIndeed there is something odd about the very idea of a disguised\noptative. Of course, it is possible to give orders or express wishes\nby means of sentences that are grammatically in the indicative mood.\nHenry IV’s “You have good leave to leave us”, is\ngrammatically in the indicative but it is merely a slightly less curt\nvariant of the obviously imperative “Worcester, get thee\ngone” (Shakespeare, Henry IV, 1.3). But when we use\nindicatives to express wishes or convey commands we are engaging in\ncommunicative acts which would misfire badly if the people we were\ntalking to failed to get the point. Even if King Henry had confined\nhimself to “You have good leave to leave us”, omitting the\nexplicitly imperative “Worcester, get thee gone”,\nWorcester would have had to be singularly obtuse not to realize that\nhe was being ordered to leave. Competent speakers are usually well\naware when a grammatically indicative sentence is being used to give a\ncommand or express a desire (indeed, this is one of the\ncriteria of linguistic competence!). But it is Russell’s\nhypothesis that, despite appearances, “X is good”\n(in the sense of good as an end) is exclusively in the optative mood\neven though, for most people, it is neither intended nor interpreted\nas such. We have been good-ing and bad-ing things up and down for\nhundreds of years whilst radically misunderstanding the meanings of\nour own utterances. To suppose this is to suppose that meaning is\nindependent of our collective intentions, which is a very large dead\nrat to swallow. Russell might reply that our usage belies our stated\nintentions, that we use “X is good” as if\nit were in the optative, and that despite our protestations to the\ncontrary, his theory provides the best explanation of our\nactual use. The problem with this reply is that it is based on an\nobviously false premise. We don’t in fact use “X is\ngood” as if it were in the optative mood—we treat as if it\nwere truth-apt. This brings me to the most obvious and perhaps the\nmost compelling objection to emotivism—what I like to call the\nDuck Argument.", "\nThe main problem for most forms of non-cognitivism is that moral\njudgments look and behave like propositions—that is, in this\nconnection, the kinds of things that can be true or false. They have,\nas the jargon has it, a “propositional surface”. We claim\nthat such sentences are true or false, we speak of knowing\nthe difference between good and bad, right and wrong (where knowledge\nwould appear to entail truth), we wonder whether our ethical\nopinions are right or wrong (in the sense of correct or incorrect) and\nbelieve that we or others are, or at least may be,\nmistaken in our moral beliefs (in the sense that they may be\nfalse). All this is difficult to make sense of except on the\nassumption that moral judgments are what they appear to\nbe—statements which express beliefs, describe some purported\nfacts and are therefore capable of truth and falsity. The argument\ndoes not show that there are such facts (after all, much the\nsame points could be made about theological discourse, and a set of\ntruth-apt sentences cannot conjure God into existence). It could be\nthat there are no moral facts corresponding to our opinions and thus\nthat they are predominately false, like the propositions of Greek\nmythology. But the way we talk strongly suggests that our moral\npronouncements are in the true/false game, and thus that they are\ntruth-apt or truth-valued. If something looks like a duck, swims like\na duck and quacks like a duck, then the chances are that it is indeed\na duck! Likewise, if something looks like a truth-apt\nexpression (since on the surface it is in the indicative mood), if it\nbehaves logically like a truth-apt expression (which again is\nwhat “X is good” undoubtedly does), if it is\ntreated by the people whose use sustains its meaning as\nif it were truth-apt, then, absent compelling arguments to the\ncontrary, it probably is truth-apt." ], "subsection_title": "8.7 Russell’s Feelings and the Duck Argument" }, { "content": [ "\nThus Russell’s brand of emotivism is subject to devastating\nobjections, some of which he was aware of. Moreover he was not that\nkeen on it. Although he thought he could show that", "\n\n\nI am not guilty of any logical inconsistency in holding to [emotivism]\nand at the same time expressing strong ethical preferences … in\nfeeling I am not satisfied. (RoE: 149/Papers 11:\n51)\n", "\nIn particular, he found himself “incapable of believing that all\nthat is wrong with wanton cruelty is that I don’t like it”. Why\nthen was he an emotivist? Because he could not “see how to\nrefute the arguments for the subjectivity of ethical values”\n(RoE: 165/Papers 11: 310–311). What were these\narguments and why did Russell find them so compelling?" ], "subsection_title": "8.8 Objections Concluded" } ] }, { "main_content": [ "\n“When I was young,” writes Russell,", "\n\n\nI agreed with G.E. Moore in believing in the objectivity of good and\nevil. Santayana’s criticism in a book called Winds of\nDoctrine, [which Russell read in 1913] caused me to abandon this\nview, though I have never been able to be as bland and comfortable\nabout it as he was. (Portraits from Memory: 91)\n", "\nAs a piece of intellectual autobiography this is not very\nilluminating. Santayana’s book abounds in mellifluous sneers, but\narguments are conspicuous by their absence. Russell’s reasons for\nrejecting a non-natural property of goodness have to be reconstructed\nfrom literary asides, delivered in passing in the course of his\nanti-War polemics." ], "section_title": "9. Objections to Objectivism", "subsections": [ { "content": [ "\nHowever, Santayana does give one reason, not for doubting the\nexistence of the Moorean Good, but for wishing that nobody believed in\nit. The idea that there are objective moral facts breeds intolerance\nand fanaticism. Accordingly, the rejection of this idea “would\ntend to render people more truly social”, specifically, more\ntolerant. “Moral warfare would continue”, he writes,\n“but not with poisoned arrows.” Russell came to agree,\nespecially after the outbreak of World War I.", "\n\n\nMy H[erbert] S[pencer] lecture was partly inspired by disgust at the\nuniversal outburst of righteousness in all nations since the war\nbegan. It seems the essence of virtue is persecution, and it has given\nme a disgust of all ethical notions, which evidently are chiefly\nuseful as an excuse for murder. (Letter to Samuel Alexander, 5/2/1915,\nRoE: 107/Papers 8: 56)\n", "\nThere is something rather paradoxical about this, since Russell was\nfirmly convinced of the rightness of his own anti-War activities:\n“When the War came, I felt as if I heard the voice of God. I\nknew it was my business to protest, however futile protest might\nbe” (Autobiography II: 18). If there are no objective\nmoral properties, there is no such thing as moral knowledge, which\nmeans that Russell cannot have literally known that he ought\nto protest. At best he could have known that he ought to protest\ngiven his values. But though he sometimes seems to talk as if\nit is objectively wrong to believe in objective values, Russell’s\nposition is (or can be made to be) coherent. It might just be a fact\nthat moral realists tend to be more intolerant and cruel than moral\nrelativists and anti-realists. Hence those who dislike intolerance and\ncruelty have a reason for running down objectivity. As Russell himself\nput it,", "\n\n\nfor my part, I should wish to see in the world less cruelty,\npersecution, punishment, and moral reprobation than exists at present;\nto this end, I believe that a recognition of the subjectivity of\nethics might conduce. (RoE: 117/Papers 13: 326)\n", "\nThe word “recognition” suggests that the\n“subjectivity of ethics” is true, and thus that there is\nno such thing as a non-natural property of goodness. But setting the\nsuccess-word to one side, it might be the case that we would\nbe better off believing in the subjectivity of ethics since believing\nin objective values leads to persecution, punishment, cruelty and\nmoral reprobation. It might pay in terms of peace, love and\nunderstanding if people came to believe Russell’s brand of emotivism.\nBut the fact that a belief pays, in some sense, does not make\nit true, as Russell himself was at pains to point out (see\nPhilosophical Essays, chs. iv & v). So even if we\nwould be better off believing that there were no objective\nvalues (a thesis Russell later came to doubt), this does not prove\nthat there are no such things." ], "subsection_title": "9.1 Persecution, Punishment and the Subjectivity of Value" }, { "content": [ "\nSo what were Russell’s reasons for rejecting a non-natural property of\ngoodness? One argument, subsequently popularized by J.L. Mackie (1977)\nas “the Argument from Relativity”, starts with the\ndiversity of moral opinion and the supposed impossibility of proof\nwhen it comes to ultimate values.", "\n\n\nIf our views as to what ought to be done were to be truly rational, we\nought to have a rational way of ascertaining what things are such as\nought to exist on their own account [that is, what things are good]\n…. On [this] point, no argument is possible. There can be\nnothing beyond an appeal to individual tastes. If, for example, one\nman thinks vindictive punishment desirable in itself, apart from any\nreformatory or deterrent effects, while another man thinks it\nundesirable in itself, it is impossible to bring any arguments in\nsupport of either side. (RoE: 112/Papers 13:\n186)\n", "\nNow it is, of course, a consequence of Russell’s later view\nboth a) that it is impossible to have a rational argument about\n“what things are such as ought to exist on their own\naccount” and b) that in such disputes there can be nothing\nbeyond “an appeal to individual tastes”. But though you\ncan argue from emotivism and the non-existence of objective\ngoodness to the truth of a) and b), can you argue\nfrom a) and b) to the non-existence of objective\ngoodness?", "\nThe argument, I suggest, is best construed as an inference to the best\nexplanation. The best explanation of a) that it is impossible to have\na rational argument about what is good or bad in itself and b) that in\nsuch disputes there can be nothing beyond “an appeal to\nindividual tastes” is the hypothesis c) that there is nothing\nobjective to disagree about since there is no such thing as\ngoodness—rather our opinions on these topics are somehow\ndependent on, or expressive of, our disparate desires and perhaps our\ndiverse upbringings.", "\nIs this a good argument? Not by itself, no. For it is not clear that\ntheses a) and b) represent genuine facts. And even if a) and b)\nare true and do represent genuine facts, is c) the\nbest explanation? Perhaps there is a property of goodness but it\nhappens to be a property that it is difficult to discern. Some people\nare just better at seeing what is good or bad than others. As Russell\nhimself put it in 1909 “the difficulty of discovering the truth\ndoes not prove that there is no truth to be discovered”\n(Philosophical Essays: 20/Papers 6: 222).", "\nHowever, the Argument From Relativity looks a little better if we\nfollow Russell’s hints and combine it with the Argument from\nExplanatory Impotence." ], "subsection_title": "9.2 Russell and the Argument from Relativity" }, { "content": [ "\nIn his polemical article “North Staffs’ Praise of War”\n(1916) Russell suggests an argument which prefigures a famous argument\nof Gilbert Harman’s 1977. (It is typical of Russell, incidentally,\nthat he develops his meta-ethical position in the course of a\nnewspaper controversy about the rights and wrongs of World War I\nrather than in an article in an academic journal.)", "\n\n\nI have been led to [the view that all ethics is subjective] by a\nnumber of reasons, some logical, some derived from observation.\nOccam’s Razor … leads me to discard the notion of absolute good\nif ethics can be accounted for without it. Observation of ethical\nvaluations leads me to think that all ethical valuations can be so\naccounted for, and that the claim of universality which men associate\nwith their ethical judgments embodies merely the impulse to\npersecution or tyranny. (RoE: 117/Papers 13:\n325–6)\n", "\nThe idea seems to be that our moral evaluations—our beliefs\nabout what is good or bad, wrong or right—can be explained\nwithout supposing that they correspond to facts involving Moorean\nproperties of “absolute” goodness or badness. And since\nour evaluations can be accounted for without supposing that there are\nany such properties, and since the only reason for we believing in\nthem is the evidence of our evaluations, we have no reason to suppose\nthat such properties exist, and some reasons (of an Occamist sort) for\nsupposing that they do not.", "\nAs it stands, this argument is inconclusive. For a Moorean might\nsimply hang tough, insisting that his own views about goodness are\nbest explained by close encounters of the Platonic kind, involving an\nintimate acquaintance with both goodness itself and the properties on\nwhich it supervenes. Of course, it is difficult to make naturalistic\nsense of such cognitions, but it is difficult to make naturalistic\nsense of our knowledge of logic, mathematics and modality. This is the\n“companions in guilt” strategy that is often deployed in\narguing for moral objectivity (for more on which, see Lillehammer\n2007). However the Argument from Explanatory Impotence gets a little\nstronger if we combine it with the Argument from Relativity. For the\nfact is that people often disagree about what is intrinsically good or\nbad, about how good or bad the good things and the bad things\nreally are, and about the relations between goodness and\nbadness and what we ought to do. We have already seen that Russell\ndisagreed with Moore about whether we ought to do that action that\nwill actually bring about the best consequences or the action\nthat it is reasonable to believe will bring about the best\nconsequences, which means that they had different intuitions about the\nrelations between goodness and obligation. Moore disagreed with\nSidgwick about whether anything besides pleasure is good as an\nend:", "\n\n\nThis proposition that “pleasure alone is good as an end,”\nthe fundamental proposition of Ethical Hedonism [is] in Professor\nSidgwick’s language, … an object of intuition. I shall try to\nshew you why my intuition denies it, just as his intuition affirms it.\nIt may always be true notwithstanding; neither intuition can\nprove whether it is true or not; I am bound to be satisfied,\nif I can “present considerations capable of determining the\nintellect” to reject it. (PE: §45)\n", "\nMore comically, the Cambridge Apostles seem to have had a serious\ndisagreement in 1899 about whether “self-abuse” was bad in\nitself, Moore intuiting that it was and his opponents arguing that it\nwas not (Levy 1981: 207–8). Now, how could Moore explain the\nintuitions of his opponents? Not by an encounter with badness, since\nanybody fully acquainted with badness and its relata would\nhave been forced to admit that self-abuse was bad. The non-natural\nfacts being impotent in this particular, he would have been driven\nback on natural causes (such as a taste for self-abuse) to explain the\nmisperceptions of his degenerate opponents. Thus he would have been\nforced to admit that some moral evaluations could be\nexplained without the aid of non-natural properties. But once this is\nadmitted, a “Why stop there?” problem opens up. For after\nall, it would have been child’s play for his opponents to return the\ncompliment, Moore’s self-denying intuitions being the obvious products\nof a Puritanical upbringing. Once we admit that some moral\nintuitions can be explained by natural, as opposed to non-natural,\ncauses—which seems pretty obvious given the prevalence of moral\n“error”—it is hard to hold the line and insist that\nthere are any of them that cannot be accounted for by\ntemperament, upbringing, desire and taste. It is possible, of\ncourse, that some moral evaluations are due to natural, and some to\nnon-natural, causes, but given that everybody admits that\nmany of our intuitions can be given a naturalistic\nexplanation (namely, the mistaken ones), Occam’s razor suggests that\nthere is no need for the non-natural to explain those moral intuitions\nthat we regard as correct. When supplemented by Relativity (which is\nwhat Russell seems to be hinting at) Explanatory Impotence provides a\npowerful argument against non-natural properties." ], "subsection_title": "9.3 Russell and Explanatory Impotence" }, { "content": [ "\nThus Russell’s explicit arguments for the “subjectivity of\nvalue” are objections to objectivism rather than arguments for a\nrival hypothesis. Moore’s theory is wrong since it presupposes\nnon-existent non-natural properties of goodness and badness. But if\nnaturalism is not an option, that still leaves two\nalternatives—some kind of non-cognitivism or an error-theory\n (see §1).\n Russell’s dominant view was to be a form of emotivism, and hence of\nnon-cognitivism. But although emotivism was Russell’s dominant view\nfrom 1913 onwards, there were two significant wobbles. In 1922 he\nproposed a version of the error theory, anticipating J. L. Mackie by\nover twenty years. And in 1954 in Human Society in Ethics and\nPolitics, he endeavored to inject a little objectivity into\nethics by developing a form of naturalism. The first wobble is more\ninteresting than the second, but neither should be neglected in an\naccount of Russell’s ethics, even though Russell abandoned the theory\nof HSEP within weeks of publication, reverting to the\nemotivism of 1935." ], "subsection_title": "9.4 Emotivism or the Error Theory?" } ] }, { "main_content": [ "\n“Is There an Absolute Good?” was apparently delivered on\nthe 14th of March 1922 at special meeting of the Apostles\n(RoE: 122–124/Papers 9: 345–346).\nRussell opens up in the fine, flippant style that the Apostles tended\nto admire:", "\n\n\nWhen the generation to which I belong were young, Moore persuaded us\nall that there is an absolute good. Most of us drew the inference that\nwe were absolutely good, but this is not an essential part of\nMoore’s position, though it is one of its most attractive parts.\n", "\nBut he soon gets down to philosophical business in what must be one of\nthe pithiest meta-ethical papers on record (it is a mere 809 words\nlong). Moore is right, he says, in thinking that “when we say a\nthing is good we do not merely mean that we have towards it a\ncertain feeling, of liking or approval or what not.” Indeed\n“ethical judgments claim objectivity”; that is, they\npurport to tell it like it is. However, this “claim [to]\nobjectivity … makes them all false”. Since there is no\nproperty of goodness corresponding to the linguistic predicate\n“good”, nothing can ever possess it. Hence, any claim that\nfriendship or anything else is good will be false, since\nthere is no such thing as goodness for friendship or pleasure to be.\nThe same goes for badness. Moreover, if there is no such thing as\ngoodness or badness, there is no such thing as rightness either, since\nfor an action to be genuinely right it must be such that it can\nreasonably be expected to produce more good and less bad than any\nalternative. But if there is no such thing as goodness to be produced,\nno action can be expected to produce more of it than any other. Of\ncourse, an action can still be relatively right: more likely\nto produce more of what somebody believes to be good and less\nof what somebody believes to be bad than any alternative. But\nno action can be genuinely right or genuinely\nobligatory, since there are no such properties as goodness or badness\nfor conscientious agents to maximize or minimize.", "\nThus far this is very like the error theory of J.L. Mackie (Mackie\n1946, 1977: ch. 1 and Joyce 2001). But there is a twist. For Mackie,\nas for Russell, “good” is a meaningful predicate even\nthough there is no property corresponding to the word. But Mackie,\nunlike Russell, is unfazed by this fact. So far as Mackie is\nconcerned, meaningful predicates that refer to non-existent properties\npose no particular problems. But for Russell, we can only talk\nmeaningfully about non-existent things if they are defined in\nterms of things with which we are acquainted. This is a consequence of\nhis Fundamental Principle that", "\n\n\nevery proposition that we can understand must be composed wholly of\nconstituents with which we are acquainted (Mysticism and\nLogic: 209/Papers 6: 154)\n", "\nor, as he was later to put it,", "\n\n\nthat sentences we can understand must be composed of words with whose\nmeaning we are acquainted. (Schilpp (ed.) 1944: 692/Papers\n11: 27)\n", "\nAccording to Russell, it", "\n\n\nseems natural to infer, as Moore did, that, since propositions in\nwhich the word “good” occurs have meaning, the word\n“good” [itself] has [a] meaning.\n", "\nThis, however, is a “fallacy”. Even though\n“good” can appear in meaningful sentences it does not have\na meaning of its own. This is very puzzling. What does Russell mean\nwhen he says that “good” has no meaning? And why is\nMoore’s view dependent on the thesis that it does?", "\nLet us start with Moore. As stated above\n (§2.1),\n Moore’s Open Question Argument goes like this:", "\nFrom (1) and (2) it follows that", "\nFrom (3) and (4) it follows that", "\nPremise (3) is crucial. Moore takes it for granted that the meaning of\na predicate is the property for which it stands. Hence, if there were\nno property of goodness corresponding to the word “good”,\n“good” would be meaningless. Since “good” is\nquite obviously not meaningless, the corresponding property\nis guaranteed. Thus we move from an obvious semantic fact—that\n“good” is plainly meaningful—to a much more\ncontentious metaphysical claim—that there is a corresponding\nproperty of goodness. What greases the wheels of this transition is\nthe apparently innocuous assumption that if a word like\n“good” is to mean something, there must be some\nthing (or at least some property) that it means. If this\ndoctrine were true, then the objections to objectivism discussed in\nthe last section would fall to the ground. The very fact that we can\ntalk meaningfully about goodness would show that there must\nindeed be such a property. It might be causally impotent and\nmetaphysically queer, but the fact that we can discuss it would entail\nthat we were stuck with it anyway.", "\nTo the end of his days Russell believed that", "\n\n\nthere are words which are only significant because there is something\nthat they mean, and if there were not this something, they would be\nempty noises not words. (Russell 1959: 177)\n", "\nBut when he was young he thought that most words were like\nthis, which explains the swollen ontology of The Principles of\nMathematics:", "\n\n\nHomeric gods, relations, chimeras and four-dimensional spaces all have\nbeing, for if they were not entities of a kind, we could make no\npropositions about them. (Russell, The Principles of\nMathematics: 449)\n", "\nThe breakthrough came with his Theory of Definite Descriptions (1905).\nPhrases such as “the present King of France” are\nincomplete symbols, which can function meaningfully in the\ncontext of a sentence even though there may be nothing that they mean.\nThey are incomplete because they have no meaning when taken in\nisolation and in the context of a sentence can be analyzed away. When\n“the King of France is bald” is analyzed in accordance\nwith Russell’s formula—“There is something which is King\nof France such that if anything is King of France, it is identical\nwith that thing, and that thing is bald”—the phrase\n“the King of France” simply disappears, though we are left\nwith the predicate “is King of France”. “The King of\nFrance is bald”, is false because there is no King of\nFrance—nothing which satisfies the propositional function\nbeing king of France—and there is no need to suppose\nthat the King of France must have some kind of being in order for this\nproposition to make sense.", "\nThis brings us back to the Open Question Argument. So far as I can\nsee, Russell continued to accept premises (1) and (2) and\nthus—with reservations—sub-conclusion (4).\n“Good” does not mean that same as any naturalistic\npredicate X—at least, it does not mean the same as any of\nthe naturalistic predicates that have been suggested so far. But he\nalso accepts something like premise (3), that the meaning of a\npredicate is the property for which it stands. It was because he\nbelieved that some predicates were among the words “which are\nonly significant because there is something that they mean”, and\nwhich would be “empty noises not words” in the absence of\nthis something, that he continued to believe in properties, right up\nuntil 1959. How then can Russell fend off Moore’s conclusion (5) that\nthere is a property of goodness that is not identical to any\nnaturalistic property of X-ness? By modifying premise (3):", "\nSome predicates are not complete symbols, and these can\nfunction meaningfully in the absence of the properties that they might\ndenote. One of these predicates is the word “good”.", "\n\n\nWithout the theory of incomplete symbols, it seemed natural to infer,\nas Moore did, that, since propositions in which the word\n“good” occurs have meaning, therefore the word\n“good” has meaning [or as we might now say, a referent];\nbut this was a fallacy.\n\n\nMy point is that the word “good” does not stand for a\npredicate [by which Russell means a property] at all, but has a\nmeaning only in the sense in which descriptive phrases have meaning,\ni.e., in use, not in isolation.\n", "\nThus “good” can be meaningful in the absence of a property\nof goodness and the error theory is safe from semantic refutation.", "\nBut Russell is not quite out of the woods. He continued to believe in\nhis Fundamental Principle that to understand a proposition we must be\nacquainted with the referents of the words that remain once the\nproposition has been boiled down to its ultimate constituents. This\nmeans, in effect, that things which don’t exist have to be defined in\nterms of things which do, indeed, that things which don’t\nexist have to be defined terms of things (including universals) with\nwhich we are acquainted. How then is “good” to be\ndefined? More pedantically, how are sentences involving\n“good” to be analyzed so that the word “good”\ncan be eliminated? According to Russell,", "\n\n\nwhen we judge “M is good”, we mean: “M\nhas that predicate [property] which is common to A, B,\nC, …[the things we approve of] but is absent in\nX, Y, Z, …[the things we disapprove\nof].”\n", "\nThe emotions of approval and disapproval, Russell notes,", "\n\n\ndo not enter into the meaning of the proposition “M is\ngood”, but only into its genesis.\n", "\nThat is, “good” is defined in terms of the things that we\napprove (and disapprove) of, even though the fact that we approve (or\ndisapprove) of them is not incorporated into the analysis. Now, in\nRussell’s opinion, the proposition", "\n\n\nM has that property which is common to A, B,\nC, … [the things we approve of] but is absent in\nX, Y, Z, … [the things we disapprove\nof],\n", "\nwill be always be false since the things we approve of have nothing in\ncommon apart from the fact that we approve of them. That is why\n“all propositions in which the word ‘good’\nhas a primary occurrence are false.” But will such propositions\nin fact be false? Surely X, Y, Z,\netc. do have a property in common, namely the property\nof being X or Y or Z or …! Perhaps Russell would reply\nthat disjunctive properties are not real properties. He took a dim\nview of disjunctive facts in\nThe Philosophy of Logical Atomism, and if disjunctive\nfacts should be rejected, then disjunctive properties would\nappear to be equally suspect (Papers 8: 185–6/The\nPhilosophy of Logical Atomism: 71–72). Even so, we cannot\nbe sure that in every case the things that we approve of\ndon’t have something in common other than a) the fact that we approve\nof them and b) that they satisfy a disjunctive predicate. Nor is this\nthe only problem. Though Russell defines “good” in terms\nof the things that “we” approve (and disapprove)\nof, what he seems to mean is that each person defines\n“good” in terms of the things that he or she\napproves (or disapproves) of. Thus if you and I approve of different\nthings, when I say “M is good” and you say\n“M is not good” what I mean is that M has\nthe property shared by X, Y, Z …\n[the things that I approve of] whereas what you mean\nis that is that it does not have the property shared by\nA, B, C … [the things that\nyou approve of]. But in that case the Problem of the\nDisappearing Dispute rears its ugly head. On Russell’s theory my\n“M is good” and your “M is not\ngood” may be quite consistent. But since they are obviously\nnot consistent, there must be something wrong with Russell’s\ntheory. We can put the point by paraphrasing Russell’s own criticisms\nof simple subjectivism:", "\n\n\nIf in asserting that A is good, [a person] X meant\nmerely to assert that A had a certain relation to himself such\nas pleasing his taste in some way [or that A had a\ncharacteristic shared by the things of which he approved] and\nY, in saying that A is not good, meant merely to deny\nthat A had a like relation to himself [or to deny that A\nhad the characteristic shared by the things of which he, Y,\napproved]; then there would be no subject of debate between them.\n(Philosophical Essays: 20–21/Papers 6:\n222)\n", "\nNor is this all. As we saw in\n §8.1,\n our moral sentiments are partly constituted by our moral beliefs.\nWhat distinguishes approval from a warm feeling of liking is not some\ndifference in phenomenological flavor but the thought that the thing\nwe approve of is good or right. Our moral sentiments are feelings\nthat, where what follows the “that” is a moral\njudgment. But if we can’t have feelings of approval or disapproval\nwithout the corresponding moral beliefs, we can’t explain the\nintellectual origins of the common conceptions of goodness and badness\nin terms of pre-existing sentiments of approval or disapproval. For\nprior to these conceptions there were no such sentiments. This is not\nthe criticism that sank the emotivist theories of Ayer and Stevenson.\nThe problem is not that Russell’s analysis of\n“good” is viciously circular because it presupposes the\nvery concept that it purports to explicate. The problem is\nthat his genealogy of “good” is viciously\ncircular (and therefore false) since it presupposes the concept it\npurports to explain. For in his capacity as an error-theorist\nRussell does not define “good” and\n“bad” in terms of approval and disapproval. Rather he\ngives a genealogy of these notions in which the feelings of\napproval and disapproval play a crucial part. As he himself puts it:\n“the emotions of approval and disapproval do not enter into the\nmeaning of the proposition ‘M is good’, but only\ninto its genesis”. But our concepts of “good” and\n“bad” cannot be caused by prior feelings of approval and\ndisapproval if those feelings are partly constituted by the very\nbeliefs they are supposed to cause. My belief that M is good\ncannot be caused by tendency to approve of M, if I cannot\napprove of M without believing that M is good.", "\nHowever, the real difficulty with Russell’s error theory and the one\nwhich probably weighed with Russell himself, seems to be this. Given\nRussell’s theory of meaning, he can make sense of non-existent\nproperties but not non-natural predicates. At least, he cannot make\nsense of predicates that are not definable in terms of things with\nwhich we are acquainted. Thus on the assumption that we are not\nacquainted with goodness (which we obviously cannot be if there is\nreally no such thing), and on the assumption that “good”\ncannot defined in terms of the things with which we are\nacquainted (which seems pretty plausible if is not equivalent to any\nnaturalistic predicate) then we cannot even understand the\npredicate “good”. At least, we cannot understand it, if it\nis construed as a descriptive predicate whose function it is to denote\na property (whether real or non-existent).", "\nAfter 1922, Russell abandoned the error theory and reverted to the\nemotivism that he had been flirting with since 1913. His reasons\nremain obscure. But perhaps it had something to do with the fact that\nhis Fundamental Principle, when combined with the OQA, made it\ndifficult, if not impossible, to make sense of “good” as\nstanding for a property that is both non-existent\nand non-natural. Since he retained his faith in the\nFundamental Principle he had to give up the error theory. And since he\nhad already rejected the objectivity of ethics—what we would\nnowadays describe as moral realism—this left him no alternative\nbut some form of non-cognitivsm. In my opinion this was the wrong\nchoice. He would have done better to give up the Fundamental Principle\nand stick with the error theory. But perhaps the thesis that moral\njudgments are mostly false was a bit too much for a dedicated moralist\nsuch as he. As he wrote to his brother, he would rather “be mad\nwith truth than sane with lies” and the idea that morality was\nlargely composed of lies—or a best useful fictions—would\nhave been too much to bear (see Pigden (ed.) 1999: 20, 121–122,\n& 189–193)." ], "section_title": "10. Russell’s Error-Theoretic Wobble: There Is No Absolute Good", "subsections": [] }, { "main_content": [ "\nRussell’s Human Society is a fun book to read, but\nmeta-ethically it is a bit of a mess. There is much wit and some\nwisdom, though both the wit and the wisdom are more conspicuous when\nhe is discussing human nature and human society than when he is\ndiscussing the finer points of ethical theory. (I particularly like\nhis frequent complaints that human behavior seldom rises to the level\nof enlightened self-interest. If only we could manage to be\nintelligently selfish, the world would be a much better place.) The\ndrift of the argument is sometimes difficult to discern, partly\nbecause of has frequent digressions to make bon mots, and\npartly because of his dialectical method of presentation, which\napproaches what he takes to be the truth via a series of successive\napproximations. Human Society in Ethics and Politics was\npublished in 1954, but the meta-ethical bits were originally written\nsome years earlier and intended for inclusion in Human Knowledge:\nIts Scope and Limits (1948). Russell held them back because he\nwas not sure whether ethical propositions rose to the dignity of\nknowledge. He continued to be doubtful about this, but by the early\n1950s his doubts had sufficiently dissipated for publication to become\na possibility. Nevertheless, there are marked analogies between the\ntwo books. Human Knowledge attempts to establish the\nexistence of a mind-independent world on the basis of private\nperceptions. Human Society attempts to establish an ethic\nthat is in some degree independent of individual minds on the\nbasis of subjective sentiments.", "\nHume looms large in Russell’s Human Knowledge. Indeed the\nwhole book can be seen as an attempt to concede the premises of Hume’s\nskeptical argument—that the data we start with are private and\npersonal and that we cannot infer an external world from such data by\nmeans of demonstrative inference—whilst resisting its\nconclusion—that we can have no knowledge of an external world.\n(Hence the need for non-demonstrative inference.) But although Hume\nwas Russell’s chief opponent in Human Knowledge, he was\nperhaps a meta-ethical ally in Human Society. In the\nEnquiry Concerning the Principles of Moral, Hume sought to\nbase an inter-subjective ethic on human sentiments, specifically the\nsentiments of approbation and disapprobation. Hume was much more at\nease in the world than Russell, and was only interested in moral\nreform in so far as morals rested on the “delusive glosses of\nsuperstition and false religion” (which in his opinion included\nall religion) or the ideological delusions of factious\npoliticians and mercantile economists. But he did want a meta-ethic\nthat would enable him to transfer the monkish virtues (whose status\nas virtues depended on the “delusive glosses”)\nfrom the catalogue of virtues to the catalogue of vices. Thus he\nwanted to be able to show that those who approved of “celibacy,\nfasting, penance, mortification, self-denial, humility, silence,\nsolitude” were making some kind of mistake. How did he\npropose to do this? By combining a definition with an empirical\nresearch program.", "\n\n\nThe hypothesis which we embrace is plain. It maintains that morality\nis determined by sentiment. It defines [my italics] virtue to\nbe whatever mental action or quality gives to a spectator the\npleasing sentiment of approbation; and vice the contrary. We then\nproceed to examine a plain matter of fact, to wit, what actions have\nthis influence. (Hume 1975 [1748]: 289)\n", "\nThe matter of fact is less plain than Hume suggests, since the\n“spectator” is an idealized observer, whose moral\nsense operates at optimum in part because (unlike the rest of us) he\nis relevantly informed. This means that we cannot simply predict the\nreactions of the spectator by observing the reactions of mankind,\nsince mankind is sometimes mistaken about the relevant facts. In\nparticular, since many people are subject to the delusive glosses of\nsuperstition and false religion, their reactions are liable to be\ndistorted by false beliefs, leading them to approve of what is really\nvicious (such as celibacy, fasting etc) and to disapprove of what is\nreally right (such as playing whist on Sundays with “modest\nwomen”). Since a virtue is whatever mental action or quality\ngives to a [suitably qualified] spectator the pleasing\nsentiment of approbation, and since nobody would approve of\nfasting, celibacy etc if they did not think they would be\nuseful in procuring an agreeable afterlife, no\nsuitably qualified person would approve of them, since being suitably\nqualified involves not being subject to the delusive glosses\nof superstition and false religion. However Hume’s meta-ethic rests\npartly on a definition (which Hume obviously conceives of as\nreporting a truth of language) and partly on the thesis that people\nshare the same moral sensibility which can therefore be\n“idealized” to serve as the criterion for virtue. In other\nwords Hume’s theory rests on the presupposition that, given the same\ninformation, we would approve or disapprove of much the same\nthings.", "\nWhat about Russell? His theory, like Hume’s rests on a set of\n“fundamental propositions and definitions”:", "\n\n\nThese definitions and propositions, if accepted provide a coherent\nbody of propositions which are true (or false) in the same sense as if\nthey were propositions of science. (RoE:\n161–162/Human Society in Ethics and Politics: 116)\n", "\nNow (1) is a variant of Sidgwick’s thesis that common-sense moralities\ntend to solidify around rules which are believed to have generally\nbeneficial consequences, where the benefit is cashed out in terms of\nhuman welfare. It is a dubious thesis, especially as Russell himself\nhad argued that many traditional moralities foster the interests of\nthe elite at the expense of other groups—foreigners, women,\nslaves and serfs. Perhaps Russell wants to exclude such moralities, by\nrestricting his claim to civilized communities, where\n“civilized” rules out societies with blatantly elitist\nmoral codes. Thesis (2) purports to define “good effects”,\nbut it does not state whose approval is to determine\ngoodness—people in general, people at their impartial best, or\njust the enlightened and well-informed? Without some clarity on this\npoint, too many things will wind up as good, since for any likely\neffect there will be some weirdo somewhere who approves of it.\nConversely, if being disapproved of means that an effect is\nnot good, the class of good effects may vanish altogether,\nsince for any likely effect there will be some weirdo somewhere who\ndisapproves of it. Paradoxically given his long career as a\nmoral radical, Russell’s meta-ethic seems to have less critical bite\nthan Hume’s, at least as regards ends. Hume’s theory allows him to\ntransfer a reputed virtue to the catalogue of vices if people approve\nof it on the basis of false beliefs. Russell seems to be stuck with\nwhatever effects people happen to approve of even if their tendency to\napprove is based on false beliefs and malodorous passions. But the\nreal problem lies with (3). It defines “right” and\n“ought” in consequentialist terms and as we have seen (and\nas Russell himself had argued many years before) such a definition is\nclearly false, at least if it is construed as a report of current\nusage. It is not a tautology to say that the right thing to do is the\naction that seems likely to produce the best consequences, which it\nwould be if Russell’s definition were correct.", "\nThe theory could be improved by retaining (1) and (2) with the class\nof approvers more carefully specified, but replacing (3) with\nsomething like:", "\nOn the assumption that the impartial spectator would retain the\nbroadly consequentialist tendencies of our rude ancestors, (1) and\n(3a) together would allow us to derive:", "\nAnd this would be a moderately plausible synthetic claim rather than a\npatently false definition. Moreover, it would provide the basis for\nthe right kind of utilitarian ethic—at least, it would do so if\nthe ethical jury in (2) is specified in such a way as to ensure that\nthey approve of the right effects.", "\nBut so far from being “true in the same sense as if they were\npropositions of science”, the definitions (2) and (3a) are\nsimply false, at least if they are construed as accounts of what the\nwords in question actually mean. Russell seems to have been aware of\nthis, as the tell-tale phrase “if they are accepted”\nindicates. Perhaps these definitions should be understood not as\nattempts to codify current usage but as proposals for linguistic\nreform (which, was a common dodge on the part of mid-century\nphilosophers when their purported analyses proved false). But in that\ncase they can be rejected without making any kind of mistake, along\nwith Russell’s entire ethic. And what can be rejected without\nintellectual error can hardly qualify as knowledge.", "\nRussell himself may have agreed. He was not at all sure that there\nwas such a thing as ethical knowledge and soon reverted to\nhis earlier emotivism. Within one month of the publication of\nHuman Society he was expressing “complete\nagreement” with the emotivism of A.J. Ayer (RoE:\n165/Papers 11: 175). The reason, I suspect, is that he came\nto see that his definitions of ‘right’ and\n‘good’ were intellectually optional. Some years later a Mr\nHarold Osborn sent him a book which attempted to provide an objective\nbasis for a humanistic ethic. Russell’s letter of thanks points out a\nproblem: “any system of ethics which claims objectivity can only\ndo so by means of a concealed ethical premise, which, if disputed,\ncannot be demonstrated” (Dear Bertrand Russell: 98).\nThat is precisely what is wrong with Human Society in Ethics and\nPolitics." ], "section_title": "11. Russell’s Humean Wobble: Human Society in Ethics and Politics", "subsections": [] }, { "main_content": [ "\nWe started out with Russell’s adverse verdict on his own meta-ethics:\n“I am not, myself, satisfied with what I have read or said on\nthe philosophical basis of ethics” (RoE:\n165/Papers 11: 310–11). And we can see in a sense that\nhe was right. Every meta-ethic that he developed seems to be subject\nto insuperable, objections. But although Russell’s writings on ethics\nare unsatisfactory, this does not mean that they are worthless.\nMeta-ethics is a difficult subject and it is hard to get it right. And\nif we ever are to get it right, we must learn from those,\nlike Russell, who got it interestingly and instructively wrong. In the\ncourse of his long philosophical career, Russell canvassed most of the\nmeta-ethical options that have dominated debate in the Twentieth and\nTwenty-First Centuries—naturalism, non-naturalism, emotivism and\nthe error-theory, and even, to some extent, subjectivism and\nrelativism. And though none of his theories quite worked out, there is\nmuch to be learned from his mistakes. Nor is this all. His\narguments as well as his theories are often\ninteresting and instructive. As we have seen, the ethical corollary to\nthe argument of “Seems Madam? Nay, It Is,” puts the kybosh\non any attempt to resolve Sidgwick’s Dualism of Practical Reason by\narguing that although we are distinct beings with different interests\nin the world of Appearance, we are, in Reality, all one\n (§3).\n Russell’s arguments against objectivism are often quite powerful, and\none anticipates Gilbert Harman’s, influential argument that objective\nvalues can be safely dismissed since they lack explanatory power\n (§9.3–9.4).\n Russell’s damning critique of Moore’s analytic consequentialism led\nMoore to abandon the view and perhaps to give up his “unduly\nanti-reforming” moral conservatism. Moreover Russell’s\nindirect influence on meta-ethics may have been profound\nsince the Open Question Argument, was probably invented to deal with\nRussell’s ideas. Finally, in the realm of normative ethics, Russell\ndeveloped a sensible and humane version of consequentialism, which\n(despite its shaky meta-ethical foundations) is resistant, if not\nimmune, to many of the standard criticisms, especially if\ncombined—as Russell thought it should be combined—with a\nhealthy dose of political skepticism. It provides a powerful tool for\nsocial and political criticism, a tool which Russell vigorously\nemployed on a vast range of topics in his writings on practical\nethics.", "\nIndeed, I should emphasize that, lengthy as this entry is, I have said\nvirtually nothing about the vast bulk of Russell’s writings on moral\nand political topics. If we are to judge by his literary output,\nRussell was much more interested in social and political questions and\nthe rights and wrongs of war and peace than in abstract questions of\nethical theory. But, when it comes to Russell’s popular writings,\nthere is no need for an intermediary. His books are easy to get hold\nof, easy to read, often very funny, and, despite the now dated\nallusions, easy to understand. Read them yourself and make up your own\nmind." ], "section_title": "12. Conclusion", "subsections": [] } ]

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One volume paperback edition\n(with introduction by Michael Foot) London: Routledge (2000).", "The Basic Writings of Bertrand Russell, 1903–1959,\nEgner and Dennon (eds.), London: Routledge, 1992 (originally published\n1961).", "Dear Bertrand Russell, London: George Allen and Unwin,\n1969.", "Fact and Fiction, London: Routledge, 1994 (originally\npublished 1961).", "In Praise of Idleness, London: Routledge, 1996\n(originally published 1935).", "Logic and Knowledge: Essays, 1901–1950, London:\nGeorge Allen and Unwin; New York: The Macmillan Company, 1956.", "Mortals and Others, volume I: Bertrand Russell’s American\nEssays 1931–1935, edited by Harry Ruja, London: Allen and\nUnwin, 1975.", "Mortals and Others, volume II: Bertrand Russell’s American\nEssays 1931–1935, edited by Harry Ruja, London: Routledge,\n1998.", "Mysticism and Logic and Other Essays, London: Routledge,\n1994 (originally published 1918).", "[PE], Philosophical Essays, London: Routledge,\n1994 (originally published in this format 1961 and in an earlier\nversion with a slightly different selection of essays in 1910).", "Portraits From Memory and Other Essays, London: George\nAllen and Unwin, 1956.", "[RoE], Russell on Ethics, edited by Charles\nPigden, London: Routledge, 1999.", "[RoM], Russell on Metaphysics, edited by Stephen\nMumford, London: Routledge, 2003.", "[RoR], Russell on Religion, edited by Louis\nGreenspan and Stefan Anderson, London: Routledge, 1999.", "The Selected Letters of Bertrand Russell: The Private\nYears, 1884–1914, edited by Nicholas Griffin, London:\nRoutledge, 2002.", "The Selected Letters of Bertrand Russell: The Public\nYears, 1914–1970, edited by Nicholas Griffin, London:\nRoutledge, 2001.", "Sceptical Essays, London: Routledge, 1977 (originally\npublished 1928).", "Unpopular Essays, London: George Allen and Unwin; New\nYork: Simon and Schuster, 1950.", "Why I am Not a Christian and Other Essays on Religion and\nRelated Subjects, edited by Paul Edwards, London: George Allen\nand Unwin, 1957.", "Yours Faitfully, Bertand Russell: A Lifelong fight\nfor Peace, Justice and Truth in Letters to the Editor, edited by\nRay Perkins, Chicago and Lasalle: Open Court, 2002.", "Vol. 1: Cambridge Essays, 1888–99, London, Boston,\nSydney: George Allen and Unwin, 1983.", "Vol. 4: Foundations of Logic, 1903–05, London and\nNew York: Routledge, 1994.", "Vol. 6: Logical and Philosophical Papers, 1909–13,\nLondon and New York: Routledge, 1992.", "Vol. 8: The Philosophy of Logical Atomism and Other Essays,\n1914–19, London: George Allen and Unwin, 1986.", "Vol. 9: Essays on Language, Mind and Matter,\n1919–26, London: Unwin Hyman, 1988.", "Vol. 10: A Fresh Look at Empiricism, 1927–42,\nLondon and New York: Routledge, 1996.", "Vol. 11: Last Philosophical Testament, 1943–68,\nLondon and New York: Routledge, 1997.", "Vol. 12: Contemplation and Action, 1902–14, London,\nBoston, Sydney: George Allen and] Unwin, 1985.", "Vol. 13: Prophecy and Dissent, 1914–16, London:\nUnwin Hyman, 1988.", "Aiken, Lillian W., 1963, Bertrand Russell’s Philosophy of\nMorals, New York: Humanities Press.", "Allard, James, 2003, “Idealism in Britain and the United\nStates” in Baldwin (ed.), 2003: 43–59.", "Ayer, A.J., 1936, Language, Truth and Logic,\n2nd edition, New York: Dover, 1952.", "Baldwin, Thomas (ed.), 2003, The Cambridge History of\nPhilosophy 1870–1945, Cambridge: Cambridge University\nPress.", "Barnes, W.H.F., 1933, “A Suggestion About Value,”\nAnalysis, 1: 45–46.", "Blackwell, Kenneth, 1985, The Spinozistic Ethics of Bertrand\nRussell, London: Allen and Unwin.", "Bradley, F.H., 1930 [1893], Appearance and Reality, ninth\nimpression, corrected, Oxford: Clarendon Press.", "Geach, P.T., 1960, “Ascriptivism”, Philosophical\nReview, 69(2); reprinted in Geach 1972: 250–254.", "–––, 1965, “Assertion”,\nPhilosophical Review, 74(4): 449–465; reprinted in Geach\n1972: 254–269.", "–––, 1972, Logic Matters, Oxford:\nBlackwell.", "Griffin, Nicholas (ed.), 2003a, The Cambridge Companion to\nBertrand Russell, Cambridge: Cambridge University Press.", "–––, 2003b, “Russell’s Philosophical\nBackground” in Griffin 2003a: 84–107.", "Harman, Gilbert, 1977, The Nature of Morality, New York:\nOxford University Press.", "Hume, David, 1978 [1739–40], A Treatise of Humean\nNature, 2nd edition, Selby-Bigge/Nidditch (eds.), Oxford:\nOxford University Press.", "–––, 1975 [1748], Enquiries Concerning Human\nUnderstanding and Concerning the Principles of Morals,\n3rd edition, Selby-Bigge/Nidditch (eds.), Oxford: Oxford\nUniversity Press.", "Joyce, Richard, 2001, The Myth of Morality, Cambridge:\nCambridge University Press.", "Langford, C.H., 1942, “The Notion of Analysis in Moore’s\nPhilosophy”, in Schilpp (ed.) 1942: 321–342.", "Levy, Paul, 1981, Moore: G.E. Moore and the Cambridge\nApostles, Oxford: Oxford University Press.", "Lewis, David, 1989, “Dispositional Theories of Value”.\nProceedings of the Aristotelian Society Supplementary Volume,\nLXIII: 113–137; reprinted in David Lewis, 2000, Papers in\nEthics and Social Philosophy, Cambridge: Cambridge University\nPress: 68–94.", "Lillehammer, Hallvard, 2007, Companions in Guilt:\nArguments for Ethical Objectivity, Basingstoke: Palgrave\nMacmillan.", "Mackie, J.L., 1946, “The Refutation of Morals”,\nAustralasian Journal of Philosophy, 24: 77–90.", "–––, 1977, Ethics: Inventing Right and\nWrong, Harmondsworth: Penguin.", "McTaggart J.E.M., 1996, Philosophical Studies, Bristol:\nThoemmes; originally published in 1934, though the passage quoted\ncomes from “The Further Determination of the Absolute”\nprivately printed in 1893.", "Miller, A., 2013, Contemporary Metaethics: an\nIntroduction, 2nd edition, Cambridge: Polity Press.", "Moore, G.E., 1903, Principia Ethica, Cambridge: Cambridge\nUniversity Press; abbreviated as PE.", "–––, 1912, Ethics, London: Williams and\nNorgate; reprinted, with new pagination, London: Oxford University\nPress, 1966 (all references to this reprint). [The more recent\nClarendon edition of 2005, with an introduction by William H. Shaw,\nhas the same pagination as the 1966 edition.]", "–––, 1942, “A Reply to My Critics,”\nin Schilpp 1942: 533–678.", "–––, 1993, Principia Ethica, revised\nedition with the Preface to the second edition and other papers,\nedited by Thomas Baldwin, Cambridge: Cambridge University Press; first\nedition published in 1903.", "Nuccetelli, S. and G. Seay (eds.), 2007, Themes from G.E.\nMoore: New Essays in Epistemology and Ethics, Oxford: Oxford\nUniversity Press.", "Perkins, Ray, 2007, “Russell’s Meta-ethics,”\nRussell: The Journal of Bertrand Russell Studies, 26:\n179–184.", "–––, 2012, “Was Russell’s Error Theory a\nMistake?” Russell: The Journal of Bertrand Russell\nStudies, 32: 30–41.", "–––, 2019, “Bertrand Russell’s Moral\nPhilosophy,” in Wahl (ed.) 2019: 334–360.", "Phillips, Paul, 2013, Contesting the Moral High Ground:\nPopular Moralists in Mid-Twentieth-Century Britain, Montreal:\nMcGill-Queen’s University Press.", "Pigden, Charles R., 2003, “Bertrand Russell: Moral\nPhilosopher or Unphilosophical Moralist?” in Griffin 2003a:\n450–474.", "–––, 2007, “Desiring to Desire: Russell,\nLewis and G.E. Moore,” in Nuccetelli and Seay 2007:\n244–260.", "–––, 2019, “Two Arguments for Emotivism\nand a Methodological Moral,” Russell: The Journal of\nBertrand Russell Studies, 39(1): 5–35.", "Potter, Michael K., 2006, Bertrand Russell’s Ethics,\nBristol: Thoemmes.", "Prior, A.N., 1949, Logic and the Basis of Ethics. Oxford:\nClarendon Press.", "Raphael, D.D. (ed.), 1991 [BM], The British\nMoralists, 2 volumes, Indianapolis: Hackett.", "Reid, Thomas, 1843, Essays on the Active Powers of the Human\nMind, edited by G.N. Wright, London: Thomas Tegg; available in a\npaperback reprint from Kessinger Publishing.", "Ross, W.D., 1930, The Right and the Good, Oxford:\nClarendon Press.", "–––, 1939, The Foundations of Ethics,\nOxford: Clarendon Press.", "Ryan, Alan, 1988, Bertrand Russell: a Political Life,\nHarmondsworth: Allen Lane", "Schilpp, Paul Arthur (ed.), 1942, The Philosophy of G.E.\nMoore (The Library of Living Philosophers), Evanston: Northwestern\nUniversity.", "––– (ed.), 1944, The Philosophy of Bertrand\nRussell (The Library of Living Philosophers), Chicago:\nNorthwestern University.", "Schulz, Bart, 2004, Henry Sidgwick: Eye of the Universe,\nCambridge: Cambridge University Press.", "Schroeder, Mark, 2010, Non-Cognitivism in Ethics, London:\nRoutledge.", "Sidgwick, Henry, 1982, The Methods of Ethics,\nIndianapolis, Hackett; this is a reprint of the 7th edition\nof 1907, first published in 1874.", "Soames, Scott, 2003, Philosophical Analysis in the Twentieth\nCentury, vol. 1: The Dawn of Analysis, Princeton:\nPrinceton University Press.", "Spinoza, Benedictus de, 1985, Ethics, in Curley ed. and\ntrans., The Collected Works of Spinoza (Volume 1), Princeton:\nPrinceton University Press.", "Stevenson, C., 1937, “The Emotive Meaning of Ethical\nTerms,” Mind, 46: 14–31.", "Stevenson, Charles, 1944, Ethics and Language, New Haven:\nYale University Press.", "Stove, David, 1991, The Plato Cult and Other Philosophical\nFollies, Oxford: Blackwell.", "Tait, Katherine, 1975, My Father Bertrand Russell, New\nYork: Harcourt, Bruce Jovanovich.", "Urmson, J.O., 1968, The Emotive Theory of Ethics, London:\nHutchinson.", "Wahl, Russell (ed.), 2019, The Bloomsbury Companion to\nBertrand Russell, London: Bloomsbury.", "Warnock, Mary, 1978, Ethics Since 1900, 3rd\nedn., Edinburg, VA: Axios Institute Press." ]

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[ "\nScientists obtain a great deal of the evidence they use by collecting\nand producing empirical results. Much of the standard philosophical\nliterature on this subject comes from 20th century logical\nempiricists, their followers, and critics who embraced their issues\nwhile objecting to some of their aims and assumptions. Discussions\nabout empirical evidence have tended to focus on epistemological\nquestions regarding its role in theory testing. This entry follows\nthat precedent, even though empirical evidence also plays important\nand philosophically interesting roles in other areas including\nscientific discovery, the development of experimental tools and\ntechniques, and the application of scientific theories to practical\nproblems.", "\nThe logical empiricists and their followers devoted much of their\nattention to the distinction between observables and unobservables,\nthe form and content of observation reports, and the epistemic bearing\nof observational evidence on theories it is used to evaluate.\nPhilosophical work in this tradition was characterized by the aim of\nconceptually separating theory and observation, so that observation\ncould serve as the pure basis of theory appraisal. More recently, the\nfocus of the philosophical literature has shifted away from these\nissues, and their close association to the languages and logics of\nscience, to investigations of how empirical data are generated,\nanalyzed, and used in practice. With this shift, we also see\nphilosophers largely setting aside the aspiration of a pure\nobservational basis for scientific knowledge and instead embracing a\nview of science in which the theoretical and empirical are usefully\nintertwined. This entry discusses these topics under the following\nheadings:" ]

[ { "content_title": "1. Introduction", "sub_toc": [] }, { "content_title": "2. Observation and data", "sub_toc": [ "2.1 Traditional empiricism", "2.2 The irrelevance of observation per se", "2.3 Data and phenomena" ] }, { "content_title": "3. Theory and value ladenness", "sub_toc": [ "3.1 Perception", "3.2 Assuming the theory to be tested", "3.3 Semantics", "3.4 Values", "3.5 Reuse" ] }, { "content_title": "4. The epistemic value of empirical evidence", "sub_toc": [ "4.1 Confirmation", "4.2 Saving the phenomena", "4.3 Empirical adequacy" ] }, { "content_title": "5. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nPhilosophers of science have traditionally recognized a special role\nfor observations in the epistemology of science. Observations are the\nconduit through which the ‘tribunal of experience’\ndelivers its verdicts on scientific hypotheses and theories. The\nevidential value of an observation has been assumed to depend on how\nsensitive it is to whatever it is used to study. But this in turn\ndepends on the adequacy of any theoretical claims its sensitivity may\ndepend on. For example, we can challenge the use of a particular\nthermometer reading to support a prediction of a patient’s\ntemperature by challenging theoretical claims having to do with\nwhether a reading from a thermometer like this one, applied in the\nsame way under similar conditions, should indicate the patient’s\ntemperature well enough to count in favor of or against the\nprediction. At least some of those theoretical claims will be such\nthat regardless of whether an investigator explicitly endorses, or is\neven aware of them, her use of the thermometer reading would be\nundermined by their falsity. All observations and uses of\nobservational evidence are theory laden in this sense (cf. Chang 2005,\nAzzouni 2004). As the example of the thermometer illustrates,\nanalogues of Norwood Hanson’s claim that seeing is a theory\nladen undertaking apply just as well to equipment generated\nobservations (Hanson 1958, 19). But if all observations and empirical\ndata are theory laden, how can they provide reality-based, objective\nepistemic constraints on scientific reasoning?", "\nRecent scholarship has turned this question on its head. Why think\nthat theory ladenness of empirical results would be problematic in the\nfirst place? If the theoretical assumptions with which the results are\nimbued are correct, what is the harm of it? After all, it is in virtue\nof those assumptions that the fruits of empirical investigation can be\n‘put in touch’ with theorizing at all. A number scribbled\nin a lab notebook can do a scientist little epistemic good unless she\ncan recruit the relevant background assumptions to even recognize it\nas a reading of the patient’s temperature. But philosophers have\nembraced an entangled picture of the theoretical and empirical that\ngoes much deeper than this. Lloyd (2012) advocates for what she calls\n“complex empiricism” in which there is “no pristine\nseparation of model and data” (397). Bogen (2016) points out\nthat “impure empirical evidence” (i.e. evidence that\nincorporates the judgements of scientists) “often tells us more\nabout the world that it could have if it were pure” (784).\nIndeed, Longino (2020) has urged that “[t]he naïve fantasy\nthat data have an immediate relation to phenomena of the world, that\nthey are ‘objective’ in some strong, ontological sense of\nthat term, that they are the facts of the world directly speaking to\nus, should be finally laid to rest” and that “even the\nprimary, original, state of data is not free from researchers’\nvalue- and theory-laden selection and organization” (391).", "\nThere is not widespread agreement among philosophers of science about\nhow to characterize the nature of scientific theories. What is a\ntheory? According to the traditional syntactic view, theories are\nconsidered to be collections of sentences couched in logical language,\nwhich must then be supplemented with correspondence rules in order to\nbe interpreted. Construed in this way, theories include maximally\ngeneral explanatory and predictive laws (Coulomb’s law of\nelectrical attraction and repulsion, and Maxwellian electromagnetism\nequations for example), along with lesser generalizations that\ndescribe more limited natural and experimental phenomena (e.g., the\nideal gas equations describing relations between temperatures and\npressures of enclosed gasses, and general descriptions of positional\nastronomical regularities). In contrast, the semantic view casts\ntheories as the space of states possible according to the theory, or\nthe set of mathematical models permissible according to the theory\n(see Suppe 1977). However, there are also significantly more\necumenical interpretations of what it means to be a scientific theory,\nwhich include elements of diverse kinds. To take just one illustrative\nexample, Borrelli (2012) characterizes the Standard Model of particle\nphysics as a theoretical framework involving what she calls\n“theoretical cores” that are composed of mathematical\nstructures, verbal stories, and analogies with empirical references\nmixed together (196). This entry aims to accommodate all of these\nviews about the nature of scientific theories.", "\nIn this entry, we trace the contours of traditional philosophical\nengagement with questions surrounding theory and observation in\nscience that attempted to segregate the theoretical from the\nobservational, and to cleanly delineate between the observable and the\nunobservable. We also discuss the more recent scholarship that\nsupplants the primacy of observation by human sensory perception with\nan instrument-inclusive conception of data production and that\nembraces the intertwining of theoretical and empirical in the\nproduction of useful scientific results. Although theory testing\ndominates much of the standard philosophical literature on\nobservation, much of what this entry says about the role of\nobservation in theory testing applies also to its role in inventing,\nand modifying theories, and applying them to tasks in engineering,\nmedicine, and other practical enterprises." ], "section_title": "1. Introduction", "subsections": [] }, { "main_content": [], "section_title": "2. Observation and data", "subsections": [ { "content": [ "\nReasoning from observations has been important to scientific practice\nat least since the time of Aristotle, who mentions a number of sources\nof observational evidence including animal dissection (Aristotle(a),\n763a/30–b/15; Aristotle(b), 511b/20–25).\nFrancis Bacon argued long ago that the best way to discover things\nabout nature is to use experiences (his term for observations as well\nas experimental results) to develop and improve scientific theories\n(Bacon 1620, 49ff). The role of observational evidence in scientific\ndiscovery was an important topic for Whewell (1858) and Mill (1872)\namong others in the 19th century. But philosophers didn’t talk\nabout observation as extensively, in as much detail, or in the way we\nhave become accustomed to, until the 20th century when\nlogical empiricists transformed philosophical thinking about it.", "\nOne important transformation, characteristic of the linguistic turn in\nphilosophy, was to concentrate on the logic of observation reports\nrather than on objects or phenomena observed. This focus made sense on\nthe assumption that a scientific theory is a system of sentences or\nsentence-like structures (propositions, statements, claims, and so on)\nto be tested by comparison to observational evidence. It was assumed\nthat the comparisons must be understood in terms of inferential\nrelations. If inferential relations hold only between sentence-like\nstructures, it follows that theories must be tested, not against\nobservations or things observed, but against sentences, propositions,\netc. used to report observations (Hempel 1935,\n50–51; Schlick 1935). Theory testing was treated as\na matter of comparing observation sentences describing observations\nmade in natural or laboratory settings to observation sentences that\nshould be true according to the theory to be tested. This was to be\naccomplished by using laws or lawlike generalizations along with\ndescriptions of initial conditions, correspondence rules, and\nauxiliary hypotheses to derive observation sentences describing the\nsensory deliverances of interest. This makes it imperative to ask what\nobservation sentences report.", "\nAccording to what Hempel called the phenomenalist account,\nobservation reports describe the observer’s subjective\nperceptual experiences.", "\n… Such experiential data might be conceived of as being\nsensations, perceptions, and similar phenomena of immediate\nexperience. (Hempel 1952, 674)\n", "\nThis view is motivated by the assumption that the epistemic value of\nan observation report depends upon its truth or accuracy, and that\nwith regard to perception, the only thing observers can know with\ncertainty to be true or accurate is how things appear to them. This\nmeans that we cannot be confident that observation reports are true or\naccurate if they describe anything beyond the observer’s own\nperceptual experience. Presumably one’s confidence in a\nconclusion should not exceed one’s confidence in one’s\nbest reasons to believe it. For the phenomenalist, it follows that\nreports of subjective experience can provide better reasons to believe\nclaims they support than reports of other kinds of evidence.", "\nHowever, given the expressive limitations of the language available\nfor reporting subjective experiences, we cannot expect phenomenalistic\nreports to be precise and unambiguous enough to test theoretical\nclaims whose evaluation requires accurate, fine-grained perceptual\ndiscriminations. Worse yet, if experiences are directly available only\nto those who have them, there is room to doubt whether different\npeople can understand the same observation sentence in the same way.\nSuppose you had to evaluate a claim on the basis of someone\nelse’s subjective report of how a litmus solution looked to her\nwhen she dripped a liquid of unknown acidity into it. How could you\ndecide whether her visual experience was the same as the one you would\nuse her words to report?", "\nSuch considerations led Hempel to propose, contrary to the\nphenomenalists, that observation sentences report ‘directly\nobservable’, ‘intersubjectively ascertainable’ facts\nabout physical objects", "\n… such as the coincidence of the pointer of an instrument with a\nnumbered mark on a dial; a change of color in a test substance or in\nthe skin of a patient; the clicking of an amplifier connected with a\nGeiger counter; etc. (ibid.)\n", "\nThat the facts expressed in observation reports be intersubjectively\nascertainable was critical for the aims of the logical empiricists.\nThey hoped to articulate and explain the authoritativeness widely\nconceded to the best natural, social, and behavioral scientific\ntheories in contrast to propaganda and pseudoscience. Some\npronouncements from astrologers and medical quacks gain wide\nacceptance, as do those of religious leaders who rest their cases on\nfaith or personal revelation, and leaders who use their political\npower to secure assent. But such claims do not enjoy the kind of\ncredibility that scientific theories can attain. The logical\nempiricists tried to account for the genuine credibility of scientific\ntheories by appeal to the objectivity and accessibility of observation\nreports, and the logic of theory testing. Part of what they meant by\ncalling observational evidence objective was that cultural and ethnic\nfactors have no bearing on what can validly be inferred about the\nmerits of a theory from observation reports. So conceived, objectivity\nwas important to the logical empiricists’ criticism of the Nazi\nidea that Jews and Aryans have fundamentally different thought\nprocesses such that physical theories suitable for Einstein and his\nkind should not be inflicted on German students. In response to this\nrationale for ethnic and cultural purging of the German educational\nsystem, the logical empiricists argued that because of its\nobjectivity, observational evidence (rather than ethnic and cultural\nfactors) should be used to evaluate scientific theories (Galison\n1990). In this way of thinking, observational evidence and its\nsubsequent bearing on scientific theories are objective also in virtue\nof being free of non-epistemic values.", "\nEnsuing generations of philosophers of science have found the logical\nempiricist focus on expressing the content of observations in a\nrarefied and basic observation language too narrow. Search for a\nsuitably universal language as required by the logical empiricist\nprogram has come up empty-handed and most philosophers of science have\ngiven up its pursuit. Moreover, as we will discuss in the following\nsection, the centrality of observation itself (and pointer readings)\nto the aims of empiricism in philosophy of science has also come under\nscrutiny. However, leaving the search for a universal pure observation\nlanguage behind does not automatically undercut the norm of\nobjectivity as it relates to the social, political, and cultural\ncontexts of scientific research. Pristine logical foundations aside,\nthe objectivity of ‘neutral’ observations in the face of\nnoxious political propaganda was appealing because it could serve as\nshared ground available for intersubjective appraisal. This appeal\nremains alive and well today, particularly as pernicious\nmisinformation campaigns are again formidable in public discourse (see\nO’Connor and Weatherall 2019). If individuals can genuinely\nappraise the significance of empirical evidence and come to\nwell-justified agreement about how the evidence bears on theorizing,\nthen they can protect their epistemic deliberations from the undue\ninfluence of fascists and other nefarious manipulators. However, this\naspiration must face subtleties arising from the social epistemology\nof science and from the nature of empirical results themselves. In\npractice, the appraisal of scientific results can often require\nexpertise that is not readily accessible to members of the public\nwithout the relevant specialized training. Additionally, precisely\nbecause empirical results are not pure observation reports, their\nappraisal across communities of inquirers operating with different\nbackground assumptions can require significant epistemic work.", "\nThe logical empiricists paid little attention to the distinction\nbetween observing and experimenting and its epistemic implications.\nFor some philosophers, to experiment is to isolate, prepare, and\nmanipulate things in hopes of producing epistemically useful evidence.\nIt had been customary to think of observing as noticing and attending\nto interesting details of things perceived under more or less natural\nconditions, or by extension, things perceived during the course of an\nexperiment. To look at a berry on a vine and attend to its color and\nshape would be to observe it. To extract its juice and apply reagents\nto test for the presence of copper compounds would be to perform an\nexperiment. By now, many philosophers have argued that contrivance and\nmanipulation influence epistemically significant features of\nobservable experimental results to such an extent that epistemologists\nignore them at their peril. Robert Boyle (1661), John Herschell\n(1830), Bruno Latour and Steve Woolgar (1979), Ian Hacking (1983),\nHarry Collins (1985) Allan Franklin (1986), Peter Galison (1987), Jim\nBogen and Jim Woodward (1988), and Hans-Jörg Rheinberger (1997),\nare some of the philosophers and philosophically-minded scientists,\nhistorians, and sociologists of science who gave serious consideration\nto the distinction between observing and experimenting. The logical\nempiricists tended to ignore it. Interestingly, the contemporary\nvantage point that attends to modeling, data processing, and empirical\nresults may suggest a re-unification of observation and intervention\nunder the same epistemological framework. When one no longer thinks of\nscientific observation as pure or direct, and recognizes the power of\ngood modeling to account for confounds without physically intervening\non the target system, the purported epistemic distinction between\nobservation and intervention loses its bite." ], "subsection_title": "2.1 Traditional empiricism" }, { "content": [ "\nObservers use magnifying glasses, microscopes, or telescopes to see\nthings that are too small or far away to be seen, or seen clearly\nenough, without them. Similarly, amplification devices are used to\nhear faint sounds. But if to observe something is to perceive it, not\nevery use of instruments to augment the senses qualifies as\nobservational.", "\nPhilosophers generally agree that you can observe the moons of Jupiter\nwith a telescope, or a heartbeat with a stethoscope. The van Fraassen\nof The Scientific Image is a notable exception, for whom to\nbe ‘observable’ meant to be something that, were it\npresent to a creature like us, would be observed. Thus, for van\nFraassen, the moons of Jupiter are observable “since astronauts\nwill no doubt be able to see them as well from close up” (1980,\n16). In contrast, microscopic entities are not observable on van\nFraassen’s account because creatures like us cannot\nstrategically maneuver ourselves to see them, present before us, with\nour unaided senses.", "\nMany philosophers have criticized van Fraassen’s view as overly\nrestrictive. Nevertheless, philosophers differ in their willingness to\ndraw the line between what counts as observable and what does not\nalong the spectrum of increasingly complicated instrumentation. Many\nphilosophers who don’t mind telescopes and microscopes still\nfind it unnatural to say that high energy physicists\n‘observe’ particles or particle interactions when they\nlook at bubble chamber photographs—let alone digital\nvisualizations of energy depositions left in calorimeters that are not\nthemselves inspected. Their intuitions come from the plausible\nassumption that one can observe only what one can see by looking, hear\nby listening, feel by touching, and so on. Investigators can neither\nlook at (direct their gazes toward and attend to) nor visually\nexperience charged particles moving through a detector. Instead they\ncan look at and see tracks in the chamber, in bubble chamber\nphotographs, calorimeter data visualizations, etc.", "\nIn more contentious examples, some philosophers have moved to speaking\nof instrument-augmented empirical research as more like tool use than\nsensing. Hacking (1981) argues that we do not see through a\nmicroscope, but rather with it. Daston and Galison (2007)\nhighlight the inherent interactivity of a scanning tunneling\nmicroscope, in which scientists image and manipulate atoms by\nexchanging electrons between the sharp tip of the microscope and the\nsurface to be imaged (397). Others have opted to stretch the meaning\nof observation to accommodate what we might otherwise be tempted to\ncall instrument-aided detections. For instance, Shapere (1982) argues\nthat while it may initially strike philosophers as counter-intuitive,\nit makes perfect sense to call the detection of neutrinos from the\ninterior of the sun “direct observation.”", "\nThe variety of views on the observable/unobservable distinction hint\nthat empiricists may have been barking up the wrong philosophical\ntree. Many of the things scientists investigate do not interact with\nhuman perceptual systems as required to produce perceptual experiences\nof them. The methods investigators use to study such things argue\nagainst the idea—however plausible it may once have\nseemed—that scientists do or should rely exclusively on their\nperceptual systems to obtain the evidence they need. Thus Feyerabend\nproposed as a thought experiment that if measuring equipment was\nrigged up to register the magnitude of a quantity of interest, a\ntheory could be tested just as well against its outputs as against\nrecords of human perceptions (Feyerabend 1969, 132–137).\nFeyerabend could have made his point with historical examples instead\nof thought experiments. A century earlier Helmholtz estimated the\nspeed of excitatory impulses traveling through a motor nerve. To\ninitiate impulses whose speed could be estimated, he implanted an\nelectrode into one end of a nerve fiber and ran a current into it from\na coil. The other end was attached to a bit of muscle whose\ncontraction signaled the arrival of the impulse. To find out how long\nit took the impulse to reach the muscle he had to know when the\nstimulating current reached the nerve. But", "\n[o]ur senses are not capable of directly perceiving an individual\nmoment of time with such small duration …\n", "\nand so Helmholtz had to resort to what he called ‘artificial\nmethods of observation’ (Olesko and Holmes 1994, 84). This meant\narranging things so that current from the coil could deflect a\ngalvanometer needle. Assuming that the magnitude of the deflection is\nproportional to the duration of current passing from the coil,\nHelmholtz could use the deflection to estimate the duration he could\nnot see (ibid). This sense of ‘artificial observation’ is\nnot to be confused e.g., with using magnifying glasses or telescopes\nto see tiny or distant objects. Such devices enable the observer to\nscrutinize visible objects. The minuscule duration of the current flow\nis not a visible object. Helmholtz studied it by cleverly concocting\ncircumstances so that the deflection of the needle would meaningfully\nconvey the information he needed. Hooke (1705,\n16–17) argued for and designed instruments to\nexecute the same kind of strategy in the 17th century.", "\nIt is of interest that records of perceptual observation are not\nalways epistemically superior to data collected via experimental\nequipment. Indeed, it is not unusual for investigators to use\nnon-perceptual evidence to evaluate perceptual data and correct for\nits errors. For example, Rutherford and Pettersson conducted similar\nexperiments to find out if certain elements disintegrated to emit\ncharged particles under radioactive bombardment. To detect emissions,\nobservers watched a scintillation screen for faint flashes produced by\nparticle strikes. Pettersson’s assistants reported seeing\nflashes from silicon and certain other elements. Rutherford’s\ndid not. Rutherford’s colleague, James Chadwick, visited\nPettersson’s laboratory to evaluate his data. Instead of watching\nthe screen and checking Pettersson’s data against what he saw,\nChadwick arranged to have Pettersson’s assistants watch the\nscreen while unbeknownst to them he manipulated the equipment,\nalternating normal operating conditions with a condition in which\nparticles, if any, could not hit the screen. Pettersson’s data\nwere discredited by the fact that his assistants reported flashes at\nclose to the same rate in both conditions (Stuewer 1985,\n284–288).", "\nWhen the process of producing data is relatively convoluted, it is\neven easier to see that human sense perception is not the ultimate\nepistemic engine. Consider functional magnetic resonance images (fMRI)\nof the brain decorated with colors to indicate magnitudes of\nelectrical activity in different regions during the performance of a\ncognitive task. To produce these images, brief magnetic pulses are\napplied to the subject’s brain. The magnetic force coordinates\nthe precessions of protons in hemoglobin and other bodily stuffs to\nmake them emit radio signals strong enough for the equipment to\nrespond to. When the magnetic force is relaxed, the signals from\nprotons in highly oxygenated hemoglobin deteriorate at a detectably\ndifferent rate than signals from blood that carries less oxygen.\nElaborate algorithms are applied to radio signal records to estimate\nblood oxygen levels at the places from which the signals are\ncalculated to have originated. There is good reason to believe that\nblood flowing just downstream from spiking neurons carries appreciably\nmore oxygen than blood in the vicinity of resting neurons. Assumptions\nabout the relevant spatial and temporal relations are used to estimate\nlevels of electrical activity in small regions of the brain\ncorresponding to pixels in the finished image. The results of all of\nthese computations are used to assign the appropriate colors to pixels\nin a computer generated image of the brain. In view of all of this,\nfunctional brain imaging differs, e.g., from looking and seeing,\nphotographing, and measuring with a thermometer or a galvanometer in\nways that make it uninformative to call it observation. And similarly\nfor many other methods scientists use to produce non-perceptual\nevidence.", "\nThe role of the senses in fMRI data production is limited to such\nthings as monitoring the equipment and keeping an eye on the subject.\nTheir epistemic role is limited to discriminating the colors in the\nfinished image, reading tables of numbers the computer used to assign\nthem, and so on. While it is true that researchers typically use their\nsense of sight to take in visualizations of processed fMRI\ndata—or numbers on a page or screen for that\nmatter—this is not the primary locus of epistemic\naction. Researchers learn about brain processes through fMRI data, to\nthe extent that they do, primarily in virtue of the suitability of the\ncausal connection between the target processes and the data records,\nand of the transformations those data undergo when they are processed\ninto the maps or other results that scientists want to use. The\ninteresting questions are not about observability, i.e. whether\nneuronal activity, blood oxygen levels, proton precessions, radio\nsignals, and so on, are properly understood as observable by creatures\nlike us. The epistemic significance of the fMRI data depends on their\ndelivering us the right sort of access to the target, but observation\nis neither necessary nor sufficient for that\naccess.", "\nFollowing Shapere (1982), one could respond by adopting an extremely\npermissive view of what counts as an ‘observation’ so as\nto allow even highly processed data to count as observations. However,\nit is hard to reconcile the idea that highly processed data like fMRI\nimages record observations with the traditional empiricist notion that\ncalculations involving theoretical assumptions and background beliefs\nmust not be allowed (on pain of loss of objectivity) to intrude into\nthe process of data production. Observation garnered its special\nepistemic status in the first place because it seemed more direct,\nmore immediate, and therefore less distorted and muddled than (say)\ndetection or inference. The production of fMRI images requires\nextensive statistical manipulation based on theories about the radio\nsignals, and a variety of factors having to do with their detection\nalong with beliefs about relations between blood oxygen levels and\nneuronal activity, sources of systematic error, and more. Insofar as\nthe use of the term ‘observation’ connotes this extra\nbaggage of traditional empiricism, it may be better to replace\nobservation-talk with terminology that is more obviously permissive,\nsuch as that of ‘empirical data’ and ‘empirical\nresults.’" ], "subsection_title": "2.2 The irrelevance of observation per se" }, { "content": [ "\nDeposing observation from its traditional perch in empiricist\nepistemologies of science need not estrange philosophers from\nscientific practice. Terms like ‘observation’ and\n‘observation reports’ do not occur nearly as much in\nscientific as in philosophical writings. In their place, working\nscientists tend to talk about data. Philosophers who adopt\nthis usage are free to think about standard examples of observation as\nmembers of a large, diverse, and growing family of data production\nmethods. Instead of trying to decide which methods to classify as\nobservational and which things qualify as observables, philosophers\ncan then concentrate on the epistemic influence of the factors that\ndifferentiate members of the family. In particular, they can focus\ntheir attention on what questions data produced by a given method can\nbe used to answer, what must be done to use that data fruitfully, and\nthe credibility of the answers they afford (Bogen 2016).", "\nSatisfactorily answering such questions warrants further philosophical\nwork. As Bogen and Woodward (1988) have argued, there is often a long\nroad between obtaining a particular dataset replete with\nidiosyncrasies born of unspecified causal nuances to any claim about\nthe phenomenon ultimately of interest to the researchers. Empirical\ndata are typically produced in ways that make it impossible to predict\nthem from the generalizations they are used to test, or to derive\ninstances of those generalizations from data and non ad hoc auxiliary\nhypotheses. Indeed, it is unusual for many members of a set of\nreasonably precise quantitative data to agree with one another, let\nalone with a quantitative prediction. That is because precise,\npublicly accessible data typically cannot be produced except through\nprocesses whose results reflect the influence of causal factors that\nare too numerous, too different in kind, and too irregular in behavior\nfor any single theory to account for them. When Bernard Katz recorded\nelectrical activity in nerve fiber preparations, the numerical values\nof his data were influenced by factors peculiar to the operation of\nhis galvanometers and other pieces of equipment, variations among the\npositions of the stimulating and recording electrodes that had to be\ninserted into the nerve, the physiological effects of their insertion,\nand changes in the condition of the nerve as it deteriorated during\nthe course of the experiment. There were variations in the\ninvestigators’ handling of the equipment. Vibrations shook the\nequipment in response to a variety of irregularly occurring causes\nranging from random error sources to the heavy tread of Katz’s\nteacher, A.V. Hill, walking up and down the stairs outside of the\nlaboratory. That’s a short list. To make matters worse, many of\nthese factors influenced the data as parts of irregularly occurring,\ntransient, and shifting assemblies of causal influences.", "\nThe effects of systematic and random sources of error are typically\nsuch that considerable analysis and interpretation are required to\ntake investigators from data sets to conclusions that can be used to\nevaluate theoretical claims. Interestingly, this applies as much to\nclear cases of perceptual data as to machine produced records. When\n19th and early 20th century astronomers looked\nthrough telescopes and pushed buttons to record the time at which they\nsaw a star pass a crosshair, the values of their data points depended,\nnot only upon light from that star, but also upon features of\nperceptual processes, reaction times, and other psychological factors\nthat varied from observer to observer. No astronomical theory has the\nresources to take such things into account.", "\nInstead of testing theoretical claims by direct comparison to the data\ninitially collected, investigators use data to infer facts about\nphenomena, i.e., events, regularities, processes, etc. whose instances\nare uniform and uncomplicated enough to make them susceptible to\nsystematic prediction and explanation (Bogen and Woodward 1988, 317).\nThe fact that lead melts at temperatures at or close to 327.5 C is an\nexample of a phenomenon, as are widespread regularities among\nelectrical quantities involved in the action potential, the motions of\nastronomical bodies, etc. Theories that cannot be expected to predict\nor explain such things as individual temperature readings can\nnevertheless be evaluated on the basis of how useful they are in\npredicting or explaining phenomena. The same\nholds for the action potential as opposed to the electrical data from\nwhich its features are calculated, and the motions of astronomical\nbodies in contrast to the data of observational astronomy. It is\nreasonable to ask a genetic theory how probable it is (given similar\nupbringings in similar environments) that the offspring of a parent or\nparents diagnosed with alcohol use disorder will develop one or more\nsymptoms the DSM classifies as indicative of alcohol use disorder. But\nit would be quite unreasonable to ask the genetic theory to predict or\nexplain one patient’s numerical score on one trial of a\nparticular diagnostic test, or why a diagnostician wrote a particular\nentry in her report of an interview with an offspring of one of such\nparents (see Bogen and Woodward, 1988,\n319–326).", "\nLeonelli has challenged Bogen and Woodward’s (1988) claim that\ndata are, as she puts it, “unavoidably embedded in one\nexperimental context” (2009, 738). She argues that when data are\nsuitably packaged, they can travel to new epistemic contexts and\nretain epistemic utility—it is not just claims about\nthe phenomena that can travel, data travel too. Preparing data for\nsafe travel involves work, and by tracing data ‘journeys,’\nphilosophers can learn about how the careful labor of researchers,\ndata archivists, and database curators can facilitate useful data\nmobility. While Leonelli’s own work has often focused on data in\nbiology, Leonelli and Tempini (2020) contains many diverse case\nstudies of data journeys from a variety of scientific disciplines that\nwill be of value to philosophers interested in the methodology and\nepistemology of science in practice.", "\nThe fact that theories typically predict and explain features of\nphenomena rather than idiosyncratic data should not be interpreted as\na failing. For many purposes, this is the more useful and illuminating\ncapacity. Suppose you could choose between a theory that predicted or\nexplained the way in which neurotransmitter release relates to\nneuronal spiking (e.g., the fact that on average, transmitters are\nreleased roughly once for every 10 spikes) and a theory which\nexplained or predicted the numbers displayed on the relevant\nexperimental equipment in one, or a few single cases. For most\npurposes, the former theory would be preferable to the latter at the\nvery least because it applies to so many more cases. And similarly for\ntheories that predict or explain something about the probability of\nalcohol use disorder conditional on some genetic factor or a theory\nthat predicted or explained the probability of faulty diagnoses of\nalcohol use disorder conditional on facts about the training that\npsychiatrists receive. For most purposes, these would be preferable to\na theory that predicted specific descriptions in a single particular\ncase history.", "\nHowever, there are circumstances in which scientists do want to\nexplain data. In empirical research it is often crucial to getting a\nuseful signal that scientists deal with sources of background noise\nand confounding signals. This is part of the long road from newly\ncollected data to useful empirical results. An important step on the\nway to eliminating unwanted noise or confounds is to determine their\nsources. Different sources of noise can have different characteristics\nthat can be derived from and explained by theory. Consider the\ndifference between ‘shot noise’ and ‘thermal\nnoise,’ two ubiquitous sources of noise in precision electronics\n(Schottky 1918; Nyquist 1928; Horowitz and Hill 2015). ‘Shot\nnoise’ arises in virtue of the discrete nature of a signal. For\ninstance, light collected by a detector does not arrive all at once or\nin perfectly continuous fashion. Photons rain onto a detector shot by\nshot on account of being quanta. Imagine building up an image one\nphoton at a time—at first the structure of the image\nis barely recognizable, but after the arrival of many photons, the\nimage eventually fills in. In fact, the contribution of noise of this\ntype goes as the square root of the signal. By contrast, thermal noise\nis due to non-zero temperature—thermal fluctuations\ncause a small current to flow in any circuit. If you cool your\ninstrument (which very many precision experiments in physics do) then\nyou can decrease thermal noise. Cooling the detector is not going to\nchange the quantum nature of photons though. Simply collecting more\nphotons will improve the signal to noise ratio with respect to shot\nnoise. Thus, determining what kind of noise is affecting one’s\ndata, i.e. explaining features of the data themselves that are\nidiosyncratic to the particular instruments and conditions prevailing\nduring a specific instance of data collection, can be critical to\neventually generating a dataset that can be used to answer questions\nabout phenomena of interest. In using data that require statistical\nanalysis, it is particularly clear that “empirical assumptions\nabout the factors influencing the measurement results may be used to\nmotivate the assumption of a particular error distribution”,\nwhich can be crucial for justifying the application of methods of\nanalysis (Woodward 2011, 173).", "\nThere are also circumstances in which scientists want to provide a\nsubstantive, detailed explanation for a particular idiosyncratic\ndatum, and even circumstances in which procuring such explanations is\nepistemically imperative. Ignoring outliers without good epistemic\nreasons is just cherry-picking data, one of the canonical\n‘questionable research practices.’ Allan Franklin has described Robert\nMillikan’s convenient exclusion of data he collected from\nobserving the second oil drop in his experiments of April 16, 1912\n(1986, 231). When Millikan initially recorded the data for this drop,\nhis notebooks indicate that he was satisfied his apparatus was working\nproperly and that the experiment was running well—he\nwrote “Publish” next to the data in his lab notebook.\nHowever, after he had later calculated the value for the fundamental\nelectric charge that these data yielded, and found it aberrant with\nrespect to the values he calculated using data collected from other\ngood observing sessions, he changed his mind, writing\n“Won’t work” next to the calculation (ibid., see\nalso Woodward 2010, 794). Millikan not only never published this\nresult, he never published why he failed to publish it. When data are\nexcluded from analysis, there ought to be some explanation justifying\ntheir omission over and above lack of agreement with the\nexperimenters’ expectations. Precisely because they are\noutliers, some data require specific, detailed, idiosyncratic causal\nexplanations. Indeed, it is often in virtue of those very explanations\nthat outliers can be responsibly rejected. Some explanation of data\nrejected as ‘spurious’ is required. Otherwise, scientists\nrisk biasing their own work.", "\nThus, while in transforming data as collected into something useful\nfor learning about phenomena, scientists often account for features of\nthe data such as different types of noise contributions, and sometimes\neven explain the odd outlying data point or artifact, they simply do\nnot explain every individual teensy tiny causal contribution to the\nexact character of a data set or datum in full detail. This is because\nscientists can neither discover such causal minutia nor would their\ninvocation be necessary for typical research questions. The fact that\nit may sometimes be important for scientists to provide detailed\nexplanations of data, and not just claims about phenomena inferred\nfrom data, should not be confused with the dubious claim that\nscientists could ‘in principle’ detail every causal quirk\nthat contributed to some data (Woodward 2010; 2011).", "\nIn view of all of this, together with the fact that a great many\ntheoretical claims can only be tested directly against facts about\nphenomena, it behooves epistemologists to think about how data are\nused to answer questions about phenomena. Lacking space for a detailed\ndiscussion, the most this entry can do is to mention two main kinds of\nthings investigators do in order to draw conclusions from data. The\nfirst is causal analysis carried out with or without the use of\nstatistical techniques. The second is non-causal statistical\nanalysis.", "\nFirst, investigators must distinguish features of the data that are\nindicative of facts about the phenomenon of interest from those which\ncan safely be ignored, and those which must be corrected for.\nSometimes background knowledge makes this easy. Under normal\ncircumstances investigators know that their thermometers are sensitive\nto temperature, and their pressure gauges, to pressure. An astronomer\nor a chemist who knows what spectrographic equipment does, and what\nshe has applied it to will know what her data indicate. Sometimes it\nis less obvious. When Santiago Ramón y Cajal looked through his\nmicroscope at a thin slice of stained nerve tissue, he had to figure\nout which, if any, of the fibers he could see at one focal length\nconnected to or extended from things he could see only at another\nfocal length, or in another slice. Analogous considerations apply to\nquantitative data. It was easy for Katz to tell when his equipment was\nresponding more to Hill’s footfalls on the stairs than to the\nelectrical quantities it was set up to measure. It can be harder to\ntell whether an abrupt jump in the amplitude of a high frequency EEG\noscillation was due to a feature of the subjects brain activity or an\nartifact of extraneous electrical activity in the laboratory or\noperating room where the measurements were made. The answers to\nquestions about which features of numerical and non-numerical data are\nindicative of a phenomenon of interest typically depend at least in\npart on what is known about the causes that conspire to produce the\ndata.", "\nStatistical arguments are often used to deal with questions about the\ninfluence of epistemically relevant causal factors. For example, when\nit is known that similar data can be produced by factors that have\nnothing to do with the phenomenon of interest, Monte Carlo\nsimulations, regression analyses of sample data, and a variety of\nother statistical techniques sometimes provide investigators with\ntheir best chance of deciding how seriously to take a putatively\nilluminating feature of their data.", "\nBut statistical techniques are also required for purposes other than\ncausal analysis. To calculate the magnitude of a quantity like the\nmelting point of lead from a scatter of numerical data, investigators\nthrow out outliers, calculate the mean and the standard deviation,\netc., and establish confidence and significance levels. Regression and\nother techniques are applied to the results to estimate how far from\nthe mean the magnitude of interest can be expected to fall in the\npopulation of interest (e.g., the range of temperatures at which pure\nsamples of lead can be expected to melt).", "\nThe fact that little can be learned from data without causal,\nstatistical, and related argumentation has interesting consequences\nfor received ideas about how the use of observational evidence\ndistinguishes science from pseudoscience, religion, and other\nnon-scientific cognitive endeavors. First, scientists are not the only\nones who use observational evidence to support their claims;\nastrologers and medical quacks use them too. To find epistemically\nsignificant differences, one must carefully consider what sorts of\ndata they use, where it comes from, and how it is employed. The\nvirtues of scientific as opposed to non-scientific theory evaluations\ndepend not only on its reliance on empirical data, but also on how the\ndata are produced, analyzed and interpreted to draw conclusions\nagainst which theories can be evaluated. Secondly, it does not take\nmany examples to refute the notion that adherence to a single,\nuniversally applicable ‘scientific method’ differentiates\nthe sciences from the non-sciences. Data are produced, and used in far\ntoo many different ways to treat informatively as instances of any\nsingle method. Thirdly, it is usually, if not always, impossible for\ninvestigators to draw conclusions to test theories against\nobservational data without explicit or implicit reliance on\ntheoretical resources.", "\nBokulich (2020) has helpfully outlined a taxonomy of various ways in\nwhich data can be model-laden to increase their epistemic utility. She\nfocuses on seven categories: data conversion, data correction, data\ninterpolation, data scaling, data fusion, data assimilation, and\nsynthetic data. Of these categories, conversion and correction are\nperhaps the most familiar. Bokulich reminds us that even in the case\nof reading a temperature from an ordinary mercury thermometer, we are\n‘converting’ the data as measured, which in this case is\nthe height of the column of mercury, to a temperature (ibid., 795). In\nmore complicated cases, such as processing the arrival times of\nacoustic signals in seismic reflection measurements to yield values\nfor subsurface depth, data conversion may involve models (ibid.). In\nthis example, models of the composition and geometry of the subsurface\nare needed in order to account for differences in the speed of sound\nin different materials. Data ‘correction’ involves common\npractices we have already discussed like modeling and mathematically\nsubtracting background noise contributions from one’s dataset\n(ibid., 796). Bokulich rightly points out that involving models in\nthese ways routinely improves the epistemic uses to which data can be\nput. Data interpolation, scaling, and ‘fusion’ are also\nrelatively widespread practices that deserve further philosophical\nanalysis. Interpolation involves filling in missing data in a patchy\ndata set, under the guidance of models. Data are scaled when they have\nbeen generated in a particular scale (temporal, spatial, energy) and\nmodeling assumptions are recruited to transform them to apply at\nanother scale. Data are ‘fused,’ in Bokulich’s\nterminology, when data collected in diverse contexts, using diverse\nmethods are combined, or integrated together. For instance, when data\nfrom ice cores, tree rings, and the historical logbooks of sea\ncaptains are merged into a joint climate dataset. Scientists must take\ncare in combining data of diverse provenance, and model new\nuncertainties arising from the very amalgamation of datasets (ibid.,\n800).", "\nBokulich contrasts ‘synthetic data’ with what she calls\n‘real data’ (ibid., 801–802). Synthetic data are virtual,\nor simulated data, and are not produced by physical interaction with\nworldly research targets. Bokulich emphasizes the role that simulated\ndata can usefully play in testing and troubleshooting aspects of data\nprocessing that are to eventually be deployed on empirical data\n(ibid., 802). It can be incredibly useful for developing and\nstress-testing a data processing pipeline to have fake datasets whose\ncharacteristics are already known in virtue of having been produced by\nthe researchers, and being available for their inspection at will.\nWhen the characteristics of a dataset are known, or indeed can be\ntailored according to need, the effects of new processing methods can\nbe more readily traced than without. In this way, researchers can\nfamiliarize themselves with the effects of a data processing pipeline,\nand make adjustments to that pipeline in light of what they learn by\nfeeding fake data through it, before attempting to use that pipeline\non actual science data. Such investigations can be critical to\neventually arguing for the credibility of the final empirical results\nand their appropriate interpretation and use.", "\nData assimilation is perhaps a less widely appreciated aspect of\nmodel-based data processing among philosophers of science, excepting\nParker (2016; 2017). Bokulich characterizes this method as “the\noptimal integration of data with dynamical model estimates to provide\na more accurate ‘assimilation estimate’ of the\nquantity” (2020, 800). Thus, data assimilation involves\nbalancing the contributions of empirical data and the output of models\nin an integrated estimate, according to the uncertainties associated\nwith these contributions.", "\nBokulich argues that the involvement of models in these various\naspects of data processing does not necessarily lead to better\nepistemic outcomes. Done wrong, integrating models and data can\nintroduce artifacts and make the processed data unreliable for the\npurpose at hand (ibid., 804). Indeed, she notes that “[t]here is\nmuch work for methodologically reflective scientists and philosophers\nof science to do in string out cases in which model-data symbiosis may\nbe problematic or circular” (ibid.)" ], "subsection_title": "2.3 Data and phenomena" } ] }, { "main_content": [ "\nEmpirical results are laden with values and theoretical commitments.\nPhilosophers have raised and appraised several possible kinds of\nepistemic problems that could be associated with theory and/or\nvalue-laden empirical results. They have worried about the extent to\nwhich human perception itself is distorted by our commitments. They\nhave worried that drawing upon theoretical resources from the very\ntheory to be appraised (or its competitors) in the generation of\nempirical results yields vicious circularity (or inconsistency). They\nhave also worried that contingent conceptual and/or linguistic\nframeworks trap bits of evidence like bees in amber so that they\ncannot carry on their epistemic lives outside of the contexts of their\norigination, and that normative values necessarily corrupt the\nintegrity of science. Do the theory and value-ladenness of empirical\nresults render them hopelessly parochial? That is, when scientists\nleave theoretical commitments behind and adopt new ones, must they\nalso relinquish the fruits of the empirical research imbued with their\nprior commitments too? In this section, we discuss these worries and\nresponses that philosophers have offered to assuage them." ], "section_title": "3. Theory and value ladenness", "subsections": [ { "content": [ "\nIf you believe that observation by human sense perception is the\nobjective basis of all scientific knowledge, then you ought to be\nparticularly worried about the potential for human perception to be\ncorrupted by theoretical assumptions, wishful thinking, framing\neffects, and so on. Daston and Galison recount the striking example of\nArthur Worthington’s symmetrical milk drops (2007, 11–16).\nWorking in 1875, Worthington investigated the hydrodynamics of falling\nfluid droplets and their evolution upon impacting a hard surface. At\nfirst, he had tried to carefully track the drop dynamics with a strobe\nlight to burn a sequence of images into his own retinas. The images he\ndrew to record what he saw were radially symmetric, with rays of the\ndrop splashes emanating evenly from the center of the impact. However,\nwhen Worthington transitioned from using his eyes and capacity to draw\nfrom memory to using photography in 1894, he was shocked to find that\nthe kind of splashes he had been observing were irregular splats\n(ibid., 13). Even curiouser, when Worthington returned to his\ndrawings, he found that he had indeed recorded some unsymmetrical\nsplashes. He had evidently dismissed them as uninformative accidents\ninstead of regarding them as revelatory of the phenomenon he was\nintent on studying (ibid.) In attempting to document the ideal form of\nthe splashes, a general and regular form, he had subconsciously\ndown-played the irregularity of individual splashes. If theoretical\ncommitments, like Worthington’s initial commitment to the\nperfect symmetry of the physics he was studying, pervasively and\nincorrigibly dictated the results of empirical inquiry, then the\nepistemic aims of science would be seriously undermined.", "\nPerceptual psychologists, Bruner and Postman, found that subjects who\nwere briefly shown anomalous playing cards, e.g., a black four of\nhearts, reported having seen their normal counterparts e.g., a red\nfour of hearts. It took repeated exposures to get subjects to say the\nanomalous cards didn’t look right, and eventually, to describe\nthem correctly (Kuhn 1962, 63). Kuhn took such studies to indicate\nthat things don’t look the same to observers with different\nconceptual resources. (For a more up-to-date discussion of theory and\nconceptual perceptual loading see Lupyan 2015.) If so, black hearts\ndidn’t look like black hearts until repeated exposures somehow\nallowed subjects to acquire the concept of a black heart. By analogy,\nKuhn supposed, when observers working in conflicting paradigms look at\nthe same thing, their conceptual limitations should keep them from\nhaving the same visual experiences (Kuhn 1962, 111,\n113–114, 115, 120–1). This would\nmean, for example, that when Priestley and Lavoisier watched the same\nexperiment, Lavoisier should have seen what accorded with his theory\nthat combustion and respiration are oxidation processes, while\nPriestley’s visual experiences should have agreed with his\ntheory that burning and respiration are processes of phlogiston\nrelease.", "\nThe example of Pettersson’s and Rutherford’s scintillation\nscreen evidence (above) attests to the fact that observers working in\ndifferent laboratories sometimes report seeing different things under\nsimilar conditions. It is plausible that their expectations influence\ntheir reports. It is plausible that their expectations are shaped by\ntheir training and by their supervisors’ and associates’\ntheory driven behavior. But as happens in other cases as well, all\nparties to the dispute agreed to reject Pettersson’s data by\nappealing to results that both laboratories could obtain and interpret\nin the same way without compromising their theoretical commitments.\nIndeed, it is possible for scientists to share empirical results, not\njust across diverse laboratory cultures, but even across serious\ndifferences in worldview. Much as they disagreed about the nature of\nrespiration and combustion, Priestley and Lavoisier gave\nquantitatively similar reports of how long their mice stayed alive and\ntheir candles kept burning in closed bell jars. Priestley taught\nLavoisier how to obtain what he took to be measurements of the\nphlogiston content of an unknown gas. A sample of the gas to be tested\nis run into a graduated tube filled with water and inverted over a\nwater bath. After noting the height of the water remaining in the\ntube, the observer adds “nitrous air” (we call it nitric\noxide) and checks the water level again. Priestley, who thought there\nwas no such thing as oxygen, believed the change in water level\nindicated how much phlogiston the gas contained. Lavoisier reported\nobserving the same water levels as Priestley even after he abandoned\nphlogiston theory and became convinced that changes in water level\nindicated free oxygen content (Conant 1957,\n74–109).", "\nA related issue is that of salience. Kuhn claimed that if Galileo and\nan Aristotelian physicist had watched the same pendulum experiment,\nthey would not have looked at or attended to the same things. The\nAristotelian’s paradigm would have required the experimenter to\nmeasure", "\n… the weight of the stone, the vertical height to which it had\nbeen raised, and the time required for it to achieve rest (Kuhn 1962,\n123)\n", "\nand ignore radius, angular displacement, and time per swing (ibid.,\n124). These last were salient to Galileo because he treated pendulum\nswings as constrained circular motions. The Galilean quantities would\nbe of no interest to an Aristotelian who treats the stone as falling\nunder constraint toward the center of the earth (ibid., 123). Thus\nGalileo and the Aristotelian would not have collected the same data.\n(Absent records of Aristotelian pendulum experiments we can think of\nthis as a thought experiment.)", "\nInterests change, however. Scientists may eventually come to\nappreciate the significance of data that had not originally been\nsalient to them in light of new presuppositions. The moral of these\nexamples is that although paradigms or theoretical commitments\nsometimes have an epistemically significant influence on what\nobservers perceive or what they attend to, it can be relatively easy\nto nullify or correct for their effects. When presuppositions cause\nepistemic damage, investigators are often able to eventually make\ncorrections. Thus, paradigms and theoretical commitments actually do\ninfluence saliency, but their influence is neither inevitable nor\nirremediable." ], "subsection_title": "3.1 Perception" }, { "content": [ "\nThomas Kuhn (1962), Norwood Hanson (1958), Paul Feyerabend (1959) and\nothers cast suspicion on the objectivity of observational evidence in\nanother way by arguing that one cannot use empirical evidence to test\na theory without committing oneself to that very theory. This would be\na problem if it leads to dogmatism but assuming the theory to be\ntested is often benign and even necessary.", "\nFor instance, Laymon (1988) demonstrates the manner in which the very\ntheory that the Michelson-Morley experiments are considered to test is\nassumed in the experimental design, but that this does not engender\ndeleterious epistemic effects (250). The Michelson-Morley apparatus\nconsists of two interferometer arms at right angles to one another,\nwhich are rotated in the course of the experiment so that, on the\noriginal construal, the path length traversed by light in the\napparatus would vary according to alignment with or against the\nEarth’s velocity (carrying the apparatus) with respect to the\nstationary aether. This difference in path length would show up as\ndisplacement in the interference fringes of light in the\ninterferometer. Although Michelson’s intention had been to\nmeasure the velocity of the Earth with respect to the all-pervading\naether, the experiments eventually came to be regarded as furnishing\ntests of the Fresnel aether theory itself. In particular, the null\nresults of these experiments were taken as evidence against the\nexistence of the aether. Naively, one might suppose that whatever\nassumptions were made in the calculation of the results of these\nexperiments, it should not be the case that the theory under the gun\nwas assumed nor that its negation was.", "\nBefore Michelson’s experiments, the Fresnel aether theory did\nnot predict any sort of length contraction. Although Michelson assumed\nno contraction in the arms of the interferometer, Laymon argues that\nhe could have assumed contraction, with no practical impact on the\nresults of the experiments. The predicted fringe shift is calculated\nfrom the anticipated difference in the distance traveled by light in\nthe two arms is the same, when higher order terms are neglected. Thus,\nin practice, the experimenters could assume either that the\ncontraction thesis was true or that it was false when determining the\nlength of the arms. Either way, the results of the experiment would be\nthe same. After Michelson’s experiments returned no evidence of\nthe anticipated aether effects, Lorentz-Fitzgerald contraction was\npostulated precisely to cancel out the expected (but not found)\neffects and save the aether theory. Morley and Miller then set out\nspecifically to test the contraction thesis, and still assumed no\ncontraction in determining the length of the arms of their\ninterferometer (ibid., 253). Thus Laymon argues that the\nMichelson-Morley experiments speak against the tempting assumption\nthat “appraisal of a theory is based on phenomena which can be\ndetected and measured without using assumptions drawn from the theory\nunder examination or from competitors to that theory”\n(ibid., 246).", "\nEpistemological hand-wringing about the use of the very theory to be\ntested in the generation of the evidence to be used for testing, seems\nto spring primarily from a concern about vicious circularity. How can\nwe have a genuine trial, if the theory in question has been presumed\ninnocent from the outset? While it is true that there would be a\nserious epistemic problem in a case where the use of the theory to be\ntested conspired to guarantee that the evidence would turn\nout to be confirmatory, this is not always the case when theories are\ninvoked in their own testing. Woodward (2011) summarizes a tidy\ncase:", "\nFor example, in Millikan’s oil drop experiment, the mere fact\nthat theoretical assumptions (e.g., that the charge of the electron is\nquantized and that all electrons have the same charge) play a role in\nmotivating his measurements or a vocabulary for describing his results\ndoes not by itself show that his design and data analysis were of such\na character as to guarantee that he would obtain results supporting\nhis theoretical assumptions. His experiment was such that he might\nwell have obtained results showing that the charge of the electron was\nnot quantized or that there was no single stable value for this\nquantity. (178)\n", "\nFor any given case, determining whether the theoretical assumptions\nbeing made are benign or straight-jacketing the results that it will\nbe possible to obtain will require investigating the particular\nrelationships between the assumptions and results in that case. When\ndata production and analysis processes are complicated, this task can\nget difficult. But the point is that merely noting the involvement of\nthe theory to be tested in the generation of empirical results does\nnot by itself imply that those results cannot be objectively useful\nfor deciding whether the theory to be tested should be accepted or\nrejected." ], "subsection_title": "3.2 Assuming the theory to be tested" }, { "content": [ "\nKuhn argued that theoretical commitments exert a strong influence on\nobservation descriptions, and what they are understood to mean (Kuhn\n1962, 127ff; Longino 1979, 38–42). If so, proponents of a caloric\naccount of heat won’t describe or understand descriptions of\nobserved results of heat experiments in the same way as investigators\nwho think of heat in terms of mean kinetic energy or radiation. They\nmight all use the same words (e.g., ‘temperature’) to\nreport an observation without understanding them in the same way. This\nposes a potential problem for communicating effectively across\nparadigms, and similarly, for attributing the appropriate significance\nto empirical results generated outside of one’s own linguistic\nframework.", "\nIt is important to bear in mind that observers do not always use\ndeclarative sentences to report observational and experimental\nresults. Instead, they often draw, photograph, make audio recordings,\netc. or set up their experimental devices to generate graphs,\npictorial images, tables of numbers, and other non-sentential records.\nObviously investigators’ conceptual resources and theoretical\nbiases can exert epistemically significant influences on what they\nrecord (or set their equipment to record), which details they include\nor emphasize, and which forms of representation they choose (Daston\nand Galison 2007, 115–190,\n309–361). But disagreements about the epistemic\nimport of a graph, picture or other non-sentential bit of data often\nturn on causal rather than semantical considerations. Anatomists may\nhave to decide whether a dark spot in a micrograph was caused by a\nstaining artifact or by light reflected from an anatomically\nsignificant structure. Physicists may wonder whether a blip in a\nGeiger counter record reflects the causal influence of the radiation\nthey wanted to monitor, or a surge in ambient radiation. Chemists may\nworry about the purity of samples used to obtain data. Such questions\nare not, and are not well represented as, semantic questions to which\nsemantic theory loading is relevant. Late 20th century\nphilosophers may have ignored such cases and exaggerated the influence\nof semantic theory loading because they thought of theory testing in\nterms of inferential relations between observation and theoretical\nsentences.", "\nNevertheless, some empirical results are reported as declarative\nsentences. Looking at a patient with red spots and a fever, an\ninvestigator might report having seen the spots, or measles symptoms,\nor a patient with measles. Watching an unknown liquid dripping into a\nlitmus solution an observer might report seeing a change in color, a\nliquid with a PH of less than 7, or an acid. The appropriateness of a\ndescription of a test outcome depends on how the relevant concepts are\noperationalized. What justifies an observer to report having observed\na case of measles according to one operationalization might require\nher to say no more than that she had observed measles symptoms, or\njust red spots according to another.", "\nIn keeping with Percy Bridgman’s view that", "\n… in general, we mean by a concept nothing more than a set of\noperations; the concept is synonymous with the corresponding sets of\noperations (Bridgman 1927, 5)\n", "\none might suppose that operationalizations are definitions or meaning\nrules such that it is analytically true, e.g., that every liquid that\nturns litmus red in a properly conducted test is acidic. But it is\nmore faithful to actual scientific practice to think of\noperationalizations as defeasible rules for the application of a\nconcept such that both the rules and their applications are subject to\nrevision on the basis of new empirical or theoretical developments. So\nunderstood, to operationalize is to adopt verbal and related practices\nfor the purpose of enabling scientists to do their work.\nOperationalizations are thus sensitive and subject to change on the\nbasis of findings that influence their usefulness (Feest 2005).", "\nDefinitional or not, investigators in different research traditions\nmay be trained to report their observations in conformity with\nconflicting operationalizations. Thus instead of training observers to\ndescribe what they see in a bubble chamber as a whitish streak or a\ntrail, one might train them to say they see a particle track or even a\nparticle. This may reflect what Kuhn meant by suggesting that some\nobservers might be justified or even required to describe themselves\nas having seen oxygen, transparent and colorless though it is, or\natoms, invisible though they are (Kuhn 1962, 127ff). To the contrary,\none might object that what one sees should not be confused with what\none is trained to say when one sees it, and therefore that talking\nabout seeing a colorless gas or an invisible particle may be nothing\nmore than a picturesque way of talking about what certain\noperationalizations entitle observers to say. Strictly speaking, the\nobjection concludes, the term ‘observation report’ should\nbe reserved for descriptions that are neutral with respect to\nconflicting operationalizations.", "\nIf observational data are just those utterances that meet\nFeyerabend’s decidability and agreeability conditions, the\nimport of semantic theory loading depends upon how quickly, and for\nwhich sentences reasonably sophisticated language users who stand in\ndifferent paradigms can non-inferentially reach the same decisions\nabout what to assert or deny. Some would expect enough agreement to\nsecure the objectivity of observational data. Others would not. Still\nothers would try to supply different standards for objectivity.", "\nWith regard to sentential observation reports, the significance of\nsemantic theory loading is less ubiquitous than one might expect. The\ninterpretation of verbal reports often depends on ideas about causal\nstructure rather than the meanings of signs. Rather than worrying\nabout the meaning of words used to describe their observations,\nscientists are more likely to wonder whether the observers made up or\nwithheld information, whether one or more details were artifacts of\nobservation conditions, whether the specimens were atypical, and so\non.", "\nNote that the worry about semantic theory loading extends beyond\nobservation reports of the sort that occupied the logical empiricists\nand their close intellectual descendents. Combining results of diverse\nmethods for making proxy measurements of paleoclimate temperatures in\nan epistemically responsible way requires careful attention to the\nvariety of operationalizations at play. Even if no ‘observation\nreports’ are involved, the sticky question about how to usefully\nmerge results obtained in different ways in order to satisfy\none’s epistemic aims remains. Happily, the remedy for the worry\nabout semantic loading in this broader sense is likely to be the\nsame—investigating the provenance of those results\nand comparing the variety of factors that have contributed to their\ncausal production.", "\nKuhn placed too much emphasis on the discontinuity between evidence\ngenerated in different paradigms. Even if we accept a broadly Kuhnian\npicture, according to which paradigms are heterogeneous collections of\nexperimental practices, theoretical principles, problems selected for\ninvestigation, approaches to their solution, etc., connections between\ncomponents are loose enough to allow investigators who disagree\nprofoundly over one or more theoretical claims to nevertheless agree\nabout how to design, execute, and record the results of their\nexperiments. That is why neuroscientists who disagreed about whether\nnerve impulses consisted of electrical currents could measure the same\nelectrical quantities, and agree on the linguistic meaning and the\naccuracy of observation reports including such terms as\n‘potential’, ‘resistance’,\n‘voltage’ and ‘current’. As we discussed\nabove, the success that scientists have in repurposing results\ngenerated by others for different purposes speaks against the\nconfinement of evidence to its native paradigm. Even when scientists\nworking with radically different core theoretical commitments cannot\nmake the same measurements themselves, with enough contextual\ninformation about how each conducts research, it can be possible to\nconstruct bridges that span the theoretical divides." ], "subsection_title": "3.3 Semantics" }, { "content": [ "\nOne could worry that the intertwining of the theoretical and empirical\nwould open the floodgates to bias in science. Human cognizing, both\nhistorical and present day, is replete with disturbing commitments\nincluding intolerance and narrow mindedness of many sorts. If such\ncommitments are integral to a theoretical framework, or endemic to the\nreasoning of a scientist or scientific community, then they threaten\nto corrupt the epistemic utility of empirical results generated using\ntheir resources. The core impetus of the ‘value-free\nideal’ is to maintain a safe distance between the appraisal of\nscientific theories according to the evidence on one hand, and the\nswarm of moral, political, social, and economic values on the other.\nWhile proponents of the value-free ideal might admit that the\nmotivation to pursue a theory or the legal protection of human\nsubjects in permissible experimental methods involve non-epistemic\nvalues, they would contend that such values ought not ought not enter\ninto the constitution of empirical results themselves, nor the\nadjudication or justification of scientific theorizing in light of the\nevidence (see Intemann 2021, 202).", "\nAs a matter of fact, values do enter into science at a variety of\nstages. Above we saw that ‘theory-ladenness’ could refer\nto the involvement of theory in perception, in semantics, and in a\nkind of circularity that some have worried begets unfalsifiability and\nthereby dogmatism. Like theory-ladenness, values can and sometimes do\naffect judgments about the salience of certain evidence and the\nconceptual framing of data. Indeed, on a permissive construal of the\nnature of theories, values can simply be understood as part of a\ntheoretical framework. Intemann (2021) highlights a striking example\nfrom medical research where key conceptual resources include notions\nlike ‘harm,’ ‘risk,’ ‘health\nbenefit,’ and ‘safety.’ She refers to research on\nthe comparative safety of giving birth at home and giving birth at a\nhospital for low-risk parents in the United States. Studies reporting\nthat home births are less safe typically attend to infant and birthing\nparent mortality rates—which are low for these\nsubjects whether at home or in hospital—but leave\nout of consideration rates of c-section and episiotomy, which are both\nrelatively high in hospital settings. Thus, a value-laden decision\nabout whether a possible outcome counts as a harm worth considering\ncan influence the outcome of the study—in this case\ntipping the balance towards the conclusion that hospital births are\nmore safe (ibid., 206).", "\nNote that the birth safety case differs from the sort of cases at\nissue in the philosophical debate about risk and thresholds for\nacceptance and rejection of hypotheses. In accepting an hypothesis, a\nperson makes a judgement that the risk of being mistaken is\nsufficiently low (Rudner 1953). When the consequences of being wrong\nare deemed grave, the threshold for acceptance may be correspondingly\nhigh. Thus, in evaluating the epistemic status of an hypothesis in\nlight of the evidence, a person may have to make a value-based\njudgement. However, in the birth safety case, the judgement comes into\nplay at an earlier stage, well before the decision to accept or reject\nthe hypothesis is to be made. The judgement occurs already in deciding\nwhat is to count as a ‘harm’ worth considering for the\npurposes of this research.", "\nThe fact that values do sometimes enter into scientific reasoning does\nnot by itself settle the question of whether it would be better if\nthey did not. In order to assess the normative proposal, philosophers\nof science have attempted to disambiguate the various ways in which\nvalues might be thought to enter into science, and the various\nreferents that get crammed under the single heading of\n‘values.’ Anderson (2004) articulates eight stages of\nscientific research where values (‘evaluative\npresuppositions’) might be employed in epistemically fruitful\nways. In paraphrase: 1) orientation in a field, 2) framing a research\nquestion, 3) conceptualizing the target, 4) identifying relevant data,\n5) data generation, 6) data analysis, 7) deciding when to cease data\nanalysis, and 8) drawing conclusions (Anderson 2004, 11). Similarly,\nIntemann (2021) lays out five ways “that values play a role in\nscientific reasoning” with which feminist philosophers of\nscience have engaged in particular:", "\n(1) the framing [of] research problems, (2) observing phenomena and\ndescribing data, (3) reasoning about value-laden concepts and\nassessing risks, (4) adopting particular models, and (5) collecting\nand interpreting evidence. (208)\n", "\nWard (2021) presents a streamlined and general taxonomy of four\nways in which values relate to choices: as reasons motivating or\njustifying choices, as causal effectors of choices, or as goods\naffected by choices. By investigating the role of values in these\nparticular stages or aspects of research, philosophers of science can\noffer higher resolution insights than just the observation that values\nare involved in science at all and untangle crosstalk.", "\nSimilarly, fine points can be made about the nature of values involved\nin these various contexts. Such clarification is likely important for\ndetermining whether the contribution of certain values in a given\ncontext is deleterious or salutary, and in what sense. Douglas (2013)\nargues that the ‘value’ of internal consistency of a\ntheory and of the empirical adequacy of a theory with respect to the\navailable evidence are minimal criteria for any viable scientific\ntheory (799–800). She contrasts these with the sort of values that\nKuhn called ‘virtues,’ i.e. scope, simplicity, and\nexplanatory power that are properties of theories themselves, and\nunification, novel prediction and precision, which are properties a\ntheory has in relation to a body of evidence (800–801). These are the\nsort of values that may be relevant to explaining and justifying\nchoices that scientists make to pursue/abandon or accept/reject\nparticular theories. Moreover, Douglas (2000) argues that what she\ncalls “non-epistemic values” (in particular, ethical value\njudgements) also enter into decisions at various stages\n“internal” to scientific reasoning, such as data\ncollection and interpretation (565). Consider a laboratory toxicology\nstudy in which animals exposed to dioxins are compared to unexposed\ncontrols. Douglas discusses researchers who want to determine the\nthreshold for safe exposure. Admitting false positives can be expected\nto lead to overregulation of the chemical industry, while false\nnegatives yield underregulation and thus pose greater risk to public\nhealth. The decision about where to set the unsafe exposure threshold,\nthat is, set the threshold for a statistically significant difference\nbetween experimental and control animal populations, involves\nbalancing the acceptability of these two types of errors. According to\nDouglas, this balancing act will depend on “whether we are more\nconcerned about protecting public health from dioxin pollution or\nwhether we are more concerned about protecting industries that produce\ndioxins from increased regulation” (ibid., 568). That scientists\ndo as a matter of fact sometimes make such decisions is clear. They\njudge, for instance, a specimen slide of a rat liver to be tumorous or\nnot, and whether borderline cases should count as benign or malignant\n(ibid., 569–572). Moreover, in such cases, it is not clear that the\nresponsibility of making such decisions could be offloaded to\nnon-scientists.", "\nMany philosophers accept that values can contribute to the generation\nof empirical results without spoiling their epistemic utility.\nAnderson’s (2004) diagnosis is as follows:", "\nDeep down, what the objectors find worrisome about allowing value\njudgments to guide scientific inquiry is not that they have evaluative\ncontent, but that these judgments might be held dogmatically, so as to\npreclude the recognition of evidence that might undermine them. We\nneed to ensure that value judgements do not operate to drive inquiry\nto a predetermined conclusion. This is our fundamental criterion for\ndistinguishing legitimate from illegitimate uses of values in science.\n(11)\n", "\nData production (including experimental design and execution) is\nheavily influenced by investigators’ background assumptions.\nSometimes these include theoretical commitments that lead\nexperimentalists to produce non-illuminating or misleading evidence.\nIn other cases they may lead experimentalists to ignore, or even fail\nto produce useful evidence. For example, in order to obtain data on\norgasms in female stumptail macaques, one researcher wired up females\nto produce radio records of orgasmic muscle contractions, heart rate\nincreases, etc. But as Elisabeth Lloyd reports, “… the\nresearcher … wired up the heart rate of the male macaques as\nthe signal to start recording the female orgasms. When I pointed out\nthat the vast majority of female stumptail orgasms occurred during sex\namong the females alone, he replied that yes he knew that, but he was\nonly interested in important orgasms” (Lloyd 1993, 142).\nAlthough female stumptail orgasms occurring during sex with males are\natypical, the experimental design was driven by the assumption that\nwhat makes features of female sexuality worth studying is their\ncontribution to reproduction (ibid., 139). This assumption influenced\nexperimental design in such a way as to preclude learning about the\nfull range of female stumptail orgasms.", "\nAnderson (2004) presents an influential analysis of the role of values\nin research on divorce. Researchers committed to an interpretive\nframework rooted in ‘traditional family values’ could\nconduct research on the assumption that divorce is mostly bad for\nspouses and any children that they have (ibid., 12). This background\nassumption, which is rooted in a normative appraisal of a certain\nmodel of good family life, could lead social science researchers to\nrestrict the questions with which they survey their research subjects\nto ones about the negative impacts of divorce on their lives, thereby\ncurtailing the possibility of discovering ways that divorce may have\nactually made the ex-spouses lives better (ibid., 13). This is an\nexample of the influence that values can have on the nature of the\nresults that research ultimately yields, which is epistemically\ndetrimental. In this case, the values in play biased the research\noutcomes to preclude recognition of countervailing evidence. Anderson\nargues that the problematic influence of values comes when research\n“is rigged in advance” to confirm certain\nhypotheses—when the influence of values amounts to incorrigible\ndogmatism (ibid., 19). “Dogmatism” in her sense is\nunfalsifiability in practice, “their stubbornness in the face of\nany conceivable evidence”(ibid., 22).", "\nFortunately, such dogmatism is not ubiquitous and when it occurs it\ncan often be corrected eventually. Above we noted that the mere\ninvolvement of the theory to be tested in the generation of an\nempirical result does not automatically yield vicious\ncircularity—it depends on how the theory is\ninvolved. Furthermore, even if the assumptions initially made in the\ngeneration of empirical results are incorrect, future scientists will\nhave opportunities to reassess those assumptions in light of new\ninformation and techniques. Thus, as long as scientists continue their\nwork there need be no time at which the epistemic value of an\nempirical result can be established once and for all. This should come\nas no surprise to anyone who is aware that science is fallible, but it\nis no grounds for skepticism. It can be perfectly reasonable to trust\nthe evidence available at present even though it is logically possible\nfor epistemic troubles to arise in the future. A similar point can be\nmade regarding values (although cf. Yap 2016).", "\nMoreover, while the inclusion of values in the generation of an\nempirical result can sometimes be epistemically bad, values properly\ndeployed can also be harmless, or even epistemically helpful. As in\nthe cases of research on female stumptail macaque orgasms and the\neffects of divorce, certain values can sometimes serve to illuminate\nthe way in which other epistemically problematic assumptions have\nhindered potential scientific insight. By valuing knowledge about\nfemale sexuality beyond its role in reproduction, scientists can\nrecognize the narrowness of an approach that only conceives of female\nsexuality insofar as it relates to reproduction. By questioning the\nabsolute value of one traditional ideal for flourishing families,\nresearchers can garner evidence that might end up destabilizing the\nempirical foundation supporting that ideal." ], "subsection_title": "3.4 Values" }, { "content": [ "\nEmpirical results are most obviously put to epistemic work in their\ncontexts of origin. Scientists conceive of empirical research, collect\nand analyze the relevant data, and then bring the results to bear on\nthe theoretical issues that inspired the research in the first place.\nHowever, philosophers have also discussed ways in which empirical\nresults are transferred out of their native contexts and applied in\ndiverse and sometimes unexpected ways (see Leonelli and Tempini 2020).\nCases of reuse, or repurposing of empirical results in different\nepistemic contexts raise several interesting issues for philosophers\nof science. For one, such cases challenge the assumption that theory\n(and value) ladenness confines the epistemic utility of empirical\nresults to a particular conceptual framework. Ancient Babylonian\neclipse records inscribed on cuneiform tablets have been used to\ngenerate constraints on contemporary geophysical theorizing about the\ncauses of the lengthening of the day on Earth (Stephenson, Morrison,\nand Hohenkerk 2016). This is surprising since the ancient observations\nwere originally recorded for the purpose of making astrological\nprognostications. Nevertheless, with enough background information,\nthe records as inscribed can be translated, the layers of assumptions\nbaked into their presentation peeled back, and the results repurposed\nusing resources of the contemporary epistemic context, the likes of\nwhich the Babylonians could have hardly dreamed.", "\nFurthermore, the potential for reuse and repurposing feeds back on the\nmethodological norms of data production and handling. In light of the\ndifficulty of reusing or repurposing data without sufficient\nbackground information about the original context, Goodman et al.\n(2014) note that “data reuse is most possible when: 1) data; 2)\nmetadata (information describing the data); and 3) information about\nthe process of generating those data, such as code, all all\nprovided” (3). Indeed, they advocate for sharing data and code\nin addition to results customarily published in science. As we have\nseen, the loading of data with theory is usually necessary to putting\nthat data to any serious epistemic\nuse—theory-loading makes theory appraisal possible.\nPhilosophers have begun to appreciate that this epistemic boon does\nnot necessarily come at the cost of rendering data “tragically\nlocal” (Wylie 2020, 285, quoting Latour 1999). But it is\nimportant to note the useful travel of data between contexts is\nsignificantly aided by foresight, curation, and management for that\naim.", "\nIn light of the mediated nature of empirical results, Boyd (2018)\nargues for an “enriched view of evidence,” in which the\nevidence that serves as the ‘tribunal of experience’ is\nunderstood to be “lines of evidence” composed of the\nproducts of data collection and all of the products of their\ntransformation on the way to the generation of empirical results that\nare ultimately compared to theoretical predictions, considered\ntogether with metadata associated with their provenance. Such metadata\nincludes information about theoretical assumptions that are made in\ndata collection, processing, and the presentation of empirical\nresults. Boyd argues that by appealing to metadata to\n‘rewind’ the processing of assumption-imbued empirical\nresults and then by re-processing them using new resources, the\nepistemic utility of empirical evidence can survive transitions to new\ncontexts. Thus, the enriched view of evidence supports the idea that\nit is not despite the intertwining of the theoretical and empirical\nthat scientists accomplish key epistemic aims, but often in virtue of\nit (ibid., 420). In addition, it makes the epistemic value of metadata\nencoding the various assumptions that have been made throughout the\ncourse of data collection and processing explicit.", "\nThe desirability of explicitly furnishing empirical data and results\nwith auxiliary information that allow them to travel can be\nappreciated in light of the ‘objectivity’ norm, construed\nas accessibility to interpersonal scrutiny. When data are repurposed\nin novel contexts, they are not only shared between subjects, but can\nin some cases be shared across radically different paradigms with\nincompatible theoretical commitments." ], "subsection_title": "3.5 Reuse" } ] }, { "main_content": [ "\nOne of the important applications of empirical evidence is its use in\nassessing the epistemic status of scientific theories. In this section\nwe briefly discuss philosophical work on the role of empirical\nevidence in confirmation/falsification of scientific theories,\n‘saving the phenomena,’ and in appraising the empirical\nadequacy of theories. However, further philosophical work ought to\nexplore the variety of ways that empirical results bear on the\nepistemic status of theories and theorizing in scientific practice\nbeyond these." ], "section_title": "4. The epistemic value of empirical evidence", "subsections": [ { "content": [ "\nIt is natural to think that computability, range of application, and\nother things being equal, true theories are better than false ones,\ngood approximations are better than bad ones, and highly probable\ntheoretical claims are better than less probable ones. One way to\ndecide whether a theory or a theoretical claim is true, close to the\ntruth, or acceptably probable is to derive predictions from it and use\nempirical data to evaluate them. Hypothetico-Deductive (HD)\nconfirmation theorists proposed that empirical evidence argues for\nthe truth of theories whose deductive consequences it verifies, and\nagainst those whose consequences it falsifies (Popper 1959, 32–34).\nBut laws and theoretical generalization seldom if ever entail\nobservational predictions unless they are conjoined with one or more\nauxiliary hypotheses taken from the theory they belong to. When the\nprediction turns out to be false, HD has trouble explaining which of\nthe conjuncts is to blame. If a theory entails a true prediction, it\nwill continue to do so in conjunction with arbitrarily selected\nirrelevant claims. HD has trouble explaining why the prediction does\nnot confirm the irrelevancies along with the theory of interest.", "\nAnother approach to confirmation by empirical evidence is Inference to the Best Explanation (IBE). The idea is roughly that an explanation of the evidence that exhibits certain desirable characteristics with respect to a family of candidate explanations is likely to be the true on (Lipton 1991). On this approach, it is in virtue of their successful explanation of the empirical evidence that theoretical claims are supported. Naturally, IBE advocates face the challenges of defending a suitable characterization of what counts as the ‘best’ and of justifying the limited pool of candidate explanations considered (Stanford 2006).", "\nBayesian approaches to scientific confirmation have garnered significant attention and are now widespread in philosophy of science. Bayesians hold that the evidential bearing of empirical evidence on a theoretical claim is to be understood in terms of likelihood or conditional probability. For example, whether empirical evidence\nargues for a theoretical claim might be thought to depend upon whether\nit is more probable (and if so how much more probable) than its denial\nconditional on a description of the evidence together with background\nbeliefs, including theoretical commitments. But by Bayes’\nTheorem, the posterior probability of the claim of interest (that is, its probability given the evidence) is proportional to that claim’s prior probability. How to justify the choice of these prior probability assignments is one of the most notorious points of contention arising for Bayesians. If one makes the assignment of priors a subjective matter decided by epistemic agents, then it is not clear that they can be justified. Once again, one’s use of evidence to evaluate a theory depends in part upon one’s theoretical commitments (Earman 1992, 33–86; Roush 2005, 149–186). If one instead appeals to chains of successive updating using Bayes’ Theorem based on past evidence, one has to invoke assumptions that generally do not obtain in actual scientific reasoning. For instance, to ‘wash out’ the influence of priors a limit theorem is invoked wherein we consider very many updating iterations, but much scientific reasoning of interest does not happen in the limit, and so in practice priors hold unjustified sway (Norton 2021, 33).", "\nRather than attempting to cast all instances of confirmation based on empirical evidence as belonging to a universal schema, a better approach may be to ‘go local’. Norton’s material theory of induction argues that inductive support arises from background knowledge, that is, from material facts that are domain specific. Norton argues that, for instance, the induction from “Some samples of the element bismuth melt at 271°C” to “all samples of the element bismuth melt at 271°C” is admissible not in virtue of some universal schema that carries us from ‘some’ to ‘all’ but matters of fact (Norton 2003). In this particular case, the fact that licenses the induction is a fact about elements: “their samples are generally uniform in their physical properties” (ibid., 650). This is a fact pertinent to chemical elements, but not to samples of material like wax (ibid.). Thus Norton repeatedly emphasizes that “all induction is local”.", " \nStill, there are those who may be skeptical about the very possibility of confirmation or of successful induction. Insofar as the bearing of evidence on theory is never totally decisive, insofar there is no single trusty universal schema that captures empirical support, perhaps the relationship between empirical evidence and scientific theory is not really about support after all. Giving up on empirical support would not automatically mean abandoning any epistemic value for empirical evidence. Rather than confirm theory, the epistemic role of evidence could be to constrain, for example by furnishing phenomena for theory to systematize or to adequately model.\n" ], "subsection_title": "4.1 Confirmation" }, { "content": [ "\nTheories are said to ‘save’ observable phenomena if they\nsatisfactorily predict, describe, or systematize them. How well a\ntheory performs any of these tasks need not depend upon the truth or\naccuracy of its basic principles. Thus according to Osiander’s\npreface to Copernicus’ On the Revolutions, a locus\nclassicus, astronomers “… cannot in any way attain to true\ncauses” of the regularities among observable astronomical\nevents, and must content themselves with saving the phenomena in the\nsense of using", "\n… whatever suppositions enable … [them] to be computed\ncorrectly from the principles of geometry for the future as well as\nthe past … (Osiander 1543, XX)\n", "\nTheorists are to use those assumptions as calculating tools without\ncommitting themselves to their truth. In particular, the assumption\nthat the planets revolve around the sun must be evaluated solely in\nterms of how useful it is in calculating their observable relative\npositions to a satisfactory approximation. Pierre Duhem’s\nAim and Structure of Physical Theory articulates a related\nconception. For Duhem a physical theory", "\n… is a system of mathematical propositions, deduced from a small\nnumber of principles, which aim to represent as simply and completely,\nand exactly as possible, a set of experimental laws. (Duhem 1906, 19)\n", "\n‘Experimental laws’ are general, mathematical descriptions\nof observable experimental results. Investigators produce them by\nperforming measuring and other experimental operations and assigning\nsymbols to perceptible results according to pre-established\noperational definitions (Duhem 1906, 19). For Duhem, the main function\nof a physical theory is to help us store and retrieve information\nabout observables we would not otherwise be able to keep track of. If\nthat is what a theory is supposed to accomplish, its main virtue\nshould be intellectual economy. Theorists are to replace reports of\nindividual observations with experimental laws and devise higher level\nlaws (the fewer, the better) from which experimental laws (the more,\nthe better) can be mathematically derived (Duhem 1906, 21ff).", "\nA theory’s experimental laws can be tested for accuracy and\ncomprehensiveness by comparing them to observational data. Let EL be\none or more experimental laws that perform acceptably well on such\ntests. Higher level laws can then be evaluated on the basis of how\nwell they integrate EL into the rest of the theory. Some data that\ndon’t fit integrated experimental laws won’t be\ninteresting enough to worry about. Other data may need to be\naccommodated by replacing or modifying one or more experimental laws\nor adding new ones. If the required additions, modifications or\nreplacements deliver experimental laws that are harder to integrate,\nthe data count against the theory. If the required changes are\nconducive to improved systematization the data count in favor of it.\nIf the required changes make no difference, the data don’t argue\nfor or against the theory." ], "subsection_title": "4.2 Saving the phenomena" }, { "content": [ "\nOn van Fraassen’s (1980) semantic account, a theory is\nempirically adequate when the empirical structure of at least one\nmodel of that theory is isomorphic to what he calls the\n“appearances” (45). In other words, when the theory\n“has at least one model that all the actual phenomena fit\ninside” (12). Thus, for van Fraassen, we continually check the\nempirical adequacy of our theories by seeing if they have the\nstructural resources to accommodate new observations. We’ll\nnever know that a given theory is totally empirically adequate, since\nfor van Fraassen, empirical adequacy obtains with respect to all that\nis observable in principle to creatures like us, not all that has\nalready been observed (69).", "\nThe primary appeal of dealing in empirical adequacy rather than\nconfirmation is its appropriate epistemic humility. Instead of\nclaiming that confirming evidence justifies belief (or boosted\nconfidence) that a theory is true, one is restricted to saying that\nthe theory continues to be consistent with the evidence as far as we\ncan tell so far. However, if the epistemic utility of empirical\nresults in appraising the status of theories is just to judge their\nempirical adequacy, then it may be difficult to account for the\ndifference between adequate but unrealistic theories, and those\nequally adequate theories that ought to be taken seriously as\nrepresentations. Appealing to extra-empirical virtues like parsimony\nmay be a way out, but one that will not appeal to philosophers\nskeptical of the connection thereby supposed between such virtues and\nrepresentational fidelity." ], "subsection_title": "4.3 Empirical adequacy" } ] }, { "main_content": [ "\nOn an earlier way of thinking, observation was to serve as the\nunmediated foundation of science—direct access to\nthe facts upon which the edifice of scientific knowledge could be\nbuilt. When conflict arose between factions with different ideological\ncommitments, observations could furnish the material for neutral\narbitration and settle the matter objectively, in virtue of being\nindependent of non-empirical commitments. According to this view,\nscientists working in different paradigms could at least appeal to the\nsame observations, and propagandists could be held accountable to the\npublicly accessible content of theory and value-free observations.\nDespite their different theories, Priestley and Lavoisier could find\nshared ground in the observations. Anti-Semites would be compelled to\nadmit the success of a theory authored by a Jewish physicist, in\nvirtue of the unassailable facts revealed by\nobservation.", "\nThis version of empiricism with respect to science does not accord\nwell with the fact that observation per se plays a relatively small\nrole in many actual scientific methodologies, and the fact that even\nthe most ‘raw’ data is often already theoretically imbued.\nThe strict contrast between theory and observation in science is more\nfruitfully supplanted by inquiry into the relationship between\ntheorizing and empirical results.", "\nContemporary philosophers of science tend to embrace the theory\nladenness of empirical results. Instead of seeing the integration of\nthe theoretical and the empirical as an impediment to furthering\nscientific knowledge, they see it as necessary. A ‘view from\nnowhere’ would not bear on our particular theories. That is, it\nis impossible to put empirical results to use without recruiting some\ntheoretical resources. In order to use an empirical result to\nconstrain or test a theory it has to be processed into a form that can\nbe compared to that theory. To get stellar spectrograms to bear on\nNewtonian or relativistic cosmology, they need to be\nprocessed—into galactic rotation curves, say. The spectrograms\nby themselves are just artifacts, pieces of paper. Scientists need\ntheoretical resources in order to even identify that such artifacts\nbear information relevant for their purposes, and certainly to put\nthem to any epistemic use in assessing theories.", "\nThis outlook does not render contemporary philosophers of science all\nconstructivists, however. Theory mediates the connection between the\ntarget of inquiry and the scientific worldview, it does not sever it.\nMoreover, vigilance is still required to ensure that the particular\nways in which theory is ‘involved’ in the production of\nempirical results are not epistemically detrimental. Theory can be\ndeployed in experiment design, data processing, and presentation of\nresults in unproductive ways, for instance, in determining whether the\nresults will speak for or against a particular theory regardless of\nwhat the world is like. Critical appraisal of the roles of theory is\nthus important for genuine learning about nature through science.\nIndeed, it seems that extra-empirical values can sometimes assist such\ncritical appraisal. Instead of viewing observation as the theory-free\nand for that reason furnishing the content with which to appraise\ntheories, we might attend to the choices and mistakes that can be made\nin collecting and generating empirical results with the help of\ntheoretical resources, and endeavor to make choices conducive to\nlearning and correct mistakes as we discover them.", "\nRecognizing the involvement of theory and values in the constitution\nand generation of empirical results does not undermine the special\nepistemic value of empirical science in contrast to propaganda and\npseudoscience. In cases where the influence of cultural, political,\nand religious values hinder scientific inquiry, it is often the case\nthat they do so by limiting or determining the nature of the empirical\nresults. Yet, by working to make the assumptions that shape results\nexplicit we can examine their suitability for our purposes and attempt\nto restructure inquiry as necessary. When disagreements arise,\nscientists can attempt to settle them by appealing to the causal\nconnections between the research target and the empirical data. The\ntribunal of experience speaks through empirical results, but it only\ndoes so through via careful fashioning with theoretical resources." ], "section_title": "5. Conclusion", "subsections": [] } ]

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[ "\nStudy of the social dimensions of scientific knowledge encompasses the\neffects of scientific research on human life and social relations, the\neffects of social relations and values on scientific research, and the\nsocial aspects of inquiry itself. Several factors have combined to\nmake these questions salient to contemporary philosophy of science.\nThese factors include the emergence of social movements, like\nenvironmentalism and feminism, critical of mainstream science;\nconcerns about the social effects of science-based technologies;\nepistemological questions made salient by big science; new trends in\nthe history of science, especially the move away from internalist\nhistoriography; anti-normative approaches in the sociology of science;\nturns in philosophy to naturalism and pragmatism. This entry reviews\nthe historical background to current research in this area and\nfeatures of contemporary science that invite philosophical attention.", "\nThe philosophical work can roughly be classified into two camps. One\nacknowledges that scientific inquiry is in fact carried out in social\nsettings and asks whether and how standard epistemology must be\nsupplemented to address this feature. The other treats sociality as a\nfundamental aspect of knowledge and asks how standard epistemology\nmust be modified or reformed from this broadly social perspective.\nConcerns in the supplementing approach include such matters as trust\nand accountability raised by multiple authorship, the division of\ncognitive labor, the reliability of peer review, the challenges of\nprivately funded science, as well as concerns arising from the role of\nscientific research in society. The reformist approach highlights the\nchallenge to normative philosophy from social, cultural, and feminist\nstudies of science while seeking to develop philosophical models of\nthe social character of scientific knowledge and inquiry. It treats\nthe questions of the division of cognitive labor, expertise and\nauthority, the interactions of science and society, etc., from the\nperspective of philosophical models of the irreducibly social\ncharacter of scientific knowledge. Philosophers employ both formal\nmodeling techniques and conceptual analysis in their efforts to\nidentify and analyze epistemologically relevant social aspects of\nscience." ]

[ { "content_title": "1. Historical Background", "sub_toc": [] }, { "content_title": "2. Big Science, Trust, and Authority", "sub_toc": [] }, { "content_title": "3. Science in Society", "sub_toc": [] }, { "content_title": "4. Social, Cultural, and Feminist Studies of Science", "sub_toc": [] }, { "content_title": "5. Models of the Social Character of Knowledge", "sub_toc": [] }, { "content_title": "6. Social Direction of Science", "sub_toc": [] }, { "content_title": "7. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Works Cited", "Further Reading" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nPhilosophers who study the social character of scientific knowledge\ncan trace their lineage at least as far as John Stuart Mill. Mill,\nCharles Sanders Peirce, and Karl Popper all took some type of critical\ninteraction among persons as central to the validation of knowledge\nclaims.", "\nMill’s arguments occur in his well-known political essay On\nLiberty, (Mill 1859) rather than in the context of his logical and\nmethodological writings, but he makes it clear that they are to apply\nto any kind of knowledge or truth claim. Mill argues from the\nfallibility of human knowers to the necessity of unobstructed\nopportunity for and practice of the critical discussion of ideas. Only\nsuch critical discussion can assure us of the justifiability of the\n(true) beliefs we do have and can help us avoid falsity or the\npartiality of belief or opinion framed in the context of just one\npoint of view. Critical interaction maintains the freshness of our\nreasons and is instrumental in the improvement of both the content and\nthe reasons of our beliefs. The achievement of knowledge, then, is a\nsocial or collective, not an individual, matter.", "\nPeirce’s contribution to the social epistemology of science is\ncommonly taken to be his consensual theory of truth: “The\nopinion which is fated to be ultimately agreed to by all who\ninvestigate is what we mean by truth, and the object represented is\nthe real.” (Peirce 1878, 133) While often read as meaning that\nthe truth is whatever the community of inquirers converges on in the\nlong run, the notion is interpretable as meaning more precisely either\nthat truth (and “the real”) depends on the agreement of\nthe community of inquirers or that it is an effect of the real that it\nwill in the end produce agreement among inquirers. Whatever the\ncorrect reading of this particular statement, Peirce elsewhere makes\nit clear that, in his view, truth is both attainable and beyond the\nreach of any individual. “We individually cannot hope to attain\nthe ultimate philosophy which we pursue; we can only seek it for the\ncommunity of philosophers.” (Peirce 1868, 40). Peirce puts great\nstock in instigating doubt and critical interaction as means to\nknowledge. Thus, whether his theory of truth is consensualist or\nrealist, his view of the practices by which we attain it grants a\ncentral place to dialogue and social interaction.", "\nPopper is often treated as a precursor of social epistemology because\nof his emphasis on the importance of criticism in the development of\nscientific knowledge. Two concepts of criticism are found in his works\n(Popper 1963, 1972) and these can be described as logical and\npractical senses of falsification. The logical sense of falsification\nis just the structure of a modus tollens argument, in which a\nhypothesis is falsified by the demonstration that one of its logical\nconsequences is false. This is one notion of criticism, but it is a\nmatter of formal relations between statements. The practical sense of\nfalsification refers to the efforts of scientists to demonstrate the\ninadequacies of one another’s theories by demonstrating\nobservational shortcomings or conceptual inconsistencies. This is a\nsocial activity. For Popper the methodology of science is\nfalsificationist in both its logical and practical senses, and science\nprogresses through the demonstration by falsification of the\nuntenability of theories and hypotheses. Popper’s logical\nfalsificationism is part of an effort to demarcate genuine science\nfrom pseudo science, and has lost its plausibility as a description of\nscientific methodology as the demarcation project has come under\nchallenge from naturalist and historicist approaches in philosophy of\nscience. While criticism does play an important role in some current\napproaches in social epistemology, Popper’s own views are more\nclosely approximated by evolutionary epistemology, especially that\nversion that treats cognitive progress as the effect of selection\nagainst incorrect theories and hypotheses. In contrast to Mill’s\nviews, for Popper the function of criticism is to eliminate false\ntheories rather than to improve them.", "\nThe work of Mill, Peirce, and Popper is a resource for philosophers\npresently exploring the social dimensions of scientific knowledge.\nHowever, the current debates are framed in the context of developments\nin both philosophy of science and in history and social studies of\nscience following the collapse of the logical empiricist consensus.\nThe philosophers of the Vienna Circle are conventionally associated\nwith an uncritical form of positivism and with the logical empiricism\nthat replaced American pragmatism in the 1940s and 1950s. According to\nsome recent scholars, however, they saw natural science as a potent\nforce for progressive social change. (Cartwright, Cat, and Chang 1996;\nGiere and Richardson, eds., 1996; Uebel 2005) With its grounding in\nobservation and public forms of verification, science for them\nconstituted a superior alternative to what they saw as metaphysical\nobscurantism, an obscurantism that led not only to bad thinking but to\nbad politics. While one development of this point of view leads to\nscientism, the view that any meaningful question can be answered by\nthe methods of science; another development leads to inquiry into what\nsocial conditions promote the growth of scientific knowledge. Logical\nempiricism, the version of Vienna Circle philosophy that developed in\nthe United States, focused on logical, internal aspects of scientific\nknowledge and discouraged philosophical inquiry into the social\ndimensions of science. These came into prominence again after the\npublication of Thomas Kuhn’s Structure of Scientific\nRevolutions (Kuhn 1962). A new generation of sociologists of\nscience, among them Barry Barnes, Steven Shapin, and Harry Collins,\ntook Kuhn’s emphasis on the role of non-evidential community\nfactors in scientific change even further than he had and argued that\nscientific judgment was determined by social factors, such as\nprofessional interests and political ideologies (Barnes 1977, Shapin\n1982, Collins 1983). This family of positions provoked a\ncounter-response among philosophers. These responses are marked by an\neffort to acknowledge some social dimensions to scientific knowledge\nwhile at the same time maintaining its epistemological legitimacy,\nwhich they take to be undermined by the new sociology. At the same\ntime, features of the organization of scientific inquiry compel\nphilosophers to consider their implications for the normative analysis\nof scientific practices." ], "section_title": "1. Historical Background", "subsections": [] }, { "main_content": [ "\nThe second half of the twentieth century saw the emergence of what has\ncome to be known as Big Science: the organization of large numbers of\nscientists bringing different bodies of expertise to a common research\nproject. The original model was the Manhattan Project, undertaken\nduring the Second World War to develop an atomic weapon in the United\nStates. Theoretical and experimental physicists located at various\nsites across the country, though principally at Los Alamos, New\nMexico, worked on sub-problems of the project under the overall\ndirection of J. Robert Oppenheimer. While academic and military\nresearch have since been to some degree separated, much experimental\nresearch in physics, especially high energy particle physics,\ncontinues to be pursued by large teams of researchers. Research in\nother areas of science as well, for example the work comprehended\nunder the umbrella of the Human Genome Project, has taken on some of\nthe properties of Big Science, requiring multiple forms of expertise.\nIn addition to the emergence of Big Science, the transition from small\nscale university or even amateur science to institutionalized research\nwith major economic impacts supported by national funding bodies and\nconnected across international borders has seemed to call for new\nethical and epistemological thinking. Moreover, the consequent\ndependence of research on central funding bodies and increasingly,\nprivate foundations or commercial entities, prompts questions about\nthe degree of independence of contemporary scientific knowledge from\nits social and economic context.", "\nJohn Hardwig (1985) articulated one philosophical dilemma posed by\nlarge teams of researchers. Each member or subgroup participating in\nsuch a project is required because each has a crucial bit of expertise\nnot possessed by any other member or subgroup. This may be knowledge\nof a part of the instrumentation, the ability to perform a certain\nkind of calculation, the ability to make a certain kind of measurement\nor observation. The other members are not in a position to evaluate\nthe results of other members’ work, and hence, all must take one\nanothers’ results on trust. The consequence is an experimental\nresult, (for example, the measurement of a property such as the decay\nrate or spin of a given particle) the evidence for which is not fully\nunderstood by any single participant in the experiment. This leads\nHardwig to ask two questions, one about the evidential status of\ntestimony, and one about the nature of the knowing subject in these\ncases. With respect to the latter, Hardwig says that either the group\nas a whole, but no single member, knows or it is possible to know\nvicariously. Neither of these is palatable to him. Talking about the\ngroup or the community knowing smacks of superorganisms and\ntranscendent entities and Hardwig shrinks from that solution.\nVicarious knowledge, knowing without oneself possessing the evidence\nfor the truth of what one knows, requires, according to Hardwig, too\nmuch of a departure from our ordinary concepts of knowledge.", "\nThe first question is, as Hardwig notes, part of a more general\ndiscussion about the epistemic value of testimony. Much of what passes\nfor common knowledge is acquired from others. We depend on experts to\ntell us what is wrong or right with our appliances, our cars, our\nbodies. Indeed, much of what we later come to know depends on what we\npreviously learned as children from our parents and teachers. We\nacquire knowledge of the world through the institutions of education,\njournalism, and scientific inquiry. Philosophers disagree about the\nstatus of beliefs acquired in this way. Here is the question: If\nA knows that p on the basis of evidence e,\nB has reason to think A trustworthy and B\nbelieves p on the basis of A’s testimony that\np, does B also know that p? Some\nphilosophers, as Locke and Hume seem to have, argue that only what one\nhas observed oneself could count as a good reason for belief, and that\nthe testimony of another is, therefore, never on its own sufficient\nwarrant for belief. Thus, B does not know simply on the basis\nof A’s testimony but must have additional evidence\nabout A’s reliability. While this result is consistent\nwith traditional philosophical empiricism and rationalism, which\nemphasized the individual’s sense experience or rational\napprehension as foundations of knowledge, it does have the consequence\nthat we do not know most of what we think we know.", "\nA number of philosophers have recently offered alternative analyses\nfocusing on one or another element in the problem. Some argue that\ntestimony by a qualified expert is itself evidential, (Schmitt 1988),\nothers that the expert’s evidence constitutes good reason for,\nbut is not itself evidential for the recipient of testimony (Hardwig\n1985, 1988), others that what is transmitted in testimony is knowledge\nand not just propositional content and thus the question of the kind\nof reason a recipient of testimony has is not to the point (Welbourne\n1981).", "\nHowever this dispute is resolved, questions of trust and authority\narise in a particularly pointed way in the sciences, and\nHardwig’s dilemma for the physics experiment is also a specific\nversion of a more general phenomenon. A popular conception of science,\nfed partly by Popper’s falsificationism, is that it is\nepistemically reliable because the results of experiments and\nobservational studies are checked by independent repetition. In\npractice, however, only some results are so checked and many are\nsimply accepted on trust. Not only must positive results be accepted\non trust, but claims of failure to replicate as well as other\ncritiques must be also. Thus, just as in the non-scientific world\ninformation is accepted on trust, so in science, knowledge grows by\ndepending on the testimony of others. What are the implications of\naccepting this fact for our conceptions of the reliability of\nscientific knowledge?", "\nThe philosopher of biology, David Hull, argued in his (1988) that\nbecause the overall structure of reward and punishment in the sciences\nis a powerful incentive not to cheat, further epistemological analysis\nof the sciences is unnecessary. What scientists have to lose is their\nreputation, which is crucial to their access to grants,\ncollaborations, prizes, etc. So the structure itself guarantees the\nveridicality of research reports. But some celebrated recent episodes,\nsuch as the purported production of “cold fusion” were\ncharacterized by the failure of replication attempts to produce the\nsame phenomenon. And, while the advocates of cold fusion were\nconvinced that their experiments had produced the phenomenon, there\nhave also been cases of outright fraud. Thus, even if the structure of\nreward and punishment is an incentive not to cheat, it does not\nguarantee the veridicality of every research report.", "\nOn Hull’s view, the scientific community seeks true theories or\nadequate models. Credit, or recognition, accrues to individuals to the\nextent they are perceived as having contributed to that community\ngoal. That is, individual scientists seek reputation and recognition,\nto have their work cited as important and as necessary to further\nscientific progress. Cheating, by misreporting experimental results or\nother misconduct, will be punished by loss of reputation. But this\ndepends on strong guarantees of detection. Absent such guarantees,\nthere is as strong an incentive to cheat, to try to obtain credit\nwithout necessarily having done the work, as not to cheat.", "\nBoth Alvin Goldman (Goldman, 1995, 1999) and Philip Kitcher (1993)\nhave treated the potential for premature, or otherwise (improperly)\ninterested reporting of results to corrupt the sciences as a question\nto be answered by means of decision theoretic models. The decision\ntheoretic approach to problems of trust and authority treats both\ncredit and truth as utilities. The challenge then is to devise\nformulas that show that actions designed to maximize credit also\nmaximize truth. Kitcher, in particular, develops formulas intended to\nshow that even in situations peopled by non-epistemically motivated\nindividuals (that is, individuals motivated more by a desire for\ncredit than by a desire for truth), the reward structure of the\ncommunity can be organized in such a way as to maximize truth and\nfoster scientific progress. One consequence of this approach is to\ntreat scientific fraud and value or interest infused science as the\nsame problem. One advantage is that it incorporates the motivation to\ncheat into the solution to the problem of cheating. But one may wonder\nhow effective this solution really is. Increasingly, we learn of\nproblematic behavior in science based industries, such as the\npharmaceutical industry. Results are withheld or distorted, authorship\nis manipulated. Hot areas, such as stem cell research, cloning, or\ngene modification, have been subjected to fraudulent research. Thus,\neven if the structure of reward and punishment is an in principle\nincentive not to cheat, it does not guarantee the reliability of every\nresearch report. The decision theoretic model needs to include at\nleast one more parameter, namely the anticipated likelihood of\ndetection within a relevant timeframe.", "\nCommunity issues have also been addressed under the banners of\nresearch ethics and of peer review. One might think that the only\nethical requirements on scientists are to protect their research\nsubjects from harm and, as professional scientists, to seek truth\nabove any other goals. This presupposes that seeking truth is a\nsufficient guide to scientific decision-making. Heather Douglas, in\nher critical study of the ideal of value-freedom (Douglas 2009),\nrejects this notion. Douglas draws on her earlier study of inductive\nrisk (Douglas 2000) to press the point that countless methodological\ndecisions required in the course of carrying out a single piece of\nresearch are underdetermined by the factual elements of the situation\nand must be guided by an assessment of the consequences of being\nwrong. Science is not value-free, but can be protected from the\ndeleterious effects of values if scientists take steps to mitigate the\ninfluence of inappropriate values. One step is to distinguish between\ndirect and indirect roles of values; another is the articulation of\nguidelines for individual scientists. Values play a direct role when\nthey provide direct motivation to accept or reject a theory; they play\nan indirect role when they play a role in evaluating the consequences\nof accepting or rejecting a claim, thus influencing what will count as\nsufficient evidence to accept or reject. The responsibility of\nscientists is to make sure that values do not play a direct role in\ntheir work and to be transparent about the indirect roles of values. A\nnumber of writers have taken issue with the tenability of\nDouglas’s distinction between direct and indirect. Steel and\nWhyte (2012) examine testing guidelines developed by pharmaceutical\ncompanies to point out that the very same decision may be motivated by\nvalues playing a direct role or playing an indirect role. If the point\nis to prohibit practices such as withholding negative results, then it\nshouldn’t matter whether the practice is motivated by values\nfunctioning directly or indirectly. Elliott (2011) questions whether\nonly harmful consequences should be considered. If science is to be\nuseful to policy makers, then questions of relative social benefit\nshould also be permitted to play a role. Finally the cognitive\nactivities demanded by Douglas’s ethical prescriptions for\nscientists seem beyond the capacities of individual scientists. This\npoint will be pursued below.", "\nTorsten Wilholt (2013) argues that the research situation is more\ncomplicated than the epistemic vs. nonepistemic tradeoff implied by\nthe decision theoretic approach. In part because of the difficulties\nin achieving the degree of knowledge required to realize\nDouglas’s ethical prescriptions, he argues that the reliance\ncalled for in science extends beyond the veridicality of reported\nresults to the values guiding the investigators relied upon. Most\nresearch involves both results expressed statistically (which requires\nchoice of significance threshold and balancing chances of Type I vs.\nType II error) and multiple steps each requiring methodological\ndecisions. These decisions, Wilholt argues, represent trade-offs among\nthe reliability of positive results, the reliability of negative\nresults, and the power of the investigation. In making these\ntradeoffs, the investigator is per force guided by an evaluation of\nthe consequences of the various possible outcomes of the study.\nWilholt extends the arguments about inductive risk offered originally\nby Richard Rudner and elaborated by Heather Douglas to propose that,\nin relying on another’s results I am relying not only on their\ncompetence and truthfulness, but on their making methodological\ndecisions informed by the same valuations of outcomes as I have. This\nattitude is more than epistemic reliance, but a deeper attitude: one\nof trust that we are guided by the same values in a shared enterprise.\nFor Wilholt, then, scientific inquiry engages ethical norms as well as\nepistemic norms. Formal or mechanical solutions such as those\nsuggested by the application of decision theoretic models are not\nsufficient, if the community must be held together by shared ethical\nvalues.", "\nPeer review and replication are methods the scientific community,\nindeed the research world in general, employs to assure consumers of\nscientific research that the work is credible. Peer review both of\nresearch proposals and of research reports submitted for publication\nscreens for quality, which includes methodological competence and\nappropriateness as well as for originality and significance, while\nreplication is intended to probe the robustness of results when\nreported experiments are carried out in different laboratories and\nwith slight changes to experimental conditions. Scholars of peer\nreview have noted various forms of bias entering into the peer review\nprocess. In a review of the literature, Lee, Sugimoto, Zhang, and\nCronin (2013) report documented bias along gender, language,\nnationality, prestige, and content as well as such problems as lack of\ninter-reviewer reliability consistency, confirmation bias, and\nreviewer conservatism. Lee (2012) argues that a Kuhnian perspective on\nvalues in science interprets lack of inter-reviewer consistency as\nvariation in interpretation, applicability, and weight assigned to\nshared values by different members of the scientific community. Lee\nand colleagues (2013) argue that journal editors must take much more\naction than is currently taken to require that researchers make their\nraw data and other relevant trial information available to enable peer\nreviewers to conduct their work adequately.", "\nOne issue that has yet to be addressed by philosophers is the gap\nbetween the ideal of replication resulting in confirmation,\nmodification, or retraction and the reality. This ideal lies behind\nthe assumptions of efficacy of structures of reward and sanction. Only\nif researchers believe that their research reports will be probed by\nefforts at replication will the threat of sanctions against faulty or\nfraudulent research be realistic. John Ioannidis and collaborators\n(Tatsioni, Bonitsis, and Ioannidis 2007; Young, N.S. Ioannidis, and\nAl-Ubaydli 2008) have shown how infrequently attempts to replicate are\nactually made and, even more strikingly, how contradicted results\npersist in the literature. This is an issue that goes beyond\nindividuals and beyond large research collaborators to the scientific\ncommunity in general. It underscores Wilholt’s contention that\nthe scientific community must be held together by bonds of trust, but\nmuch more empirical and philosophical work is needed to address how to\nproceed when such trust is not justified. The demonstration of\nwidespread lack of replicability on studies in psychology and in\nbiomedical research has prompted debate about the causes and the\nseriousness of the alleged crisis (Loken and Gelman 2017; Ioannidis\n2007; Redish, Kummerfeld, Morris, and Love 2018).", "\nWinsberg, Huebner, and Kukla (2013) draw attention to a different kind\nof supra-empirical, ethical issue raised by the contemporary situation\nof multiple authorship. What they call “radically collaborative\nresearch” involves investigators with different forms of\nexpertise, as in Hardwig’s example, and as is now common across\nmany fields, collaborating to generate an experimental result. For\nWinsberg, Huebner, and Kukla, the question is not merely reliability,\nbut accountability. Who can speak for the integrity of the research\nwhen it has been conducted by researchers with a variety not just of\ninterests, but of methodological standards, most opaque one to\nanother? Winsberg, Huebner, and Kukla argue that a model of the social\ncollaboration is needed as much as a model of the data or of the\ninstruments. They argue further that the laissez-faire Wisdom of\nCrowds model (according to which local differences in methodological\nstandards will cancel each other out), while perhaps adequate if the\nquestion is one of reliability, is not adequate for addressing these\nissues of accountability. They do not themselves, however, offer an\nalternative model." ], "section_title": "2. Big Science, Trust, and Authority", "subsections": [] }, { "main_content": [ "\nWork on the role of science in society encompasses both general models\nof the public authority of science and analysis of particular research\nprograms that have a bearing on public life. In their early work,\nSteve Fuller and Joseph Rouse were both concerned with political\ndimensions of cognitive authority. Rouse, whose (1987) integrated\nanalytic and continental philosophy of science and technology, sought\nto develop what might be called a critical pragmatism. This\nperspective facilitated an analysis of the transformative impact of\nscience on human life and social relations. Rouse emphasized the\nincreased power over individual lives that developments in science\nmake possible. This can only be said to have increased with the\ndevelopment of information technology. Fuller (1988) partially\naccepted the empirical sociologists’ claim that traditional\nnormative accounts of scientific knowledge fail to get a purchase on\nactual scientific practices, but took this as a challenge to relocate\nthe normative concerns of philosophers. These should include the\ndistribution and circulation of knowledge claims. The task of social\nepistemology of science, according to Fuller, should be regulation of\nthe production of knowledge by regulating the rhetorical,\ntechnological, and administrative means of its communication. While\nthere has not been much uptake of Fuller’s proposals as\narticulated, Lee’s work mentioned above begins to make detailed\nrecommendations that take into account the current structures of\nfunding and communication.", "\nOne key area of socially relevant interdisciplinary science is risk\nassessment, which involves both research on the effects of various\nsubstances or practices and the evaluation of those effects once\nidentified. The idea is to gain an understanding of both positive\neffects and of negative effects and a method of evaluating these. This\ninvolves integrating the work of specialists in the kind of substance\nwhose risks are under assessment (geneticists, chemists, physicists),\nbiomedical specialists, epidemiologists, statisticians, and so on. In\nthese cases, we are dealing not only with the problems of trust and\nauthority among specialists from different disciplines, but also with\nthe effects of introducing new technologies or new substances into the\nworld. The risks studied are generally of harm to human health or to\nthe environment. Interest in applying philosophical analysis to risk\nassessment originated in response to debates about the development and\nexpansion of nuclear power-generating technologies. In addition, the\napplication of cost-benefit analysis and attempts to understand\ndecision-making under conditions of uncertainty became topics of\ninterest as extensions of formal modeling techniques (Giere 1991).\nThese discussions intersect with debates about the scope of rational\ndecision theory and have expanded to include other technologies as\nwell as applications of scientific research in agriculture and in the\nmyriad forms of biological engineering. Essays on the relation between\nscience and social values in risk research collected in the volume\nedited by Deborah Mayo and Rachelle Hollander (1991) attempt to steer\na course between uncritical reliance on cost-benefit models and their\nabsolute rejection. Coming from a slightly different angle, the\nprecautionary principle represents an approach shifting the burden of\nproof in regulatory decisions from demonstration of harm to\ndemonstration of safety of substances and practices. Carl Cranor\n(2004) explores versions of the principle and defends its use in\ncertain decision contexts. Shrader-Frechette (2002) has advocated\nmodels of ethically weighted cost-benefit analysis and greater public\ninvolvement in risk assessment. In particular she (Shrader-Frechette\n1994, 2002) has argued for including members of the public in\ndeliberations about health effects of and reasonable exposure limits\non environmental pollutants, especially radioactive materials.\nPhilosophers of science have also worked to make visible the ways in\nwhich values play a role in the research assessing the effects of\ntechno-scientifically produced substances and practices themselves, as\ndistinct from the challenges of assigning values to identified risks\nand benefits.", "\nDouglas (2000) is an influential study of toxicological research on\neffects of exposure to dioxins. Douglas set her analysis in the\nframework of inductive risk introduced by Richard Rudner (1953) and\nalso explored by Carl Hempel (1965). The ampliative character of\ninductive inference means that the premises can be true (and even\nstrongly supportive) and the conclusion false. Rudner argued that this\nfeature of inductive inference means that scientists ought to take the\nconsequences of being wrong into account when determining how strong\nthe evidence for a hypothesis needs to be before accepting the\nhypothesis. [But see Jeffrey (1956) for a different view.] Douglas\nproposes that such considerations reach deeper into the scientific\nprocess than the acceptance of a conclusion based on the evidence to\nthe construction of the evidence itself. Scientists must make\ndecisions about levels of statistical significance, how to balance the\nchance of false positives against the chance of false negatives. They\nmust determine protocols for deciding borderline cases in their tissue\nsamples. They must select among possible dose-response models.\nDeciding in one way has one set of social consequences, and in another\nway another, opposing, set of consequences. Douglas claims that\nscientists ought to take these risks into account when making the\nrelevant methodological decisions. Since, even in her examples, public\nhealth considerations point in one direction and economic\nconsiderations point in another, in the end it is not clear just what\nresponsibility can reasonably be assigned to the individual\nscientist.", "\nIn addition to risk assessment, philosophers have begun thinking about\na variety of research programs and methods that affect human\nwellbeing. Lacey (2005), for example, delineates the contrasting\nvalues informing industrial, conventional agriculture on the one hand\nand small-scale agroecology on the other. Cartwright (2012),\nelaborated in Cartwright and Hardie (2012), is primarily a critical\nanalysis of the reliance on randomized control trials to support\npolicy decisions in economic development, medicine, and education.\nThese fail to take account of variations in contexts of application\nthat will affect the outcome. Cartwright’s focus on a particular\nmethodological approach is an extension of philosophers’\ntraditional engagement in areas of controversy in which philosophical\nanalysis might make a difference. Philip Kitcher’s (1985), which\ntook on sociobiology, and Elliott Sober and David Sloan Wilson’s\n(1998), an extensive argument for group level selection, are examples\nthat focus on content and methodology of extensions of evolutionary\ntheory.", "\nClimate change research has provoked several quite different kinds of\nanalysis. As a complex interdisciplinary field, its evidential\nstructure leaves it vulnerable to challenge. Opponents of limiting the\nuse of fossil fuels have exploited those vulnerabilities to sow public\ndoubts about the reality and/or causes of climate change (Oreskes and\nConway 2011). Parker 2006, Lloyd 2010, Parker 2010, Winsberg 2012\nhave, respectively, investigated strategies for reconciling apparent\ninconsistencies among climate models, the differences between\nmodel-based projections and strictly inductive projections, methods\nfor assessing and communicating the uncertainties inherent in climate\nmodels. Philosophers have also considered how to interpret the\n(American) public’s susceptibility to the climate change\ndeniers. Philip Kitcher (2012) interprets it as lack of information\namid a plethora of misinformation and proposes methods for more\neffective communication of reputable science to the public. Anderson\n(2011), on the contrary, contends that members of the public are\nperfectly able to evaluate the reliability of contradictory\nassessments by following citation trails, etc., whether on the\ninternet or in hard copies of journals. Her view is that the\nreluctance to accept the reality of climate change is a reluctance to\nabandon familiar ways of life, which is what averting climate-caused\ndisaster requires all to do. Finally, there is an ethical and\npolitical question once the inevitability of climate change is\naccepted: how should the burdens of taking action be distributed? The\nindustrialized West is responsible for most of the carbon pollution up\nto the end of the 20th century, but developing nations trying to\nindustrialize have contributed an increasing share, and will continue\nto do so, in the 21st century. Who bears the burden? And if the\neffects will only be felt by generations in the future, why should\npresent generations take actions whose harms will be felt now and\nwhose benefits lie in the future and will not be experienced by those\nbearing the costs? Broome (2008) explores the intergenerational\nissues, while Raina (2015) explores the global dimensions.", "\nTwo additional areas of ongoing scientific controversy are the\nbiological reality (or not) of race and the biology of gender\ndifferences. Developments in genetics, and documented racial\ndifferences in health, have thrown doubt on earlier anti-realist views\nof race, such as those articulated by Stephen J. Gould (1981) and\nRichard Lewontin (Lewontin, Rose, and Kamin 1984). Spencer (2012,\n2014) argues for a sophisticated form of biological racial realism.\nGannett (2003) argues that biological populations are not independent\nobjects that can provide data relevant to racial realism, while Kaplan\nand Winther (2013) argue that no claims about race can be read from\nbiological theory or data. The reality and basis of observed gender\ndifferences were the subject of much debate in the late 20th\ncentury(See Fausto-Sterling 1992). These issues have crystallized in\nthe early 21st century in debates about the brain and cognition\ndrawing the attention of philosophers of biology and cognitive\nscientists. Rebecca Jordan-Young (2010), Cordelia Fine (2010), and\nBluhn, Jacobson and Maibom, eds. (2012) all explore, with an aim of\ndebunking, claims of gendered brains. " ], "section_title": "3. Science in Society", "subsections": [] }, { "main_content": [ "\nKuhn’s critique of logical empiricism included a strong\nnaturalism. Scientific rationality was to be understood by studying\nactual episodes in the history of science, not by formal analyses\ndeveloped from a priori concepts of knowledge and reason (Kuhn 1962,\n1977). Sociologists and sociologically inclined historians of science\ntook this as a mandate for the examination of the full spectrum of\nscientists’ practices without any prior prejudice as to which\nwere epistemically legitimate and which not. That very distinction\ncame under suspicion from the new social scholars, often labeled\n“social constructivists.” They urged that understanding\nthe production of scientific knowledge required looking at all the\nfactors causally relevant to the acceptance of a scientific idea, not\njust at those the researcher thinks should be relevant.", "\nA wide range of approaches in social and cultural studies of science\nhas come under the umbrella label of “social\nconstructivism.” Both terms in the label are understood\ndifferently in different programs of research. While constructivists\nagree in holding that those factors treated as evidential, or as\nrationally justifying acceptance, should not be privileged at the\nexpense of other causally relevant factors, they differ in their view\nof which factors are causal or worth examination. Macro-analytic\napproaches, such as those associated with the so-called Strong\nProgramme in the Sociology of Scientific Knowledge, treat social\nrelations as an external, independent factor and scientific judgment\nand content as a dependent outcome. Micro-analyses or laboratory\nstudies, on the other hand, abjure the implied separation of social\ncontext and scientific practice and focus on the social relations\nwithin scientific research programs and communities and on those that\nbind research-productive and research-receptive communities\ntogether.", "\nResearchers also differ in the degree to which they treat the social\nand the cognitive dimensions of inquiry as independent or interactive.\nThe researchers associated with the macro-analytic Strong Programme in\nthe Sociology of Scientific Knowledge (Barry Barnes, David Bloor,\nHarry Collins, Donald MacKenzie, Andrew Pickering, Steve Shapin) were\nparticularly interested in the role of large scale social phenomena,\nwhether widely held social/political ideologies or group professional\ninterests, on the settlement of scientific controversies. Some\nlandmark studies in this genre include Andrew Pickering’s (1984)\nstudy of competing professional interests in the interpretation of\nhigh energy particle physics experiments, and Steven Shapin and Simon\nShaffer’s (1985) study of the controversy between Robert Boyle\nand Thomas Hobbes about the epistemological relevance of experiments\nwith vacuum pumps.", "\nThe micro-sociological or laboratory studies approach features\nethnographic study of particular research groups, tracing the myriad\nactivities and interactions that eventuate in the production and\nacceptance of a scientific fact or datum. Karin Knorr Cetina’s\n(1981) reports her year-long study of a plant science laboratory at UC\nBerkeley. Bruno Latour and Steven Woolgar’s (1986) study of\nRoger Guillemin’s neuroendocrinology laboratory at the Salk\nInstitute is another classic in this genre. These scholars argued in\nsubsequent work (Knorr-Cetina 1983; Latour, 1987) that their form of\nstudy showed that philosophical analyses of rationality, of evidence,\nof truth and knowledge, were irrelevant to understanding scientific\nknowledge. Sharon Traweek’s (1988) comparative study of the\ncultures of Japanese and North American high energy physics\ncommunities pointed to the parallels between cosmology and social\norganization but abstained from making extravagant or provocative\nepistemological claims. The efforts of philosophers of science to\narticulate norms of scientific reasoning and judgment were, in the\nview of both macro- and micro-oriented scholars, misdirected, because\nactual scientists relied on quite different kinds of considerations in\nthe practice of science.", "\nUntil recently, apart from a few anomalous figures like Caroline\nHerschel, Barbara McClintock, and Marie Curie, the sciences were a\nmale preserve. Feminist scholars have asked what bearing the\nmasculinity of the scientific profession has had on the content of\nscience and on conceptions of scientific knowledge and practice.\nDrawing both on work by feminist scientists that exposed and critiqued\ngender biased science and on theories of gender, feminist historians\nand philosophers of science have offered a variety of models of\nscientific knowledge and reasoning intended to accommodate the\ncriticism of accepted science and the concomitant proposal and\nadvocacy of alternatives. Evelyn Keller (1985) proposed a\npsycho-dynamic model of knowledge and objectivity, arguing that a\ncertain psychological profile, facilitated by typical patterns of\nmasculine psychological development, associated knowledge and\nobjectivity with domination. The association of knowledge and control\ncontinues to be a topic of concern for feminist thinkers as it is also\nfor environmentally concerned critics of the sciences. In this\nconnection, see especially Lacey’s (2005) study of the\ncontroversy concerning transgenic crops. Other feminists turned to\nMarxist models of social relations and developed versions of\nstandpoint theory, which holds that the beliefs held by a group\nreflect the social interests of that group. As a consequence, the\nscientific theories accepted in a context marked by divisions of power\nsuch as gender will reflect the interests of those in power.\nAlternative theoretical perspectives can be expected from those\nsystematically excluded from power. (Harding 1986; Rose 1983; Haraway\n1978).", "\nStill other feminists have argued that some standard philosophical\napproaches to the sciences can be used to express feminist concerns.\nNelson (1990) adopts Quine’s holism and naturalism to analyze\ndebates in recent biology. Elizabeth Potter (2001) adapts Mary\nHesse’s network theory of scientific inference to analyse\ngendered aspects of 17th century physics. Helen Longino (1990)\ndevelops a contextual empiricism to analyze research in human\nevolution and in neuroendocrinology. In addition to the direct role\nplayed by gender bias, scholars have attended to the ways shared\nvalues in the context of reception can confer an a priori\nimplausibility on certain ideas. Keller (1983) argued that this was\nthe fate of Barbara McClintock’s unorthodox proposals of genetic\ntransposition. Stephen Kellert (1993) made a similar suggestion\nregarding the then resistance to so-called chaos theory, that is the\nuse of non-linear dynamics to model processes like climate change.", "\nWhat the feminist and empirical sociological analyses have in common\nis the view that the social organization of the scientific community\nhas a bearing on the knowledge produced by that community. There are\ndeep differences, however, in their views as to what features of that\nsocial organization are deemed relevant and how they are expressed in\nthe theories and models accepted by a given community. The gender\nrelations focused on by feminists went unrecognized by sociologists\npursuing macro- or microsociological research programs. The feminist\nscientists and scholars further differ from the scholars in empirical\nsocial and cultural studies of science in their call for alternative\ntheories and approaches in the sciences. These calls imply that\nphilosophical concerns with truth and justification are not only\nlegitimate but useful tools in advancing feminist transformative goals\nfor the sciences. As can be seen in their varying treatments of\nobjectivity, however, philosophical concepts are often reworked in\norder to be made applicable to the content or episodes of interest\n(See Anderson 2004, Haraway 1988, Harding 1993, Keller 1985, Longino\n1990, Nelson 1990, Wylie 2005)", "\nIn addition to differences in analysis of philosophical concepts like\nobjectivity, rationality, or truth, feminist philosophers of science\nhave also debated the proper role of contextual (sometimes called,\n“external” or “social”) values. Some feminists\nargue that, given that values do play a role in scientific inquiry,\nsocially progressive values ought to shape not only decisions about\nwhat to investigate but also the processes of justification.\nPhilosophers of science should incorporate exemplification of the\nright values in their accounts of confirmation or justification.\nOthers are less certain about the identification of the values that\nshould and those that should not inform the conduct of science. These\nphilosophers are dubious that a consensus exists, or is even possible\nin a pluralistic society, on what constitute the values that ought to\nguide inquiry. In an exchange with Ronald Giere, Janet Kourany (2003a,\n2003b) argues that not only science, but philosophy of science ought\nto be concerned with the promotion of socially progressive values.\nGiere (2003) replies that what counts as socially progressive will\nvary among philosophers, and that in a democracy, it is unlikely that\na unanimous or near unanimous consensus regarding the values to inform\nphilosophical analysis or scientific inquiry could be achieved either\nin the larger society or in the smaller social subset of philosophers\nof science." ], "section_title": "3. Social, Cultural, and Feminist Studies of Science", "subsections": [] }, { "main_content": [ "\nSince 1980, interest in developing philosophical accounts of\nscientific knowledge that incorporate the social dimensions of\nscientific practice has been on the increase. Some philosophers see\nattention to the social as a straightforward extension of already\ndeveloped approaches in epistemology. Others, inclined toward some\nform of naturalism, have taken the work in empirical social studies of\nscience discussed above seriously. They have, however, diverged quite\nconsiderably in their treatment of the social. Some understand the\nsocial as biasing or distorting, and hence see the social as opposed\nto or competing with the cognitive or epistemic. These philosophers\nsee the sociologists’ disdain for normative philosophical\nconcerns as part of a general debunking of science that demands a\nresponse and defense. Some philosophers see the social aspects of\nscience as incidental to deep questions about knowledge, but\ninformative about certain tendencies in scientific communities. Others\ntreat the social as instead constitutive of rationality. These\ndifferences in conception of the role and nature of the social inform\ndifferences in the several approaches to modeling the sociality of\ninquiry and knowledge discussed below.", "\nContemporary philosophers pursue both formal and informal modeling\napproaches in addressing the social character of knowledge. Those\npursuing formal models tend to bracket questions about rationality,\nobjectivity, or justification and concentrate on mathematically\ninvestigating the effects of community structures on features of the\npursuit of knowledge and its diffusion in a community. Those pursuing\ninformal models are more interested in understanding the role of the\ncommunity in enhancing or constituting desired features of inquiry\nsuch as rationality and objectivity and in thinking about the ways\nknowledge is realized", "\nCommunication and the division of cognitive labor. Among the\nfirst issues to be investigated using formal techniques was the\ndivision of cognitive labor. While big science projects such as\ndiscussed by Hardwig pose a problem of integrating disparate elements\nof the solution to a question, the division of cognitive labor\nconcerns the appropriate or optimal distribution of efforts towards\nsolving a given problem. If everyone follows the same research\nstrategy to solve a problem or answer a question, then a solution\nlying outside that strategy will not be reached. If such a solution is\nbetter than any attainable via the shared strategy, the community\nfails to attain the better solution. But how can it be rational to\nadopt a research strategy other than the one deemed at the time most\nlikely to succeed? Philip Kitcher in his (1993) was concerned to offer\nan alternative to the strong programme’s proposal that\ncontroversy and the persistence of alternative research programs were\na function of the varying social or ideological commitments of\nresearchers. However, he also acknowledged that if researchers\nfollowed only the strategy judged at the time most likely to lead to\ntruth, they would not pursue unorthodox strategies that might lead to\nnew discoveries. He therefore labeled the observed fact that\nresearchers pursued different approaches to the same problem as the\ndivision of cognitive labor and proposed a decision model that\nattributed the pursuit of a nonorthodox (maverick) research strategy\nto a rational calculation about the chances of a positive payoff. This\nchance was calculated on the basis of the likelihood of the maverick\nstrategy being successful (or more successful than the orthodox\napproach), the numbers of peers pursuing orthodox or other maverick\nstrategies, and the anticipated reward of success. A community can\nallocate research resources in such a way as to maintain the balance\nof orthodox and maverick scientists most likely to facilitate\nprogress. Thus, scientific progress can tolerate and indeed benefits\nfrom a certain amount of “impure” motivation. Michael\nStrevens (2003) argued instead that the pursuit of maverick research\nstrategies was to be expected as a consequence of the priority rule.\nThe priority rule refers to the practice of referring to a law or\nobject with the name of the first individual to articulate or perceive\nand identify it. Think of Boyle’s Law, Halley’s comet, the\nPlanck constant, Avogadro’s number, etc. There’s no such\nreward attached to pursuing a research strategy devised by another and\n“merely” adding to what that individual has already\ndiscovered. The rewards of research come from being first. And to be\nfirst requires pursuing a novel problem or strategy. The division of\ncognitive labor, understood as different researchers pursuing\ndifferent research strategies, is a simple effect of the priority\nrule. Muldoon and Weisberg (2011) reject both Kitcher’s and\nStrevens’s accounts as presupposing unrealistically uniform and\nideal agents. In reality, they observe, scientists have at best\nimperfect knowledge of the entire research situation, do not know the\nentirety of the research landscape, and when they do know, know\ndifferent things. They do not have sufficient information to employ\nthe decision methods Kitcher and Strevens attribute to them. Muldoon\nand Weisberg propose agent-based modeling as a means to represent the\nimperfect, non-overlapping, and partial knowledge of the agents\ndeciding what research problems and strategies to pursue.\nSolomon’s advocacy of dissensus discussed below can be\nunderstood as rejecting the premises of the problem. From that point\nof view the aim of scientific organization ought to be to promote\ndisagreement.", "\nKevin Zollman, following Bala and Goyal (1998), used network theory to\nmodel different possible communication structures. The aim of Zollman\n(2007, 2013) is to investigate what difference communication\nstructures make to the chances of a scientific community settling on a\ncorrect (or incorrect) theory or hypothesis and to the speed by which\nsuch a consensus is reached. Networks consist of nodes and edges that\nconnect them. The nodes can represent individuals or any group that\nhas uniform beliefs. The nodes can have values of believe or not\nbelieve and consensus consists in all nodes in the network taking the\nsame value. Zollman investigates three possible communication\nstructures: the cycle, in which each node is connected only to nodes\non either side of it in the cycle; the wheel, in which there is a\ncentral node to which all other nodes are exclusively connected; and\nthe complete, in which each node is connected to every other node.\nUsing the mathematics of network theory, Zollman proves the somewhat\ncounterintuitive thesis that the network with limited communication,\nthe cycle, has the highest probability of consensus on the correct\nhypothesis, while the network with the densest communication, the\ncomplete, has a non-negligible probability of consensus (from which\ndeparture is not possible) on the incorrect hypothesis. Zollman (2010)\nalso uses this method to investigate the division of labor problem,\nalthough he comes at it from a slightly different point of view that\ndo Kitcher or Strevens. Structures with sparse or limited\ncommunication are more likely to arrive at the correct hypothesis, but\nbecause they take longer to reach consensus, different research\napproaches may persist in such communities. Under the right\ncircumstances, this will prevent foreclosure on the incorrect\nhypothesis. Zollman implicitly blames a dense communication structure\nfor the premature abandonment of the bacterial hypothesis of peptic\nulcers. Diversity is a good thing as long as the evidence is not\ndecisive, and if the acid hypothesis, which held sway until a new\nstaining method showed the presence of Helicobacter pylori, had\nbeen slower to diffuse into the community, the bacterial hypothesis\nmight have been preserved long enough to be better supported.", "\nWhile Zollman presents his results as an alternative method to the\nreward mechanisms discussed by Kitcher, Strevens, and Muldoon and\nWeisberg, they do not include a mechanism for establishing any of the\nnetwork structures as the preferred communication system for a\nscientific community. Kitcher and the others were concerned with how\nagents might be motivated to pursue a theory or method whose chance of\nsuccess was either unknown or thought unlikely. Funding bodies like\ngovernmental science foundations and private foundations provide or\ncan provide the relevant reward structure. Prize-giving bodies, like\nthe Nobel Foundation or the Kavli Foundation, as well as historical\npractice, entrench the priority rule. Both of these are community\nmethods that can motivate the choice to pursue high risk, high reward\nresearch. It is not clear how communities would select communication\nstructures, nor what kind of system would be able to enforce a\nstructure. Rosenstock, O’Connor, and Bruner (2017) point out in\naddition that Zollman’s results are very sensitive to how\nparameters of the models are set. Adjust the number of nodes or the\nprobabilities assigned to the alternative strategies/hypotheses and\nthe Zollman effect disappears. The probability of consensus on the\nincorrect hypothesis in the densely connected communication structure\nreduces to close to zero with more nodes or greater disparity of\nassigned probabilities to alternatives. ", "\nO’Connor and other colleagues have used evolutionary game theory\nto model other community phenomena such as the persistence of minority\ndisadvantage in scientific communities (Rubin & O’Connor\n2018), scientific polarization (O’Connor & Weatherall 2017),\ndiversity (O’Connor & Bruner 2017), conservatism in science\n(O’Connor forthcoming). While not necessarily claiming that\nthese game theoretic models are fully descriptive of the phenomena\nthey model, these theorists do claim that given certain initial\nconditions, certain undesirable social situations (like the\ndisadvantage accruing to minority status) are to be expected rather\nthan being understood as perversions of scientific practice. This\nwould suggest that some ways of addressing those undesirable social\noutcomes may not be effective and that alternative measures ought to\nbe sought in case of failure.", "\nSociality, rationality, and objectivity. Philosophers who treat\nthe social as biasing or distorting tend to focus on the\nconstructivists’ view that there are no universal principles of\nrationality or principles of evidence that can be used to identify in\nany context-independent way which factors are evidential and which\nnot. Reconciliationists tend to argue that what is correct in the\nsociologists’ accounts can be accommodated in orthodox accounts\nof scientific knowledge. The key is sifting the correct from the\nexaggerated or misguided. Integrationists read the relevance of the\nsociologists’ accounts as supporting the development of new\naccounts of rationality or objectivity, rather than as grounds for\nrejecting the cogency of such normative ideals. ", "\nPhilosophers concerned to defend the rationality of science against\nsociological misrepresentations include Larry Laudan (1984) James\nBrown (1989, 1994), Alvin Goldman (1987, 1995) and Susan Haack (1996).\nThe details of these philosophers’ approaches differ, but they\nagree in holding that scientists are persuaded by what they regard as\nthe best evidence or argument, the evidence most indicative of the\ntruth by their lights, and in holding that arguments and evidence are\nthe appropriate focus of attention for understanding the production of\nscientific knowledge. When evidential considerations have not trumped\nnon-evidential considerations, we have an instance of bad science.\nThey read the sociologists as arguing that a principled distinction\nbetween evidential and nonevidential considerations cannot be drawn\nand devote considerable effort to refuting those arguments. In their\npositive proposals for accommodating the social character of science,\nsociality is understood as a matter of the aggregation of individuals,\nnot their interactions, and public knowledge as simply the additive\noutcome of many individuals making sound epistemic judgments.\nIndividual rationality and individual knowledge are thus the proper\nfocus of philosophers of science. Exhibiting principles of rationality\napplicable to individual reasoning is sufficient to demonstrate the\nrationality of science, at least in its ideal form.", "\nReconciliationists include Ronald Giere, Mary Hesse, and Philip\nKitcher. Giere (1988) models scientific judgment using decision\ntheory. This permits incorporating scientists’ interests as one\nof the parameters of the decision matrix. He also advocates a\nsatisficing, rather than optimizing, approach to modeling the decision\nsituation, thus enabling different interests interacting with the same\nempirical base to support different selections as long as they are\nconsistent with that base. Mary Hesse (1980) employs a network model\nof scientific inference that resembles W.V.O. Quine’s web of\nbelief in that its constituents are heterogeneous in character, but\nall subject to revision in relation to changes elsewhere in the\nnetwork. She understands the social factors as coherence conditions\noperating in tandem with logical constraints to determine the relative\nplausibility of beliefs in the network.", "\nThe most elaborate reconciliationist position is that developed in\nPhilip Kitcher’s (1993). In addition to modeling relations of\nauthority and the division of cognitive labor as described above, he\noffers what he terms a compromise between extreme rationalists and\nsociological debunkers. The compromise model appeals to a principle of\nrationality, which Kitcher calls the External Standard. It is deemed\nexternal because it is proposed as holding independently of any\nparticular historical, cultural or social context. Thus, not only is\nit external, but it is also universal. The principle applies to change\nof belief (or shift from one practice to another, in Kitcher’s\nbroader locution), not to belief. It treats a shift (in practice or\nbelief) as rational if and only “the process through which the\nshift was made has a success ratio at least as high as that of any\nother process used by human beings (ever) ...” (Kitcher 1993,\n303). Kitcher’s compromise proposes that scientific ideas\ndevelop over time and benefit from the contributions of many\ndifferently motivated researchers. This is the concession to the\nsociologically oriented scholars. In the end, however, those theories\nthat are rationally accepted are those that satisfy Kitcher’s\nExternal Standard. Kitcher thus joins Goldman, Haack, and Laudan in\nthe view that it is possible to articulate a priori conditions of\nrationality or of epistemic warrant that operate independently of, or,\nperhaps one might say, orthogonally to, the social relations of\nscience.", "\nA third set of models is integrationist in character. Integrationists\nuse the observations of sociologists of science to develop alternative\naccounts of scientific rationality and objectivity. Nelson (1990)\nfocuses on a slightly different aspect of Quine’s holism than\ndoes Hesse. Nelson uses Quine’s arguments against the\nindependently foundational status of observation statements as the\nbasis for what she calls a feminist empiricism. According to Nelson,\nno principled distinction can be made between the theories,\nobservations, or values of a community. What counts as evidence, in\nher view, is fixed by the entire complex of a community’s\ntheories, value commitments, and observations. There is neither\nknowledge nor evidence apart from such a shared complex. The community\nis the primary knower on this view and individual knowledge is\ndependent on the knowledge and values of the community.", "\nMiriam Solomon’s social empiricism is focused on scientific\nrationality (Solomon 2001). It, too, involves denying a universal\nprincipled distinction among the causes of belief. Solomon draws on\ncontemporary cognitive science literature to argue that what are\ntraditionally called biases are simply among the kinds of\n“decision vector” that influence belief. They are not\nnecessarily undesirable elements from which science needs to be\nprotected, and can be productive of insight and rational belief.\nSalience and availability (of data, of measurement technologies), also\ncalled cold biases, are decision vectors as much as social ideologies\nor other motivational factors, “hot biases.” The\ndistinctive feature of Solomon’s social empiricism is her\ncontrast between individual and community rationality. Her (2001)\nurges the pluralistic view that a community is rational when the\ntheories it accepts are those that have unique empirical successes.\nIndividuals can persist in beliefs that are (from a panoptic\nperspective) less well supported than others on this view, if the\ntotality of available evidence (or empirical data) is not available to\nthem, or when their favored theory accounts for phenomena not\naccounted for other theories, even when those may have a greater\nquantity of empirical successes. What matters to science, however, is\nthat the aggregated judgments of a community be rational. A community\nis rational when the theories it accepts are those with all or with\nunique empirical successes. It is collectively irrational to jettison\na theory with unique empirical successes. Thus, the community can be\nrational even when its members are, as judged by traditional epistemic\nstandards, individually irrational. Indeed, individual irrationality\ncan contribute to community rationality in that individuals committed\nto a theory that accounts for their data keep that data in the range\nof phenomena any theory accepted by the entire community must\neventually explain. In addition to empirical success, Solomon proposes\nan additional normative criterion. In order to secure appropriate\ndistribution of scientific effort, biases must be appropriately\ndistributed in the community. Solomon proposes a scheme for\nascertaining when a distribution is normatively appropriate. Thus, for\nSolomon, a scientific community is rational when biases are\nappropriately distributed and it accepts only a theory with all or\ntheories with unique empirical successes as the normative\nepistemological condition. Rationality accrues only to a community,\nand not to the individuals constituting the community. As in\nZollman’s network models, consensus just is all members of the\ncommunity assigning the same value (T/F) to a hypothesis or\ntheory.", "\nFinally, in Longino’s critical contextual empiricism, the\ncognitive processes that eventuate in scientific knowledge are\nthemselves social (Longino 1990, 2002). Longino’s starting point\nis a version of the underdetermination argument: the semantic gap\nbetween statements describing data and statements expressing\nhypotheses or theories to be confirmed or disconfirmed by that data.\nThis gap, created by the difference in descriptive terms used in the\ndescription of data and in the expression of hypotheses, means that\nevidential relations cannot be formally specified and that data cannot\nsupport one theory or hypothesis to the exclusion of all alternatives.\nInstead, such relations are mediated by background assumptions.\nEventually, in the chain of justification, one reaches assumptions for\nwhich no evidence is available. If these are the context in which\nevidential relations are constituted, questions arise concerning how\nthe acceptance of such assumptions can be legitimated. According to\nLongino, the only check against the arbitrary dominance of subjective\n(metaphysical, political, aesthetic) preference in such cases is\ncritical interaction among the members of the scientific community or\namong members of different communities. There is no higher authority\nor transcendent aperspectival position from which it is possible to\nadjudicate among foundational assumptions. Longino takes the\nunderdetermination argument to express in logical terms the point made\nby the sociologically oriented researchers: the individuals\nparticipating in the production of scientific knowledge are\nhistorically, geographically, and socially situated and their\nobservations and reasoning reflect their situations. This fact does\nnot undermine the normative enterprise of philosophy, but requires its\nexpansion to include within its scope the social interactions within\nand between scientific communities. What counts as knowledge is\ndetermined by such interactions.", "\nLongino claims that scientific communities do institutionalize some\ncritical practices (for example, peer review), but argues that such\npractices and institutions must satisfy conditions of effectiveness in\norder to qualify as objective. She argues, therefore, for the\nexpansion of scientific norms such as accuracy and consistency to\ninclude norms that apply to communities. These are (1) the provision\nof venues in which critical interaction can take place, (2) the uptake\nof critical intervention as demonstrated in change of belief\ndistribution in the community over time in a way that is sensitive to\nthe critical discourse taking place within that community, (3) public\naccessibility of the standards that regulate discourse, and (4)\ntempered equality of intellectual authority. By this latter condition,\nperhaps the most controversial of her proposed norms, Longino means\nthat any perspective has a prima facie capacity to contribute to the\ncritical interactions of a community, though equal standing can be\nlost owing to failure to engage or to respond to criticism. In her\n2002, Longino argues that the cognitive processes of science, such as\nobservation and reasoning, are themselves social processes. Thus the\ninteractions subject to community norms extend not only to discussion\nof assumptions in finished research, but to the constructive processes\nof research as well.", "\nSolomon and Longino differ on where they locate normativity and on the\nrole and effectiveness of deliberative processes in actual scientific\ninquiry. Solomon attends to the patterns of acceptance and to the\ndistribution of decision vectors, regardless of the interactions among\ncommunity members, while Longino attends to deliberative processes and\ninteractions. They may also differ in their views of what constitutes\nscientific success.", "\nOne set of issues that has yet to give rise to extended philosophical\nreflection is the question how civilizational differences are\nexpressed in scientific work (See Bala 2008). Here, too, there is a\nmicro- and a macro- version. At the micro level, one might ask how the\ninteractional culture of individual laboratories or theoretical\nsubcommunities is or is not expressed in the outcome of their\nresearch. At the macro level one might be asking how large scale\ncultural features are reflected in the content and practice of science\nin a given cultural formation. For example, Joseph Needham argued that\nfeatures of the culture of ancient China directed their technical and\nintellectual ingenuity into channels that foreclosed the development\nof anything like the science that developed in Western Europe in the\n14th through the 17th centuries. Other cultures developed some aspects\nof what we now think of as a cosmopolitan or global scientific culture\n(for example, the mathematics and astronomy of 10th through 14th\ncentury Islamic and South Asian scholars) independently of the early\nmodern physics developed in Western and Central Europe. The papers in\nHabib and Raina (2001) address aspects of these questions with respect\nto the history of science in India.", "\nUnity, Plurality and the Aims of Inquiry. The variety of views\non the degree of sociality assignable to the epistemological concepts\nof science lead to different views concerning the ultimate character\nof the outcome of inquiry. This difference can be summarized as the\ndifference between monism and pluralism. Monism, as characterized in\nKellert, Longino, and Waters (2006), holds that the goal of inquiry is\nand should be a unified, comprehensive, and complete account of\nphenomena (whether all phenomena, or the phenomena specific to a\nparticular domain of inquiry). If this is so, then the norms of\nassessment should be informed by this goal and there should be one\nstandard by which theories, models, and hypotheses in the sciences are\nassessed. Deviation from an accepted theoretical framework is\nproblematic and requires explanation, such as the explanations offered\nfor the division of cognitive labor. Monism, with its commitment to\nultimate unity, requires ways to reconcile competing theories or to\nadjudicate controversy so as to eliminate competition in favor of the\none true or best theory. Pluralism, on the other hand, holds that the\nobserved plurality of approaches within a science is not necessarily a\nflaw but rather reflects the complexity of the phenomena under\ninvestigation in interaction with the limitations of human cognitive\ncapacities and the variety of human cognitive as well as pragmatic\ninterests in representations of those phenomena.", "\nAmong pluralists, a diversity of views is to be found. Suppes (1978)\nemphasized the mutual untranslatability of the descriptive terms\ndeveloped in the course of scientific specialization. Such\nincommensurability will resist evaluation by a common measure.\nCartwright’s (1999) invocation of a dappled world emphasizes the\ncomplexity and diversity of the natural (and social) world. Scientific\ntheories and models are representations of varying degrees of\nabstraction that manage to apply at best partially to whatever\nphenomena they purport to represent. To the extent they are taken to\nrepresent actual process in the real world, they must be hedged by\nceteris paribus clauses. Scientific laws and models attach to patches\nof the world, but not to a seamlessly law-governed whole.\nMitchell’s (2002, 2009) integrative pluralism is a rejection of\nthe goal of unification by either reduction to a single (fundamental)\nlevel of explanation or abstraction to a single theoretical\nrepresentation, in favor of a more pragmatically inflected set of\nexplanatory strategies. The success for any particular investigation\nis answerable to the goals of the investigation, but there may be\nmultiple compatible accounts reflecting both the contingency and\npartiality of the laws/generalizations that can figure in explanations\nand the different goals one may bring to investigation of the same\nphenomenon. The explanations sought in any particular explanatory\nsituation will draw on these multiple accounts as appropriate for the\nlevel of representation adequate to achieve its pragmatic ends.\nMitchell’s defense of integrative pluralism rests on both the\npartiality of representation and the complexity of the phenomena to be\nexplained.", "\nKellert, Longino, and Waters advance a pluralism that sees\nmultiplicity not only among but within levels of analysis. Furthermore\nthey see no reason to require that the multiple accounts be\ncompatible. The multiplicity of noncongruent empirically adequate\naccounts helps us appreciate the complexity of a phenomenon without\nbeing in a position to generate a single account of that complexity.\nThey do not hold that all phenomena will support ineliminable\npluralism, but that there are some phenomena that will require\nmutually irreducible or incompatible models. Which these are is\ndetermined by examining the phenomena, the models, and the match\nbetween phenomena and models. Like Mitchell, Kellert, Longino, and\nWaters hold that pragmatic considerations (broadly understood) will\ngovern the choice of model to be used in particular circumstances.\nBoth forms of pluralism (compatibilist and noncompatibilist) abandon\nthe notion that there is a set of natural kinds whose causal\ninteractions are the basis for fundamental explanations of natural\nprocesses. The noncompatibilist is open to multiple classification\nschemes answerable to different pragmatic interests in classifying. To\nthis extent the noncompatibilist pluralist embraces a view close to\nthe promiscuous realism articulated by John Dupré (1993). The\ncompatibilist, or integrative pluralist, on the other hand, must hold\nthat there is a way that different classification schemes can be\nreconciled to support the envisioned integration of explanatory\nmodels.", "\nPluralism receives support from several additional approaches. Giere\n(2006) uses the phenomenon of color vision to support a position he\ncalls perspectival realism. Like the colors of objects, scientific\nrepresentations are the result of interactions between human cognitive\nfaculties and the world. Other species have different visual equipment\nand perceive the world differently. Our human cognitive faculties,\nthen, constitute perspectives. We could have been built differently\nand hence perceived the world differently. Perspectival realism leads\nto pluralism, because perspectives are partial. While van\nFraassen’s (2008) does not take a position on pluralism vs.\nmonism (and as an empiricist and antirealist van Fraassen would not\nhave to), its emphasis on the partiality and perspective dependence of\nmeasurement provides a complementary point of entry to such diversity.\nSolomon (2006) urges a yet more welcoming attitude towards\nmultiplicity. In her view, dissensus is a necessary component of\nwell-functioning scientific communities and consensus can be\nepistemologically pernicious. In an extension of the arguments in\nSolomon (2001) she argues that different models and theoretical\nrepresentations will be associated with particular insights or\nspecific data that are likely to be lost if the aim is to integrate or\notherwise combine the models to achieve a consensus understanding. The\nactivity of integrating two or more models is different from the\nprocess of one model from a set of alternatives coming eventually to\nhave all the empirical successes distributed among the other models.\nIn her examination of consensus conferences called by the United\nStates National Institutes of Health (Solomon 2011), Solomon finds\nthat such conferences do not resolve existing dissent in the\nscientific community. Instead, they tend to take place after a\nconsensus has emerged in the research community and are directed more\nto the communication of such consensus to outside communities (such as\nclinicians, insurers, health policy experts, and the public) than to\nthe assessment of evidence that might warrant consensus.", "\nResearchers committed to a monist or unified science will see\nplurality as a problem to be overcome, while researchers already\ncommitted to a deeply social view of science will see plurality as a\nresource of communities rather than a problem. The diversity and\npartiality that characterizes both a local and the global scientific\ncommunity characterize the products of those communities as well as\nthe producers. Universalism and unification require the elimination of\nepistemologically relevant diversity, while a pluralist stance\npromotes it and the deeply social conception of knowledge that\nfollows. ", "\nSociality and the structure of scientific knowledge. Attention\nto the social dimensions of scientific knowledge and the consequent\npotential for plurality has prompted philosophers to rethink the\nstructure of what is known. Many philosophers (including Giere,\nKitcher, and Longino) who advocate forms of pluralism invoke the\nmetaphor of maps to explain how scientific representations can be both\npartial and adequate. Maps only represent those features of the\nterritory mapped that are relevant for the purpose for which the map\nis drawn. Some maps may represent the physical area bounded by state\nboundaries, others may represent the population size, or the relative\nabundance/poverty of natural resources. Winther (forthcoming) explores\nthe variety of kinds of maps used in science and philosophical use of\nthe map metaphor. But the map metaphor is only one of several ways to\nrethink the structure of scientific knowledge.", "\nOther philosophers draw more heavily on cognitive science. Giere\n(2002) takes a naturalist approach to modeling, not so much the\ndistribution of cognitive labor, but the distribution of cognition.\nThis approach takes a system or interactive community as the locus of\ncognition, rather than the individual agent. Nersessian (2006) extends\ndistributed cognition to model-based reasoning in the sciences. Models\nare artifacts that focus the cognitive activity of multiple\nindividuals in particular settings. Knowledge is distributed across\nthe minds interacting about the artifacts in that setting. Paul\nThagard draws on the increasingly interdisciplinary (and hence social)\nnature of cognitive science itself to argue that not only does\ncognitive science (or certain lines of analysis in cognitive science)\nsupport a conception of cognition as distributed among interacting\nagents, but that this conception can be turned back upon cognitive\nscience itself. (Thagard 2012). Finally Alexander Bird (2010) reflects\non the sense of knowledge required for attributions such as:\n“the biomedical community now knows that peptic ulcers are often\ncaused by the bacterium Helicobacter pylori.” Or\n“There was an explosive growth in scientific knowledge in the\ntwentieth century.” Bird faults other social epistemologists for\nstill making such collective knowledge supervenient on the states of\nindividuals. Instead, he argues, we should understand social knowing\nas a functional analogue of individual knowing. Both are dependent on\nthe existence and proper functioning of the relevant structures:\nreasoning and perception for individuals; libraries and journals and\nother social structures, for collectivities. Scientific knowledge is\nan emergent effect of collective epistemic interactions, concretized\nin the texts that have been designated as vehicles for the\npreservation and communication of that knowledge" ], "section_title": "4. Models of the Social Character of Knowledge", "subsections": [] }, { "main_content": [ "\nModern science has been regarded as both a model of democratic\nself-governance and an activity requiring and facilitating democratic\npractices in its supporting social context (Popper 1950, Bronowski\n1956). In this perspective, science is seen as embedded in and\ndependent on its supporting social context, but insulated in its\npractices from the influence of that context. As the reach of science\nand science-based technologies has extended further and further into\nthe economy and daily life of industrialized societies, new attention\nis paid to the governance of science. Regardless of one’s views\nabout the social character of knowledge, there are further questions\nconcerning what research to pursue, what social resources to devote to\nit, who should make such decisions, and how they should be made.", "\nPhilip Kitcher (2001) has opened these questions to philosophical\nscrutiny. While Kitcher largely endorses the epistemological views of\nhis (1993), in the later work he argues that there is no absolute\nstandard of the significance (practical or epistemic) of research\nprojects, nor any standard of the good apart from subjective\npreferences. The only non-arbitrary way to defend judgments concerning\nresearch agendas in the absence of absolute standards is through\ndemocratic means of establishing collective preferences. Kitcher,\nthus, attempts to spell out procedures by which decisions concerning\nwhat research directions to pursue can be made in a democratic manner.\nThe result, which he calls well-ordered science, is a system in which\nthe decisions actually made track the decisions that would be a made\nby a suitably constituted representative body collectively\ndeliberating with the assistance of relevant information (concerning,\ne.g., cost and feasibility) supplied by experts.", "\nKitcher’s “well-ordered science” has attracted\nattention from other philosophers, from scientists, and from scholars\nof public policy. Winning praise as a first step, it has also elicited\na variety of criticisms and further questions. The criticisms of his\nproposal range from worries about the excessive idealism of the\nconception to worries that it will enshrine the preferences of a much\nsmaller group than those who will be affected by research decisions.\nKitcher’s proposal at best works for a system in which all or\nmost scientific research is publicly funded. But the proportion of\nprivate, corporate, funding of science compared to that of public\nfunding has been increasing, thus calling into question the\neffectiveness of a model that presupposes largely public control\n(Mirowski and Sent 2002, Krimsky 2003). Kitcher’s model, it\nshould be noted, still effects a significant separation between the\nactual conduct of research and decisions concerning the direction of\nresearch and scholars who see a more intimate relation between social\nprocesses and values in the context and those in the conduct of\nresearch will be dissatisfied with it. Kitcher himself (Kitcher 2011)\nseems to relax the separation somewhat.", "\nThe counterfactual character of the proposal raises questions about\nthe extent to which well-ordered science really is democratic. If the\nactual decisions do not need to be the result of democratic procedures\nbut only to be the same as those that would result from such\nprocedures, how do we know which decisions those are without actually\ngoing through the deliberative exercise? Even if the process is\nactually carried out, there are places, e.g. in choice of experts\nwhose advice is sought, which permit individual preferences to subvert\nor bias the preferences of the whole (Roth 2003). Furthermore, given\nthat the effects of scientific research are potentially global, while\ndemocratic decisions are at best national, national decisions will\nhave an effect well beyond the population represented by the decision\nmakers. Sheila Jasanoff has also commented that even in contemporary\nindustrialized democracies there are quite different science\ngovernance regimes. There is not one model of democratic decision\nmaking, but many, and the differences translate into quite different\npolicies (Jasanoff 2005).", "\nIn his (2011) Kitcher abandons the counterfactual approach as he\nbrings the ideal of well-orderedness into contact with actual debates\nin and about contemporary science. His concern here is the variety of\nways in which scientific authority has been eroded by what he terms\n“chimeric epistemologies.” It’s not enough to say\nthat the scientific community has concluded that, say, the MMR vaccine\nis safe, or that the climate is changing in a way that requires a\nchange in human activities. In a democratic society, there are many\nother voices claiming authority, whether on presumed evidential\ngrounds or as part of campaigns to manipulate public opinion. Kitcher\nsuggests mechanisms whereby small groups trusted by their communities\nmight develop the understanding of complicated technical issues\nthrough tutoring by members of the relevant research communities and\nthen carry this understanding back to the public. He also endorses\nJames Fishkin’s (2009) experiments in deliberative polling as a\nmeans to bring members of the public committed to different sides of a\ntechnical issue together with the scientific exponents of the issue\nand in a series of exchanges that cover the evidence, the different\nkinds of import different lines of reasoning possess, and the other\nelements of a reasoned discussion, bring the group to a consensus on\nthe correct view. The pluralist and pragmatically inclined\nphilosophers discussed in the previous section might worry that there\nis not a single correct view towards which such an encounter ought to\nconverge, but that a broader discussion that incorporates deliberation\nabout aims and values might produce sufficient (temporary) convergence\nto ground action or policy." ], "section_title": "5. Social Direction of Science", "subsections": [] }, { "main_content": [ "\nPhilosophical study of the social dimensions of scientific knowledge\nhas been intensifying in the decades since 1970. Social controversies\nabout the sciences and science based technologies as well as\ndevelopments in philosophical naturalism and social epistemology\ncombine to drive thinking in this area forward. Scholars in a number\nof cognate disciplines continue to investigate the myriad social\nrelations within scientific communities and between them and their\nsocial, economic, and institutional contexts.", "\nWhile this area first came to prominence in the so-called science wars\nof the 1980s, attending to social dimensions of science has brought a\nnumber of topics to philosophical attention. The phenomenon of Big\nScience has encouraged philosophers to consider the epistemological\nsignificance of such phenomena as trust and cognitive interdependence\nand the division of cognitive labor. The increased economic and social\ndependence on science-based technologies has prompted attention to\nquestions of inductive risk and the role of values in assessing\nhypotheses with social consequences. The controversies over health\nrisks of certain vaccines, over the measurement of environmental\npollution, and over the causes of climate change have expanded\nphilosophy of science from its more accustomed areas of logical and\nepistemological analysis to incorporate concerns about the\ncommunication and uptake of scientific knowledge and the ethical\ndimensions of superficially factual debates.", "\nPartly in response to the work of scholars in the social studies of\nscience, partly in response to the changing role of scientific inquiry\nthrough the 20th and into the 21st centuries, philosophers have sought\nways to either accommodate the (tenable) results of the sociologists\nand cultural historians or to modify traditional epistemological\nconcepts used in the analysis of scientific knowledge. These\ninvestigations in turn lead to new thinking about the structure and\nlocation of the content of knowledge. While debates within philosophy\nof science between and among adherents to one or another of the models\nof the sociality of knowledge will continue, an important future step\nwill be a fuller encounter between individual-based social\nepistemology with its focus on testimony and disagreement as\ntransactions among individuals and the more fully social\nepistemologies that take social relations or interaction as partially\nconstitutive of empirical knowledge." ], "section_title": "6. Conclusion", "subsections": [] } ]

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[ "\nScientific inquiry has led to immense explanatory and technological\nsuccesses, partly as a result of the pervasiveness of scientific\ntheories. Relativity theory, evolutionary theory, and plate tectonics\nwere, and continue to be, wildly successful families of theories\nwithin physics, biology, and geology. Other powerful theory clusters\ninhabit comparatively recent disciplines such as cognitive science,\nclimate science, molecular biology, microeconomics, and Geographic\nInformation Science (GIS). Effective scientific theories magnify\nunderstanding, help supply legitimate explanations, and assist in\nformulating predictions. Moving from their knowledge-producing\nrepresentational functions to their interventional roles (Hacking\n1983), theories are integral to building technologies used within\nconsumer, industrial, and scientific milieus.", "\nThis entry explores the structure of scientific theories from the\nperspective of the Syntactic, Semantic, and Pragmatic Views. Each of\nthese answers questions such as the following in unique ways. What is\nthe best characterization of the composition and function of\nscientific theory? How is theory linked with world? Which\nphilosophical tools can and should be employed in describing and\nreconstructing scientific theory? Is an understanding of practice and\napplication necessary for a comprehension of the core structure of a\nscientific theory? Finally, and most generally, how are these three\nviews ultimately related?" ]

[ { "content_title": "1. Introduction", "sub_toc": [ "1.1 Syntactic, Semantic, and Pragmatic Views: The Basics", "1.2 Two Examples: Newtonian Mechanics and Population Genetics" ] }, { "content_title": "2. The Syntactic View", "sub_toc": [ "2.1 Theory Structure per the Syntactic View", "2.2 A Running Example: Newtonian Mechanics", "2.3 Interpreting Theory Structure per the Syntactic View", "2.4 Taking Stock: Syntactic View" ] }, { "content_title": "3. The Semantic View", "sub_toc": [ "3.1 Theory Structure per the Semantic View", "3.2 A Running Example: Newtonian Mechanics", "3.3 Interpreting Theory Structure per the Semantic View", "3.4 Taking Stock: Semantic View" ] }, { "content_title": "4. The Pragmatic View", "sub_toc": [ "4.1 Theory Structure per the Pragmatic View", "4.2 A Running Example: Newtonian Mechanics", "4.3 Interpreting Theory Structure per the Pragmatic View", "4.4 Taking Stock: Pragmatic View" ] }, { "content_title": "5. Population Genetics", "sub_toc": [] }, { "content_title": "6. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nIn philosophy, three families of perspectives on scientific theory are\noperative: the Syntactic View, the Semantic View,\nand the Pragmatic View. Savage distills these philosophical\nperspectives thus:", "\nThe syntactic view that a theory is an axiomatized collection\nof sentences has been challenged by the semantic view that a\ntheory is a collection of nonlinguistic models, and both are\nchallenged by the view that a theory is an amorphous entity consisting\nperhaps of sentences and models, but just as importantly of exemplars,\nproblems, standards, skills, practices and tendencies. (Savage 1990,\nvii–viii)\n", "\nMormann (2007) characterizes the Syntactic and Semantic Views in\nsimilar terms, and is among the first to use the term “Pragmatic\nView” to capture the third view (137). The three views are\nbaptized via a trichotomy from linguistics deriving from the work of\nCharles Morris, following Charles S. Peirce. In a classic exposition,\nthe logical positivist Carnap writes:", "\nIf in an investigation explicit reference is made to the speaker, or,\nto put it in more general terms, to the user of a language, then we\nassign it to the field of pragmatics. (Whether in this case\nreference to designata is made or not makes no difference for this\nclassification.) If we abstract from the user of the language and\nanalyze only the expressions and their designata, we are in the field\nof semantics. And if, finally, we abstract from the designata\nalso and analyze only the relations between the expressions, we are in\n(logical) syntax. The whole science of language, consisting\nof the three parts mentioned, is called semiotic. (1942, 9;\nsee also Carnap 1939, 3–5, 16)\n", "\nTo summarize, syntax concerns grammar and abstract structures;\nsemantics investigates meaning and representation; and pragmatics\nexplores use. Importantly, while no view is oblivious to the syntax,\nsemantics, or pragmatics of theory, the baptism of each is a product\nof how one of the three aspects of language is perceived to be\ndominant: theory as syntactic logical reconstruction (Syntactic View);\ntheory as semantically meaningful mathematical modeling (Semantic\nView); or theory structure as complex and as closely tied to theory\npragmatics, i.e., function and context (Pragmatic View). Each of these\nphilosophical perspectives on scientific theory will be reviewed in\nthis entry. Their relations will be briefly considered in the\nConclusion." ], "section_title": "1. Introduction", "subsections": [ { "content": [ "\nIt will be helpful to pare each perspective down to its essence. Each\nendorses a substantive thesis about the structure of scientific\ntheories.", "\nFor the Syntactic View, the structure of a scientific theory is its\nreconstruction in terms of sentences cast in a metamathematical\nlanguage. Metamathematics is the axiomatic machinery for building\nclear foundations of mathematics, and includes predicate logic, set\ntheory, and model theory (e.g., Zach 2009; Hacking 2014). A central\nquestion of the Syntactic View is: in which logical language should we\nrecast scientific theory?", "\nSome defenders of the Semantic View keep important aspects of this\nreconstructive agenda, moving the metamathematical apparatus from\npredicate logic to set theory. Other advocates of the Semantic View\ninsist that the structure of scientific theory is solely mathematical.\nThey argue that we should remain at the mathematical level, rather\nthan move up (or down) a level, into foundations of mathematics. A\ncentral question for the Semantic View is: which mathematical models\nare actually used in science?", "\nFinally, for the Pragmatic View, scientific theory is internally and\nexternally complex. Mathematical components, while often present, are\nneither necessary nor sufficient for characterizing the core structure\nof scientific theories. Theory also consists of a rich variety of\nnonformal components (e.g., analogies and natural kinds). Thus, the\nPragmatic View argues, a proper analysis of the grammar (syntax) and\nmeaning (semantics) of theory must pay heed to scientific theory\ncomplexity, as well as to the multifarious assumptions, purposes,\nvalues, and practices informing theory. A central question the\nPragmatic View poses is: which theory components and which modes of\ntheorizing are present in scientific theories found across a variety\nof disciplines?", "\nIn adopting a descriptive perspective on the structure of\nscientific theories, each view also deploys, at least implicitly, a\nprescriptive characterization of our central topic. In other\nwords, postulating that scientific theory is \\(X\\) (e.g., \\(X\\) = a\nset-theoretic structure, as per Suppes 1960, 1962, 1967, 1968, 2002)\nalso implies that what is not \\(X\\) (or could not be recast as \\(X\\))\nis not (or could not possibly be) a scientific theory, and would not\nhelp us in providing scientific understanding, explanation,\nprediction, and intervention. For the Syntactic View, what is not (or\ncannot be) reconstructed axiomatically is not theoretical, while for\nthe Semantic View, what is not (or cannot be) modeled mathematically\nis not theoretical. In contrast, in part due to its pluralism about\nwhat a scientific theory actually (and possibly) is, and because it\ninterprets theory structure as distributed in practices, the Pragmatic\nView resists the definitional and normative terms set by the other two\nviews. As a result, the Pragmatic View ultimately reforms the very\nconcepts of “theory” and “theory structure.”\n", "\nThis encyclopedia entry will be organized as follows. After presenting\nthis piece’s two sustained examples, immediately below, the\nthree views are reviewed in as many substantive sections. Each section\nstarts with a brief overview before characterizing that\nperspective’s account of theory structure. Newtonian mechanics\nis used as a running example within each section. The interpretation\nof theory structure—viz., how theory “hooks up” with\nphenomena, experiment, and the world—is also reviewed in each\nsection. In the final section of this entry, we turn to population\ngenetics and an analysis of the Hardy-Weinberg Principle (HWP) to\ncompare and contrast each view. The Conclusion suggests, and remains\nnon-committal about, three kinds of relations among the views:\nidentity, combat, and complementarity.\nTheory is not a single, static entity that we are seeing from three\ndifferent perspectives, as we might represent the Earth using three\ndistinct mathematical map projections. Rather, theory itself changes\nas a consequence of perspective adopted." ], "subsection_title": "1.1 Syntactic, Semantic, and Pragmatic Views: The Basics" }, { "content": [ "\nTwo examples will be used to illustrate differences between the three\nviews: Newtonian mechanics and population genetics. While relativity\ntheory is the preferred theory of the Syntactic View,\nNewtonian mechanics is more straightforward. Somewhat permissively\nconstrued, the theory of Newtonian mechanics employs the basic\nconceptual machinery of inertial reference frames, centers of mass,\nNewton’s laws of motion, etc., to describe the dynamics and\nkinematics of, among other phenomena, point masses acting\nvis-à-vis gravitational forces (e.g. the solar system) or with\nrespect to forces involved in collisions (e.g., pool balls on a pool\ntable; a closed container filled with gas). Newtonian mechanics is\nexplored in each section.", "\nPopulation genetics investigates the genetic composition of\npopulations of natural and domesticated species, including the\ndynamics and causes of changes in gene frequencies in such populations\n(for overviews, see Lloyd 1994 [1988]; Gould 2002; Pigliucci and\nMüller 2010; Okasha 2012). Population genetics emerged as a\ndiscipline with the early 20th century work of R.A. Fisher,\nSewall Wright, and J.B.S. Haldane, who synthesized Darwinian\nevolutionary theory and Mendelian genetics. One important part of\npopulation genetic theory is the Hardy-Weinberg Principle. HWP is a\nnull model mathematically stating that gene frequencies remain\nunchanged across generations when there is no selection, migration,\nrandom genetic drift, or other evolutionary forces acting in a given\npopulation. HWP peppers early chapters of many introductory textbooks\n(e.g., Crow and Kimura 1970; Hartl and Clark 1989; Bergstrom and\nDugatkin 2012). We return to HWP in Section 5 and here merely state\nquestions each view might ask about population genetics.", "\nThe Syntactic View focuses on questions regarding the highest\naxiomatic level of population genetics (e.g., Williams 1970, 1973; Van\nValen 1976; Lewis 1980; Tuomi 1981, 1992). Examples of such queries\nare:", "\nInvestigations of the axiomatized rational reconstruction of theory\nshed light on the power and promises, and weaknesses and\nincompleteness, of the highest-level theoretical edifice of population\ngenetics. ", "\nSecondly, the Semantic View primarily examines questions regarding the\nmathematical structure of population genetics (Lewontin 1974, Beatty\n1981; López Beltrán 1987; Thompson 1989, 2007; Lloyd\n1994 [1988]). Very generally, this exploration involves the following\nquestions:", "\nThe main subject of investigation is mathematical structure, rather\nthan metamathematics or even alternative model types or modeling\nmethods. ", "\nFinally, the Pragmatic View asks about the internal complexity of\npopulation genetic theory, as well as about the development and\ncontext of population genetics. In so doing, it inquires into how\npurposes and values have influenced the theoretical structure of\nevolutionary theory, selecting and shaping current population genetics\nfrom a wide variety of possible alternative theoretical articulations.\nThe following questions about the structure of population genetic\ntheory might be here addressed:", "\nAs when studying an organism, the structure of theory cannot be\nunderstood independently of its history and function." ], "subsection_title": "1.2 Two Examples: Newtonian Mechanics and Population Genetics" } ] }, { "main_content": [ "\nAccording to the Syntactic View, which emerged mainly out of work of\nthe Vienna Circle and Logical Empiricism (see Coffa 1991; Friedman\n1999; Creath 2014; Uebel 2014), philosophy most generally practiced\nis, and should be, the study of the logic of natural science, or\nWissenschaftslogik (Carnap 1937, 1966; Hempel 1966). Robust\nand clear logical languages allow us to axiomatically reconstruct\ntheories, which—by the Syntacticists’ definition—are\nsets of sentences in a given logical domain language (e.g.,\nCampbell 1920, 122; Hempel 1958, 46; cf. Carnap 1967 [1928],\n§156, “Theses about the Constructional System”). Domain languages\ninclude “the language of physics, the language of\nanthropology” (Carnap 1966, 58). ", "\nThis view has been variously baptized as the Received View (Putnam\n1962; Hempel 1970), the Syntactic Approach (van Fraassen 1970, 1989),\nthe Syntactic View (Wessels 1976), the Standard Conception (Hempel\n1970), the Orthodox View (Feigl 1970), the Statement View (Moulines\n1976, 2002; Stegmüller 1976), the Axiomatic Approach (van\nFraassen 1989), and the Once Received View (Craver 2002). For\nhistorical reasons, and because of the linguistic trichotomy discussed\nabove, the “Syntactic View” shall be the name of choice in\nthis entry." ], "section_title": "2. The Syntactic View", "subsections": [ { "content": [ "\nSome conceptual taxonomy is required in order to understand the\nlogical framework of the structure of scientific theories for the\nSyntactic View. We shall distinguish terms,\nsentences, and languages (see Table 1). ", "\nBuilding upwards from the bottom, let us start with the three kinds of\nterms or vocabularies contained in a scientific language: theoretical,\nlogical, and observational. Examples of theoretical terms are\n“molecule,” “atom,” “proton,” and\n“protein,” and perhaps even macro-level objects and properties\nsuch as “proletariat” and “aggregate demand.”\nTheoretical terms or concepts can be classificatory (e.g.,\n“cat” or “proton”), comparative (e.g.,\n“warmer”), or quantitative (e.g.,\n“temperature”) (Hempel 1952; Carnap 1966, Chapter 5).\nMoreover, theoretical terms are “theoretical constructs”\nintroduced “jointly” as a “theoretical system”\n(Hempel 1952, 32). Logical terms include quantifiers (e.g., \\(\\forall,\n\\exists\\)) and connectives (e.g., \\(\\wedge, \\rightarrow\\)). Predicates\nsuch as “hard,” “blue,” and “hot,”\nand relations such as “to the left of” and “smoother\nthan,” are observational terms. ", "\nTerms can be strung together into three kinds of sentences:\ntheoretical, correspondence, and observational. \\(T_S\\) is the set of\ntheoretical sentences that are the axioms, theorems, and laws of the\ntheory. Theoretical sentences include the laws of Newtonian mechanics\nand of the Kinetic Theory of Gases, all suitably axiomatized (e.g.,\nCarnap 1966; Hempel 1966). Primitive theoretical sentences (e.g.,\naxioms) can be distinguished from derivative theoretical sentences\n(e.g., theorems; see Reichenbach 1969 [1924]; Hempel 1958; Feigl\n1970). \\(C_S\\) is the set of correspondence sentences tying\ntheoretical sentences to observable phenomena or “to a\n‘piece of reality’” (Reichenbach 1969 [1924], 8; cf.\nEinstein 1934, 1936 [1936], 351). To simplify, they provide the\ntheoretical syntax with an interpretation and an application, i.e., a\nsemantics. Suitably axiomatized version of the following sentences\nprovide semantics to Boyle’s law, \\(PV = nRT\\): “\\(V\\) in\nBoyle’s law is equivalent to the measurable volume \\(xyz\\) of a\nphysical container such as a glass cube that is \\(x\\), \\(y\\), and\n\\(z\\) centimeters in length, width, and height, and in which the gas\nmeasured is contained” and “\\(T\\) in Boyle’s law is\nequivalent to the temperature indicated on a reliable thermometer or\nother relevant measuring device properly calibrated, attached to the\nphysical system, and read.” Carnap (1987 [1932], 466) presents\ntwo examples of observational sentences, \\(O_S\\): “Here (in a\nlaboratory on the surface of the earth) is a pendulum of such and such\na kind,” and “the length of the pendulum is 245.3\ncm.” Importantly, theoretical sentences can only contain\ntheoretical and logical terms; correspondence sentences involve all\nthree kinds of terms; and observational sentences comprise only\nlogical and observational terms.", "\nThe total domain language of science consists of two languages: the\ntheoretical language, \\(L_T\\), and the observational language, \\(L_O\\)\n(e.g., Hempel 1966, Chapter 6; Carnap 1966, Chapter 23; the index\nentry for “Language,” of Feigl, Scriven, and Maxwell 1958,\n548 has three subheadings: “observation,”\n“theoretical,” and “ordinary”). The\ntheoretical language includes theoretical vocabulary, while the\nobservational language involves observational terms. Both languages\ncontain logical terms. Finally, the theoretical language includes, and\nis constrained by, the logical calculus, Calc, of the\naxiomatic system adopted (e.g., Hempel 1958, 46; Suppe 1977, 50-53).\nThis calculus specifies sentence grammaticality as well as appropriate\ndeductive and non-ampliative inference rules (e.g., modus ponens)\npertinent to, especially, theoretical sentences. Calc can\nitself be written in theoretical sentences.", "\nTable 1 summarizes the Syntactic View’s account of theory\nstructure:", "\nThe salient divide is between theory and observation. Building on\nTable 1, there are three different levels of scientific knowledge,\naccording to the Syntactic View:", "\n\\(\\{T_S\\} =\\) The uninterpreted syntactic system of the scientific\ntheory.\n\n\\(\\{T_S, C_S\\} =\\) The scientific theory structure of a particular\ndomain (e.g., physics, anthropology).\n\n\\(\\{T_S,C_S,O_S\\} =\\) All of the science of a particular domain. ", "\nScientific theory is thus taken to be a syntactically formulated set\nof theoretical sentences (axioms, theorems, and laws) together with\ntheir interpretation via correspondence sentences. As we have seen,\ntheoretical sentences and correspondence sentences are cleanly\ndistinct, even if both are included in the structure of a scientific\ntheory.", "\nOpen questions remain. Is the observation language a sub-language of\nthe theoretical language, or are they both parts of a fuller language\nincluding all the vocabulary? Can the theoretical vocabulary or\nlanguage be eliminated in favor of a purely observational vocabulary\nor language? Are there other ways of carving up kinds of languages?\nFirst, a “dialectical opposition” between “logic and\nexperience,” “form and content,” “constitutive\nprinciples and empirical laws,” and “‘from\nabove’… [and] ‘from below’” pervades\nthe work of the syntacticists (Friedman 1999, 34, 63). Whether\nsyntacticists believe that a synthesis or unification of this general\nopposition between the theoretical (i.e., logic, form) and the\nobservational (i.e., experience, content) is desirable remains a topic\nof ongoing discussion. Regarding the second question, Hempel 1958\ndeflates what he calls “the theoretician’s\ndilemma”—i.e., the putative reduction without remainder of\ntheoretical concepts and sentences to observational concepts and\nsentences. Finally, other language divisions are possible, as Carnap\n1937 argues (see Friedman 1999, Chapter 7). Returning to the main\nthread of this section, the distinction toolkit of theoretical and\nobservational terms, sentences, and languages (Table 1) permit the\nsyntacticists to render theoretical structure sharply, thereby aiming\nat the reconstructive “logic of science”\n(Wissenschafstlogik) that they so desire." ], "subsection_title": "2.1 Theory Structure per the Syntactic View" }, { "content": [ "\nReichenbach 1969 [1924] stands as a canonical attempt by a central\ndeveloper of the Syntactic View of axiomatizing a physical theory,\nviz., relativity theory (cf. Friedman 1983, 1999; see also Reichenbach\n1965 [1920]). For the purposes of this encyclopedia entry, it is\npreferable to turn to another syntactic axiomatization effort. In\naxiomatizing Newtonian mechanics, the mid-20th century\nmathematical logician Hans Hermes spent significant energy defining\nthe concept of mass (Hermes 1938, 1959; Jammer 1961). More precisely,\nhe defines the theoretical concept of “mass ratio” of two\nparticles colliding inelastically in an inertial reference frame\n\\(S\\). Here is his full definition of mass ratio (1959, 287):", "\nOne paraphrase of this definition is, “‘the mass of \\(x\\)\nis α times that of \\(x_0\\)’ is equivalent to ‘there\nexists a system \\(S\\), an instant \\(t\\), momentary mass points \\(y\\)\nand \\(y_0\\), and initial velocities \\(v\\) and \\(v_0\\), such that \\(y\\)\nand \\(y_0\\) are genidentical, respectively, with \\(x\\) and \\(x_0\\);\nthe joined mass points move with a velocity of 0 with respect to frame\n\\(S\\) immediately upon colliding at time \\(t\\); and \\(y\\) and \\(y_0\\)\nhave determinate velocities \\(v\\) and \\(v_0\\) before the collision in\nthe ratio α, which could also be 1 if \\(x\\) and \\(x_0\\) are\nthemselves genidentical.’” Hermes employs the notion of\n“genidentical” to describe the relation between two\ntemporal sections of a given particle’s world line\n(Jammer 1961, 113). Set aside the worry that two distinct particles\ncannot be genidentical per Hermes’ definition, though they can\nhave identical properties. In short, this definition is syntactically\ncomplete and is written in first-order predicate logic, as are the\nother axioms and definitions in Hermes (1938, 1959). Correspondence\nrules connecting a postulated mass \\(x\\) with an actual mass were not\narticulated by Hermes." ], "subsection_title": "2.2 A Running Example: Newtonian Mechanics" }, { "content": [ "\nThe link between theory structure and the world, under the Syntactic\nView, is contained in the theory itself: \\(C_S\\), the set of\ncorrespondence rules. The term “correspondence rules”\n(Margenau 1950; Nagel 1961, 97–105; Carnap 1966, Chapter 24) has\na variety of near-synonyms:", "\nImportant differences among these terms cannot be mapped out here.\nHowever, in order to better understand correspondence rules, two of\ntheir functions will be considered: (i) theory interpretation\n(Carnap, Hempel) and (ii) theory reduction (Nagel,\nSchaffner). The dominant perspective on correspondence rules is that\nthey interpret theoretical terms. Unlike “mathematical\ntheories,” the axiomatic system of physics “cannot\nhave… a splendid isolation from the world” (Carnap 1966,\n237). Instead, scientific theories require observational\ninterpretation through correspondence rules. Even so, surplus meaning\nalways remains in the theoretical structure (Hempel 1958, 87; Carnap\n1966). Second, correspondence rules are seen as necessary for\ninter-theoretic reduction (van Riel and Van Gulick 2014). For\ninstance, they connect observation terms such as\n“temperature” in phenomenological thermodynamics (the\nreduced theory) to theoretical concepts such as “mean kinetic\nenergy” in statistical mechanics (the reducing theory).\nCorrespondence rules unleash the reducing theory’s epistemic\npower. Notably, Nagel (1961, Chapter 11; 1979) and Schaffner (1969,\n1976, 1993) allow for multiple kinds of correspondence rules, between\nterms of either vocabulary, in the reducing and the reduced theory\n(cf. Callender 1999; Winther 2009; Dizadji-Bahmani, Frigg, and\nHartmann 2010). Correspondence rules are a core part of the structure\nof scientific theories and serve as glue between theory and\nobservation.", "\nFinally, while they are not part of the theory structure, and although\nwe saw some examples above, observation sentences are worth briefly\nreviewing. Correspondence rules attach to the content of observational\nsentences. Observational sentences were analyzed as (i) protocol\nsentences or Protokollsätze (e.g., Schlick 1934;\nCarnap 1987 [1932], 1937, cf. 1963; Neurath 1983 [1932]), and as (ii)\nexperimental laws (e.g., Campbell 1920; Nagel 1961; Carnap\n1966; cf. Duhem 1954 [1906]). Although constrained by Calc,\nthe grammar of these sentences is determined primarily by the order of\nnature, as it were. In general, syntacticists do not consider methods\nof data acquisition, experiment, and measurement to be philosophically\ninteresting. In contrast, the confirmation relation between\n(collected) data and theory, especially as developed in inductive\nlogic (e.g., Reichenbach 1938, 1978; Carnap 1962 [1950], 1952), as\nwell as questions about the conventionality, grammaticality,\nfoundationalism, atomism, and content of sense-data and synthetic\nstatements, are considered philosophically important (e.g., Carnap\n1987 [1932], 1937, 1966; Neurath 1983 [1932]; Reichenbach 1951;\nSchlick 1925 [1918], 1934; for contemporary commentary, see, e.g.,\nCreath 1987, 2014; Rutte 1991; Friedman 1999)." ], "subsection_title": "2.3 Interpreting Theory Structure per the Syntactic View" }, { "content": [ "\nTo summarize, the Syntactic View holds that there are three kinds of\nterms or vocabularies: logical, theoretical, and observational; three\nkinds of sentences: \\(T_S\\), \\(C_S\\), and \\(O_S\\); and two languages:\n\\(L_T\\) and \\(L_O\\). Moreover, the structure of scientific theories\ncould be analyzed using the logical tools of metamathematics. The goal\nis to reconstruct the logic of science, viz. to articulate an\naxiomatic system.", "\nInterestingly, this perspective has able and active defenders today,\nwho discuss constitutive and axiomatized principles of the historical\n“relativized a priori” (Friedman 2001, cf. 2013), argue\nthat “the semantic view, if plausible, is syntactic”\n(Halvorson 2013), and explore “logicism” for, and in, the\nphilosophy of science (Demopulous 2003, 2013; van Benthem 2012).\nFurthermore, for purposes of the syntactic reconstruction of\nscientific theories, some continue espousing—or perhaps plea for\nthe resurrection of—predicate logic (e.g., Lutz 2012, 2014),\nwhile other contemporary syntacticists (e.g., Halvorson 2012, 2013,\n2019) endorse more recently developed metamathematical and\nmathematical equipment, such as category theory, which “turns\nout to be a kind of universal mathematical language like set\ntheory” (Awodey 2006, 2; see Eilenberg and MacLane 1945).\nImportantly, Halvorson (2019) urges that interlocutors adopt\n“structured” rather than “flat” views of\ntheories. For the case of the syntactic view this would mean that\nrather than accept the usual formulation that a theory is a\nset of sentences, “… [we] might say that a\ntheory consists of both sentences and inferential relations between\nthose sentences” (Halvorson 2019, 277–8). Classical\nsyntacticists such as Rudolf Carnap (Friedman 1999, 2011; Carus 2007;\nBlatti and Lapointe 2016; Koellner ms. in Other Internet Resources)\nand Joseph Henry Woodger (Nicholson and Gawne 2014) have recently\nreceived increasing attention." ], "subsection_title": "2.4 Taking Stock: Syntactic View" } ] }, { "main_content": [ "\nAn overarching theme of the Semantic View is that analyzing theory\nstructure requires employing mathematical tools rather than predicate\nlogic. After all, defining scientific concepts within a specific\nformal language makes any axiomatizing effort dependent on the choice,\nnature, and idiosyncrasies of that narrowly-defined language. For\ninstance, Suppes understands first-order predicate logic, with its\n“linguistic” rather than “set-theoretical”\nentities, as “utterly impractical” for the formalization\nof “theories with more complicated structures like probability\ntheory” (Suppes 1957, 232, 248–9; cf. Suppes 2002). Van\nFraassen, another influential defender of the Semantic View, believes\nthat the logical apparatus of the Syntactic View “had moved us\nmille milles de toute habitation scientifique, isolated in\nour own abstract dreams” (van Fraassen 1989, 225). Indeed, what\nwould the appropriate logical language for specific mathematical\nstructures be, especially when such structures could be reconstructed\nin a variety of formal languages? Why should we imprison mathematics\nand mathematical scientific theory in syntactically defined\nlanguage(s) when we could, instead, directly investigate the\nmathematical objects, relations, and functions of scientific theory?\n", "\nConsistent with the combat strategy (discussed in the Conclusion),\nhere is a list of grievances against the Syntactic View discussed at\nlength in the work of some semanticists.", "\nWhat, then, does the Semantic View propose to put in the Syntactic\nView’s place?" ], "section_title": "3. The Semantic View", "subsections": [ { "content": [ "\nEven a minimal description of the Semantic View must acknowledge two\ndistinct strategies of characterizing and comprehending theory\nstructure: the state-space and the\nset-/model-theoretic approaches. ", "\nThe state-space approach emphasizes the mathematical models of actual\nscience, and draws a clear line between mathematics and\nmetamathematics. The structure of a scientific theory is identified\nwith the “class,” “family” or\n“cluster” of mathematical models constituting it, rather\nthan with any metamathematical axioms “yoked to a particular\nsyntax” (van Fraassen 1989, 366). Under this analysis,\n“the correct tool for philosophy of science is mathematics, not\nmetamathematics”—this is Suppes’ slogan, per van\nFraassen (1989, 221; 1980, 65). In particular, a state space or phase\nspace is an \\(N\\)-dimensional space, where each of the relevant\nvariables of a theory correspond to a single dimension and each point\nin that space represents a possible state of a real system.\nAn actual, real system can take on, and change, states according to\ndifferent kinds of laws, viz., laws of succession determining\npossible trajectories through that space (e.g., Newtonian kinematic\nlaws); laws of co-existence specifying the permitted regions\nof the total space (e.g., Boyle’s law); and laws of\ninteraction combining multiple laws of succession or\nco-existence, or both (e.g., population genetic models combining laws\nof succession for selection and genetic drift, Wright 1969; Lloyd 1994\n[1988]; Rice 2004; Clatterbuck, Sober, and Lewontin 2013). Different\nmodels of a given theory will share some dimensions of their state\nspace while differing in others. Such models will also partially\noverlap in laws (for further discussion of state spaces, laws, and\nmodels pertinent to the Semantic View, see Suppe 1977, 224–8;\nLloyd 1994, Chapter 2; Nolte 2010; Weisberg 2013, 26–9).", "\nHistorically, the state-space approach emerged from work by Evert\nBeth, John von Neumann, and Hermann Weyl, and has important parallels\nwith Przełęcki (1969) and Dalla Chiara Scabia and Toraldo di\nFrancia (1973) (on the history of the approach see: Suppe 1977; van\nFraassen 1980, 65–67; Lorenzano 2013; advocates of the approach\ninclude: Beatty 1981; Giere 1988, 2004; Giere, Bickle, and Mauldin\n2006; Lloyd 1983, 1994 [1988], 2013 In Press; Suppe 1977, 1989;\nThompson, 1989, 2007; van Fraassen 1980, 1989, 2008; for alternative\nearly analyses of models see, e.g., Braithwaite 1962; Hesse 1966,\n1967). Interestingly, van Fraassen (1967, 1970) provides a potential\nreconstruction of state spaces via an analysis of\n“semi-interpreted languages.” Weisberg (2013), building on\nmany insights from Giere’s work, presents a broad view of\nmodeling that includes mathematical structures that are\n“trajectories in state spaces” (29), but also permits\nconcrete objects and computational structures such as algorithms to be\ndeemed models. Lorenzano (2013) calls Giere’s (and, by\nextension, Weisberg’s and even Godfrey-Smith’s 2006)\napproach “model-based,” separating it out from the\nstate-space approach. A more fine-grained classification of the\nstate-space approach is desirable, particularly if we wish to\nunderstand important lessons stemming from the Pragmatic View of\nTheories, as we shall see below.", "\nAs an example of a state-space analysis of modeling, consider a\ncapsule traveling in outer space. An empirically and dynamically\nadequate mathematical model of the capsule’s behavior would\ncapture the position of the capsule (i.e., three dimensions\nof the formal state space), as well as the velocity and\nacceleration vectors for each of the three standard spatial\ndimensions (i.e., six more dimensions in the formal state space). If\nthe mass were unknown or permitted to vary, we would have to add one\nmore dimension. Possible and actual trajectories of our capsule, with\nknown mass, within this abstract 9-dimensional state space could be\ninferred via Newtonian dynamical laws of motion (example in Lewontin\n1974, 6–8; consult Suppe 1989, 4). Importantly, under the\nstate-space approach, the interesting philosophical work of\ncharacterizing theory structure (e.g., as classes of models), theory\nmeaning (e.g., data models mapped to theoretical models), and theory\nfunction (e.g., explaining and predicting) happens at the level of\nmathematical models. ", "\nLurking in the background of the state-space conception is the fact\nthat mathematics actually includes set theory and model\ntheory—i.e., mathematical logic. Indeed, according to some\ninterlocutors, “metamathematics is part of mathematics”\n(Halvorson 2012, 204). Historically, a set-/model-theoretic approach\nemerged from Tarski’s work and was extensively articulated by\nSuppes and his associates (van Fraassen 1980, 67). Set theory is a\ngeneral language for formalizing mathematical structures as\ncollections—i.e., sets—of abstract objects (which can\nthemselves be relations or functions; see Krivine 2013 [1971]). Model\ntheory investigates the relations between, on the one hand, the formal\naxioms, theorems, and laws of a particular theory and, on the other\nhand, the mathematical structures—the models—that provide\nan interpretation of that theory, or put differently, that make the\ntheory’s axioms, theorems, and laws true (Hodges 1997, Chapter\n2; Jones 2005). Interestingly, model theory often uses set theory\n(e.g., Marker 2002); set theory can, in turn, be extended to link\naxiomatic theories and semantic models via “set-theoretical\npredicates” (e.g., Suppes 1957, 2002). Finally, there are\ncertain hybrids of these two branches of mathematical logic, including\n“partial structures” (e.g., da Costa and French 1990,\n2003; Bueno 1997; French 2017; French and Ladyman 1999, 2003; Vickers\n2009; Bueno, French, and Ladyman 2012). Lorenzano (2013) provides a\nmore complex taxonomy of the intellectual landscape of the Semantic\nView, including a discussion of Structuralism, a kind of\nset-/model-theoretic perspective. Structuralism involves theses about\n“theory-nets,” theory-relative theoretical vs.\nnon-theoretical terms, a diversity of intra- and inter-theoretic laws\nwith different degrees of generality, a typology of inter-theoretic\nrelations, and a rich account of correspondence rules in scientific\npractice (see Moulines 2002; Pereda 2013; Schmidt 2014; Ladyman 2014).\nOn the whole, the set-/model-theoretic approach of the Semantic View\ninsists on the inseparability of metamathematics and mathematics. In\npreferring to characterize a theory axiomatically in terms of its\nintension rather than its extension, it shares the Syntactic\nView’s aims of reconstructive axiomatization (e.g., Sneed 1979;\nStegmüller 1979; Frigg and Votsis 2011; Halvorson 2013, 2019;\nLutz 2012, 2014, 2017).", "\nAn example will help motivate the relation between theory and model.\nTwo qualifications are required: (i) we return to a more standard\nset-/model-theoretic illustration below, viz., McKinsey, Sugar, and\nSuppes’ (1953) axiomatization of particle mechanics, and (ii)\nthis motivational example is not from the heartland of model theory\n(see Hodges 2013). Following van Fraassen’s intuitive case of\n“seven-point geometry” (1980, 41–44; 1989,\n218–220), also known as “the Fano plane” we see how\na particular geometric figure, the model, interprets and\nmakes true a set of axioms and theorems, the theory. In\ntopology and geometry there is rich background theory regarding how to\nclose Euclidean planes and spaces to make finite geometries by, for\ninstance, eliminating parallel lines. Consider the axioms of a\nprojective plane:", "\nA figure of a geometric model that makes this theory true is:", "\nThis is the smallest geometrical model satisfying the three axioms of\nthe projective plane theory. Indeed, this example fits van\nFraassen’s succinct characterization of the theory-model\nrelation:", "\nA model is called a model of a theory exactly if the theory is\nentirely true if considered with respect to this model alone.\n(Figuratively: the theory would be true if this model was the whole\nworld.) (1989, 218)\n", "\nThat is, if the entire universe consisted solely of these seven points\nand seven lines, the projective plane theory would be true. Of course,\nour universe is bigger. Because Euclidean geometry includes parallel\nlines, the Fano plane is not a model of Euclidean geometry. Even so,\nby drawing the plane, we have shown it to be isomorphic to\nparts of the Euclidean plane. In other words, the Fano plane has been\nembedded in a Euclidean plane. Below we return to the\nconcepts of embedding and isomorphism, but this example shall suffice\nfor now to indicate how a geometric model can provide a semantics for\nthe axioms of a theory.", "\nIn short, for the Semantic View the structure of a scientific theory\nis its class of mathematical models. According to some advocates of\nthis view, the family of models can itself be axiomatized, with those\nvery models (or other models) serving as axiom truth-makers. " ], "subsection_title": "3.1 Theory Structure per the Semantic View" }, { "content": [ "\nReturning to our running example, consider Suppes’ 1957\nmodel-theoretic articulation of particle mechanics, which builds on\nhis 1953 article with J.C.C. McKinsey and A.C. Sugar. Under this\nanalysis, there is a domain of set-theoretic objects of the form \\(\\{\nP, T, s, m, f, g \\}\\), where \\(P\\) and \\(T\\) are themselves sets,\n\\(s\\) and \\(g\\) are binary functions, \\(m\\) is a unary and \\(f\\) a\nternary function. \\(P\\) is the set of particles; \\(T\\) is a set of\nreal numbers measuring elapsed times; \\(s(p, t)\\) is the position of\nparticle \\(p\\) at time \\(t\\); \\(m(p)\\) is the mass of particle \\(p\\);\n\\(f(p, q, t)\\) is the force particle \\(q\\) exerts on \\(p\\) at time\n\\(t\\); and \\(g(p, t)\\) is the total resultant force (by all other\nparticles) on \\(p\\) at time \\(t\\). Suppes and his collaborators\ndefined seven axioms—three kinematical and four\ndynamical—characterizing Newtonian particle mechanics (see also\nSimon 1954, 1970). Such axioms include Newton’s third law\nreconstructed in set-theoretic formulation thus (Suppes 1957,\n294):", "\nImportantly, the set-theoretic objects are found in more than one of\nthe axioms of the theory, and Newton’s calculus is reconstructed\nin a novel, set-theoretic form. Set-theoretic predicates such as\n“is a binary relation” and “is a function” are\nalso involved in axiomatizing particle mechanics (Suppes 1957, 249).\nOnce these axioms are made explicit, their models can be specified and\nthese can, in turn, be applied to actual systems, thereby providing a\nsemantics for the axioms (e.g., as described in Section 3.3.1 below).\nA particular system satisfying these seven axioms is a particle\nmechanics system. (For an example of Newtonian mechanics from the\nstate-space approach, recall the space capsule of Section 3.1.1.)" ], "subsection_title": "3.2 A Running Example: Newtonian Mechanics" }, { "content": [ "\nHow is the theory structure, described in Section 3.1, applied to\nempirical phenomena? How do we connect theory and data via observation\nand experimental and measuring techniques? The Semantic View\ndistinguishes theory individuation from both theory-phenomena and\ntheory-world relations. Three types of analysis of theory\ninterpretation are worth investigating: (i) a hierarchy of\nmodels (e.g., Suppes; Suppe), (ii) similarity (e.g.,\nGiere; Weisberg), and (iii) isomorphism (e.g., van Fraassen;\nFrench and Ladyman).", "\nOne way of analyzing theory structure interpretation is through a\nseries of models falling under the highest-level axiomatizations. This\nseries has been called “a hierarchy of models,” though it\nneed not be considered a nested hierarchy. These models include models\nof theory, models of experiment, and models of data (Suppes 1962,\n2002). Here is a summary of important parts of the hierarchy (Suppes\n1962, Table 1, 259; cf. Giere 2010, Figure 1, 270): ", "\nThe temptation to place phenomena at the bottom of the\nhierarchy must be resisted because phenomena permeate all levels.\nIndeed, the “class of phenomena” pertinent to a scientific\ntheory is its “intended scope” (Suppe 1977, 223; Weisberg\n2013, 40). Furthermore, this temptation raises fundamental questions\nabout scientific representation: “there is the more profound\nissue of the relationship between the lower most representation in the\nhierarchy—the data model perhaps—and reality itself, but\nof course this is hardly something that the semantic approach alone\ncan be expected to address” (French and Ladyman 1999, 113; cf.\nvan Fraassen 2008, 257–258, “The ‘link’ to\nreality”). Borrowing from David Chalmers, the “hard\nproblem” of philosophy of science remains connecting abstract\nstructures to concrete phenomena, data, and world. ", "\nThe similarity analysis of theory interpretation combines semantic and\npragmatic dimensions (Giere 1988, 2004, 2010; Giere, Bickle, and\nMauldin 2006; Weisberg 2013). According to Giere, interpretation is\nmediated by theoretical hypotheses positing representational relations\nbetween a model and relevant parts of the world. Such relations may be\nstated as follows:", "\nHere \\(S\\) is a scientist, research group or community, \\(W\\) is a\npart of the world, and \\(X\\) is, broadly speaking, any one of a\nvariety of models (Giere 2004, 743, 747, 2010). Model-world similarity\njudgments are conventional and intentional:", "\nNote that I am not saying that the model itself represents an aspect\nof the world because it is similar to that aspect. …Anything is\nsimilar to anything else in countless respects, but not anything\nrepresents anything else. It is not the model that is doing the\nrepresenting; it is the scientist using the model who is doing the\nrepresenting. (2004, 747)\n", "\nRelatedly, Weisberg (2013) draws upon Tversky (1977) to develop a\nsimilarity metric for model interpretation (equation 8.10, 148). This\nmetric combines (i) model-target semantics (90–97), and (ii) the\npragmatics of “context, conceptualization of the target, and the\ntheoretical goals of the scientist” (149). Giere and Weisberg\nthus endorse an abundance of adequate mapping relations between a\ngiven model and the world. From this diversity, scientists and\nscientific communities must select particularly useful similarity\nrelationships for contextual modeling purposes. Because of semantic\npluralism and irreducible intentionality, this similarity analysis of\ntheory interpretation cannot be accommodated within a hierarchy of\nmodels approach, interpreted as a neat model nesting based on\npre-given semantic relations among models at different levels.", "\nThe term “isomorphism” is a composite of the Greek words\nfor “equal” and “shape” or “form.”\nIndeed, in mathematics, isomorphism is a perfect one-to-one, bijective\nmapping between two structures or sets. Figure (2) literally and\nfiguratively captures the term:", "\nEspecially in set theory, category theory, algebra, and topology,\nthere are various kinds of “-morphisms,” viz., of mapping\nrelations between two structures or models. Figure\n(3) indicates five different kinds of homomorphism, arranged in a Venn\ndiagram.", "\nAlthough philosophers have focused on isomorphism, other morphisms\nsuch as monomorphism (i.e., an injective homomorphism where some\nelements in the co-domain remain unmapped from the domain) might also\nbe interesting to investigate, especially for embedding data (i.e.,\nthe domain) into rich theoretical structures (i.e., the co-domain). To\ncomplete the visualization above, an epimorphism is a surjective\nhomomorphism, and an endomorphism is a mapping from a structure to\nitself, although it need not be a symmetrical—i.e.,\ninvertible—mapping, which would be an automorph. ", "\nPerhaps the most avid supporter of isomorphism and embedding as the\nway to understand theory interpretation is van Fraassen. In a\nnutshell, if we distinguish (i) theoretical models, (ii)\n“empirical substructures” (van Fraassen 1980, 64, 1989,\n227; alternatively: “surface models” 2008, 168), and (iii)\n“observable phenomena” (1989, 227, 2008, 168), then, van\nFraassen argues, theory interpretation is a relation of isomorphism\nbetween observable phenomena and empirical substructures, which are\nthemselves isomorphic with one or more theoretical models.\nMoreover, if a relation of isomorphism holds between \\(X\\) and a\nricher \\(Y\\), we say that we have embedded \\(X\\) in \\(Y\\). For\ninstance, with respect to the seven-point geometry above (Figure 1),\nvan Fraassen contends that isomorphism gives embeddability, and that\nthe relation of isomorphism “is important because it is also the\nexact relation a phenomenon bears to some model or theory, if that\ntheory is empirically adequate” (1989, 219–20; this kind\nof statement seems to be simultaneously descriptive and prescriptive\nabout scientific representation, see Section 1.1 above). In The\nScientific Image he is even clearer about fleshing out the\nempirical adequacy of a theory (with its theoretical models) in terms\nof isomorphism between “appearances” (i.e., “the\nstructures which can be described in experimental and measurement\nreports,” 1980, 64, italics removed) and empirical\nsubstructures. Speaking metaphorically,", "\nthe phenomena are, from a theoretical point of view, small, arbitrary,\nand chaotic—even nasty, brutish, and short…—but can\nbe understood as embeddable in beautifully simple but much larger\nmathematical models. (2008, 247; see also van Fraassen 1981, 666 and\n1989, 230)\n", "\nInterestingly, and as a defender of an identity strategy (see\nConclusion), Friedman also appeals to embedding and subsumption\nrelations between theory and phenomena in his analyses of theory\ninterpretation (Friedman 1981, 1983).\nBueno, da Costa, French, and Ladyman also employ embedding and\n(partial) isomorphism in the empirical interpretation of partial\nstructures (Bueno 1997; Bueno, French, and Ladyman 2012; da Costa and\nFrench 1990, 2003; French 2017; French and Ladyman 1997, 1999, 2003;\nLadyman 2004). Suárez discusses complexities in van\nFraassen’s analyses of scientific representation and theory\ninterpretation (Suárez 1999, 2011). On the one hand,\nrepresentation is structural identity between the theoretical and the\nempirical. On the other hand, “There is no representation except\nin the sense that some things are used, made, or taken, to represent\nsome things as thus or so” (van Fraassen 2008, 23, italics\nremoved). The reader interested in learning how van Fraassen\nsimultaneously endorses acontextually structural and contextually\npragmatic aspects of representation and interpretation should refer to\nvan Fraassen’s (2008) investigations of maps and “the\nessential indexical.” [To complement the structure vs. function\ndistinction, see van Fraassen 2008, 309–311 for a structure\n(“structural relations”) vs. history (“the\nintellectual processes that lead to those models”) distinction;\ncf. Ladyman et al. 2011] In all of this, embedding via isomorphism is\na clear contender for theory interpretation under the Semantic\nView." ], "subsection_title": "3.3 Interpreting Theory Structure per the Semantic View" }, { "content": [ "\nIn short, committing to either a state-space or a set-/model-theoretic\nview on theory structure does not imply any particular perspective on\ntheory interpretation (e.g., hierarchy of models, similarity,\nembedding). Instead, commitments to the former are logically and\nactually separable from positions on the latter (e.g., Suppes and\nSuppe endorse different accounts of theory structure, but share an\nunderstanding of theory interpretation in terms of a hierarchy of\nmodels). The Semantic View is alive and well as a family of analyses\nof theory structure, and continues to be developed in interesting ways\nboth in its state-space and set-/model-theoretic approaches. " ], "subsection_title": "3.4 Taking Stock: Semantic View" } ] }, { "main_content": [ "\nThe Pragmatic View recognizes that a number of assumptions about\nscientific theory seem to be shared by the Syntactic and Semantic\nViews. Both perspectives agree, very roughly, that theory is (1)\nexplicit, (2) mathematical, (3) abstract, (4) systematic, (5) readily\nindividualizable, (6) distinct from data and experiment, and (7)\nhighly explanatory and predictive (see Flyvbjerg 2001, 38–39;\ncf. Dreyfus 1986). The Pragmatic View imagines the structure of\nscientific theories rather differently, arguing for a variety of\ntheses:", "\nThese are core commitments of the Pragmatic View.", "\nIt is important to note at the outset that the Pragmatic View takes\nits name from the linguistic trichotomy discussed above, in the\nIntroduction. This perspective need not imply commitment to, or\nassociation with, American Pragmatism (e.g. the work of Charles S.\nPeirce, William James, or John Dewey; cf. Hookway 2013; Richardson\n2002). For instance, Hacking (2007a) distinguishes his pragmatic\nattitudes from the school of Pragmatism. He maps out alternative\nhistorical routes of influence, in general and on him,\nvis-à-vis fallibilism (via Imre Lakatos, Karl Popper; Hacking\n2007a, §1), historically conditioned truthfulness (via Bernard\nWilliams; Hacking 2007a, §3), and realism as intervening (via\nFrancis Everitt, Melissa Franklin; Hacking 2007a, §4). To borrow\na term from phylogenetics, the Pragmatic View is\n“polyphyletic.” The components of its analytical framework\nhave multiple, independent origins, some of which circumnavigate\nAmerican Pragmatism.", "\nWith this qualification and the five theses above in mind, let us now\nturn to the Pragmatic View’s analysis of theory structure and\ntheory interpretation." ], "section_title": "4. The Pragmatic View", "subsections": [ { "content": [ "\nWe should distinguish two strands of the Pragmatic View: the\nPragmatic View of Models and a proper Pragmatic View of\nTheories. ", "\nNancy Cartwright’s How the Laws of Physics Lie\ncrystallized the Pragmatic View of Models. Under Cartwright’s\nanalysis, models are the appropriate level of investigation for\nphilosophers trying to understand science. She argues for significant\nlimitations of theory (thesis #1), claiming that laws of nature are\nrarely true, and are epistemically weak. Theory as a collection of\nlaws cannot, therefore, support the many kinds of inferences and\nexplanations that we have come to expect it to license. Cartwright\nurges us to turn to models and modeling, which are central to\nscientific practice. Moreover, models\n“lie”—figuratively and literally—between\ntheory and the world (cf. Derman 2011). That is, “to explain a\nphenomenon is to find a model that fits it into the basic framework of\nthe theory and that thus allows us to derive analogues for the messy\nand complicated phenomenological laws which are true of it.” A\nplurality of models exist, and models “serve a variety of\npurposes” (Cartwright 1983, 152; cf. Suppes 1978). Cartwright is\ninterested in the practices and purposes of scientific models, and\nasks us to focus on models rather than theories.", "\nCartwright’s insights into model pluralism and model practices\nstand as a significant contribution of “The Stanford\nSchool” (cf. Cat 2014), and were further developed by the\n“models as mediators” group, with participants at LSE,\nUniversity of Amsterdam, and University of Toronto (Morgan and\nMorrison 1999; Chang 2011; cf. Martínez 2003). This group\ninsisted on the internal pluralism of model components (thesis #2).\nAccording to Morgan and Morrison, building a model involves\n“fitting together… bits which come from disparate\nsources,” including “stories” (Morgan and Morrison\n1999, 15). Boumans (1999) writes:", "\n\n\nmodel building is like baking a cake without a recipe. The ingredients\nare theoretical ideas, policy views, mathematisations of the cycle,\nmetaphors and empirical facts. (67)\n\n\nMathematical moulding is shaping the ingredients in such a\nmathematical form that integration is possible… (90)\n", "\nIn an instructive diagram, Boumans suggests that a variety of factors\nbesides theory and data feed into a model: metaphors, analogies,\npolicy views, stylised facts, mathematical techniques, and\nmathematical concepts (93). The full range of components involved in a\nmodel will likely vary according to discipline, and with respect to\nexplanations and interventions sought (e.g., analogies but not policy\nviews will be important in theoretical physics). In short, model\nbuilding involves a complex variety of internal nonformal aspects,\nsome of which are implicit (theses #2 and #3).", "\nAs one example of a nonformal component of model construction and\nmodel structure, consider metaphors and analogies (e.g., Bailer-Jones\n2002). Geary (2011) states the “simplest equation” of\nmetaphor thus: “\\(X = Y\\)” (8, following Aristotle:\n“Metaphor consists in giving the thing a name that belongs to\nsomething else… ,” Poetics, 1457b). The line\nbetween metaphor and analogy in science is blurry. Some interlocutors\nsynonymize them (e.g., Hoffman 1980; Brown 2003), others reduce one to\nthe other (analogy is a form of metaphor, Geary 2011; metaphor is a\nkind of analogy, Gentner 1982, 2003), and yet others bracket one to\nfocus on the other (e.g., Oppenheimer 1956 sets aside metaphor). One\nway to distinguish them is to reserve “analogy” for\nconcrete comparisons, with clearly identifiable and demarcated source\nand target domains, and with specific histories, and use\n“metaphor” for much broader and indeterminate comparisons,\nwith diffuse trajectories across discourses. Analogies include the\n“lines of force” of electricity and magnetism (Maxwell and\nFaraday), the atom as a planetary system (Rutherford and Bohr), the\nbenzene ring as a snake biting its own tail (Kekulé),\nDarwin’s “natural selection” and “entangled\nbank,” and behavioral “drives” (Tinbergen) (e.g.,\nHesse 1966, 1967; Bartha 2010). Examples of metaphor are\ngenetic information, superorganism, and networks (e.g., Keller 1995).\nMore could be said about other informal model components, but this\ndiscussion of metaphors and analogies shall suffice to hint at how\nmodels do not merely lie between theory and world. Models express a\nrich internal pluralism (see also de Chadarevian and Hopwood 2004;\nMorgan 2012). ", "\nModel complexity can also be seen in the external plurality of models\n(thesis #2). Not all models are mathematical, or even ideally recast\nas mathematical. Non-formalized (i.e., non–state-space,\nnon-set-/model-theoretic) models such as physical, diagrammatic,\nmaterial, historical, “remnant,” and fictional models are\nubiquitous across the sciences (e.g., Frigg and Hartmann 2012; for the\nbiological sciences, see Hull 1975; Beatty 1980; Griesemer 1990, 1991\na, b, 2013; Downes 1992; Richards 1992; Winther 2006a; Leonelli\n2008; Weisberg 2013). Moreover, computer simulations differ in\nimportant respects from more standard analytical mathematical models\n(e.g., Smith 1996; Winsberg 2010; Weisberg 2013). According to some\n(e.g., Griesemer 2013; Downes 1992; Godfrey-Smith 2006; Thomson-Jones\n2012), this diversity belies claims by semanticists that models can\nalways be cast “into set theoretic terms” (Lloyd 2013 In\nPress), are “always a mathematical structure” (van\nFraassen 1970, 327), or that “formalisation of a theory is an\nabstract representation of the theory expressed in a formal deductive\nframework… in first-order predicate logic with identity, in set\ntheory, in matrix algebra and indeed, any branch of\nmathematics...” (Thompson 2007, 485–6). Even so, internal\npluralism has been interpreted as supporting a “deflationary\nsemantic view,” which is minimally committed to the perspective\nthat “model construction is an important part of scientific\ntheorizing” (Downes 1992, 151). Given the formal and\nmathematical framework of the Semantic View (see above), however, the\nbroad plurality of kinds of models seems to properly belong under a\nPragmatic View of Models.", "\nInterestingly, while critiquing the Syntactic and Semantic Views on\nmost matters, the Pragmatic View of Models construed theory, the\nprocess of theorizing, and the structure of scientific theories,\naccording to terms set by the two earlier views. For instance,\nCartwright tends to conceive of theory as explicit, mathematical,\nabstract, and so forth (see the first paragraph of Section 4). She\nalways resisted “the traditional syntactic/semantic view of\ntheory” for its “vending machine” view, in which a\ntheory is a deductive and automated machine that upon receiving\nempirical input “gurgitates” and then “drops out the\nsought-for representation” (1999a, 184–5). Rather than\nreform Syntactic and Semantic accounts of theory and theory structure,\nhowever, she invites us, as we just saw, to think of science as\nmodeling, “with theory as one small component”\n(Cartwright, Shomar, and Suárez 1995, 138; Suárez and\nCartwright 2008). Many have followed her. Kitcher’s predilection\nis also to accept the terms of the Syntactic and Semantic Views. For\ninstance, he defines theories as “axiomatic deductive\nsystems” (1993, 93). In a strategy complementary to\nCartwright’s modeling turn, Kitcher encourages us to focus on\npractice, including practices of modeling and even practices of\ntheorizing. In The Advancement of Science, practice is\nanalyzed as a 7-tuple, with the following highly abbreviated\ncomponents: (i) a language; (ii) questions; (iii) statements\n(pictures, diagrams); (iv) explanatory patterns; (v) standard\nexamples; (vi) paradigms of experimentation and observation, plus\ninstruments and tools; and (vii) methodology (Kitcher 1993, 74).\nScientific practice is also center stage for those singing the praises\nof “the experimental life” (e.g., Hacking 1983; Shapin and\nSchaffer 1985; Galison 1987), and those highlighting the cognitive\ngrounds of science (e.g., Giere 1988; Martínez 2014) and\nscience’s social and normative context (e.g., Kitcher 1993,\n2001; Longino 1995, 2002; Ziman 2000; cf. Simon 1957). Indeed, the\nmodeling and practice turns in the philosophy of science were\nreasonable reactions to the power of axiomatic reconstructive and\nmathematical modeling analyses of the structure of scientific\ntheories. ", "\nYet, a Pragmatic View of Theories is also afoot, one\nresisting orthodox characterizations of theory often embraced, at\nleast early on, by Pragmatic View philosophers such as Cartwright,\nHacking, Kitcher, and Longino. For instance, Craver (2002) accepts\nboth the Syntactic and Semantic Views, which he humorously and not\ninaccurately calls “the Once Received View” and the\n“Model Model View.” But he also observes:", "\nWhile these analyses have advanced our understanding of some formal\naspects of theories and their uses, they have neglected or obscured\nthose aspects dependent upon nonformal patterns in theories.\nProgress can be made in understanding scientific theories by attending\nto their diverse nonformal patterns and by identifying the axes along\nwhich such patterns might differ from one another. (55)\n", "\nCraver then turns to mechanistic theory as a third theory type (and a\nthird philosophical analysis of theory structure) that highlights\nnonformal patterns:", "\nDifferent types of mechanisms can be distinguished on the basis of\nrecurrent patterns in their organization. Mechanisms may be organized\nin series, in parallel, or in cycles. They may contain branches and\njoins, and they often include feedback and feedforward subcomponents.\n(71)\n", "\nConsistent with theses #2 and #3 of the Pragmatic View, we must\nrecognize the internal pluralism of theories as including nonformal\ncomponents. Some of these are used to represent organizational and\ncompositional relations of complex systems (Craver 2007; Wimsatt 2007; Winther 2011; Walsh 2015). While mechanistic analyses such as\nCraver’s may not wish to follow every aspect of the Pragmatic\nView of Theories, there are important and deep resonances between the\ntwo.", "\nIn a review of da Costa and French (2003), Contessa (2006) writes:", "\nPhilosophers of science are increasingly realizing that the\ndifferences between the syntactic and the semantic view are less\nsignificant than semanticists would have it and that, ultimately,\nneither is a suitable framework within which to think about scientific\ntheories and models. The crucial divide in philosophy of science, I\nthink, is not the one between advocates of the syntactic view and\nadvocates of the semantic view, but the one between those who think\nthat philosophy of science needs a formal framework or other and those\nwho think otherwise. (376)\n", "\nAgain, we are invited to develop a non-formal framework of science and\npresumably also of scientific theory. (Halvorson 2012, 203 takes\nContessa 2006 to task for advocating “informal philosophy of\nscience.”) Moreover, in asking “what should the content of\na given theory be taken to be on a given occasion?”, Vickers\n(2009) answers:", "\nIt seems clear that, in addition to theories being vague objects in\nthe way that ‘heaps’ of sand are, there will be\nfundamentally different ways to put together theoretical assumptions\ndepending on the particular investigation one is undertaking. For\nexample, sometimes it will be more appropriate to focus on the\nassumptions which were used by scientists, rather than the\nones that were believed to be true. (247, footnote\nsuppressed)\n", "\nA Pragmatic View of Theories helps make explicit nonformal internal\ncomponents of theory structure. ", "\nKey early defenders of the modeling and practice turns have also\nrecently begun to envision theory in a way distinct from the terms set\nby the Syntactic and Semantic Views. Suárez and Cartwright\n(2008) extend and distribute theory by arguing that “What we\nknow ‘theoretically’ is recorded in a vast number of\nplaces in a vast number of different ways—not just in words and\nformulae but in machines, techniques, experiments and applications as\nwell” (79). And while her influence lies primarily in the\nmodeling turn, even in characterizing the “vending\nmachine” view, Cartwright calls for a “reasonable\nphilosophical account of theories” that is “much more\ntextured, and… much more laborious” than that adopted by\nthe Syntactic and Semantic Views (1999a, 185). The theory-data and\ntheory-world axes need to be rethought. In her 2019 book on\n“artful modeling”, Cartwright emphasizes the importance of\nknow-how and creativity in scientific practice, and “praise[s]\nengineers and cooks and inventors, as well as experimental physicists\nlike Millikan and Melissa Franklin” (Cartwright 2019, 76).\nKitcher wishes to transform talk of theories into discussion of\n“significance graphs” (2001, 78 ff.). These are network\ndiagrams illustrating which (and how) questions are considered\nsignificant in the context of particular scientific communities and\nnorms (cf. Brown 2010). Consistently with a Pragmatic View of\nTheories, Morrison (2007) reconsiders and reforms canonical\nconceptualizations of “theory.” Finally, Longino (2013)\nproposes an archaeology of assumptions behind and under different\nresearch programs and theories of human behavior such as\nneurobiological, molecular behavioral genetic, and\nsocial-environmental approaches (e.g., Oyama 2000). For instance, two\nshared or recurring assumptions across programs and theories are:", "\n(1) that the approach in question has methods of measuring both the\nbehavioral outcome that is the object of investigation and the factors\nwhose association with it are the topic of investigation and (2) that\nthe resulting measurements are exportable beyond the confines of the\napproach within which they are made. (Longino 2013, 117)\n", "\nA Pragmatic View of Theories expands the notion of theory to include\nnonformal aspects, which surely must include elements from\nBoumans’ list above (e.g., metaphors, analogies, policy views),\nas well as more standard components such as ontological assumptions\n(e.g., Kuhn 1970; Levins and Lewontin 1985; Winther 2006b), natural\nkinds (e.g., Hacking 2007b), and conditions of application or scope\n(e.g., Longino 2013).", "\nIn addition to exploring internal theory diversity and in parallel\nwith plurality of modeling, a Pragmatic View of Theories could also\nexplore pluralism of modes of theorizing, and of philosophically\nanalyzing theoretical structure (thesis #2). Craver (2002) provides a\nstart in this direction in that he accepts three kinds of scientific\ntheory and of philosophical analysis of scientific theory. A more\nsynoptic view of the broader pragmatic context in which theories are\nembedded can be found in the literature on different\n“styles” of scientific reasoning and theorizing (e.g.,\nCrombie 1994, 1996; Vicedo 1995; Pickstone 2000; Davidson 2001;\nHacking 2002, 2009; Winther 2012b; Elwick 2007; Mancosu\n2010). While there is no univocal or dominant classification of\nstyles, two lessons are important. First, a rough consensus exists\nthat theoretical investigations of especially historical, mechanistic,\nand mathematical structures and relations will involve different\nstyles. Second, each style integrates theoretical products and\ntheorizing processes in unique ways, thus inviting an irreducible\npragmatic methodological pluralism in our philosophical analysis of\nthe structure of scientific theories. For instance, the structure of\ntheories of mechanisms in molecular biology or neuroscience involves\nflow charts, and is distinct from the\nstructure of theories of historical processes and patterns as found in\nsystematics and phylogenetics, which involves phylogenetic trees. As Crombie suggests, we need a\n“comparative historical anthropology of thinking.” (1996,\n71; see Hacking 2009) Mathematical theory hardly remains regnant. It\ngives way to a pluralism of theory forms and theory processes. Indeed,\neven mathematical theorizing is a pluralistic motley, as Hacking\n(2014) argues. Although a “deflationary” Semantic View\ncould account for pluralism of theory forms, the Pragmatic View of\nTheories, drawing on styles, is required to do justice to the immense\nvariety of theorizing processes, and of philosophical accounts of\ntheory and theory structure. ", "\nFinally, outstanding work remains in sorting out the philosophical\nutility of a variety of proposed units in addition to styles, such as\nKuhn’s (1970) paradigms, Lakatos’ (1980) research\nprogrammes, Laudan’s (1977) research traditions, and\nHolton’s (1988) themata. A rational comparative historical\nanthropology of both theorizing and philosophical analyses of\ntheorizing remains mostly unmapped (cf. Matheson and Dallmann 2014).\nSuch a comparative meta-philosophical analysis should also address\nDavidson’s (1974) worries about “conceptual schemes”\nand Popper’s (1996 [1976]) critique of “the myth of the\nframework” (see Hacking 2002; Godfrey-Smith 2003)." ], "subsection_title": "4.1 Theory Structure per the Pragmatic View" }, { "content": [ "\nCartwright has done much to develop a Pragmatic View. Start by\nconsidering Newton’s second law:", "\nHere \\(F\\) is the resultant force on a mass \\(m\\), and \\(a\\) is the\nnet acceleration of \\(m\\); both \\(F\\) and \\(a\\) are vectors. This law\nis considered a “general” (Cartwright 1999a, 187) law\nexpressed with “abstract quantities” (Cartwright 1999b,\n249). Newton’s second law can be complemented with other laws,\nsuch as (i) Hooke’s law for an ideal spring:", "\nHere \\(k\\) is the force constant of the spring, and \\(x\\) the distance\nalong the x-axis from the equilibrium position, and (ii)\nCoulomb’s law modeling the force between two charged\nparticles:", "\nHere \\(K\\) is Coulomb’s electrical constant, \\(q\\) and \\(q'\\)\nare the charges of the two objects, and \\(r\\) the distance between the\ntwo objects. The picture Cartwright draws for us is that\nNewton’s, Hooke’s, and Coulomb’s laws are abstract,\nleaving out many details. They can be used to derive mathematical\nmodels of concrete systems. For instance, by combining (1) and (2),\nthe law of gravitation (a “fundamental” law, Cartwright\n1983, 58–59), other source laws, and various simplifying\nassumptions, we might create a model for the orbit of Mars, treating\nthe Sun and Mars as a 2-body system, ignoring the other planets,\nasteroids, and Mars’ moons. Indeed, the Solar System is a\npowerful “nomological machine” (Cartwright 1999a,\n50–53), which “is a fixed (enough) arrangement of\ncomponents, or factors, with stable (enough) capacities that in the\nright sort of stable (enough) environment will, with repeated\noperation, give rise to the kind of regular behaviour that we\nrepresent in our scientific laws” (Cartwright 1999a, 50).\nImportantly, most natural systems are complex and irregular, and\ncannot be neatly characterized as nomological machines. For these\ncases, abstract laws “run out” (Cartwright 1983) and are\nrarely smoothly “deidealised” (Suárez 1999). In\ngeneral, abstract laws predict and explain only within a given domain\nof application, and only under ideal conditions. More concrete laws or\nmodels are not directly deduced from them (e.g., Suárez 1999,\nSuárez and Cartwright 2008), and they can rarely be combined to\nform effective “super-laws” (Cartwright 1983,\n70–73). In short, the move from (1) and (2) or from (1) and (3)\nto appropriate phenomenological models, is not fully specified by\neither abstract law pairing. Indeed, Cartwright developed her notion\nof “capacities” to discuss how “the principles of\nphysics” “are far better rendered as claims about\ncapacities, capacities that can be assembled and reassembled in\ndifferent nomological machines, unending in their variety, to give\nrise to different laws” (1999a, 52). Articulating concrete\nmodels requires integrating a mix of mathematical and nonformal\ncomponents. Laws (1), (2), and (3) remain only one component, among\nmany, of the models useful for, e.g., exploring the behavior of the\nSolar System, balls on a pool table, or the behavior of charges in\nelectrical fields.", "\nShifting examples but not philosophical research program,\nSuárez and Cartwright (2008) explains how analogies such as\nsuperconductors as diamagnets (as opposed to ferromagnets) were an\nintegral part of the mathematical model of superconductivity developed\nby Fritz and Heinz London in the 1930s (63; cf. London and London\n1935). Suárez and Cartwright gladly accept that this model\n“is uncontroversially grounded in classic electromagnetic\ntheory” (64). However, contra Semantic View Structuralists such\nas Bueno, da Costa, French, and Ladyman, they view nonformal aspects\nas essential to practices of scientific modeling and theorizing:\n“The analogy [of diamagnets] helps us to understand how the\nLondons work with their model… which assumptions they add and\nwhich not… a formal reconstruction of the model on its own\ncannot help us to understand that” (69). In short, the running\nexample of Newtonian mechanics, in conjunction with a glimpse into the\nuse of analogies in mathematical modeling, illustrates the Pragmatic\nView’s account of theory syntax: theory is constituted by a\nplurality of formal and informal components." ], "subsection_title": "4.2 A Running Example: Newtonian Mechanics" }, { "content": [ "\nAs we have explored throughout this section, models and theories have\ninformal internal components, and there are distinct modes of modeling\nand theorizing. Because of the Pragmatic View’s attention to\npractice, function, and application, distinguishing structure\nfrom interpretation is more difficult here than under the\nSyntactic and Semantic Views. Any synchronic analysis of the structure\nof models and theories must respect intentional diachronic processes\nof interpreting and using, as we shall now see.", "\nRegarding the import of function in models and theories (thesis #4),\nalready the Belgian philosopher of science Apostel defined modeling\nthus: “Let then \\(R(S,P,M,T)\\) indicate the main variables of\nthe modelling relationship. The subject \\(S\\) takes, in view of the\npurpose \\(P\\), the entity \\(M\\) as a model for the prototype\n\\(T\\)” (1960, 128, see also Apostel 1970). Purposes took\ncenter-stage in his article title: “Towards the Formal Study of\nModels in the Non-Formal Sciences.” MIT Artificial Intelligence\ntrailblazer Minsky also provided a pragmatic analysis:", "\nWe use the term “model” in the following sense: To an\nobserver \\(B\\), an object \\(A^*\\) is a model of an object \\(A\\) to the\nextent that \\(B\\) can use \\(A^*\\) to answer questions that interest\nhim about \\(A\\). The model relation is inherently ternary. Any\nattempt to suppress the role of the intentions of the investigator\n\\(B\\) leads to circular definitions or to ambiguities about\n“essential features” and the like. (1965, 45)\n", "\nThis account is thoroughly intentionalist and anti-essentialist. That\nis, mapping relations between model and world are left open and\noverdetermined. Specifying the relevant relations depends on\ncontextual factors such as questions asked, and the kinds of\nsimilarities and isomorphisms deemed to be of interest. The\nappropriate relations are selected from an infinite (or, at least,\nnear-infinite) variety of possible relations (e.g., Rosenblueth and\nWiener 1945; Lowry 1965).", "\nRegarding practice (thesis #5), in addition to ample work on the\nexperimental life mentioned above, consider a small example. A full\nunderstanding of the content and structure of the London\nbrothers’ model of superconductivity requires attention to\ninformal aspects such as analogies. Even London and London (1935)\nstate in the summary of their paper that “the current [”in\na supraconductor“] is characterized as a kind of diamagnetic\nvolume current” (88). They too saw the diamagnetic analogy as\ncentral to their theoretical practices. Criteria and practices of\ntheory confirmation also differ from the ones typical of the Syntactic\nand Semantic Views. While predictive and explanatory power as well as\nempirical adequacy remain important, the Pragmatic View also insists\non a variety of other justificatory criteria, including pragmatic\nvirtues (sensu Kuhn 1977; Longino 1995) such as fruitfulness and\nutility. In a nutshell, the Pragmatic View argues that scientific\ntheory structure is deeply shaped and constrained by functions and\npractices, and that theory can be interpreted and applied validly\naccording to many different criteria." ], "subsection_title": "4.3 Interpreting Theory Structure per the Pragmatic View" }, { "content": [ "\nThe analytical framework of the Pragmatic View remains under\nconstruction. The emphasis is on internal diversity, and on the\nexternal pluralism of models and theories, of modeling and theorizing,\nand of philosophical analyses of scientific theories. The Pragmatic\nView acknowledges that scientists use and need different kinds of\ntheories for a variety of purposes. There is no one-size-fits-all\nstructure of scientific theories. Notably, although the Pragmatic View\ndoes not necessarily endorse the views of the tradition of American\nPragmatism, it has important resonances with the latter school’s\nemphasis on truth and knowledge as processual, purposive, pluralist,\nand context-dependent, and on the social and cognitive structure of\nscientific inquiry.", "\nA further qualification in addition to the one above regarding\nAmerican Pragmatism is in order. The Pragmatic View has important\nprecursors in the historicist or “world view” perspectives\nof Feyerabend, Hanson, Kuhn, and Toulmin, which were an influential\nset of critiques of the Syntactic View utterly distinct from the\nSemantic View. This philosophical tradition focused on themes such as\nmeaning change and incommensurability of terms across world views\n(e.g., paradigms), scientific change (e.g., revolutionary: Kuhn 1970;\nevolutionary: Toulmin 1972), the interweaving of context of discovery\nand context of justification, and scientific rationality (Preston\n2012; Bird 2013; Swoyer 2014). The historicists also opposed the idea\nthat theories can secure meaning and empirical support from a\ntheory-neutral and purely observational source, as the Syntactic View\nhad insisted on with its strong distinction between theoretical and\nobservational vocabularies (cf. Galison 1988). Kuhn’s paradigms\nor, more precisely, “disciplinary matrices” even had an\ninternal anatomy with four components: (i) laws or symbolic\ngeneralizations, (ii) ontological assumptions, (iii) values, and (iv)\nexemplars (Kuhn 1970, postscript; Godfrey-Smith 2003; Hacking 2012).\nThis work was concerned more with theory change than with theory\nstructure and had fewer conceptual resources from sociology of science\nand history of science than contemporary Pragmatic View work.\nMoreover, paradigms never quite caught on the way analyses of models\nand modeling have. Even so, this work did much to convince later\nscholars, including many of the Pragmatic View, of certain weaknesses\nin understanding theories as deductive axiomatic structures." ], "subsection_title": "4.4 Taking Stock: Pragmatic View" } ] }, { "main_content": [ "\nAs a final way to contrast the three views, we return to population\ngenetics and, especially, to the Hardy-Weinberg Principle (HWP). Both\nWoodger (1937, 1959) and Williams (1970, 1973) provide detailed\naxiomatizations of certain parts of biology, especially genetics,\ndevelopmental biology, and phylogenetics. For instance, Woodger (1937)\nconstructs an axiomatic system based on ten logical predicates or\nrelations, including \\(\\bP\\) (part of), \\(\\bT\\) (before\nin time), \\(\\bU\\) (reproduced by cell division or cell\nfusion), \\(\\bm\\) (male gamete), \\(\\bff\\) (female\ngamete), and \\(\\bgenet\\) (genetic property) (cf.\nNicholson and Gawne 2014). Woodger (1959) elaborates these logical\npredicates or relations to produce a careful reconstruction of\nMendelian genetics. Here are two axioms in his system (which are\nrewritten in contemporary notation, since Woodger used Russell and\nWhitehead’s Principia Mathematica notation):", "\nThe first axiom should be read thus: “no gamete is both male and\nfemale” (1959, 416). In the second axiom, given that \\(DLZxyz\\)\nis a primitive relation defined as “\\(x\\) is a zygote which\ndevelops in the environment \\(y\\) into the life \\(z\\)” (1959,\n415), the translation is “every life develops in one and only\none environment from one and only one zygote” (416). Woodger\nclaims that “the whole of Mendel’s work can be\nexpressed…” via this axiomatic system. Woodger briefly\nmentions that if one assumes that the entire system or population is\nrandom with respect to gamete fusions, “then the Pearson-Hardy\nlaw is derivable” (1959, 427). This was a reference to HWP. In\nher explorations of various axiomatizations of Darwinian lineages and\n“subclans,” and the process of the “expansion of the\nfitter,” Williams (1970, 1973) also carefully defines concepts,\nand axiomatizes basic biological principles of reproduction, natural\nselection, fitness, and so forth. However, she does not address HWP.\nOf interest is the lack of axiomatization of HWP or other mathematical\nprinciples of population genetics in Woodger’s and\nWilliams’ work. Were such principles considered secondary or\nuninteresting by Woodger and Williams? Might Woodger’s and\nWilliams’ respective axiomatic systems simply lack the power and\nconceptual resources to axiomatically reconstruct a mathematical\nedifice actually cast in terms of probability theory? Finally, other\nfriends of the Syntactic View, such as the early Michael Ruse, do not\nprovide an axiomatization of HWP (Ruse 1975, 241).", "\nProponents of the Semantic View claim that their perspective on\nscientific theory accurately portrays the theoretical structure of\npopulation genetics. Thompson (2007) provides both set-theoretical and\nstate-space renditions of Mendelian genetics. The first involves\ndefining a set-theoretic predicate for the system, viz., \\(\\{P, A, f,\ng\\}\\), where \\(P\\) and \\(A\\) are sets representing, respectively, the\ntotal collection of alleles and loci in the population, while \\(f\\)\nand \\(g\\) are functions assigning an allele to a specific location in,\nrespectively, the diploid cells of an individual or the haploid\ngametic cells. Axioms in this set-theoretic formalization include\n“The sets \\(P\\) and \\(A\\) are finite and non empty” (2007,\n498). In contrast, the state-space approach of the Semantic View\narticulates a phase space with each dimension representing allelic (or\ngenotypic) frequencies (e.g., cover and Chapter 3 of Lloyd 1994\n[1988]). As an example, “for population genetic theory, a\ncentral law of succession is the Hardy-Weinberg law” (Thompson\n2007, 499). Mathematically, the diploid version of HWP is written\nthus:", "\nHere \\(p\\) and \\(q\\) are the frequencies of two distinct alleles at a\nbiallelic locus. The left-hand side represents the allele frequencies\nin the parental generation and a random mating pattern, while the\nright-hand side captures genotype frequencies in the offspring\ngeneration, as predicted from the parental generation. This is a null\ntheoretical model—actual genotypic and allelic frequencies of\nthe offspring generation often deviate from predicted frequencies\n(e.g., a lethal homozygote recessive would make the\n\\(q^2_{\\text{off}}\\) term = 0). Indeed, HWP holds strictly only in\nabstracted and idealized populations with very specific properties\n(e.g., infinitely large, individuals reproduce randomly) and only when\nthere are no evolutionary forces operating in the population\n(e.g., no selection, mutation, migration, or drift) (e.g., Hartl and\nClark 1989; Winther et al. 2015). HWP is useful also in the way it\ninteracts with laws of succession for selection, mutation, and so\nforth (e.g., Okasha 2012). This powerful population genetic principle\nis central to Semantic View analyses of the mathematical articulation\nof the theoretical structure of population genetics (see also\nLorenzano 2014, Ginnobili 2016).", "\nRecall that the Pragmatic View highlights the internal and external\npluralism—as well as the purposiveness—of model and theory\nstructure. Consider recent uses of population genetic theory to\nspecify the kinds and amounts of population structure existing in\nHomo sapiens. In particular, different measures and\nmathematical modeling methodologies are employed in investigating\nhuman genomic diversity (e.g., Jobling et al. 2004; Barbujani et al.\n2013; Kaplan and Winther 2013). It is possible to\ndistinguish at least two different research projects, each of which\nhas a unique pragmatic content (e.g., aims, values, and methods).\nDiversity partitioning assesses genetic variation within and\namong pre-determined groups using Analysis of Variance (also crucial\nto estimating heritability, Downes 2014). Clustering analysis\nuses Bayesian modeling techniques to simultaneously produce clusters\nand assign individuals to these “unsupervised” cluster\nclassifications. The robust result of the first modeling project is\nthat (approximately) 85% of all genetic variance is found within human\nsubpopulations (e.g., Han Chinese or Sami), 10% across subpopulations\nwithin a continental region, and only 5% is found across continents\n(i.e., “African,” “Asian,” and\n“European” – Lewontin 1972, 1974). (Recall also that\nwe are all already identical at, on average, 999 out of 1000\nnucleotides.) To calculate diversity partitions at these three nested\nlevels, Lewontin (1972) used a Shannon information-theoretic measure\nclosely related to Sewall Wright’s \\(F\\)-statistic:", "\nHere \\(H_T\\) is the total heterozygosity of the population assessed,\nand \\(\\bar{H}_S\\) is the heterozygosity of each subpopulation (group)\nof the relevant population, averaged across all the subpopulations.\n\\(F_{ST}\\) is bounded by 0 and 1, and is a measure of population\nstructure, with higher \\(F_{ST}\\) values suggesting more structure,\nviz., more group differentiation. HWP appears implicitly in both\n\\(H_T\\) and \\(\\bar{H}_S\\), which take heterozygosity (\\(2pq\\)) to be\nequal to the expected proportion of heterozygotes under HWP\nrather than the actual frequency of heterozygotes. \\(H_T\\) is\ncomputed by using the grand population average of \\(p\\) and \\(q\\),\nwhereas calculating \\(\\bar{H}_S\\) involves averaging across the\nexpected heterozygosities of each subpopulation. If random mating\noccurs—and thus HWP applies—across the entire population\nwithout respecting subpopulation borders, then \\(H_T\\) and\n\\(\\bar{H}_S\\) will be equal (i.e., \\(p\\) of the total population and\nof each individual subpopulation will be the same; likewise for\n\\(q\\)). If, instead, HWP applies only within subpopulations but not\nacross the population as a whole, then \\(\\bar{H}_S\\) will be smaller\nthan \\(H_T\\), and \\(F_{ST}\\) will be positive (i.e., there will be\n“excess homozygosity” across subpopulations, which is\nknown as the “Wahlund Principle” in population genetics).\nThis is one way among many to deploy the population-genetic principle\nof HWP. Thus, the Lewontin-style diversity partitioning result that\nonly roughly 5% of the total genetic variance is among races is\nequivalent to saying that \\(F_{ST}\\) across the big three continental\npopulations in Lewontin’s three-level model is 0.05 (e.g.,\nBarbujani et al. 1997). The basic philosophical tendency is to\nassociate the diversity partitioning research project’s\n(approximately) 85%-10%-5% result with an anti-realist\ninterpretation of biological race.", "\nIn contrast, clustering analysis (e.g., Pritchard et al. 2000;\nRosenberg et al. 2002; cf. Edwards 2003) can be readily\nperformed even with the small amount of among-continent genetic\nvariance in Homo sapiens. For instance, when the Bayesian\nmodeling computer program STRUCTURE is asked to produce 5\nclusters, continental “races” appear—African,\nAmerindian, Asian, European, and Pacific Islanders. Interestingly,\nthis modeling technique is also intimately linked to HWP: “Our\nmain modeling assumptions are Hardy-Weinberg equilibrium within\npopulations and complete linkage equilibrium between loci within\npopulations” (Pritchard et al. 2000, 946). That is, for a cluster to eventually be robust in the\nmodeling runs, it should meet HWP expectations. Clustering analysis\nhas sometimes been interpreted as a justification for a\nrealist stance towards biological race (see discussions in\nHochman 2013; Winther and Kaplan 2013; Edge and Rosenberg 2015; Spencer 2015).", "\nThis example of the mathematical modeling of human genomic diversity\nteaches that basic and simple formal components can be used in\ndifferent ways to develop and apply theory, both inside and outside of\nscience. In contrast to the Syntactic and Semantic Views, the\nPragmatic View foregrounds tensions vis-à-vis ontological\nassumptions and political consequences regarding the existence (or\nnot) of biological race between diversity partitioning (Lewontin 1972)\nand clustering analysis (Pritchard et al. 2000) research packages.\nThese ontological ruptures can be identified despite the fact that\nboth research projects assess population structure by examining\ndepartures from HWP (i.e., they measure excess homozygosity), and are\ncompletely consistent (e.g., Winther 2014; Ludwig 2015; Edge and\nRosenberg 2015).", "\nThis exploration of how the three views on the structure of scientific\ntheory address population genetics, and in particular HWP, invites a\ncertain meta-pluralism. That is, the Syntactic View carefully breaks\ndown fundamental concepts and principles in genetics and population\ngenetics, articulating definitions and relations among terms. The\nSemantic View insightfully decomposes and interweaves the complex\nmathematical edifice of population genetics. The Pragmatic View sheds\nlight on modeling choices and on distinct interpretations and\napplications of the same theory or model, both within and without\nscience. The three perspectives are hardly mutually exclusive. (N.B.,\nthe two running examples concern theory structure in Newtonian\nmechanics and population genetics, independently considered. While\ninteresting, debates about “evolutionary forces” are\nbeyond the scope of the current entry; see, e.g., Hitchcock and\nVelasco 2014.)" ], "section_title": "5. Population Genetics", "subsections": [] }, { "main_content": [ "\nThe structure of scientific theories is a rich topic. Theorizing and\nmodeling are core activities across the sciences, whether old (e.g.,\nrelativity theory, evolutionary theory) or new (e.g., climate\nmodeling, cognitive science, and systems biology). Furthermore, theory\nremains essential to developing multipurpose tools such as statistical\nmodels and procedures (e.g., Bayesian models for data analysis,\nagent-based models for simulation, network theory for systems\nanalysis). Given the strength and relevance of theory and theorizing\nto the natural sciences, and even to the social sciences (e.g.,\nmicroeconomics, physical, if not cultural, anthropology),\nphilosophical attention to the structure of scientific theories could\nand should increase. This piece has focused on a comparison of three\nmajor perspectives: Syntactic View, Semantic View, and Pragmatic View.\nIn order to handle these complex debates effectively, we have\nsidestepped certain key philosophical questions, including questions\nabout scientific realism; scientific explanation and prediction;\ntheoretical and ontological reductionism; knowledge-production and\nepistemic inference; the distinction between science and technology;\nand the relationship between science and society. Each of these topics\nbears further philosophical investigation in light of the three\nperspectives here explored.", "\nA table helps summarize general aspects of the three views’\nanalyses of the structure of scientific theories:", "\nThe Syntactic, Semantic, and Pragmatic views are often taken to be\nmutually exclusive and, thus, to be in competition with one another.\nThey indeed make distinct claims about the anatomy of scientific\ntheories. But one can also imagine them to be complementary, focusing\non different aspects and questions of the structure of scientific\ntheories and the process of scientific theorizing. For instance, in\nexploring nonformal and implicit components of theory, the Pragmatic\nView accepts that scientific theories often include mathematical\nparts, but tends to be less interested in these components. Moreover,\nthere is overlap in questions—e.g., Syntactic and Semantic Views\nshare an interest in formalizing theory; the Semantic and Pragmatic\nViews both exhibit concern for scientific practice.", "\nHow are these three views ultimately related? A standard philosophical\nmove is to generalize and abstract, understanding a situation from a\nhigher level. One “meta” hypothesis is that a given\nphilosophical analysis of theory structure tends to be associated with\na perceived relationship among the three views here discussed. The\nSyntactic View is inclined to interpret the Semantic View’s\nformal machinery as continuous with its own generalizing axiomatic\nstrategy, and hence diagnoses many standard Semantic View critiques\n(Section 3) as missing their mark (the strategy of identity;\ne.g., Friedman 1982; Worrall 1984; Halvorson 2012, 2013, 2019; Lutz\n2012, 2017; cf. Chakravartty 2001). The Semantic View explicitly\ncontrasts its characterization of theory structure with the\n“linguistic” or “metamathematical” apparatus\nof the Syntactic View (the strategy of combat; e.g., Suppe\n1977; van Fraassen 1980, 1989; Lloyd 1994 [1988]). Finally, the\nPragmatic View, which did not exist as a perspective until relatively\nrecently, imagines theory as pluralistic and can thus ground a\nholistic philosophical investigation. It envisions a meta-pluralism in\nwhich reconstructive axiomatization and mathematical modeling remain\nimportant, though not necessary for all theories. This third view\nendorses a panoply of theoretical structures and theorizing styles,\nnegotiating continuity both between theorizing and “the\nexperimental life,” and among philosophical analyses of the\nstructure of scientific theories (the strategy of\ncomplementarity; e.g., Hacking 1983, 2009; Galison 1988,\n1997; Craver 2002; Suárez and Cartwright 2008; Griesemer 2013). Interestingly, Suárez and Pero\n(2019) explicitly concur with the Pragmatic View as described in this\narticle, but believe that “the semantic conception in its bare\nminimal expression” is compatible with, if not sufficient for,\ncapturing “pragmatic elements and themes involved in a more\nflexible and open-ended approach to scientific theory”\n(Suárez and Pero 2019, 348). By design, the ecumenical\nmeta-pluralism sanctioned by the Pragmatic View does not completely\noffset identity and combat strategies. Moreover, only “partial\nacceptance” of the respective views may ultimately be possible.\nEven so, the complementarity strategy might be worth developing\nfurther. Compared to identity and combat meta-perspectives, it\nprovides broader—or at least different—insights into the\nstructure of scientific theories. More generally, exploring the\nrelations among these views is itself a rich topic for future\nphilosophical work, as is investigating their role in, and\ninterpretation of, active scientific fields ripe for further\nphilosophical analysis such as climate change (e.g., Winsberg 2018),\nmodel organisms (e.g., Ankeny and Leonelli 2020), and cartography and\nGIS (e.g., Winther 2020)." ], "section_title": "6. Conclusion", "subsections": [] } ]

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A Story of Two Mathematical Methods,”\nCritical Philosophy of Race, 2 (2): 204–223.", "–––, 2020, When Maps Become the World,\nChicago, IL: University of Chicago Press.", "Winther, R.G., R. Giordano, M.D. Edge, and R. Nielsen, 2015,\n“The Mind, the Lab, and the Field: Three Kinds of Populations in\nScientific Practice,” Studies in History and Philosophy of\nBiological and Biomedical Sciences, 52: 12–21.", "Winther, R.G. and J.M. Kaplan, 2013, “Ontologies and\nPolitics of Biogenomic ‘Race’,” Theoria. A\nJournal of Social and Political Theory (South Africa), 60 (3):\n54–80.", "Woodger J.H., 1937, The Axiomatic Method in Biology,\nCambridge: Cambridge University Press.", "–––, 1959, “Studies in the Foundations of\nGenetics,” in The Axiomatic Method with Special Reference to\nGeometry and Physics: Proceedings of an International Symposium Held\nat the University of California, Berkeley, December 26,\n1957–January 4, 1958, L. Henkin, P. 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[ "\nFor phenomenologists, the immediate and first-personal givenness of\nexperience is accounted for in terms of a pre-reflective\nself-consciousness. In the most basic sense of the term,\nself-consciousness is not something that comes about the moment one\nattentively inspects or reflectively introspects one’s\nexperiences, or recognizes one’s specular image in the mirror,\nor refers to oneself with the use of the first-person pronoun, or\nconstructs a self-narrative. Rather, these different kinds of\nself-consciousness are to be distinguished from the pre-reflective\nself-consciousness which is present whenever I am living through or\nundergoing an experience, e.g., whenever I am consciously perceiving\nthe world, remembering a past event, imagining a future event,\nthinking an occurrent thought, or feeling sad or happy, thirsty or in\npain, and so forth." ]

[ { "content_title": "1. Pre-reflective self-consciousness", "sub_toc": [] }, { "content_title": "2. Philosophical issues and objections", "sub_toc": [] }, { "content_title": "3. Temporality and the limits of reflective self-consciousness", "sub_toc": [] }, { "content_title": "4. Bodily self-awareness", "sub_toc": [] }, { "content_title": "5. Social forms of self-consciousness", "sub_toc": [] }, { "content_title": "6. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "References", "Related Bibliography" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nOne can get a bearing on the notion of pre-reflective\nself-consciousness by contrasting it with reflective\nself-consciousness. If you ask me to give you a description of the\npain I feel in my right foot, or of what I was just thinking about, I\nwould reflect on it and thereby take up a certain perspective that was\none order removed from the pain or the thought. Thus, reflective\nself-consciousness is at least a second-order cognition. It may be the\nbasis for a report on one’s experience, although not all reports\ninvolve a significant amount of reflection.", "\nIn contrast, pre-reflective self-consciousness is pre-reflective in\nthe sense that (1) it is an awareness we have before we do any\nreflecting on our experience; (2) it is an implicit and first-order\nawareness rather than an explicit or higher-order form of\nself-consciousness. Indeed, an explicit reflective self-consciousness\nis possible only because there is a pre-reflective self-awareness that\nis an on-going and more primary kind of self-consciousness. Although\nphenomenologists do not always agree on important questions about\nmethod, focus, or even whether there is an ego or self, they are in\nclose to unanimous agreement about the idea that the experiential\ndimension always involves such an implicit pre-reflective\n self-awareness.[1]\n In line with Edmund Husserl (1959, 189, 412), who maintains that\nconsciousness always involves a self-appearance\n(Für-sich-selbst-erscheinens), and in agreement with\nMichel Henry (1963, 1965), who notes that experience is always\nself-manifesting, and with Maurice Merleau-Ponty who states that\nconsciousness is always given to itself and that the word\n‘consciousness’ has no meaning independently of this\nself-givenness (Merleau-Ponty 1945, 488), Jean-Paul Sartre writes that\npre-reflective self-consciousness is not simply a quality added to the\nexperience, an accessory; rather, it constitutes the very mode of\nbeing of the experience:", "\nThis self-consciousness we ought to consider not as a new\nconsciousness, but as the only mode of existence which is possible\nfor a consciousness of something (Sartre 1943, 20 [1956, liv]).\n", "\nIn short, unless a mental process is pre-reflectively self-conscious\nthere will be nothing it is like to undergo the process, and it\ntherefore cannot be a phenomenally conscious process (Zahavi 1999,\n2005, 2014). An implication of this is obviously that the\nself-consciousness in question is so fundamental and basic that it can\nbe ascribed to all creatures that are phenomenally conscious,\nincluding various non-human animals.", "\nThe notion of pre-reflective self-awareness is related to the idea\nthat experiences have a subjective ‘feel’ to them, a\ncertain (phenomenal) quality of ‘what it is like’ or what\nit ‘feels’ like to have them. As it is usually expressed\noutside of phenomenological texts, to undergo a conscious experience\nnecessarily means that there is something it is like for the subject\nto have that experience (Nagel 1974; Searle 1992). This is obviously\ntrue of bodily sensations like pain. But it is also the case for\nperceptual experiences, experiences of desiring, feeling, and\nthinking. There is something it is like to taste chocolate, and this\nis different from what it is like to remember or imagine what it is\nlike to taste chocolate, or to smell vanilla, to run, to stand still,\nto feel envious, nervous, depressed or happy, or to entertain an\nabstract belief.", "\nAll of these different experiences are, however, also characterized by\ntheir distinct first-personal character. The what-it-is-likeness of\nphenomenal episodes is properly speaking a\nwhat-it-is-like-for-me-ness. This for-me-ness doesn’t refer\nto a specific experiential quality like sour or soft, rather it refers\nto the distinct first-personal givenness of experience. It refers to\nthe fact that the experiences I am living through are given\ndifferently (but not necessarily better) to me than to anybody else. I\nmay see that you are sad, but my seeing your sadness is qualitatively\ndifferent from my living through my sadness. It could consequently be\nclaimed that anybody who denies the for-me-ness of experience simply\nfails to recognize an essential constitutive aspect of experience.\nSuch a denial would be tantamount to a denial of the first-person\nperspective. It would entail the view that my own mind is either not\ngiven to me at all—I would be mind- or self-blind—or is presented\nto me in exactly the same way as the minds of others.", "\nOne sometimes distinguishes two uses of the term\n‘conscious’, a transitive and an intransitive use. On the\none hand, we can speak of our being conscious of something, be\nit x, y, or z. On the other, we can speak of our\nbeing conscious simpliciter (rather than non-conscious). For\nsome time a widespread way to account for intransitive consciousness\nin cognitive science and analytic philosophy of mind has been by means\nof some kind of higher-order theory. The distinction between conscious\nand non-conscious mental states has been taken to rest upon the\npresence or absence of a relevant meta-mental state (e.g., Armstrong\n1968; Carruthers 1996, 2000; Lycan 1987, 1996; Rosenthal 1997). Thus,\nintransitive consciousness has been taken to depend upon the mind\ndirecting its intentional aim at its own states and operations. As\nCarruthers puts it, the subjective feel of experience presupposes a\ncapacity for higher-order awareness: “such self-awareness is a\nconceptually necessary condition for an organism to be a subject of\nphenomenal feelings, or for there to be anything that its experiences\nare like” (1996, 152). But for Carruthers, the self-awareness in\nquestion is a type of reflection. In his view, a creature must be\ncapable of reflecting upon, thinking about, and hence conceptualizing\nits own mental states if those mental states are to be states of which\nthe creature is aware (1996, 155, 157).", "\nOne might share the view that there is a close link between\nconsciousness and self-consciousness and still disagree about the\nnature of the link. And although the phenomenological view might\nsuperficially resemble the view of the higher-order theories, we are\nultimately confronted with two quite different accounts. The\nphenomenologists explicitly deny that the self-consciousness that is\npresent the moment I consciously experience something is to be\nunderstood in terms of some kind of higher-order monitoring. It does\nnot involve an additional mental state, but is rather to be understood\nas an intrinsic feature of the primary experience. That is, in\ncontrast to higher-order accounts of consciousness that claim that\nconsciousness is an extrinsic or relational property of those mental\nstates that have it, a property bestowed upon them from without by\nsome further state, the phenomenologists would typically argue that\nthe feature in virtue of which a mental state is conscious is an\nintrinsic property of those mental states that have it. Moreover, the\nphenomenologists also reject the attempt to construe intransitive\nconsciousness in terms of transitive consciousness, that is, they\nreject the view that a conscious state is a state we are conscious of\nas object. To put it differently, not only do they reject the view\nthat a mental state becomes conscious by being taken as an object by a\nhigher-order state, they also reject the view (generally associated\nwith Brentano) according to which a mental state becomes conscious by\ntaking itself as an object (cf. Zahavi 2004; 2014).", "\nWhat arguments support the phenomenological claims, however?\nPhenomenologists don’t simply appeal to a correct phenomenological\ndescription but provide additional, more theoretical, arguments. One\nline of reasoning found in virtually all of the phenomenologists is\nthe view that the attempt to let (intransitive) consciousness be a\nresult of a higher-order monitoring will generate an infinite regress.\nOn the face of it, this is a rather old idea. Typically, the regress\nargument has been understood in the following manner. If all occurrent\nmental states are conscious in the sense of being taken as objects by\noccurrent second-order mental states, then these second-order mental\nstates must themselves be taken as objects by occurrent third-order\nmental states, and so forth ad infinitum. The standard\nresponse to this objection is that the regress can easily be avoided\nby accepting the existence of non-conscious mental states. This is\nprecisely the position adopted by the defenders of higher-order\ntheory. For them a second-order perception or thought does not have to\nbe conscious. It would be conscious only if accompanied by a\n(non-conscious) third-order thought or perception (Rosenthal 1997,\n745). The phenomenological reply to this solution is rather\nstraightforward, however. The phenomenologists would concede that it\nis possible to halt the regress by postulating the existence of\nnon-conscious mental states, but they would maintain that such an\nappeal to the non-conscious leaves us with a case of explanatory\nvacuity. That is, they would find it quite unclear why the relation\nbetween two otherwise non-conscious processes should make one of them\nconscious. Or to put it differently, they would be quite unconvinced\nby the claim that a state without subjective or phenomenal qualities\ncan be transformed into one with such qualities, i.e., into an\nexperience with first-personal character, by the mere addition of a\nnon-conscious meta-state having the first-state as its intentional\nobject.", "\nThe phenomenological alternative avoids the regress. As Sartre writes:\n“[T]here is no infinite regress here, since a consciousness has no\nneed at all of a reflecting [higher-order] consciousness in order to\nbe conscious of itself. It simply does not posit itself as an\nobject” (1936, 29 [1957, 45]). That is, pre-reflective\nself-consciousness is not transitive in relation to the state (of)\nwhich it is aware. It is, as Sartre puts it, the mode of existence of\nconsciousness itself. This does not mean that a higher-order\nmeta-consciousness is impossible, but merely that it always\npresupposes the existence of a prior non-objectifying, pre-reflective\nself-consciousness as its condition of possibility. To quote Sartre\nagain, “it is the non-reflective consciousness which renders the\nreflection [and any higher-order representation of it] possible”\n(1943, 20 [1956, liii]). ", "\nThere are also lines of argumentation in contemporary analytical\nphilosophy of mind that are close to and consistent with the\nphenomenological conception of pre-reflective self-awareness. Alvin\nGoldman provides an example:", "\n[Consider] the case of thinking about x or attending to\nx. In the process of thinking about x there is\nalready an implicit awareness that one is thinking about x.\nThere is no need for reflection here, for taking a step back from\nthinking about x in order to examine it…When we are\nthinking about x, the mind is focused on x, not on\nour thinking of x. Nevertheless, the process of thinking\nabout x carries with it a non-reflective self-awareness\n(Goldman 1970, 96).\n", "\nA similar view has been defended by Owen Flanagan, who not only argues\nthat consciousness involves self-consciousness in the weak sense that\nthere is something it is like for the subject to have the experience,\nbut also speaks of the low-level self-consciousness involved in\nexperiencing my experiences as mine (Flanagan 1992, 194). As Flanagan\nquite correctly points out, this primary type of self-consciousness\nshould not be confused with the much stronger notion of\nself-consciousness that is in play when we are thinking about our own\nnarrative self. The latter form of reflective self-consciousness\npresupposes both conceptual knowledge and narrative competence. It\nrequires maturation and socialization, and the ability to access and\nissue reports about the states, traits, dispositions that make one the\nperson one is. Other philosophers who have defended comparable views,\ninclude José Luis Bermúdez (1998), who has argued that that\nthere are a variety of nonconceptual forms of self-consciousness that\nare “logically and ontogenetically more primitive than the higher\nforms of self-consciousness that are usually the focus of\nphilosophical debate” (1998, 274; also see Poellner 2003), and Uriah\nKriegel (2009) who has defended the existence of a type of\nself-consciousness that is intrinsic to and inherent in phenomenal\nconsciousness. Across a variety of philosophical studies, then, one\nfinds support for the phenomenological conception of pre-reflective\nself-awareness.", "\nThat pre-reflective self-awareness is implicit, then, means that I am\nnot confronted with a thematic or explicit awareness of the experience\nas belonging to myself. Rather we are dealing with a non-observational\nself-acquaintance. Here is how Heidegger and Sartre put the point:", "\nDasein [human existence] as existing, is there for itself, even when\nthe ego does not expressly direct itself to itself in the manner of\nits own peculiar turning around and turning back, which in\nphenomenology is called inner perception as contrasted with outer. The\nself is there for the Dasein itself without reflection and without\ninner perception, before all reflection. Reflection, in the\nsense of a turning back, is only a mode of self-apprehension,\nbut not the mode of primary self-disclosure (Heidegger 1989, 226\n[1982, 159]).\n\n\nIn other words, every positional consciousness of an object is at the\nsame time a non-positional consciousness of itself. If I count the\ncigarettes which are in that case, I have the impression of disclosing\nan objective property of this collection of cigarettes: they are a\ndozen. This property appears to my consciousness as a property\nexisting in the world. It is very possible that I have no positional\nconsciousness of counting them. Then I do not know myself as counting.\nYet at the moment when these cigarettes are revealed to me as a dozen,\nI have a non-thetic consciousness of my adding activity. If anyone\nquestioned me, indeed, if anyone should ask, “What are you doing\nthere?” I should reply at once, “I am counting.”\n(Sartre 1943, 19–20 [1956, liii]).\n", "\nIt might be clarifying to compare the phenomenological notion of\npre-reflective self-consciousness with the one defended by Brentano.\nAccording to Brentano as I listen to a melody I am aware that I am\nlistening to the melody. He acknowledges that I do not have two\ndifferent mental states: my consciousness of the melody is one and the\nsame as my awareness of perceiving it; they constitute one single\npsychical phenomenon. On this point, and in opposition to higher-order\nrepresentation theories, Brentano and the phenomenologists are in\ngeneral agreement. But for Brentano, by means of this unified mental\nstate, I have an awareness of two objects: the melody and my\nperceptual experience. ", "\nIn the same mental phenomenon in which the sound is present to our\nminds we simultaneously apprehend the mental phenomenon itself. What\nis more, we apprehend it in accordance with its dual nature insofar as\nit has the sound as content within it, and insofar as it has itself as\ncontent at the same time. We can say that the sound is the primary\nobject of the act of hearing, and that the act of\nhearing itself is the secondary object (Brentano 1874,\n179–180 [1973, 127–128]).\n", "\nHusserl disagrees on just this point, as do Sartre and Heidegger: my\nawareness of my experience is not an awareness of it as an\n object.[2]\n My awareness is non-objectifying in the sense that I do not occupy\nthe position or perspective of a spectator or in(tro)spector who\nattends to this experience in a thematic way. That a psychological\nstate is experienced, “and is in this sense conscious, does not\nand cannot mean that this is the object of an act of consciousness, in\nthe sense that a perception, a presentation or a judgment is directed\nupon it” (Husserl 1984a, 165 [2001, I, 273]). In pre-reflective\nself-awareness, experience is given, not as an object, but precisely\nas subjective experience. For phenomenologists, intentional experience\nis lived through (erlebt), but does not appear in an\nobjectified manner. Experience is conscious of itself without being\nthe intentional object of consciousness (Husserl 1984b, 399; Sartre\n1936, 28–29). That we are aware of our lived experiences even if\nwe do not direct our attention towards them is not to deny that we can\ndirect our attention towards our experiences, and thereby take them as\nobjects of reflection (Husserl 1984b, 424).", "\nTo be self-aware is not to capture a pure self or self-object that\nexists separately from the stream of experience, rather it is to be\nconscious of one’s experience in its intrinsic first-person mode\nof givenness. When Hume, in a famous passage in A Treatise of\nHuman Nature (1739), declares that he cannot find a self when he\nsearches his experiences, but finds only particular perceptions or\nfeelings, it could be argued that he overlooks something in his\nanalysis, namely the specific givenness of his own experiences.\nIndeed, he was looking only among his own experiences, and\nseemingly recognized them as his own, and could do so only on the\nbasis of that immediate self-awareness that he seemed to miss. As C.O.\nEvans puts it: “[F]rom the fact that the self is not an object\nof experience it does not follow that it is non-experiential”\n(Evans 1970, 145). Accordingly, we should not think of the self, in\nthis most basic sense, as a substance, or as some kind of ineffable\ntranscendental precondition, or as a social construct that gets\ngenerated through time; rather it is an integral aspect of conscious\nlife, and involves this immediate experiential character.", "\nOne advantage of the phenomenological view is that it is capable of\naccounting for some degree of diachronic unity, without actually\nhaving to posit the self as a separate entity over and above the\nstream of consciousness (see the discussion of time-consciousness in\nSection 3 below). Although we live through a number of different\nexperiences, the experiencing itself remains a constant in regard to\nwhose experience it is. This is not accounted for by a substantial\nself or a mental theater. On this point Hume was right. There is no\npure or empty field of consciousness upon which the concrete\nexperiences subsequently make their entry. The field of experiencing\nis nothing apart from the specific experiences. Yet we are naturally\ninclined to distinguish the strict singularity of an experience from\nthe continuous stream of changing experiences. What remains constant\nand consistent across these changes is the sense of for-me-ness (or\nperspectival ownership) constituted by pre-reflective self-awareness.\nOnly a being with this sense of ownership could go on to form concepts\nabout herself, consider her own aims, ideals, and aspirations as her\nown, construct stories about herself, and plan and execute actions for\nwhich she will take responsibility. " ], "section_title": "1. Pre-reflective self-consciousness", "subsections": [] }, { "main_content": [ "\nThe concept of pre-reflective self-awareness is related to a variety\nof philosophical issues, including epistemic asymmetry, immunity to\nerror through misidentification and self-reference. We will examine\nthese issues each in turn.", "\nIt seems clear that the objects of my visual perception are\nintersubjectively accessible in the sense that they can in principle\nbe the objects of another’s perception. A subject’s\nperceptual experience itself, however, is given in a unique way to the\nsubject herself. Although two people, A and B, can\nperceive a numerically identical object, they each have their own\ndistinct perceptual experience of it; just as they cannot share each\nother’s pain, they cannot literally share these perceptual\nexperiences. Their experiences are epistemically asymmetrical in this\nregard. B might realize that A is in pain; he might\nsympathize with A, he might even have the same kind of pain\n(same qualitative aspects, same intensity, same proprioceptive\nlocation), but he cannot literally feel A’s pain the\nsame way A does. The subject’s epistemic access to her\nown experience, whether it is a pain or a perceptual experience, is\nprimarily a matter of pre-reflective self-awareness. If secondarily,\nin an act of introspective reflection I begin to examine my perceptual\nexperience, I will recognize it as my perceptual experience only\nbecause I have been pre-reflectively aware of it, as I have been\nliving through it. Thus, phenomenology maintains, the access that\nreflective self-consciousness has to first-order phenomenal experience\nis routed through pre-reflective consciousness, for if we were not\npre-reflectively aware of our experience, our reflection on it would\nnever be motivated. When I do reflect, I reflect on something with\nwhich I am already experientially familiar.", "\nThe ease with which we self-ascribe experiences is partially to be\nexplained by appeal to pre-reflective self-awareness. It is important\nto emphasize, however, that pre-reflective self-awareness is only a\nnecessary and not a sufficient condition for reflective\nself-ascription and first-person knowledge. Many animals who possess\npre-reflective self-consciousness obviously lack the cognitive\nresources needed for reflective self-ascriptions. ", "\nWhen I experience an occurrent pain, perception, or thought, the\nexperience in question is given immediately and noninferentially. I do\nnot have to judge or appeal to some criteria in order to identify it\nas my experience. There are no free-floating experiences;\neven the experience of freely-floating belongs to someone. As William\nJames (1890) put it, all experience is “personal.” Even in\npathological cases, as in depersonalization or schizophrenic symptoms\nof delusions of control or thought insertion, a feeling or experience\nthat the subject claims not to be his is nonetheless experienced by\nhim as being part of his stream of consciousness. The complaint of\nthought insertion, for example, necessarily acknowledges that the\ninserted thoughts are thoughts that belong to the subject’s\nexperience, even as the agency for such thoughts are attributed to\nothers. This first-person character entails an implicit experiential\nself-reference. If I feel hungry or see my friend, I cannot be\nmistaken about who the subject of that experience is, even if I can be\nmistaken about it being hunger (perhaps it’s really thirst), or\nabout it being my friend (perhaps it’s his twin), or even about\nwhether I am actually seeing him (I may be hallucinating). As\nWittgenstein (1958), Shoemaker (1968), and others have pointed out, it\nis nonsensical to ask whether I am sure that I am the one who\nfeels hungry. This is the phenomenon known as “immunity to error\nthrough misidentification relative to the first-person pronoun.”\nTo this idea of immunity to error through misidentification, the\nphenomenologist adds that whether a certain experience is experienced\nas mine, or not, does not depend upon something apart from the\nexperience, but depends precisely upon the pre-reflective givenness\nthat belongs to the structure of the experience (Husserl 1959, 175;\nHusserl 1973a, 28, 56, 307, 443; see Zahavi 1999, 6ff.).", "\nSome philosophers who are inclined to take self-consciousness to be\nintrinsically linked to the issue of self-reference would argue that\nthe latter depends on a first-person concept. One attains\nself-consciousness only when one can conceive of oneself\nas oneself, and has the linguistic ability to use the\nfirst-person pronoun to refer to oneself (Baker 2000, 68; cf. Lowe\n2000, 264). On this view, self-consciousness is something that emerges\nin the course of a developmental process, and depends on the\nacquisition of concepts and language. Accordingly, some philosophers\ndeny that young children are capable of self-consciousness (Carruthers\n1996; Dennett 1976; Wilkes 1988; also see Flavell 1993). Evidence from\ndevelopmental psychology and ecological psychology, however, suggests\nthat there is a primitive, proprioceptive form of self-consciousness\nalready in place from\n birth.[3]\n This primitive self-awareness precedes the mastery of language and\nthe ability to form conceptually informed judgments, and it may serve\nas a basis for more advanced types of self-consciousness (see, e.g.,\nButterworth 1995, 1999; Gibson 1986; Meltzoff 1990a, 1990b; Neisser\n1988; and Stern 1985). The phenomenological view is consistent with\nsuch findings.", "\nThe notion of pre-reflective self-awareness is much\nmore accepted today than it was 20 years ago and has become part of\nthe standard repertoire in philosophy of mind. The notion’s\nincreasing popularity not surprisingly has also led to an increasing\namount of criticism. One line of attack has focused on what might be\ncalled the universality question. Is it truly the case that all\nconscious mental states involve pre-reflective self-awareness,\nfor-me-ness, and a sense of ownership? Does the link hold by necessity\nsuch that it characterizes all experiences, however primitive or\ndisordered they might be, or might it, for instance, be something that\nonly holds true for a more limited group of experiences, say, normal,\nadult, experiences (Lane 2012; Dainton 2016; Guillot 2017; Howell\n& Thompson 2017). Whether infantile or pathological or\nhallucinogenic experiences constitute relevant exceptions, i.e.,\nexperiences that lack pre-reflective self-awareness, for-me-ness and\nsense of ownership, is to a large extent dependent upon how robustly\none interprets these notions. If pre-reflective self-awareness is\ninterpreted simply as a non-inferential awareness of the experience\none is having rather than as an awareness of some self-object, and if\nfor-me-ness and sense of ownership are interpreted not as involving an\nawareness of the possessive relation between oneself and the\nexperience, but rather as the distinct perspectival givenness or\nfirst-personal presence of experience, it is far from obvious that\nthere really are exceptions to be found (Zahavi 2014, 2018, 2019).\nSome critics have also claimed that the sense of ownership is a\nby-product of reflective or introspective processes (e.g., Bermúdez\n2011; 2018; Dainton 2007). They insist that there is nothing like a\npre-reflective sense of ownership that is “something over and above\nthe changing stream of thought, perception, volition, emotion, memory,\nbodily sensation, and so on” (Dainton 2007, 240; emphasis added).\nBut as should already be clear, phenomenologists do not claim that\npre-reflective self-awareness or the sense of ownership is something\n“over and above” experience, something extra that is added as a\nsecond experience. Rather, the claim is that it is an intrinsic\nfeature of experience itself. In this respect, the phenomenological\nclaim is as deflationary as the critics would want (Gallagher 2017a)." ], "section_title": "2. Philosophical issues and objections", "subsections": [] }, { "main_content": [ "\nAlthough, as pre-reflectively self-aware of my experience I am not\nunconscious of it, I do not attend to it; rather I tend to overlook it\nin favor of the object that I am perceiving, the thing I am\nremembering, etc. In my everyday life, I am absorbed by and\npreoccupied with projects and objects in the world, and as such I do\nnot attend to my experiential life. Therefore, this pervasive\npre-reflective self-consciousness is not to be understood as complete\nself-comprehension. One can accept the notion of a pervasive\nself-consciousness and still accept the existence of the unconscious\nin the sense of subjective components which remain ambiguous, obscure,\nand resistant to comprehension. Thus, one should distinguish between\nthe claim that consciousness is characterized by an immediate\nfirst-person character and the claim that consciousness is\ncharacterized by total self-transparency. One can easily accept the\nfirst and reject the latter (Ricoeur 1950, 354–355). ", "\nIn contrast to pre-reflective self-consciousness, which delivers an\nimplicit sense of self at an experiential or phenomenal level,\nreflective self-consciousness is an explicit, conceptual, and\nobjectifying awareness that takes a lower-order consciousness as its\nattentional theme. I am able at any time to attend directly to the\ncognitive experience itself, turning my experience itself into the\nobject of my consideration.", "\nPhenomenologists do not claim the infallible authority of reflection\nover subjective experience. There are no epistemic guarantees\nconnected with self-consciousness other than immunity to error through\nmisidentification. If I cannot be wrong about who is living through my\nexperiences, I can be wrong about all kinds of other things about my\nexperiences. A brief consideration of the phenomenology of temporality\nwill help to explain this, namely, why reflective self-consciousness\nis characterized by certain limitations. It will also help to clarify\nhow pre-reflective self-consciousness, as a mode of existence, is\npossible in the first place, as well as elucidate the phenomenological\naccount of diachronic unity, an account that does not posit something\ncalled the “self” as a separate entity over and above the\nstream of consciousness (cf. Zahavi 2014).", "\nAccording to Husserl’s analysis, experience of any sort\n(perception, memory, imagination, etc.) has a common temporal\nstructure such that any moment of experience contains a retentional\nreference to past moments of experience, a current openness (primal\nimpression) to what is present, and a protentional anticipation of the\nmoments of experience that are just about to happen (Husserl 1966; see\nGallagher 1998). The retentional structure of experience, that is, the\nfact that when I am experiencing something, each passing moment of\nconsciousness does not simply disappear at the next moment but is kept\nin intentional currency, constitutes a coherency that stretches over\nan experienced temporal duration. Husserl’s favorite example is\na melody. When I experience a melody, I don’t simply experience\na knife-edge presentation (primal impression) of one note, which is\nthen completely washed away and replaced with the next discrete\nknife-edge presentation of the next note. Rather, consciousness\nretains the sense of the first note as just past, as I hear the second\nnote, a hearing that is also enriched by an anticipation (protention)\nof the next note (or at least, in case I do not know the melody, a\nsense that there will be a next note, or some next auditory event).\nHusserl claims that we actually do perceive melodies—in\nopposition to an earlier view propounded by Brentano, viz., that with\nthe help of our imagination or recollection we construct or\nreconstruct such unities out of a synthesis of mental acts. That we\nactually perceive melodies (without first constructing them using\nmemory and imagination) is possible only because consciousness is so\nstructured to allow for this temporal presentation.", "\nImportantly, the temporal (retentional-impressional-protentional)\nstructure of consciousness not only allows for the experience of\ntemporally extended objects or intentional contents, but also entails\nthe self-manifestation of consciousness, that is, its pre-reflective\nself-awareness. The retention of past notes of the melody is\naccomplished, not by a “real” or literal re-presentation\nof the notes (as if I were hearing them a second time and\nsimultaneously with the current note), but by an intentional retaining\nof my just past experience of the melody as just past. This\nmeans that this retentional structure gives me an immediate awareness\nof my ongoing experience in the ongoing flow of experience, a\nself-awareness that is implicit in my experience of the object. At the\nsame time that I am aware of a melody, for example, I am co-aware of\nmy ongoing experience of the melody through the retentional structure\nof that very experience—and this just is the pre-reflective\nself-awareness of experience (see Zahavi 1999, 2003).", "\nThe temporal structure that accounts for pre-reflective self-awareness\nis also the structural feature that accounts for the limitations\nimposed on reflective self-consciousness. Reflective\nself-consciousness yields knowledge of pre-reflective subjectivity\nthat is always after the fact. Reflective self-consciousness, which\ntakes pre-reflective experience as its object, is itself (like any\nconscious experience) characterized by the same temporal structure. In\nprinciple, however, the retentional-impressional-protentional\nstructure of reflection cannot overlay the\nretentional-impressional-protentional structure of pre-reflective\nexperience in complete simultaneity. There is always a slight delay\nbetween reflection and the pre-reflective object of reflection. One\nmight say that the pre-reflective experience must first be there if I\nam to turn my reflective attention to it and make it an object of\nreflection. Husserl writes: “When I say I, I grasp\nmyself in a simple reflection. But this self-experience\n[Selbsterfahrung] is like every experience\n[Erfahrung], and in particular every perception, a mere\ndirecting myself towards something that was already there for me, that\nwas already conscious, but not thematically experienced, not\nnoticed” (Husserl 1973b, 492–493). This delay is one of\nthe reasons why there remains a difference or distance between the\nreflecting subject and the reflected object, even though the reflected\nobject is my own experience. As a reflecting subject, I never fully\ncoincide with myself.", "\nAs Merleau-Ponty puts it, our temporal existence is both a condition\nfor and an obstacle to our self-comprehension. Temporality contains an\ninternal fracture that permits us to return to our past experiences in\norder to investigate them reflectively, but this very fracture also\nprevents us from fully coinciding with ourselves. There will always\nremain a difference between the lived and the understood\n(Merleau-Ponty 1945, 76, 397, 399, 460). Self-consciousness provides\nus with the sense that we are always already in play. This leads some\nphenomenologists to note that we are born (or “thrown”\ninto the world) and not self-generated. We are caught up in a life\nthat is in excess of our full comprehension (Heidegger 1986). There is\nalways something about ourselves that we cannot fully capture in the\nmoment of self-conscious reflection.", "\nIf reflective self-consciousness is limited in this way, this should\nnot prevent us from exercising it. Indeed, reflective\nself-consciousness is a necessary condition for moral\nself-responsibility, as Husserl points out. Reflection is a\nprecondition for self-critical deliberation. If we are to subject our\ndifferent beliefs and desires to a critical, normative evaluation, it\nis not sufficient simply to have immediate first-personal access to\nthe states in question. ", "\nWe take as our point of departure the essential ability for\nself-consciousness in the full sense of personal self-inspection\n(inspectio sui), and the ability that is based on this for\ntaking up positions that are reflectively directed back on oneself and\none’s own life, on personal acts of self-knowledge,\nself-evaluation, and practical acts of self-determination,\nself-willing, and self-formation. (Husserl 1988, 23).\n", "\nSelf-consciousness is, therefore, not epiphenomenal. Our ability to\nmake reflective judgments about our own beliefs and desires also\nallows us to modify them.", "\nOne might see the position of Husserl, Sartre and Merleau-Ponty as\nbeing situated between two extremes. On the one hand, we have the view\nthat reflection merely copies or mirrors pre-reflective experience\nfaithfully, and on the other hand we have the view that reflection\ndistorts lived experience. The middle course is to recognize that\nreflection involves a gain and a loss. For Husserl, Sartre, and\nMerleau-Ponty, reflection is constrained by what is pre-reflectively\nlived through. It is answerable to experiential facts and is not\nconstitutively self-fulfilling. At the same time, however, they\nrecognized that reflection qua thematic self-experience does not\nsimply reproduce the lived experiences unaltered and that this is\nprecisely what makes reflection cognitively valuable. The experiences\nreflected upon are transformed in the process, to various degrees and\nmanners depending upon the type of reflection at work. Subjectivity\nconsequently seems to be constituted in such a fashion that it can\nand, at times, must relate to itself in an “othering”\nmanner. This self-alteration is something inherent to reflection; it\nis not something that reflection can overcome." ], "section_title": "3. Temporality and the limits of reflective self-consciousness", "subsections": [] }, { "main_content": [ "\nMuch of what we have said about self-consciousness may still seem\noverly mentalistic. It is important to note that for phenomenologists\nlike Husserl and Merleau-Ponty, pre-reflective self-awareness is both\nembodied and embedded in the world. The first-person point of view on\nthe world is never a view from nowhere; it is always defined by the\nsituation of the perceiver’s body, which concerns not simply\nlocation and posture, but action in pragmatic contexts and interaction\nwith other people. Pre-reflective self-awareness includes aspects that\nare both bodily and intersubjective.", "\nThe claim is not simply that the perceiver/actor is objectively\nembodied, but that the body is in some fashion experientially present\nin the perception or action. Phenomenologists distinguish the\npre-reflective body-awareness that accompanies and shapes every\nspatial experience, from a reflective consciousness of the body. To\ncapture this difference, Husserl introduced a terminological\ndistinction between Leib and Körper, that is,\nbetween the pre-reflectively lived body, i.e., the body as an embodied\nfirst-person perspective, and the subsequent thematic experience\nof the body as an object (Husserl 1973a, 57). Pre-reflective\nbody- (Leib-) awareness is not a type of object-perception,\nbut it is an essential element of every such perception. If I reach\nfor a tool, I know where to reach because I have a sense of where it\nis in relation to myself. I also sense that I will be able to reach\nit, or that I will have to take two steps towards it. My perception of\nthe tool must involve proprioceptive and kinaesthetic information\nabout my bodily situation and the position of my limbs, otherwise I\nwould not be able to reach for it or use it. If in such cases, we want\nto say that I have an awareness of my body, such bodily awareness is\nquite different from the perception that I have of the tool. I may\nhave to look or feel around in order to find where the tool is; but,\nunder normal circumstances, I never have to do that in regard to my\nbody. I am tacitly aware, not only of where my hands and feet are, but\nalso of what I can do with them. This tacit awareness of my body\nalways registers as an “I can” (or “I can’t,” as the\ncase may be). Primarily, my body is experienced, not as an object, but\nas a field of activity and affectivity, as a potentiality of mobility\nand volition, as an “I do” and “I can.” ", "\nThe body provides not only the egocentric spatial framework for\norientation towards the world, but also the constitutive contribution\nof its mobility. Perception does not involve a passive reception, but\nan active exploration of the environment. Husserl calls attention to\nthe importance of bodily movements (the movements of the eye,\nmanipulations by the hand, the locomotion of the body, etc.) for the\nexperience of space and spatial objects. He further claims that\nperception is correlated to and accompanied by\nproprioceptive-kinaesthetic self-sensation or self-affection (Husserl\n1973c). Every visual or tactile appearance is given in correlation to\na kinaesthetic experience. When I touch a shaped surface, it is given\nin conjunction with a sensation of finger movements. When I watch the\nflight of a bird, the moving bird is given in conjunction with the\nkinaesthetic sensations of eye movement and perhaps neck movement.\nSuch kinaesthetic activation during perception produces an implicit\nand pervasive reference to one’s own body. The implicit\nself-awareness of the actual and possible movements of my body helps\nshape the experience that I have of the world. To be clear, however,\nbodily self-awareness is not an awareness of the body in isolation\nfrom the world; it is embedded in action and perception. We do not\nfirst become aware of the body and subsequently use it to engage with\nthe world. We experience the world bodily, and the body is revealed to\nus in our exploration of the world. Primarily, the body attains\nself-awareness in action (or in our dispositions to action, or in our\naction possibilities) when it relates to something, uses something, or\nmoves through the\n world.[4]\n ", "\nBodily self-awareness, like self-consciousness more generally, has\nlimitations. I am never fully aware of everything that is going on\nwith my body. Indeed, my body tends to efface itself as I perceive and\nact in the world. When I jump to catch a ball that is thrown over my\nhead, I certainly have a sense of what I can do, but I am not aware of\nmy precise movements or postures—for example, that my right leg\nbends at a certain angle as I reach with my left hand. I can execute\nmovements without being explicitly conscious of them, and even what I\nam tacitly aware of is somewhat limited—for example, I am not\naware of the shape of my grasp as I reach to grab the ball. Although I\nmay not be aware of certain details about my bodily performance, this\ndoes not mean however that I am unconscious of my body. Rather it\nmeans that the way that I am aware of my body is fully integrated with\nthe intentional action that I am performing. I know that I am jumping\nto catch the ball, and implicit in that, as an immediate sense rather\nthan an inference, I experience my body jumping to catch the ball.", "\nFurthermore, experiential aspects of my embodiment permeate my\npre-reflective self-consciousness. There is something it is like to\njump to catch a ball, and part of what it is like is that I am in fact\njumping. There is something different about what it is like to sit and\nimagine (or remember) myself jumping to catch the ball, and at least\npart of that difference has to do with the fact that I am sitting\nrather than jumping, although none of this may be explicit in my\nexperience.", "\nAnother way to think of the self-awareness involved in action is to\nconsider the sense of agency that is normally an aspect of\npre-reflective self-awareness in action. If, as I am walking down the\nstreet, I am pushed from behind, I am instantly aware of my body\nmoving in a way that I did not intend. The fact that I feel a loss of\ncontrol over my actions suggests that there had been an implicit sense\nof agency or control in my walking prior to being pushed. In voluntary\naction, I experience the movements of my body as my own actions, and\nthis is replaced by a feeling of loss of bodily control in the case of\ninvoluntary movement. Voluntary actions feel different from\ninvoluntary actions, and this difference depends respectively, on the\nexperience of agency or the experience of a lack of agency—as\nthe case may be if my body is being moved by someone\n else.[5]\n ", "\nHubert Dreyfus has famously argued that in the case of expert\nperformance we are not self-conscious, but rather “usually involved\nin coping in a mindless way” (Dreyfus 2007a, 356). On his account,\nour immersed bodily life is so completely and totally world-engaged\nthat it is entirely oblivious to itself. Indeed, in total absorption,\none ceases being a subject altogether (Dreyfus 2007b, 373). It is only\nwhen this bodily absorption is interrupted that something like\nself-consciousness emerges. Dreyfus consequently doesn’t deny the\nexistence of self-consciousness, but he definitely wants to see it as\na capacity that is only exercised or actualized on special occasions.\nMoreover, when this capacity is exercised it necessarily disrupts our\ncoping and radically transform the kind of affordances that are given\nto it (Dreyfus 2005, 61; 2007, 354). A number of theorists, however,\nhave taken issue with this characterization of expert performance and\nhave argued that in the performing arts (e.g., in dance, musical\nperformance) and in athletics (e.g., baseball, cricket) expert\nperformers may employ an enhanced but still pre-reflective awareness\n(Legrand 2007), a heedful consciousness of the situation (e.g., Sutton\net al. 2011), or even a skillful reflective monitoring (Montero 2010;\n2014), or some variable combination of these (Høffding 2018), and\nthat such consciousness does not impede performance but improves it.\n" ], "section_title": "4. Bodily self-awareness", "subsections": [] }, { "main_content": [ "\nA focus on embodied self-experience inevitably leads to a decisive\nwidening of the discussion. The externality of embodiment puts me, and\nmy actions, in the public sphere. Self-consciousness, which involves\nan ability to make reflective judgments about our own beliefs and\ndesires, is always shaped by others and what we have learned from\nothers. This intersubjective or social influence can also affect\npre-reflective self-awareness, including my sense of embodied\nagency.", "\nI can become aware of myself through the eyes of other people, and\nthis can happen in a number of different ways. Thus, embodiment brings\nintersubjectivity and sociality into the picture, and draws attention\nto the question of how certain forms of self-consciousness are\nintersubjectively mediated, and may depend on one’s social\nrelations to others. My awareness of myself as one person among\nothers, an awareness that I may frame from the perspective of others,\nattempting to see myself as they see me, involves a change in the\nattitude of self-consciousness. Within this attitude, judgments that I\nmake about myself are constrained by social expectations and cultural\nvalues. This kind of social self-consciousness is always\ncontextualized, as I try to understand how I appear to others, both in\nthe way I look, and in the meaning of my actions. I find myself in\nparticular contexts, with specific capabilities and dispositions,\nhabits and convictions, and I express myself in a way that is\nreflected off of others, in relevant (socially defined) roles through\nmy language and my actions.", "\nThe role of the other in this mode of self-consciousness is not\nunessential. According to Husserl, I become aware of myself\nspecifically as a human person only in such intersubjective relations\n(Husserl 1973b, 175; 1952, 204–05; see Hart 1992, 71; Zahavi\n1999, 157ff. Also see Taylor 1989, 34–36 for a similar idea).\nThus Husserl distinguishes the subject taken in its bare formality\nfrom the personalized subject and claims that the origin and status of\nbeing a person must be located in the social dimension. I am a person,\nsocially contextualized, with abilities, dispositions, habits,\ninterests, character traits, and convictions, all of which have been\ndeveloped through my interactions with others. When considering the\nfullness of human selfhood, the idea of an isolated, pure and formal\nsubject of experience is an abstraction (Husserl 1968, 210). Given the\nright conditions and circumstances, the self acquires a personalizing\nself-apprehension, i.e., it develops into a person and as a person\n(cf. Husserl 1952, 265). And this development depends heavily upon\nsocial interaction (Husserl 1973b, 170–171). ", "\nThis kind of self-consciousness also opens up the possibility of\nself-alienation, famously explicated by Sartre in terms of the\nother’s gaze. For Sartre, because “our being, along with\nits being-for-itself, is also for-others; the being which is revealed\nto the reflective consciousness is for-itself-for-others” (1956,\n282). On this view, the primary experience of the other is not that I\nperceive her as some kind of object in which I must find a person, but\nI perceive the other as a subject who perceives me as an object. My\nexperience of the other is at the same time an experience that\ninvolves my own self-consciousness, a self-consciousness in which I am\npre-reflectively aware that I am an object for another. This\nexperience can further motivate a reflective self-consciousness, as I\nconsider how I must appear to the other.", "\nMerleau-Ponty (1945, 415) suggests that the other’s gaze can\nmotivate this kind of self-consciousness only if I already have a\nsense of my own visibility to the other. This sense of my own\nvisibility, however, is immediately linked with the pre-reflective,\nproprioceptive-kinaesthetic sense of my body, an insight that goes\nback to Husserl’s analysis (mentioned above). Merleau-Ponty\nnotes its connection to the infant’s capability for imitation,\nand this is carried forward to more recent advances in developmental\npsychology (see Merleau-Ponty, 1945, 165, 404–405; 2010; Gallagher and\nZahavi 2012; Zahavi 1999, 171–72). Indeed, although much emphasis has\nfallen on vision and the gaze of the other in phenomenological\naccounts of self-consciousness, proprioceptive and tactile experiences\nhave a developmental primacy and emerge in the pre-natal environment\nin ways that allow for very basic relational experiences of\nself-movement versus movement of the mother’s body (Lymer 2010;\n2014; Ciaunica & Crucianelli 2019; Ciaunica & Fotopoulou\n2016), and continue to play a significant role in embodied\ninteractions with caregivers during early infancy. In this respect,\nintersubjective/intercorporeal experiences can affect pre-reflective\nbody self-awareness. This complicates any claim that the\npre-reflective experience of body ownership is primarily for\nself-preservation (Ciaunica & Crucianelli 2019; de Vignemont\n2018).", "\nThis is not the place to enter into a detailed discussion of these\nrich and complex issues, issues that extend to analyses of phenomena\nsuch as empathy, shame, guilt, and so on (see Zahavi 2010, 2014). But\nit is important to realize that self-consciousness is a multifaceted\nconcept. It is not something that can be exhaustively analyzed simply\nby examining the inner workings of the mind. " ], "section_title": "5. Intersubjective and social forms of self-consciousness", "subsections": [] }, { "main_content": [ "\nThe notion of self-consciousness has been the subject of a rich and\ncomplex analysis in the phenomenological tradition. Aspects of the\nphenomenological analysis also show up in other areas of research,\nincluding feminism (Stawarska 2006; Young 2005; Heinämaa 2003),\necological psychology (Gibson 1966), and recent analyses of enactive\nperception (Gallagher 2017b; Noë 2004; Thompson 2008). The\nrecognition of the existence of a primitive form of pre-reflective\nself-consciousness is an important starting point for an understanding\nof more elaborate forms of self-consciousness that are concept- and\nlanguage-dependent. Phenomenological analyses show these processes to\nbe more than purely mental or cognitive events since they integrally\ninvolve embodiment and intersubjective dimensions. " ], "section_title": "6. Conclusion", "subsections": [] } ]

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[ "\nMontague semantics is a theory of natural language semantics and of\nits relation with syntax. It was originally developed by the logician\nRichard Montague (1930–1971) and subsequently modified and\nextended by linguists, philosophers, and logicians. The most important\nfeatures of the theory are its use of model theoretic semantics which\nis nowadays commonly used for the semantics of logical languages and\nits adherence to the principle of compositionality—that is, the\nmeaning of the whole is a function of the meanings of its parts and\ntheir mode of syntactic combination. This entry presents the origins\nof Montague Semantics, summarizes important aspects of the classical\ntheory, and sketches more recent developments. We conclude with a\nsmall example, which illustrates some modern features." ]

[ { "content_title": "1. Introduction", "sub_toc": [ "1.1 Background", "1.2 Basic Aspects" ] }, { "content_title": "2. Components of Montague Semantics", "sub_toc": [ "2.1 Unicorns and Meaning Postulates", "2.2 Noun Phrases and Generalized Quantifiers", "2.3 Logic and Translating", "2.4 Intensionality and Tautologies", "2.5 Scope and Derivational History" ] }, { "content_title": "3. Philosophical Aspects", "sub_toc": [ "3.1 From Frege to Intensions", "3.2 Compositionality", "3.3 Syntactic Categories and Semantic Types", "3.4 Pragmatics", "3.5 Ontology" ] }, { "content_title": "4. Concluding Remarks", "sub_toc": [ "4.1 Legacy", "4.2 Further Reading", "4.3 Example" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Introduction", "subsections": [ { "content": [ "\nMontague semantics is the approach to the semantics of natural\nlanguage introduced by Richard Montague in the 1970s. He described the\naim of his enterprise as follows:", "\nThe basic aim of semantics is to characterize the notion of a true\nsentence (under a given interpretation) and of entailment (Montague\n1970c, 373 fn).\n", "\nThe salient points of Montague’s approach are a model theoretic\nsemantics, a systematic relation between syntax and semantics, and a\nfully explicit description of a fragment of natural language. His\napproach constituted a revolution: after the Chomskyan revolution that\nbrought mathematical methods into syntax, now such methods were\nintroduced in semantics.", "\nMontague’s approach became influential, as many authors began to\nwork in his framework and conferences were devoted to ‘Montague\ngrammar’. Later on, certain aspects of his approach were adapted\nor changed, became generally accepted or were entirely abandoned.\nNowadays not many authors would describe their own work as\n‘Montague semantics’ given the many differences that have\ntaken shape in semantics since Montague’s own work, but his\nideas have left important traces, and changed the semantic landscape\nforever. In our presentation of Montague semantics the focus will be\non these developments.", "\nRichard Montague was a mathematical logician who had specialized in\nset theory and modal logic. His views on natural language must be\nunderstood with his mathematical background in mind. Montague held the\nview that natural language was a formal language very much in the same\nsense as predicate logic was a formal language. As such, in\nMontague’s view, the study of natural language belonged to\nmathematics, and not to psychology (Thomason 1974, 2). Montague\nformulated his views:", "\nThere is in my opinion no important theoretical difference between\nnatural languages and the artificial languages of logicians; indeed I\nconsider it possible to comprehend the syntax and semantics of both\nkinds of languages with a single natural and mathematically precise\ntheory. (Montague 1970c, 373)\n", "\nSometimes only the first part of the quote is recalled, and that might\nraise the question whether he did not notice the great differences:\nfor instance that natural languages develop without an a priori set of\nrules whereas artificial languages have an explicit syntax and are\ndesigned for a special purpose. But the quote as a whole expresses\nclearly what Montague meant by ‘no important theoretical\ndifference’; the ‘single natural and mathematically\nprecise theory’ which he aimed at, is presented in his paper\n‘Universal Grammar’ (Montague 1970c). He became most\nwell-known after the appearance of Montague 1973, in which the theory\nis applied to some phenomena which were discussed intensively in the\nphilosophical literature of those days.", "\nAccording to Caponigro (forthcoming), Montague’s interest in the\nfield arose when preparing a seminar on the philosophy of language as\na visiting professor in Amsterdam in 1966. Only a couple of years\nearlier, he had deemed the “systematic exploration of the\nEnglish language, indeed of what might be called the ‘logic of\nordinary English’, […] either extremely laborious or\nimpossible” and did ‘not find it rewarding’\n(Montague and Kalish 1964, 10). Yet he appears to have changed his\nmind after perusing Quine’s (1960) Word and Object as\nwell as Chomsky’s (1965) Aspects of the Theory of\nSyntax: the latter opened the perspective of treating the syntax\nof natural language as a formal system but failed to provide any\nserious analysis of linguistic meaning; the former offered a\nsystematic connection between traditional grammar and formal logic\n– and much more systematically so than contemporary logic texts.\nIn fact, Montague’s semantic work owes a lot to Quine’s\ndescriptive insights into the ‘logic of ordinary English’,\nbut differs from his predecessor by making the connection between\nlanguage and logic in rigorous, mathematical terms:", "\nIt should be emphasized that this is not a matter of vague intuition,\nas in elementary logic courses, but an assertion to which we have\nassigned exact significance. (Montague 1973, 237)\n", "\nWe next describe the basic ideas of Montague semantics. Section\n 2\n presents several components of Montague semantics in more detail.\nSection\n 3\n includes a discussion of philosophically interesting aspects, and\nSection\n 4\n provides a detailed example and further reading." ], "subsection_title": "1.1 Background" }, { "content": [ "\nTo implement his objective, Montague applied the method which is\nstandard for logical languages: model theoretic semantics. This means\nthat, using constructions from set theory, a model is defined, and\nthat natural language expressions are interpreted as elements (or\nsets, or functions) in this universe. Such a model should not be\nconceived of as a model of reality. On the one hand, the model gives\nmore than reality: natural language does not only speak about past,\npresent and future of the real world, but also about situations that\nmight be the case, or are imaginary, or cannot be the case at all. On\nthe other hand, however, the model offers less: it merely specifies\nreality as conceived by language. An example: we speak about mass\nnouns such as water as if every part of water is water again,\nas if it has no minimal parts, which physically is not correct. For\nmore information on natural language metaphysics, see Bach 1986b.", "\nMontague semantics is not interested in a particular situation (e.g.\nthe real world) but in semantical properties of language. When\nformalizing such properties, reference to a class of models has to be\nmade, and therefore the interpretation of a language will be defined\nwith respect to a set of (suitable) models. For example, in the\nintroduction we mentioned that the characterization of entailment was\na basic goal of semantics. That notion is defined as follows. Sentence\n\\(A\\) entails sentence \\(B\\) if in all models in which the\ninterpretation of \\(A\\) is true, also the interpretation of \\(B\\) is\ntrue. Likewise, a tautology is true in all models, and a contradiction\nis true in no model.", "\nAn essential feature of Montague semantics is the systematic relation\nbetween syntax and semantics. This relation is described by the\nPrinciple of Compositionality, which reads, in a formulation\nthat is standard nowadays:", "\nThe meaning of a compound expression is a function of the meanings of\nits parts and of the way they are syntactically combined. (Partee\n1984, 281)\n", "\nAn example: Suppose that the meaning of walk, or\nsing is (for each model in the class) defined as the set of\nindividuals who share respectively the property of (being an\nindividual that is) walking or the property of (being an individual\nthat is) singing. By appealing to the principle of compositionality,\nif there is a rule that combines these two expressions to the verb\nphrase walk and sing, there must be a corresponding rule that\ndetermines the meaning of that verb phrase. In this case, the\nresulting meaning will be the intersection of the two sets.\nConsequently, in all models the meaning of walk and sing is a\nsubset of the meaning of walk. Furthermore, we have a rule\nthat combines the noun phrase John with a verb phrase. The\nresulting sentence John walks and sings means that John is an\nelement of the set denoted by the verb phrase. Note that in any model\nin which John is element of the intersection of walkers and singers,\nhe is an element of the set of walkers. So John walks and\nsings entails John walks.", "\nAn important consequence of the principle of compositionality is that\nall the parts that play a role in the syntactic composition of a\nsentence must also have a meaning. And furthermore, each syntactic\nrule must be accompanied by a semantic rule which says how the meaning\nof the compound is obtained. Thus, the meaning of an expression is\ndetermined by the way in which the expression is formed, and as such\nthe derivational history plays a role in determining the meaning. For\nfurther discussion, see Section\n 2.5.", "\nThe formulation of the aim of Montague semantics mentioned in the\nintroduction (‘to characterize truth and entailment of\nsentences’) suggests that the method is restricted to\ndeclarative sentences. But this need not be the case. In Montague 1973\n(241 fn) we already find suggestions for how to deal with imperatives\nand questions. Hamblin (1973) and Karttunen (1977) have given a\nsemantics for questions by analyzing them as expressing sets of\npropositions, viz. those expressed by their (declarative) answers; an\nalternative approach, taken by Groenendijk and Stokhof (1989)\nconsiders questions as partitioning logical space into mutually\nexcluding possibilities.", "\nSince Montague only considered sentences in isolation, certain\ncommentators pointed out that the sentence boundary was a serious\nlimitation for the approach. But what about discourse? An obvious\nrequirement is that the sentences from a discourse are interpreted one\nby one. How then to treat co-referentiality of anaphora over sentence\nboundaries? The solution which was proposed first was Discourse\nRepresentation Theory (Kamp 1981). On the one hand, that was an\noffspring of Montague’s approach because it used model theoretic\nsemantics; on the other hand, it was a deviation because (discourse)\nrepresentations were an essential ingredient. Nowadays there are\nseveral reformulations of DRT that fit into Montague’s framework\n(see van Eijck and Kamp 1997). A later solution was based upon a\nchange of the logic; dynamic Montague semantics was developed and that\ngave a procedure for binding free variables in logic which has an\neffect on subsequent formulas (Groenendijk and Stokhof 1990, 1991).\nHence the sentence boundary is not a fundamental obstacle for Montague\nsemantics." ], "subsection_title": "1.2 Basic Aspects" } ] }, { "main_content": [], "section_title": "2. Components of Montague Semantics", "subsections": [ { "content": [ "\nMontague’s most influential article was ‘The Proper\nTreatment of Quantification in Ordinary English’ (Montague\n1973), commonly abbreviated as ‘PTQ’. It presented a\nfragment of English that covered several phenomena which were in those\ndays discussed extensively. One of the examples gave rise to the\ntrademark of Montague grammar: the unicorn (several publications on\nMontague grammar are illustrated with unicorns).", "\nConsider the two sentences John finds a unicorn and John\nseeks a unicorn. These are syntactically alike\n(subject-verb-object), but are semantically very different. From the\nfirst sentence follows that there exists at least one unicorn, whereas\nthe second sentence is ambiguous between the so called de\ndicto (or non-specific, or notional) reading\nwhich does not imply the existence of unicorns, and the de re\n(or specific, or objectual) reading from which\nexistence of unicorns follows.", "\nThe two sentences are examples of a traditional problem called\n‘quantification into intensional contexts’. Traditionally,\nthe second sentence as a whole was seen as an intensional context, and\nthe novelty of Montague’s solution was that he considered the\nobject position of seek as the source of the phenomenon. He\nformalized seek not as a relation between two individuals,\nbut as a relation between an individual and a more abstract entity\n(see section 2.2). Under this analysis the existence of a unicorn does\nnot follow. The de re reading is obtained in a different way\n(see section 2.5).", "\nIt was Montague’s strategy to apply to all expressions of a\ncategory the most general approach, and narrow this down, when\nrequired, by meaning postulates (and, in some cases, logical\ndecomposition). So initially, find is also considered to be a\nrelation between an individual and such an abstract entity, but some\nmeaning postulate restricts the class of models in which we interpret\nthe fragment to only those models in which the relation for\nfind is the (classical) relation between individuals.", "\nAs a consequence of this strategy, Montague’s paper has many\nmeaning postulates. Nowadays semanticists often prefer to express the\nsemantic properties of individual lexical items directly in their\nlexical meaning, and then find is directly interpreted as a\nrelation between individuals. Meaning postulates are mainly used to\nexpress structural properties of the models (for instance, the\nstructure of the time axis), and to express relations between the\nmeanings of words. For a discussion of the role of meaning postulates,\nsee Zimmermann 1999." ], "subsection_title": "2.1 Unicorns and Meaning Postulates" }, { "content": [ "\nNoun phrases like a pig, every pig, and\nBabe, behave in many respects syntactically alike: they can\noccur in the same positions, can be conjoined, etc. But a uniform\nsemantics seems problematic. There were proposals which said that\nevery pig denotes the universally generic pig, and a\npig an arbitrary pig. Such proposals were famously rejected by\nLewis (1970), who raised, for instance, the question which would be\nthe color of the universal pig, all colors, or would it be\ncolorless?", "\nMontague proposed the denotation of a descriptive phrase to be a set\nof properties. For instance, the denotation of John is the\nset consisting of properties which hold for him, and of every\nman the set of properties which hold for every man. Thus they are\nsemantically uniform, and then conjunction and/or disjunction of\narbitrary quantifier phrases (including e.g. most but not\nall) can be dealt with in a uniform way.", "\nThis abstract approach has led to generalized quantifier theory, see\nBarwise and Cooper 1981 as well as Peters and Westerståhl 2006.\nAmong the most popular achievements of generalized quantifier theory\nis a semantic characterization of so-called ‘negative polarity\nitems’: words like yet and ever. Their\noccurrence can be licensed by negation: The 6:05 has arrived\nyet is out, whereas The 6:05 hasn’t arrived yet is\nOK. But there are more contexts in which negative polarity items may\noccur, and syntacticians did not succeed in characterizing them.\nLadusaw (1980) did so by using a characterization from generalized\nquantifier theory. This has been widely acknowledged as a great\nsuccess for formal semantics. His proposal roughly was as follows.\nDownward entailing expressions are expressions that license inferences\nfrom supersets to subsets. No is downward entailing because\nfrom No man walks it follows that No father walks. A\nnegative polarity item is acceptable only if it is interpreted in the\nscope of a downward entailing expression, e.g. No man ever\nwalks. Further research showed that the analysis needed refining,\nand that a hierarchy of negative polarity items should be used\n(Ladusaw 1996, Homer 2021)." ], "subsection_title": "2.2 Noun Phrases and Generalized Quantifiers" }, { "content": [ "\nAn expression may directly be associated with some element from the\nmodel. For instance, walk with some set of individuals. Then\nalso the operations on meanings have to be specified directly, and\nthat leads to formulations such as:", "\n\\(G_3 (\\ulcorner\\)is\\(\\urcorner)\\) is that function \\(f \\in\n((2^I)^{A\\times A})^{A^{ \\omega}}\\) such that, for all \\(x \\in\nA^{\\omega}\\), all \\(u,t \\in A\\) and all \\(i \\in I : f(x)(t,u)(i) = 1\\)\nif and only if \\(t = u\\). (Montague 1970a, 195)\n", "\nSuch descriptions are not easy to understand, nor convenient to work\nwith. Montague (1973, 228) said, ‘it is probably more\nperspicuous to proceed indirectly’. For this purpose he\nintroduced a language, called ‘intensional logic’. The\noperation described above is then represented by \\(^{\\wedge}\\lambda\nt\\lambda u[t = u\\)]. The \\(\\lambda t\\) says that it is a function that\ntakes \\(t\\) as argument, likewise for \\(\\lambda u\\). So \\(\\lambda\nt\\lambda u[t = u\\)] is a function which takes two arguments, and\nyields true if the arguments are equal, and otherwise false. The\npreceding \\(^{\\wedge}\\) says that we consider a function from possible\nworlds and moments of time to the thus defined function.", "\nThree features of the Montague’s ‘intensional logic’\nattracted attention:", "\nThis motivation for indirect interpretation – by way of\ncompositional translation as a tool for obtaining perspicuous\nrepresentations of meaning – has a number of important\nconsequences:", "\nThe method of using logical notation for representing meanings has a\nlong history, going back at least to philosophers such as Dalgarno and\nLeibniz who developed formal languages in order to express philosophy\nclearly. In the 19th century, there were several proposals for\nartificial languages in order to make mathematical argumentation more\ntransparent, for instance by Frege and by Peano. Frege’s\n‘Begriffsschrift’ (Frege 1879) can be seen as the birth of\npredicate logic: he introduced quantifiers. His motivation came from\nmathematical needs; he did not use his Begriffsschrift in his papers\non natural language. Russell (1905) used logic to represent the\nmeanings of natural language. A classical example in his paper is the\nanalysis of The king of France is bald. Syntactically it has\nthe form subject-predicate, but if it were constructed logically as a\nsubject-predicate, then the king of France, which denotes\nnothing, cannot be the subject. So syntactic form and logical form may\ndiverge: natural language obscures the view of the real meaning. This\nbecame known as the ‘misleading form thesis’. Therefore,\nphilosophers of language saw, in those days, the role of logic as a\ntool to improve natural language, an aim that is alien to Montague\nsemantics. In fact, using higher-order functional type theory (Church\n1940) as the target of his translation, Montague (1970c) developed a\n‘compositional’ version of Russell‘s analysis, which\ndoes preserve the constituent structure of the source language\n(English). An interesting overview of the history of translating\nnatural language into logic is given in Stokhof 2007." ], "subsection_title": "2.3 Logic and Translation" }, { "content": [ "\nMontague defined the denotation of a sentence as a function from\npossible worlds and moments of time to truth values. Such a function\nis called an ‘intension’. As he said (Montague 1970a,\n220), this made it possible to deal with the semantics of common\nphenomena such as modifiers, e.g. in Necessarily the father of\nCain is Adam. Its denotation cannot be obtained from the truth\nvalue of The father of Cain is Adam: one needs to know the\ntruth value for other possible worlds and moments of time. The\nintensional approach also made it possible to deal with several\nclassical puzzles. Two examples from Montague 1973 are: The\ntemperature is rising, which should not be analyzed as stating\nthat some number is rising; and John wishes to catch a fish and\neat it, which should not be analyzed as implying that John has a\nparticular fish in mind.", "\nIntensional semantics has been criticized for the fact that all\ntautologies get the same meaning (are synonymous). Indeed, a tautology\nas John is ill or he is not ill gets as intension the\nfunction that constantly yields true, and the same holds for\nother tautologies. If one is interested in discriminating semantically\nbetween tautologies, then a refinement of the notions\n‘meaning’ and ‘equivalence’ is needed:\n‘meaning’ should see distinctions between tautologies, and\n‘equivalence’ should be sensitive for the thus refined\nnotion of meaning. The oldest proposals to account for this problem\ngoes back to Carnap (1947, §14) and was later taken up by Lewis\n(1970, sec. 5): propositions are structured by including in their\nmeanings also the meanings of their parts. Then indeed Green grass\nis green and White snow is white have different\nmeanings. However, lexical synonyms still pose a problem. Since\nwoodchuck and groundhog are names for the same\nspecies, John believes that Phil is a groundhog is, under\nthis view, equivalent with John believes that Phil is a\nwoodchuck. One could consider belief contexts a separate problem,\nbut most authors see it as part of the problem of equivalence of all\ntautologies.", "\nLater several proposals for dealing with this have been developed;\nsurveys can be found in Bäuerle and Cresswell (2003), Fox and\nLappin (2005), and Egré (2021). The latter authors explain that\nthere are two strategies: the first is to introduce impossible worlds\nin which woodchuck and groundhog are not equivalent,\nand the second is to introduce an entailment relation with the\nproperty that identity does not follow from reciprocal entailment. Fox\nand Lappin follow the second strategy." ], "subsection_title": "2.4 Intensionality and Tautologies" }, { "content": [ "\nA well known example of scope ambiguity is Every man loves a\nwoman. Is there only one woman involved (e.g. Mother Mary), or\ndoes every man love a different woman? The sentence has no lexically\nambiguous words, and there are no syntactic arguments to assign them\nmore than one constituent structure. How to account for the\nambiguity?", "\nIn Montague 1973, the scope ambiguity is dealt with by providing for\nthe sentence two different derivations. On the reading that\nevery has wide scope, the sentence is produced from every\nman and loves a woman. On the reading that only one\nwoman is involved, the sentence is obtained from Every man loves\nhim\\(_1\\). The him\\(_1\\) is an artifact, a placeholder,\nor, one might say, a syntactic variable. A special kind of rule,\ncalled a ‘quantifying-in rule’, will replace this\nhim\\(_1\\) by a noun phrase or a pronoun (in case there are\nmore occurrences of this placeholder). The placeholder corresponds\nwith a logical variable that becomes bound by the semantic counterpart\nof the quantifying-in rule. For the sentence under discussion, the\neffect of the application of the quantifying-in rule to a\nwoman and Every man loves him\\(_1\\) is that the desired\nsentence is produced and that the quantifier corresponding with a\nwoman gets wide scope. When we would depict its derivation as a\ntree, this tree would be larger than the constituent structure of the\nsentence due to the introduction and later removal of\nhim\\(_1\\).", "\nThis quantifying-in rule is used by Montague for other phenomena as\nwell. An example is co-referentiality: Mary loves the man whom she\nkissed is obtained from He\\(_1\\) loves the man whom\nhe\\(_1\\) kissed. And the de re reading of\nJohn seeks a unicorn is obtained from a unicorn and\nJohn seeks him\\(_1\\).", "\nMany researchers did not like this analysis in which powerful\nsyntactic rules and artificial symbols (him\\(_1)\\) are used.\nBelow we consider two strategies to remedy.", "\nThe first strategy was to deny the ambiguity. Some linguists have\nargued that the scope order is the same as the surface order; this is\nknown as ‘Jackendoff’s principle’ (Jackendoff 1972).\nBut there are sentences where this does not work. Others said that it\nis sufficient only to obtain the weakest reading (every wide\nscope), and that the stronger reading is inferred when additional\ninformation is available. But there are sentences for which the\ndifferent scope readings are logically independent, as in Every\nwoman loves one man.", "\nThe second strategy was to capture the ambiguity in another way than\nby the quantifying-in rules. Historically the first method was to put\nthe interpretations of the noun phrases in a store from which these\ninterpretations could be retrieved when needed: different stages of\nretrieving correspond with differences in scope. One might see this as\na grammar in which the direct correspondence between syntax and\nsemantics has been relaxed. The method is called ‘Cooper\nStore’, after the author who proposed this (Cooper 1983). A\nlater proposal is DRT \\((=\\) Discourse Representation Theory), where\nrepresentations are used to account for such ambiguities (van Eijck\nand Kamp 1997).", "\nA recent method is by means of ‘lifting rules’ (see\nsection 3.3): the meaning of a noun-phrase is ‘lifted’ to\na more abstract level, and different levels yield different scope\nreadings (see Hendriks 2001 and Jacobson 2014).", "\nEven if the role of derivational history can be avoided for scope and\nco-referentiality, other phenomena remain for which derivational\nhistories have a role. An example is John wondered when Alice said\nshe would leave. This is ambiguous between John asking for the\ntime of leaving, or for the time of saying. So the sentence is\nambiguous, even though there are no arguments for assigning to it more\nthan one constituent structure. Pelletier (1993) presents this\nsentence and others, and says: ‘In order to maintain the\nCompositionality Principle, theorists have resorted to a number of\ndevices which are all more or less unmotivated (except to maintain the\nPrinciple): Montagovian “quantifying-in” rules, traces,\ngaps, […].’ Pelletier’s objection can be\nappreciated if one assumes that meaning assignment is directly linked\nwith constituent structure. But, as explained in Section\n 1.2,\n this is not the case. The derivation specifies which rules are\ncombined in which order, and this derivation constitutes the input to\nthe meaning assignment function. The constituent structure is\ndetermined by the output of the syntactic rules, and different\nderivation processes may generate one and the same constituent\nstructure. In this way, semantic ambiguities are accounted for. One\nshould not call something ‘constituent structure’ if it is\nnot intended as such, and next refute it because it does not have the\ndesired properties.", "\nThe distinction between a derivation tree and a constituent tree is\nmade in several theories of grammar. In Tree Adjoining Grammars (TAGs)\nthe different scope readings of the sentence about loving a woman\ndiffer in the order in which the noun-phrases are substituted in the\nbasic tree. A classical example in Chomskyan grammar is The\nshooting of the hunters was bloody, which is ambiguous between\nthe hunters shooting, or the hunters being shot at. The two readings\ncome from two different sources: one in which the hunters is\nthe subject of the sentence, and one in which it is the object." ], "subsection_title": "2.5 Scope and Derivational History" } ] }, { "main_content": [], "section_title": "3. Philosophical Aspects", "subsections": [ { "content": [ "\nThroughout most of his semantic work, Montague avowedly adopted a\nversion of Frege’s (1892) distinction between\n‘sense’ and ‘denotation’. Frege’s\noriginal line of thought concerns sentences like The Greeks did\nnot know that the morning star is the evening star, which does\nnot seem to express that the Greeks were confused about the\nself-identity of Venus. Frege’s analysis accounts for this\nobservation by having descriptive names like the morning star\ndenote their referents in ordinary contexts, but something different\nin embedded clauses (or, more generally, in ‘indirect\ncontexts’): their ‘sense’ – a semantic value\nthat captures the way in which an object is referred to. Since\nreferring to a celestial object by the morning star differs\nfrom referring to it by the evening star, the embedded clause\ndoes not denote an analytic truth but a contingent proposition, whose\ntruth may well have escaped the Greeks.", "\nFrege’s approach is known to run into a number of problems. One\nof them concerns the iteration of indirect contexts, as in Gottlob\nsuspected that the Greeks did not know that the morning star is the\nevening star. Though he did not explicitly address the issue,\nFrege is usually understood as resorting to an infinite hierarchy of\never more indirect senses to be associated with each otherwise\nnon-ambiguous expression (Dummett 1981, 267; Carnap 1947, §30;\nKripke 2008, 183; see however Parsons 1981 for a more cautious\ninterpretation). The purported Fregean line of analysis has been\ncriticized for multiplying ambiguity beyond necessity (Janssen 2012)\nas well as raising serious learnability issues (Davidson 1968, 11).\nThough Montague did acknowledge a hierarchy of senses, he did not\nemploy it for the analysis of iterated indirect contexts. Instead, he\nidentified Frege’s (1892) senses with intensions along\nthe lines of Carnap (1947) – set theoretic functions on a\nlogical space of possible worlds (or world-time-pairs) whose values\nare the denotations of expressions – their extensions.\nIn particular, the way in which a description refers to its referent\nis captured by its dependence on contingent facts. As a case in point,\nthe famous Fregean descriptions differ in intension as long as there\nis a possible world in which the brightest star at dawn is not the\nsame object as the brightest star at night.", "\nThe replacement of senses by intensions paves the way to an\nalternative approach to iterated intensionality: generalizing\nKripke’s (1963) semantics of modality, Montague (1970b, 73)\naccounted for clausal embedding in terms of propositional operators\nwhose extension, like that of their argument, depends on a given point\nin logical space. As it turns out, this so-called ‘neighborhood\nsemantics’ of clausal embedding does without reference to a\nsense hierarchy even in iterated indirect environments\n(ibid., 76), which is why Montague used it as the basis for\nhis general compositional analysis of natural language. Montague\n(ibid., 75f.) still presented his approach as being in line\nwith Frege’s, thereby emphasizing the commonalities in the\noverall architecture of semantic theory, which he identified as\n‘Frege’s functionality principle’:", "\nthe extension of a formula is a function of the extensions (ordinary\nextensions) of those of its parts not standing within indirect\ncontexts (that is […] not standing within the scope of an\noperator), together with the intensions (what Frege also called\nindirect extensions) of those parts that do stand within\nindirect contexts. (Montague 1970b, 74f.)\n", "\nMoreover, Montague (1970c, 390) called one of the key constructions of\nhis general theory of reference ‘Fregean interpretation’;\nand in his type-logical hierarchy, intensions are marked by the letter\n‘\\(s\\)’, which is short for ‘sense’\n(ibid., 379). This notation has become quite common in\nlinguistic semantics, although the ‘\\(s\\)’ is frequently\ntaken to stand for possible \\(s\\)ituations!", "\nOnly at one point in his semantic work did Montague abandon his\nFregean stance: in his essay ‘English as a formal\nlanguage’ (1970a), he employed a one-level architecture of\n‘Russellian’ denotations and expressed his doubts about\nthe cogency of Frege’s motivation for non-propositional senses\n(ibid., sec. 9, remark xi), thereby foreshadowing\nKaplan’s (1975) comparison between the frameworks of Frege 1892\nand Russell 1905. Yet in his ‘Universal Grammar’, Montague\ncommented:", "\nI should like, however, to withdraw my emphasis […] on the\npossibility of doing without a distinction between sense and\ndenotation. While such a distinction can be avoided in special cases,\nit remains necessary for the general theory, and probably provides the\nclearest approach even to the special cases in question. (Montague\n1970c, 374, fn.)\n", "\nEven though Montague tended to play down the difference, the switch\nfrom senses to intensions is known to have dramatic consequences on\nthe fine-grainedness of semantic analysis. In particular, as mentioned\nin section 2.4, any two logically equivalent sentences come out as\nhaving the same intension; yet their senses will diverge if their\ntruth value is not determined in the same way. Montague indicated how\nthis unwelcome consequence may be avoided in terms of mismatches\nbetween worlds and contexts, creating what he called\n‘“unactualizable” points of reference’\n(ibid., 382), but he did not provide a detailed analysis to\nsubstantiate his sketchy remarks." ], "subsection_title": "3.1 From Frege to Intensions" }, { "content": [ "\nFor Montague the principle of compositionality did not seem to be a\nsubject of deliberation or discussion, but the only way to proceed. In\neffect he made compositionality the core part of his ‘theory of\nmeaning’ (Montague 1970c, 378), which was later summed up in the\nslogan: ‘Syntax is an algebra, semantics is an algebra, and\nmeaning is a homomorphism between them’ (Janssen 1983, 25). Yet\nalthough Montague used the term ‘Frege’s functionality\nprinciple’ for the way in which extension and intension are\ncompositionally intertwined, he did not have a special term for\ncompositionality in general. Later authors, who identified the\nPrinciple of Compositionality as a cornerstone of Montague’s\nwork, also used the term ‘Frege’s Principle’\n(originating with Cresswell 1973, 75); Thomason 1980 is an early\nsource for the term ‘compositional’.", "\nIt has been claimed that Montague’s analysis of pronouns is not compositional. This is, however, not the case. In order to\nexplain the compositional nature of his treatment of pronouns, both\nJanssen (1997) and Dowty (2007) explain how variables are interpreted\nin logic; we follow their explanations. Consider the following clauses\nfrom the traditional Tarskian interpretation of predicate logic.", "\nThe first clause says: \\(\\varphi \\wedge \\psi\\) is true when using\nassignment \\(g\\) if and only if \\(\\varphi\\) and \\(\\psi\\) are true when\nthe assignment \\(g\\) is used. In the second clause assignments \\(h\\)\nare introduced (by \\(\\sim_x g)\\) which are equal to \\(g\\) except maybe\nfor the value they assign to variable \\(x\\). Montague uses the same\nformat, with the difference that besides \\(g\\) he also has \\(i\\), the\ntime of reference and \\(j\\), the possible world, as superscripts.", "\nIn the formulation of the clauses there is nothing which can be\npointed at as ‘the meaning’, in fact it is a definition of\ntruth with \\(g\\) and \\(h\\) as parameters. So how is it possible that\nthis (and Montague’s work) are compositional?", "\nThe answer requires a shift in perspective. The meaning of a formula\n\\(\\varphi\\), shortly \\(M(\\varphi)\\), is the set of assignments for\nwhich the formula is true. Then the first clause says that", "\nso a simple set-theoretic combination on the two meanings is\nperformed. And", "\ni.e., \\(\\{g \\mid \\text{for some }h \\in\nM(\\varphi), g \\sim_x h \\}\\), which can be described as: extend the set\n\\(M(\\varphi)\\) with all \\(x\\)-variants. (The reference to\n‘\\(x\\)’ may be felt as problematic, but Montague even\neliminated this trace of non-compositionality by assigning appropriate\nmeanings to variables; see Zimmermann and Sternefeld 2013, ch. 10, for\npertinent details.) In general, in Montague semantics the meaning of\nan expression is a function which has as domain the triples\n\\(\\langle\\)moment of time, possible world, assignment to\nvariables\\(\\rangle\\).", "\nIs it possible to achieve compositionality for natural language?\nObvious candidates for counterexamples are idioms, because their\nmeanings seem not to be built from their constituting words. However,\nWesterståhl (2002) presents a collection of methods, varying\nfrom compound basic expressions, to deviant meanings for constituting\nparts. Janssen (1997) refutes several other counterexamples that are\nput forward in the literature.", "\nHow strong is compositionality? Mathematical results show that any\nlanguage can be given a compositional semantics, either by using an\nunorthodox syntax (Janssen 1997) or by using an unorthodox semantics\n(Zadrozny 1994). However their proofs are not helpful in practice.\nHodges (2001) showed under which circumstances a given compositional\nsemantics for a fragment can be extended to a larger language.", "\nThere is no general agreement among formal semanticists about the role\nand status of compositionality; at least the following four positions\nhave been held (nearly the same list is given in Partee 1996):", "\nAn extensive discussion of compositionality is given in Janssen 1997,\nand in the entry on\n compositionality." ], "subsection_title": "3.2 Compositionality" }, { "content": [ "\nAccording to Montague, the purpose of syntax is to provide the input\nto semantics:", "\nI fail to see any interest in syntax except as a preliminary to\nsemantics. (Montague 1970c, 223)\n", "\nAlthough syntax was in his eyes subordinate, he was fully explicit in\nhis rules in which he used some ad hoc syntactic tools.", "\nIn Montague 1970a and 1970c, the relation between syntactic categories\nand semantic types is given only by a list. Montague (1973) defines a\nsystematic relation which amounts to the same relation as one would\nhave in categorial grammar. However, Montague’s syntax is not a\ncategorial syntax because the rules are not always category driven and\nbecause some of the rules are not concatenation rules.", "\nFor each of these two aspects, proposals have been put forward to\nchange the situation. One direction was to stay closer to the ideals\nof categorial grammar, with only type-driven rules, sometimes allowing\nfor a restricted extension of the power of concatenation rules (see,\nfor example, Morrill 1994, Carpenter 1998). The other approach was to\nincorporate in Montague grammar as much as possible the insights from\nsyntactic theories, especially originating from the tradition of\nChomsky. A first step was made by Partee (1973), who let the grammar\nproduce structures (labelled bracketings); a syntactically\nsophisticated grammar (with Chomskyan movement rules) was used in the\nRosetta translation project (Rosetta 1994). The influential textbook\nby Heim and Kratzer (1998) combined the two approaches by applying\ntype-driven interpretation to the syntactic level of (Chomskyan)\nLogical Forms.", "\nIn his syntactic accounts, Montague tended to treat\n‘logical‘ words like determiners (the, a,\nevery) and conjunctions (and, or, not)\nsyncategorematically, i.e., not by means of lexical entries, but as\nthe effect of specific syntactic rules; the reason for this decision\nis unknown, but it may be speculated that it was part of a\ncharacterization of grammatical meaning in terms of logicality,\npresumably along the lines of Tarski’s 1986 invariance\ncriterion. As a consequence, a different rule is needed for John\nwalks and sings than for John walks and Mary sings:\nsyntactically the first one is a conjunction of verb phrases and the\nsecond one of sentences. However, the two meanings of and are\nclosely related and a generalization is missed. As a general solution\nit was proposed to use rules (or alternatively general principles)\nthat change the category of an expression – a change that\ncorresponds with a semantic rule that ‘lifts’ the meaning.\nFor instance, the meaning of and as a connective between verb\nphrases is obtained by lifting the meaning of the sentence connective\n\\(\\wedge\\) to \\(\\lambda P\\lambda Q\\lambda x[P(x) \\wedge Q(x)].\\) The\nline of analysis has been extensively studied in Partee and Rooth\n1983, Partee 1987, Hendriks 2001, and Winter 2001.", "\nMontague’s method of defining fragments with a fully explicit\nsyntax has become far less popular than it was in the heyday of\nMontague Grammar in the 1980s. Nowadays semanticists prefer to focus\non specific phenomena, suggesting rules which are only explicit\nconcerning the semantic side. This tendency has been criticized by\nPartee in Janssen 1997 and Jacobson 2014, where a fragment is actually\nprovided." ], "subsection_title": "3.3 Syntactic Categories and Semantic Types" }, { "content": [ "\nThe truth conditions of sentences sometimes vary with the context of\nuse. Thus, whether I am happy is true, depends on who the\nspeaker is; other examples include the referents of here and\nthis. Montague (1968; 1970b) addressed these factors,\nindicating that they could be treated by introducing additional\nparameters besides the time and the possible world. Despite occasional\ncritcism (Cresswell 1973, 111; Lewis 1980, 86f.), the treatment of\ncontextual dependence by way of a fixed finite list of parameters has\nbecome quite standard in formal semantics.", "\nMontague initially treated contextual parameters on a par with times\nand worlds, but in ‘Universal Grammar’ (Montague 1970c) he\nindicated that a distinction should be made between those that\ndetermine the content (which, following Frege 1892, is what is denoted\nin indirect contexts) from those that constitute it:", "\nThus meanings are functions of two arguments– a possible world\nand a context of use. The second argument is introduced in order to\npermit a treatment […] of such indexical locutions as\ndemonstratives, first- and second-person singular pronouns, and free\nvariables (which are treated […] as a kind of demonstrative).\nSenses on the other hand […] are functions of only one\nargument, regarded as a possible world. The intuitive distinction is\nthis: meanings are those entities that serve as interpretations of\nexpressions (and hence, if the interpretation of a compound is always\nto be a function of the interpretations of its components, cannot be\nidentified with functions of possible worlds alone), while senses are\nthose intensional entities that are sometimes denoted by expressions.\n(Montague 1970c, 379)\n", "\nWhile these remarks are still a far cry from double-indexing\napproaches to context dependence (Kamp 1971), they do exhibit the\nbasic idea underlying the shiftability criterion for distinguishing\ncontext and index (Lewis 1980). In particular, Montague’s\nmeanings share a core feature with Kaplan’s (1989) characters:\nboth map paramteterized contexts to propositions, understood as\n(characteristic functions of) sets of possible worlds.", "\nMontague (1970c, 68) followed Bar-Hillel 1954 in treating context\ndependence as part of pragmatics. It was only after his death, that\nhis framework was connected to other aspects of pragmatics. In\nparticular, in early work on Montague grammar, various proposals were\nmade to give compositional characterizations of presuppositions and\n(conventional) implicatures (Peters 1979; Karttunen and Peters 1979),\nbut later treatments were not always completely compositional, taking\nseveral contextual factors into account (Beaver 1997). In a similar\nvein, early work in the tradition was rather optimistic about directly\napplying Montague semantics to non-declarative uses of (declarative)\nsentences (Cresswell 1973), but later accounts had to invoke a lot\nmore than linguistic meaning, including models of interlocutors’\nperspectives (Gunlogson 2003)." ], "subsection_title": "3.4 Pragmatics" }, { "content": [ "\nMontague’s semantic analyses were given in terms of a\ntype-logical hierarchy whose basic ingredients were truth values,\npossible individuals, and possible worlds. While the exact nature of\nindividuals and worlds depends on the (arbitrary) choice of a\nparticular model (or ‘Fregean interpretation’), the truth\nvalues 1 (true) and 0 (false) transcend the class of all models, thus\nemphasizing their status as logical objects. A lot of work in current\nlinguistic semantics still applies Montague’s type-logical\nhierarchy, which is however often enriched by events (or,\nmore generally: eventualities) that serve as the referents of\nverbs and verb phrases (Bach 1986a; Parsons 1990).", "\nIn early work on intensional analysis (Carnap 1947, Kaplan 1964),\npossible worlds had been identified with models of a suitable\nextensional language. For reasons indicated in section 3.1, Montague\n(1969, 164) broke with this tradition, appealing to Kripke’s\naccount of modality based on possible worlds as unstructured basic\nobjects. In his essay ‘On the nature of certain philosophical\nentities’ (Montague 1969), he argued that this seemingly minor\ntechnical innovation opens a new perspective in philosophical\nanalysis, by reducing certain ‘dubious’ entities to\npredicate intensions or properties – functions mapping\npossible worlds to sets of objects. The idea was that, once the\nconceptual and techical problems of the semantics of intensional\nlanguages had been overcome, they may replace extensional predicate\nlogic as a basis of philosophical argument:", "\nPhilosophy is always capable of enlarging itself; that is, by\nmetamathematical or model-theoretic means – means available\nwithin set theory – one can “justify” a language or\ntheory that transcends set theory, and then proceed to transact a new\nbranch of philosophy within the new language. It is now time to take\nsuch a step and to lay the foundations of intensional languages.\n(Montague 1969,165f.)\n", "\nMontague illustrated his claim by detailed analyses of (talk about)\npains, tasks, obligations, and events in terms of second-order\nintensional logic, which contained the core elements of his (slightly)\nlater compositional interpretation of English.", "\nAlthough it has since become common in linguistic semantics to analyse\ncontent in terms of possible worlds, they are not always taken to be\ntotally devoid of structure. As a case in point, Kratzer (2002) has\nargued that the verb know relates subjects to facts and thus\nits interpretation requires appeal to the mereology of worlds: facts\nare concrete parts worlds. Moreover, as in Kripke’s original\napproach, semantic theory frequently imposes some external structure\non logical space. Thus, accessibility relations and distance measures\nbetween worlds are invoked to account for, respectively, propositional\nattitudes (along the lines of Hinitkka 1969) and counterfactual\nconditionals (following Lewis 1973). In a similar vein, the universe\nof individuals (or ‘entities’, in Montague’s\nparlance) nowadays gives way to a richer domain of structured objects,\nincluding substances and their parts, which may serve as extensions of\nmass nouns such as water (Pelletier & Schubert 2003), as\nwell as groups and their members, which are denoted by plural noun\nphrases (Link 1983). Also when properties (loving John) are\nconsidered as entities for which predicates may hold (Mary likes\nloving John), additional structure is needed: property theory\ngives the tools to incorporate them (Turner 1983).", "\nOccasional doubts have been raised as to the adequacy of\nMontague’s higher-order intensional logic as a tool for the\nsemantic interpretation of natural language:", "\nIt seems to me that this is the strategy employed by Montague\nGrammarians, who are in fact strongly committed to compositionality.\n[…]. There is a price to be paid however. The higher order\nentities evoked in this “type theoretical ascent” are much\nless realistic philosophically and psycholinguistically than our\noriginal individuals. Hence the ascent is bound to detract from the\npsycholinguistic and methodological realism of one’s theory.\n(Hintikka 1983, 20)\n", "\nThis objection does not appreciate the role played by higher-order\nabstraction in compositional semantics, which is not to form sentences\nabout higher-order functions. Rather, \\(\\lambda\\)-abstraction is used\nas a heuristic tool to describe compositional contributions of\nexpressions to larger syntactic environments (cf. Zimmermann 2021,\nsec. 2.1). Thus, e.g., the extension of a determiner is defined as its\ncontribution to the truth value of a sentence in which it occurs (in\nsubject position), which can be described in terms of the extensions\nof the nouns and verb phrases it combines with – and these\nextensions are themselves sets (by a similar reasoning). The abstract\nhigher-order objects are thus merely convenient ways of describing the\nkinematics of compositionality and do not serve as the objects that\nthe sentences of the language so described are about, or that its\nterms refer to. As a case in point, it can be shown that even though\nthe (indirect) interpretation of the English fragment of Montague 1973\nmakes use of \\(\\lambda\\)-abstraction over second-order variables, its\nexpressive power is much weaker than higher-order type logic and does\nnot even have the resources to formulate certain meaning postulates to\nwhich its lexical items abide (Zimmermann 1983). In fact,\nHintikka’s alternative (game-theoretical) semantics fares no\nbetter once it is formulated in a compositional way (see Hodges 1997\nor Caicedo et al. 2009)." ], "subsection_title": "3.5 Ontology" } ] }, { "main_content": [], "section_title": "4. Concluding Remarks", "subsections": [ { "content": [ "\nMontague revolutionized the field of semantic theory. He introduced\nmethods and tools from mathematical logic, and set standards for\nexplicitness in semantics. Now all semanticists know that logic has\nmore to offer than first-order logic only." ], "subsection_title": "4.1 Legacy" }, { "content": [ "\nA recent introduction is Jacobson 2014. It is a gentle introduction to\nthe field, especially for linguists and philosophers. It presents\nseveral successes obtained by the approach. Older introductions are\nDowty et al. 1981 and Gamut 1991, which are more technical\nand prepare for Montague’s original papers. An overview of the\nhistory of the field is given by Partee and Hendriks (1997) as well as\nPartee (2011); Caponigro (forthcoming) provides an extensive\nbiographical background on Montague. Collections of important papers\nare Portner and Partee (eds.) 2002 and Partee 2004; further\ninformation is provided in the volume edited by McNally and\nSzabó (forthcoming). The ‘Handbook of\ncompositionality’(Werning et al. 2011) discusses many aspects of\nthe approach. The most important journals in the field are\nLinguistics and Philosophy, the Journal of\nSemantics, Natural Language Semantics, and Semantics\nand Pragmatics." ], "subsection_title": "4.2 Further Reading" } ] } ]

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[ "\n\nProof-theoretic semantics is an alternative to truth-condition\nsemantics. It is based on the fundamental assumption that the central\nnotion in terms of which meanings are assigned to certain expressions\nof our language, in particular to logical constants, is that of\nproof rather than truth. In this sense\nproof-theoretic semantics is semantics in terms of proof.\nProof-theoretic semantics also means the semantics of proofs,\ni.e., the semantics of entities which describe how we arrive at certain\nassertions given certain assumptions. Both aspects of proof-theoretic\nsemantics can be intertwined, i.e. the semantics of proofs is itself\noften given in terms of proofs.", "\n\nProof-theoretic semantics has several roots, the most specific one\nbeing Gentzen’s remarks that the introduction rules in his\ncalculus of natural deduction define the meanings of logical constants,\nwhile the elimination rules can be obtained as a consequence of this\ndefinition (see section\n 2.2.1).\n More\nbroadly, it belongs to what Prawitz called general proof\ntheory (see section\n 1.1).\n Even more\nbroadly, it is part of the tradition according to which the meaning of\na term should be explained by reference to the way it is used\nin our language.", "\n\nWithin philosophy, proof-theoretic semantics has mostly figured\nunder the heading “theory of meaning”. This terminology\nfollows Dummett, who claimed that the theory of meaning is the basis of\ntheoretical philosophy, a view which he attributed to Frege. The term\n“proof-theoretic semantics” was proposed by\nSchroeder-Heister (1991; used already in 1987 lectures in Stockholm) in order not to leave the term\n“semantics” to denotationalism alone—after all,\n“semantics” is the standard term for investigations dealing\nwith the meaning of linguistic expressions. Furthermore, unlike\n“theory of meaning”, the term “proof-theoretic\nsemantics” covers philosophical and technical aspects likewise.\nIn 1999, the first conference with this title took place in\nTübingen, the second one in 2013. The first textbook with this title appeared in 2015. " ]

[ { "content_title": "1. Background", "sub_toc": [ "1.1 General proof theory: consequence vs. proofs", "1.2 Inferentialism, intuitionism, anti-realism", "1.3 Gentzen-style proof theory: Reduction, normalization, cut elimination" ] }, { "content_title": "2. Some versions of proof-theoretic semantics", "sub_toc": [ "2.1 The semantics of implications: Admissibility, derivability, rules", "2.2 The Semantics of derivations as based on introduction rules", "2.3 Clausal definitions and definitional reasoning", "2.4 Structural characterization of logical constants", "2.5 Categorial proof theory" ] }, { "content_title": "3. Extensions and alternatives to standard proof-theoretic semantics", "sub_toc": [ "3.1 Elimination rules as basic", "3.2 Negation and denial", "3.3 Harmony and reflection in the sequent calculus", "3.4 Subatomic structure and natural language", "3.5 Classical logic", "3.6 Hypothetical reasoning", "3.7 Intensional proof-theoretic semantics" ] }, { "content_title": "4. Conclusion and outlook", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] }, { "content_title": "Examples of Proof-theoretic Validity", "sub_toc": [] }, { "content_title": "Definitional Reflection and Paradoxes", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Background", "subsections": [ { "content": [ "\n\nThe term “general proof theory” was coined by Prawitz.\nIn general proof theory, “proofs are studied in their own right\nin the hope of understanding their nature”, in contradistinction\nto Hilbert-style “reductive proof theory”, which is the\n“attempt to analyze the proofs of mathematical theories with the\nintention of reducing them to some more elementary part of mathematics\nsuch as finitistic or constructive mathematics” (Prawitz, 1972,\np. 123). In a similar way, Kreisel (1971) asks for a re-orientation of\nproof theory. He wants to explain “recent work in proof theory\nfrom a neglected point of view. Proofs and their representations by\nformal derivations are treated as principal objects of study, not as\nmere tools for analyzing the consequence relation.” (Kreisel,\n1971, p. 109) Whereas Kreisel focuses on the dichotomy between a theory\nof proofs and a theory of provability, Prawitz concentrates on the\ndifferent goals proof theory may pursue. However, both stress the\nnecessity of studying proofs as fundamental entities by means of which\nwe acquire demonstrative (especially mathematical) knowledge. This\nmeans in particular that proofs are epistemic entities which should not\nbe conflated with formal proofs or derivations. They are rather what\nderivations denote when they are considered to be representations of\narguments. (However, in the following we often use “proof”\nsynonymously with “derivation”, leaving it to the reader to\ndetermine whether formal proofs or proofs as epistemic entities are\nmeant.) In discussing Prawitz’s (1971) survey, Kreisel (1971,\np. 111) explicitly speaks of a “mapping” between\nderivations and mental acts and considers it as a task of proof theory\nto elucidate this mapping, including the investigation of the identity\nof proofs, a topic that Prawitz and Martin-Löf had put on the\nagenda.", "\n\nThis means that in general proof theory we are not solely interested\nin whether B follows from A, but in the way by means\nof which we arrive at B starting from A. In this\nsense general proof theory is intensional and epistemological in\ncharacter, whereas model theory, which is interested in the consequence\nrelation and not in the way of establishing it, is extensional and\nmetaphysical." ], "subsection_title": "1.1 General proof theory: consequence vs. proofs" }, { "content": [ "\n\nProof-theoretic semantics is inherently inferential, as it is\ninferential activity which manifests itself in proofs. It thus belongs\nto inferentialism (see Brandom, 2000) according to which\ninferences and the rules of inference establish the meaning of\nexpressions, in contradistinction to denotationalism,\naccording to which denotations are the primary sort of meaning.\nInferentialism and the ‘meaning-as-use’ view of semantics\nis the broad philosophical framework of proof-theoretic semantics. This\ngeneral philosophical and semantical perspective merged with\nconstructive views which originated in the philosophy of mathematics,\nespecially in mathematical intuitionism. Most forms of proof-theoretic\nsemantics are intuitionistic in spirit, which means in particular that\nprinciples of classical logic such as the law of excluded middle or the\ndouble negation law are rejected or at least considered problematic.\nThis is partly due to the fact that the main tool of proof-theoretic\nsemantics, the calculus of natural deduction, is biased towards\nintuitionistic logic, in the sense that the straightforward formulation\nof its elimination rules is the intuitionistic one. There classical\nlogic is only available by means of some rule of indirect proof, which,\nat least to some extent, destroys the symmetry of the reasoning\nprinciples (see section\n 3.5).\n If one adopts\nthe standpoint of natural deduction, then intuitionistic logic is a\nnatural logical system. Also the BHK (Brouwer-Heyting-Kolmogorov)\ninterpretation of the logical signs plays a significant role. This\ninterpretation is not a unique approach to semantics, but comprises\nvarious ideas which are often more informally than formally described.\nOf particular importance is its functional view of implication,\naccording to which a proof of A → B is a\nconstructive function which, when applied to a proof of A\nyields a proof of B. This functional perspective underlies\nmany conceptions of proof-theoretic semantics, in particular those of\nLorenzen, Prawitz and Martin Löf (see sections\n 2.1.1,\n 2.2.2,\n 2.2.3).", "\n\nAccording to Dummett, the logical position of intuitionism\ncorresponds to the philosophical position of anti-realism. The realist\nview of a recognition independent reality is the metaphysical\ncounterpart of the view that all sentences are either true or false\nindependent of our means of recognizing it. Following Dummett, major\nparts of proof-theoretic semantics are associated with\nanti-realism." ], "subsection_title": "1.2 Inferentialism, intuitionism, anti-realism" }, { "content": [ "\n\nGentzen’s calculus of natural deduction and its rendering by\nPrawitz is the background to most approaches to proof-theoretic\nsemantics. Natural deduction is based on at least three major\nideas:", "\n\nIn Gentzen’s natural deduction system for first-order logic\nderivations are written in tree form and based on the well-known rules.\nFor example, implication has the following introduction and elimination\nrules", "\n\n\n\n \n \n [A]\n \n \n \n B\n   →I\n \n \n A→B\n \n \n\n        \n\n\n \n  \n \n A→B  A\n   →E\n \n \n B\n \n \n\n\n\n", "\n\nwhere the brackets indicate the possibility to discharge occurrences\nof the assumption A. The open assumptions of a\nderivation are those assumptions on which the end-formula depends. A\nderivation is called closed, if it has no open assumption,\notherwise it is called open. If we deal with quantifiers, we\nhave to consider open individual variables (sometimes called\n“parameters”), too. Metalogical features crucial for\nproof-theoretic semantics and for the first time systematically\ninvestigated and published by Prawitz (1965) include:", "\n\nReduction: For every detour consisting of an introduction\nimmediately followed by an elimination there is a reduction step\nremoving this detour.", "\n\nNormalization: By successive applications of reductions,\nderivations can be transformed into normal forms which contain no\ndetours.", "\n\nFor implication the standard reduction step removing detours is the\nfollowing:", "\n\n\n\n \n [A] \n ⋮ \n B\n     \n |\n A→B\n     \n A\n B\n \n\n\n     reduces to     \n\n\n \n |A⋮B\n \n\n\n\n", "\n\nA simple, but very important corollary of normalization is the\nfollowing: Every closed derivation in intuitionistic logic can be\nreduced to a derivation using an introduction rule in the last\nstep. We also say that intuitionistic natural deduction satisfies\nthe “introduction form property”. In\nproof-theoretic semantics this result figures prominently under the\nheading “fundamental assumption” (Dummett, 1991,\np. 254). The “fundamental assumption” is a typical\nexample of a philosophical re-interpretation of a technical\nproof-theoretic result.", "Further Reading:", "\n\nFor the general orientation of proof-theoretic semantics\nthe special issue of Synthese (Kahle and Schroeder-Heister,\n2006) the reader edited by Piecha and Schroeder-Heister (2016b), the textbook by Francez (2015), Schroeder-Heister (2008b, 2016a), and Wansing (2000).", "\n\nFor the philosophical position and development of proof\ntheory the entries on\n Hilbert’s program\nand the\n development of proof theory\nas well as Prawitz (1971).", "\n\nFor intuitionism the entries on\n intuitionistic logic,\n intuitionism in the philosophy of mathematics\nand the\n development of intuitionistic logic.", "\n\nFor anti-realism the entry on \n challenges to metaphysical realism\n as well as Tennant (1987); Tennant (1997), Tranchini (2010);\nTranchini (2012a).", "\n\nFor Gentzen-style proof-theory and the theory of natural\ndeduction: besides Gentzen’s (1934/35) original presentation,\nJaśkowski’s (1934) theory of suppositions and Prawitz’s (1965)\nclassic monograph, Tennant (1978), Troelstra and Schwichtenberg\n(2000), and Negri and von Plato (2001)." ], "subsection_title": "1.3 Gentzen-style proof theory: Reduction, normalization, cut elimination" } ] }, { "main_content": [], "section_title": "2. Some versions of proof-theoretic semantics", "subsections": [ { "content": [ "\n\nThe semantics of implication lies at the heart of proof-theoretic\nsemantics. In contradistinction to classical truth-condition semantics,\nimplication is a logical constant in its own right. It has also the\ncharacteristic feature that it is tied to the concept of consequence.\nIt can be viewed as expressing consequence at the sentential level due\nto modus ponens and to what in Hilbert-style systems is called the\ndeduction theorem, i.e. the equivalence of Γ,A ⊢\nB and Γ ⊢ A → B.", "\n\nA very natural understanding of an implication A →\nB is reading it as expressing the inference rule which allows\none to pass over from A to B. Licensing the step from\nA to B on the basis of A → B\nis exactly, what modus ponens says. And the deduction theorem can be\nviewed as the means of establishing a rule: Having shown that\nB can be deduced from A justifies the rule that from\nA we may pass over to B. A rule-based semantics of\nimplication along such lines underlies several conceptions of\nproof-theoretic semantics, notably those by Lorenzen, von Kutschera and\nSchroeder-Heister.", "\n\nLorenzen, in his Introduction to Operative Logics and\nMathematics (1955) starts with logic-free (atomic) calculi, which\ncorrespond to production systems or grammars. He calls a rule\nadmissible in such a system if it can be added to it without\nenlarging the set of its derivable atoms. The implication arrow →\nis interpreted as expressing admissibility. An implication A\n→ B is considered to be valid, if, when read as a rule,\nit is admissible (with respect to the underlying calculus). For\niterated implications (= rules) Lorenzen develops a theory of\nadmissibility statements of higher levels. Certain statements such as\nA →A or ((A →B),\n(B →C)) → (A →C)\nhold independently of the underlying calculus. They are called\nuniversally admissible\n[“allgemeinzulässig”]), and constitute a system of\npositive implicational logic. In a related way, laws for universal\nquantification ∀ are justified using admissibility\nstatements for rules with schematic variables.", "\n\nFor the justification of the laws for the logical constants ∧,\n∨, ∃ and ⊥, Lorenzen uses an inversion\nprinciple (a term he coined). In a very simplified form, without\ntaking variables in rules into account, the inversion principle says\nthat everything that can be obtained from every defining condition of\nA can be obtained from A itself. For example, in the\ncase of disjunction, let A and B each be a\ndefining condition of A∨B as expressed by the\nprimitive rules A → A∨B and\nB → A∨B. Then the inversion\nprinciple says that A∨B →C is\nadmissible assuming A →C and B\n→C, which justifies the elimination rule for disjunction.\nThe remaining connectives are dealt with in a similar way. In the case\nof ⊥, the absurdity rule ⊥→ A is obtained from\nthe fact that there is no defining condition for ⊥.", "\n\nIn what he calls “Gentzen semantics”, von Kutschera\n(1968) gives, as Lorenzen, a semantics of logically complex\nimplication-like statements\nA1,…,An\n→ B with respect to calculi K which govern the\nreasoning with atomic sentences. The fundamental difference to Lorenzen\nis the fact that\nA1,…,An\n→ B now expresses a derivability rather than an\nadmissibility statement.", "\n\nIn order to turn this into a semantics of the logical constants of\npropositional logic, von Kutschera argues as follows: When giving up\nbivalence, we can no longer use classical truth-value assignments to\natomic formulas. Instead we can use calculi which prove or refute\natomic sentences. Moreover, since calculi not only generate proofs or\nrefutations but arbitrary derivability relations, the idea is to start\ndirectly with derivability in an atomic system and extend it with rules\nthat characterize the logical connectives. For that von Kutschera gives\na sequent calculus with rules for the introduction of n-ary\npropositional connectives in the succedent and antecedent, yielding a\nsequent system for generalized propositional connectives. Von Kutschera\nthen goes on to show that the generalized connectives so defined can\nall be expressed by the standard connectives of intuitionistic logic\n(conjunction, disjunction, implication, absurdity).", "\n\nWithin a programme of developing a general schema for rules for\narbitrary logical constants, Schroeder-Heister (1984) proposed that a\nlogically complex formula should express the content or common\ncontent of systems of rules. This means that not the\nintroduction rules are considered basic but the consequences of\ndefining conditions. A rule R is either a formula A\nor has the form\nR1,…,Rn\n⇒ A, where\nR1,…,Rn\nare themselves rules. These so-called “higher-level rules”\ngeneralize the idea that rules may discharge assumptions to the case\nwhere these assumptions can themselves be rules. For the standard\nlogical constants this means that A∧B expresses\nthe content of the pair (A,B); A → B\nexpresses the content of the rule A ⇒ B;\nA∨B expresses the common content of A and\nB; and absurdity ⊥ expresses the common content of the\nempty family of rule systems. In the case of arbitrary n-ary\npropositional connectives this leads to a natural deduction system with\ngeneralized introduction and elimination rules. These general\nconnectives are shown to be definable in terms of the standard ones,\nestablishing the expressive completeness of the standard intuitionistic\nconnectives.", "\n\nFor Lorenzen’s approach in relation to Prawitz-style\nproof-theoretic semantics: Schroeder-Heister (2008a). For extensions of\nexpressive completeness in the style of von Kutschera: Wansing\n(1993a)." ], "subsection_title": "2.1 The semantics of implications: Admissibility, derivability, rules" }, { "content": [ "\n\nIn his Investigations into Logical Deduction, Gentzen makes\nsome, nowadays very frequently quoted, programmatic remarks on the\nsemantic relationship between introduction and elimination inferences\nin natural deduction.", "\n\nThe introductions represent, as it were, the\n‘definitions’ of the symbols concerned, and the\neliminations are no more, in the final analysis, than the consequences\nof these definitions. This fact may be expressed as follows: In\neliminating a symbol, we may use the formula with whose terminal symbol\nwe are dealing only ‘in the sense afforded it by the introduction\nof that symbol’. (Gentzen, 1934/35, p. 80)", "\n\nThis cannot mean, of course, that the elimination rules are\ndeducible from the introduction rules in the literal sense of\nthe word; in fact, they are not. It can only mean that they can be\njustified by them in some way.", "\n\nBy making these ideas more precise it should be possible to display\nthe E-inferences as unique functions of their corresponding\nI-inferences, on the basis of certain requirements. (ibid.,\np. 81)", "\n\nSo the idea underlying Gentzen’s programme is that we have\n“definitions” in the form of introduction rules and some\nsort of semantic reasoning which, by using “certain\nrequirements”, validate the elimination rules.", "\n\nBy adopting Lorenzen’s term and adapting its underlying idea\nto the context of natural deduction, Prawitz (1965) formulated an\n“inversion principle” to make Gentzen’s remarks more\nprecise:", "\n\nLet α be an application of an elimination rule that\nhas B as consequence. Then, deductions that satisfy the\nsufficient condition […] for deriving the major premiss of\nα, when combined with deductions of the minor premisses\nof α (if any), already “contain” a deduction\nof B; the deduction of B is thus obtainable directly\nfrom the given deductions without the addition of α.\n(p. 33)", "\n\nHere the sufficient conditions are given by the premisses of the\ncorresponding introduction rules. Thus the inversion principle says\nthat a derivation of the conclusion of an elimination rule can be\nobtained without an application of the elimination rule if its major\npremiss has been derived using an introduction rule in the last step,\nwhich means that a combination", "\n\n\n\n \n ⋮\n I-inference\n \n A\n \n\n\n {Di}\n\n E-inference\n\n\n\nB\n\n\n", "\n\nof steps, where {Di} stands for a\n(possibly empty) list of deductions of minor premisses, can be\navoided.", "\n\nThe relationship between introduction and elimination rules is often\ndescribed as “harmony”, or as governed by a\n“principle of harmony” (see, e.g. Tennant, 1978,\np. 74). This terminology is not uniform and sometimes not even\nfully clear. It essentially expresses what is also meant by\n“inversion”. Even if “harmony” is a term which\nsuggests a symmetric relationship, it is frequently understood as\nexpressing a conception based on introduction rules as, e.g., in\nRead’s (2010) “general elimination harmony” (although\noccasionally one includes elimination based conceptions as well).\nSometimes harmony is supposed to mean that connectives are strongest or\nweakest in a certain sense given their introduction or their\nelimination rules. This idea underlies Tennant’s (1978) harmony\nprinciple, and also Popper’s and Koslow’s structural\ncharacterizations (see section\n 2.4).\n The\nspecific relationship between introduction and elimination rules as\nformulated in an inversion principle excludes alleged inferential\ndefinitions such as that of the connective tonk, which\ncombines an introduction rule for disjunction with an elimination rule\nfor conjunction, and which has given rise to a still ongoing debate on\nthe format of inferential definitions (see Humberstone, 2010).", "\n\nProof-theoretic validity is the dominating approach to\nproof-theoretic semantics. As a technical concept it was developed by\nPrawitz (1971; 1973; 1974), by turning a proof-theoretic validity\nnotion based on ideas by Tait (1967) and originally used to prove\nstrong normalization, into a semantical concept. Dummett provided much\nphilosophical underpinning to this notion (see Dummett, 1991). The\nobjects which are primarily valid are proofs as representations of\narguments. In a secondary sense, single rules can be valid if they lead\nfrom valid proofs to valid proofs. In this sense, validity is a global\nrather than a local notion. It applies to arbitrary derivations over a\ngiven atomic system, which defines derivability for atoms. Calling a\nproof which uses an introduction rule in the last step\ncanonical, it is based on the following three ideas:", "\n\nAd 1: The definition of validity is based on\nGentzen’s idea that introduction rules are\n‘self-justifying’ and give the logical constants their\nmeaning. This self-justifying feature is only used for closed proofs,\nwhich are considered primary over open ones.", "\n\nAd 2: Noncanonical proofs are justified by reducing them to\ncanonical ones. Thus reduction procedures (detour reductions) as used\nin normalization proofs play a crucial role. As they justify arguments,\nthey are also called “justifications” by Prawitz. This\ndefinition again only applies to closed proofs, corresponding to the\nintroduction form property of closed normal derivations in natural\ndeduction (see section\n 1.3).", "\n\nAd 3: Open proofs are justified by considering their closed\ninstances. These closed instances are obtained by replacing their open\nassumptions with closed proofs of them, and their open variables with\nclosed terms. For example, a proof of B from A is\nconsidered valid, if every closed proof, which is obtained by replacing\nthe open assumption A with a closed proof of A, is\nvalid. In this way, open assumptions are considered to be placeholders\nfor closed proofs, for which reason we may speak of a substitutional\ninterpretation of open proofs.", "\n\nThis yields the following definition of proof-theoretic\nvalidity:", "\n\nFormally, this definition has to be relativized to the atomic system\nconsidered, and to the set of justifications (proof reductions)\nconsidered. Furthermore, proofs are here understood as\ncandidates of valid proofs, which means that the rules from\nwhich they are composed are not fixed. They look like proof trees, but\ntheir individual steps can have an arbitrary (finite) number of\npremisses and can eliminate arbitrary assumptions. The definition of\nvalidity singles out those proof structures which are\n‘real’ proofs on the basis of the given reduction\nprocedures.", "\n\nValidity with respect to every choice of an atomic system can be\nviewed as a generalized notion of logical validity. In fact, if we\nconsider the standard reductions of intuitionistic logic, then all\nderivations in intuitionistic logic are valid independent of the atomic\nsystem considered. This is semantical correctness. We may ask\nif the converse holds, viz. whether, given that a derivation is valid\nfor every atomic system, there is a corresponding derivation in\nintuitionistic logic. That intuitionistic logic is complete in this\nsense is known as Prawitz’s conjecture (see Prawitz, 1973;\nPrawitz, 2013). However, no satisfactory proof of it has been given.\nThere are considerable doubts concerning the validity of this\nconjecture for systems that go beyond implicational logic. In any case\nit will depend on the precise formulation of the notion of validity, in\nparticular on its handling of atomic systems.", "\n\nFor a more formal definition and detailed examples demonstrating\nvalidity, as well as some remarks on Prawitz’s conjecture\n see the", "\n Supplement on Examples of proof-theoretic validity.\n", "\n\nMartin-Löf’s type theory (Martin-Löf, 1984) is a\nleading approach in constructive logic and mathematics.\nPhilosophically, it shares with Prawitz the three fundamental\nassumptions of standard proof-theoretic semantics, mentioned in\n section\n 2.2.2:\n the priority of closed canonical\nproofs, the reduction of closed non-canonical proofs to canonical ones\nand the substitutional view of open proofs. However,\nMartin-Löf’s type theory has at least two characteristic\nfeatures which go beyond other approaches in proof-theoretic\nsemantics:", "\n\nThe first idea goes back to the Curry-Howard correspondence (see de\nGroote, 1995; Sørensen and Urzyczyn, 2006), according to which\nthe fact that a formula A has a certain proof can be codified\nas the fact that a certain term t is of type A,\nwhereby the formula A is identified with the type A.\nThis can be formalized in a calculus for type assignment, whose\nstatements are of the form t : A. A proof of\nt : A in this system can be read as showing that\nt is a proof of A. Martin-Löf (1995; 1998) has\nput this into a philosophical perspective by distinguishing this\ntwo-fold sense of proof in the following way. First we have proofs of\nstatements of the form t : A. These statements are\ncalled judgements, their proofs are called\ndemonstrations. Within such judgements the term\nt represents a proof of the proposition\nA. A proof in the latter sense is also called a proof\nobject. When demonstrating a judgement t : A, we\ndemonstrate that t is a proof (object) for the proposition\nA. Within this two-layer system the demonstration\nlayer is the layer of argumentation. Unlike proof objects,\ndemonstrations have epistemic significance; their judgements carry\nassertoric force. The proof layer is the layer at which meanings are\nexplained: The meaning of a proposition A is explained by\ntelling what counts as a proof (object) for A. The distinction\nmade between canonical and non-canonical proofs is a distinction at the\npropositional and not at the judgement al layer. This implies a certain\nexplicitness requirement. When I have proved something, I must not\nonly have a justification for my proof at my disposal as in\nPrawitz’s notion of validity, but at the same time have to be\ncertain that this justification fulfills its purpose. This\ncertainty is guaranteed by a demonstration. Mathematically, this\ntwo-fold sense of proof develops its real power only when types may\nthemselves depend on terms. Dependent types are a basic ingredient of\nof Martin-Löf’s type theory and related approaches.", "\n\nThe second idea makes Martin-Löf’s approach strongly\ndiffer from all other definitions of proof-theoretic validity. The\ncrucial difference, for example, to Prawitz’s procedure is that\nit is not metalinguistic in character, where\n“metalinguistic” means that propositions and candidates of\nproofs are specified first and then, by means of a definition in the\nmetalanguage, it is fixed which of them are valid and which are not.\nRather, propositions and proofs come into play only in the context of\ndemonstrations. For example, if we assume that something is a proof of\nan implication A → B, we need not necessarily\nshow that both A and B are well-formed propositions\noutright, but, in addition to knowing that A is a proposition,\nwe only need to know that B is a proposition provided\nthat A has been proved. Being a proposition is\nexpressed by a specific form of judgement, which is established in the\nsame system of demonstration which is used to establish that a proof of\na proposition has been achieved.", "\n\nIn Martin-Löf’s theory, proof-theoretic semantics\nreceives a strongly ontological component. A recent debate deals with\nthe question of whether proof objects have a purely ontological status\nor whether they codify knowledge, even if they are not epistemic acts\nthemselves.", "\n\nFor inversion principles see Schroeder-Heister (2007).", "\n\nFor variants of proof-theoretic harmony see Francez (2015) and Schroeder-Heister (2016a). \n\nFor Prawitz’s definition of proof-theoretic validity\nsee Schroeder-Heister (2006).", "\n\nFor Matin-Löf’s type theory, see the entry on\n type theory\nas well as Sommaruga (2000)." ], "subsection_title": "2.2 The Semantics of derivations as based on introduction rules" }, { "content": [ "\n\nProof-theoretic semantics normally focuses on logical constants.\nThis focus is practically never questioned, apparently because it is\nconsidered so obvious. In proof theory, little attention has been paid\nto atomic systems, although there has been Lorenzen’s early work\n(see section\n 2.1.1),\n where the\njustification of logical rules is embedded in a theory of arbitrary\nrules, and Martin-Löf’s (1971) theory of iterated inductive\ndefinitions where introduction and elimination rules for atomic\nformulas are proposed. The rise of logic programming has widened this\nperspective. From the proof-theoretic point of view, logic programming\nis a theory of atomic reasoning with respect to clausal definitions of\natoms. Definitional reflection is an approach to proof-theoretic\nsemantics that takes up this challenge and attempts to build a theory\nwhose range of application goes beyond logical constants.", "\n\nIn logic programming we are dealing with program clauses of the\nform", "\n A ⇐ B1, …, Bm\n", "\n\nwhich define atomic formulas. Such clauses can naturally be\ninterpreted as describing introduction rules for atoms. From the point\nof view of proof-theoretic semantics the following two points are\nessential:", "\n\n(1)  Introduction rules (clauses) for logically compound\nformulas are not distinguished in principle from introduction rules\n(clauses) for atoms. Interpreting logic programming proof-theoretically\nmotivates an extension of proof-theoretic semantics to arbitrary atoms,\nwhich yields a semantics with a much wider realm of applications.", "\n\n(2)  Program clauses are not necessarily well-founded. For\nexample, the head of a clause may occur in its body. Well-founded\nprograms are just a particular sort of programs. The use of arbitrary\nclauses without further requirements in logic programming is a\nmotivation to pursue the same idea in proof-theoretic semantics,\nadmitting just any sort of introduction rules and not just those of a\nspecial form, and in particular not necessarily ones which are\nwell-founded. This carries the idea of definitional freedom, which is a\ncornerstone of logic programming, over to semantics, again widening the\nrealm of application of proof-theoretic semantics.", "\n\nThe idea of considering introduction rules as meaning-giving rules\nfor atoms is closely related to the theory of inductive definitions in\nits general form, according to which inductive definitions are systems\nof rules (see Aczel, 1977).", "\n\nThe theory of definitional reflection (Hallnäs, 1991;\nHallnäs, 2006; Hallnäs and Schroeder-Heister, 1990/91;\nSchroeder-Heister, 1993) takes up the challenge from logic programming\nand gives a proof-theoretic semantics not just for logical constants\nbut for arbitrary expressions, for which a clausal definition can be\ngiven. Formally, this approach starts with a list of clauses which is\nthe definition considered. Each clause has the form", "\n A ⇐ Δ\n", "\n\nwhere the head A is an atomic formula (atom). In the\nsimplest case, the body Δ is a list of atoms\nB1,…,Bm,\nin which case a definition looks like a definite logic program. We\noften consider an extended case where Δ may also contain some\nstructural implication ‘⇒’, and sometimes even some\nstructural universal implication, which essentially is handled by\nrestricting substitution. If the definition of A has the\nform", "\n \n", "\n\nthen A has the following introduction and elimination\nrules", "\n\n\n \n Δ1\n   · · ·  \n Δn\n \n A\n A\n\n\n\n\n\n \n [Δ1]\n \n [Δn]\n \n \n A  \n C\n  · · · \n C\n \n C\n \n\n\n", "\n\nThe introduction rules, also called rules of definitional\nclosure, express reasoning ‘along’ the clauses. The\nelimination rule is called the principle of definitional\nreflection, as it reflects upon the definition as a whole. If\nΔ1,…,\nΔn exhaust all possible conditions\nto generate A according to the given definition, and if each\nof these conditions entails the very same conclusion C, then\nA itself entails this conclusion. If the clausal definition \nis viewed as an inductive definition, this principle can be viewed as\nexpressing the extremal clause in inductive definitions: Nothing else\nbeyond the clauses given defines A. Obviously, definitional\nreflection is a generalized form of the inversion principles discussed.\nIt develops its genuine power in definitional contexts with free\nvariables that go beyond purely propositional reasoning, and in\ncontexts which are not well-founded. An example of a non-wellfounded\ndefinition is the definition of an atom R by its own\nnegation:", "\n \n", "\n\nThis example is discussed in detail in the", "\n Supplement on Definitional reflection and paradoxes.\n", "\n\nFor non-wellfoundedness and paradoxes see the entries\non\n self-reference and\n Russell’s paradox,\nas well as the references quoted in the supplement linked to." ], "subsection_title": "2.3 Clausal definitions and definitional reasoning" }, { "content": [ "\n\nThere is a large field of ideas and results concerning what might be\ncalled the “structural characterization” of logical\nconstants, where “structural” is here meant both in the\nproof-theoretic sense of “structural rules” and in the\nsense of a framework that bears a certain structure, where this\nframework is again proof-theoretically described. Some of its authors\nuse a semantical vocabulary and at least implicitly suggest that their\ntopic belongs to proof-theoretic semantics. Others explicitly deny\nthese connotations, emphasizing that they are interested in a\ncharacterization which establishes the logicality of a constant. The\nquestion “What is a logical constant?” can be answered in\nproof-theoretic terms, even if the semantics of the constants\nthemselves is truth-conditional: Namely by requiring that the (perhaps\ntruth-conditionally defined) constants show a certain inferential\nbehaviour that can be described in proof-theoretic terms. However, as\nsome of the authors consider their characterization at the same time as\na semantics, it is appropriate that we mention some of these approaches\nhere.", "\n\nThe most outspoken structuralist with respect to logical constants,\nwho explicitly understands himself as such, is Koslow. In his\nStructuralist Theory of Logic (1992) he develops a theory of\nlogical constants, in which he characterizes them by certain\n“implication relations”, where an implication relation\nroughly corresponds to a finite consequence relation in Tarski’s\nsense (which again can be described by certain structural rules of a\nsequent-style system). Koslow develops a structural theory in the\nprecise metamathematical sense, which does not specify the domain of\nobjects in any way beyond the axioms given. If a language or any other\ndomain of objects equipped with an implication relation is given, the\nstructural approach can be used to single out logical compounds by\nchecking their implicational properties.", "\n\nIn his early papers on the foundations of logic, Popper (1947a;\n1947b) gives inferential characterizations of logical constants in\nproof-theoretic terms. He uses a calculus of sequents and characterizes\nlogical constants by certain derivability conditions of such sequents.\nHis terminology clearly suggests that he intends a proof-theoretic\nsemantics of logical constants, as he speaks of “inferential\ndefinitions” and the “trivialization of mathematical\nlogic” achieved by defining constants in the way described.\nAlthough his presentation is not free from conceptual imprecision and\nerrors, he was the first to consider the sequent-style inferential\nbehaviour of logical constants to characterize them. This is all the\nmore remarkable as he was probably not at all, and definitely not fully\naware of Gentzen’s sequent calculus and Gentzen’s further\nachievements (he was in correspondence with Bernays, though). However,\nagainst his own opinion, his work can better be understood as an\nattempt to define the logicality of constants and to structurally\ncharacterize them, than as a proof-theoretic semantics in the genuine\nsense. He nevertheless anticipated many ideas now common in\nproof-theoretic semantics, such as the characterization of logical\nconstants by means of certain minimality or maximality conditions with\nrespect to introduction or elimination rules.", "\n\nImportant contributions to the logicality debate that characterize\nlogical constants inferentially in terms of sequent calculus rules are\nthose by Kneale (1956) and Hacking (1979). A thorough account of\nlogicality is proposed by Došen (1980; 1989) in\nhis theory of logical constants as “punctuation marks”,\nexpressing structural features at the logical level. He understands\nlogical constants as being characterized by certain double-line rules\nfor sequents which can be read in both directions. For example,\nconjunction and disjunction are (in classical logic, with\nmultiple-formulae succedents) characterized by the double-line\nrules", "\n\n\n\n \n \n Γ⊢A, Δ     Γ⊢B, Δ \n \n\n \n Γ⊢ A∧B, Δ\n \n \n\n       \n\n \n \n Γ, A⊢ Δ     Γ, B⊢ Δ \n \n\n \n Γ⊢ A∨B, Δ\n \n \n\n\n\n", "\n\nDošen is able to give characterizations which include systems\nof modal logic. He explicitly considers his work as a contribution to\nthe logicality debate and not to any conception of proof-theoretic\nsemantics. Sambin et al., in their Basic Logic (Sambin, Battilotti, and\nFaggian, 2000), explicitly understand what Došen calls\ndouble-line rules as fundamental meaning giving rules. The double-line\nrules for conjunction and disjunction are read as implicit definitions\nof these constants, which by some procedure can be turned into the\nexplicit sequent-style rules we are used to. So Sambin et al. use the\nsame starting point as Došen, but interpret it not as a\nstructural description of the behaviour of constants, but semantically\nas their implicit definition (see Schroeder-Heister, 2013).", "\n\nThere are several other approaches to a uniform proof-theoretic\ncharacterization of logical constants, all of whom at least touch upon\nissues of proof-theoretic semantics. Such theories are Belnap’s\nDisplay Logic (Belnap, 1982), Wansing’s Logic of Information\nStructures (Wansing, 1993b), generic proof editing systems and their\nimplementations such as the Edinburgh logical framework (Harper,\nHonsell, and Plotkin, 1987) and many successors which allow the\nspecification of a variety of logical systems. Since the rise of linear\nand, more generally, substructural logics (Di Cosmo and Miller, 2010;\nRestall, 2009) there are various approaches dealing with logics that\ndiffer with respect to restrictions on their structural rules. A\nrecent movement away from singling out a particular logic as the true\none towards a more pluralist stance (see, e.g., Beall and Restall,\n2006) which is interested in what different logics have in common\nwithout any preference for a particular logic can be seen as a shift\naway from semantical justification towards structural\ncharacterization." ], "subsection_title": "2.4 Structural characterization of logical constants" }, { "content": [ "\n\n\nThere is a considerable literature on category theory in relation to\nproof theory, and, following seminal work by Lawvere, Lambek and others\n(see Lambek and Scott, 1986, and the references therein), category\nitself can be viewed as a kind of abstract proof theory. If one looks\nat an arrow A → B in a category as a kind of\nabstract proof of B from A, we have a representation\nwhich goes beyond pure derivability of B from A (as\nthe arrow has its individuality), but does not deal with the particular\nsyntactic structure of this proof. For intuitionistic systems,\nproof-theoretic semantics in categorial form comes probably closest to\nwhat denotational semantics is in the classical case.", "\n\nOne of the most highly developed approaches to categorial proof theory is due to Došen. He has not only advanced the application of categorial methods in proofs theory (e.g., Došen and Petrić, 2004), but also shown how proof-theoretic methods can be used in category theory itself (Došen, 2000). Most important for categorial logic in relation to proof-theoretic semantics is that in categorial logic, arrows always come together with an identity relation, which in proof-theory corresponds to the identity of proofs. In this way, ideas and results of categorial proof theory pertain to what may be called intensional proof-theoretic semantics, that is, the study of proofs as entities in their own right, not just as vehicles to establish consequences (Došen, 2006, 2016). Another feature of categorial proof-theory is that it is inherently hypothetical in character, which means that it starts from hypothetical entities. It this way it overcomes a paradigm of standard, in particular validity-based, proof-theoretic semantics (see section 3.6 below).", "\nFurther Reading:", "\n\nFor Popper’s theory of logical constants see\nSchroeder-Heister (2005).", "\n\nFor logical constants and their logicality see the\nentry on\n logical constants.", "\n\nFor categorial approaches see the entry on\n category theory." ], "subsection_title": "2.5 Categorial proof theory" } ] }, { "main_content": [], "section_title": "3. Extensions and alternatives to standard proof-theoretic semantics", "subsections": [ { "content": [ "\n\nMost approaches to proof-theoretic semantics consider introduction\nrules as basic, meaning giving, or self-justifying, whereas the\nelimination inferences are justified as valid with respect to the given\nintroduction rules. This conception has at least three roots: The first\nis a verificationist theory of meaning according to which the\nassertibility conditions of a sentence constitute its meaning. The\nsecond is the idea that we must distinguish between what gives the\nmeaning and what are the consequences of this meaning, as not all\ninferential knowledge can consist of applications of definitions. The\nthird one is the primacy of assertion over other speech acts such as\nassuming or denying, which is implicit in all approaches considered so\nfar.", "\n\nOne might investigate how far one gets by considering elimination\nrules rather than introduction rules as a basis of proof-theoretic\nsemantics. Some ideas towards a proof-theoretic semantics based on\nelimination rather than introduction rules have been sketched by\nDummett (1991, Ch. 13), albeit in a very rudimentary form. A more\nprecise definition of validity based on elimination inferences is due\nto Prawitz (1971; 2007; see also Schroeder-Heister 2015). Its essential idea is that a closed proof is\nconsidered valid, if the result of applying an elimination rule to its\nend formula is a valid proof or reduces to one. For example, a closed\nproof of an implication A → B is valid, if, for\nany given closed proof of A, the result of applying modus\nponens", "\n\n A → B   A\n B\n\n\n", "\n\nto these two proofs is a valid proof of B, or reduces to\nsuch a proof. This conception keeps two of the three basic ingredients\nof Prawitz-style proof-theoretic semantics (see section\n 2.2.2):\n the role of proof reduction and the\nsubstitutional view of assumptions. Only the canonicity of proofs\nending with introductions is changed into the canonicity of proofs\nending with eliminations." ], "subsection_title": "3.1 Elimination rules as basic" }, { "content": [ "\n\nStandard proof-theoretic semantics is assertion-centred in that\nassertibility conditions determine the meaning of logical constants.\nCorresponding to the intuitionistic way of proceeding, the negation\n¬A of a formula A is normally understood as\nimplying absurdity A →⊥, where ⊥ is a\nconstant which cannot be asserted, i.e., for which no assertibility\ncondition is defined. This is an ‘indirect’ way of\nunderstanding negation. In the literature there has been the discussion\nof what, following von Kutschera (1969), might be called\n‘direct’ negation. By that one understands a one-place\nprimitive operator of negation, which cannot be, or at least is not,\nreduced to implying absurdity. It is not classical negation either. It\nrather obeys rules which dualize the usual rules for the logical\nconstants. Sometimes it is called the “denial” of a\nsentence, sometimes also “strong negation” (see Odintsov,\n2008). Typical rules for the denial ~A of A are", "\n\n \n ~A   ~B\n       \n ~A\n    \n ~B\n \n \n ~(A∨B)\n \n ~(A∧B)\n \n ~(A∧B)\n \n\n\n", "\n\nEssentially, the denial rules for an operator correspond to the\nassertion rules for the dual operator. Several logics of denial have\nbeen investigated, in particular Nelson’s logics of\n“constructible falsity” motivated first by Nelson (1949)\nwith respect to a certain realizability semantics. The main focus has\nbeen on his systems later called N3 and N4 which differ with respect to\nthe treatment of contradiction (N4 is N3 without ex contradictione\nquodlibet). Using denial any approach to proof-theoretic semantics\ncan be dualized by just exchanging assertion and denial and turning\nfrom logical constants to their duals. In doing so, one obtains a\nsystem based on refutation (= proof of denial) rather than proof. It\ncan be understood as applying a Popperian view to proof-theoretic\nsemantics.", "\n\nAnother approach would be to not just dualize assertion-centered\nproof-theoretic semantics in favour of a denial-centered\nrefutation-theoretic semantics, but to see the relation between rules\nfor assertion and for denial as governed by an inversion principle or\nprinciple of definitional reflection of its own. This would be a\nprinciple of what might be called\n“assertion-denial-harmony”. Whereas in standard\nproof-theoretic semantics, inversion principles control the\nrelationship between assertions and assumptions (or consequences), such\na principle would now govern the relationship between assertion and\ndenial. Given certain defining conditions of A, it would say\nthat the denial of every defining condition of A leads to the\ndenial of A itself. For conjunction and disjunction it leads\nto the common pairs of assertion and denial rules", "\n\n\n \n A\n    \n B\n       \n ~A   ~B\n \n \n A∨B\n \n A∨B\n \n ~(A∨B)\n \n\n\n\n\n\n \n A   B\n       \n ~A\n    \n ~B\n \n \n A∧B\n \n ~(A∧B)\n \n ~(A∧B)\n \n\n\n", "\n\nThis idea can easily be generalized to definitional reflection,\nyielding a reasoning system in which assertion and denial are\nintertwined. It has parallels to the deductive relations between the\nforms of judgement studied in the traditional square of opposition\n(Schroeder-Heister, 2012a; Zeilberger, 2008). It should be emphasized\nthat the denial operator is here an external sign indicating a form of\njudgement and not as a logical operator. This means in particular that\nit cannot be iterated." ], "subsection_title": "3.2 Negation and denial" }, { "content": [ "\n\nGentzen’s sequent calculus exhibits a symmetry between right\nand left introduction rules which suggest to look for a harmony\nprinciple that makes this symmetry significant to proof-theoretic\nsemantics. At least three lines have been pursued to deal with this\nphenomenon. (i) Either the right-introduction or or the\nleft-introduction rules are considered to be introduction rules. The\nopposite rules (left-introductions and right-introductions,\nrespectively) are then justified using the corresponding elimination\nrules. This means that the methods discussed before are applied to\nwhole sequents rather than formulas within sequents. Unlike these\nformulas, the sequents are not logically structured. Therefore this\napproach builds on definitional reflection, which applies harmony and\ninversion to rules for arbitrarily structured entities rather than for\nlogical composites only. It has been pursued by de Campos Sanz and\nPiecha (2009). (ii) The right- and left-introduction rules are derived\nfrom a characterization in the sense of Došen’s double\nline rules (section\n 2.4),\n which is then read\nas a definition of some sort. The top-down direction of a double-line\nrule is already a right- or a left-introduction rule. The other one can\nbe derived from the bottom-up direction by means of certain principles.\nThis is the basic meaning-theoretic ingredient of Sambin et al.’s\nBasic Logic (Sambin, Battilotti, and Faggian, 2000). (iii) The\nright- and left-introduction rules are seen as expressing an\ninteraction between sequents using the rule of cut. Given either the\nright- or the left-rules, the complementary rules express that\neverything that interacts with its premisses in a certain way so does\nwith its conclusion. This idea of interaction is a generalized\nsymmetric principle of definitional reflection. It can be considered to\nbe a generalization of the inversion principle, using the notion of\ninteraction rather than the derivability of consequences (see\nSchroeder-Heister, 2013). All three approaches apply to the sequent\ncalculus in its classical form, with possibly more than one formula in\nthe succedent of a sequent, including structurally restricted versions\nas investigated in linear and other logics." ], "subsection_title": "3.3 Harmony and reflection in the sequent calculus" }, { "content": [ "\n\nEven if, as in definitional reflection, we are considering\ndefinitional rules for atoms, their defining conditions do not normally\ndecompose these atoms. A proof-theoretic approach that takes the\ninternal structure of atomic sentences into account, has been proposed\nby Wieckowski (2008; 2011; 2016). He uses introduction and elimination rules\nfor atomic sentences, where these atomic sentences are not just reduced\nto other atomic sentences, but to subatomic expressions representing\nthe meaning of predicates and individual names. This can be seen as a\nfirst step towards natural language applications of proof-theoretic\nsemantics. A further step in this direction has been undertaken by\nFrancez, who developed a proof-theoretic semantics for several\nfragments of English (see Francez, Dyckhoff, and Ben-Avi, 2010; Francez\nand Dyckhoff, 2010, Francez and Ben-Avi 2015)." ], "subsection_title": "3.4 Subatomic structure and natural language" }, { "content": [ "\n\nProof-theoretic semantics is intuitionistically biased. This is due\nto the fact that natural deduction as its preferred framework has\ncertain features which make it particularly suited for intuitionistic\nlogic. In classical natural deduction the ex falso\nquodlibet", "\n\n ⊥\n A\n\n\n", "\n\nis replaced with the rule of classical reductio ad\nabsurdum", "\n\n [A → ⊥]\n \n\n\n ⊥\n A\n\n\n \n\n\n", "\n\nIn allowing to discharge A →⊥ in order to infer\nA, this rule undermines the subformula principle.\nFurthermore, in containing both ⊥ and A\n→⊥, it refers to two different logical constants in a single\nrule, so there is no separation of logical constants any more.\nFinally, as an elimination rule for ⊥ it does not follow the\ngeneral pattern of introductions and eliminations. As a consequence, it\ndestroys the introduction form property that every closed\nderivation can be reduced to one which uses an introduction rule in the\nlast step.", "\n\nClassical logic fits very well with the multiple-succedent sequent\ncalculus. There we do not need any additional principles beyond those\nassumed in the intuitionistic case. Just the structural feature of\nallowing for more than one formula in the succedent suffices to obtain\nclassical logic. As there are plausible approaches to establish a\nharmony between right-introductions and left-introduction in the\nsequent calculus (see section\n 3.3),\n classical logic appears to be perfectly\njustified. However, this is only convincing if reasoning is\nappropriately framed as a multiple-conclusion process, even if this\ndoes not correspond to our standard practice where we focus on single\nconclusions. One could try to develop an appropriate intuition by\narguing that reasoning towards multiple conclusions delineates the area\nin which truth lies rather than establishing a single proposition as\ntrue. However, this intuition is hard to maintain and cannot be\nformally captured without serious difficulties. Philosophical\napproaches such as those by Shoesmith and Smiley (1978) and\nproof-theoretic approaches such as proof-nets (see Girard, 1987; Di\nCosmo and Miller, 2010) are attempts in this direction.", "\n\nA fundamental reason for the failure of the introduction form\nproperty in classical logic is the indeterminism inherent in the laws\nfor disjunction. A∨B can be inferred from \nA as well as from B. Therefore, if the disjunction laws were the\nonly way of inferring A∨B, the derivability of\nA∨¬A, which is a key principle of classical\nlogic, would entail that of either A or of ¬A,\nwhich is absurd. A way out of this difficulty is to abolish\nindeterministic disjunction and use instead its classical de Morgan\nequivalent ¬(¬A ∧¬B). This leads\nessentially to a logic without proper disjunction. In the quantifier\ncase, there would be no proper existential quantifier either, as\n∃xA would be understood in the sense of\n¬∀x¬A. If one is prepared to accept\nthis restriction, then certain harmony principles can be formulated for\nclassical logic." ], "subsection_title": "3.5 Classical logic" }, { "content": [ "\n\nStandard approaches to proof-theoretic semantics, especially Prawitz’s\nvalidity-based approach (section 2.2.2), take closed derivations as\nbasic. The validity of open derivations is defined as the transmission\nof validity from closed derivations of the assumptions to a closed\nderivation of the assertion, where the latter is obtained by\nsubstituting a closed derivation for an open assumption. Therefore, if\none calls closed derivations ‘categorical’ and open derivations\n‘hypothetical’, one may characterize this approach as following two\nfundamental ideas: (I) The primacy of the categorical over the\nhypothetical, (II) the transmission view of consequence. These two\nassumptions (I) and (II) may be viewed as dogmas of standard semantics\n(see Schroeder-Heister 2012c). “Standard semantics” here not only\nmeans standard proof-theoretic semantics, but also classical\nmodel-theoretic semantics, where these dogmas are assumed as\nwell. There one starts with the definition of truth, which is the\ncategorical concept, and defines consequence, the hypothetical\nconcept, as the transmission of truth from conditions to\nconsequent. From this point of view, constructive semantics, including\nproof-theoretic semantics, exchange the concept of truth with a\nconcept of construction or proof, and interpret “transmission” in\nterms of a constructive function or procedure, but otherwise leave the\nframework untouched.", "\n\nThere is nothing wrong in principle with these dogmas. However, there\nare phenomena that are difficult to deal with in the standard\nframework. Such a phenomenon is non-wellfoundedness, especially\ncircularity, where we may have consequences without transmission of\ntruth and provability. Another phenomenon are substructural\ndistinctions, where it is crucial to include the structuring of\nassumptions from the very beginning. Moreover, and this is most\ncrucial, we might define things in a certain way without knowing in\nadvance of whether our definition or chain of definitions is\nwell-founded or not. We do not first involve ourselves into the\nmetalinguistic study of the definition we start with, but would like\nto start to reason immediately. This problem does not obtain if we\nrestrict ourselves to the case of logical constants, where the\ndefining rules are trivially well-founded. But the problem arises\nimmediately, when we consider more complicated cases that go beyond\nlogical constants.", "\n\nThis makes it worthwhile to proceed in the other direction and start with the hypothetical concept of consequence, i.e., characterize consequence directly without reducing\nit to the categorical case. Philosophically this means that the categorical concept is a\nlimiting concept of the hypothetical one. In the classical case, truth would be a limiting case of consequence, namely consequence without hypotheses. This program is closely related to the approach of categorial proof theory (section 2.5), which is based on the primacy of hypothetical entities (“arrows”). Formally, it would give preference to the sequent calculus over natural deduction, since the sequent calculus allows the manipulation of the assumption side of a sequence by means of left-introduction rules. " ], "subsection_title": "3.6 Hypothetical reasoning" }, { "content": [ "\n\n A    B\n A∧B\n\n\n", "\n\n \n A∧B\n       \n A∧B\n    \n \n \n A\n \n B\n \n \n\n\n", "\n\nor the pair", "\n\n \n A∧B\n       \n A∧B  A\n    \n \n \n A\n \n B\n \n \n\n\n", "\n\nas the elimination rules for conjunction. The second pair of rules would often be considered to be just a more complicated variant of the pair of projections. However, from an intensional point of view, these two pairs of rules are not identical. Identifying them corresponds to identifying A ∧ B and A ∧ (A → B), which is only extensionally, but not intensionally correct. As Došen has frequently argued (e.g., Došen 1997, 2006), formulas such as A ∧ B and A ∧ (A → B) are equivalent, but not isomorphic. Here “isomorphic” means that when proving one formula from the other and vice versa, we obtain, by combining these two proofs, the identity proof. This is not the case in this example. ", " Pursuing this idea leads to principles of harmony and inversion which are different from the the standard ones. As harmony and inversion lie at the heart of proof-theoretic semantics, many of its issues are touched. Taking the topic of intensionality seriously may reshape many fields of proof-theoretic semantics. And since the identity of proofs is a basic topic of categorial proof theory, the latter will need to receive stronger attention in proof-theoretic semantics than is currently the case. ", "\n\nFurther Reading", "\n\nFor negation and denial see Tranchini (2012b); Wansing\n(2001).", "\n\nFor natural language semantics see \n Francez (2015).", "\n\nFor classical logic see the entry on\n classical logic.", "\n\nFor hypothetical reasoning and intensional proof theoretic semantics see \n Došen (2003, 2016) and Schroeder-Heister (2016a)." ], "subsection_title": "3.7 Intensional proof-theoretic semantics" } ] }, { "main_content": [ "\n\nStandard proof-theoretic semantics has practically exclusively been\noccupied with logical constants. Logical constants play a central role\nin reasoning and inference, but are definitely not the exclusive, and\nperhaps not even the most typical sort of entities that can be defined\ninferentially. A framework is needed that deals with inferential\ndefinitions in a wider sense and covers both logical and extra-logical\ninferential definitions alike. The idea of definitional reflection with\nrespect to arbitrary definitional rules (see\n 2.3.2)\n and also natural language applications\n (see\n 3.4)\n point in this direction, but farther\nreaching conceptions can be imagined. Furthermore, the concentration on\nharmony, inversion principles, definitional reflection and the like is\nsomewhat misleading, as it might suggest that proof-theoretic semantics\nconsists of only that. It should be emphasized that already when it\ncomes to arithmetic, stronger principles are needed in addition to\ninversion. However, in spite of these limitations, proof-theoretic\nsemantics has already gained very substantial achievements that can\ncompete with more widespread approaches to semantics." ], "section_title": "4. Conclusion and outlook", "subsections": [] } ]

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[ "\nTwo-dimensional (2D) semantics is a formal framework that is used to\ncharacterize the meaning of certain linguistic expressions and the\nentailment relations among sentences containing them. Two-dimensional\nsemantics has also been applied to thought contents. In contrast with\nstandard possible worlds semantics, 2D semantics assigns extensions\nand truth-values to expressions relative to two possible world\nparameters, rather than just one. So a 2D semantic framework provides\nfiner-grained semantic values than those available within standard\npossible world semantics, while using the same basic model-theoretic\nresources. The 2D framework itself is just a formal tool. To develop a\nsemantic theory for someone’s language, a proponent of 2D\nsemantics must do three things: (i) explain what exactly the two\npossible world parameters represent, (ii) explain the rules for\nassigning 2D semantic values to a person’s words and sentences,\nand (iii) explain how 2D semantic values help in understanding the\nmeanings of the person’s words and sentences.", "\nThe two-dimensional framework has been interpreted in different ways\nfor different explanatory purposes. The two most widely accepted\napplications of two-dimensional semantics target restricted classes of\nexpressions. David Kaplan’s 2D semantic framework for indexicals\nis widely used to explain conventional semantic rules governing\ncontext-dependent expressions like ‘I’,\n‘that’, or ‘here’, which pick out different\nthings depending on the context in which the expression is used. And\nlogicians working on tense and modal logic use 2D semantics to\ncharacterize the logical implications of operators like\n‘now’, ‘actually’, and\n‘necessarily’. Such restricted applications of 2D\nsemantics are intended to systematize and explain uncontroversial\naspects of linguistic understanding.", "\nTwo-dimensional semantics has also been used for more ambitious\nphilosophical purposes. Influential theorists like David Lewis, Frank\nJackson and David Chalmers argue that a generalized 2D semantic\nframework can be used to isolate an apriori aspect of meaning.\nRoughly, the idea is that speakers always have apriori access to the\ntruth-conditions associated with their own sentences. On the face of\nit, this apriority claim seems to conflict with the observation that\ncertain necessary truths, such as ‘water =\nH2O’, can be known only on the basis of empirical\ninquiry. But proponents of generalized 2D semantics argue that the 2D\nframework undercuts this objection, by showing how such aposteriori\nnecessities are consistent with apriori access to truth-conditions.\nThe positive reasons to accept generalized 2D semantics, however, are\nbound up with larger (and partly disjoint) explanatory projects. As a\nconsequence, debates over the merits of generalized 2D semantics touch\non broader controversies about apriority, modality, semantic theory\nand philosophical methodology.", "\nThe two-dimensional framework can also figure in a theory of ad\nhoc language use, instead of a theory of literal meanings. Robert\nStalnaker’s influential 2D account of assertion falls in this\ncategory. His “metasemantic” interpretation of the 2D\nframework is intended to characterize what is communicated when\nconversational partners are partially ignorant or mistaken about the\nliteral meaning of their own words. Although it is formally similar to\ngeneralized 2D semantics, Stalnaker’s use of the 2D framework\navoids apriori accessible truth-conditions of the sort posited by\ngeneralized 2D semantics." ]

[ { "content_title": "1. Restricted 2D Semantics", "sub_toc": [ "1.1 Indexicals", "1.2. Modal operators" ] }, { "content_title": "2. Generalized 2D Semantics", "sub_toc": [ "2.1 Vindicating the traditional approach to meaning", "2.2 The empiricist project", "2.3 The rationalist project", "2.4 Objections to generalized 2D semantics" ] }, { "content_title": "3. The Metasemantic Interpretation", "sub_toc": [ "3.1 2D semantics for externalists", "3.2 A 2D account of assertoric content", "3.3 Propositional attitudes", "3.4 Metasemantic vs. semantic", "Supplement: Objections to the metasemantic interpretation" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nTwo-dimensional semantics was introduced to model the semantics of\ncontext-sensitive expressions in natural language, like indexicals and\ndemonstratives. A similar 2D framework was developed to model\nimportant aspects of tense and modal logic." ], "section_title": "1. Restricted 2D Semantics", "subsections": [ { "content": [ "\nSemantic theories explain how the truth or falsity of whole sentences\ndepends on the meanings of their parts by stating rules governing the\ninterpretation of subsentential expressions and their modes of\ncombination. A semantic framework provides a standard formalism for\nstating such rules. The simplest (0-dimensional) semantic frameworks\nwork by assigning extensions as the semantic values of\nparticular expressions. Intuitively, the extension includes those\nthings in the actual world to which the expression applies: e.g., the\nextension of the name ‘Barack Obama’ is the man Obama, the\nextension of the predicate ‘is cool’ is the set of all the\nactual cool things, and the extension of a two-place predicate\n‘is cooler than’ is the set of pairs of actually existing\nthings the first of which is cooler than the second. A whole sentence\nis assigned a truth-value (True or False) as its extension, which is\ncomputed on the basis of the extensions of the component expressions:\ne.g., the sentence, ‘Barack Obama is cool’, will have the\nsemantic value True just in case Obama is a member of the set of\nactual cool things. A two-dimensional semantic framework is the result\nof enriching this simple extensional framework in two distinct\nways.", "\nThe first enrichment, standard possible worlds semantics, is\nintroduced to explain the meaning of modal operators like\n‘possible’ and ‘necessary’ and to distinguish\nthe intuitive subject matter represented by particular subsentential\nexpressions. Consider the expressions ‘Roger Federer’,\n‘the greatest tennis player of all time’, and ‘the\nmost famous Swiss citizen in 2020’. Let’s assume all three\nexpressions happen to have exactly the same extension: a particular\nindividual RF. So a simple extensional semantics will assign exactly\nthe same semantic value to all three expressions. But clearly they\ndiffer in meaning: if events had unfolded only slightly differently\nthan they actually did, the three expressions would pick out different\npeople. In general, definite descriptions like ‘the greatest\ntennis player’ or ‘the most famous Swiss citizen’\npick out different individuals depending on who happens to have the\nrelevant properties in counterfactual situations; whereas proper names\nlike ‘Roger Federer’ rigidly pick out the very\nsame individual in every possible\n situation.[1]\n [See entry on\n rigid designators.]\n Moreover, such differences in what expressions pick out in\ncounterfactual situations affect the truth of modal claims: e.g.,\n‘Federer is necessarily Federer’ is true, but\n‘Federer is necessarily the greatest tennis player’ is\nfalse. So there is an aspect of meaning that is not captured in simple\nextensional semantics. The basic idea behind possible world semantics\nis to map out such differences in meaning by specifying what an\nexpression picks out relative to every possible way the world\ncould be (every “possible world”).", "\nIn standard (1-dimensional) possible worlds semantics, the semantic\nvalue of an expression is an intension, a function that\nassigns an extension to the expression “at” every possible\nworld. For instance, the semantic value of a definite description like\n‘the best known Swiss citizen’ is a function that takes as\ninput a possible world and yields as output whoever happens to satisfy\nthat description in that world, and the semantic value of a proper\nname like ‘Roger Federer’ is a constant function that maps\nevery possible world to the very same individual, RF. Such intensions\nreflect commonsense intuitions about the “modal profile”\nof the objects, kinds, or properties picked out by our words –\ni.e. different possible ways those features could be\n instantiated.[2]\n This framework is also used to explain the meaning of modal operators\nlike ‘necessarily’ and ‘possibly’: a sentence\nis necessarily true just in case it is true at every possible world,\nand it is possibly true just in case it is true at some possible\nworld. [See the entries on\n intensional logic\n and\n modal logic.]", "\nThe second enrichment of the basic extensional semantic\nframework—the one that is distinctive of two-dimensional\nsemantics—requires us to take possible worlds into account in a\ndifferent way. To see why this might be necessary for an adequate\naccount of meaning, let’s focus on context-sensitive expressions\nlike ‘I’, ‘here’ or ‘this’. In one\nrespect, these terms function like names, picking out the very same\nthing in every possible world. For instance, if Hillary Clinton says\n‘I could have been president’, her word ‘I’\nrefers rigidly to the same woman, HC, in every possible world and her\nclaim is true just in case there is a possible way the world could be\nin which HC is president. In standard possible worlds semantics, then,\nthe intension o of ‘I’ is exactly the same as the\nintension of the name ‘Hillary Clinton’: a function that\nyields the individual HC for every possible world. But clearly the\nEnglish word ‘I’ is not synonymous with the name\n‘Hillary Clinton’—for John McCain might utter the\nsentence ‘I could have been president’ and in his mouth\nthe word ‘I’ would refer rigidly to a different person,\nJM, in every possible world. What’s distinctive of\ncontext-sensitive expressions like ‘I’ or\n‘this’ is that they represent different things depending\non the context in which they are used. David Kaplan\n (1989a)[3]\n first brought widespread attention to this phenomenon of\ncontext-dependence by proposing his influential two-dimensional\nsemantic theory to clarify the rules governing such expressions.", "\nKaplan distinguishes two different aspects of the meaning of\nexpressions in a public language. The first aspect, content,\nreflects the modal profile of the object, kind or property\nrepresented. This is the aspect of meaning that is modeled by standard\npossible world semantics. The second aspect of meaning,\ncharacter, reflects semantic rules governing how the content\nof an expression may vary from one context of use to the next. A\ncontext-invariant expression like ‘Hillary Clinton’ has a\nconstant character, picking out the very same object in every context\nin which it’s used, whereas indexical expressions like\n‘I’ or ‘this’ have variable character, picking\nout different things in different contexts of use.", "\nFormally, character is defined as a function that maps possible\ncontexts of use to contents, and content is defined as a function\nmapping possible worlds to extensions. Thus, a character is a function\nthat takes as input a context and yields as output a function from\npossible worlds to extensions. This is a two-dimensional\nintension, since there are two distinct roles that possibilities\nplay here: as a context of use, and as a circumstance of evaluation (a\npossible situation relative to which we evaluate whether the relevant\nobject exists or property is instantiated). Contexts of use can be\nthought of as “centered” worlds: possible worlds with a\ndesignated agent and time within that world, which serve to locate a\nparticular situation in which the expression is used. We can then\nrepresent a context as an ordered triple, \\(\\langle w,a,t\\rangle\\) ,\nof a possible world w, an agent a\nwithin that world, and a time t\nwhen the agent exists in that\n world.[4]\n So possible worlds play two distinct roles in Kaplan’s\nformalism: contexts of use determine which content is expressed and\ncircumstances of evaluation reflect the modal profile of that content.\nThe conventional semantic rules governing an expression like\n‘I’ can be easily represented using Kaplan’s 2D\nframework: in any possible context, \\(\\langle w,a,t\\rangle\\), an\nutterance of ‘I’ rigidly designates the agent of\nthat context, a, in all possible circumstances of evaluation.\n[See the entry on\n indexicals\n for a more detailed discussion].", "\nA useful way of visualizing the dual role played by possible worlds in\na 2D framework is to construct a two-dimensional matrix\n(Stalnaker 1978). To represent Kaplan’s theory of indexicals, we\narray possible circumstances of evaluation along the horizontal axis\nand possible contexts of utterance along the vertical axis. Each\nhorizontal row of the matrix represents the content the\ntarget expression would have if used in the context specified for that\nrow. This content is (partially) represented by recording the\nextension of the term at each possible circumstance arrayed along the\nhorizontal axis. This procedure is then repeated for each context\nlisted along the vertical axis.", "\nFor instance, consider a particular utterance of ‘I’ made\nby Barack Obama during his inaugural presidential address. This\ncontext of use can be represented as the world \\(w_1\\), centered on\nthe man BO, at time \\(t_0\\). We can (partially) represent the content\nof ‘I’ in this centered world thus:", "\nThis simple one-dimensional matrix reflects the fact that, when used\nin this context, ‘I’ refers rigidly to Obama at every\npossible circumstance of evaluation—even at the counterfactual\nworlds \\(w_2\\) and \\(w_3\\), in which John McCain or Hillary Rodham\nClinton won the 2008 presidential election. The context-dependence of\nthe expression ‘I’ is revealed when we evaluate the use of\n‘I’ with respect to different possible contexts of use.\nLet’s consider two other contexts: \\(\\langle w_2, \\JM,\nt_0\\rangle\\) is a world in which McCain won the election, centered on\nhim at his inaugural address; and \\(\\langle w_3, \\HC, t_0\\rangle\\) is\na world in which Clinton won, centered on her at her inaugural\naddress. We then rely on our implicit understanding of the semantic\nrules governing ‘I’ to generate two more rows for our\nmatrix:", "\nWhat the matrix reveals is that the expression ‘I’ rigidly\ndesignates different individuals, depending on the context in which it\nis used. Thus the 2D matrix provides a graphic illustration of how\ncontent of the expression ‘I’ varies, depending on the\ncontext in which it is used.", "\nSuch 2D matrices can be used to represent the differences between the\nsemantic rules governing indexicals, definite descriptions, and names.\nFor instance, the definite description ‘the inaugural speaker in\n2009’ will generate the following Kaplanian matrix:", "\nUnlike the matrix for ‘I’, the horizontal rows of this 2D\nmatrix are all exactly the same. This reflects the fact that the\nexpression ‘the inaugural speaker in 2009’ is not\ncontext-sensitive: it always represents the very same property\nirrespective of the context in which it is used—namely, the\nproperty of being the person who delivers the inaugural US\npresidential address in 2009. This property is exemplified by\ndifferent individuals at different possible worlds: the person who is\nthe inaugural speaker at \\(w_1\\) is Obama, at \\(w_2\\) it’s\nMcCain, and at \\(w_3\\) it’s Clinton. In general, the sequence\narrayed along the rows of this matrix reflects the variety of\ndifferent individuals who could instantiate the property represented\nby ‘the inaugural speaker’ in different circumstances. Of\ncourse, no finite matrix can fully capture the range of variation, but\nit can give a useful partial representation of the property in\nquestion.", "\nThe matrix for a proper name like ‘Barack Obama’ reveals\nanother very different pattern:", "\nAccording to Kaplan, proper names are context-invariant: they always\nhave the very same content irrespective of the context in which they\nare used. Proper names are also rigid designators: they pick out a\nsingle individual at every possible world. The upshot is that the 2D\nmatrix for a proper name will be completely uniform: the very same\nindividual appears in every cell of the matrix. This reflects the idea\nthat the semantic function of a name in a public language is simply to\npick out a particular individual, not to convey any information about\nhow to identify the individual in question. [For a different account\nof proper names, see §2.2 below.]", "\nKaplan’s semantic rules for indexicals guarantee that certain\nsentences will be true whenever they are uttered, and certain\ninferences will be truth preserving. This account paved the way for\nKaplan’s formal logic of indexicals (Kaplan 1989a). In this\nsystem, logical validity is defined in terms of different possible\ncontexts of use: a sentence is valid iff it is true in every possible\ncontext of use; and an inference is valid iff the truth of the\npremises ensures the truth of the conclusion in every possible context\nof use.", "\nOn Kaplan’s account, sentences can be logically valid, even if\nthey express contingent propositions. For instance, the semantic rules\ngoverning indexicals ensures that the sentence ‘I am here’\nwill be true in any context of use. But the content expressed is\nnormally contingent: I could easily not have been here right\nnow, but at the beach instead.", "\nTo illustrate, we can construct a partial 2D matrix for the sentence\nusing our previous example. Suppose ‘I am here now’ is\nuttered by the new president at the inauguration\n(t0) in \\(w_1\\) where Obama won, \\(w_2\\), where\nMcCain won, and \\(w_3\\) where Clinton won. Let’s assume Obama\nwould attend the inaugural address of McCain but not of Clinton,\nMcCain would avoid the inauguration of anyone who defeated him, and\nClinton would attend Obama’s inauguration but not\nMcCain’s. This yields the following 2D matrix:", "\nThe horizontal rows of the matrix represent the different propositions\nexpressed by the sentence in each context of use. Each utterance\nexpresses a different contingent proposition, as can be seen by the\nfact that each contains both ‘T’s and ‘F’s,\nand that the patterns differ. The 2D matrix also graphically\nrepresents the fact that the sentence is guaranteed to be true\nwhenever uttered. Notice the diagonal of the matrix running from the\ntop left corner to the bottom right, which contains all\n‘T’s. This reflects the fact that the sentence is\nguaranteed to be true whenever uttered. With a nod to Stalnaker\n(1978), we can call this the diagonal intension of the\nsentence. In Kaplan’s semantic framework, a necessary diagonal\nintension indicates that a sentence is logically valid and\n analytic.[5]" ], "subsection_title": "1.1 Indexicals" }, { "content": [ "\nAt around the same time that Kaplan began developing his account of\nindexicals, logicians working on tense and modal logic had begun using\n2D semantic frameworks to explain the behavior of sentential operators\nlike ‘now’ and ‘actually’ (Åqvist 1973;\nKamp 1971; Segerberg 1973; Vlach 1973). Unlike Kaplan, these logicians\nwere not primarily concerned with the semantic rules governing natural\nlanguages. In particular, modal logicians were not focused on how the\ncontext in which an expression is used can affect its reference.\nRather, they were interested in developing formal systems for\nrepresenting valid inferences about time and possibility. It turns out\nthat tense and modal logic are formally very similar and that both\nrequire double-indexing for expressive adequacy. Thus, to fully\ncapture reasoning about what’s necessary and possible, we need\nto move from standard possible worlds semantics to a 2D semantic\nframework.", "\nConsider the following sentence:", "\nStandard possible worlds semantics lacks the expressive power to\ncapture what is said by this sentence (Crossley and Humberstone 1977;\nHazen 1976, 1978). The claim is not that there is a possible world\nsuch that all the things that are red in that world are also shiny in\nthat world (they’re supposed to be red in the actual\nworld, not the counterfactual one). Nor is the claim that for each\nobject that is red, there is a possible world in which it is shiny\n(the objects are all supposed to be shiny together within a\nsingle possible world). So here is a relation among objects in\npossible worlds that cannot be expressed in standard possible world\nsemantics. To capture the relation, we need to introduce an extra\nelement into the formal framework: we simply designate one world\nwithin the model (the set of possible worlds) to play the role of the\nactual world. We can then introduce a sentential operator\n‘\\(\\mathcal{A}\\)’ (read as ‘Actually’), which\nrequires us to evaluate any claim within its scope at the\ndesignated world, even when the operator is embedded within the\nscope of other modal operators. Using this enriched possible worlds\nframework, we can represent the truth-conditions of our sample\nsentence in a straightforward way:", "\nThis sentence is true just in case there is some possible world, w,\nin which everything that is red in the designated\nworld, \\(w_@\\), is shiny in w.", "\nOne awkward consequence of this 2D semantic account of\n‘Actually’ is the way this operator interacts with the\nstandard modal operator ‘Necessarily’. Intuitively, what\nthe actual world is like seems logically and metaphysically\ncontingent. But according to the proposed semantics for\n‘Actually’, any true sentence S will\nyield a necessary truth when embedded within the\nscope of the operator ‘\\(\\mathcal{A}\\)’. For instance,\nconsider the following sentence:", "\nIf Obama won in the designated world of our model, then it’s\ntrue at every possible world in that model that Obama won at its\ndesignated world. So on the proposed 2D semantics, the sentence is\nnecessarily true. (When we embed (2) within the necessity\noperator ‘\\(\\Box\\)’ we get a truth; and any claim of the\nform \\(\\mathcal{A}S \\rightarrow \\Box \\mathcal{A}S\\) will be logically\nvalid.) But intuitively it’s a contingent matter how\nthe 2008 elections turned out. To mitigate this counterintuitive\nconsequence, Crossley and Humberstone introduce a new logical\noperator, ‘Fixedly’ (‘\\(\\mathcal{F}\\)’) in\nsuch a way that the complex operator ‘Fixedly Actually’\n(‘\\(\\mathcal{F}\\mathcal{A}\\)’), captures the sense of\nnecessity we have in mind when we deny that (2) is necessary. A\nsentence is fixedly actually true just in case it is true no\nmatter which world is designated as\n actual.[6]", "\nOnce again, 2D matrices can be used to graphically depict how the\nsemantic theory works. Let’s take our universe of possible\nworlds to contain just three worlds: \\(w_1\\) is a world where Obama\nwon, \\(w_2\\) a world where McCain won, and \\(w_3\\) a world where\nClinton won. To explain the ‘Fixedly Actually’ operator,\nwe need to consider possible worlds playing two different roles: the\nstandard role as a circumstance of evaluation and the special role of\nbeing designated as the actual world. To construct a 2D matrix, we\narray possible worlds playing the standard role along the horizontal\naxis, and along the vertical axis we array the same worlds playing the\nrole of being designated as actual. Each horizontal row of this matrix\nrepresents a different model with a particular world designated as\n actual.[7]\n On this account, the truth of a sentence embedded within the\n‘Actually’ operator depends entirely on what’s true\nin the world designated as actual in a given model. So we can fill in\nthe 2D matrix as follows:", "\nIn any world in a model (a row in the matrix), ‘Actually S’\nis always evaluated by looking at the\ndesignated world of that model. So such sentences are either\nnecessarily true (True at every world in the model) or necessarily\nfalse (False at every world in the model). This is the sense of\nnecessity that corresponds to the standard modal operator\n‘\\(\\Box\\)’. On this understanding of necessity, the target\nsentence is necessarily true (since \\(w_1\\) represents the\nactual actual world). But intuitively there is a sense in\nwhich the sentence seems contingent, since a different world could\nhave been actual: if \\(w_2\\) or \\(w_3\\) had been actual, the sentence\n‘Obama actually won’ would have been false. This fact is\nreflected in the 2D matrix by the diagonal intension, where the\nsentence comes out true with respect to \\(\\langle w_1, w_1\\rangle\\),\nbut false with respect to \\(\\langle w_2, w_2\\rangle\\) and \\(\\langle\nw_3, w_3\\rangle\\). The ‘Fixedly Actually’ operator is\nsensitive to the necessity or contingency of the diagonal intension.\nThe sense in which the target sentence (2) is not necessary is that\nit’s not fixedly actually true.", "\nWhile this double-indexing model has become standard in the\nliterature, as (Rabern 2012b) points out, the same expressive adequacy\nconsiderations Crossley and Humberstone (1977) used to support two\nindices for modal and temporal operators also support\nmultiple-indexing for those operators. For instance,\nconsider the following sentence:", "\nTo generate the correct analysis, we need to invoke three distinct\nworlds: the actual world \\(w_1\\), where the Titanic hit an iceberg, a\ncounterfactual world \\(w_2\\) where it did not, and another\ncounterfactual world \\(w_3\\) where all survivors of the voyage in\n\\(w_2\\) died. So double-indexing and 2D matrices cannot fully capture\nthe compositional semantics of modal sentences: we will need an\ninfinite sequence of possible world indices. For further work on\nmultiple-indexed semantics, see (Ninan 2010; Yalcin 2015).", "\nAn influential paper by Martin Davies and Lloyd Humberstone\n(1980) brought the formal tools developed in 2D modal logic to bear on\nphilosophical puzzles about modality. Following Gareth Evans (1979),\nDavies and Humberstone suggest that there are two notions of\nmetaphysical necessity involved in ordinary modal thinking: deep and\nsuperficial necessity. They argue that the two logical operators,\n‘\\(\\mathcal{F}\\mathcal{A}\\)’ and ‘\\(\\Box\\)’,\nrespectively, provide a\nclear formal elucidation of these two notions.", "\nThese two notions of necessity, they argue, help explain some of Saul\nKripke’s (1980) puzzling examples in which necessity and\napriority come apart. Using 2D modal logic, it’s easy to\nconstruct necessary aposteriori truths. The semantic rules governing\nthe modal operator ‘\\(\\mathcal{A}\\)’ guarantee that every\nclaim of the form \\(\\mathcal{A}S\\) will be either necessarily true or\nnecessarily false in the sense of ‘\\(\\Box\\)’. But when the\nembedded sentence S is an ordinary empirical truth\nlike ‘Obama won’, \\(\\mathcal{A}S\\) will be knowable only\naposteriori: so \\(\\mathcal{A}S\\) will be a necessary aposteriori\ntruth. The ‘Actually’ operator can also be used to\nconstruct contingent apriori truths. Any claim of the form\n\\((\\mathcal{A}S \\rightarrow S)\\) is guaranteed by the semantic rules\ngoverning ‘Actually’ to be true at the designated world no\nmatter which world is designated as actual (i.e., it’s fixedly\nactually true). But when S is an ordinary empirical\ntruth, the complex claim is not necessary in the sense of\n‘\\(\\Box\\)’: there will be some worlds in the model where\nS is false while \\(\\mathcal{A}S\\) is true. In such\ncases, the complex sentence will be a contingent apriori truth.", "\nDavies and Humberstone also suggest that the 2D modal operator\n‘Actually’ might help analyze certain referring\nexpressions in natural language. In particular, they focus on\nEvans’ (1982) notion of a ‘descriptive name’ (a name\nwhose reference is fixed by a description) and on natural kind terms.\nSuppose the following definitions capture the semantic rules governing\nthe relevant expressions in natural language:", "\nIf such analyses are correct, then the semantics for\n‘actually’ will allow us to explain why ‘Julius\ninvented the zip’ is contingent and apriori and ‘water =\nH2O’ is necessary\n aposteriori.[8]\n [See the entries on\n names\n and\n descriptions.\n For a survey of other philosophical applications of the 2D framework\nin modal logic see (Humberstone 2004).]", "\nDavies and Humberstone themselves express reservations about the\nadequacy of analyses using ‘actually’ for natural language\nexpressions, particularly in the case of proper names (1980,\n17–21). As a consequence, they did not take 2D modal logic to\nprovide a complete response to Kripke’s puzzles about necessary\naposteriori and contingent apriori truths. However, the use of the 2D\nframework to explain these puzzles was subsequently taken up and\nrefined by proponents of generalized 2D semantics." ], "subsection_title": "1.2 Modal Operators" } ] }, { "main_content": [], "section_title": "2. Generalized 2D Semantics", "subsections": [ { "content": [ "\nIn the previous sections, we considered applications of the 2D\nframework that seek to explain the meaning of specific types of\nexpression: indexicals and modal operators. In contrast, proponents of\ngeneralized 2D semantics (G2D) believe that the 2D framework can be\nused to explain an important aspect of the meaning of all\nexpressions. In particular, G2D is meant to vindicate the traditional\nidea that we have apriori access to our own meanings through armchair\nreflection.", "\nAccording to the philosophical tradition, to know the meaning of a\nsubsentential expression like ‘bachelor’ is to implicitly\ngrasp a criterion that determines exactly which individuals count as\nbachelors in any possible situation. (Accounts of meaning broadly\nalong these lines were advanced by Plato, Descartes, Locke, Hume,\nFrege, Russell, Carnap, and many others.) On the traditional account,\nspeakers’ implicit grasp of a criterion plays two key\ntheoretical roles:", "\nThe first claim requires that speakers who share the same meaning must\nshare a criterion for identifying the reference; while the second\nrequires that this criterion be veridical. If this traditional account\nof meaning is correct, then one can make one’s own meanings\nexplicit by engaging in apriori conceptual analysis. Such\nconceptual analysis allows you to determine what exactly it takes to\ncount as a bachelor in any possible world; and it allows you to\nspecify what exactly someone must be prepared to accept in order to\ngenuinely agree or disagree about bachelors.", "\nG2D is a strategy for defending a variant of this traditional view of\nmeaning against a series of influential objections. In the\n1970s and 80s, semantic externalists used a variety of persuasive\nexamples to argue that the traditional account of meaning yields an\nunrealistic picture of (i) semantic competence, (ii) reference\ndetermination, and (iii) epistemic access to modal facts. Proper names\nand natural kind terms seem especially problematic for the traditional\n account.[9]\n By commonsense standards, you don’t need to know a specific\nrule for identifying Gödel in any possible world in order to\ncount as competent with the name ‘Gödel’; and no such\nknowledge seems required for your use of the name to pick out the\nrelevant man in every possible world (Donnellan 1970; Kripke\n 1980).[10]\n Similarly, you don’t need to know precisely what it takes for\nsomething to count as water in any possible world to be competent with\nthe word ‘water’ or for your word to pick out the chemical\nsubstance H2O in every possible world (Kripke 1980; Putnam\n1970, 1972). Indeed, making room for the possibility of ignorance and\nerror about reference-conditions seems crucial to explaining empirical\ninquiry into the nature of familiar things, and to vindicating the\ncommonsense realist idea that we can refer to things whose nature we\ndon’t fully understand (Burge 1979, 1986; Putnam 1972, 1973). If\nthese critics are right, then the traditional account of meaning is\nuntenable. Implicit knowledge of reference-conditions is not\nrequired either for linguistic competence or for determinate\nreference. And apriori conceptual analysis cannot be trusted to reveal\nwhat’s genuinely possible—at best, it reveals one’s\ncurrent fallible assumptions about the topic in question. [See the\nentry on\n externalism about mental content.]", "\nProponents of G2D believe this pessimistic conclusion is unwarranted.\nWhat critics’ examples really show, they argue, is that the\ntraditional view of meaning should be refined, not junked. Moreover,\nthe 2D semantics developed for indexicals and modal operators suggests\na promising strategy for accommodating putative externalist\ncounterexamples within a broadly traditional account of meaning. In\nthe case of indexicals and rigidified definite descriptions, competent\nspeakers grasp a reference-fixing criterion without grasping\nthe modal profile of the object, kind, or property picked out\nby the expression. For instance, you can know that ‘I’\nalways refers to the speaker whenever it is uttered without knowing\nthe nature of the person who is actually picked (e.g., what it takes\nto be Barack Obama in any possible world). Perhaps our understanding\nof names and natural kind terms is structured in a similar way:\ncompetent speakers always have apriori access to the reference-fixing\ncriterion for their own use of the name ‘Barack Obama’,\nbut they have only aposteriori access to the associated modal profile.\nIf this suggestion is on the right track, then a G2D framework could\nbe used to clarify the nature of this semantic understanding. Moreover\nwe may be able to explain certain epistemic operators, like ‘it\nis conceptually possible that’ or ‘it is apriori\nthat’, as operating on such 2D semantic values.", "\nThe basic philosophical idea behind G2D—that subjects have\napriori access to reference-fixing criteria for their words but not to\nthe modal profile of the subject matter picked out—has been\nsuggested by a number of theorists. David Lewis, in particular, was a\npowerful champion of the idea that we can give apriori definitions for\nterms whose precise reference we do not understand. Lewis articulated\nthe ‘analytic functionalist’ approach to specifying the\nmeaning of mental predicates and of theoretical terms in science\n(1966; 1970; 1972; 1979; 1980; 1994); and he was also an early\nadvocate of a generalized 2D approach to semantics (1981; 1994). Other\ninfluential proponents of the idea that we can have implicit knowledge\nof reference-fixing criteria without knowing the modal profile of the\nreference include Michael Dummett (1973; 1981), Gareth Evans (1982),\nand John Searle (1983). Early proponents of an explicitly\ntwo-dimensional semantics for names and natural kind terms include\nHarry Deutsch (1990, 1993), Ulrike Haas-Spohn (1995), and Kai-Yee Wong\n(1996). However, it is two later theorists—Frank Jackson (1994;\n1998a; 1998b; 2004) and David Chalmers (1996; 2002b; 2002c; 2004;\n2006a)—who have most systematically developed and defended G2D\nas a way of reconciling the lessons of semantic externalism with the\ntraditional apriori approach to meaning and modality.", "\nIt’s worth noting that G2D has been motivated primarily by\nepistemic, metasemantic, and metaphysical concerns, rather than by\nissues in compositional semantics. In particular, G2D seeks to\nvindicate the traditional idea that we can know the truth-conditions\nof our own sentences via armchair reasoning about hypothetical cases.\nThe approach promises to explain why certain necessary truths can only\nbe known aposteriori by appealing to the structure of our implicit\nsemantic understanding. Proponents of G2D make claims about how the\ntwo types of intension may interact with modal and epistemic\noperators. However, working out the details of the compositional\nsemantics has been a relatively recent concern of proponents of G2D\n(e.g. Chalmers 2011a, c; Chalmers and Rabern 2014; Johannesson and\nPackalén 2016; Kipper 2017).", "\nThe 2D semantic frameworks proposed by Jackson and Chalmers are very\nsimilar in their broad aims and formal structure, and commentators\noften treat the two versions as interchangeable. However, the two\nframeworks are developed in the service of two quite different\nphilosophical projects, emphasizing different aspects of the\ntraditional approach to meaning. Jackson takes up the traditional\nempiricist project of explaining empirical facts about language use\nand communication, while Chalmers pursues a broadly rationalist\nproject of explaining key structural interconnections between meaning,\napriority, and possibility. This difference in explanatory aims leads\nto different interpretations of the 2D framework." ], "subsection_title": "2.1 Vindicating the traditional approach to meaning" }, { "content": [ "\nAn empiricist account of meaning is a high-level causal explanation of\nuncontroversial facts about language use. In particular, the\nempiricist seeks to characterize the psychological states that guide\nindividuals’ application of an expression to particular cases,\nand to explain how linguistic coordination within a linguistic\ncommunity is achieved.", "\nClearly individual speakers must have some implicit assumptions about\nthe reference of a word that guide their verdicts about whether it\napplies to particular cases (Jackson 1998a, 29–42). Your\njudgments about whether a particular Gettier case counts as knowledge,\nfor instance, are guided by your prior understanding of the term\n‘knowledge’, and your answer is only justified insofar as\nit reflects that prior understanding. An empiricist seeks to explain\nthese facts by positing a stable internal psychological\nstate—something like an internal reference-fixing\ntemplate—that guides your verdicts no matter what the\nactual world turns out to be like.", "\nIt’s equally clear that members of the same linguistic community\ngenerally manage to use words to reliably coordinate their beliefs and\nactions (Jackson 1998b, 2004). When I ask you to pass the salt, you\nknow roughly which white granular substance I’m asking\nfor—you know, for instance, that it would be inappropriate to\npass the sugar bowl or the pepper grinder. This sort of everyday\ncoordination requires speakers to have similar dispositions to\nclassify things as falling into the extension of words, and it\nrequires that these similarities in classificatory dispositions be\nmutually obvious to all concerned: for it to make sense for me to say\n‘please pass the salt’ in order to get salt, it must be\ncommon knowledge between us that we’re inclined to classify\nroughly the same things as ‘salt’. An empiricist explains\nthis common knowledge by positing implicit conventions that\nrequire everyone to associate the very same reference-fixing template\nwith a given word (Jackson 1998b; Lewis 1969).", "\nAn empiricist use of the 2D framework is intended to show that this\ncore explanatory project is not undermined by the intuitions about\nnames and natural kind terms highlighted by semantic externalists\n(Jackson 1998a;\n 1998b).[11]", "\nExternalists argue that ordinary speakers are often ignorant or\nmistaken about the precise nature (modal profile) of the objects,\nkinds or properties their words pick out. But linguistic conventions\ndon’t always fix the reference by specifying the nature of the\nreference. Perhaps the conventions governing names and natural kind\nterms are structured in a similar way to indexicals. For instance, we\nmight have an implicit semantic rule requiring us to take\n‘water’ to pick out whatever chemical kind\nactually explains a certain suite of superficial observable\nproperties: e.g., being a clear, potable, odorless liquid that fills\nlakes and streams around here (Jackson 1998a, 1998b). On this\nanalysis, ‘water’ just is an implicitly indexical\nexpression, picking out different chemical kinds depending on which\nworld is actual. If this rule is what one must accept to count as\ncompetent with the meaning of the expression type ‘water’,\nthen it is no surprise that competent speakers often fail to realize\nthat water = H2O.", "\nOf course, it is an empirical question whether names and natural kind\nterms are in fact governed by indirect reference-fixing rules of this\nsort. But according to Jackson, you can test whether your implicit\nunderstanding of ‘water’ is structured in this way by\nconsidering possible situations in two different roles: as your\nactual environment or as a mere counterfactual\npossibility (Jackson 1998a, ch. 2). Consider two different\npossible worlds based on Putnam’s Twin Earth thought experiment\n(Putnam 1972). In the first world, Earth, the clear potable stuff that\nfills lakes and streams and is habitually called ‘water’\nby English speakers is H2O. The second world, Twin Earth,\nis exactly the same except that the stuff that has these properties is\nthe complex chemical kind, XYZ. If your commonsense understanding of\n‘water’ is governed by the proposed reference-fixing\nconvention, it would lead you to identify different chemical\nsubstances as water depending on what your actual environment is like:\nif your actual environment is Earth, then water is H2O; but\nif your actual environment is Twin Earth, then water is XYZ. If you\nassume that water is actually H2O, moreover, you\nwill judge that water is essentially H2O in all\ncounterfactual circumstances. And if you assume water is\nactually XYZ, then you’ll judge water is\nessentially XYZ.", "\nThis pattern of dispositions to apply the term ‘water’ can\nbe depicted on a 2D matrix as follows:", "\nAlong the vertical axis are ranged centered possible worlds (a\npossible world, with a designated agent a and time\nt within that world) representing different ways\nyour actual environment could be like; and the same worlds are ranged\nalong the horizontal axis representing different counterfactual\ncircumstances of evaluation. This matrix reflects your commonsense\ndispositions to apply the term ‘water’ to different\nchemical kinds on the basis of whether it actually plays certain\nsuperficial roles described in other commonsense terms\n(‘clear’, ‘potable’, ‘liquid’,\n etc).[12]", "\nSemantic externalists take these sorts of judgments about Twin Earth\nto militate against a traditional account of meaning—for they\nsuggest that your understanding does not fully determine the nature of\nthe reference. But according to Jackson, the only conclusion that is\nwarranted is that the meaning of your term is more complex than the\ntradition suggests: your verdicts about possible worlds considered as\nactual reflect your naïve reference-fixing criterion,\nand your verdicts about possible worlds considered as counterfactual\nreflect the theoretical criterion you would accept after you\nlearned all the relevant empirical facts about your actual\nenvironment. These two types of criterion can be modeled in possible\nworld semantics as intensions: an A-intension (for\n‘Actual’) is a function from worlds considered as actual\nto extensions, while a C-intension (for ‘Counterfactual’)\nis a function from worlds considered as counterfactual to extensions\n(Jackson 1998a, ch.2). The diagonal of our matrix corresponds to the\nA-intension you associate with ‘water’; and the first\nhorizontal row corresponds to the C-intension of your term\n‘water’ (assuming that \\(\\langle\\)Earth, \\(a, t\\rangle\\)\nrepresents your real-world environment).", "\nSemantic externalists acknowledge only the C-intension as modeling an\nexpression’s semantic content, but 2D empiricists insist that\nboth A- and C-intensions reflect important aspects of a competent\nEnglish speaker’s understanding of a word like\n‘water’. In particular, they take A-intensions to reflect\nwhat is understood and communicated by minimally competent English\nspeakers and what guides their everyday classifications. The\nsuggestion, then, is that A-intensions capture the shared,\nconventionally entrenched understanding of reference-fixing conditions\nposited by the empiricist approach to meaning.", "\nBy itself, this 2D framework offers no guarantee that the hypothetical\njudgments recorded by an A-intension are produced by a stable\nreference-fixing criterion. Nor does it guarantee that the very same\nA-intension will be generated for all competent speakers in your\nlinguistic community. However, according to Jackson, we have solid\nempirical reasons to think these conditions are satisfied in the case\nof names and natural kind terms. First, the widespread acceptance of\nthe externalist thought experiments demonstrates that we do in fact\nshare similar reference-fixing criteria for terms like\n‘water’ and ‘Gödel’ (Jackson 1998a,\n38–39). Second, the empiricist model of meaning provides the\nbest psychological explanation of how such linguistic coordination is\nachieved (Jackson\n 1998b).[13]", "\nIn addition to clarifying the structure of our semantic understanding,\nthe 2D framework can help justify specific conceptual analyses. The\ncriteria that implicitly guide our everyday use of a term are often\nembodied in recognitional or inferential dispositions rather than in\nconsciously accessible rules. Indeed, Jackson likens grasp of\nreference-fixing criteria for particular expressions to our ability to\nrecognize the grammaticality of sentences in one’s own language\n(2000). Just as linguists can construct a grammar for your language on\nthe basis of your judgments about the acceptability of particular\nsentences, you can construct an analysis of the meaning you associate\nwith an expression on the basis of your application of a term to\nhypothetical cases. The correct analysis must capture the full range\nof your confident judgments involving the target expression, while\nabstracting away from performance errors and other interfering factors\n(Jackson 1998a, 31–37).", "\nThis psychological model helps explain how you can come to know the\ncorrect analysis of your term ‘water’ by noting which\nproperties you treat as “obvious and central” when filling\nin a 2D matrix like the one above (Jackson 1998a, 31). The 2D\nframework prompts you to consider possible cases in two different\nways–as actual or as counterfactual. This allows you to know\nwhether the content of your term varies depending on what your actual\nenvironment is like (e.g. ‘water’) or whether it is stable\n(e.g. ‘bachelor’). Moreover, careful attention to your\nreactions to these suppositions will allow you to make explicit which\nsuperficial properties implicitly guide your application of the term.\nFor instance, you may discover that your implicit criterion for\napplying ‘water’ is that water \\(=_{df}\\) the actual\nchemical kind in your environment that is a clear, potable, odorless\nliquid that falls as rain and fills lakes and streams. Alternatively,\nyour use of the term ‘water’ may be guided by the types of\ncausal relations invoked in causal theories of reference: water\n\\(=_{df}\\) the actual natural kind that has been the dominant cause of\nyour community’s past use of the term ‘water’.\nIndeed, Jackson suggests that standard causal theories of reference\nare based on this method of conceptual analysis (1998a, 37–41).\n[See the entry on\n causal theories of mental content.]", "\nThe conceptual analyses produced by this method count as apriori,\naccording to the 2D empiricist, because you can know them to be\ncorrect “independently of knowing what the actual world is\nlike” (Jackson 1998a, 51). The evidence that supports such\nanalyses consists in purely hypothetical judgments: judgments about\nhow to classify cases on the supposition that your\nenvironment is like X, or like Y.\nSince such hypothetical judgments don’t\nrequire you to determine what your real environment is like,\nyour justification for accepting an analysis is not based on empirical\nknowledge. And to change your judgment about a purely hypothetical\ncase would be to change the meaning of your term (Jackson 1998a,\n44–46).", "\nJackson claims that apriori conceptual analysis plays a crucial role\nin metaphysics (Jackson 1994; 1998a). Metaphysical reductions provide\na constitutive account of some target domain (e.g., beliefs, free\nwill, water, moral rightness) in terms of more basic features of the\nworld (e.g., the properties postulated by an idealized physics, ideas\nin the mind of God, the mosaic of sense data). A physicalist about\nmental states, for instance, is committed to there being specific\nfacts about the microphysical structure of the world that suffice for\nthe existence of beliefs, desires and sensory experiences. The\nphysicalist is thus committed to metaphysically necessary\n“entailments” connecting claims about the two domains:\nit’s metaphysically necessary that if such-and-such physical\nfacts obtain, then such-and-such mental facts obtain. This\nmetaphysical entailment relation can arguably be cashed out in terms\nof global supervenience (Jackson 1998a, 6–14). [See the entry on\n supervenience.]", "\nThe role of conceptual analysis is to show that a putative reduction\nrespects the original meaning of the target expression (Jackson 1998a,\n28). A physicalist won’t succeed in accounting for free will if\nshe identifies free will with having a temperature of 37.4º C\n– such a “reduction” would simply change the subject\nunder discussion. A successful reduction must be answerable to our\noriginal shared understanding of the target expression—and\nelucidating this original understanding just is what conceptual\nanalysis does. So if conceptual analyses are knowable apriori, it\nfollows that metaphysical reductions must always be backed by apriori\nentailments between the base-level claim (such as a physical\ndescription of the world) and the target claim (such as the claim that\nhumans have free will).", "\nOn this empiricist account, conceptual analysis plays a modest\nmetaphysical role. Conceptual analysis captures apriori entailment\nrelations among your ideas; but it cannot tell you whether there\nare any objects, kinds, or properties that satisfy your\ncurrent reference-fixing assumptions (Jackson 1998a, 42–4).\nMoreover, the meaning you currently associate with a term may be\npragmatically deficient: e.g., it may not be determinate enough to\nsettle certain hard cases or it may not allow you to draw useful\ndistinctions in your actual environment. In such cases, you would have\ngood pragmatic reasons to change the meaning of your term (Jackson\n1998a, 44–6, 53–4). What the empiricist denies is that\nchanging your current criteria for applying a term can ever get you\ncloser to the truth about what you meant all along." ], "subsection_title": "2.2 The empiricist project" }, { "content": [ "\nFor an empiricist, an expression’s meaning reflects the causal\nmechanisms guiding everyday classification and communication. For a\nrationalist, in contrast, an expression’s meaning reflects what\nis apriori accessible to the speaker on the basis of ideal reflection.\nThe empiricist is primarily concerned with causal explanation of\nlinguistic facts, while the rationalist is primarily concerned with\nidealized apriori rationality and insights into objective possibility.\nThis difference in emphasis can have significant ramifications for\nG2D.", "\nDavid Chalmers has developed a detailed and influential rationalist\ninterpretation of the 2D framework. This semantic project is situated\nwithin a broadly rationalist tradition that posits a “golden\ntriangle” of necessary constitutive relations between meaning,\napriority, and possibility (2004; 2006a; 2012).", "\nFollowing Frege (1892), Chalmers is interested in capturing a notion\nof meaning that is finer-grained than reference. Frege pointed out\nthat sentences containing co-referential expressions like\n‘Hesperus’ and ‘Phosphorus’ can differ in\ncognitive significance: someone who is competent with these\ntwo names may not realize they are co-referential and may therefore\nuse them differently in making and justifying claims. Frege took\nsameness of cognitive significance to be the mark of sameness of\nmeaning. According to a 2D rationalist, sameness of cognitive\nsignificance can in most cases be elucidated in terms of apriori\nequivalence: two expressions are associated with the same meaning\niff one can know that they pick out the very same things on the basis\nof apriori reflection alone (Chalmers\n 2002b).[14]\n This constitutive link between meaning and apriority constitutes the\nfirst side of the “golden triangle”.", "\nThe second side of the “golden triangle” connects meaning\nwith possibility. Following Carnap (1947), Chalmers suggests that we\ncan use possible worlds semantics to individuate particular meanings\nin terms of their representational properties. In standard possible\nworld semantics, the meaning of ‘doctor’ is identified\nwith an intension that maps possible worlds to extensions. An\nexpression’s intension reflects the modal profile of the object,\nkind, or property picked out. Identifying meanings with intensions\ntherefore establishes an important constitutive connection between\nmeanings and modal claims. If ‘doctor’ and\n‘physician’ are associated with the same meaning, then\nit’s true in all possible worlds that all doctors are\nphysicians and all physicians are doctors. And conversely if two\nexpressions are co-extensive in all possible worlds, then\nthey have the same meaning.", "\nThe third side of the “golden triangle” connects\npossibility with apriority. Following Kant (1787), a rationalist about\nmodality holds that what is necessary is always knowable apriori and\nwhat is knowable apriori is always necessary. Thus ideal apriori\nreflection can be trusted to reveal the space of possibility.", "\nThis “golden triangle” of constitutive relations generates\na distinctive rationalist account of meaning. To be competent with an\nexpression’s meaning is to be in an internal cognitive state\nthat puts one in a position to identify its extension in any possible\nworld on the basis of apriori reflection alone. Apriori reflection\nwill also suffice to determine whether two expressions are associated\nwith the same or different meanings. This rationalist approach to\nmeaning contrasts with the empiricist one: whereas the empiricist uses\ncausally efficacious cognitive mechanisms to isolate the\nreference-fixing criteria currently associated with an expression, the\nrationalist uses the subject’s ideally rational\njudgments to isolate the complex cognitive states that would\nground those reflective judgments. As a consequence, the aspect of\nunderstanding that corresponds to a rationalist meaning may turn out\nto be more heterogeneous and less stable than the shared, causally\nefficacious ‘templates’ postulated by the empiricist. The\n“golden triangle” also involves a distinctive rationalist\naccount of modal epistemology, according to which ideal apriori\nconceivability is a fail-safe guide to metaphysical possibility. This\nmodal rationalism affords a simple and attractive account of our\naccess to modal facts (Chalmers 1996, 136–8; 1999, 488–91;\n 2002a).[15]", "\nThis simple rationalist picture of meaning and modality, however, was\nundermined by externalist thought experiments. Kripke’s (1980)\nobservation that certain necessary truths, like ‘Hesperus =\nPhosphorus’, are only knowable aposteriori threatens both the\nidea that linguistic competence affords apriori access to the truth-\nand applicability-conditions of one’s words and the idea that\nnecessary truths are always apriori knowable. The guiding idea behind\n2D rationalism is that a rationalist can accommodate Kripke’s\nexamples by moving to a 2D semantic framework. In particular, the 2D\nframework can be used to isolate an aspect of meaning that satisfies\nthe “golden triangle” of constitutive relations among\nmeaning, apriority and modality.", "\nRoughly, the idea is that ‘Hesperus = Phosphorus’ is\naposteriori because we associate distinct reference-fixing criteria\nwith the two names: e.g., being the brightest star visible in the\nevening and the brightest star visible the morning. According to the\n2D rationalist, these reference-fixing criteria are (i) an aspect of\nmeaning, (ii) which can be known apriori via conceptual analysis, and\n(iii) which suffices to fix the applicability conditions for every\npossible world considered as one’s actual environment. If the 2D\nframework can be used to isolate such an aspect of meaning for all\nexpressions, we will have vindicated the rationalist’s\n“golden triangle” connecting meaning, apriority and\npossibility.", "\nVindicating this “golden triangle” constitutes a primary\ntheoretical constraint for a rationalist interpretation of 2D\nsemantics. A 2D semantics that meets this constraint would play a\nwide-ranging role in philosophy. It would account for core semantic\nroles associated with the Fregean notion of sense (Chalmers 2002b) and\nthe traditional notion of a proposition (Chalmers 2011a). In addition,\nrationalist 2D semantics promises to define a versatile notion of\nnarrow thought content suited to playing key explanatory and\nevaluative roles in commonsense psychology (Chalmers 2002c).\nFurthermore, the rationalist approach to meaning and modality\nunderwrites a distinctive form of apriori reasoning about the nature\nof the actual world:", "\nThere is a long tradition in philosophy of using apriori methods to\ndraw conclusions about what is possible and what is necessary, and\noften in turn to draw conclusions about matters of substantive\nmetaphysics. Arguments like this typically have three steps: first an\nepistemic claim (about what can be known or conceived), from there to\na modal claim (about what is possible or necessary), and from there to\na metaphysical claim (about the nature of things in the world).\n(Chalmers 2002a, 145)\n", "\nChalmers has developed an influential anti-physicalist argument\nalong these lines, which relies on a rationalist 2D semantic framework\nto establish that facts about phenomenal consciousness cannot be\nreduced to physical or functional facts about the brain (1996; 2009).\nSee the supplementary document:", "\n The 2D argument against materialism.\n ", "\nAny interpretation of the 2D framework must answer the following two\nquestions:", "\nBut the rationalist project imposes specific constraints on how these\nquestions are answered. To vindicate the “golden\ntriangle”, the rationalist must identify a way of mapping an\nindividual speaker’s understanding of particular expressions\nonto possible worlds that affords apriori access to the entire space\nof possibility. This is not a trivial requirement: standard ways of\ninterpreting the 2D framework cannot vindicate the rationalist\nproject. However Chalmers has developed a distinctive\n“epistemic” interpretation of the 2D framework that he\nbelieves can establish the relevant constitutive links between\nmeaning, apriority and possibility (2004, 2006a).", "\nA rationalist 2D semantics must vindicate the following principle:", "\nCore Thesis: For any sentence \\(S,\\) \\(S\\) is apriori iff \\(S\\)\nhas a necessary 1-intension. (Chalmers 2004, 165)\n", "\nA sentence’s 1-intension is an intension that corresponds to the\ndiagonal of a 2D matrix. So the Core Thesis affirms that a token\nsentence is apriori (for a subject at a particular time) just in case\nthere is no possible way the world might be that, if it actually\nobtained, would make S false. In effect, the Core\nThesis sums up the “golden triangle” of constitutive\nconnections the rationalist hopes to establish between meaning,\napriority, and possibility: (i) it postulates a possible way the world\ncould be for every apriori coherent hypothesis, and vice versa; and\n(ii) this tight connection between apriority and possibility is\nreflected in an aspect of linguistic meaning, the\n 1-intension.[16]", "\nThe major obstacle to vindicating the Core Thesis for standard\ninterpretations of the 2D framework is the assignment\nprinciple—the way 2D theories assign extensions relative to\n“worlds considered as actual”. A natural way of\nunderstanding the injunction to consider a possible world as actual is\nto simply imagine a possible world, locate a person in it at a time,\nand then rely on ordinary interpretive methods to decide what exactly\nthat person in those empirical circumstances is referring to when\nusing a given expression. Chalmers calls this strategy for assigning\n1-intensions to expressions a “contextualist”\ninterpretation of the 2D framework. What’s distinctive of a\ncontextualist approach is (i) that a token of the target expression\nmust be located within the world considered as actual, and (ii) that\nthe expression is assigned an extension on the basis of how it’s\nused in that world. On this approach, a 1-intension will be\nundefined for possible worlds that do not contain a token of\nthe target expression: no extension can be assigned for such worlds,\nnot even an empty extension.", "\nThis contextualist approach to assigning 1-intensions is incompatible\nwith the Core Thesis (Chalmers 2004, 167­–176). Consider\nsentences like ‘Language exists’ or ‘A sentient\nbeing exists’: the meaning of these sentences seems to guarantee\nthat they will be true in every possible context in which they are\nused. So on the contextualist approach, these sentences should be\nassigned necessary 1-intensions, mapping every possible context of use\nto the truth-value True. But contrary to the Core Thesis, these\nsentences are not apriori truths knowable independently of\nany empirical evidence. There’s no contradiction in the very\nidea of a world without language or thought and we can easily imagine\nwhat such a world would be like; it’s just that our everyday\nexperience allows us to immediately rule out the possibility that our\nactual environment is like that. The problem is that contextualist\n1-intensions are undefined for worlds without thought or language,\neven though they are both apriori coherent and metaphysically\npossible. So a necessary contextual 1-intension does not track\napriority or metaphysical necessity. Contextualist 1-intensions,\ntherefore, cannot satisfy the rationalist’s Core\n Thesis.[17]", "\nThis difficulty can be avoided, Chalmers argues, if we rely on a\nnotion of epistemic possibility—what seems\npossible after ideal rational reflection—to interpret the 2D\nframework. More specifically, he focuses on the notion of apriori\ncoherence: claims that could be true for all one can tell on the basis\nof idealized apriori\n reasoning.[18]\n This notion of apriori coherence is used to answer the two\ninterpretive questions highlighted above: (i) apriori coherence is\nused to characterize the possibilities relative to which 1-intensions\nare defined, and (ii) apriori coherence is invoked to assign\n1-intensions to a speaker’s expressions.", "\nFirst consider the possibilities that define 1-intensions. On the\nepistemic interpretation, the possibilities are not metaphysically\npossible contexts of use, but epistemically possible\n“scenarios”: maximally specific hypotheses about what\none’s actual environment might be like that cannot be ruled out\nthrough apriori reasoning alone. Scenarios provide a complete\ncharacterization of the entire history of a universe, down to the last\nmicrophysical detail. They also provide perspectival\ninformation—a notional “center”—that indicates\nthe location from which the hypothetical universe is to be considered.\nThe crucial point is that scenarios are defined by their epistemic\nrole: they represent ways we can conceive of the actual world, within\nwhich we can try to identify familiar objects, kinds or\n properties.[19]", "\nThe second distinctive element of the epistemic interpretation of 2D\nsemantics is the procedure for assigning 1-intensions to a\nspeaker’s expressions. On the epistemic approach, 1-intensions\nreflect relations of apriori coherence between descriptions of\npossible scenarios and ordinary language sentences:", "\nThe epistemic 1-intension for a sentence S is True\nat a scenario W iff \\((W\\) & not\\(-S)\\) is\napriori incoherent. (Chalmers 2004, 180–4)\n", "\nThis principle for assigning 1-intensions relies on the\nspeaker’s ordinary ability to engage in object-level reasoning\nabout combinations of hypotheses: given the assumption that the\nscenario description W is true, you’re asked\nto decide whether S must be true as well. If\nit’s incoherent to accept \\((W\\) & not\\(-S)\\), your\nepistemic intension for S maps W\nto True, otherwise W is mapped to False. This\nepistemic assignment principle contrasts sharply with the\ncontextualist principle. The contextualist approach requires us to\nengage in explicit meta-linguistic reasoning to interpret the\nexpression ‘S’ as it’s\nused within the possible world W. On the\nepistemic approach, in contrast, an extension is assigned to\n‘S’ on the basis of the subject’s\nown object-level reasoning using the expressions ‘W’\nand ‘S’.", "\nUnlike the contextualist approach, therefore, the epistemic assignment\nprinciple does not explicitly require that a scenario contain a token\nof the relevant expression type in order to assign an extension\nrelative to that scenario. As a consequence, sentences like\n‘Language exists’ seem to pose no special problem for\nsatisfying the Core Thesis. The sentence ‘Language exists’\nwill have a contingent epistemic 1-intension, because there are\npossible scenarios that are apriori consistent with both the truth and\nfalsity of that sentence. For instance, consider a scenario in which\nthe only object is a giant lump of salt. To test whether your sentence\n‘Language exists’ is true at this scenario considered as\nactual, you ask whether there is any incoherence in combining the\nclaim ‘The only object that exists is a lump of salt’ with\nthe claim ‘It’s not the case that language exists’.\nIntuitively, this combination is coherent: there is no language in the\nsalt world. So the epistemic 1-intension for your sentence\n‘Language exists’ yields the value False for that\nscenario. Since there are other scenarios relative to which the\nsentence ‘Language exists’ will have the value True, your\nsentence will have a contingent epistemic 1-intension. This contingent\nepistemic intension for your sentence ‘Language exists’\nreflects the fact that it’s not apriori true that language\nexists. So it seems the epistemic assignment principle will allow\napriority and necessity of the 1-intension to go hand in hand, as\nrequired by the Core Thesis.", "\nThere is further work to do in spelling out Chalmers’ E2D\nframework in such a way as to vindicate his rationalist project. One\nway to think about the rationalist project is as a combination of the\nfollowing theses:", "\nTogether, 1 and 2 constitute a sort of semantic reductionism: the\nmeaning of any ordinary language expression is reduced to the meanings\nof the base vocabulary via the epistemic exercise of considering\nscenarios as actual and worlds as counterfactual. And 3 ensures that\nthis epistemic exercise is an accurate guide to metaphysical\npossibility. Chalmers’ Core Thesis is meant to capture this\ntight relationship between grasp of meaning, apriori reflection, and\nmetaphysical possibility.", "\nHowever, simply rejecting C2D in favor of E2D does not yet provide any\npositive account of what it is to entertain an epistemic scenario W,\nand how we should update our beliefs in the light of the supposition\nthat W is actual. Without these details, it’s impossible to\ndetermine whether the Core Thesis is true. Perhaps it’s\nimpossible to consider a scenario as actual without presupposing\none’s own existence, or perhaps our best epistemic methods for\nupdating our beliefs presupposes the existence of those very beliefs;\nor perhaps there is no way of thinking about the world that\ndoesn’t rely on some further empirical assumptions about the\nworld.", "\nChalmers has entered into these interpretive questions in considerable\ndetail over many publications. The starting point for his approach is\noutlined in (Chalmers and Jackson 2001), where he suggests that\nscenarios can be understood as PQTI sentences: where P states\nmicrophysical truths, Q states phenomenal truths, T is a\n‘that’s all’ clause indicating that P and Q provide\na complete description of a possible universe, and I indicates the\nsubject’s notional location within that universe. P and Q employ\na canonical vocabulary that fully specifies the essential nature of\nthe fundamental properties upon which all other properties in a\npossible world supervene. Thus, PQTI sentences provide an\nepistemically transparent access to the space of epistemic and\nmetaphysical possibility (simply removing the self-locating\ninformation from a PQTI sentence yields a complete description of a\ncorresponding possible world, PQT). The 1-intensions of one’s\nordinary language expressions are then determined by the individual\nsubject’s ideally reflective dispositions to judge sentences\ntrue, assuming the truth of different PQTI-sentences. And 2-intensions\nare fixed by one’s reasoning about PQT sentences considered as\ncounterfactual (given assumptions about PQTI). (Chalmers 2006, 2011b)\nfurther articulates how the space of epistemic possibility can be\nunderstood, how scenarios are related to possible worlds, and how 1-\nand 2-intensions are assigned to token representations.", "\nMore recently, in Constructing the World (2012), Chalmers has focused\nsquarely on the epistemic ‘scrutability’ relation that\nconnects our understanding of ordinary language expressions to\nbase-level descriptions of scenarios.", "\nApriori Scrutability: There is a compact class of basic truths D such\nthat for any truth S, one can conclusively know ‘D \\(\\supset\\)\nS’ apriori.", "\nChalmers still takes PQTI sentences to be a promising candidate for\nspecifying a scrutability base D, but he is open to the possibility\nthat the descriptive vocabulary in PQTI may need to be supplemented in\norder to capture some truths, such as truths about causal relations or\nquiddities. But while he can afford to be flexible about the exact\nnature of the scrutability base, Chalmers’ rationalist program\ndepends on vindicating Apriori Scrutability for any sentence that is\nevaluable as possibly true or false (169–71). A good deal thus\nhangs on whether he is right that ideal epistemic procedures allow for\napriori justification, given an exhaustive base-level description of a\nscenario. Chalmers offers arguments to support the plausibility of\nthis view in (2012, ch. 4.).", "\nAccording to the ‘frontloading’ argument, we can have\nconclusive apriori knowledge of material conditionals of the form\n(PQTI \\(\\supset\\)\nS). Chalmers argues that all empirical information relevant to\njustifying a verdict about S can be ‘frontloaded’ into the\nantecedent of the conditional, so information about one’s\nreal-world environment, E, cannot play any essential role in\njustifying verdicts about the conditional. If E is itself apriori\nentailed by PQTI, it is not needed to justify a verdict about the\nconditional. And if E is not apriori entailed by PQTI, E will be\nirrelevant to justifying a verdict about the conditional. So our\njustification for the application conditionals that ground\n1-intensions is wholly apriori, and immune to empirical\n defeat.[20]", "\nEpistemic 2D semantics differs in important respects from traditional\naccounts of meaning. Semantic theories normally describe general\nsemantic rules governing expression types, whereas epistemic\n2D semantics is based on a single individual’s current\nunderstanding of a token expression. Kaplan and Jackson, for\ninstance, use the 2D framework to characterize the implicit\nconventions governing syntactically individuated expressions like\n‘I’ or ‘water’ in our linguistic community. In\ncontrast, Chalmers uses the 2D framework to characterize your\npotentially idiosyncratic understanding of a particular use of an\nexpression on a given occasion—e.g., the way you understood Al\nGore’s fifth use of ‘water’ during a speech on\nclimate change. Moreover, on this account 2D semantic values depend on\nthe upshot of ideal rational reflection about apriori coherence\nrelations. Just what is involved in ideal rational reflection is an\nopen question. But it’s plausible that it may depend on\nsubstantive constructive theorizing about the empirical scenario in\nquestion and on various non-obvious and idiosyncratic aspects of the\nsubject’s initial cognitive state. In that case, identifying the\nprecise epistemic 1-intension associated with your understanding of\n‘water’ will be a highly non-trivial matter, and it may be\nfar from obvious when your understanding of the term shifts so that\ntwo tokens no longer share the same epistemic 1-intension. This is\nwhy, in contrast with 2D empiricists like Jackson, a rationalist like\nChalmers denies that epistemic 1-intensions reflect the\nsubject’s “implicit knowledge” of a reference-fixing\ncriterion (e.g., Chalmers 2002a, 185; 2006b, §5).", "\nOf course, it’s possible that some epistemic intensions will\nreflect stable reference-fixing rules that are entrenched by implicit\nlinguistic conventions. But it’s also possible that some\nepistemic intensions will reflect highly abstract, heterogeneous,\nunstable, and idiosyncratic aspects of a speaker’s understanding\nat a given time. As a consequence, epistemic intensions are not\nguaranteed to line up with conventional linguistic meanings (Chalmers\n2002b). Given this divergence from standard semantic theories, one may\nwonder whether epistemic intensions deserve to be considered a kind of\nmeaning.", "\nHowever, according to the 2D rationalist, epistemic intensions play\nthe core semantic roles associated with Fregean senses (Chalmers\n2002b). Like Fregean senses, epistemic 1-intensions lend themselves to\na compositional semantic theory: the epistemic intension of a sentence\nis determined by the epistemic intensions of the component\nexpressions. Moreover, epistemic 1-intensions, like Fregean senses,\nreflect the speaker’s own rational perspective on what her words\nrepresent. Two token names ‘A’ and\n‘B’ have the same Fregean senses iff\nthe identity ‘A = B’ would strike the speaker as\ntrivially true. Similarly, a subject associates two token\nexpressions with the same epistemic intension iff they are apriori\n equivalent.[21]\n Finally, epistemic intensions may play a role similar to that of\nFregean senses in the semantics of attitude reports (Chalmers 2011a).\nOverall, then, epistemic intensions seem to provide an attractive\ntheoretical refinement of the Fregean notion of sense.", "\nIn addition, epistemic intensions arguably carve out a well-defined\nnotion of narrow content suited to playing key roles in commonsense\npsychology (Chalmers 2002c). Epistemic intensions reflect rational\nrelations among token mental states. Epistemic intensions can then be\nused to specify representational state types that are relevant to\nassessing a person’s rationality and to explaining rational\nthought processes.", "\nIt’s important to note that epistemic 1-intensions are intended\nto explain only one aspect of meaning. The 2D semantic\nframework also posits 2-intensions (“counterfactual” or\n“subjunctive” intensions), which reflect the modal profile\nof the object, kind or property picked out by an expression. But\nChalmers emphasizes that his E2D does not exclude positing further\naspects of meaning:", "\nTwo-dimensionalism is naturally combined with a semantic\npluralism, according to which expressions and utterances can be\nassociated with many different semantic (or quasi-semantic) values, by\nmany different semantic (or quasi-semantic) relations. On this view\nthere should be no question about whether the primary intension or the\nsecondary intension is the content of an utterance. Both can\nbe systematically associated with utterances, and both can play some\nof the roles that we want contents to play. Furthermore, there will\ncertainly be explanatory roles that neither of them play, so\ntwo-dimensionalism should not be seen as offering an exhaustive\naccount of the content of an utterance. Rather it is characterizing\nsome aspects of utterance content, aspects that can play a useful role\nin the epistemic and modal domains. (Chalmers 2006a, §3.5)\n", "\nIn sum, Chalmers’ highly idealized E2D framework is intended to\nearn its semantic keep by defining a kind of meaning capable of\nforging traditional rationalist connections between meaning,\nrationality and possibility. But he is happy to allow that there may\nbe other types of semantic values or structures that are needed to\nplay other semantic roles. [See entry on\n propositions,\n and\n structured propositions.]" ], "subsection_title": "2.3 The rationalist project" }, { "content": [ "\nThe G2D framework has attracted a wide variety of criticisms,\ntargeting its commitment to apriori conceptual analysis, its claim\nthat 1-intentions capture a type of meaning, and its internalist\napproach to assigning contents. The specific rationalist and\nempiricist applications of the G2D framework have also been\ncriticized. For a survey of these lines of criticism: see the\nsupplementary document:", "\n Objections to generalized 2D semantics\n " ], "subsection_title": "2.4 Objections to generalized 2D semantics" } ] }, { "main_content": [], "section_title": "3. The Metasemantic Interpretation", "subsections": [ { "content": [ "\nGeneralized 2D semantics seeks to vindicate a traditional internalist\nconception of meaning: it posits an extra aspect of meaning for all\nexpressions (the intension corresponding to the diagonal of a 2D\nmatrix) that is fully determined by a subject’s internal states,\nand which in turn determines objective truth-conditions for their\nsentences. By enriching compositional semantics in this way, G2D\npromises a straightforward explanation of a variety of epistemic\nproperties of sentences: e.g., why a necessary sentence like\n‘Hesperus is Phosphorus’ is not apriori knowable, what the\nsubject learns by accepting the sentence, or how the subject uses the\nsentence in reasoning.", "\nBut using the 2D framework to characterize the subject’s\nepistemic perspective is not beholden to this internalist project.\nSemantic externalists reject the traditional view that our purely\ninternal states afford apriori access to reference-fixing conditions\nfor our words and thoughts. According to externalists, the basic\nassignments in a compositional semantics relate the subject’s\nwords and thoughts to objective features of her\nenvironment—objects, kinds and properties whose nature is\ncaptured by standard (1D) possible world semantics. Even externalists,\nhowever, can define 2D matrices that reflect the subject’s\nepistemic perspective on the reference of her words and thoughts. For\nthe externalist, however, these 2D matrices will not represent\nmeanings—a specific aspect of understanding that is\nrequired for linguistic or conceptual competence and which figures in\na compositional semantic theory that determines truth-conditions for\nsentences. On an externalist interpretation, 2D matrices merely\nreflect one aspect of a subject’s partial semantic\nunderstanding of what her words and thoughts represent. Because\nexternalist 2D matrices don’t represent meanings, moreover, the\nexternalist is free to use the 2D framework strategically to focus on\ndifferent aspects of the subject’s understanding for different\nexplanatory purposes.", "\nRobert Stalnaker has articulated such an externalist interpretation of\nthe 2D framework in a series of influential papers spanning some\nthirty years. He was the first to introduce 2D matrices to specify\nwhat is communicated in situations where conversational partners are\npartly ignorant or mistaken about the nature of the objects, kinds or\nproperties their words pick out (1978), and he later extended his 2D\nframework to characterize the content of certain thoughts and attitude\nattributions (1981; 1987; 1988). In both cases, the 2D framework is\nused to define “diagonal” intensions that reflect the\nsubject’s partial understanding of which objects, kinds or\nproperties her words and thoughts represent. These diagonal intensions\nare not meanings or semantic values, since they do not figure in a\ncompositional semantic theory and they do not reflect conditions for\nconceptual or linguistic competence. The only meaning of an expression\non this account is its ordinary “horizontal” intension. In\neffect, Stalnaker’s 2D matrices represent different meanings\nthat an expression could have had if it had occurred in\ndifferent empirical circumstances. This “metasemantic”\ninterpretation of the 2D framework contrasts sharply the\n“semantic” interpretations favored by G2D theorists like\nJackson and Chalmers (Stalnaker 2001, 2004).", "\nProponents of G2D were influenced by Stalnaker’s early papers\ndeveloping the 2D framework, and their views are often presented as\ncontinuous in motivation and form. But there are important theoretical\nconsequences that flow from the choice between 2D metasemantics and\ngeneralized 2D semantics. Indeed, Stalnaker himself is a vocal critic\nof generalized 2D semantics, rejecting its commitment to the semantic\nstatus of 2D matrices, its commitment to apriori conceptual analysis,\nand its internalist approach to reference determination." ], "subsection_title": "3.1 2D semantics for externalists" }, { "content": [ "\nThe metasemantic interpretation of the 2D framework was originally\ndeveloped as a way of explaining how the propositions conveyed by the\nassertion of a sentence can vary depending on the conversational\ncontext (Stalnaker 1978). In this seminal paper, Stalnaker proposes an\nattractive theoretical account of the role of assertion in a\nconversation, which is then used to explain how the assertoric use of\na necessary sentence like ‘Hesperus = Phosphorus’, can\nconvey a specific empirical proposition within a given conversation.\nIn particular, Stalnaker argues that our commitment to construing such\nsentences as making felicitous and informative assertions will lead us\nto reinterpret their content in ways that can be modeled\nusing the 2D framework.", "\nThe guiding idea is that in making an assertion the speaker is trying\nto get the audience to rule out certain possibilities. In asserting\n‘It’s cold today’, for instance, I may be trying to\nget you to rule out possibilities in which today’s temperature\nin Melbourne is over 10° C. We can model what my assertion\nconveys, then, as a function that maps possible worlds in which\ntoday’s temperature is under 10° C to True and all other\nworlds to False. However, the precise truth-conditions communicated by\nan assertoric use of a sentence depend in part on the conversational\ncontext in which it takes place. Just which temperatures count as\ncold, for instance, depends on shared background assumptions in a\nparticular conversational context: what’s cold in Melbourne is\nmild in Manitoba.", "\nA second guiding idea is that the proposition actually conveyed by the\nassertion of a particular sentence depends on presuppositions\nshared by the participants in the conversation—including\npresuppositions about what particular words represent and\npresuppositions about actual empirical circumstances. If you’re\na Chinese speaker who doesn’t understand anything at all about\nwhat the term ‘cold’ represents in English, then I cannot\nuse ‘It’s cold today‘ to convey facts about\nMelbourne’s weather. And if you’re a Canadian who\ndoesn’t understand anything about Australian weather conditions,\nyou won’t understand precisely what I am saying to my fellow\nMelburnians when I assert that sentence. Stalnaker calls the set of\npresuppositions that conversational partners treat as common knowledge\nthat they can rely on to get their point across the “context\nset”—which he models as the set of possible worlds that\nsatisfy all of these mutual presuppositions. The context set will\nencode shared assumptions about the meaning of words, about general\nempirical facts, about the what’s happened so far in the\nconversation, and so on.", "\nThe goal of assertion, Stalnaker suggests, is to shrink the context\nset. In making an assertion, the speaker tries to get the audience to\naccept a new proposition as one of their shared presuppositions,\nthereby shrinking the set of possible worlds that are considered live\noptions. For instance, in asserting ‘It’ll be very cold\ntoday’ to a group of Melburnians, I exploit background knowledge\nof local weather conditions in June to get my audience to accept that\nthe temperature outside is somewhere between 5–10° C, ruling\nout live possibilities that it might be in the 15–20° C\nrange. If all goes well, further planning will proceed on the basis of\na smaller and more accurate range of possibilities. In contrast, if I\nwere to assert ‘It’s cold’ to the monolingual\nChinese speaker or to the parochial Canadian, my assertion would be\ndefective, since my audience wouldn’t be able to figure out\nwhich temperatures are ruled out by my assertion.", "\nIdentity claims, however, do not seem to fit this simple model of\nassertion. As Kripke (1980) argued, identities are either necessarily\ntrue or necessarily false. So accepting an identity will either leave\nthe context set unchanged or it will eliminate it altogether. Either\nway, asserting an identity would be pointless. But clearly it is not.\nAsserting an identity such as ‘Lloyd is I.L. Humberstone’\ncan be genuinely informative, ruling out empirical possibilities\npreviously taken to be live options. According to the metasemantic\naccount, (i) the goal of assertion can explain why the assertion of a\nnecessary sentence will lead to a reinterpretation of the content of\nthe asserted sentence, and (ii) the 2D framework helps to specify just\nwhich proposition will be conveyed by the sentence within a given\nconversation.", "\nIn general, an identity claim is appropriate when one of the parties\nto a conversation is (partially) ignorant about which object is picked\nout by a name like ‘Lloyd’. For an externalist like\nStalnaker, this is a case of semantic ignorance. If\nO’Leary doesn’t know that ‘Lloyd’ is\nco-referential with ‘I.L. Humberstone’, then he does not\nfully understand the semantic rules governing these names: i.e., that\nboth names are associated with a constant function from any possible\nworld to a specific individual. But O’Leary isn’t utterly\nincompetent with the meaning of these terms: he implicitly understands\nboth names as rigid designators, and he has some substantive\nunderstanding of the object each name picks out. For instance, he may\nunderstand that ‘Lloyd’ refers to the person to whom\nhe’s just been introduced and that ‘I.L.\nHumberstone’ refers to the author of ‘Direction of\nFit’. O’Leary’s semantic deficiency—his\nfailure to fully understand the meaning of these names in a\ncontextually appropriate way—is grounded in his ignorance of the\nordinary empirical fact that the man to whom he has been introduced is\nthe author of ‘Direction of Fit’.", "\n2D matrices can be used to represent this sort of partial semantic\nunderstanding. O’Leary knows that \\(if\\) the man in front of him\nis the author of the famous article, then ‘Lloyd = I.L.\nHumberstone’ expresses a necessary truth; and he knows that\n\\(if\\) the man in front of him isn’t the author, the sentence\nexpresses a necessary falsehood. What O’Leary doesn’t know\nis which of these two possibilities corresponds to his actual\nsituation. Call the first possibility i and the\nsecond j. O’Leary’s epistemic situation\ncan then be summed up in a 2D matrix:", "\nThe matrix is defined only with respect to a specific set of relevant\nalternative possibilities, i and j,\nchosen in such a way as to reflect the\nsubjects’ semantic understanding and our own explanatory\ninterests. The vertical axis represents these possible worlds in their\nrole as contexts of use, which determine the literal semantic\ncontent of the expressions used in them. The horizontal axis\nrepresents those same possible worlds as circumstances of\nevaluation, relative to which we evaluate the truth or falsity of\nthe proposition expressed. Each row of the matrix thus represents a\ndifferent proposition that might be literally expressed by the\nsentence. Stalnaker calls such matrices propositional\nconcepts, since they reflect the subject’s current\nimperfect conception of the meaning of the\n sentence.[22]\n This particular matrix reflects the fact that O’Leary’s\ncurrent epistemic state is compatible with the identity sentence\nexpressing either a necessary truth or a necessary falsehood,\ndepending on empirical facts about the actual context of use.", "\nWhat does O’Leary learn when he comes to accept Daniels’\nassertion of ‘Lloyd is I.L. Humberstone’? Since the actual\nworld is like i, the literal semantic content of\nthe asserted sentence is a necessary truth. But necessary truths rule\nout no empirical possibilities whatsoever, so this cannot be the\ninformative proposition that is conveyed by Daniels’ assertion.\nMoreover, O’Leary is not in a position to recognize that this is\nthe literal semantic content of the sentence, since he doesn’t\nknow whether the actual world is like i or j.\nThe natural suggestion is that the information\nconveyed by Daniels’ assertion is that the real world is like\ni and not j. When O’Leary\naccepts ‘Lloyd is I.L. Humberstone’, he will no longer\ntreat the possibility that the man in front of him is not the\nauthor of the famous article as a live option: this empirical\npossibility will be eliminated from his context set. Thus, the\nproposition that seems to be conveyed by Daniels’ assertion\ncorresponds to the diagonal intension determined by our 2D matrix for\nthat assertion. Moreover, this observation generalizes: when subjects\nare partially ignorant of the semantic values of their words, the\ndiagonal proposition determined by the propositional concept can\ncapture the empirical information conveyed by the assertion.", "\nBut why is this so? To explain why assertions sometimes express the\ndiagonal proposition, the metasemantic account appeals to rational\nmaxims governing conversational cooperation. The following maxim seems\nto govern the practice of assertion:", "\nThe very same proposition should be expressed relative to every\npossible world in the context set. (Stalnaker 1978, 88)\n", "\nSpeakers should conform to this maxim, because assertion involves an\nintention to get one’s audience to eliminate worlds from the\ncontext set in accordance with the proposition expressed—and in\norder for this intention to succeed the audience must be in a position\nto figure out just which worlds they are being asked to eliminate.\nWhen this sort of rational maxim governing the communication of\ninformation is flouted, the audience will look for a non-standard\ninterpretation of the utterance that would bring it back into\nconformity with the maxims (Grice 1989). [See the entries on\n pragmatics\n and on\n implicature.]", "\nAccording to Stalnaker, this is precisely what is going on in the case\nof identity claims like the one we have been considering.\nDaniels’ assertion of ‘Lloyd is I.L. Humberstone’\nclearly flouts the proposed maxim. We can assume that Daniels is aware\nthat O’Leary doesn’t know whether he is in a world like\ni, where the man to whom he’s been introduced\nis the famous author, or a world like j where they are distinct. Yet\nDaniels utters a sentence that expresses a different proposition\ndepending on whether the actual world is like i or\nlike j. In such circumstances, the audience should\nlook for an alternative interpretation of the assertion.\nDaniels’ assertion can be brought back into conformity with the\nmaxim by re-interpreting it as conveying the proposition expressed by\nthe diagonal of the matrix. At a rough intuitive level, we can say\nthat Daniels is trying to get O’Leary to accept that the\nsentence ‘Lloyd is I.L. Humberstone’ expresses a truth.\nBut the 2D framework also allows us to specify more precisely just\nwhat empirical information is conveyed within a given conversational\ncontext. Given O’Leary’s and Daniels’ common\npresuppositions about what the two names represent, Daniels’\nassertion also expresses the proposition that the man to whom\nO’Leary has just been introduced is the author of\n‘Direction of Fit’.", "\nIt’s worth emphasizing, however, that the very same sentence\nasserted in a different conversational context could express an\nentirely different empirical proposition: just which proposition is\nexpressed, on this metasemantic account, depends on what the\nindividual parties to the conversation are currently presupposing\nabout the meanings of the expressions used.", "\nIn recent work, Stalnaker has enriched his notion of a context. In\naddition to a sets of possible worlds, he introduces (i) multiple\ncenters within those worlds representing the participants in a\nconversation, and (ii) accessibility relations among the centers\nrepresenting interlocutors’ ways of identifying each other\n(Stalnaker 2008, 2014). This added structure is intended to capture\nself-locating presuppositions that can help explain what’s\ncommunicated by indexical expressions like ‘I’,\n‘you’ and ‘now’. For a helpful overview of the\nmotivation for such an approach, see (Ninan 2010a) and for further\ndevelopment of multi-centered accounts of propositional content see\n(Torre 2010, Ninan 2013)." ], "subsection_title": "3.2 A 2D account of assertoric content" }, { "content": [ "\nThe metasemantic 2D framework was originally developed to explain\ncommunication, but the framework can also be used to specify the\ncontent of certain beliefs and the content of assertions that\nattribute beliefs.", "\nStalnaker (1984) defends a coarse-grained account of belief contents,\nwhich individuates particular belief states in terms of a set of\npossible worlds that would make them true. If this project is to\nsucceed, it must be possible to fully specify beliefs without invoking\nanything like Fregean senses or conceptual structure. But there is an\nimportant class of beliefs that seem to pose insuperable problems for\na simple possible worlds account of their content: beliefs in\nnecessary truths. The problem for a standard possible worlds analysis\nis that all necessary truths have precisely the same content (the\nfunction mapping every world to True). So the belief that Hesperus\n= Phosphorus will have exactly the same content as a belief\nthat Hesperus = Hesperus & Fermat’s last theorem is\ntrue. But these are clearly distinct belief states. Beliefs in\nidentities have been particularly important in motivating theories of\nfiner-grained thought contents.", "\nBut fine-grained Fregean senses or conceptual structures are not\nstrictly required to distinguish beliefs in identities. Stalnaker\n(1981; 1987) argues that the metasemantic 2D framework he developed to\nexplain what is communicated by an assertion of an identity\nsentence can also explain the content of the belief states\nattributed using an identity sentence to specify its content. If\nO’Leary were to notice the pole star and think to himself\nthat’s Mars, for instance, the truth-conditions of his\nthought can be captured by a judiciously defined diagonal proposition\n(Stalnaker 1987, 125). In this case, the worlds we include in the\ncontext set may involve facts about which object is the target of\nO’Leary’s visual attention and facts about salient\nempirical properties he associates with the name ‘Mars’.\nOn the metasemantic approach, then, the proposition we attribute in\nsaying O’Leary believes that that is Mars is the\nproposition that the visually salient object is the object that has\nthose Martian properties.", "\nA further complication arises in specifying the content of attitude\nattributions. On the metasemantic account of assertion, the content\nconveyed by a sentence depends on the shared presuppositions of the\nspeaker and audience. But sometimes the parties to a discussion are\nbetter informed than the person they are describing. In philosophical\ndiscussions, for instance, it is standardly presupposed that\n‘Hesperus’ and ‘Phosphorus’ are\nco-referential. So the diagonal intension associated with the sentence\n‘Hesperus \\(\\ne\\) Phosphorus’ will be necessarily\nfalse when it’s asserted in philosophical contexts (i.e.,\nit will be false when uttered in any situation compatible with what is\nbeing presupposed in the philosophical conversation). And yet when a\nphilosopher says that O’Leary doesn’t know that Hesperus\nis Phosphorus, she still manages to communicate that O’Leary\nfails to grasp some contingent empirical proposition. On the face of\nit, the metasemantic account of assertion cannot explain how this is\npossible, since every cell of the metasemantic matrix for the identity\nclaim in this philosophical conversation will be assigned the value\nTrue.", "\nStalnaker’s response to this problem is to suggest that the\ncontext set for a belief report must be expanded so as to include\nworlds that correspond to the way that the believer himself (i.e.\nO’Leary) takes things to be. The diagonal proposition of the\nphilosopher’s sentence is thus determined by considering what\nshe would be saying if her sentence were asserted in contexts\ncompatible with O’Leary’s beliefs (1987; 1988). However,\nthere is no general rule for choosing which worlds are the relevant\nones:", "\nThe procedure I am proposing for extending propositional concepts so\nthat the diagonalization strategy can be applied to problematic belief\nattributions takes examples case by case. It is not, as yet, very\nsatisfactory if we are looking for a systematic way to explain why the\ncomplements of belief attributions denote the propositions that they\nseem to denote. But if, using this procedure, we can find a possible\nworlds proposition that is a plausible candidate to be the object of\nbelief being attributed in the various problematic examples, then\n[…] it will not be completely mysterious how these propositions\ncan be expressed by the sentences that seem to express them.\n(Stalnaker 1987, 129)\n", "\nThus, the metasemantic 2D framework provides adequate descriptive\nresources for characterizing mental states and our discourse about\nthem, without invoking fine-grained Fregean senses, concepts, or\nsyntactic structures. However, the metasemantic theory used to\nconstruct the relevant 2D matrices relies on unsystematic norms of\ncharitable interpretation to identify the precise contents of\nparticular attitudes and attitude reports (Stalnaker 1999b,\n 18–19).[23]" ], "subsection_title": "3.3 Propositional attitudes" } ] } ]

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Casullo and J. Thurow (eds.), Oxford:\nOxford University Press.", "Wilson, M., 2014, “David Chalmers versus the boll\nweevil”, Philosophy and Phenomenological Research, 89:\n238–248.", "Wittmer, G., 2013, “Review of J. Kipper, A\nTwo-Dimensionalist Guide to Conceptual Analysis”, Notre\nDame Philosophical Reviews, 11 January 2013,\n available online/.", "Wong, K-Y., 1996, “Sentence-Relativity and the Necessary\nAposteriori”, Philosophical Studies, 83:\n53–91.", "Yablo, S., 1999, “Concepts and Consciousness”,\nPhilosophy and Phenomenological Research, 59:\n455–463.", "–––, 2000a, “Red, Bitter, Best”,\nPhilosophical Books, 48: 17–23.", "–––, 2000b, “Textbook Kripkeanism and the\nOpen Texture of Concepts”, Pacific Philosophical\nQuarterly, 81 (1): 98–122.", "–––, 2002, “Coulda, Woulda,\nShoulda”, in Conceivability and Possibility, T. Gendler\nand J. Hawthorne (eds.), Oxford: Oxford University Press, pp.\n441–492.", "–––, 2006, “No Fool’s Cold: Notes on\nIllusions of Possibility”, in Two-Dimensional\nSemantics, M. Garcia-Carpintero and J. Macia (eds.), Oxford:\nOxford University Press, pp. 327–346.", "–––, 2008, Thoughts: Papers on Mind,\nMeaning, and Modality, Oxford: Oxford University Press.", "Yalcin, S., 2015, “Semantics and Metasemantics in the\nContext of Generative Grammar”, in Metasemantics: New Essays\non the Foundations of Meaning, A. Burgess and B. Sherman (ed.),\nOxford: Oxford University Press, pp. 17–54." ]

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[ "\n\nThis entry intends to give an account of the most important stages\nof the medieval history of semiotics by providing a general\nchronological survey of the main sources and theoretical developments\nof the medieval notion of sign." ]

[ { "content_title": "1. Semiotics:its place in the framework of scholastic disciplines", "sub_toc": [] }, { "content_title": "2. The late ancient sources of medieval semiotics", "sub_toc": [ "2.1 Augustine (354–430)", "2.2 Boethius (480–528)" ] }, { "content_title": "3. Semiotic beginnings in the 11th and 12th century", "sub_toc": [] }, { "content_title": "4. The genesis of an elaborate theory of signs in the second half of 13th century", "sub_toc": [ "4.1 Ps.-Robert Kilwardby", "4.2 Roger Bacon (ca. 1214-ca. 1293)" ] }, { "content_title": "5. Grammatica Speculativa and its critics", "sub_toc": [] }, { "content_title": "6. Mental concepts as signs", "sub_toc": [] }, { "content_title": "7. The sign as a central notion in 14th-century logic", "sub_toc": [] }, { "content_title": "8. The concept of sign in scholastic logic of 15th and early 16th-century", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nTo speak of medieval semiotics is not to speak of a precisely\ndefined discipline besides, and distinct from, other medieval arts and\nsciences; it is rather to speak of a complex field of more or less\n— mostly more — elaborate reflections on the concept of\nsign, its nature, function, and classification. In order to understand\nthe enormous extent to which such theories grew during the Middle Ages\nsome basic formal features of the scholastic organization of knowledge\nhas to be kept in mind. First, scholastic learning is essentially a\ncommentary tradition. Most of the writings either are explicit\ncommentaries on what at a time were taken to be canonical texts (as\ne.g., the works of Aristotle, the Sentences of Peter Lombard,\nthe Grammar of Priscian, or the Summulae Logicales of\nPeter of Spain or Buridan) or are at least composed with constant\nreference to the topics treated there. A second point, closely related\nto the first, is the common scholastic practice of putting great effort\ninto the conceptual analysis of the basic terms and notions. Thus,\nwherever terms like ‘sign’ (signum) or\n‘representation’ (repraesentatio) appeared in the\ntexts commented on, scholastic authors felt obliged either to give an\nexplicit account of these concepts or at least to be able to refer to a\nplace where this has been done. In view of this, the fact that\nAristotle in his On Interpretation had incidentally called the\nword a ‘sign’ (semeion, symbol) of the mental\nconcept or that Augustine had termed the sacrament a ‘sacred\nsign’ (signum sacrum) became most important for the\nlater development of semiotics. For in both cases the outcome was a\nlarge number of detailed explorations of the nature and divisions of\nsign. Both points combined resulted in a general tendency towards an\nincreasing complexity and refinement of the scholastic discourse. For\nit is part of the intrinsic logic of any commentary tradition — a\nclose parallel can be found in the Indian tradition of logic and\nsemiotics that we do not discuss here — that all later\ncommentaries, which in many cases are actually meta-commentaries, have\nto compete with the previous ones and to surpass them in elaboration by\ntaking up, evaluating, or commenting on their arguments and\nterminological distinctions.", "\n\nThere are various areas within the scholastic system of arts and\nsciences where a rich tradition of semiotic questions and answers\naccumulated over the centuries (Maierù 1981; Meier-Oeser 1997,\n42–170; Fuchs 1999). Most important are those places located in the\nrealm of the so-called trivium (i.e., grammar, rhetoric and\nlogic), especially in logic where already the determination of its\nprimary subject as well as the discussion of the basic logical notions\n(like ‘term’ or ‘signification’) gave rise to\nexplicit remarks on the concept of sign. The most relevant loci\nclassici of logical contributions to a general theory of sign and\nsignification are: the comments on Aristotle's introductory chapter of\nOn Interpretation (esp. 1. 16a3–8), “the common starting\npoint for virtually all medieval theories of semantics” (Magee\n1989, 8), as well as the commentaries (especially from the\n15th and early 16th century) on the first tract\nof the so-called Summulae Logicales of Peter of Spain, and all\ntexts or parts of logical textbooks that are related to one of the\naforementioned passages. Further considerations with relevance to\nsemiotics within the sphere of logic are to be found, though less\nfrequently, in the commentaries on the final chapter of the Prior\nAnalytics (2, 27 70a-b) where Aristotle had outlined his doctrine\nof inference from\n signs.[1]\n Still within the sphere of trivium,\nvarious efforts to develop grammar into a regular science matching the\nAristotelian standards led, during the second half of 13th\ncentury, to approaches to language either starting from the general\nconcept of sign (Bacon, Ps.-Kilwardby) or taking grammar as a theory\nreflecting on the fundamental structure of sign systems (grammatica\nspeculativa).", "\n\nA rich source of semiotic material is also to be found in the\ntheologico-philosophical tradition. The loci classici of\nsemiotic discussions in the Commentaries on the Book of\nSentences (Liber Sententiarum) of Peter Lombard,\nthe basic scholastic textbook in theology, are particularly\nthe comments on book 1, distinction 1: the sign as subject and means of\nall instruction; bk. 1, dist. 3: the differences between images and\ntraces and their respective epistemic value; bk. 1, dist. 27: mental\nconcepts, spoken words and their signification; bk. 2, dist. 10: the\ncommunication of\n angels;[2]\n and, last but not least, bk. 4, dist. 1: the\nsacramental sign and the sign in\n general.[3]\n Outside the\nphilosophical and theological discourse, the notion of sign\ntraditionally played an important role in the theory and practice of\nmedical diagnostics (Maierù 1981: 64ff)." ], "section_title": "1. Semiotics: its place in the framework of scholastic disciplines", "subsections": [] }, { "main_content": [ "\n\nThe core set of ideas and doctrines from which medieval philosophers\ndeveloped their semiotic theories was provided to them mainly by two\nlate ancient authors. Besides Boethius (480–528), who transmitted\nAristotelian semantics to the Latin Middle Ages, Augustine's (354–430)\ndoctrine of sign is the most important junction of ancient and medieval\ntheories of sign and signification. Augustine's doctrine also has to be\nseen as a decisive turning point in the history of semiotics." ], "section_title": "2. The late ancient sources of medieval semiotics", "subsections": [ { "content": [ "\n\nAugustine's assertions and remarks, even though they do not offer a\ncompletely uniform concept of sign, were fundamental to the development\nof medieval semiotic, and they constituted the only elaborate theory of\nsigns until the 13th century (apart from the original theory\nof Peter Abelard). In his incomplete early work, De\nDialectica, Augustine massively draws on the terminology of the\nStoic philosophy of language, though in many points fundamentally\nmodifying its sense.[4]\n It is especially in the concept of sign\nwhere his difference from Stoic doctrines becomes apparent. For\naccording to the most refined theory of Stoic logicians, a sign in the\nproper technical sense (semeion) was seen as the abstract\npropositional content of a sentence insofar it is functioning as the\nantecedent in a true implication by means of which a hitherto unknown\ntruth is revealed. By contrast, Augustine is favoring a reifying\nconcept of sign. A sign, as he defines it in line with the descriptions\ngiven by Cicero and the Latin tradition of\n rhetoric,[5]\n is “something that shows itself to the senses and something other\nthan itself to the mind” (Signum est quod se ipsum sensui et\npraeter se aliquid animo ostendit) (Augustine De dial.\n1975, 86). The concept of sign, thus defined in terms of a triadic\nrelation (a sign is always a sign of something to\nsome mind), provides the general basis for Augustine's theory of\nlanguage: “To speak is to give a sign in articulate voice”\n(Loqui est articulata voce signum dare) (Augustine De\ndial. 1975, 86). Speech, in further contrast to Stoic semantics,\nis essentially characterized by its communicative function. A word, by\ndefinition, is a “sign of something, which can be understood by\nthe hearer when pronounced by the speaker” (uniuscuiusque rei\nsignum, quod ab audiente possit intelligi, a loquente prolatum)\n(Augustine De dial. 1975, 86). The communicative\nfunction[6]\n is thus essential to the linguistic sign:\n“There is no reason for signifying, i.e., for giving signs except\nto convey into another's mind what the sign-giver has in his own\nmind” (Nec ulla causa est nobis significandi, id est signi\ndandi, nisi ad … traiciendum in alterius animum id quod animo\ngerit qui signum dat) (Augustine De doctr. chr. II 3,\n1963, 34: 17–20). In his dialogue De Magistro (On the\nTeacher), however, written shortly after De Dialectica,\nAugustine denies that words or signs have the power of\n‘showing’ anything in the sense of making something present\nto the understanding (Non … mihi rem, quam significat,\nostendit verbum…) (Augustine De magistro X 32,\n1974, 191). For this reason, still influenced by the tenets of the\nskeptical tradition at that\n time,[7]\n Augustine was limiting\nthe capacity of the sign to its admonitory or commemorative function\n(Augustine De magistro XI 36, 1974, 194).", "\n\nBut in De Doctrina Christiana, after abandoning the\nskeptical position, Augustine redefines the sign accordingly, claiming\nthat “a sign is something which, offering itself to the senses,\nconveys something other to the intellect (Signum … est res\npraeter speciem quam ingerit sensibus, aliud aliquid ex se faciens in\ncogitationem venire) (Augustine De doctr. chr. II 1,\n1963, 33). In contrast to his former view, he is now attributing a\nfundamental epistemic function to the sign, claiming that “all\ninstruction is either about things or about signs; but things are\nlearnt by means of signs” (Omnis doctrina vel rerum est vel\nsignorum, sed res per signa discuntur) (Augustine De doctr.\nchr. I 1, 1963, 9). The borderline between things and signs and\nthus the sign itself is defined functionally rather than ontologically:\nsigns are things employed to signify something (res … quae\nad significandum aliquid adhibentur) (Augustine De doctr.\nchr. I 1, 1963, 9). Augustine divides the sign into the two main\nclasses of natural signs (signa naturalia) and given signs\n(signa data). “Natural signs are those which, apart from\nany intention or desire of using them as signs, do yet lead to the\nknowledge of something\n else”,[8]\n as, for example, smoke\nwhen it indicates fire, the footprint of an animal passing by, or the\ncountenance of an angry or sorrowful man. “Conventional signs, on\nthe other hand, are those which living beings mutually exchange in\norder to show, as well as they can, the feelings of their minds, or\ntheir perceptions, or their\n thoughts.”[9]\n Whether and to what\nextent such an “intention to signify” (voluntas\nsignificandi) can be assumed in cases of animal sign communication\nAugustine leaves\n open.[10]", "\n\nThe signs used in human communication are further subdivided with\nregard to the senses to which they address themselves: “some\nrelate to the sense of sight, some to that of hearing, a very few to\nthe other senses”. The preeminent role among all sorts of\n“given signs”, that Augustine is claiming for the words,\ndoes not result from their quantitative preponderance but rather from\nthe fact that, as he points out, everything that is indicated by\nnonverbal signs can be put into words but not vice versa\n(Augustine De doctr. chr. II 7, 1963, 35). ‘Word’\n(verbum) in its proper sense means — at least for the\nearly Augustine — ‘spoken word’. Writing\n(litterae), introduced by man in order to impart permanency to\nspoken language, is just a secondary system of signs, consisting of\n“signs of words” (signa verborum) rather than of\nwords itself (Augustine, De doctr. chr. II 8, (Ibid.); De\ndial. 1975, 86f.).", "\n\nIn close analogy to this devaluation of the written word against the\nspoken one, Augustine in his later theory of verbum mentis\n(mental word) is advocating the devaluation of the spoken word\nand the external sign in general against the internal sphere of mental\ncognition. It is now the mental or interior word (verbum\ninterius), i.e., the mental concept, that is considered as word in\nits most proper sense, whereas the spoken word appears as a mere sign\nor voice of the word (signum verbi, vox verbi)\n(Augustine, De Trinitate XV 11 20, 1968,\n 486f.).[11]\n Thoughts\n(cogitationes) are performed in mental words. The verbum\nmentis, corresponding to what later was called the conceptus\nmentis or intellectus, is by no means a\n‘linguistic’ entity in the proper sense, for it is\n“nullius linguae”, i.e., it does not belong to any\nparticular spoken language like Latin or Greek. So we are confronted\nwith the paradoxical situation that linguistic terminology (e.g.,\nverbum, locutio, oratio, dicere, etc.) is used to describe a\nphenomenon whose independence from any language is strongly emphasized\nat the same time.", "\n\nDespite all the internal ruptures and inconsistencies, Augustine's\ndoctrine of sign is based on a definition of the sign that, for the\nfirst time, intends to embrace both the natural indexical sign and the\nconventional linguistic sign as species of an all-embracing generic\nnotion of sign, thus marking a turning point in the history of\nsemiotics." ], "subsection_title": "2.1 Augustine (354–430)" }, { "content": [ "\n\nEven though Boethius, in line with the Aristotelian writings he\ncommented on, focuses on the concept of linguistic signification and\nhardly ever explicitly speaks of signs (notae) in general\n(Magee 1989, 61ff.), he is, besides Augustine, the main source for\nmedieval theories of signs. This is explained by the fact that, due to\nAugustine's influence, the semantics of linguistic signs became the\nfocus of semiotic theory, and that Boethius with his translations of\nand comments on parts of the Aristotelian Organon (especially\nPeri Hermeneias) is the most important, and for a long time\nthe only available, source for medieval acquaintance with the semantics\nof Aristotle and his Neoplatonic commentators of late antiquity. Thus,\nthe medieval philosophers viewed Aristotle's logic at first through the\neyes of Boethius, who has made some influential decisions concerning\nsemantic terminology (Engels 1963), as well as the interpretation of\nthe Aristotelian text. What they learned through his writings were\ninter alia the insight into the conventional character of\nlanguage, the view that meaning is established by an act of\n‘imposition’, i.e., name-giving or reference-setting, and\nthe influential idea that to signify (significare) is to\n“establish an understanding” (intellectum\nconstituere).\n\n", "\n\nEspecially in his more elaborate second commentary on Peri\nHermeneias, Boethius discusses at length the interrelations\nbetween the four elements of linguistic semeiosis mentioned by\nAristotle, i.e., between external objects or things (res),\nmental concepts or representations (passiones,\nintellectus), spoken words (voces), and written words\n(scripta). These elements are arranged so that they build up\nwhat Boethius calls the “order of speaking” (ordo\norandi) (Magee 1989, 64–92) which is characterized by the fact\nthat among the elements mentioned the former in each case ontologically\nprecedes the latter. Thus, without the existence of things there would\nbe no concepts, without concepts no spoken words, and without spoken\nwords no written ones. This, however, is not reversible in that sense\nthat the use of written characters in any case demands the knowledge of\nthe vocal expressions denoted by them, that there is always a concept\nbehind a spoken word, and that every concept refers to a real thing as\nits object (Boethius In Periherm. ed. sec., 1880: 21, 28–30).\nIn any case, the ordo orandi determines the direction of\nlinguistic signification: written characters signify spoken words,\nwhereas spoken words primarily signify mental concepts and, by means of\nthe latter, secondaryly denote the things. Thus, scriptura\nleft aside, the remaining three elements are structurally organized\nalong the lines of the prominent ‘semiotic triangle’\naccording to which signs refer to things by means of concepts (Boethius\nIn Periherm. ed. sec., 1880: 24, 33). In his further\ndiscussion of the ordo orandi Boethius divides, with reference\nto Porphyrius and the Aristotelians (peripatetici), three\nlevels of speech: besides — or rather at the fundament of —\nwritten and spoken discourse there is a mental speech (oratio\nmentis) in which thinking is\n performed.[12]\n It is, just like the\nAugustinian mental word, not made up from words of any national\nlanguages but rather from transidiomatic or even non-linguistic mental\nconcepts which are, as Aristotle has claimed, the same for all men." ], "subsection_title": "2.2 Boethius (480–528)" } ] }, { "main_content": [ "\n\nIn the late 11th century Anselm of Canterbury (1033–1109)\nrevived the Augustinian doctrine of the verbum mentis,\ncombining it with the Aristotelian view on mental concepts outlined in\nthe opening chapter of Peri Hermeneias. Thus, the two aspects\nof the mental word — which are found more or less implicitly in\nAugustine's work already — became explicit in Anselm. First:\nmental words are natural words and thus identical for all human beings\n(they are “verba … naturalia … et apud omnes\ngentes eadem”) (Anselm of Canterbury, Monolog.,\n1968: 25); and second: they are similitudes and mental images of things\n(similitudines et imagines\n rerum).[13]\n Due to this, they\nsignify their objects in a more expressive way (expressius\nsignant) than any other kind of words, and thus they are, as\nAnselm agrees with Augustine, what has to be termed ‘word’\nin its most proper sense (Anselm of Canterbury, Monolog.,\n1968: 25).", "\n\nA constitutive factor of the emergence of a medieval theory of signs\nwithin the context of grammar and logic is the resumption of\nAugustine's practice of embedding the concept of language into the\ngeneric notion of sign. Already Peter Abelard (1079–1142), in many\nrespects the most important author of the 12th century,\npoints out, that the phenomenon of linguistic signification\n(significatio vocum), falling into the sphere of competence of\nlogic, does not cover the whole range of sign processes (Abelard:\nDe dial., 1956: 111). For things in the broadest sense may\nfunction as signs, too, if they are connected to each other in such a\nway that the perception of one leads to the cognition of the other.\nThis can be the case when the one thing is an image of the other, when\nthings are either arbitrarily imposed to exercise the function of\nsignifying (significandi officium), as for instance the famous\ncirculus vini, a wreath of foliage, attached outside the\ntavern, indicating that wine is sold inside, or the conventional\ngestures of monastic sign\n languages,[14]\n or when two things, by being repeatedly noticed in conjunction, are\ncustomarily (secundum consuetudinem) associated with each\nother, or, finally, when they bear some sort of relationship to each\nother (secundum aliquam earum ad se\n habitudinem).[15]", "\n\nAbelard apparently is well aware of the fact that the concept of\nsign that results from taking into account all these cases as instances\nof signification is not only general but also unspecific. In order to\nbe able to single out cases of “properly signifying”\n(proprie significare) from such a ‘pansemiotic’\nsetting, he introduces a distinction, distinguishing between signs that\nsimply signify (signa significantia) and signs that are, as\nsignificative signs (signa significativa), i.e., as bearers of\nmeaning, involved in processes of intended sign-giving (Abelard De\ndial., 1956: 111; Log. ‘Ingredientibus’,\n1927: 336ff)." ], "section_title": "3. Semiotic beginnings in the 11th and 12th century", "subsections": [] }, { "main_content": [ "\n\nThe genesis of an elaborate theory of signs in the second half of\nthe 13th century is the result of a complex interplay of\nAristotelian and Augustinian influences. Since the mid-13th\ncentury Augustinian views, until then effective mainly in theological\ndiscussions, begin to invade the faculties of arts. Due to this, the\nsign is increasingly taken as the basic concept of the\n‘linguistic science’ (scientia\nsermocinalis):[16]\n “Speech is nothing but a sign”\n(Sermo totaliter signum est), Robert Kilwardby asserts\n(Kilwardby De ortu scientiarum, 1976, 160). Roger Bacon\npraises the sign even as the principal instrument of all Liberal\n Arts.[17]\n It is true, the consciousness of words\nbeing signs is nothing new. From this point onward, however, it gives\nrise, at first in the framework of grammar theory, to semiotic\nreflections that go beyond what is known from earlier centuries." ], "section_title": "4. The genesis of an elaborate theory of signs in the second half of 13th century", "subsections": [ { "content": [ "\n\nThe unknown author, now commonly named Ps.-Robert Kilwardby, opens\nhis commentary on Priscianus maior (written somewhere between\n1250 and 1280)[18]\n by modifying Augustine's prominent dictum\nthat “all instruction is either about things or about\nsigns” into the stronger and more ‘semiotic-minded’\nthesis that “every science is about signs or things\nsignified” (scientia omnis aut est de signis aut de rebus\nsignificatis) (Ps.-Robert Kilwardby: Comment. on “Prisc.\nMaior”, 1975, 1). This statement he takes as starting point\nof a detailed discussion of the questions of whether there can be a\n(special) science of\n signs[19]\n and, if so, what its relationship towards\nthe sciences dealing with things would be\n like.[20]\n Ps.-Kilwardby points\nout that there are several ‘sciences of signs’\n(diversae sunt scientiae de signis) according to the various\nkinds of signs (Ps.-Robert Kilwardby: Comment. on “Prisc.\nMaior”, 1975, 3). Since, however, any discipline, in order\nto meet the Aristotelian standard of science as it began to be accepted\nat that time, must have a general subject matter, the scientia de\nsignis necessarily contemplates the sign “in terms of a\nuniversal notion abstracted from the particular signs” (sub\nratione universalis abstracti a particularibus signis) (Ps.-Robert\nKilwardby: Comment. on “Prisc. Maior”, 1975, 4).\nIn case of natural signs (signa naturalia) as well as\n“moral signs” (signa moralia), as e.g., actions in\nrelation to the good or bad will, the theory of signs cannot be\nseparated from the theory of things signified; therefore, these signs\nfall under natural and moral science, respectively (Ps.-Robert\nKilwardby: Comment. on “Prisc. Maior”, 1975, 6).\nThe linguistic signs, however, produced by the human understanding for\nthe purpose of communicating its ideas, are the subject-matter of a\nrational science (scientia rationalis), the science of\nsigns." ], "subsection_title": "4.1 Ps.-Robert Kilwardby" }, { "content": [ "\n\nRoger Bacon is probably the most important medieval theorist of sign\n— at least he is the author of the most extensive medieval tract\non signs known so\n far.[21]\n Starting from a minute analysis of the\nnotion of sign and its various divisions, Bacon develops both in De\nsignis (ca. 1267) and in his Compendium studii theologiae\n(1292) a general conception of signification as well as a detailed\ntheory of the linguistic sign, so that here, as in Augustine, semantics\nis integrated into a broader theory of sign in general. According to\nBacon, the concept of sign belongs to the category of relation. To be\nmore precise, a sign, as it was pointed out already in Augustine's\ndefinition, is a triadic relation, such that it is — in principle\n— a sign of something to someone. This way of\nputting the point, however, gives rise to the question of whether both\nrelata of this relation are equally essential for its\nexistence. What would happen if one of these relata did not\nexist? What if the designated thing ceased to exist? And what if there\nwere no cognitive power taking notice or even being able to take notice\nof the sign?", "\n\nBonaventura (ca. 1217–1274), one of the most renowned theologians of\nthe time, explicitly places emphasis on the sign's relation to the\nsignificate, claiming that", "… a sign has a twofold comparison: both to that\nwhich it signifies, and to that to which it signifies; and the first is\nessential and the sign always has it in act, but the second it has in\nhabit; and it is from the first that it is called a sign, not\nfrom the second. Whence a circle above a tavern is always a sign, even\nif no one looks at\n it.[22]", "\n\nIn direct opposition to this commonly accepted manner of\npresentation, Bacon lay stress on the ‘pragmatic’ relation\nto the sign-interpreter, for the notion of sign is, as he claims,\n“essentially predicated with respect to someone to whom it\nsignifies. … For if no one could conceive something through the\nsign, it would be void and vain, nay, it wouldn't be a sign.”\n(Roger Bacon, De signis, 1978, 81). Other than the essential\nrelation of an actual sign to its interpreter, which must be in any a\ncase what was called a ‘real relation’ (relatio\nrealis), the relation to the significate can be a so-called a\n‘relation of reason’ (relatio rationis), for, as\nBacon adds: “It does not follow ‘a sign is in act,\ntherefore the thing signified exists’, because nonentities can be\nsignified by words just like entities” (Roger Bacon, De\nsignis, 1978, 81). There are other important points in which Bacon\ndeviates from the common opinion: He defines the sign as “that\nwhich upon being offered to the sense or intellect designates something\nto the intellect itself” (illud quod oblatum sensui vel\nintellectui aliquid designat ipsi intellectui), and emphasizes\nthat, contrary to what the common description says, there are signs\nwhich are offered only to the\n intellect.[23]", "\n\nBacon presents a detailed classification of\n signs[24]\n by\ntaking up, combining, and modifying elements of several prior sign\ntypologies. The division of the two main classes of natural and given\nsigns is taken from Augustine, the distinction between necessary and\nprobable signs is borrowed from Aristotle (an. pr. II, 27, 70a3-b5),\nand their subdivision according to their temporal reference is a\ntraditional element in the theories of the sacramental\n sign.[25]", "\n\nThe general class of natural signs signifying unintentionally by\ntheir essence (1) is divided according to the relation between a sign\nand its significate into the three subclasses of (1.1) inferential\nsigns based on a more or less constant concomitance of sign and\nsignificate, (1.2) iconic signs, based on similarity in appearance, and\n(1.3) signs based on a causal relation between the sign and the\nsignified thing. The signs of inference (illatio) are\nsubdivided into (1.1.1) necessary and (1.1.2) probable signs, both of\nwhich are further differentiated according to the three possible\ndirections of temporal reference (present, past, future). Bacon gives\nto understand that he takes inferential and iconic signs to be signs\nmore properly than the members of third class, i.e., signs based on a\ncausal relation (later in the Compendium studii theologiae he\nwill drop this class entirely). He justifies this by pointing to the\nfundamental difference between sign relations and causal relation:\nwhereas sign relations are necessarily constituted by an interpreter,\ncausal relations exist independently of any such one alone by reason of\nthe order of\n nature.[26]", "\n\nThe general class of signs given and directed by a soul (signa\nordinata ab anima) (2) is divided according to whether the living\nbeing brings forth the sign (2.1) together with a deliberation by\nreason and choice of will (cum deliberatione rationis et electione\nvoluntatis), or (2.2) by a natural instinct or impulse\n(instictu naturali et impetu naturae). The reason for\ndistinguishing two modes of natural signifying, as they appear in (1)\nand (2.1), is, on the one hand, an equivocation of the concept of\nnature, meaning “substance or essence of something”\n(substantia sive essentia cuiuslibet), as well as “force\nacting without deliberation” (virtus agens sine\ndeliberatione) (De signis, 1978, 85f.) and, on the other\nhand, the insight that, contrary to what holds for the natural signs in\nthe first sense, in the case of the latter there is always a\nsign-giver, not only someone taking something as a sign. Interjections\n(2.3) are considered as a hybrid of the two other sorts of given\nsigns.", "\n\nIt has to be noticed that in Bacon's, as well as in any other\nmedieval sign-typology, the classes of signs — even though this\nis not explicitly stated by the authors themselves — distinguish\nmodes of signifying rather than signs in the sense of sign-vehicles.\nTherefore, one and the same thing, fact, or event may, in different\nrespects, fall under various and even opposite sign-classes. This fact\nis especially important for the full account of sign-processes in which\nspoken language is involved.", "\n\nThe primary intention of Bacon's semiotic analyses is, as it was\nalready with Augustine, to provide the foundations for the semantics of\nspoken language.[27]\n According to Bacon, an adequate and\ncomplete account of the “difficult issue” (difficilis\ndubitatio) of what the significate of a vocal expression is has to\nconsider three different aspects: 1) the signification of vocal\nexpressions apart from impositio, i.e., apart from their being\nendowed with (conventional) meaning by ‘imposition’, 2)\ntheir signification according to imposition, and 3) their signification\nover and above imposition.", "\n\n1) Each vocal expression may serve independently from its imposition\nas a natural sign (De signis, 1978, 86f.) Words indicate for\ninstance the speaker being close, and they may ‘tell’\nsomething about him in the same way as an artwork is indicating the\nskills of the artist. Furthermore, the spoken word is a natural sign\nimplying that the speaker possesses the concept of the object meant by\nthe word according to its regular meaning. For the significative use of\nlanguage presupposes the presence of a concept in the speaker's mind\nthat corresponds to the object denoted (De signis, 1978, 85f.,\nComp. studii theol., 1988, 64). Thus, the relation between the\nvocal expression and the mental concept is, contrary to what was the\ncommon opinion since the days of Augustine and Boethius, not a relation\nof expression but rather of indexical signification.", "\n\n2) In his account of signification of words regarding their\n‘impositio’ Bacon accentuates the arbitrariness of\nmeaning.[28]\n But even though the first\n‘impositor’ (name-giver) is free to impose a word or sign\non anything whatsoever, he does perform the act of imposition according\nto the paradigm of baptism: “all names which we impose on things\nwe impose inasmuch as they are present to us, as in the case of names\nof people in\n Baptism”.[29]\n Contrary to the venerable tradition of\nAristotelian, Boethian or Porphyrian\n Semantics,[30]\n holding that spoken\nwords, at least immediately, signify mental concepts, Bacon favors the\nview that words, according to their imposition, immediately and\nproperly signify the things themselves. With this account of linguistic\nsignification Bacon abandons the model of the semantic\n triangle[31]\n and\nmarks an important turning point on the way from the traditional\nintensionalist semantics to the extensionalist reference semantics as\nit became increasingly accepted in the 14th\n century.[32]", "\n\nBacon is, however, well aware of the fact that the use of names and\nwords in general is not restricted to the meaning endowed through the\nfirst act of imposition (the term ‘homo’ does not only\ndenote those men that have been present when the original act of its\nimposition took place); nor do words cease to be used when their\noriginal significata (things signified) no longer physically\nexist (Bacon, De signis, 1978, 128). Bacon intends to solve\nthe resulting difficulties (which every causal theory of meaning based\non the concepts of ‘reference setting’ and ‘reference\nborrowing’ has to face) by distinguishing two modes of\nimposition. This can be seen as his most inventive contribution to\nsemantics.[33]\n Besides the ‘formal’ mode of\nimposition conducted by a ‘perlocutionary’ vocal expression\nlike “I call this …” (modus imponendi sub forma\nimpositionis vocaliter expressa) there is another kind taking\nplace tacitly (sine forma imponendi vocaliter expressa)\nwhenever a term is applied (transumitur) to any object other\nthan the first name-giver has ‘baptized’ (Bacon, De\nsignis, 1978, 130). Whereas the formal mode of imposition refers\neither to the mythical situation of a first invention of language or to\nthe act of explicitly coining a new word, the second kind of imposition\ndescribes what actually happens during the everyday use of language.\nThis modification of the meaning of words is constantly taking place\nwithout the speaker or anyone else being actually aware of it. For just\nby using language we “all day long impose names without being\nconscious of when and how” (nos tota die imponimus nomina et\nnon advertimus quando et quomodo) (Bacon, De signis,\n1978, 100, 130f.)", "\n\n3) Even if impositio in the described sense is of pivotal\nimportance for the constitution of linguistic meaning, the\nsignification of words is by no means limited to it: “a vocal\nexpression signifies many things for which it is not imposed, as it\nsignifies all those things that bear an essential relation to the thing\nfor which the word is\n imposed.”[34]\n In this way, Bacon\nclaims, words signify, as it were, infinitely many\n things.[35]" ], "subsection_title": "4.2 Roger Bacon (ca. 1214-ca. 1293)" } ] }, { "main_content": [ "\n\nThe idea, fundamental both for Bacon and Ps.-Kilwardby, that grammar\nis a regular science rather than a propaedeutic art, is shared by the\nschool of the so-called “modist grammarians”\n(modistae) emerging around 1270 in the Faculty of Arts of the\nUniversity of Paris and culminating in the Grammatica\nSpeculativa of Thomas of Erfurt around 1300. The members of this\nschool, taking it for granted that the objective of any regular science\nwas to explain the facts by giving reasons for them rather than to\nsimply describe them, make it their business to deduce the grammatical\nfeatures common to all languages from universal modes of being by means\nof corresponding modes of understanding. Thus the tradition of\nspeculative grammar (grammatica speculativa) develops the\ncommonly accepted Aristotelian claim (De Interpretatione\n1.16a3–9) that the mental concepts, just as the things, are the same\nfor all men (eadem apud omnes) further to the thesis of a\nuniversal grammar based on the structural analogy between the\n“modes of being” (modi essendi), the “modes\nof understanding” (modi intelligendi), and the\n“modes of signifying” (modi significandi) that are\nthe same for all languages. Along this line, Boethius Dacus (Boethius\nthe Dane), one of the most important theoreticians of speculative\ngrammar,[36]\n states that", "… all national languages are grammatically\nidentical. The reason for this is that the whole grammar is borrowed\nfrom the things … and just as the natures of things are similar\nfor those who speak different languages, so are the modes of being and\nthe modes of understanding; and consequently the modes of signifying\nare similar, whence, so are the modes of grammatical construction or\nspeech. And therefore the whole grammar which is in one language is\nsimilar to the one which is in another\n language.[37]", "\n\nEven though the words are arbitrarily imposed (whence arise the\ndifferences between all languages), the modes of signifying are\nuniformly related to the modes of being by means of the modes of\nunderstanding (whence arise the grammatical similarities among all\nlanguages). Focusing on the terms of ‘sign’ and\n‘signification’, speculative grammar, as a science of\ngeneral cognitive-linguistic structures, prescinds from all the\ndifferent national languages — and even from vocal language as\nsuch. For it is, as Martinus Dacus points out, not essential for\nspeculative grammar to deal with vocal expressions or with structures\nof vocal sign systems, because any kind of signs could be the object of\nthe considerations of a modist grammarian. The fact that he is\nconcerned with linguistic signs rather than with gestures or the\n“language of eyes” is only due to the fact that vocal\nexpressions are, compared to other kind of signs, more apt for human\ncommunication.[38]", "\n\nSoon after 1300 the modistic approach came under substantial\ncriticism. The main point that critics like Ockham oppose is not the\nassumption of a basic universal grammar, for such a claim is implied in\nOckham's concept of mental grammar, too. Two other aspects of modism\nare in the focus of these criticisms: (1) the assertion of a close\nstructural analogy between spoken or mental language and external\nreality (consimilis distinctio inter voces vel intentiones in anima\nsignificantes et inter ipsa significata) (William of Ockham,\nExpos. in lIbid. Porphyrii de praed., 1978, 158); (2) the\ninadmissible reification of the modus significandi adherent to\nits description as some quality or form added to the articulate voice\n(dictioni superadditum) through the act of imposition. To say\nthat vocal expressions ‘have’ different modes of signifying\nis, as Ockham points out, just a metaphorical manner of speaking; for\nwhat is meant is simply the fact that different words signify whatever\nthey signify in different\n ways.[39]\n According to John\nAurifaber (fl. ca. 1300), a vocal term is significative, or is a sign,\nsolely by being used significatively, not on grounds of something\ninherent in the\n sound.[40]\n In order to assign signification a proper\nplace in reality, it must be ascribed to the intellect rather than to\nthe vocal sound (significare est accidens intellectus; sed vox est\nillud quo significat intellectus) (Aurifaber, Determ. de modis\nsignif., 1967, 226). The criticism of modist grammar is based on a\nfundamental redefinition of the concept of sign, coming about after the\nmid-13th century. For the translocation of signification in\nthe proper sense from the word to the intellect is based on the\npresupposition that, whatever Augustine may have said, mental concepts\nare signs themselves." ], "section_title": "5. Grammatica Speculativa and its critics", "subsections": [] }, { "main_content": [ "\n\nIn 12th- and early 13th-century logical\ntextbooks the concept of sign does not play an important role yet.\n‘Sign’ in its technical sense is taken as the name of the\nso-called syncategorematic terms (e.g., omnis [every],\nnullus [no] as signa universalia or universal signs,\nquidam [a certain], aliquis [some] as signa\nparticularia or particular signs) (L. M. de Rijk, 1965–67,\nII/2.383).[41]\n In line with the text of Aristotle's\nPeri Hermeneias and its translation by Boethius, only written\nand spoken words were said to signify. Mental concepts (passiones\nanimae, intellectus, conceptus) were seen as\nlikenesses (similitudines) rather than as signs of things.\nOnce again, it is the mid-13th century where a conceptual\nchange is taking place which, although at first it may seem to be a\nmatter of nuance, turns out to be one of the most important junctures\nin the history of semiotics: mental concepts — without at first\nlosing their status of being likenesses of things — begin to be\ncharacterized as signs of things (signa rerum). It is true\nthat there are some few passages in Boethius, Anselm, and Abelard\nalready pointing in this direction (Boethius, In Periherm. ed.\nsec., 1880, 24; cf. Magee, 1989, 71; Anselm of Canterbury,\nMonolog., 1968, 25; Abelard, Log.\n‘Ingredientibus’, 1927, 315f.). But it is not until\nthe second half of 13th century that this idea achieves\ngeneral acceptance and gains relevance to the theory of\n sign.[42]", "\n\nThe consequences of this view are many: for instance, the rejection,\nor at least the modification, of Augustine's venerable definition of\nthe sign, and the new possibility to describe the relationship between\nthe concept and its object without referring to the notion of\nsimilitude. Furthermore, in the semantic triangle, the Boethian\nordo orandi now can be described entirely in terms of sign and\nsignificate.[43]\n Insofar as concepts agree with vocal\nexpressions in their function of being signs, it makes sense to\nconceive of thought processes as a kind of mental speech (oratio\nmentalis) showing close analogies to spoken discourse. This again\npaves the way for the development of a mentalist logic, the principal\nobjects of which are not the vocal terms and propositions any longer,\nbut rather the corresponding mental acts. The definition of mental\nconcepts as signa rerum also provides the basis of a close\ninterconnection of logic and epistemology as it is characteristic\nespecially of the later Middle Ages. In conjunction with this, a\nredefinition of the notion of signification (significare) is\ntaking place. For where the mental concepts, i.e., the acts of\nunderstanding (intellectus), are considered to be signs\nthemselves, the Aristotelian definition of significare\n(signifying) as to constitute an understanding (constituere\nintellectum) can no longer be regarded as adequate. As a result,\nthe terminology of ‘representation’\n(repraesentatio, repraesentare, facere\npraesens), originally used mainly in epistemological contexts,\nachieves an increasing importance for logical semantics by being fused\nwith the terminology of ‘signification’. Finally, the\ndescription of mental concepts as signs can also be seen as one of the\nmain motifs for the general account of signs as it emerges in late\nmedieval logic. For it is only under this condition that logic is no\nlonger concerned exclusively with arbitrary signs but also — and\neven primarily — with natural signs." ], "section_title": "6. Mental concepts as signs", "subsections": [] }, { "main_content": [ "\n\nEven though in 13th-century terminist logic\n‘significatio’ is seen as the foundation of all\n‘properties of terms’ (proprietates terminorum),\nthe generation of William of Sherwood and Peter of Spain is not\nparticularly interested in the concept of signification.\nSignificatio is shortly described as “presentation of\nsome form to the intellect” (praesentatio alicuius formae ad\nintellectus)[44]\n or as “representation of a thing by\nmeans of a conventional vocal expression” (rei per vocem\nsecundum placitum repraesentatio) (Peter of Spain, Summule\nlogicales, 1972, 79). But the detailed logical discussion\nstarts right away with the concept of suppositio\n(supposition), i.e., from the capacity of substantive terms to stand\nfor something in a propositional context.", "\n\nWith William of Ockham (ca. 1285–1347/49), however, the concepts of\nsign and signification begin to take center stage in logic (Biard\n1981, 452; Biard 1989, Lenz 2003, Panaccio 2004). Logic is seen as\nexclusively concerned with signs, primarily with mental signs,\nsecondarily with vocal or written signs. Ockham integrates the\nconcept of supposition into his definition of sign. He recognizes that\nthe general notion of sign as something that makes something else come\ninto cognition is too broad to be useful in logic and semantic theory;\ntherefore, he adds to the definition the criterion that a sign, as far\nas its use in logic is concerned, has to be apt to stand for the thing\nit makes come into cognition, or else it has to be such that it could\nbe added to such a sign standing for something (natum est pro illo\nsupponere vel tali addi in propositione) (William of\nOckham, Summa log., 1974, 9).[45] Thus, Ockham's logical concept of sign is\nrestricted to what later will be termed a ‘propositional\nsign’ (signum propositionale) (John Raulin, In log.\nArist. comment., 1500, fol. a5rb). Due to the central\nposition of the notion of sign in his logic, one is entitled to\ncharacterize Ockham's logic as “ruled by the concept of\nsign” (“régie par le concept de signe”)\n(Biard 1989, 102). Ockham, constantly referring to the notion of sign,\nventures in many cases a semiological redefinition of basic logical\nconcepts (Biard 1989, 102–25), which in turn allows him to reformulate\ntraditional ontological issues, as for instance the questions of\nuniversals, the number of categories, or the ontological status of\nrelations, as semantic questions.", "\n\nOckham's logic marks an important, though not the only important,\nstep in the process that might be described as a progressive\n‘mentalization’ of sign. The idea behind this process is\nthe contention that without some sort of ‘intentionality’\nthe phenomena of sign, signification and semiosis in general must\nremain inconceivable. This tendency of relocating the notions of sign\nand signification from the realm of spoken words to the sphere of the\nmind is characteristic of the mentalist logic arising in the early\n14th century, and remaining dominant throughout the later\nMiddle Ages. Words or signs, insofar as they concern rational\ndiscourse, were traditionally held to be the essential subject matter\nof logic. According to mentalist logic, however, the\n‘words’ or ‘signs’ primarily relevant to logic\nare not the spoken words, but the trans-idiomatic mental words\n(verba mentis) or mental concepts. Thus, in later medieval\nlogic, as already in Burleigh and Ockham, the mental sign will be the\nfocus of logical semantics. According to a distinction introduced by\nPeter of Ailly (1330–1421) in the second half of 14th\ncentury,", "…a thing can be called a sign in two senses. In the\nfirst sense, because it leads to an act of knowing the thing of which\nit is a sign. In a second sense, because it is itself the act of\nknowing the thing. In the second sense we may say that a concept is a\nsign of a thing of which such a concept is a natural likeness —\nnot that it leads to an act of knowing that thing, but because it is\nthe very act itself of knowing the thing, [an act that] naturally and\nproperly represents that thing (Peter of Ailly, Concepts,\n1980, 17).", "\n\nEven if Ockham's semantics, as well as his theory of mental language\ngoverned by a trans-idiomatic mental grammar transforming the theorems\nof terminist logic into a theory of thought processes (William of\nOckham, Summa log., 1974,\n 11ff),[46]\n was by no means\nundisputed, and came under severe criticism by his opponents as well as\nno less severe modifications by his ‘followers’. What,\ndespite all the differences, logical authors from the\n14thcentury on generally have in common is their awareness\nof the importance of the concept of sign — even though, of\ncourse, there were exceptions to this rule. Some realistic-minded\ntheologians, such as John Wyclif (1330–1384) or Stanislas of Znoymo\n(fl. ca. 1400), harshly criticize the alleged overestimation of the\nsign by the “teachers of signs” (doctores\nsignorum), as the latter calls them. According to Stanislas, the\nhuman ‘errantry through the vain and useless signs’ of\nlogic is nothing but the necessary consequence of the fall of mankind\n(in penam peccati sumus necessitati in his vacuis et inanis signis\nerranter ambulare) (Stanislas of Znoymo, De vero et\nfalso, 1971,\n 207).[47]" ], "section_title": "7. The sign as a central notion in 14th-century logic", "subsections": [] }, { "main_content": [ "\n\nWith Ockham, the concept of sign becomes a central notion of logical\ntheory. However, as a result of Ockham's focus on the propositional\nsign as the only sign relevant to logic, initially only a narrow\nsection of semiotic topics were dealt with in logic. In contrast to\nOckham, late scholastic terminist logic is characterized by an approach\nof discussing logico-semantic topics on the basis of a most general\nunderstanding of the pertinent vocabulary (e.g., terminus,\nsignificare, repraesentare, signum etc.).\nDue to this practice, topics of semiotic relevance, even though not of\ndirect logical concern, began to accumulate at the margins of the\nlogical discourse. The culmination point of this development is reached\nin the Paris school of John Major (John Mair, 1469–1547), the most\nimportant and most influential center of late-scholastic logical\nstudies.[48]", "\n\nThe members of this school take signification or “to\nsignify” in the general sense of to “make (someone) know\n(something)” (facere cognoscere) (Petrus Margallus,\nLog. utriusque scholia, 1520,\n 148),[49]\n and conceive it along\nthe lines of the older description of ‘repraesentare’ in\nits broadest sense according to which the function of representation\ncould be ascribed to all which “in some way contributes to a\nthing being known” (quod aliquo modo facit ad hoc quod res\ncognoscatur).[50]\n Consequently, “to signify”\noften is characterized as “to represent something to an\nintellect” (aliquid intellectui respraesentare) (Albert\nof Saxony, Quaest. in artem vet, 1988, 472; John Raulin,\nIn log. Arist. Comment, 1500, fol. g4vb). In order\nto make this definition cover cases of non intellectual sign\ninterpreters (animals)[51]\n as well as the so-called syncategorematic\nterms which do not properly signify ‘something’\n(aliquid), a still more general version was put forward,\ndefining the act of signifying as “to represent something or some\nthings or somehow to a cognitive power (aliquid vel aliqua vel\naliqualiter potentiae cognitivae repraesentare) (Gaspar Lax,\nParve divis. term., ca. 1502, fol a4vb). This\ndefinition roughly expresses what is basically uncontroversial\nregarding the concept of signification among logicians from late\n14th to early 16th century. Even if there were\nnumerous definitional variants of the concept of signification, which\noften gave occasion to controversies, nevertheless, common to all these\nvariations was their primarily epistemological orientation. Contrary to\nOckham's concept of sign, it is not the logical function of referring\nto a significatum that stands in the foreground, but rather\nthe sign's relation to a cognitive power. In other words, the sign is\nnot primarily characterized by its appropriateness to fulfill a\nsemantic function in the context of a proposition, but rather by its\ncapability to act in an epistemologically efficient way on a cognitive\npower: “A sign is something that makes think” (signum\nest res faciens cogitare) (Petrus Margallus, Log. utriusque\nscholia, 1520, 146). Unlike Ockham's semantic concept of sign, the\none favored by the later authors is predominantly pragmatic.", "\n\nThis tendency is already obvious when Peter of Ailly defines the act\nof signifying as “to represent something, or some things, or\nsomehow to a cognitive power by vitally changing it” (aliquid\nvel aliqua vel aliqualiter potentiae cognitivae ipsam vitaliter\nimmutando repraesentare) (Peter of Ailly, Concepts, 1980,\n16).[52]\n With the particle “vitally changing\nit” (vitaliter immutare) entering into the definition of\n‘significare’ the relatedness to cognition or to a\ncognitive power becomes an essential factor of signification. For, as\nJohn Gebwiler later underlines: “without such a vital change\nnothing is signified to whomsoever” (absque vitali\nimmutatione nihil cuipiam significatur) (John Gebwiler,\nMagistralis totius parvuli artis log. compil., 1511, fol.\nh4r-h4v).", "\n\nIn view of this it should be clear that the widespread opinion\naccording to which in medieval philosophy the sign was characterized by\nthe “classical definition” or the “famous formula of\naliquid stat pro aliquo” (something stands for\nsomething)[53]\n is mistaken. It is suppositio,\nnot significatio, that is characterized by that\nformula.[54]\n Even in Ockham's concept of sign, which\ncomes closest to such a description, the aptitude ‘to stand for\nsomething’ is just one component of the whole function of the\nsign. In no case has the sign or act of signifying been conceived as a\nsimple two-term relation of “something standing for\nsomething”.", "\n\nOn the basis of an extended notion of sign, the authors of late\n15th- and early 16th-century logic discussed at\nlength topics like the different kinds of signification and\nrepresentation (Gaspar Lax, Parve divis. term., ca. 1502, fol.\na5[55]\n or the traditional distinction of natural\nand conventional signs, showing that there exist intermediate forms,\nlike those signs that signify by custom (ex consuetudine)\n(Hagenau, Comment. in prim. et quart. tract. Petri Hisp, 1495,\nfol. a7v; Conrad Pschlacher, Compendiarius parv. log.\nLiber, 1512, fol. 6r-6v), which are\ninstituted neither by nature nor by an act of imposition, but rather\nare established by repetition (frequentatio) (Juan de Oria,\nSummul. vol. Primum, 1987, 109).", "\n\nThe universality of the concept of sign, according to which in some\nrespect “anything in the world is a sign” (omnis res\nmundi est signum) (Peter Margallus, Logices utriusque\nscholia, 1520, 146f.), is counterbalanced by the emphasis laid on\nthe mental sign (signum mentale) providing the basis for the\nwhole range of sign processes. Spoken words, just like any external\nsigns in general, can signify only by mediation of an immediate\nsignification, provided by the mental\n concepts.[56]\n Thus, as Petrus a\nSpinosa says, the whole signification depends on the mental term\n(tota significatio dependet a [termino]\nmentali) (Pedro de Espinosa, Tractatus terminorum,\ncited in Muñoz Delgado, 1983, 152f.) In some respect this claim\neven goes beyond John Gerson's thesis, that “signification is not\nproperly or aptly understood except with respect to an intellectual\nnature that is able to use the sign” (Significatio nec\nproprie nec convenienter accipitur, nisi per respectum ad naturam\nintellectualem, quae potest uti signo) (John Gerson, De modis\nsignificandi, 1706, 816). For what makes any signification\npossible, the cognitive act, is conceived to be a sign or an act of\nsignification in the most proper sense, so that any other sign or\nsignification can be termed a such only with reference to the mental\nsign (ipsa cognitio formalis… est propriissima significatio,\nita quod alia dicuntur significare per attributionem ad istam)\n(Hieronymus de S. Marcho, Compendium praeclarum, 1507, fol.\nB1[57]", "\n\nWhereas according to Augustine the sign, being an external entity by\ndefinition, was precluded from the sphere of the mind, it is now the\nmental sign, i.e., the mental concept or mental term (terminus\nmentalis), that is seen as the primary and most principal sign\n(signum mentale est primum et principalissimum signum, sine quo\nvoces et scripta significare non possunt) (Florentius Diel,\nModernorum summulae log., 1489, fol. a5v) as well\nas the ultimate ground of all\n signification.[58]\n Without such an\nultimate and immediate signification instantiated in the formal\nsignification of the mental concept, there would be, as John Raulin\nremarks, an infinite regress (processus in infinitum) in any\nsignification, something like a Peircean ‘infinite\nsemeiosis’.[59]\n Unlike the infinite semeiosis of Peirce,\nhowever, such a regress, according to late medieval authors, would not\nhave the character of a steady and permanent differentiation of\nsignification but rather would be, as John Major calls it, an\n“abyss in signifying” (abyssus in significando)\n(John Major: Introd. perutile in Arist. dial. (1527: fol.\n14ra), i.e., a process never resulting in a actual\nsignification.", "\n\nTogether with the deliberately extended notions of\n‘sign’ and ‘term’ and the emphasis of the role\nof the mental sign, a fundamental redefinition of written signs, i.e.,\ninscriptions is emerging in logic around 1500. Taking their cue from\nthe view introduced by Peter of Ailly, the later authors free the\nwritten sign from its traditional subordination to the vocal sign by\nimmediately subordinating it to the mental sign (Florentius Diel,\nModernorum summulae log., 1489, fol. d5v; Peter\nTartaretus, Expos. in summulas Petri Hisp, 1514, fol.\n37rb-va; Antonius Coronel, Termini,\n1506, fol. B3ra-b; Hieronymus Pardo, Medulla\ndyalect., 1505, fol. 7rb; John Eck, In summulis\nPetri Hisp., 1516, fol. 5 vb). Thus scriptura,\nno longer viewed as a secondary sign system and as a mere supplement of\nvocal speech, is no longer restricted to alphabetic writing. This in\nturn provides the ground for a dramatic generalization of the notion of\nwritten sign as well. When logical discourse extends its boundaries in\norder to give an account of all sorts of signs, integrating the whole\nrange of signs into the traditional framework of logic and, at the same\ntime, these signs have to be described along the lines of the\ntraditional distinction of mental, vocal, and written terms, then it is\nthe written term (terminus scriptus) that provides the most\nsuitable opportunity for such an integration. This, of course,\npresupposes a radically extended notion of inscriptions as it arose in\nParisian logic around 1500, where an inscription is no longer\ncharacterized in terms of its derivative relation to spoken language,\nbut rather in terms of its specific relation to the human sensory\napparatus. In this sense, John Major and others define the written term\nas a “term that can be perceived by a corporeal eye”\n(terminus scriptus est terminus qui oculo corporali percipi\npotest) (John Major, Libri quos in artibus in collegio Montis\nAcuti Parisius regentando compilavit, 1508, fol.\n 4[60]\n And Juan\nde Oria more explicitly states: “A written term is not called so\nbecause of being an inscription made up from characters or letters but\nrather because of representing something to the cognitive faculty by\nmeans of sight” (non enim dicitur terminus scriptus, quia sit\nscriptura ex caracteribus aut litteris constans, sed quia potentie\ncognitive aliquid proprie representat, mediante visu) (Juan de\nOria, Summul. vol. Primum, 1987, 106). The written term being\nthus defined, even the circulus vini can count as a written\nterm (John Maior , Libri…, 1508, fol. 4va).\nSome authors extend the notion of writing even further and call\nterminus scriptus “a term perceptible by senses other\nthan haering” (terminus alio sensu quam auditu\nperceptibilis) (Peter Margallus, Log. utriusque scholia,\n1520, 92) so that every corporeal being perceivable by one of the four\nexternal senses different from hearing may be an instance of written\nterms (omne sensibile corpus quattuor externis sensibus posse esse\nterminum scriptum) (Peter Margallus, Log. utriusque\nscholia, 1520, 162f.)", "\n\nThe basic idea behind this theoretical extension of the notion of\ninscription is the indifference of de sign-function to the material\ninstantiation of the sign. This arbitrariness of the medium of the sign\nholds for the signs not only with regard to their communicative\ncapacity, but also with regard to their function in logical operations.\nAs Paul of Venice points out, in principle it would be possible to form\nsyllogisms or to draw conclusions by using sticks and stones instead of\nwords or sentences (… possemus cum baculis syllogizare et\ncum lapidibus concludere) (Paul of Venice, Logica magna, prima\npars, Tract. de terminis, 1979, 78). The fact that we, in general,\ndo not do so, and that we do not communicate by means of sensible\nqualities like warms or smell, but rather use vocal or written terms in\nthe strict sense, is only due to their greater operability (Paul of\nVenice, Logica magna, prima pars, Tract. de terminis, 1979,\n78).[61]\n For we can utter articulated sounds\nwhenever we want to but cannot produce with the same ease and\ndistinctness the possible objects of the other senses like certain\ncolors or smells.[62]", "\n\nExtending the notion of terminus opens the horizon for\ntaking into account further semiotic issues, such as the distinction\nbetween terms that signify absolutely (terminus absolute\nsignificans) and terms that signify on account of circumstances\n(terminus ex circumstantia significans) (Juan de Oria,\nSummul. vol. Primum, 1987, 106f.) Whereas spoken or written\nwords are members of the first class, the second class is made up from\nany other kind of conventional signs, like the toll of bells, the\ncrucifix or the circulus vini. With this distinction, Johannes\nde Oria underscores the influence of the situational context on the\nsignification of non-linguistic signs. As he notices, it depends on the\ncircumstances of time and place whether the toll of a bell is an\ninvitation to go to the chapter congregation or to a meal; an image of\nthe crucified Christ denotes that he has to be adored only in the\nsituational context of a church building, but not in the studio of the\npainter or sculptor (imago crucifixi in ecclesia posita,\nrepresentat quod est adoranda, ubi non sic representaret in domo\npictoris vel statuifici) (Juan de Oria, Summul. vol.\nPrimum, 1987, 106f.); a wreath of foliage denotes the vine-selling\nonly when attached outside a tavern, but not in the woods (Peter\nMargallus, Log. utriusque scholia, 1965, 166). Moreover, the\nterms that signify on account of circumstances are characterized\naccording to John of Oria by the fact that they regularly signify a\nstate of affairs and thus function as propositional signs (terminus\nex circumstantia significans regulariter representat aliquid esse vel\nnon esse. Ex quo fit quod omnis talis terminus est propositio)\n(Juan de Oria, Summul. vol. Primum, 1987, 106).", "\n\nWhereas in Western Europe, under the growing influence of humanism,\nthe scholastic tradition of terminist logic came to an end in the third\ndecade of the 16th century, it had a vigorous, though not\nunaltered, continuation on the Iberian Peninsula until the\n18th century. From there it was re-imported to the\nuniversities and academic schools in Western Europe, after the late\n16th and early 17th century, mainly but not\nexclusively in Catholic areas. Even if the scholastic doctrine of signs\nwas presented in a so to speak “light version” by authors\nlike Domingo de Soto[63]\n and Franciscus Toletus, the rudiments of\nmedieval semiotics transmitted through their writings, provided the\ngroundwork on which a great number of 17th-century logicians\nwere developing a highly elaborated sign theory (Meier-Oeser 1997,\n171–335). The most important of these are the so-called Conimbricenses,\nJohn of St. Thomas (alias John Poinsot), Peter of Candamo and Silvester\nAranha, but a large number of texts is still awaiting to be\nexplored." ], "section_title": "8. The concept of sign in scholastic logic of 15th and early 16th-century", "subsections": [] } ]

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G. Braakhuis, C. H. Kneepkens, and\nL. M. de Rijk, Nijmegen: Ingenium, 167–191.", "Fuchs, Michael: 1999, Zeichen und Wissen. Das Verhältnis der\nZeichentheorie zur Theorie des Wissens und der Wissenschaften im\ndreizehnten Jahrhundert, Aschendorff, Münster in Westfalen.", "Gill, Harjeet Singh: 1999, “The Abélardian Tradition\nof Semiotics”. In Signs and Signification, vol. 1, ed.\nH. Singh Gill and G. Manetti, New Delhi: Bahri, 35–67.", "Glidden, David: 1983, “Skeptic semiotics”,\nPhronesis, 28: 213–55.", "Grassi, Onorato: 1986, Intuizione e significato. Adam Wodeham\ned il problema della conoscenza nel XIV secolo, Jaca,\nMailand.", "Haller, Rudolf: 1962, “Untersuchungen zum Bedeutungsproblem\nin der antiken und mittelalterlichen Philosophie”, Archiv\nfür Begriffgeschichte, 7: 57–119.", "Häring, Nikolaus M.: 1956, “Caracter, Signum und\nSignaculum. Der Weg von Petrus Damiani bis zur eigentlichen Aufnahme in\ndie Sakramentenlehre im 12. Jahrhundert”, Scholastik, 31:\n41–69.", "Howell, Kenneth: 1987, “Two aspects of Roger Bacon's semiotic\ntheory in De signis”, Semiotica, 63: 73–81.", "Hübener, Wolfgang: 1968, Studien zur kognitiven\nRepräsentation in der mittelalterlichen Philosophie.\nUnpublished Habilitationsschrift. Berlin.", "Hübener, Wolfgang: 1974, “Der theologisch-philosophische\nKonservativismus des Jean Gerson”. In Antiqui und moderni:\nTraditionsbewusstsein und Fortschrittsbewusstsein im späten\nMittelalter (= Miscellanea mediaevalia 9), ed. A. Zimmermann,\nBerlin, New York: W. de Gruyter, 171–200.", "Hübener, Wolfgang: 1981, “‘Oratio mentalis’\nund ‘oratio vocalis’ in der Philosophie des 14.\nJahrhunderts”. In Sprache und Erkenntnis im Mittelalter\n(= Miscellanea Mediaevalia 13/1–2), W. Kluxen et al. (eds.),\nBerlin, New York: W. de Gruyter, vol. 1, 488–97.", "Hübener, Wolfgang: 1990, “Wyclifs Kritik an den Doctores\nsignorum”. In Die Gegenwart Ockhams, ed. W. Vossenkuhl\nand R. Schönberger, Weinheim: VCH, 128–46.", "Jackson, B. Darrell: 1969, “The Theory of Signs in St.\nAugustine's De doctrina christiana”, Revue des Études\nAugustiniennes, 15: 9–49.", "Jolivet, Jean: 1969, Arts du langage et théologie chez\nAbélard, Paris: Vrin.", "Kaczmarek, Ludger: 1983, Significatio in der Zeichen- und\nSprachtheorie Ockhams. In History of Semiotics, ed. Achim\nEschbach and Jürgen Trabant, Benjamins, Amsterdam, Philadelphia,\n87–104.", "Kneepkens, C. H.: 1995, “The Priscianic Tradition,” in\nSprachtheorien in Spätantike und Mittelalter, ed. Sten\nEbbesen, Gunter Narr Verlag, Tübingen, 239–64.", "Kretzmann, Norman (ed.): 1988, Meaning and Inference in Medieval\nPhilosophy, Dordrecht: Kluwer.", "Lenz, Martin: 2003, Mentale Sätze: Wilhelm von Ockhams\nThesen zur Sprachlichkeit des Denkens, Wiesbaden: Franz Steiner\nVerlag.", "Magee, John: 1989, Boethius on signification and mind,\nLeiden: Brill.", "Maierù, Alfonso: 1981, “'Signum’ dans la culture\nmédiévale”. 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Friedman, Royal Danish Academy of Sciences and Letters,\nCopenhagen: C. A. Reitzel, 83–104.", "Panaccio, Claude: 1996, “Le langage mental en discussion:\n1320–1355”. Les Études philosophiques, 3:\n323–39.", "Panaccio, Claude: 1999a: “Grammar and Mental Language in\nPseudo-Kilwardby”, in Medieval Analyses in Language and\nCognition, Acts of the Symposium, ‘The Copenhagen School of\nMedieval Philosophy’, January 10–13, 1996, ed. Sten Ebbesen and\nRussell L. Friedman, Royal Danish Academy of Sciences and Letters,\nCopenhagen: Reitzel, 397–413.", "Panaccio, Claude: 1999b, Le discours intérieur de Platon\na Guillaume d'Ockham, Paris: Seuil.", "Panaccio, Claude: 2004, Ockham on Concepts, Aldershot:\nAshgate.", "Pinborg, Jan: 1962, “Das Sprachdenken der Stoa und Augustins\nDialektik”, Classica et Mediaevalia, 23: 148–77.", "Pinborg, Jan: 1967, Die Entwicklung der Sprachtheorie im\nMittelalter, Beiträge zur Geschichte der Philosophie und\nTheologie im Mittelalter XLII.2, Münster: Aschendorff.", "Pinborg, Jan: 1971, “Bezeichnung in der Logik des XIII\nJahrhunderts”. in Der Begriff der repraesentatio im\nMittelalter, Stellvertretung – Symbol – Zeichen –\nBild, ed. A. Zimmermann (= Miscellanea mediaevalia 8) Berlin,\nNew York: W. de Gruyter, 237–281.", "Pinborg, Jan: 1972, Logik und Semantik im Mittelalter. Ein\nÜberblick, Stuttgart-Bad Cannstatt: Frommann-Holzboog.", "Pinborg, Jan: 1976, “Some Problems of Semantic Representation\nin Medieval Logic”. In History of Linguistic Thought and\nContemporary Linguistics, ed. H. Parret, Berlin, New York: W. de\nGruyter, 254–78.", "Pinborg, Jan: 1981, “Roger Bacon on Signs: A Newly Recovered\nPart of the Opus maius”, in Sprache und Erkenntnis im\nMittelalter, ed. W. Kluxen et al. (= Miscellanea Mediaevalia\n13/1–2), Berlin, New York: W. de Gruyter, vol. 1, 403–412.", "Pinborg, Jan: 1982, “Speculative Grammar,” in The\nCambridge History of Later Medieval Philosophy, ed. Norman\nKretzmann, Anthony Kenny, and Jan Pinborg, Cambridge: Cambridge\nUniversity Press, 254–69.", "Posner, Roland, Robering, Klaus and Sebeok, Thomas A. (Eds.): 1997,\nSemiotik – Semiotics. Ein Handbuch zu den zeichentheoretischen\nGrundlagen von Natur und Kultur, vol. 1, Berlin, New York: W. de\nGruyter.", "Rosier, Irène: 1994, La parole comme acte. Sur la\ngrammaire et la sémantique au XIIIe siècle, Paris:\nVrin.", "Rosier, Irène: 1995, “Res significata et modus\nsignificandi: Les implications d'une distinction\nmédiévale,” in Sprachtheorien in\nSpätantike und Mittelalter, ed. Sten Ebbesen, Gunter Narr\nVerlag, Tübingen, 135–68.", "Rosier-Catach, Irène: 2000, Aristotle and Augustine. Two\nModels of Occidental Medieval Semantics, in: In Signs and\nSignification, vol. 2, ed. H. Singh Gill and G. Manetti, New\nDelhi: Bahri, 41–62.", "Rosier-Catach, Irène: forthcoming Signes et sacrements.\nLa parole efficace, Paris: Seuil.", "Ruef, Hans 1981, Augustin über Semiotik und Sprache.\nSprachtheoretische Analysen zu Augustins Schrift “De\nDialectica”, Bern: Wyss Erben.", "Simone, Raffaele: 1972, “Sémiologie\naugustinienne”. Semiotica, 6: 1–31.", "Sirridge, Mary: 1999, “‘Quam videndo intus\ndicimus’: Seeing and Saying in De Trinitate XV” in\nMedieval Analyses in Language and Cognition, Acts of the\nSymposium, ‘The Copenhagen School of Medieval Philosophy’,\nJanuary 10–13, 1996, ed. Sten Ebbesen and Russell L. Friedman, Royal\nDanish Academy of Sciences and Letters, Copenhagen: Reitzel,\n318–330.", "Tabarroni, Andrea: 1989, “Mental signs and the theory of\nrepresentation in Ockham”, in On the Medieval Theory of\nSigns, ed. U. Eco and C. Marmo, Amsterdam: Benjamins,\n195–224.", "Tweedale, Martin: 1990. “Mental Representation in Later\nMedieval Scholasticism”, in: Historical Foundations of\nCognitive Science, ed. J.-C. Smith, Dordrecht: Kluwer, 35-52.", "Umiker-Sebeok, J. and Sebeok, Thomas A. (Eds.): 1987, Monastic\nSign Languages, Approaches to Semiotics 76, Amsterdam:\nBenjamins." ]

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[ "\nBy “alternative set theories” we mean systems of set\ntheory differing significantly from the dominant ZF\n(Zermelo-Frankel set theory) and its close relatives (though we will\nreview these systems in the article). Among the systems we will review\nare typed theories of sets, Zermelo set theory and its variations, New\nFoundations and related systems, positive set theories, and\nconstructive set theories. An interest in the range of alternative set\ntheories does not presuppose an interest in replacing the dominant set\ntheory with one of the alternatives; acquainting ourselves with\nfoundations of mathematics formulated in terms of an alternative\nsystem can be instructive as showing us what any set theory (including\nthe usual one) is supposed to do for us. The study of alternative set\ntheories can dispel a facile identification of “set\ntheory” with “Zermelo-Fraenkel set theory”; they are\nnot the same thing." ]

[ { "content_title": "1. Why Set Theory?", "sub_toc": [ "1.1 The Dedekind construction of the reals", "1.2 The Frege-Russell definition of the natural numbers" ] }, { "content_title": "2. Naive Set Theory", "sub_toc": [ "2.1 The other paradoxes of naive set theory" ] }, { "content_title": "3. Typed Theories", "sub_toc": [] }, { "content_title": "4. Zermelo Set Theory and Its Refinements", "sub_toc": [ "4.1 Zermelo set theory", "4.2 From Zermelo set theory to ZFC", "4.3 Critique of Zermelo set theory", "4.4 Weak variations and theories with hypersets" ] }, { "content_title": "5. Theories with Classes", "sub_toc": [ "5.1 Class theory over ZFC", "5.2 Ackermann set theory" ] }, { "content_title": "6. New Foundations and Related Systems", "sub_toc": [ "6.1 The definition of NF", "6.2 The consistency problem for NF; the known consistent subsystems", "6.3 Mathematics in NFU + Infinity + Choice", "6.4 Critique of NFU" ] }, { "content_title": "7. Positive Set Theories", "sub_toc": [ "7.1 Topological motivation of positive set theory", "7.2 The system GPK\\(^{+}_{\\infty}\\) of Olivier Esser", "7.3 Critique of positive set theory" ] }, { "content_title": "8. Logically and Philosophically Motivated Variations", "sub_toc": [ "8.1 Constructive set theory", "8.2 Set theory for nonstandard analysis", "8.3 The multiverse view of set theory" ] }, { "content_title": "9. Small Set Theories", "sub_toc": [ "9.1 Pocket set theory", "9.2 Vopenka’s alternative set theory" ] }, { "content_title": "10. Double Extension Set Theory: A Curiosity", "sub_toc": [] }, { "content_title": "11. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nWhy do we do set theory in the first place? The most immediately\nfamiliar objects of mathematics which might seem to be sets are\ngeometric figures: but the view that these are best understood as sets\nof points is a modern view. Classical Greeks, while certainly aware of\nthe formal possibility of viewing geometric figures as sets of points,\nrejected this view because of their insistence on rejecting the actual\ninfinite. Even an early modern thinker like Spinoza could comment that\nit is obvious that a line is not a collection of points (whereas for\nus it may hard to see what else it could be; Ethics, I.15,\nscholium IV, 96).", "\nCantor’s set theory (which we will not address directly here as\nit was not formalized) arose out of an analysis of complicated\nsubcollections of the real line defined using tools of what we would\nnow call topology (Cantor 1872). A better advertisement for the\nusefulness of set theory for foundations of mathematics (or at least\none easier to understand for the layman) is Dedekind’s\ndefinition of real numbers using “cuts” in the rational\nnumbers (Dedekind 1872) and the definition of the natural numbers as\nsets due to Frege and Russell (Frege 1884).", "\nMost of us agree on what the theories of natural numbers, real\nnumbers, and Euclidean space ought to look like (though constructivist\nmathematicians will have differences with classical mathematics even\nhere). There was at least initially less agreement as to what a theory\nof sets ought to look like (or even whether there ought to be a theory\nof sets). The confidence of at least some mathematicians in their\nunderstanding of this subject (or in its coherence as a subject at\nall) was shaken by the discovery of paradoxes in “naive”\nset theory around the beginning of the twentieth century. A number of\nalternative approaches were considered then and later, but a single\ntheory, the Zermelo-Fraenkel theory with the Axiom of Choice\n(ZFC) dominates the field in practice. One of the strengths\nof the Zermelo-Fraenkel set theory is that it comes with an image of\nwhat the world of set theory is (just as most of us have a common\nnotion of what the natural numbers, the real numbers, and Euclidean\nspace are like): this image is what is called the “cumulative\nhierarchy” of sets." ], "section_title": "1. Why Set Theory?", "subsections": [ { "content": [ "\nIn the nineteenth century, analysis (the theory of the real numbers)\nneeded to be put on a firm logical footing. Dedekind’s\ndefinition of the reals (Dedekind 1872) was a tool for this\npurpose.", "\nSuppose that the rational numbers are understood (this is of course a\nmajor assumption, but certainly the rationals are more easily\nunderstood than the reals).", "\nDedekind proposed that the real numbers could be uniquely correlated\nwith cuts in the rationals, where a cut was determined by a\npair of sets \\((L, R)\\) with the following properties: \\(L\\) and \\(R\\)\nare sets of rationals. \\(L\\) and \\(R\\) are both nonempty and every\nelement of \\(L\\) is less than every element of \\(R\\) (so the two sets\nare disjoint). \\(L\\) has no greatest element. The union of \\(L\\) and\n\\(R\\) contains all rationals.", "\nIf we understand the theory of the reals prior to the cuts, we can say\nthat each cut is of the form \\(L = (-\\infty , r) \\cap \\mathbf{Q}, R =\n[r, \\infty) \\cap \\mathbf{Q}\\), where \\(\\mathbf{Q}\\) is the set of all\nrationals and \\(r\\) is a unique real number uniquely determining and\nuniquely determined by the cut. It is obvious that each real number\n\\(r\\) uniquely determines a cut in this way (but we need to show that\nthere are no other cuts). Given an arbitrary cut \\((L, R)\\), we\npropose that \\(r\\) will be the least upper bound of \\(L\\). The Least\nUpper Bound Axiom of the usual theory of the reals tells us that \\(L\\)\nhas a least upper bound \\((L\\) is nonempty and any element of \\(R\\)\n(which is also nonempty) is an upper bound of \\(L\\), so \\(L\\) has a\nleast upper bound). Because \\(L\\) has no greatest element, its least\nupper bound \\(r\\) cannot belong to \\(L\\). Any rational number less\nthan \\(r\\) is easily shown to belong to \\(L\\) and any rational number\ngreater than or equal to \\(r\\) is easily shown to belong to \\(R\\), so\nwe see that the cut we chose arbitrarily (and so any cut) is of the\nform \\(L = (-\\infty , r) \\cap \\mathbf{Q}, R = [r, \\infty) \\cap\n\\mathbf{Q}\\).", "\nA bolder move (given a theory of the rationals but no prior theory of\nthe reals) is to define the real numbers as cuts. Notice that\nthis requires us to have not only a theory of the rational numbers\n(not difficult to develop) but also a theory of sets of rational\nnumbers: if we are to understand a real number to be identified with a\ncut in the rational numbers, where a cut is a pair of sets of rational\nnumbers, we do need to understand what a set of rational numbers is.\nIf we are to demonstrate the existence of particular real numbers, we\nneed to have some idea what sets of rational numbers there are.", "\nAn example: when we have defined the rationals, and then defined the\nreals as the collection of Dedekind cuts, how do we define the square\nroot of 2? It is reasonably straightforward to show that \\((\\{x \\in\n\\mathbf{Q} \\mid x \\lt 0 \\vee x^2 \\lt 2\\}, \\{x \\in \\mathbf{Q} \\mid x\n\\gt 0 \\amp x^2 \\ge 2\\})\\) is a cut and (once we define arithmetic\noperations) that it is the positive square root of two. When we\nformulate this definition, we appear to presuppose that any property\nof rational numbers determines a set containing just those rational\nnumbers that have that property." ], "subsection_title": "1.1 The Dedekind construction of the reals" }, { "content": [ "\nFrege (1884) and Russell (1903) suggested that the simpler concept\n“natural number” also admits analysis in terms of sets.\nThe simplest application of natural numbers is to count finite sets.\nWe are all familiar with finite collections with 1, 2, 3, …\nelements. Additional sophistication may acquaint us with the empty set\nwith 0 elements.", "\nNow consider the number 3. It is associated with a particular property\nof finite sets: having three elements. With that property it may be\nargued that we may naturally associate an object, the collection of\nall sets with three elements. It seems reasonable to identify this set\nas the number 3. This definition might seem circular (3 is the set of\nall sets with 3 elements?) but can actually be put on a firm,\nnon-circular footing.", "\nDefine 0 as the set whose only element is the empty set. Let \\(A\\) be\nany set; define \\(A + 1\\) as the collection of all sets \\(a \\cup\n\\{x\\}\\) where \\(a \\in A\\) and \\(x \\not\\in a\\) (all sets obtained by\nadding a new element to an element of \\(A)\\). Then \\(0 + 1\\) is\nclearly the set we want to understand as \\(1, 1 + 1\\) is the set we\nwant to understand as \\(2, 2 + 1\\) is the set we want to understand as\n3, and so forth.", "\nWe can go further and define the set \\(\\mathbf{N}\\) of natural\nnumbers. 0 is a natural number and if \\(A\\) is a natural number, so is\n\\(A + 1\\). If a set \\(S\\) contains 0 and is closed under successor, it\nwill contain all natural numbers (this is one form of the principle of\nmathematical induction). Define \\(\\mathbf{N}\\) as the intersection of\nall sets \\(I\\) which contain 0 and contain \\(A + 1\\) whenever \\(A\\) is\nin \\(I\\) and \\(A + 1\\) exists. One might doubt that there is any\ninductive set, but consider the set \\(V\\) of all \\(x\\) such that \\(x =\nx\\) (the universe). There is a formal possibility that \\(V\\) itself is\nfinite, in which case there would be a last natural number \\(\\{V\\}\\);\none usually assumes an Axiom of Infinity to rule out such\npossibilities." ], "subsection_title": "1.2 The Frege-Russell definition of the natural numbers" } ] }, { "main_content": [ "\nIn the previous section, we took a completely intuitive approach to\nour applications of set theory. We assumed that the reader would go\nalong with certain ideas of what sets are like.", "\nWhat are the identity conditions on sets? It seems entirely in accord\nwith common sense to stipulate that a set is precisely determined by\nits elements: two sets \\(A\\) and \\(B\\) are the same if for every\n\\(x\\), either \\(x \\in A\\) and \\(x \\in B\\) or \\(x \\not\\in A\\) and \\(x\n\\not\\in B\\):", "\nThis is called the axiom of extensionality.", "\nIt also seems reasonable to suppose that there are things which are\nnot sets, but which are capable of being members of sets (such objects\nare often called atoms or urelements). These objects\nwill have no elements (like the empty set) but will be distinct from\none another and from the empty set. This suggests the alternative\nweaker axiom of extensionality (perhaps actually closer to common\nsense),", "\nwith an accompanying axiom of sethood", "\nWhat sets are there? The simplest collections are given by enumeration\n(the set {Tom, Dick, Harry} of men I see\nover there, or (more abstractly) the set \\(\\{-2, 2\\}\\) of square roots\nof 4. But even for finite sets it is often more convenient to give a\ndefining property for elements of the set: consider the set of all\ngrandmothers who have a legal address in Boise, Idaho; this is a\nfinite collection but it is inconvenient to list its members. The\ngeneral idea is that for any property \\(P\\), there is a set of all\nobjects with property \\(P\\). This can be formalized as follows: For\nany formula \\(P(x)\\), there is a set \\(A\\) (the variable \\(A\\) should\nnot be free in \\(P(x))\\) such that", "\nThis is called the axiom of comprehension. If we have weak\nextensionality and a sethood predicate, we might want to say", "\nThe theory with these two axioms of extensionality and comprehension\n(usually without sethood predicates) is called naive set\ntheory.", "\nIt is clear that comprehension allows the definition of finite sets:\nour set of men {Tom, Dick, Harry} can also\nbe written \\(\\{x \\mid {}\\) \\(x = \\textit{Tom}\\) \\({}\\lor{}\\) \\(x =\n\\textit{Dick}\\) \\({}\\lor{}\\) \\(x = \\textit{Harry}\\}\\). It also appears\nto allow for the definition of infinite sets, such as the set\n\\((\\{x \\in \\mathbf{Q} \\mid x \\lt 0 \\lor x^2 \\lt 2\\}\\) mentioned above\nin our definition of the square root of 2.", "\nUnfortunately, naive set theory is inconsistent. Russell gave the most\nconvincing proof of this, although his was not the first paradox to be\ndiscovered: let \\(P(x)\\) be the property \\(x \\not\\in x\\). By the axiom\nof comprehension, there is a set \\(R\\) such that for any \\(x, x \\in\nR\\) iff \\(x \\not\\in x\\). But it follows immediately that \\(R \\in R\\)\niff \\(R \\not\\in R\\), which is a contradiction.", "\nIt must be noted that our formalization of naive set theory is an\nanachronism. Cantor did not fully formalize his set theory, so it\ncannot be determined whether his system falls afoul of the paradoxes\n(he did not think so, and there are some who agree with him now).\nFrege formalized his system more explicitly, but his system was not\nprecisely a set theory in the modern sense: the most that can be said\nis that his system is inconsistent, for basically the reason given\nhere, and a full account of the differences between Frege’s\nsystem and our “naive set theory” is beside the point\n(though historically certainly interesting)." ], "section_title": "2. Naive Set Theory", "subsections": [ { "content": [ "\nTwo other paradoxes of naive set theory are usually mentioned, the\nparadox of Burali-Forti (1897)—which has historical\nprecedence—and the paradox of Cantor. To review these other\nparadoxes is a convenient way to review as well what the early set\ntheorists were up to, so we will do it. Our formal presentation of\nthese paradoxes is anachronistic; we are interested in their\nmathematical content, but not necessarily in the exact way that they\nwere originally presented.", "\nCantor in his theory of sets was concerned with defining notions of\ninfinite cardinal number and infinite ordinal number. Consideration of\nthe largest ordinal number gave rise to the Burali-Forti paradox, and\nconsideration of the largest cardinal number gave rise to the Cantor\nparadox.", "\nInfinite ordinals can be presented in naive set theory as isomorphism\nclasses of well-orderings (a well-ordering is a linear order \\(\\le\\)\nwith the property that any nonempty subset of its domain has a\n\\(\\le\\)-least element). We use reflexive, antisymmetric, transitive\nrelations \\(\\le\\) as our linear orders rather than the associated\nirreflexive, asymmetric, transitive relations \\(\\lt\\), because this\nallows us to distinguish between the ordinal numbers 0 and 1 (Russell\nand Whitehead took the latter approach and were unable to define an\nordinal number 1 in their Principia Mathematica).", "\nThere is a natural order on ordinal numbers (induced by the fact that\nof any two well-orderings, at least one will be isomorphic to an\ninitial segment of the other) and it is straightforward to show that\nit is a well-ordering. Since it is a well-ordering, it belongs to an\nisomorphism class (an ordinal number!) \\(\\Omega\\).", "\nIt is also straightforward to show that the order type of the natural\norder on the ordinals restricted to the ordinals less than \\(\\alpha\\)\nis \\(\\alpha\\): the order on \\(\\{0, 1, 2\\}\\) is of order type 3, the\norder on the finite ordinals \\(\\{0, 1, 2, \\ldots \\}\\) is the first\ninfinite ordinal \\(\\omega\\), and so forth.", "\nBut then the order type of the ordinals \\(\\lt \\Omega\\) is \\(\\Omega\\)\nitself, which means that the order type of all the ordinals\n(including \\(\\Omega)\\) is “greater”—but \\(\\Omega\\)\nwas defined as the order type of all the ordinals and should not be\ngreater than itself!", "\nThis paradox was presented first (Cantor was aware of it) and Cantor\ndid not think that it invalidated his system.", "\nCantor defined two sets as having the same cardinal number if there\nwas a bijection between them. This is of course simply common sense in\nthe finite realm; his originality lay in extending it to the infinite\nrealm and refusing to shy from the apparently paradoxical results. In\nthe infinite realm, cardinal and ordinal number are not isomorphic\nnotions as they are in the finite realm: a well-ordering of order type\n\\(\\omega\\) (say, the usual order on the natural numbers) and a\nwell-ordering of order type \\(\\omega + \\omega\\) (say, the order on the\nnatural numbers which puts all odd numbers before all even numbers and\nputs the sets of odd and even numbers in their usual order) represent\ndifferent ordinal numbers but their fields (being the same set!) are\ncertainly of the same size. Such “paradoxes” as the\napparent equinumerousness of the natural numbers and the perfect\nsquares (noted by Galileo) and the one-to-one correspondence between\nthe points on concentric circles of different radii, noted since the\nMiddle Ages, were viewed as matter-of-fact evidence for\nequinumerousness of particular infinite sets by Cantor.", "\nNovel with Cantor was the demonstration (1872) that there are infinite\nsets of different sizes according to this criterion. Cantor’s\nparadox, for which an original reference is difficult to find, is an\nimmediate corollary of this result. If \\(A\\) is a set, define the\npower set of \\(A\\) as the set of all subsets of \\(A: \\wp(A) =\n\\{B \\mid \\forall x(x \\in B \\rightarrow x \\in A)\\}\\). Cantor proved\nthat there can be no bijection between \\(A\\) and \\(\\wp(A)\\) for any\nset \\(A\\). Suppose that \\(f\\) is a bijection from \\(A\\) to \\(\\wp(A)\\).\nDefine \\(C\\) as \\(\\{a \\in A \\mid a \\not\\in f(a)\\}\\). Because \\(f\\) is\na bijection there must be \\(c\\) such that \\(f(c) = C\\). Now we notice\nthat \\(c \\in C \\leftrightarrow c \\not\\in f (c) = C\\), which is a\ncontradiction.", "\nCantor’s theorem just proved shows that for any set \\(A\\), there\nis a set \\(\\wp(A)\\) which is larger. Cantor’s paradox arises if\nwe try to apply Cantor’s theorem to the set of all sets (or to\nthe universal set, if we suppose (with common sense) that not all\nobjects are sets). If \\(V\\) is the universal set, then \\(\\wp(V)\\), the\npower set of the universal set (the set of all sets) must have larger\ncardinality than \\(V\\). But clearly no set can be larger in\ncardinality than the set which contains everything!", "\nCantor’s response to both of these paradoxes was telling (and\ncan be formalized in ZFC or in the related systems which\nadmit proper classes, as we will see below). He essentially reinvoked\nthe classical objections to infinite sets on a higher level. Both the\nlargest cardinal and the largest ordinal arise from considering the\nvery largest collections (such as the universe \\(V)\\). Cantor drew a\ndistinction between legitimate mathematical infinities such as the\ncountable infinity of the natural numbers (with its associated\ncardinal number \\(\\aleph_0\\) and many ordinal numbers \\(\\omega ,\n\\omega + 1, \\ldots ,\\omega + \\omega ,\\ldots)\\), the larger infinity of\nthe continuum, and further infinities derived from these, which he\ncalled transfinite, and what he called the Absolute Infinite,\nthe infinity of the collection containing everything and of such\nrelated notions as the largest cardinal and the largest ordinal. In\nthis he followed St. Augustine (De Civitate Dei) who argued\nin late classical times that the infinite collection of natural\nnumbers certainly existed as an actual infinity because God was aware\nof each and every natural number, but because God’s knowledge\nencompassed all the natural numbers their totality was somehow finite\nin His sight. The fact that his defense of set theory against the\nBurali-Forti and Cantor paradoxes was subsequently successfully\nformalized in ZFC and the related class systems leads some to\nbelieve that Cantor’s own set theory was not implicated in the\nparadoxes." ], "subsection_title": "2.1 The other paradoxes of naive set theory" } ] }, { "main_content": [ "\nAn early response to the paradoxes of set theory (by Russell, who\ndiscovered one of them) was the development of type theory (see the\nappendix to Russell’s The Principles of Mathematics\n(1903) or Whitehead & Russell’s Principia\nMathematica (1910–1913).", "\nThe simplest theory of this kind, which we call TST (Théorie\nSimple des Types, from the French, following Forster and others) is\nobtained as follows. We admit sorts of object indexed by the natural\nnumbers (this is purely a typographical convenience; no actual\nreference to natural numbers is involved). Type 0 is inhabited by\n“individuals” with no specified structure. Type 1 is\ninhabited by sets of type 0 objects, and in general type \\(n + 1\\) is\ninhabited by sets of type \\(n\\) objects.", "\nThe type system is enforced by the grammar of the language. Atomic\nsentences are equations or membership statements, and they are only\nwell-formed if they take one of the forms \\(x^{n} = y^{n}\\) or \\(x^{n}\n\\in y^{n+1}\\).", "\nThe axioms of extensionality of TST take the form", "\nthere is a separate axiom for each \\(n\\).", "\nThe axioms of comprehension of TST take the form (for any\nchoice of a type \\(n\\), a formula \\(\\phi\\), and a variable \\(A^{n+1}\\)\nnot free in \\(\\phi)\\)", "\nIt is interesting to observe that the axioms of TST are\nprecisely analogous to those of naive set theory.", "\nThis is not the original type theory of Russell. Leaving aside\nRussell’s use of “propositional functions” instead\nof classes and relations, the system of Principia Mathematica\n(Whitehead & Russell 1910–1913), hereinafter PM\nfails to be a set theory because it has separate types for relations\n(propositional functions of arity \\(\\gt 1)\\). It was not until Norbert\nWiener observed in 1914 that it was possible to define the ordered\npair as a set (his definition of \\(\\lt x, y \\gt\\) was not the current\n\\(\\{\\{x\\},\\{x, y\\}\\}\\), due to Kuratowski (1921), but \\(\\{\\{\\{x\\},\n\\varnothing \\},\\{\\{y\\}\\}\\})\\) that it became clear that it is possible\nto code relation types into set types. Russell frequently said in\nEnglish that relations could be understood as sets of pairs (or longer\ntuples) but he had no implementation of this idea (in fact, he defined\nordered pairs as relations in PM rather than the now usual\nreverse!) For a discussion of the history of this simplified type\ntheory, see Wang 1970.", "\nFurther, Russell was worried about circularity in definitions of sets\n(which he believed to be the cause of the paradoxes) to the extent\nthat he did not permit a set of a given type to be defined by a\ncondition which involved quantification over the same type or a higher\ntype. This predicativity restriction weakens the mathematical\npower of set theory to an extreme degree.", "\nIn Russell’s system, the restriction is implemented by\ncharacterizing a type not only by the type of its elements but by an\nadditional integer parameter called its “order”. For any\nobject with elements, the order of its type is higher than the order\nof the type of its elements. Further, the comprehension axiom is\nrestricted so that the condition defining a set of a type of order\n\\(n\\) can contain parameters only of types with order \\(\\le n\\) and\nquantifiers only over types with order \\(\\lt n\\). Russell’s\nsystem is further complicated by the fact that it is not a theory of\nsets, as we noted above, because it also contains relation types (this\nmakes a full account of it here inappropriate). Even if we restrict to\ntypes of sets, a simple linear hierarchy of types is not possible if\ntypes have order, because each type has “power set” types\nof each order higher than its own.", "\nWe present a typed theory of sets with predicativity restrictions (we\nhave seen this in work of Marcel Crabbé, but it may be older).\nIn this system, the types do not have orders, but Russell’s\nramified type theory with orders (complete with relation types) can be\ninterpreted in it (a technical result of which we do not give an\naccount here).", "\nThe syntax of predicative TST is the same as that of the\noriginal system. The axioms of extensionality are also the same. The\naxioms of comprehension of predicative TST take the form (for\nany choice of a type \\(n\\), a formula \\(\\phi\\), and a variable\n\\(A^{n+1}\\) not free in \\(\\phi\\), satisfying the restriction that no\nparameter of type \\(n + 2\\) or greater appears in \\(\\phi\\), nor does\nany quantifier over type \\(n + 1\\) or higher appear in \\(\\phi)\\)", "\nPredicative mathematics does not permit unrestricted mathematical\ninduction: In impredicative type theory, we can define 0 and the\n“successor” \\(A^+\\) of a set just as we did above in naive\nset theory (in a given type \\(n)\\) then define the set of natural\nnumbers:", "\nRussell would object that the set \\(\\mathbf{N}^{n+1}\\) is being\n“defined” in terms of facts about all sets\n\\(A^{n+1}\\): something is a type \\(n + 1\\) natural number just in case\nit belongs to all type \\(n + 1\\) inductive sets. But one of the type\n\\(n + 1\\) sets in terms of which it is being “defined” is\n\\(\\mathbf{N}^{n+1}\\) itself. (Independently of predicativist scruples,\none does need an Axiom of Infinity to ensure that all natural numbers\nexist; this is frequently added to TST, as is the Axiom of\nChoice).", "\nFor similar reasons, predicative mathematics does not permit the Least\nUpper Bound Axiom of analysis (the proof of this axiom in a set\ntheoretical implementation of the reals as Dedekind cuts fails for the\nsame kind of reason).", "\nRussell solved these problems in PM by adopting an Axiom of\nReducibility which in effect eliminated the predicativity\nrestrictions, but in later comments on PM he advocated\nabandoning this axiom.", "\nMost mathematicians are not predicativists; in our opinion the best\nanswer to predicativist objections is to deny that comprehension\naxioms can properly be construed as definitions (though we admit that\nwe seem to find ourselves frequently speaking loosely of \\(\\phi\\) as\nthe condition which “defines” \\(\\{x \\mid \\phi \\})\\).", "\nIt should be noted that it is possible to do a significant amount of\nmathematics while obeying predicativist scruples. The set of natural\nnumbers cannot be defined in the predicative version of TST,\nbut the set of singletons of natural numbers can be defined and can be\nused to prove some instances of induction (enough to do quite a bit of\nelementary mathematics). Similarly, a version of the Dedekind\nconstruction of the real numbers can be carried out, in which many\nimportant instances of the least upper bound axiom will be\nprovable.", "\nType theories are still in use, mostly in theoretical computer\nscience, but these are type theories of functions, with\ncomplexity similar to or greater than the complexity of the system of\nPM, and fortunately outside the scope of this study." ], "section_title": "3. Typed Theories", "subsections": [] }, { "main_content": [ "\nIn this section we discuss the development of the usual set theory\nZFC. It did not spring up full-grown like Athena from the\nhead of Zeus!" ], "section_title": "4. Zermelo Set Theory and Its Refinements", "subsections": [ { "content": [ "\nThe original theory Z of Zermelo (1908) had the following\naxioms:", "\nWe note that we do not need an axiom asserting the existence of\n\\(\\varnothing\\) (which is frequently included in axiom lists as it was\nin Zermelo’s original axiom set): the existence of any object\n(guaranteed by logic unless we use a free logic) along with separation\nwill do the trick, and even if we use a free logic the set provided by\nInfinity will serve (the axiom of Infinity can be reframed to say that\nthere is a set which contains all sets with no elements (without\npresupposing that there are any) and is closed under the desired\nsuccessor operation).", "\nEvery axiom of Zermelo set theory except Choice is an axiom of naive\nset theory. Zermelo chose enough axioms so that the mathematical\napplications of set theory could be carried out and restricted the\naxioms sufficiently that the paradoxes could not apparently be\nderived.", "\nThe most general comprehension axiom of Z is the axiom of\nSeparation. If we try to replicate the Russell paradox by constructing\nthe set \\(R' = \\{x \\in A \\mid x \\not\\in x\\}\\), we discover that \\(R'\n\\in R' \\leftrightarrow R' \\in A \\amp R' \\not\\in R'\\), from which we\ndeduce \\(R' \\not\\in A\\). For any set \\(A\\), we can construct a set\nwhich does not belong to it. Another way to put this is that\nZ proves that there is no universal set: if we had the\nuniversal set \\(V\\), we would have naive comprehension, because we\ncould define \\(\\{x \\mid P(x)\\}\\) as \\(\\{x \\in V \\mid P(x)\\}\\) for any\nproperty \\(P(x)\\), including the fatal \\(x \\not\\in x\\).", "\nIn order to apply the axiom of separation, we need to have some sets\n\\(A\\) from which to carve out subsets using properties. The other\naxioms allow the construction of a lot of sets (all sets needed for\nclassical mathematics outside of set theory, though not all of the\nsets that even Cantor had constructed with apparent safety).", "\nThe elimination of the universal set seems to arouse resistance in\nsome quarters (many of the alternative set theories recover it, and\nthe theories with sets and classes recover at least a universe of all\nsets). On the other hand, the elimination of the universal set seems\nto go along with Cantor’s idea that the problem with the\nparadoxes was that they involved Absolutely Infinite\ncollections—purported “sets” that are too large." ], "subsection_title": "4.1 Zermelo set theory" }, { "content": [ "\nZermelo set theory came to be modified in certain ways.", "\nThe formulation of the axiom of separation was made explicit:\n“for each formula \\(\\phi\\) of the first-order language with\nequality and membership, \\(\\{x \\in A \\mid \\phi \\}\\) exists”.\nZermelo’s original formulation referred more vaguely to\nproperties in general (and Zermelo himself seems to have objected to\nthe modern formulation as too restrictive).", "\nThe non-sets are usually abandoned (so the formulation of\nExtensionality is stronger) though ZFA (Zermelo-Fraenkel set\ntheory with atoms) was used in the first independence proofs for the\nAxiom of Choice.", "\nThe axiom scheme of Replacement was added by Fraenkel to make it\npossible to construct larger sets (even \\(\\aleph_{\\omega}\\) cannot be\nproved to exist in Zermelo set theory). The basic idea is that any\ncollection the same size as a set is a set, which can be logically\nformulated as follows: if \\(\\phi(x,y)\\) is a functional formula\n\\(\\forall x\\forall y\\forall z[(\\phi(x,y) \\amp \\phi(x,z)) \\rightarrow y\n= z\\)] and \\(A\\) is a set then there is a set \\(\\{y \\mid \\exists x \\in\nA(\\phi(x,y))\\}\\).", "\nThe axiom scheme of Foundation was added as a definite conception of\nwhat the universe of sets is like. The idea of the cumulative\nhierarchy of sets is that we construct sets in a sequence of stages\nindexed by the ordinals: at stage 0, the empty set is constructed; at\nstage \\(\\alpha + 1\\), all subsets of the set of stage \\(\\alpha\\) sets\nare constructed; at a limit stage \\(\\lambda\\), the union of all stages\nwith index less than \\(\\lambda\\) is constructed. Replacement is\nimportant for the implementation of this idea, as Z only\npermits one to construct sets belonging to the stages \\(V_n\\) and\n\\(V_{\\omega +n}\\) for \\(n\\) a natural number (we use the notation\n\\(V_{\\alpha}\\) for the collection of all sets constructed at stage\n\\(\\alpha)\\). The intention of the Foundation Axiom is to assert that\nevery set belongs to some \\(V_{\\alpha}\\) ; the commonest formulation\nis the mysterious assertion that for any nonempty set \\(A\\), there is\nan element \\(x\\) of \\(A\\) such that \\(x\\) is disjoint from \\(A\\). To\nsee that this is at least implied by Foundation, consider that there\nmust be a smallest \\(\\alpha\\) such that \\(A\\) meets \\(V_{\\alpha}\\),\nand any \\(x\\) in this \\(V_{\\alpha}\\) will have elements (if any) only\nof smaller rank and so not in \\(A\\).", "\nZermelo set theory has difficulties with the cumulative hierarchy. The\nusual form of the Zermelo axioms (or Zermelo’s original form)\ndoes not prove the existence of \\(V_{\\alpha}\\) as a set unless\n\\(\\alpha\\) is finite. If the Axiom of Infinity is reformulated to\nassert the existence of \\(V_{\\omega}\\), then the ranks proved to exist\nas sets by Zermelo set theory are exactly those which appear in the\nnatural model \\(V_{\\omega +\\omega}\\) of this theory. Also, Zermelo set\ntheory does not prove the existence of transitive closures of sets,\nwhich makes it difficult to assign ranks to sets in general. Zermelo\nset theory plus the assertion that every set belongs to a rank\n\\(V_{\\alpha}\\) which is a set implies Foundation, the existence of\nexpected ranks \\(V_{\\alpha}\\) (not the existence of such ranks for all\nordinals \\(\\alpha\\) but the existence of such a rank containing each\nset which can be shown to exist), and the existence of transitive\nclosures, and can be interpreted in Zermelo set theory without\nadditional assumptions.", "\nThe Axiom of Choice is an object of suspicion to some mathematicians\nbecause it is not constructive. It has become customary to indicate\nwhen a proof in set theory uses Choice, although most mathematicians\naccept it as an axiom. The Axiom of Replacement is sometimes replaced\nwith the Axiom of Collection, which asserts, for any formula\n\\(\\phi(x,y)\\):", "\nNote that \\(\\phi\\) here does not need to be functional; if for every\n\\(x \\in A\\), there are some \\(y\\)s such that \\(\\phi(x, y)\\), there is\na set such that for every \\(x \\in A\\), there is \\(y\\) in that\nset such that \\(\\phi(x, y)\\). One way to build this set is to\ntake, for each \\(x \\in A\\), all the \\(y\\)s of minimal rank such that\n\\(\\phi(x, y)\\) and put them in \\(C\\). In the presence of all other\naxioms of ZFC, Replacement and Collection are equivalent;\nwhen the axiomatics is perturbed (or when the logic is perturbed, as\nin intuitionistic set theory) the difference becomes important. The\nAxiom of Foundation is equivalent to \\(\\in\\)-Induction here but not in\nother contexts: \\(\\in\\)-Induction is the assertion that for any\nformula \\(\\phi\\):", "\ni.e., anything which is true of any set if it is true of all its\nelements is true of every set without exception." ], "subsection_title": "4.2 From Zermelo set theory to ZFC" }, { "content": [ "\nA common criticism of Zermelo set theory is that it is an ad\nhoc selection of axioms chosen to avoid paradox, and we have no\nreason to believe that it actually achieves this end. We believe such\nobjections to be unfounded, for two reasons. The first is that the\ntheory of types (which is the result of a principled single\nmodification of naive set theory) is easily shown to be precisely\nequivalent in consistency strength and expressive power to Z\nwith the restriction that all quantifiers in the formulas \\(\\phi\\) in\ninstances of separation must be bounded in a set; this casts doubt on\nthe idea that the choice of axioms in Z is particularly\narbitrary. The fact that the von Neumann-Gödel-Bernays class\ntheory (discussed below) turns out to be a conservative extension of\nZFC suggests that full ZFC is a precise formulation\nof Cantor’s ideas about the Absolute Infinite (and so not\narbitrary). Further, the introduction of the Foundation Axiom\nidentifies the set theories of this class as the theories of a\nparticular class of structures (the well-founded sets) of which the\nZermelo axioms certainly seem to hold (whether Replacement holds so\nevidently is another matter).", "\nThese theories are frequently extended with large cardinal axioms (the\nexistence of inaccessible cardinals, Mahlo cardinals, weakly compact\ncardinals, measurable cardinals and so forth). These do not to us\nsignal a new kind of set theory, but represent answers to the question\nas to how large the universe of Zermelo-style set theory is.", "\nThe choice of Zermelo set theory (leaving aside whether one goes on to\nZFC) rules out the use of equivalence classes of equinumerous\nsets as cardinals (and so the use of the Frege natural numbers) or the\nuse of equivalence classes of well-orderings as ordinals. There is no\ndifficulty with the use of the Dedekind cut formulation of the reals\n(once the rationals have been introduced). Instead of the equivalence\nclass formulations of cardinal and ordinal numbers, the von\nNeumann ordinals are used: a von Neumann ordinal is a transitive\nset (all of its elements are among its subsets) which is well-ordered\nby membership. The order type of a well-ordering is the von Neumann\nordinal of the same length (the axiom of Replacement is needed to\nprove that every set well-ordering has an order type; this can fail to\nbe true in Zermelo set theory, where the von Neumann ordinal \\(\\omega\n+ \\omega\\) cannot be proven to exist but there are certainly\nwell-orderings of this and longer types). The cardinal number \\(|A|\\)\nis defined as the smallest order type of a well-ordering of \\(A\\)\n(this requires Choice to work; without choice, we can use Foundation\nto define the cardinal of a set \\(A\\) as the set of all sets\nequinumerous with \\(A\\) and belonging to the first \\(V_{\\alpha}\\)\ncontaining sets equinumerous with \\(A)\\). This is one respect in which\nCantor’s ideas do not agree with the modern conception; he\nappears to have thought that he could define at least cardinal numbers\nas equivalence classes (or at least that is one way to interpret what\nhe says), although such equivalence classes would of course be\nAbsolutely Infinite." ], "subsection_title": "4.3 Critique of Zermelo set theory" }, { "content": [ "\nSome weaker subsystems of ZFC are used. Zermelo set theory,\nthe system Z described above, is still studied. The further\nrestriction of the axiom of separation to formulas in which all\nquantifiers are bounded in sets \\((\\Delta_0\\) separation) yields\n“bounded Zermelo set theory” or “Mac Lane set\ntheory”, so called because it has been advocated as a foundation\nfor mathematics by Saunders Mac Lane (1986). It is interesting to\nobserve that Mac Lane set theory is precisely equivalent in\nconsistency strength and expressive power to TST with the\nAxiom of Infinity. Z is strictly stronger than Mac Lane set\ntheory; the former theory proves the consistency of the latter. See\nMathias 2001a for an extensive discussion.", "\nThe set theory KPU (Kripke-Platek set theory with urelements,\nfor which see Barwise 1975) is of interest for technical reasons in\nmodel theory. The axioms of KPU are the weak Extensionality\nwhich allows urelements, Pairing, Union, \\(\\Delta_0\\) separation,\n\\(\\Delta_0\\) collection, and \\(\\in\\)-induction for arbitrary formulas.\nNote the absence of Power Set. The technical advantage of KPU\nis that all of its constructions are “absolute” in a\nsuitable sense. This makes the theory suitable for the development of\nan extension of recursion theory to sets.", "\nThe dominance of ZFC is nowhere more evident than in the\ngreat enthusiasm and sense of a new departure found in reactions to\nthe very slight variation of this kind of set theory embodied in\nversions of ZFC without the foundation axiom. It should be\nnoted that the Foundation Axiom was not part of the original\nsystem!", "\nWe describe two theories out of a range of possible theories of\nhypersets (Zermelo-Frankel set theory without foundation). A\nsource for theories of this kind is Aczel 1988.", "\nIn the following paragraphs, we will use the term “graph”\nfor a relation, and “extensional graph” for a relation\n\\(R\\) satisfying", "\nA decoration of a graph \\(G\\) is a function \\(f\\) with the property\nthat \\(f(x) = \\{f(y) \\mid yGx\\}\\) for all \\(x\\) in the field of \\(G\\).\nIn ZFC, all well-founded relations have unique decorations,\nand non-well-founded relations have no decorations. Aczel proposed his\nAnti-Foundation Axiom: every set graph has a unique\ndecoration. Maurice Boffa considered a stronger axiom: every\npartial, injective decoration of an extensional set graph \\(G\\) whose\ndomain contains the \\(G\\)-preimages of all its elements can be\nextended to an injective decoration of all of \\(G\\).", "\nThe Aczel system is distinct from the Boffa system in having fewer\nill-founded objects. For example, the Aczel theory proves that there\nis just one object which is its own sole element, while the Boffa\ntheory provides a proper class of such objects. The Aczel system has\nbeen especially popular, and we ourselves witnessed a great deal of\nenthusiasm for this subversion of the cumulative hierarchy. We are\ndoubtless not the only ones to point this out, but we did notice and\npoint out to others that at least the Aczel theory has a perfectly\nobvious analogue of the cumulative hierarchy. If \\(A_{\\alpha}\\) is a\nrank, the successor rank \\(A_{\\alpha +1}\\) will consist of all those\nsets which can be associated with graphs \\(G\\) with a selected point\n\\(t\\) with all elements of the field of \\(G\\) taken from\n\\(A_{\\alpha}\\). The zero and limit ranks are constructed just as in\nZFC. Every set belongs to an \\(A_{\\alpha}\\) for \\(\\alpha\\)\nless than or equal to the cardinality of its transitive closure. (It\nseems harder to impose rank on the world of the Boffa theory, though\nit can be done: the proper class of self-singletons is an obvious\ndifficulty, to begin with!).", "\nIt is true (and has been the object of applications in computer\nscience) that it is useful to admit reflexive structures for some\npurposes. The kind of reflexivity permitted by Aczel’s theory\nhas been useful for some such applications. However, such structures\nare modelled in well-founded set theory (using relations other than\nmembership) with hardly more difficulty, and the reflexivity admitted\nby Aczel’s theory (or even by a more liberal theory like that of\nBoffa) doesn’t come near the kind of non-well-foundedness found\nin genuinely alternative set theories, especially those with universal\nset. These theories are close variants of the usual theory\nZFC, caused by perturbing the last axiom to be added to this\nsystem historically (although, to be fair, the Axiom of Foundation is\nthe one which arguably defines the unique structure which the usual\nset theory is about; the anti-foundation axioms thus invite us to\ncontemplate different, even if closely related, universal\nstructures)." ], "subsection_title": "4.4 Weak variations and theories with hypersets" } ] }, { "main_content": [], "section_title": "5. Theories with Classes", "subsections": [ { "content": [ "\nEven those mathematicians who accepted the Zermelo-style set theories\nas the standard (most of them!) often found themselves wanting to talk\nabout “all sets”, or “all ordinals”, or\nsimilar concepts.", "\nVon Neumann (who actually formulated a theory of functions, not sets),\nGödel, and Bernays developed closely related systems which admit,\nin addition to the sets found in ZFC, general collections of\nthese sets. (In Hallett 1984, it is argued that the system of von\nNeumann was the first system in which the Axiom of Replacement was\nimplemented correctly [there were technical problems with\nFraenkel’s formulation], so it may actually be the first\nimplementation of ZFC.)", "\nWe present a theory of this kind. Its objects are classes.\nAmong the classes we identify those which are elements as sets.", "\nThe axiom scheme of class comprehension with quantification only over\nsets admits a finite axiomatization (a finite selection of formulas\n\\(\\phi\\) (most with parameters) suffices) and was historically first\npresented in this way. It is an immediate consequence of class\ncomprehension that the Russell class \\(\\{x \\mid x \\not\\in x\\}\\) cannot\nbe a set (so there is at least one proper class).", "\nThis elegant axiom is essentially due to von Neumann. A class\nbijection is a class of ordered pairs; there might be pathology here\nif we did not have enough pairs as sets, but other axioms do provide\nfor their existence. It is interesting to observe that this axiom\nimplies Replacement (a class which is the same size as a set cannot be\nthe same size as the universe) and, surprisingly, implies Choice (the\nvon Neumann ordinals make up a proper class essentially by the\nBurali-Forti paradox, so the universe must be the same size as the\nclass of ordinals, and the class bijection between the universe and\nthe ordinals allows us to define a global well-ordering of the\nuniverse, whose existence immediately implies Choice).", "\nAlthough Class Comprehension and Limitation of Size appear to tell us\nexactly what classes there are and what sets there are, more axioms\nare required to make our universe large enough. These can be taken to\nbe the axioms of Z (other than extensionality and choice,\nwhich are not needed): the sethood of pairs of sets, unions of sets,\npower sets of sets, and the existence of an infinite set are enough to\ngive us the world of ZFC. Foundation is usually added. The\nresulting theory is a conservative extension of ZFC: it\nproves all the theorems of ZFC about sets, and it does not\nprove any theorem about sets which is not provable in ZFC.\nFor those with qualms about choice (or about global choice),\nLimitation of Size can be restricted to merely assert that the image\nof a set under a class function is a set.", "\nWe have two comments about this. First, the mental furniture of set\ntheorists does seem to include proper classes, though usually it is\nimportant to them that all talk of proper classes can be explained\naway (the proper classes are in some sense “virtual”).\nSecond, this theory (especially the version with the strong axiom of\nLimitation of Size) seems to capture the intuition of Cantor about the\nAbsolute Infinite.", "\nA stronger theory with classes, but still essentially a version of\nstandard set theory, is the Kelley-Morse set theory in which Class\nComprehension is strengthened to allow quantification over all classes\nin the formulas defining classes. Kelley-Morse set theory is not\nfinitely axiomatizable, and it is stronger than ZFC in the\nsense that it allows a proof of the consistency of ZFC." ], "subsection_title": "5.1 Class theory over ZFC" }, { "content": [ "\nThe next theory we present was actually embedded in the set\ntheoretical proposals of Paul Finsler, which were (taken as a whole)\nincoherent (see the notes on Finsler set theory available in the\n Other Internet Resources).\n Ackermann later (and apparently independently) presented it again. It\nis to all appearances a different theory from the standard one (it is\nour first genuine “alternative set theory”) but it turns\nout to be essentially the same theory as ZF (and choice can\nbe added to make it essentially the same as ZFC).", "\nAckermann set theory is a theory of classes in which some\nclasses are sets, but there is no simple definition of which\nclasses are sets (in fact, the whole power of the theory is that the\nnotion of set is indefinable!)", "\nAll objects are classes. The primitive notions are equality,\nmembership and sethood. The axioms are", "\nOne can conveniently add axioms of Foundation and Choice to this\nsystem.", "\nTo see the point (mainly, to understand what Set Comprehension says)\nit is a good idea to go through some derivations.", "\nThe formula \\(x = a \\lor x = b\\) (where \\(a\\) and \\(b\\) are sets) does\nnot mention sethood, has only the sets \\(a\\) and \\(b\\) as parameters,\nand is true only of sets. Thus it defines a set, and Pairing is true\nfor sets.", "\nThe formula \\(\\exists y(x \\in y \\amp y \\in a)\\), where \\(a\\) is a set,\ndoes not mention sethood, has only the set \\(a\\) as a parameter, and\nis true only of sets by the Axiom of Elements (any witness \\(y\\)\nbelongs to the set \\(a\\), so \\(y\\) is a set, and \\(x\\) belongs to the\nset \\(y\\), so \\(x\\) is a set). Thus Union is true for sets.", "\nThe formula \\(\\forall y(y \\in x \\rightarrow y \\in a)\\), where \\(a\\) is\na set, does not mention sethood, has only the set \\(a\\) as a\nparameter, and is true only of sets by the Axiom of Subsets. Thus\nPower Set is true for sets.", "\nThe big surprise is that this system proves Infinity. The formula \\(x\n\\ne x\\) clearly defines a set, the empty set \\(\\varnothing\\). Consider\nthe formula", "\nThis formula does not mention sethood and has no parameters (or just\nthe set parameter \\(\\varnothing)\\). The class \\(V\\) of all sets has\n\\(\\varnothing\\) as a member and contains \\(y \\cup \\{y\\}\\) if it\ncontains \\(y\\) by Pairing and Union for sets (already shown). Thus any\n\\(x\\) satisfying this formula is a set, whence the extension of the\nformula is a set (clearly the usual set of von Neumann natural\nnumbers). So Infinity is true in the sets of Ackermann set theory.", "\nIt is possible (but harder) to prove Replacement as well in the realm\nof well-founded sets (which can be the entire universe of sets if\nFoundation for classes is added as an axiom). It is demonstrable that\nthe theorems of Ackermann set theory about well-founded sets are\nexactly the theorems of ZF (Lévy 1959; Reinhardt\n1970).", "\nWe attempt to motivate this theory (in terms of the cumulative\nhierarchy). Think of classes as collections which merely exist\npotentially. The sets are those classes which actually get\nconstructed. Extensionality for classes seems unproblematic. All\ncollections of the actual sets could have been constructed by\nconstructing one more stage of the cumulative hierarchy: this\njustifies class comprehension. Elements of actual sets are actual\nsets; subcollections of actual sets are actual sets; these do not seem\nproblematic. Finally, we assert that any collection of classes which\nis defined without reference to the realm of actual sets, which is\ndefined in terms of specific objects which are actual, and which turns\nout only to contain actual elements is actual. When one gets\none’s mind around this last assertion, it can seem reasonable. A\nparticular thing to note about such a definition is that it is\n“absolute”: the collection of all actual sets is a proper\nclass and not itself an actual set, because we are not committed to\nstopping the construction of actual sets at any particular point; but\nthe elements of a collection satisfying the conditions of set\ncomprehension do not depend on how many potential collections we make\nactual (this is why the actuality predicate is not allowed to appear\nin the “defining” formula).", "\nIt may be a minority opinion, but we believe (after some\ncontemplation) that the Ackermann axioms have their own distinctive\nphilosophical motivation which deserves consideration, particularly\nsince it turns out to yield basically the same theory as ZF\nfrom an apparently quite different starting point.", "\nAckermann set theory actually proves that there are classes which have\nnon-set classes as elements; the difference between sets and classes\nprovably cannot be as in von Neumann-Gödel-Bernays class theory.\nA quick proof of this concerns ordinals. There is a proper class von\nNeumann ordinal \\(\\Omega\\), the class of all set von Neumann ordinals.\nWe can prove the existence of \\(\\Omega + 1\\) using set comprehension:\nif \\(\\Omega\\) were the last ordinal, then “\\(x\\) is a von\nNeumann ordinal with a successor” would be a predicate not\nmentioning sethood, with no parameters (so all parameters sets), and\ntrue only of sets. But this would make the class of all set ordinals a\nset, and the class of all set ordinals is \\(\\Omega\\) itself, which\nwould lead to the Burali-Forti paradox. So \\(\\Omega + 1\\) must exist,\nand is a proper class with the proper class \\(\\Omega\\) as an\nelement.", "\nThere is a meta-theorem of ZF called the Reflection Principle\nwhich asserts that any first-order assertion which is true of the\nuniverse \\(V\\) is also true of some set. This means that for any\nparticular proof in ZF, there is a set \\(M\\) which might as\nwell be the universe (because any proof uses only finitely many\naxioms). A suitable such set \\(M\\) can be construed as the universe of\nsets and the actual universe \\(V\\) can be construed as the universe of\nclasses. The set \\(M\\) has the closure properties asserted in Elements\nand Subsets if it is a limit rank; it can be chosen to have as many of\nthe closure properties asserted in Set Comprehension (translated into\nterms of \\(M)\\) as a proof in Ackermann set theory requires. This\nmachinery is what is used to show that Ackermann set theory proves\nnothing about sets that ZF cannot prove: one translates a\nproof in Ackermann set theory into a proof in ZFC using the\nReflection Principle." ], "subsection_title": "5.2 Ackermann set theory" } ] }, { "main_content": [], "section_title": "6. New Foundations and Related Systems", "subsections": [ { "content": [ "\nWe have alluded already to the fact that the simple typed theory of\nsets TST can be shown to be equivalent to an untyped theory\n(Mac Lane set theory, aka bounded Zermelo set theory). We briefly\nindicate how to do this: choose any map \\(f\\) in the model which is an\ninjection with domain the set of singletons of type 0 objects and\nrange included in type 1 (the identity on singletons of type 0 objects\nis an example). Identify each type 0 object \\(x^0\\) with the type 1\nobject \\(f (\\{x^0\\})\\); then introduce exactly those identifications\nbetween objects of different types which are required by\nextensionality: every type 0 object is identified with a type 1\nobject, and an easy meta-induction shows that every type \\(n\\) object\nis identified with some type \\(n + 1\\) object. The resulting structure\nwill satisfy all the axioms of Zermelo set theory except Separation,\nand will satisfy all instances of Separation in which each quantifier\nis bounded in a set (this boundedness comes in because each instance\nof Comprehension in TST has each quantifier bounded in a\ntype, which becomes a bounding set for that quantifier in the\ninterpretation of Mac Lane set theory). It will satisfy Infinity and\nChoice if the original model of TST satisfies these axioms.\nThe simplest map \\(f\\) is just the identity on singletons of type 0\nobjects, which will have the effect of identifying each type 0 object\nwith its own singleton (a failure of foundation). It can be arranged\nfor the structure to satisfy Foundation: for example, if Choice holds\ntype 0 can be well-ordered and each element of type 0 identified with\nthe corresponding segment in the well-ordering, so that type 0 becomes\na von Neumann ordinal. (A structure of this kind will never model\nReplacement, as there will be a countable sequence of cardinals [the\ncardinalities of the types] which is definable and cofinal below the\ncardinality of the universe.) See Mathias 2001a for a full\naccount.", "\nQuine’s set theory New Foundations (abbreviated NF,\nproposed in 1937 in his paper “New Foundations for Mathematical\nLogic”), is also based on a procedure for identifying the\nobjects in successive types in order to obtain an untyped theory.\nHowever, in the case of NF and related theories, the idea is\nto identify the entirety of type \\(n + 1\\) with type \\(n\\); the type\nhierarchy is to be collapsed completely. An obvious difficulty with\nthis is that Cantor’s theorem suggests that type \\(n + 1\\)\n(being the “power set” of type \\(n)\\) should be\nintrinsically larger than type \\(n\\) (and in some senses this is\ndemonstrably true).", "\nWe first outline the reason that Quine believed that it might be\npossible to collapse the type hierarchy. We recall from\n above:", "\n\n\nWe admit sorts of object indexed by the natural numbers (this is\npurely a typographical convenience; no actual reference to natural\nnumbers is involved). Type 0 is inhabited by “individuals”\nwith no specified structure. Type 1 is inhabited by sets of type 0\nobjects, and in general type \\(n + 1\\) is inhabited by sets of type\n\\(n\\) objects.\n", "\nThe type system is enforced by the grammar of the language. Atomic\nsentences are equations or membership statements, and they are only\nwell-formed if they take one of the forms \\(x^{n} = y^{n}\\) or \\(x^{n}\n\\in y^{n+1}\\).", "\nThe axioms of extensionality of TST take the form", "\nthere is a separate axiom for each \\(n\\).", "\nThe axioms of comprehension of TST take the form (for any\nchoice of a type \\(n\\), a formula \\(\\phi\\), and a variable \\(A^{n+1}\\)\nnot free in \\(\\phi)\\)", "\nIt is interesting to observe that the axioms of TST are\nprecisely analogous to those of naive set theory.", "\nFor any formula \\(\\phi\\), define \\(\\phi^+\\) as the formula obtained by\nraising every type index on a variable in \\(\\phi\\) by one. Quine\nobserves that any proof of \\(\\phi\\) can be converted into a proof of\n\\(\\phi^+\\) by raising all type indices in the original proof. Further,\nevery object \\(\\{x^n \\mid \\phi \\}^{n+1}\\) that the theory permits us\nto define has a precise analogue \\(\\{x^{n+1} \\mid \\phi^{+}\\}^{n+2}\\)\nin the next higher type; this can be iterated to produce\n“copies” of any defined object in each higher type.", "\nFor example, the Frege definition of the natural numbers works in\nTST. The number \\(3^2\\) can be defined as the (type 2) set of\nall (type 1) sets with three (type 0) elements. The number \\(3^3\\) can\nbe defined as the (type 3) set of all (type 2) sets with three (type\n1) elements. The number \\(3^{27}\\) can be defined as the (type 27) set\nof all (type 26) sets with three (type 25) elements. And so forth. Our\nlogic does not even permit us to say that these are a sequence of\ndistinct objects; we cannot ask the question as to whether they are\nequal or not.", "\nQuine suggested, in effect, that we tentatively suppose that \\(\\phi\n\\equiv \\phi^+\\) for all \\(\\phi\\) ; it is not just the case that if we\ncan prove \\(\\phi\\), we can prove \\(\\phi^+\\), but that the truth values\nof these sentences are the same. It then becomes strongly tempting to\nidentify \\(\\{x^n \\mid \\phi \\}^{n+1}\\) with \\(\\{x^{n+1} \\mid\n\\phi^{+}\\}^{n+2}\\), since anything we can say about these two objects\nis the same (and our new assumption implies that we will assign the\nsame truth values to corresponding assertions about these two\nobjects).", "\nThe theory NF which we obtain can be described briefly (but\ndeceptively) as being the first-order untyped theory with equality and\nmembership having the same axioms as TST but without the\ndistinctions of type. If this is not read very carefully, it may be\nseen as implying that we have adopted the comprehension axioms of\nnaive set theory,", "\nfor each formula \\(\\phi\\). But we have not. We have only adopted those\naxioms for formulas \\(\\phi\\) which can be obtained from formulas of\nTST by dropping distinctions of type between the variables\n(without introducing any identifications between variables of\ndifferent types). For example, there is no way that \\(x \\not\\in x\\)\ncan be obtained by dropping distinctions of type from a formula of\nTST, without identifying two variables of different type.\nFormulas of the untyped language of set theory in which it is possible\nto assign a type to each variable (the same type wherever it occurs)\nin such a way as to get a formula of TST are said to be\nstratified. The axioms of NF are strong\nextensionality (no non-sets) and stratified comprehension.", "\nThough the set \\(\\{x \\mid x \\not\\in x\\}\\) is not provided by\nstratified comprehension, some other sets which are not found in any\nvariant of Zermelo set theory are provided. For example, \\(x = x\\) is\na stratified formula, and the universal set \\(V = \\{x \\mid x = x\\}\\)\nis provided by an instance of comprehension. Moreover, \\(V \\in V\\) is\ntrue.", "\nAll mathematical constructions which can be carried out in\nTST can be carried out in NF. For example, the Frege\nnatural numbers can be constructed, and so can the set \\(\\mathbf{N}\\)\nof Frege natural numbers. For example, the Frege natural number 1, the\nset of all one-element sets, is provided by NF." ], "subsection_title": "6.1 The definition of NF" }, { "content": [ "\nNo contradictions are known to follow from NF, but some\nuncomfortable consequences do follow. The Axiom of Choice is known to\nfail in NF: Specker (1953) proved that the universe cannot be\nwell-ordered. (Since the universe cannot be well-ordered, it follows\nthat the “Axiom” of Infinity is a theorem of NF:\nif the universe were finite, it could be well-ordered.) This might be\nthought to be what one would expect on adopting such a dangerous\ncomprehension scheme, but this turns out not to be the problem. The\nproblem is with extensionality.", "\nJensen (1968) showed that NFU (New Foundations with\nurelements), the version of New Foundations in which extensionality is\nweakened to allow many non-sets (as described above under naive set\ntheory) is consistent, is consistent with Infinity and Choice, and is\nalso consistent with the negation of Infinity (which of course implies\nChoice). NFU, which has the full stratified comprehension\naxiom of NF with all its frighteningly big sets, is weaker in\nconsistency strength than Peano arithmetic; NFU + Infinity +\nChoice is of the same strength as TST with Infinity and\nChoice or Mac Lane set theory.", "\nSome other fragments of NF, obtained by weakening\ncomprehension rather than extensionality, are known to be consistent.\nNF3, the version of NF in which one\naccepts only those instances of the axiom of comprehension which can\nbe typed using three types, was shown to be consistent by Grishin\n(1969).", "\nNFP (predicative NF), the version of NF in\nwhich one accepts only instances of the axiom of comprehension which\ncan be typed so as to be instances of comprehension of predicative\nTST (described above under type theories) was shown to be\nconsistent by Marcel Crabbé (1982). He also demonstrated the\nconsistency of the theory NFI in which one allows all\ninstances of stratified comprehension in which no variable appears of\ntype higher than that assigned to the set being defined (bound\nvariables of the same type as that of the set being defined are\npermitted, which allows some impredicativity). One would like to read\nthe name NFI as “impredicative NF” but\none cannot, as it is more impredicative than NFP, not more\nimpredicative than NF itself.", "\nNF3+Infinity has the same strength as second-order\narithmetic. So does NFI (which has just enough\nimpredicativity to define the natural numbers, and not enough for the\nLeast Upper Bound Axiom). NFP is equivalent to a weaker\nfragment of arithmetic, but does (unlike NFU) prove Infinity:\nthis is the only application of the Specker proof of the negation of\nthe Axiom of Choice to a provably consistent theory. Either Union is\ntrue (in which case we readily get all of NF and\nSpecker’s proof of Infinity goes through) or Union is not true,\nin which case we note that all finite sets have unions, so there must\nbe an infinite set. NF3 has considerable interest\nfor a surprising reason: it turns out that all infinite\nmodels of TST3 (simple type theory with three\ntypes) satisfy the ambiguity schema \\(\\phi \\equiv \\phi^+\\) (of course\nthis only makes sense for formulas with one or two types) and this\nturns out to be enough to show that for any infinite model of\nTST3 there is a model of NF3\nwith the same theory. NF4 is the same theory as\nNF (Grishin 1969), and we have no idea how to get a model of\nTST4 to satisfy ambiguity.", "\nVery recently, Sergei Tupailo (2010) has proved the consistency of\nNFSI, the fragment of NF consisting of\nextensionality and those instances of Comprehension (\\(\\{x \\in A \\mid\n\\phi \\}\\) exists) which are stratified and in which the variable \\(x\\)\nis assigned the lowest type. Tupailo’s proof is highly\ntechnical, but Marcel Crabbé pointed out that a structure for\nthe language of set theory in which the sets are exactly the finite\nand cofinite collections satisfies this theory (so it is very weak).\nIt should be noted that Tupailo’s model of NFSI\nsatisfies additional propositions of interest not satisfied by the\nvery simple model of Crabbé, such as the existence of each\nFrege natural number. It is of some interest whether this new fragment\nrepresents an independent way of getting a consistent fragment of\nNF. Note that NFU+NFSI is NF\nbecause NFSI has strong extensionality. Also,\nNFP+NFSI is NF because NFSI\nincludes Union. The relationship of NFSI to NF\\(_3\\)\nhas been clarified by Marcel Crabbé in 2016. Tupailo’s\ntheory is shown not to be a fragment of Grishin’s, and thus\nrepresents a fourth known method of getting consistent fragments." ], "subsection_title": "6.2 The consistency problem for NF; the known consistent subsystems" }, { "content": [ "\nOf these set theories, only NFU with Infinity, Choice and\npossibly further strong axioms of infinity (of which more anon) is\nreally mathematically serviceable. We examine the construction of\nmodels of this theory and the way mathematics works inside this\ntheory. A source for this development is Holmes 1998. Rosser 1973\ndevelops the foundations of mathematics in NF: it can adapted\nto NFU fairly easily).", "\nA model of NFU can be constructed as follows. Well-known\nresults of model theory allow the construction of a nonstandard model\nof ZFC (actually, a model of Mac Lane set theory suffices)\nwith an external automorphism \\(j\\) which moves a rank \\(V_{\\alpha}\\).\nWe stipulate without loss of generality that \\(j(\\alpha) \\lt \\alpha\\).\nThe universe of our model of NFU will be \\(V_{\\alpha}\\) and\nthe membership relation will be defined as", "\n(where \\(\\in\\) is the membership relation of the nonstandard model).\nThe proof that this is a model of NFU is not long, but it is\ninvolved enough that we refer the reader elsewhere. The basic idea is\nthat the automorphism allows us to code the (apparent) power set\n\\(V_{\\alpha +1}\\) of our universe \\(V_{\\alpha}\\) into the\n“smaller” \\(V_{j(\\alpha)+1}\\) which is included in our\nuniverse; the left over objects in \\(V_{\\alpha} - V_{j(\\alpha)+1}\\)\nbecome urelements. Note that \\(V_{\\alpha} - V_{j(\\alpha)+1}\\) is most\nof the domain of the model of NFU in a quite strong sense:\nalmost all of the universe is made up of urelements (note that each\n\\(V_{\\beta +1}\\) is the power set of \\(V_{\\beta}\\), and so is strictly\nlarger in size, and not one but many stages intervene between\n\\(V_{j(\\alpha)+1}\\) (the collection of “sets”) and\n\\(V_{\\alpha}\\) (the “universe”)). This construction is\nrelated to the construction used by Jensen, but is apparently first\ndescribed explicitly in Boffa 1988.", "\nIn any model of NFU, a structure which looks just like one of\nthese models can be constructed in the isomorphism classes of\nwell-founded extensional relations. The theory of isomorphism classes\nof well-founded extensional relations with a top element looks like\nthe theory of (an initial segment of) the usual cumulative hierarchy,\nbecause every set in Zermelo-style set theory is uniquely determined\nby the isomorphism type of the restriction of the membership relation\nto its transitive closure. The surprise is that we not only see a\nstructure which looks like an initial segment of the cumulative\nhierarchy: we also see an external endomorphism of this structure\nwhich moves a rank (and therefore cannot be a set), in terms of which\nwe can replicate the model construction above and get an\ninterpretation of NFU of this kind inside NFU! The\nendomorphism is induced by the map \\(T\\) which sends the isomorphism\ntype of a relation \\(R\\) to the isomorphism type of \\(R^{\\iota} = \\{\n\\langle \\{x\\}, \\{y\\}\\rangle \\mid xRy\\}\\). There is no reason to\nbelieve that \\(T\\) is a function: it sends any relation \\(R\\) to a\nrelation \\(R^{\\iota}\\) which is one type higher in terms of\nTST. It is demonstrable that \\(T\\) on the isomorphism types\nof well-founded extensional relations is not a set function (we will\nnot show this here, but our discussion of the Burali-Forti paradox\nbelow should give a good idea of the reasons for this). See Holmes\n(1998) for the full discussion.", "\nThis suggests that the underlying world view of NFU, in spite\nof the presence of the universal set, Frege natural numbers, and other\nlarge objects, may not be that different from the world view of\nZermelo-style set theory; we build models of NFU in a certain\nway in Zermelo-style set theory, and NFU itself reflects this\nkind of construction internally. A further, surprising result (Holmes\n2012) is that in models of NFU constructed from a nonstandard\n\\(V_{\\alpha}\\) with automorphism as above, the membership relation on\nthe nonstandard \\(V_{\\alpha}\\) is first-order definable (in a very\nelaborate way) in terms of the relation \\(\\in_{NFU}\\); this is very\nsurprising, since it seems superficially as if all information about\nthe extensions of the urelements has been discarded in this\nconstruction. But this turns out not to be the case (and this means\nthat the urelements, which seem to have no internal information,\nnonetheless have a great deal of structure in these models).", "\nModels of NFU can have a “finite” (but externally\ninfinite) universe if the ordinal \\(\\alpha\\) in the construction is a\nnonstandard natural number. If \\(\\alpha\\) is infinite, the model of\nNFU will satisfy Infinity. If the Axiom of Choice holds in\nthe model of Zermelo-style set theory, it will hold in the model of\nNFU.", "\nNow we look at the mathematical universe according to NFU,\nrather than looking at models of NFU from the outside.", "\nThe Frege construction of the natural numbers works perfectly in\nNFU. If Infinity holds, there will be no last natural number\nand we can define the usual set \\(\\mathbf{N}\\) of natural numbers just\nas we did above.", "\nAny of the usual ordered pair constructions works in NFU. The\nusual Kuratowski pair is inconvenient in NF or in\nNFU, because the pair is two types higher than its\nprojections in terms of TST. This means that functions and\nrelations are three types higher than the elements of their domains\nand ranges. There is a type-level pair defined by Quine (1945;\ntype-level because it is the same type as its projections) which is\ndefinable in NF and also on \\(V_{\\alpha}\\) for any infinite\nordinal \\(\\alpha\\); this pair can be defined and used in NF\nand the fact that it is definable on infinite \\(V_{\\alpha}\\) means\nthat it can be assumed in NFU+Infinity that there is a\ntype-level ordered pair (the existence of such a pair also follows\nfrom Infinity and Choice together). This would make the type\ndisplacement between functions and relations and elements of their\ndomains and ranges just one, the same as the displacement between the\ntypes of sets and their elements. We will assume that ordered pairs\nare of the same type as their projections in the sequel, but we will\nnot present the rather complicated definition of the Quine pair.", "\nOnce pairs are defined, the definition of relations and functions\nproceeds exactly as in the usual set theory. The definitions of\nintegers and rational numbers present no problem, and the Dedekind\nconstruction of the reals can be carried out as usual. We will focus\nhere on developing the solutions to the paradoxes of Cantor and\nBurali-Forti in NFU, which give a good picture of the odd\ncharacter of this set theory, and also set things up nicely for a\nbrief discussion of natural strong axioms of infinity for\nNFU. It is important to realize as we read the ways in which\nNFU evades the paradoxes that this evasion is successful:\nNFU is known to be consistent if the usual set theory is\nconsistent, and close examination of the models of NFU shows\nexactly why these apparent dodges work.", "\nTwo sets are said to be of the same cardinality just in case there is\na bijection between them. This is standard. But we then proceed to\ndefine \\(|A|\\) (the cardinality of a set \\(A)\\) as the set of all sets\nwhich are the same size as \\(A\\), realizing the definition intended by\nFrege and Russell, and apparently intended by Cantor as well. Notice\nthat \\(|A|\\) is one type higher than \\(A\\). The Frege natural numbers\nare the same objects as the finite cardinal numbers.", "\nThe Cantor theorem of the usual set theory asserts that \\(|A| \\lt\n|\\wp(A)|\\). This is clearly not true in NFU, since | \\(V|\\)\nis the cardinality of the universe and \\(|\\wp(V)|\\) is the cardinality\nof the set of sets, and in fact \\(|V| \\gt \\gt |\\wp(V)|\\) in all known\nmodels of NFU (there are many intervening cardinals in all\nsuch models). But \\(|A| \\lt |\\wp(A)|\\) does not make sense in\nTST: it is ill-typed. The correct theorem in TST,\nwhich is inherited by NFU, is \\(|\\wp_1 (A)| \\lt |\\wp(A)|\\),\nwhere \\(\\wp_1 (A)\\) is the set of one-element subsets of \\(A\\), which\nis at the same type as the power set of \\(A\\). So we have \\(|\\wp_1\n(V)| \\lt |\\wp(V)|\\): there are more sets than there are singleton\nsets. The apparent bijection \\(x \\mapsto \\{x\\}\\) between \\(\\wp_1 (V)\\)\nand \\(V\\) cannot be a set (and there is no reason to expect it to be a\nset, since it has an unstratified definition).", "\nA set which satisfies \\(|A| = |\\wp_1 (A)|\\) is called a\ncantorian set, since it satisfies the usual form of\nCantor’s theorem. A set \\(A\\) which satisfies the stronger\ncondition that the restriction of the singleton map to \\(A\\) is a set\nis said to be strongly cantorian (s.c.). Strongly cantorian\nsets are important because it is not necessary to assign a relative\ntype to a variable known to be restricted to a strongly cantorian set,\nas it is possible to use the restriction of the singleton map and its\ninverse to freely adjust the type of any such variable for purposes of\nstratification. The strongly cantorian sets are can be thought of as\nanalogues of the small sets of the usual set theory.", "\nOrdinal numbers are defined as equivalence classes of well-orderings\nunder similarity. There is a natural order on ordinal numbers, and in\nNFU as in the usual set theory it turns out to be a\nwell-ordering—and, as in naive set theory, a set! Since the\nnatural order on the ordinal numbers is a set, it has an order type\n\\(\\Omega\\) which is itself one of the ordinal numbers. Now in the\nusual set theory we prove that the order type of the restriction of\nthe natural order on the ordinals to the ordinals less than \\(\\alpha\\)\nis the ordinal \\(\\alpha\\) itself; however, this is an ill-typed\nstatement in TST, where, assuming a type level ordered pair,\nthe second occurrence of \\(\\alpha\\) is two types higher than the first\n(it would be four types higher if the Kuratowski ordered pair were\nused). Since the ordinals are isomorphism types of relations, we can\ndefine the operation \\(T\\) on them as above.", "\n\n\nThe order type of the restriction of the natural order on the ordinals\nto the ordinals less than \\(\\alpha\\) is the ordinal \\(T^2\n(\\alpha)\\)\n", "\nis an assertion which makes sense in TST and is in fact true\nin TST and so in NFU. We thus find that the order\ntype of the restriction of the natural order on the ordinals to the\nordinals less than \\(\\Omega\\) is \\(T^2 (\\Omega)\\), whence we find that\n\\(T^2 (\\Omega)\\) (as the order type of a proper initial segment of the\nordinals) is strictly less than \\(\\Omega\\) (which is the order type of\nall the ordinals). Once again, the fact that the singleton\nmap is not a function eliminates the “intuitively obvious”\nsimilarity between these orders. This also shows that \\(T\\) is not a\nfunction. \\(T\\) is an order endomorphism of the ordinals, though,\nwhence we have \\(\\Omega \\gt T^2 (\\Omega) \\gt T^4 (\\Omega)\\ldots\\),\nwhich may be vaguely disturbing, though this “sequence” is\nnot a set. A perhaps useful comment is that in the models of\nNFU described above, the action of \\(T\\) on ordinals exactly\nparallels the action of \\(j\\) on order types of well-orderings \\((j\\)\ndoes not send NFU ordinals to ordinals, exactly, so this\nneeds to be phrased carefully): the “descending sequence”\nalready has an analogue in the sequence \\(\\alpha \\gt j(\\alpha) \\gt j^2\n(\\alpha)\\ldots\\) in the original nonstandard model. Some have asserted\nthat this phenomenon (that the ordinals in any model of NFU\nare not externally well-ordered) can be phrased as “NFU\nhas no standard model”. We reserve judgement on this—we do\nnote that the theorem “the ordinals in any (set!) model of\nNFU are not well-ordered” is a theorem of NFU\nitself; note that NFU does not see the universe as a model of\nNFU (even though it is a set) because the membership relation\nis not a set relation (if it were, the singleton map certainly would\nbe).", "\nNFU + Infinity + Choice is a relatively weak theory: like\nZermelo set theory it does not prove even that \\(\\aleph_{\\omega}\\)\nexists. As is the case with Zermelo set theory, natural extensions of\nthis theory make it much stronger. We give just one example. The Axiom\nof Cantorian Sets is the deceptively simple statement (to which there\nare no evident counterexamples) that “every cantorian set is\nstrongly cantorian”. NFU + Infinity + Choice +\nCantorian Sets is a considerably stronger theory than NFU +\nInfinity + Choice: in its theory of isomorphism types of well-founded\nextensional relations with top element, the cantorian types with the\nobvious “membership” relation satisfy the axioms of\nZFC + “there is an \\(n\\)-Mahlo cardinal” for each\nconcrete \\(n\\). There is no mathematical need for the devious\ninterpretation: this theory proves the existence of \\(n\\)-Mahlo\ncardinals and supports all mathematical constructions at that level of\nconsistency strength in its own terms without any need to refer to the\ntheory of well-founded extensional relations. More elaborate\nstatements about such properties as “cantorian” and\n“strongly cantorian” (applied to order types as well as\ncardinality) yield even stronger axioms of infinity.", "\nOur basic claim about NFU + Infinity + Choice (and its\nextensions) is that it is a mathematically serviceable alternative set\ntheory with its own intrinsic motivation (although we have used\nZermelo style set theory to prove its consistency here, the entire\ndevelopment can be carried out in terms of TST alone: one can\nuse TST as meta-theory, show in TST that consistency\nof TST implies consistency of NFU, and use this\nresult to amend one’s meta-theory to NFU, thus\nabandoning the distinctions between types). We do not claim that it is\nbetter than ZFC, but we do claim that it is adequate, and\nthat it is important to know that adequate alternatives exist; we do\nclaim that it is useful to know that there are different ways to found\nmathematics, as we have encountered the absurd assertion that\n“mathematics is whatever is formalized in\nZFC”." ], "subsection_title": "6.3 Mathematics in NFU + Infinity + Choice" }, { "content": [ "\nLike Zermelo set theory, NFU has advantages and\ndisadvantages. An advantage, which corresponds to one of the few clear\ndisadvantages of Zermelo set theory, is that it is possible to define\nnatural numbers, cardinal numbers, and ordinal numbers in the natural\nway intended by Frege, Russell, and Whitehead.", "\nMany but not all of the purported disadvantages of NFU as a\nworking foundation for mathematics reduce to complaints by\nmathematicians used to working in ZFC that “this is not\nwhat we are used to”. The fact that there are fewer singletons\nthan objects (in spite of an obvious external one to one\ncorrespondence) takes getting used to. In otherwise familiar\nconstructions, one sometimes has to make technical use of the\nsingleton map or \\(T\\) operations to adjust types to get\nstratification. This author can testify that it is perfectly possible\nto develop good intuition for NFU and work effectively with\nstratified comprehension; part of this but not all of it is a good\nfamiliarity with how things are done in TST, as one also has\nto develop a feel for how to use principles that subvert\nstratification.", "\nAs Sol Feferman has pointed out, one place where the treatments in\nNFU (at least those given so far) are clearly quite involved\nare situations in which one needs to work with indexed families of\nobjects. The proof of König’s Lemma of set theory in Holmes\n1998 is a good example of how complicated this kind of thing can get\nin NFU. We have a notion that the use of sets of “Quine\natoms” (self-singletons) as index sets (necessarily for s.c.\nsets) might relieve this difficulty, but we haven’t proved this\nin practice, and problems would remain for the noncantorian\nsituation.", "\nThe fact that “NFU has no standard models” (the\nordinals are not well-ordered in any set model of NFU) is a\ncriticism of NFU which has merit. We observe, though, that\nthere are other set theories in which nonstandard objects are\ndeliberately provided (we will review some of these below), and some\nof the applications of those set theories to “nonstandard\nanalysis” might be duplicated in suitable versions of\nNFU. We also observe that strong principles which minimize\nthe nonstandard behavior of the ordinals turn out to give surprisingly\nstrong axioms of infinity in NFU; the nonstandard structure\nof the ordinals allows insight into phenomena associated with large\ncardinals.", "\nSome have thought that the fact that NFU combines a universal\nset and other big structures with mathematical fluency in treating\nthese structures might make it a suitable medium for category theory.\nAlthough we have some inclination to be partial to this class of set\ntheories, we note that there are strong counterarguments to this view.\nIt is true that there are big categories, such as the category of all\nsets (as objects) and functions (as the morphisms between them), the\ncategory of all topological spaces and homeomorphism, and even the\ncategory of all categories and functors. However, the category of all\nsets and functions, for example, while it is a set, is not\n“cartesian closed” (a technical property which this\ncategory is expected to have): see McLarty 1992. Moreover, if one\nrestricts to the s.c. sets and functions, one obtains a cartesian\nclosed category, which is much more closely analogous to the category\nof all sets and functions over ZFC—and shares with it\nthe disadvantage of being a proper class! Contemplation of the models\nonly confirms the impression that the correct analogue of the proper\nclass category of sets and functions in ZFC is the proper\nclass category of s.c. sets and functions in NFU! There may\nbe some applications for the big set categories in NFU, but\nthey are not likely to prove to be as useful as some have\noptimistically suggested. See Feferman 2006 for an extensive\ndiscussion.", "\nAn important point is that there is a relativity of viewpoint here:\nthe NFU world can be understood to be a nonstandard initial\nsegment of the world of ZFC (which could be arranged to\ninclude its entire standard part!) with an automorphism and the\nZFC world (or an initial segment of it) can be interpreted in\nNFU as the theory of isomorphism classes of well-founded\nextensional relations with top (often restricted to its strongly\ncantorian part); these two theories are mutually interpretable, so the\ncorresponding views of the world admit mutual translation.", "\nZFC might be viewed as motivated by a generalization of the\ntheory of sets in extension (as generalizations of the notion of\nfinite set, replacing the finite with the transfinite and the rejected\ninfinite with the rejected Absolute Infinite of Cantor) while the\nmotivation of NFU can be seen as a correction of the theory\nof sets as intensions (that is, as determined by predicates) which led\nto the disaster of naive set theory. Nino Cocchiarella (1985) has\nnoted that Frege’s theory of concepts could be saved if one\ncould motivate a restriction to stratified concepts (the abandonment\nof strong extensionality is merely a return to common sense). But the\nimpression of a fundamental contrast should be tempered by the\nobservation that the two theories nonetheless seem to be looking at\nthe same universe in different ways!" ], "subsection_title": "6.4 Critique of NFU" } ] }, { "main_content": [], "section_title": "7. Positive Set Theories", "subsections": [ { "content": [ "\nWe will not attempt an exhaustive survey of positive set theory; our\naim here is to motivate and exhibit the axioms of the strongest system\nof this kind familiar to us, which is the third of the systems of\nclassical set theory which we regard as genuinely mathematically\nserviceable (the other two being ZFC and suitable strong\nextensions of NFU + Infinity + Choice).", "\nA positive formula is a formula which belongs to the smallest\nclass of formulas containing a false statement \\(\\bot\\), all atomic\nmembership and equality formulas and closed under the formation of\nconjunctions, disjunctions, universal and existential quantifications.\nA generalized positive formula is obtained if we allow\nbounded universal and existential quantifications (the\nadditional strength comes from allowing \\((\\forall x \\in A \\mid \\phi)\n\\equiv \\forall x(x \\in A \\rightarrow \\phi)\\); bounded existential\nquantification is positive in any case).", "\nPositive comprehension is motivated superficially by an attack on one\nof the elements of Russell’s paradox (the negation): a positive\nset theory will be expected to support the axiom of extensionality (as\nusual) and the axiom of (generalized) positive comprehension:\nfor any (generalized) positive formula \\(\\phi , \\{x \\mid \\phi \\}\\)\nexists.", "\nWe mention that we are aware that positive comprehension with the\nadditional generalization of positive formulas allowing one to include\nset abstracts \\(\\{x \\mid \\phi \\}\\) (with \\(\\phi\\) generalized\npositive) in generalized positive formulas is consistent, but turns\nout not to be consistent with extensionality. We are not very familiar\nwith this theory, so have no additional comments to make about it; do\nnotice that the translations of formulas with set abstracts in them\ninto first order logic without abstracts are definitely not positive\nin our more restricted sense, and so one may expect some kind of\ntrouble!", "\nThe motivation for the kinds of positive set theory we are familiar\nwith is topological. We are to understand the sets as closed\nsets under some topology. Finite unions and intersections of closed\nsets are closed; this supports the inclusion of \\(\\{x \\mid \\phi \\lor\n\\psi \\}\\) and \\(\\{x \\mid \\phi \\amp \\psi \\}\\) as sets if \\(\\{x \\mid\n\\phi \\}\\) and \\(\\{x \\mid \\psi \\}\\) are sets. Arbitrary intersections\nof closed sets are closed: this supports our adoption of even bounded\nuniversal quantification (if each \\(\\{x \\mid \\phi(y)\\}\\) is a set,\nthen \\(\\{x \\mid \\forall y\\phi(y)\\}\\) is the intersection of all of\nthese sets, and so should be closed, and \\(\\{x \\in A \\mid \\forall\ny\\phi(y)\\}\\) is also an intersection of closed sets and so should be\nclosed. The motivation for permitting \\(\\{x \\mid \\exists y\\phi(y)\\}\\)\nwhen each \\(\\{x \\mid \\phi(y)\\}\\) exists is more subtle, since infinite\nunions do not as a rule preserve closedness: the idea is that the set\nof pairs \\((x, y)\\) such that \\(\\phi(x, y)\\) is closed, and the\ntopology is such that the projection of a closed set is closed.\nCompactness of the topology suffices. Moreover, we now need to be\naware that formulas with several parameters need to be considered in\nterms of a product topology.", "\nAn additional very powerful principle should be expected to hold in a\ntopological model: for any class \\(C\\) whatsoever (any collection of\nsets), the intersection of all sets which include \\(C\\) as a subclass\nshould be a set. Every class has a set closure.", "\nWe attempt the construction of a model of such a topological theory.\nTo bring out an analogy with Mac Lane set theory and NF, we\ninitially present a model built by collapsing TST in yet\nanother manner.", "\nThe model of TST that we use contains one type 0 object\n\\(u\\). Note that this means that each type is finite. Objects of each\ntype are construed as better and better approximations to the untyped\nobjects of the final set theory. \\(u\\) approximates any set. The type\n\\(n + 1\\) approximant to any set \\(A\\) is intended to be the set of\ntype \\(n\\) approximants of the elements of \\(A\\).", "\nThis means that we should be able to specify when a type \\(n + 2\\) set\n\\(A^{n+2}\\) refines a type \\(n + 1\\) set \\(A^{n+1}\\): each (type \\(n +\n1)\\) element of \\(A^{n+2}\\) should refine a (type \\(n)\\) element of\n\\(A^{n+1}\\), and each element of \\(A^{n+1}\\) should be refined by one\nor more elements of \\(A^{n+2}\\). Along with the information that the\ntype 0 object \\(u\\) refines both of the elements of type 1, this gives\na complete recursive definition of the notion of refinement of a type\n\\(n\\) set by a type \\(n + 1\\) set. Each type \\(n + 1\\) set refines a\nunique type \\(n\\) set but may be refined by many type \\(n + 2\\) sets.\n(The “hereditarily finite” sets without \\(u\\) in their\ntransitive closure are refined by just one precisely analogous set at\nthe next higher level.) Define a general relation \\(x \\sim y\\) on all\nelements of the model of set theory as holding when \\(x = y\\) (if they\nare of the same type) or if there is a chain of refinements leading\nfrom the one of \\(x, y\\) of lower type to the one of higher type.", "\nThe objects of our first model of positive set theory are sequences\n\\(s_n\\) with each \\(s_n\\) a type \\(n\\) set and with \\(s_{n+1}\\)\nrefining \\(s_n\\) for each \\(n\\). We say that \\(s \\in t\\) when \\(s_{n}\n\\in t_{n+1}\\) for all \\(n\\). It is straightforward to establish that\nif \\(s_{n} \\in t_{n+1}\\) or \\(s_{n} = t_{n}\\) is false, then \\(s_k \\in\nt_{k+1}\\) or (respectively) \\(s_k = t_k\\) is false for all \\(k \\gt\nn\\). More generally, if \\(s_m \\sim t_n\\) is false, then \\(s_{m+k} \\sim\nt_{n+k}\\) is false for all \\(k \\ge 0\\).", "\nFormulas in the language of the typed theory with \\(\\in\\) and \\(\\sim\\)\nhave a monotonicity property: if \\(\\phi\\) is a generalized positive\nformula and one of its typed versions is false, then any version of\nthe same formula obtained by raising types and refining the values of\nfree variables in the formula will continue to be false. It is not\nhard to see why this will fail to work if negation is allowed.", "\nIt is also not too hard to show that if all typed versions of a\ngeneralized positive formula \\(\\phi\\) in the language of the intended\nmodel (with sequences \\(s\\) appearing as values of free variables\nreplaced by their values at the appropriate types) are true, then the\noriginal formula \\(\\phi\\) is true in the intended model. The one\ndifficulty comes in with existential quantification: the fact that one\nhas a witness to \\((\\exists x.\\phi(x))\\) in each typed version does\nnot immediately give a sequence witnessing this in the intended model.\nThe tree property of \\(\\omega\\) helps here: only finitely many\napproximants to sets exist at each level, so one can at each level\nchoose an approximant refinements of which are used at infinitely many\nhigher levels as witnesses to \\((\\exists x.\\phi(x))\\), then restrict\nattention to refinements of that approximant; in this way one gets not\nan arbitrary sequence of witnesses at various types but a\n“convergent” sequence (an element of the intended\nmodel).", "\nOne then shows that any generalized positive formula \\(\\phi(x)\\) has\nan extension \\(\\{x \\mid \\phi(x)\\}\\) by considering the sets of\nwitnesses to \\(\\phi(x)\\) in each type \\(n\\); these sets themselves can\nbe used to construct a convergent sequence (with the proviso that some\napparent elements found at any given stage may need to be discarded;\none defines \\(s_{n+1}\\) as the set of those type \\(n\\) approximants\nwhich not only witness \\(\\phi(x)\\) at the current type \\(n\\) but have\nrefinements which witness \\(\\phi(x)\\) at each subsequent type. The\nsequence of sets \\(s\\) obtained will be an element of the intended\nmodel and have the intended extension.", "\nFinally, for any class of sequences (elements of the intended model)\n\\(C\\), there is a smallest set which contains all elements of\n\\(C\\): let \\(c_{n+1}\\) be the set of terms \\(s_n\\) of sequences \\(s\\)\nbelonging to \\(C\\) at each type \\(n\\) to construct a sequence \\(c\\)\nwhich will have the desired property.", "\nThis theory can be made stronger by indicating how to pass to\ntransfinite typed approximations. The type \\(\\alpha + 1\\)\napproximation to a set will always be the set of type \\(\\alpha\\)\napproximations; if \\(\\lambda\\) is a limit ordinal, the type\n\\(\\lambda\\) approximation will be the sequence \\(\\{s_{\\beta} \\}_{\\beta\n\\lt \\lambda}\\) of approximants to the set at earlier levels (so our\n“intended model” above is the set of type \\(\\omega\\)\napproximations in a larger model).", "\nEverything above will work at any limit stage except the treatment of\nthe existential quantifier. The existential quantifier argument will\nwork if the ordinal stage at which the model is being constructed is a\nweakly compact cardinal. This is a moderately strong large cardinal\nproperty (for an uncountable cardinal): it implies, for example, the\nexistence of proper classes of inaccessibles and of \\(n\\)-Mahlo\ncardinals for each \\(n\\).", "\nSo for each weakly compact cardinal \\(\\kappa\\) (including \\(\\kappa =\n\\omega)\\) the approximants of level \\(\\kappa\\) in the transfinite type\ntheory just outlined make up a model of set theory with\nextensionality, generalized positive comprehension, and the closure\nproperty. We will refer to this model as the\n“\\(\\kappa\\)-hyperuniverse”." ], "subsection_title": "7.1 Topological motivation of positive set theory" }, { "content": [ "\nWe now present an axiomatic theory which has the\n\\(\\kappa\\)-hyperuniverses with \\(\\kappa \\gt \\omega\\) as (some of its)\nmodels. This is a first-order theory with equality and membership as\nprimitive relations. This system is called\nGPK\\(^{+}_{\\infty}\\) and is described in Esser 1999.", "\nAs one might expect, some of the basic concepts of this set theory are\ntopological (sets being the closed classes of the topology on the\nuniverse).", "\nThis set theory interprets ZF. This is shown by demonstrating\nfirst that the discrete sets (and more particularly the (closed) sets\nof isolated points in the topology) satisfy an analogue of Replacement\n(a definable function (defined by a formula which need not be\npositive) with a discrete domain is a set), and so an analogue of\nseparation, then by showing that well-founded sets are isolated in the\ntopology and the class of well-founded sets is closed under the\nconstructions of ZF.", "\nNot only ZF but also Kelley-Morse class theory can be\ninterpreted; any definable class of well-founded sets has a closure\nwhose well-founded members will be exactly the desired members (it\nwill as a rule have other, non-well-founded members). Quantification\nover these “classes” defines sets just as easily as\nquantification over mere sets in this context; so we get an\nimpredicative class theory. Further, one can prove internally to this\ntheory that the “proper class ordinal” in the interpreted\n\\(KM\\) has the tree property, and so is in effect a weakly compact\ncardinal; this shows that this theory has considerable consistency\nstrength (for example, its version of ZF proves that there is\na proper class of inaccessible cardinals, a proper class of\n\\(n\\)-Mahlos for each \\(n\\), and so forth): the use of large cardinals\nin the outlined model construction above was essential.", "\nThe Axiom of Choice in any global form is inconsistent with this\ntheory, but it is consistent for all well-founded sets to be\nwell-orderable (in fact, this will be true in the models described\nabove if the construction is carried out in an environment in which\nChoice is true). This is sufficient for the usual mathematical\napplications.", "\nSince ZF is entirely immersed in this theory, it is clearly\nserviceable for the usual classical applications. The Frege natural\nnumbers are not definable in this theory (except for 0 and 1); it is\nbetter to work with the finite von Neumann ordinals. The ability to\nprove strong results about large cardinals using the properties of the\nproper class ordinal suggests that the superstructure of large sets\ncan be used for mathematical purposes as well. Familiarity with\ntechniques of topology of \\(\\kappa\\)-compact spaces would be useful\nfor understanding what can be done with the big sets in this\ntheory.", "\nWith the negation of the Axiom of Infinity, we get the theory of the\n\\(\\omega\\)-hyperuniverse, which is equiconsistent with second-order\narithmetic, and so actually has a fair amount of mathematical\nstrength. In this theory, the class of natural numbers (considered as\nfinite ordinals) is not closed and acquires an extra element “at\ninfinity” (which happens to be the closure of the class of\nnatural numbers itself). Individual real numbers can be coded (using\nthe usual Dedekind construction, actually) but the theory of sets of\nreal numbers will begin to look quite different." ], "subsection_title": "7.2 The system GPK\\(^{+}_{\\infty}\\) of Olivier Esser" }, { "content": [ "\nOne obvious criticism is that this theory is extremely\nstrong, compared with the other systems given here. This could be a\ngood thing or a bad thing, depending on one’s attitude. If one\nis worried about the consistency of a weakly compact, the level of\nconsistency strength here is certainly a problem (though the theory of\nthe \\(\\omega\\) -hyperuniverse will stay around in any case). On the\nother hand, the fact that the topological motivation for set theory\nseems to work and yields a higher level of consistency strength than\none might expect (“weakly compact” infinity following from\nmerely uncountable infinity) might be taken as evidence that these are\nvery powerful ideas.", "\nThe mathematical constructions that are readily accessible to this\nauthor are simply carried over from ZF or ZFC; the\nwell-founded sets are considered within the world of positive set\ntheory, and we find that they have exactly the properties we expect\nthem to have from the usual viewpoint. It is rather nice that we get\n(fuzzier) objects in our set theory suitable to represent all of the\nusual proper classes; it is less clear what we can do with the other\nlarge objects than it is in NFU. A topologist might find this\nsystem quite interesting; in any event, topological expertise seems\nrequired to evaluate what can be done with the extra machinery in this\nsystem.", "\nWe briefly review the paradoxes: the Russell paradox doesn’t\nwork because \\(x \\not\\in x\\) is not a positive formula; notice that\n\\(\\{x \\mid x \\in x\\}\\) exists! The Cantor paradox does not work\nbecause the proof of the Cantor theorem relies on an instance of\ncomprehension which is not positive. \\(\\wp(V)\\) does exist and is\nequal to \\(V\\). The ordinals are defined by a non-positive condition,\nand do not make up a set, but it is interesting to note that the\nclosure \\(\\mathbf{CL}(On)\\) of the class \\(On\\) of ordinals is equal\nto \\(On \\cup \\{\\mathbf{CL}(On)\\}\\); the closure has itself as its only\nunexpected element." ], "subsection_title": "7.3 Critique of positive set theory" } ] }, { "main_content": [ "\nIn the preceding set theories, the properties of the usual objects of\nmathematics accord closely with their properties as\n“intuitively” understood by most mathematicians (or lay\npeople). (Strictly speaking, this is not quite true in NFU +\nInfinity without the additional assumption of Rosser’s Axiom of\nCounting, but the latter axiom (“\\(\\mathbf{N}\\) is strongly\ncantorian”) is almost always assumed in practice).", "\nIn the first two classes of system discussed in this section, logical\nconsiderations lead to the construction of theories in which\n“familiar” parts of the world look quite different.\nConstructive mathematicians do not see the same continuum that we do,\nand if they are willing to venture into the higher reaches of set\ntheory, they find a different world there, too. The proponents of\nnonstandard analysis also find it useful to look at a different\ncontinuum (and even different natural numbers) though they do see the\nusual continuum and natural numbers embedded therein.", "\nIt is not entirely clear that the final item discussed in this\nsection, the multiverse view of set theory proposed by Joel Hamkins,\nshould be described as a view of the world of set theory at all: it\nproposes that we should consider that there are multiple different\nconcepts of set each of which describes its own universe (and loosely\nwe might speak of the complex of universes as a\n“multiverse”), but at bottom it is being questioned\nwhether there is properly a single world of set theory at all. But the\ntentative list of proposed axioms he gives for relationships between\nuniverses have some of the flavor of an alternative set theory." ], "section_title": "8. Logically and Philosophically Motivated Variations", "subsections": [ { "content": [ "\nThere are a number of attempts at constructive (intuitionistic)\ntheories of types and set theories. We will describe a few systems\nhere, quite briefly as we are not expert in constructive\nmathematics.", "\nAn intuitionistic typed theory of sets is readily obtained by simply\nadopting the intuitionistic versions of the axioms of TST as\naxioms. An Axiom of Infinity would be wanted to ensure that an\ninterpretation of Heyting arithmetic could be embedded in the theory;\nit might be simplest to provide type 0 with the primitives of Heyting\narithmetic (just as the earliest versions of TST had the\nprimitives of classical arithmetic provided for type 0). We believe\nthat this would give a quite comfortable environment for doing\nconstructive mathematics.", "\nDaniel Dzierzgowski has gone so far as to study an intuitionistic\nversion of NF constructed in the same way; all that we can\nusefully report here is that it is not clear that the resulting theory\nINF is as strong as NF (in particular, it is unclear\nwhether INF interprets Heyting Arithmetic, because\nSpecker’s proof of Infinity in NF does not seem to go\nthrough in any useful way) but the consistency problem for\nINF remains open in spite of the apparent weakness of the\ntheory.", "\nA more ambitious theory is IZF (intuitionistic ZF).\nAn interesting feature of the development of IZF is that one\nmust be very careful in one’s choice of axioms: some\nformulations of the axioms of set theory have (constructively\ndeducible) consequences which are not considered constructively valid\n(such as Excluded Middle), while other (classically equivalent)\nformulations of the axioms appear not to have such consequences: the\nlatter forms, obviously to be preferred for a constructive development\nof set theory, often are not the most familiar ones in the classical\ncontext.", "\nA set of axioms which seems to yield a nontrivial system of\nconstructive mathematics is the following:", "\nSee Friedman 1973 and\n Other Internet Resources\n for further information about IZF.", "\nAs is often the case in constructive mathematics generally, very\nsimple notions of classical set theory (such as the notion of an\nordinal) require careful reformulation to obtain the appropriate\ndefinition for the constructive environment (and the formulations\noften appear more complicated than familiar ones to the classical\neye). Being inexpert, we will not involve ourselves further in this.\nIt is worth noting that IZF, like many but not all\nconstructive systems, admits a double negation interpretation of the\ncorresponding classical theory ZF; we might think of\nIZF as a weakened version of ZF from the classical\nstandpoint, but in its own terms it is the theory of a larger, more\ncomplex realm in which a copy of the classical universe of set theory\nis embedded.", "\nThe theories we have described so far are criticized by some\nconstructive mathematicians for allowing an unrestricted power set\noperation. A weaker system CZF (constructive ZF has\nbeen proposed which does not have this operation (and which has the\nsame level of strength as the weak set theory KPU without\nPower Set described earlier).", "\nCZF omits Power Set. It replaces Foundation with\n\\(\\in\\)-Induction for the same reasons as above. The axioms of\nExtensionality, Pairing, and Union are as in ordinary set theory. The\naxiom of Separation is restricted to bounded \\((\\Delta_0)\\) formulas\nas in Mac Lane set theory or KPU.", "\nThe Collection axiom is replaced by two weaker axioms.", "\nThe Strong Collection axiom scheme asserts that if for every \\(x \\in\nA\\) there is \\(y\\) such that \\(\\phi (x, y)\\), then there is a set\n\\(B\\) such that for every \\(x \\in A\\) there is \\(y \\in B\\) such that\n\\(\\phi(x, y)\\) (as in the usual scheme) but also for every \\(y \\in B\\)\nthere is \\(x \\in A\\) such that \\(\\phi(x, y)\\) (\\(B\\) doesn’t\ncontain any redundant elements). The additional restriction is useful\nbecause of the weaker form of the Separation Axiom.", "\nThe Subset Collection scheme can be regarded as containing a very weak\nform of Power Set. It asserts, for each formula \\(\\phi(x, y, z)\\) that\nfor every \\(A\\) and \\(B\\), there is a set \\(C\\) such that for each\n\\(z\\) such that \\(\\forall x \\in A\\exists y \\in B[\\phi(x, y, z)\\)]\nthere is \\(R_z \\in C\\) such that for every \\(x \\in A\\) there is \\(y\n\\in R_z\\) such that \\(\\phi(x, y, z)\\) and for every \\(y \\in\nR_z\\) there is \\(x \\in A\\) such that \\(\\phi(x, y, z)\\) (this is the\nsame restriction as in the Strong Collection axiom; notice that not\nonly are images under the relation constructed, but the images are\nfurther collected into a set).", "\nThe Subset Collection scheme is powerful enough to allow the\nconstruction of the set of all functions from a set \\(A\\) to a set\n\\(B\\) as a set (which suggests that the classical version of this\ntheory is as strong as ZF, since the existence of the set of\nfunctions from \\(A\\) to \\(\\{0, 1\\}\\) is classically as strong as the\nexistence of the power set of \\(A\\), and strong collection should\nallow the proof of strong separation in a classical environment).", "\nThis theory is known to be at the same level of consistency strength\nas the classical set theory KPU. It admits an interpretation\nin Martin-Löf constructive type theory (as IZF does\nnot).", "\nSee Aczel (1978, 1982, 1986) for further information about this\ntheory." ], "subsection_title": "8.1 Constructive set theory" }, { "content": [ "\nNonstandard analysis originated with Abraham Robinson (1966), who\nnoticed that the use of nonstandard models of the continuum would\nallow one to make sense of the infinitesimal numbers of Leibniz, and\nso obtain an elegant formulation of the calculus with fewer\nalternations of quantifiers.", "\nLater exponents of nonstandard analysis observed that the constant\nreference to the model theory made the exposition less elementary than\nit could be; they had the idea of working in a set theory which was\ninherently “nonstandard”.", "\nWe present a system of this kind, a version of the set theory\nIST (Internal Set Theory) of Nelson (1977). The primitives of\nthe theory are equality, membership, and a primitive notion of\nstandardness. The axioms follow.", "\nOur form of Idealization is simpler than the usual version but has the\nsame effect.", "\nTransfer immediately implies that any uniquely definable object\n(defined without reference to standardness) is in fact a standard\nobject. So the empty set is standard, \\(\\omega\\) is standard, and so\nforth. But it is not the case that all elements of standard objects\nare standard. For consider the cardinality of a finite set containing\nall standard objects; this is clearly greater that any standard\nnatural number (usual element of \\(\\omega)\\) yet it is equally clearly\nan element of \\(\\omega\\). It turns out to be provable that every set\nall of whose elements are standard is a standard finite set.", "\nRelative consistency of this theory with the usual set theory\nZFC is established via familiar results of model theory.\nWorking in this theory makes it possible to use the techniques of\nnonstandard analysis in a “elementary” way, without ever\nappealing explicitly to the properties of nonstandard models." ], "subsection_title": "8.2 Set theory for nonstandard analysis" }, { "content": [ "\nWe examine the theory of the set theoretic multiverse proposed by Joel\nDavid Hamkins, whose purpose is to address philosophical questions\nabout independence questions in standard set theory, but which when\nspelled out formally has some of the flavor of an alternative set\ntheory. A set theoretic Platonist might say about the Continuum\nHypothesis (CH) that, since there is “of course”\na single universe of sets, CH is either true or false in that\nworld, but that we cannot determine which of CH and\n\\(\\neg\\)CH actually holds. Hamkins proposes as an alternative\n(taking the same realist standpoint as the classical Platonist, it\nmust be noted) that there are many distinct concepts of set, which we\nmay suppose for the moment all satisfy the usual axioms of\nZFC, each concept determining its own universe of sets, and\nin some of these universes CH holds and in some it does not\nhold. He says further, provocatively, that in his view CH is\na solved problem, because we have an excellent understanding of the\nconditions under which CH holds in \\(a\\) universe of sets\n(note the article used) and the conditions in which it does not hold,\nand even more provocatively, he argues that an “ideal”\nsolution to the CH problem in which a generally accepted\naxiom arises which causes most mathematicians to conclude that\nCH is “self-evidently” true or false (deciding\nthe question in the usual sense) is now actually impossible, because\nset theorists are now very conversant with universes in which both\nalternatives hold, and understand very well that neither alternative\nis “self-evidently” true (the force of his argument is\nreally that the complementary conclusion that one of the alternatives\nis self-evidently false is now impossible to draw, because we are too\nwell acquainted with actual “worlds” in which each\nalternative holds to believe that either is absurd).", "\nWe could write an entire essay on questions raised in our summary in\nthe previous paragraph, but Hamkins has already done this in Hamkins\n2012. Our aim here is to summarize the tentative axioms that Hamkins\npresents for the multiverse conception. This is not really a formal\nset of axioms, but it does have some of the qualities of an\naxiomatization of an alternative set theory. We note that the list of\naxioms presented here unavoidably presupposes more knowledge of\nadvanced set theory than other parts of this article.", "\nOne thing to note here is that Hamkins is open to the idea that some\nuniverses may be models of theories other than ZFC (weaker\ntheories such as Zermelo set theory or Peano arithmetic, or even\ndifferent theories such as ZFA or NF/NFU). But it\nappears to be difficult philosophically to articulate exact boundaries\nfor what counts as a “concept of set theory” which would\ndefine a universe. And this is fine, because there is no notion of\n“the multiverse” of universes as a completed totality here\nat all—this would amount to smuggling in the single Platonic\nuniverse again through the back door! Some of the axioms which follow\ndo presume that the universes discussed are models of ZFC or\nvery similar theories.", "\nThis asserts that our forcing extensions are concretely real worlds.\nHamkins discusses the metaphysical difficulties of the status of\nforcing extensions at length in Hamkins 2012.", "\nWe quote Hamkins:", "\n\n\nthe principle asserts that no universe is correct about the height of\nthe ordinals, and every universe looks like an initial segment of a\nmuch taller universe having the same truths. (2012: 438)\n", "\nHere we are presuming that the universes we are talking about are\nmodels of ZFC or a ZFC-like theory.", "\nThis definitely has the flavor of an alternative set theory axiom! The\nmodel theoretic motivation is obvious: this amounts to taking\nSkolem’s paradox seriously. Hamkins notes that the Forcing\nExtension principle above already implies this, but it is clear in any\ncase that his list of tentative axioms is intended to be neither\nindependent nor complete.", "\nHamkins says that this may be the most provocative of all his axioms.\nHe states that he intends this to imply that even our notion of\nnatural numbers is defective in any universe: the collection of\nnatural numbers as defined in any universe is seen to contain\nnonstandard elements from the standpoint of a further universe.", "\nWe merely quote this astonishing assertion, which says that for any\nelementary embedding of a universe \\(V\\) into a model \\(M\\) included\nin \\(V\\), our understanding of this embedding locally to \\(V\\) itself\nis seriously incomplete.", "\nWe are used to thinking of the constructible universe \\(L\\) as a\n“restricted” universe. Here Hamkins turns this inside out\n(he discusses at length why this is a reasonable way to think in the\npaper Hamkins 2012).", "\nWe leave it to the reader who is interested to pursue this\nfurther." ], "subsection_title": "8.3 The multiverse view of set theory" } ] }, { "main_content": [ "\nIt is commonly noted that set theory produces far more superstructure\nthan is needed to support classical mathematics. In this section, we\ndescribe two miniature theories which purport to provide enough\nfoundations without nearly as much superstructure. Our “pocket\nset theory” (motivated by a suggestion of Rudy Rucker) is just\nsmall; Vopenka’s alternative set theory is also\n“nonstandard” in its approach." ], "section_title": "9. Small Set Theories", "subsections": [ { "content": [ "\nThis theory is a proposal of ours, which elaborates on a suggestion of\nRudy Rucker. We (and many others) have observed that of all the orders\nof infinity in Cantor’s paradise, only two actually occur in\nclassical mathematical practice outside set theory: these are\n\\(\\aleph_0\\) and \\(c\\), the infinity of the natural numbers and the\ninfinity of the continuum. Pocket set theory is a theory motivated by\nthe idea that these are the only infinities (Vopenka’s\nalternative set theory also has this property, by the way).", "\nThe objects of pocket set theory are classes. A class is said to be a\nset iff it is an element (as in the usual class theories over\nZFC).", "\nThe ordered pair is defined using the usual Kuratowski definition, but\nwithout assuming that there are any ordered pairs. The notions of\nrelation, function, bijection and equinumerousness are defined as\nusual (still without any assumptions as to the existence of any\nordered pairs). An infinite set is defined as a set which is\nequinumerous with one of its proper subsets. A proper class is defined\nas a class which is not a set.", "\nThe axioms of pocket set theory are", "\nWe cannot resist proving the main results (because the proofs are\nfunny).", "\nCantor’s theorem (no set is the same size as the class of its\nsubsets) and the Schröder-Bernstein theorem (if there are\ninjections from each of two classes into the other, there is a\nbijection between them) have their standard proofs.", "\nThe Russell class can be shown to be the same size as the universe\nusing Schröder-Bernstein: the injection from \\(R\\) into \\(V\\) is\nobvious, and \\(V\\) can be embedded into \\(R\\) using the map \\(x\n\\mapsto \\{\\{x\\}, \\varnothing \\}\\) (clearly no set \\(\\{\\{x\\},\n\\varnothing \\}\\) belongs to itself). So a class is proper iff it is\nthe same size as the universe (limitation of size).", "\nDefine the von Neumann ordinals as classes which are strictly\nwell-ordered by membership. Each finite ordinal can be proved to be a\nset (because it is smaller than its successor and is a subclass of the\nRussell class). The class of all ordinals is not a set (but is the\nlast ordinal), for the usual reasons, and so is the same size as the\nuniverse, and so the universe can be well-ordered.", "\nThere is an infinite ordinal, because there is an ordinal which can be\nplaced in one-to-one correspondence with one’s favorite infinite\nset \\(I\\). Since there is an infinite ordinal, every finite ordinal is\na set and the first infinite ordinal \\(\\omega\\) is a set. It follows\nthat all infinite sets are countably infinite.", "\nThe power set of an infinite set \\(I\\) is not the same size as \\(I\\)\nby Cantor’s theorem, is certainly infinite, and so cannot be a\nset, and so must be the same size as the universe. It follows by usual\nconsiderations that the universe is the same size as \\(\\wp(\\omega)\\)\nor as \\(\\mathbf{R}\\) (the set of real numbers, defined in any of the\nusual ways), and its “cardinal” is \\(c\\). Further, the\nfirst uncountable ordinal \\(\\omega_1\\) is the cardinality of the\nuniverse, so the Continuum Hypothesis holds.", "\nIt is well-known that coding tricks allow one to do classical\nmathematics without ever going above cardinality \\(c\\): for example,\nthe class of all functions from the reals to the reals, is\ntoo large to be even a proper class here, but the class of\ncontinuous functions is of cardinality \\(c\\). An individual\ncontinuous function \\(f\\) might seem to be a proper class, but it can\nbe coded as a hereditarily countable set by (for example) letting the\ncountable set of pairs of rationals \\(\\langle p, q\\rangle\\) such that\n\\(p \\lt f(q)\\) code the function \\(f\\). In fact, it is claimed that\nmost of classical mathematics can be carried out using just natural\nnumbers and sets of natural numbers (second-order arithmetic) or in\neven weaker systems, so pocket set theory (having the strength of\nthird order arithmetic) can be thought to be rather\ngenerous.", "\nWe do remark that it is not necessarily the case that the hypothetical\nadvocate of pocket set theory thinks that the universe is small; he or\nshe might instead think that the continuum is very large…" ], "subsection_title": "9.1 Pocket set theory" }, { "content": [ "\nPetr Vopenka has presented the following alternative set\ntheory (1979).", "\nThe theory has sets and classes. The following axioms hold of\nsets.", "\nThe theory of sets appears to be the theory of \\(V_{\\omega}\\) (the\nhereditarily finite sets) in the usual set theory!", "\nWe now pass to consideration of classes.", "\nA proper semiset is a signal that the set which contains it is\nnonstandard (recall that all sets seem to be hereditarily\nfinite!)", "\nA finite set has standard size (the use of “finite” here\ncould be confusing: all sets are nonstandard finite here,\nafter all).", "\nAn ordering of type \\(\\omega\\) has the same length as the\nstandard natural numbers. We can prove that there is such an\nordering: consider the order on the finite (i.e., standard finite) von\nNeumann ordinals. There must be infinite von Neumann ordinals because\nthere is a set theoretically definable bijection between the von\nNeumann ordinals and the whole universe of sets: any proper semiset\ncan be converted to a proper semiset of a set of von Neumann\nordinals.", "\nThe Prolongation Axiom has a role similar to that of the\nStandardization Axiom in the “nonstandard” set theory\nIST above.", "\nVopenka considers representations of superclasses of classes using\nrelations on sets. A class relation \\(R\\) on a class \\(A\\) is said to\ncode the superclass of inverse images of elements of \\(A\\) under\n\\(R\\). A class relation \\(R\\) on a class \\(A\\) is said to\nextensionally code this superclass if distinct elements of \\(A\\) have\ndistinct preimages. He “tidies up” the theory of such\ncodings by adopting the", "\nIt is worth noting that this can be phrased in a way which makes no\nreference to superclasses: for any class relation \\(R\\), there is a\nclass relation \\(R'\\) such that for any \\(x\\) there is \\(x'\\) with\npreimage under \\(R'\\) equal to the preimage of \\(x\\) under \\(R\\), and\ndistinct elements of the field of \\(R'\\) have distinct preimages.", "\nHis notion of coding is more general: we can further code collections\nof classes by taking a pair \\(\\langle K, R\\rangle\\) where \\(K\\) is a\nsubclass of the field of \\(R\\); clearly any collection of classes\ncodable in this way can be extensionally coded by using the axiom in\nthe form we give.", "\nThe final axiom is", "\nThis implies (as in pocket set theory) that there are two infinite\ncardinalities, which can be thought of as \\(\\aleph_0\\) and \\(c\\),\nthough in this context their behavior is less familiar than it is in\npocket set theory. For example, the set of all natural numbers (as\nVopenka defines it) is of cardinality \\(c\\), while there is an initial\nsegment of the natural numbers (the finite natural numbers) which has\nthe expected cardinality \\(\\omega\\).", "\nOne gets the axiom of choice from the axioms of cardinalities and\nextensional codings; the details are technical. One might think that\nthis would go as in pocket set theory: the order type of all the\nordinals is not a set and so has the same cardinality as the universe.\nBut this doesn’t work here, because the “ordinals”\nin the obvious sense are all nonstandard finite ordinals, which, from\na class standpoint, are not well-ordered at all. However, there is a\ndevious way to code an uncountable well-ordering using the axiom of\nextensional coding, and since its domain is uncountable it must be the\nsame size as the universe.", "\nThis is a rather difficult theory. A model of the alternative set\ntheory in the usual set theory is a nonstandard model of\n\\(V_{\\omega}\\) of size \\(\\omega_1\\) in which every countable external\nfunction extends to a function in the model. It might be best to\nsuppose that this model is constructed inside \\(L\\) (the constructible\nuniverse) so that the axiom of cardinalities will be satisfied. The\naxiom of extensional coding follows from Choice in the ambient set\ntheory.", "\nThe constructions of the natural numbers and the real numbers with\nwhich we started go much as usual, except that we get two kinds of\nnatural numbers (the finite von Neumann ordinals in the set universe\n(nonstandard), and the finite von Neumann set ordinals\n(standard)). The classical reals can be defined as Dedekind cuts in\nthe standard rationals; these are not sets, but any real can then be\napproximated by a nonstandard rational. One can proceed to do analysis\nwith some (but not quite all) of the tools of the usual nonstandard\nanalysis." ], "subsection_title": "9.2 Vopenka’s alternative set theory" } ] }, { "main_content": [ "\nA recent proposal of Andrzej Kisielewicz (1998) is that the paradoxes\nof set theory might be evaded by having two different membership\nrelations \\(\\in\\) and \\(\\varepsilon\\), with each membership relation\nused to define extensions for the other.", "\nWe present the axiomatics. The primitive notions of this theory are\nequality \\((=)\\) and the two flavors \\(\\in\\) and \\(\\varepsilon\\) of\nmembership. A formula \\(\\phi\\) is uniform if it does not\nmention \\(\\varepsilon\\). If \\(\\phi\\) is a uniform formula, \\(\\phi^*\\)\nis the corresponding formula with \\(\\in\\) replaced by \\(\\varepsilon\\)\nthroughout. A set \\(A\\) is regular iff it has the same\nextension with respect to both membership relations: \\(x \\in A \\equiv\nx \\varepsilon A\\).", "\nThe comprehension axiom asserts that for any uniform formula\n\\(\\phi(x)\\) in which all parameters (free variables other than \\(x\\))\nare regular, there is an object \\(A\\), for which we use the notation\n\\(\\{x \\mid \\phi(x)\\}\\), such that \\(\\forall x ((x \\in A \\equiv \\phi^*)\n\\amp (x \\varepsilon A \\equiv \\phi))\\).", "\nThe extensionality axiom asserts that for any \\(A\\) and \\(B\\),\n\\(\\forall x(x \\in A \\equiv x \\varepsilon B) \\rightarrow A = B\\).\nNotice that any object to which this axiom applies is regular.", "\nFinally, a special axiom asserts that any set one of whose extensions\nis included in a regular set is itself regular.", "\nThis theory can be shown to interpret ZF in the realm of\nhereditarily regular sets. Formally, the proof has the same\nstructure as the proof for Ackermann set theory. It is unclear whether\nthis theory is actually consistent; natural ways to strengthen it\n(including the first version proposed by Kisielewicz) turn out to be\ninconsistent. It is also extremely hard to think about!", "\nAn example of the curious properties of this theory is that the\nordinals under one membership relation are exactly the regular\nordinals while under the other they are longer; this means that the\napparent symmetry between the two membership relations breaks!" ], "section_title": "10. Double Extension Set Theory: A Curiosity", "subsections": [] }, { "main_content": [ "\nWe have presented a wide range of theories here. The theories\nmotivated by essentially different views of the realm of mathematics\n(the constructive theories and the theories which support nonstandard\nanalysis) we set to one side. Similarly, the theories motivated by the\ndesire to keep the universe small can be set to one side. The\nalternative classical set theories which support a fluent development\nof mathematics seem to be ZFC or its variants with classes\n(including Ackermann), NFU + Infinity + Choice with suitable\nstrong infinity axioms (to get s.c. sets to behave nicely), and the\npositive set theory of Esser. Any of these is adequate for the\npurpose, in our opinion, including the one currently in use. There is\nno compelling reason for mathematicians to use a different foundation\nthan ZFC; but there is a good reason for mathematicians who\nhave occasion to think about foundations to be aware that there are\nalternatives; otherwise there is a danger that accidental features of\nthe dominant system of set theory will be mistaken for essential\nfeatures of any foundation of mathematics. For example, it is\nfrequently said that the universal set (an extension which is actually\ntrivially easy to obtain in a weak set theory) is an inconsistent\ntotality; the actual situation is merely that one cannot have a\nuniversal set while assuming Zermelo’s axiom of separation." ], "section_title": "11. Conclusion", "subsections": [] } ]

[ "Aczel, Peter, 1978, “The Type Theoretic Interpretation of\nConstructive Set Theory”, in A. MacIntyre, L. Pacholski, J.\nParis (eds.), Logic Colloquium ‘77, (Studies in Logic\nand the Foundations of Mathematics, 96), Amsterdam: North-Holland, pp.\n55–66. doi:10.1016/S0049-237X(08)71989-X", "–––, 1982, “The Type Theoretic\nInterpretation of Constructive Set Theory: Choice Principles”,\nin A.S. Troelstra and D. van Dalen (eds.), The L.E.J. Brouwer\nCentenary Symposium, (Studies in Logic and the Foundations of\nMathematics, 110), Amsterdam: North-Holland, pp. 1–40.\ndoi:10.1016/S0049-237X(09)70120-X", "–––, 1986, “The Type Theoretic\nInterpretation of Constructive Set Theory: Inductive\nDefinitions”, in Ruth Barcan Marcus, Georg J.W.Dorn, and Paul\nWeingartner (eds.), Logic, Methodology, and Philosophy of Science\nVII, (Studies in Logic and the Foundations of Mathematics, 114),\nAmsterdam: North-Holland, pp. 17–49.\ndoi:10.1016/S0049-237X(09)70683-4", "–––, 1988, Non-Well-Founded Sets (CSLI\nLecture Notes, 14), Stanford: CSLI Publications.", "St. Augustine, De Civitate Dei, Book 12, chapter 18.", "Barwise, Jon, 1975, Admissible Sets and Structures: An\nApproach to Definability Theory, (Perspectives in Mathematical\nLogic, 7), Berlin: Springer-Verlag.", "Boffa, M., 1988, “ZFJ and the Consistency Problem for\nNF”, Jahrbuch der Kurt Gödel Gesellschaft, Vienna,\npp. 102–106", "Burali-Forti, C., 1897, “Una questione sui numeri\ntransfiniti”, Rendiconti del Circolo matematico di\nPalermo, 11(1): 154–164. A correction appears in\n“Sulle classi ben ordinate”, Rendiconti del Circolo\nmatematico di Palermo, 11(1): 260. It is not clear that\nBurali-Forti ever correctly understood his paradox.\ndoi:10.1007/BF03015911 and doi:10.1007/BF03015919", "Cantor, Georg, 1872, “Über die Ausdehnung eines Satzes\naus der Theorie der trigonometrischen Reihen”,\nMathematischen Annalen, 5: 123–32.", "–––, 1891, “Über eine elementare\nFrage der Mannigfaltigkeitslehre”, Jahresbericht der\ndeutschen Mathematiker-Vereiningung, 1: 75–8.", "Cocchiarella, Nino B., 1985, “Frege’s\nDouble-Correlation Thesis and Quine’s Set Theories NF and\nML”, Journal of Philosophical Logic, 14(1): 1–39.\ndoi:10.1007/BF00542647", "Crabbé, Marcel, 1982, “On the Consistency of an\nImpredicative Subsystem of Quine’s NF”,\nJournal of Symbolic Logic, 47(1): 131–36.\ndoi:10.2307/2273386", "–––, 2016, “NFSI is not included\nin NF3”, Journal of Symbolic Logic,\n81(3): 948–950. doi:10.1017/jsl.2015.29", "Dedekind, Richard, 1872, Stetigkeit und irrationale\nZahlen, Brannschweig: Friedrich Vieweg und Sohn (second edition,\n1892).", "Esser, Olivier, 1999, “On the Consistency of a Positive\nTheory”, Mathematical Logic Quarterly, 45(1):\n105–116. doi:10.1002/malq.19990450110", "Feferman, Sol, 2006, “Enriched Stratified Systems for the\nFoundations of Category Theory” in Giandomenico Sica (ed.),\nWhat is Category Theory?, Milan: Polimetrica.\n [Feferman 2006 preprint available online (PDF)]", "Frege, Gottlob, 1884, Die Grundlagen der Arithmetik,\nEnglish translation by J.L. Austin, The Foundations of\nArithmetic, Oxford: Blackwell, 1974.", "Friedman, Harvey, 1973, “Some Applications of Kleene’s\nMethods for Intuitionistic Systems”, in A.R.D. Mathias and H.\nRogers (eds.), Cambridge Summer School in Mathematical Logic,\n(Lecture Notes in Mathematics, 337), Berlin: Springer-Verlag, pp.\n113–170. doi:10.1007/BFb0066773", "Grishin, V.N., 1969, “Consistency of a Fragment of\nQuine’s NF System”, Soviet Mathematics\nDoklady, 10: 1387–1390.", "Hallett, Michael, 1984, Cantorian Set Theory and Limitation of\nSize, Oxford: Clarendon, pp. 280–286.", "Hamkins, Joel David, 2012, “The Set-Theoretic\nMultiverse”, Review of Symbolic Logic, 5(3):\n416–449. doi:10.1017/S1755020311000359", "Holmes, M. Randall, 1998, Elementary Set Theory with a\nUniversal Set, (Cahiers du Centre de logique, 10),\nLouvain-la-Neuve: Academia. (See chapter 20 for the discussion of\nwell-founded extensional relation types.)\n [Holmes 1998 revised and corrected version available online (PDF)]", "–––, 2012, “The Usual Model Construction\nfor NFU Preserves Information”, Notre Dame Journal\nof Formal Logic, 53(4): 571–580.\ndoi:10.1215/00294527-1722764", "Jensen, Ronald Bjorn, 1968, “On the Consistency of a Slight\n(?) Modification of Quine’s ‘New\nFoundations’”, Synthese, 19(1): 250–63.\ndoi:10.1007/BF00568059", "Kisielewicz, Andrzej, 1998, “A Very Strong Set\nTheory?”, Studia Logica, 61(2): 171–178.\ndoi:10.1023/A:1005048329677", "Kuratowski, Casimir [Kazimierz], 1921, “Sur la notion de\nl’ordre dans la Théorie des Ensembles”,\nFundamenta Mathematicae, 2(1): 161–171.\n [Kuratowski 1921 available online]", "Lévy, Azriel, 1959, “On Ackermann’s Set\nTheory”, Journal of Symbolic Logic, 24(2):\n154–166. doi:10.2307/2964757", "Mac Lane, Saunders, 1986, Mathematics, Form and Function,\nBerlin: Springer-Verlag.", "Mathias, A.R.D., 2001a, “The Strength of Mac Lane Set\nTheory”, Annals of Pure and Applied Logic,\n110(1–3): 107–234. doi:10.1016/S0168-0072(00)00031-2", "–––, 2001b, “Slim Models of Zermelo Set\nTheory”, The Journal of Symbolic Logic, 66(2):\n487–496. doi:10.2307/2695026", "McLarty, Colin, 1992, “Failure of Cartesian Closedness in\nNF”, Journal of Symbolic Logic, 57(2):\n555–6. doi:10.2307/2275291", "Nelson, Edward, 1977, “Internal Set Theory, a New Approach\nto Nonstandard Analysis”, Bulletin of the American\nMathematical Society, 83(6): 1165–1198.\ndoi:10.1090/S0002-9904-1977-14398-X", "Quine, W.V.O., 1937, “New Foundations for Mathematical\nLogic”, American Mathematical Monthly, 44(2):\n70–80. doi:10.2307/2300564", "–––, 1945, “On Ordered Pairs”,\nJournal of Symbolic Logic, 10(3): 95–96.\ndoi:10.2307/2267028", "Reinhardt, William N., 1970, “Ackermann’s Set Theory\nEquals ZF”, Annals of Mathematical Logic, 2(2):\n189–249. doi:10.1016/0003-4843(70)90011-2", "Robinson, Abraham, 1966, Non-standard Analysis,\nAmsterdam: North-Holland.", "Rosser, J. Barkley, 1973, Logic for Mathematicians,\nsecond edition, New York: Chelsea.", "Russell, Bertrand, 1903, The Principles of Mathematics,\nLondon: George Allen and Unwin.", "Specker, Ernst P., 1953, “The Axiom of Choice in\nQuine’s ‘New Foundations for Mathematical\nLogic’”, Proceedings of the National Academy of\nSciences of the United States of America, 39(9): 972–5.\n [Specker 1953 available online]", "Spinoza, Benedict de, 1677, Ethics, reprinted and\ntranslated in A Spinoza Reader: the “Ethics” and Other\nWorks, Edwin Curley (ed. and trans.), Princeton: Princeton\nUniversity Press, 1994.", "Tupailo, Sergei, 2010, “Consistency of Strictly\nImpredicative NF and a Little More …”,\nJournal of Symbolic Logic, 75(4): 1326–1338.\ndoi:10.2178/jsl/1286198149", "Vopěnka, Petr, 1979, Mathematics in the Alternative Set\nTheory, Leipzig: Teubner-Verlag.", "Wang, Hao, 1970, Logic, Computers, and Sets, New York:\nChelsea, p. 406.", "Whitehead, Alfred North and Bertrand Russell, [PM]\n1910–1913, Principia Mathematica, 3 volumes, Cambridge:\nCambridge University Press.", "Wiener, Norbert, 1914, “A Simplification of the Logic of\nRelations”, Proceedings of the Cambridge Philosophical\nSociety, 17: 387–390.", "Zermelo, Ernst, 1908, “Untersuchen über die Grundlagen\nder Mengenlehre I”, Mathematische Annalen, 65:\n261–281." ]

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[ "\n\nConstructive and intuitionistic Zermelo-Fraenkel set theories\nare\n axiomatic theories of sets\n in the\nstyle of\n Zermelo-Fraenkel set theory (ZF)\n which are based on\n intuitionistic logic.\n They were introduced in the 1970’s and they represent a formal context\n within which to codify mathematics based on intuitionistic logic (see the entry\non\n constructive mathematics).\nThey are formulated on the standard first order language of \nZermelo-Fraenkel set theory and make no direct use of inherently \nconstructive ideas. In working in constructive and intuitionistic \nZF we can thus to some extent rely on our familiarity with ZF and \nits heuristics.", "\n\nNotwithstanding the similarities with classical set theory, the\nconcepts of set defined by constructive and\nintuitionistic set theories differ considerably from that of\nthe classical tradition; they also differ from each other. The\ntechniques utilised to work within them, as well as to obtain\nmetamathematical results about them, also diverge in some respects\nfrom the classical tradition because of their commitment to\nintuitionistic logic. In fact, as is common in intuitionistic\nsettings, a plethora of semantic and proof-theoretic methods are\navailable for the study of constructive and intuitionistic set\ntheories.", "\n\nThis entry introduces the main features of constructive and intuitionistic set theories. As the field is expanding at a fast \npace, we can only briefly recall some key aspects of results and available techniques. We focus more on\nconstructive set theory to highlight important\nfoundational issues that arise within it.\nNote that we omit a conspicuous part of the literature \non constructive and intuitionistic ZF which relates to their categorical \ninterpretations. This area has seen major developments over the years, so much \nso that an adequate treatment of that progress would require a \nsubstantial extension of this entry. \nThe interested reader might wish to consult the entry on \n category theory \n and its references (see also its\n supplement Programmatic Reading Guide). " ]

[ { "content_title": "1. The Essence of Constructive and Intuitionistic Set Theory", "sub_toc": [ "1.1 Axiomatic freedom", "1.2 Constructive versus intuitionistic set theory", "1.3 Predicativity in constructive set theory" ] }, { "content_title": "2. Origins of Constructive and Intuitionistic Set Theories", "sub_toc": [] }, { "content_title": "3. The Axioms Systems CZF and IZF", "sub_toc": [] }, { "content_title": "4. Constructive Choice Principles", "sub_toc": [] }, { "content_title": "5. Proof Theory and Semantics of Constructive and Intuitionistic ZF", "sub_toc": [ "5.1 Proof-theoretic strength", "5.2 Large sets in constructive and intuitionistic ZF", "5.3 Metamathematical properties of constructive and intuitionistic ZF and semantic techniques" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nConstructive and intuitionistic Zermelo-Fraenkel set theories are\nbased on intuitionistic rather than classical logic, and \nrepresent a natural environment within which to codify and study \nmathematics based on intuitionistic logic. \nFor constructive ZF, the main focus has been \nto represent the mathematical\npractice of Bishop (Bishop 1967, Bishop and Bridges\n1985).", "\n\nFor the basic concepts and the driving ideas of intuitionistic logic,\nconstructive mathematics and intuitionism, the reader may wish to\nconsult the following entries:", "\n\nFor classical set theory, see the entry on\n set theory.", "\n\nConstructive and intuitionistic ZF are based on the same first-order\nlanguage as classical ZF set theory,\nwhich has only the binary predicate symbol \\(\\in\\) (membership) as\nnon-logical symbol. That is, they are formulated on the basis of\nintuitionistic first-order logic with equality, plus the binary\npredicate symbol \\(\\in\\). We can thus take advantage of the simplicity\nof the set-theoretic language and of our familiarity with it (Myhill\n1975). As with Bishop-style constructive mathematics, Constructive and\nintuitionistic ZF are compatible with the classical\ntradition, in the sense that all of their theorems are classically\ntrue. In fact, the two formal systems that we shall consider,\nConstructive Zermelo-Fraenkel (CZF) and Intuitionistic\nZermelo-Fraenkel (IZF), give rise to full classical ZF by the simple\naddition of the principle of the excluded middle." ], "section_title": "1. The Essence of Constructive and Intuitionistic Set Theory", "subsections": [ { "content": [ "\n\nClassical Zermelo-Fraenkel set theory is based on classical\nfirst-order predicate logic with equality. On top of the logical\nprinciples are axioms and schemata which describe the notion of set\nthe theory codifies. These principles can be classified into three\nkinds. First, there are principles that enable us to form new sets\nfrom given ones. For example, the axiom of pair allows us to form a\nset which is the pair of two given sets. Secondly, there are\nprinciples that establish properties of the set theoretic\nstructure. For example, the axiom of extensionality identifies all\nsets having the same elements. Third, and finally, there are axioms\nasserting the existence of specific sets. Thus the axiom of infinity\nstates that there is an infinite set. These principles all together\nare usually called the set-theoretic principles.", "\n\nWhen introducing versions of ZF based on intuitionistic logic, the\nfirst step is to eliminate from the logic the principle of the\nexcluded middle (EM). The next step is to choose a good stock of\nset-theoretic principles which faithfully represent the desired notion\nof constructive set. These tasks turn out to be more challenging than\none at first might have expected. In fact, as is well known, systems\nbased on a “weaker” logic have the ability to distinguish\nbetween statements which are equivalent from the point of view of a\n“stronger” logic. In the case of set theory, some of the\nZF axioms or schemata are often presented by one of many classically\nequivalent formulations. Classically it is only a matter of\nconvenience which one to use at a specific time. When working on the\nbasis of intuitionistic logic, however, various formulations of a\nclassical axiom may turn out to be distinct (non-equivalent). In fact,\none can envisage new statements which are classically equivalent to a\nZF axiom but intuitionistically separate from it (for example CZF’s\nsubset collection axiom (Aczel 1978)).\n", "\nAs to the first step, consisting in eliminating the principle of\nexcluded middle from the logic, it turns out that simply evicting this\nprinciple from the underlying logic is insufficient; that is, it is\nnot enough to take the intuitionistic rather than the classical\npredicate calculus as our basis. We also need to ensure that the set\ntheoretic axioms do not bring undesirable forms of excluded middle\nback into our theory. For example, as noted by Myhill (1973), we need\nextra care in choosing an appropriate statement for the axiom of\nfoundation. Foundation is introduced in set theory to rule out sets\nwhich are members of themselves and thus \\(\\in\\)-chains of sets. The\nusual formulation of foundation asserts that each inhabited set (a set\nwith at least one element) has a least element with respect to the\nmembership relation. This statement, however, can be shown to yield\nconstructively unacceptable instances of excluded middle on the basis\nof modest set-theoretic assumptions. Therefore the usual formulation\nof foundation has to be omitted from a set theory based on\nintuitionistic logic. For a proof, see the supplementary document:", "Set-theoretic principles incompatible with intuitionistic logic.", "The typical move in formulating set theories based on\nintuitionistic logic is then to replace foundation with the\nclassically equivalent schema of set induction, which does not have\nthe same “side effects” but has similar\n consequences.[1]", "As to the second step, related to the selection of a good stock of \nset-theoretic principles, the schemata of replacement and\nseparation, and the axiom of power set have attracted most attention. For\nthe exact formulation of these principles see the supplementary\ndocument:", "Axioms of CZF and IZF.", "\n\nHere the following is a typical scenario. Given what are classically two variants\nof a single set-theoretic principle, their classical proof of equivalence requires \nat some point an instance of the excluded middle. However, in general this\nproof of equivalence will not carry through to an\nintuitionistic context, and thus what are classically two forms of one principle\nmay result into two distinct principles when working intuitionistically. \nChoosing one rather than\nthe other of them may therefore influence the notion of set we thus define. \nIn the context of constructive set theories like CZF, power set and \nseparation are \nreplaced by intuitionistically weaker principles. One reason for this is that \nthe full strenght of power set and full separation are seen as unnecessary, \nsince their weaker substitutes seem to \nsuffice for carrying out constructive mathematics. Another reason is that they \nare seen as philosophically problematic, since they may introduce forms of\nimpredicativity within the set theory (see the section on\n Predicativity in constructive set theory).\nThe case of replacement versus collection is somehow more complex (see,\nfor example, the articles (Friedman and Scedrov 1985), (Rathjen 2005)\nand (Rathjen 2012)). It is worth stressing that while adopting the\nusual formulation of foundation goes against the very assumption of\nintuitionistic logic as background logic, the principles of separation\nand power set have no incompatibility with intuitionistic logic at\nall, so much so that they are integral part of the intuitionistic\ntheory of sets IZF (Friedman 1973a).\n", "\n\nTo summarise, in formulating a set theory based on intuitionistic\nlogic, the first task is to expel the principle of excluded middle,\nincluding those instances of it which might be hidden in familiar\nformulations of set-theoretic axioms. The next task is to choose one\nversion of each classical principle which best characterises the\ndesired notion of set. This opens up a range of choices one can make,\nas a plurality of intuitionistic principles may correspond to one\nclassical principle. It should be stressed that from a constructive\npoint of view this plurality of options (and thus systems), rather\nthan causing uneasiness, is a highly desirable situation, as it\nconstitutes a form of “axiomatic freedom”. For example, it\nallows us to differentiate between a number of mathematical notions,\nthus better capturing our intuitions of them as distinct. It also\ngives us the freedom to choose the notions and theories which best\nsuit a given context. In addition, by adopting intuitionistic logic\nwe can include within our theories principles which are classically\nvery strong, without having to commit to their classical strength. For\nexample, one can add a notion of inaccessible set to a weak\nconstructive set theory and obtain a predicative theory,\nwhile the same notion embedded in a classical context becomes\nextremely strong (see the sections on\n Predicativity in constructive set theory and \nLarge sets in constructive and intuitionistic ZF).\nFinally, a rich area of (meta-theoretical) study of the relations\nbetween the resulting distinct set-theoretic systems naturally\narises. As one could expect, this freedom also has a price, as a\nhighly technical study of the axiomatic theories might be necessary to\ndistinguish their principles as well as to unveil some of their\nsubtleties. This again can be seen as an advantage, since it forces us\nto a deeper and clearer analysis of the mathematical notions involved\nand prompts us to develop new sophisticated tools." ], "subsection_title": "1.1 Axiomatic freedom" }, { "content": [ "\n\nAlthough there are many systems of sets based on\nintuitionistic logic, we can distinguish two main trends within the\nliterature. According to the first one, we take all of what is\navailable in classical ZF set theory and only modify those principles,\nsuch as foundation, which have a clear incompatibility with\nintuitionistic logic. This gives rise to set theories such as\nIntuitionistic Zermelo-Fraenkel,\n IZF,\na variant of which was introduced as early as in (Friedman\n1973a). (See Beeson 1985, Chapters 8 and 9 and Scedrov 1985 for two\nsurveys on IZF.) The rationale behind these theories appears to be\nthat of granting the mathematician the most powerful tools possible,\nas long as compatibility with intuitionistic logic is\npreserved. According to the second approach, in addition to the\nadherence to intuitionistic logic we also introduce restrictions on\nthe set-theoretic principles admitted, as far as the resulting system\ncomplies with the constructive mathematical practice. Theories of\nthis second kind can thus be seen as the outcome of a double process\nof restriction with respect to classical ZF. First there is a\nrestriction to intuitionistic logic, then a restriction is imposed on\nthe set-theoretic constructions allowed. The latter is motivated by\n(1) the observation that weaker principles appear to suffice for the\nconstructive mathematical practice and (2) the desire to adhere to a\nform of predicativity (see the next section for a clarification of\nthis notion of predicativity). Paradigmatic examples of the latter\nkind of systems are Myhill’s Constructive Set Theory (Myhill 1975),\nFriedman’s system B (Friedman 1977) and Aczel’s Constructive\nZermelo-Fraenkel set theory\n CZF\n (Aczel 1978; 1982; 1986, Aczel & Rathjen\n2001; Aczel & Rathjen 2010, Other Internet Resources). We can also say that in this second approach the foundational\nmotivation influences the practice to a higher degree.", "\n\nIn the following we make use of a convention which is often in\nplace today, according to which the adjective\n“intuitionistic” refers to those set theories, such as\nIZF, which are impredicative, while “constructive” refers\nto set theories, such as CZF, which comply with a form of\npredicativity. Note, however, that this convention is\nnot always followed in the literature. In fact, the adjective\n“constructive” has also been used to denote impredicative\ntheories, and “intuitionistic” to refer to predicative\nfoundational theories such as Martin-Löf type theory\n(Martin-Löf 1975; 1984). It is also worth noting that the present\nconvention on the use of the words “constructive” and\n“intuitionistic” differs from that made in the context of\nconstructive mathematics (see, for example, the entry\non constructive mathematics\nand also Bridges and Richman 1987)." ], "subsection_title": "1.2 Constructive versus intuitionistic set theory" }, { "content": [ "\n\nPredicativism has its origins in the writings of Poincaré and\nRussell, who responded to the paradoxes that were discovered in\nCantor’s and Frege’s set theories in the early 20th\ncentury. Subsequently Weyl made fundamental contributions to the study\nof predicative mathematics (Weyl 1918, see also Feferman 1988).\nAccording to one notion, a definition is impredicative if it\ndefines an object by reference to a totality which includes the object\nto be defined. With his Vicious Circle Principle (VCP), Russell\nintended to eliminate the circularity in mathematics that arises from\nsuch impredicative definitions. Russell gave various formulations of the VCP, one of which is:", "\n Whatever contains an apparent variable must not be a possible value\n of that variable (Russell 1908, in van Heijenoort 1967, 163).\n", "\n\nPoincaré, Russell and Weyl’s foundational analysis of\npredicativity has paved the way for a variety of logical analyses of\nthe notion. The most commonly accepted analysis is due to Feferman and\nSchütte (independently) following lines indicated by Kreisel\n(Kreisel 1958, Feferman 1964 and Schütte 1965; 1965a). Here\nproof theory has played a pivotal role. In very rough terms, the idea\nwas to single out a collection of theories (a transfinite progression\nof systems of ramified second order arithmetic indexed by ordinals) by\nmeans of which to characterise a certain notion of predicative\nordinal. Feferman and Schütte’s proof theoretic analysis of these\ntheories has identified an ordinal, usually referred to as\n\\(\\Gamma_0\\), which is the least non-predicative ordinal\naccording to this notion. A formal system is considered \npredicatively justifiable if it is proof-theoretically reducible to a\nsystem of ramified second order arthmetic indexed by an ordinal less\nthen \\(\\Gamma_0\\). Therefore in proof theory\n\\(\\Gamma_0\\) is usually considered as representing the limit of\npredicativity. (See Feferman 2005 for a more accurate informal\naccount of this notion of predicativity and for further\nreferences. See also Crosilla 2017. The reader may also consult the section on\n predicativism\n in the entry on philosophy of mathematics and the entry on\n paradoxes and contemporary\nlogic).", "\n\nFor constructive foundational theories a more\n“liberal” approach to predicativism has been suggested,\nstarting from work in the late 1950’s of Lorenzen, Myhill and Wang\n(see e.g. Lorenzen and Myhill 1959). The driving idea is that\nso-called inductive definitions ought to be allowed in the\nrealm of constructive mathematics. The intuitive justification of\ninductive definitions is related to the fact that they can be\nexpressed by means of finite rules, in a “bottom-up” way.\nThe proof-theoretic strength of theories of inductive definitions goes\nwell beyond Feferman and Schütte’s bound (Buchholz, Feferman,\nPohlers and Sieg 1981). Thus relatively strong theories are considered\npredicative in today’s foundations of constructive mathematics. This\nmore liberal notion of predicativity has often been\ntermed generalised predicativity. In this entry we \nsimply write predicativity for generalised predicativity and call \npredicativity given the natural numbers the better known form of predicativity which arises in the classical context and was analysed by Kreisel, Feferman and Schütte.", "An example of a predicative theory in this sense is the\nconstructive set theory CZF, as its proof-theoretic strength is the\nsame as that of a theory of one inductive definition known as\nID\\(_1\\). The system IZF, instead, is impredicative, as its\nproof-theoretic strength equates that of the whole of classical ZF\n(Friedman 1973a).", "\n\nIn set theories based on intuitionistic logic, predicativity is usually\nachieved by restricting the principles of separation and power set, as\nthese appear to be the main sources of impredicativity (when the\ninfinity axiom is assumed). ", "\n\nThe schema of separation allows us to form a subset of a given set\nwhose elements satisfy a given property (expressed by a formula in the\nlanguage of set theory). Given a set \\(B\\) and a formula \\(\\phi(X)\\),\nseparation allows us to construct a new set, the set of those elements\n\\(X\\) of \\(B\\) for which \\(\\phi\\) holds. This is usually informally\nrepresented as: \\(\\{X \\in B : \\phi(X)\\}\\). Separation may lead to\nimpredicativity in case the formula \\(\\phi\\) contains unbounded\nquantifiers ranging over the whole universe of sets; in fact, in\ndefining the new set by separation we may thus refer to this very set,\ncontradicting Russell’s VCP. For example, if we define a set\n\\(C\\) by separation as \\(\\{X\\in B : \\forall Y \\psi(X,Y)\\}\\), then\n\\(C\\) is among the \\(Y\\)’s that need to be checked for the\nproperty \\(\\psi\\). This form of impredicativity is avoided in\nconstructive set theory by restricting the separation schema: by\nrequiring that all quantifiers occurring in the formula \\(\\phi\\) range\nonly over “previously constructed” sets. Syntactically,\nthis means that given a set \\(B\\), we can form a new set \\(\\{X \\in B :\n\\phi(X)\\}\\) by separation only if all quantifiers in \\(\\phi\\) are\nbounded; that is, only if all quantifiers in \\(\\phi\\) are of the form\n\\(\\forall X (X\\in Y \\rightarrow \\ldots)\\) or \\(\\exists X(X\\in Y \\wedge\n\\ldots)\\), for some set \\(Y\\).", "\nWe can see that constraining separation in this way avoids impredicativity, by \nobserving that the\nproof theoretic strength of CZF, which has only restricted separation,\nis within the range of predicativity. However, by adding full\nseparation to CZF one obtains an impredicative theory, in fact, one\nwith the same proof-theoretic strength as full second order arithmetic\n(Lubarsky 2006). See also Section 5 for a discussion of the role of proof theory\nin analysing constructive and intuitionistic set theories. ", "\n\nThe power set axiom allows us to form a set of all subsets of\na given set. An example of impredicative use of power set is given by\nthe definition of a subset of the natural numbers, \\(N\\), as follows:\n\\(B := \\{n \\in N : \\forall C \\subseteq N \\phi(n, C)\\}\\), where\n\\(\\phi\\) can be taken to be a bounded formula. A form of circularity\narises here as \\(B\\) itself is among the subsets of \\(N\\) which need\nto be checked for \\(\\phi\\). As emphasized by Myhill (1975, 354), power\nset is hard to justify from a constructive point of view: it gathers\ntogether all the subsets of a given set, but does not prescribe a rule\nthat \"constructs\" the set out of previously given sets, as\npredicativity would seem to require.\n", "Myhill writes:", "Power set seems especially nonconstructive and\nimpredicative compared with the other axioms: it does not involve, as\nthe others do, putting together or taking apart sets that one has\nalready constructed but rather selecting out of the totality of all\nsets those that stand in the relation of inclusion to a given\nset. (Myhill 1975, 351).", "\nPower set seems particularly problematic in the case of infinite sets, \nas \"we have no idea of what an arbitrary subset of an infinite set is; there is no way of generating them all and so we have no way to form the set of all of them\" (Myhill 1975, 354).\nAs a consequence, there seems to be no way of giving constructive sense to the set of all subsets of an infinite set. ", "\nMyhill crucially observes that power set is not needed for constructive \nmathematics Bishop-style, as it can be replaced by one of its\nconsequences. This is often called Myhill’s exponentiation\naxiom and states that we can form a set of all functions\nfrom one given set to another. This axiom is clearly\nequivalent to power set in a classical context, where subsets of a\ngiven set may be represented by characteristic functions. In the\nabsence of the principle of excluded middle, however, power set and\nexponentiation are not equivalent.\nMyhill’s fundamental observation is that exponentiation suffices to carry out \nthe mathematics of (Bishop 1967); for example, it allows for \nthe construction of the (Cauchy) real numbers within constructive set theory. \nMyhill claims that exponentiation is constructively meaningful because a function is a rule, \na finite object which can actually be given.", "\nHe also writes that the case of power set is different from that of\nexponentiation as:", "even in the case of infinite sets \\(A\\) and \\(B\\) we do\nhave an idea of an arbitrary mapping from \\(A\\) into \\(B\\). An\narbitrary mapping from \\(\\mathbf{Z}\\) into \\(\\mathbf{Z}\\) is a partial\nrecursive function together with a proof that the computation always\nterminates; a similar account can be given of an arbitrary real\nfunction. There is no corresponding explanation of\n“arbitrary subset”. (Myhill 1975,\n354).", "\n\nMyhill’s exponentiation axiom is now part of all major systems of\nconstructive set theory. In the case of CZF, in fact, one has a\nstrengthening of exponentiation, known as subset collection, which is\nalso a weakening of power set. A generalisation of exponentiation can\nalso be found in constructive type theory.", "\nIn the case of CZF, the claim that adding the power set axiom \ninduces a form of impredicativity can\nbe substantiated by a technical result. Rathjen (2012b) shows that CZF\naugmented by the power set axiom exceeds the strength of classical Zermelo set theory,\nand thus the addition of the power set axiom to CZF \nbrings us to a fully impredicative theory. This also shows that the\nimplication from power set to subset collection can not be reversed,\nas CZF’s proof-theoretic strength is way below that of Zermleo\nset-theory. In other terms, the power set axiom is much stronger than \nboth exponentiation and subset collection. ", "\n\nHaving introduced appropriate constraints to power set and separation,\nwe could now face a substantial objection. Constructive and\nintuitionistic set theories can be seen as modifications of classical\nZF set theory that are obtained by: (1) replacing classical with\nintuitionistic logic, and (2) accurately choosing, among various\nclassically equivalent principles, those which seem more appropriate\nfor given purposes. For example, we might choose principles which\nsuffice to represent a certain mathematical practice, like, for\nexample, Bishop style mathematics. The resulting notion of set,\nhowever, might become obscure and the choice of the set-theoretic\nprinciples might appear to a certain degree as arbitrary. In the case\nof intuitionistic ZF, one can justify the choice of the set-theoretic\nprinciples by examining its semantical interpretations, as Heyting\nsemantics, or by looking at its categorical models. In the case of\nconstructive set theory, to hinder this kind of objection, Aczel has\ngiven an interpretation of CZF in a version of Martin-Löf type\ntheory (Aczel 1978). The claim is that a clear constructive meaning is\nthus assigned to CZF’s notion of set by looking at its meaning in\nMartin-Löf type theory, since the latter is usually considered as\nrepresenting an accurate and fully motivated formulation of a\nconstructive notion of set. Aczel’s interpretation of CZF in\nconstructive type theory is given by interpeting sets\nas trees in type theory. That is, in constructive type theory \nthe universe of sets of CZF is represented by a type, V, of iterative sets built over the\nuniverse, U, of small types (Aczel 1978;\nMartin-Löf 1984). This interpretation clearly highlights the\n(generalised) predicativity of CZF, whose sets can be seen as trees built up inductively, and whose set theoretic universe also has a clear inductive\nstructure.\n", "The predicativity of CZF and related systems is consonant with\nphilosophical positions which are often associated with the use of\nintuitionistic logic. In particular, it would seem that if\nwe construct the mathematical objects, for example, if the\nmathematical objects are mental constructions of some kind, then\nresorting to impredicative definitions would produce an undesirable\nform of circularity. This clearly contrasts with a view often\nassociated to classical set theory, for which our mathematical\nactivity can be seen as a gradual disclosure of properties of the\nuniverse of sets, whose existence is independent from us. Such a view is\nusually bound up with the use of classical logic and impredicativity\nin studying the set-theoretic universe. Predicativity is also often\nseen as related to the time-honoured distinction between actual and\npotential infinity. Predicative (and thus, in particular,\nconstructive) theories are often seen as avoiding reference to actual\ninfinity, and only committing to potential infinity (Dummett 2000,\nFletcher 2007). This again seems particularly in harmony with those\nphilosophical positions which highlight the human dimension of our\nmathematical activity, by seeing, for example, the mathematical\nobjects and the truth of statements about them as dependent on\nus. Another related aspect is often seen as pertaining to\npredicativity: if the universe of sets is built up in stages by our\nown mathematical activity, then it would be natural also to see it\nas open ended. For this reason, in a constructive context,\nwhere the rejection of classical logic meets the requirement of\npredicativity, the universe of sets is often described as an open\nconcept, a universe “in fieri”. This idea is especially\nwell exemplified within constructive type theory, where the notion of\ntype-theoretic universe has been deliberately left open by Per\nMartin-Löf (by not postulating specific elimination rules for\nit). The open ended nature of the universe of sets has paved the way\nfor extensions of it by reflection principles. These have been\ninvestigated both within type theory and constructive set theory. See\n(Rathjen 2005a) for a survey of results and a foundational discussion,\nand also section 5.2. \nFor a formal analysis of the constructive universe of sets and a comparison with the Von Neumann hierarchy, see (Ziegler 2014). " ], "subsection_title": "1.3 Predicativity in constructive set theory" } ] }, { "main_content": [ "\n\nIntuitionistic versions of Zermelo-Fraenkel set theories were\nintroduced in the early 1970s by Friedman and Myhill. In (Friedman\n1973) the author presents a study of formal properties of various\nintuitionistic systems and introduces for them an extension of\nKleene’s realisability method. The realisability technique is applied\nin (Myhill 1973) to show the existence property for a version of\nintuitionistic Zermelo-Fraenkel set theory (with replacement in place\nof collection). In another fundamental contribution Friedman extends\nthe double negation translation of intuitonistic logic to relate\nclassical and intuitionistic set theories (Friedman 1973a). These\nfirst papers already address the relation between some major\nintuitionistic set theories and classical ZF. They also clarify a key\nfeature of set theory based on intuitionistic logic, mainly that it is\namenable to powerful constructive semantic interpretations, like\nrealizability. These techniques are applied to the study of crucial\nmetatheoretical properties which are typical of the constructive\napproach and which are enjoyed by some constructive set theories (see\nthe section on\n Semantic techniques). \nThis groundbreaking work has been fully exploited and substantially\nextended in work by Beeson and McCarty (see Beeson 1985; McCarty\n1984).", "\n\nConstructive set theory from the very start has a more distinctive\nfoundational vocation and it is bound up with Bishop’s mathematics. In\nfact, in 1967 Bishop published the book “Foundations of\nconstructive analysis” (Bishop 1967), which opened up a new era\nfor mathematics based on intuitionistic logic (see the entry on\n constructive mathematics).\nThe monograph stimulated fresh attempts in the logical community to\nclarify and formally represent the principles which were used by\nBishop, though only at an informal level. First attempts by Goodman\nand Myhill (Goodman and Myhill 1972) made use of versions of\nGödel’s system T (see also (Bishop 1970) for a similar\nattempt). Myhill, however, reached the conclusion that the resulting\nformalisation was too complex and artificial (Myhill 1975,\n347). Myhill proposed instead a system which is closer to the informal\nnotion of set originally utilised by Bishop and also closer to the\nset-theoretic tradition. Myhill writes (1975, 347):", "We refuse to believe that things have to be this complicated -\nthe argumentation of (Bishop 1967) looks very smooth and seems to \nfall directly from a certain concept of what sets, functions, etc. are, and\nwe wish to discover a formalism which isolates the principles underlying \nthis conception in the same way that Zermelo-Fraenkel set theory\nisolates the principles underlying classical (nonconstructive)\nmathematics. We want these principles to be such as to make the\nprocess of formalization completely trivial, as it is in the classical\ncase.", "\n\nWe observe here that Myhill’s constructive set theory had\ndistinguished notions of function, natural number and set; it thus\nclosely represented a constructive tradition in which functions and\nnatural numbers are conceptually independent from sets. Another\nfundamental step in the development of constructive set theory was\nFriedman’s “Set-theoretical foundations for constructive\nanalysis” (Friedman 1977). Here, among other systems, a system\ncalled B is defined which has further restrictions on the\nset-theoretic principles compared with Myhill’s (in particular, it has\nno set induction). It also has a restricted form of the axiom of\ndependent choice. System B is there shown to be expressive enough to\nrepresent the constructive analysis of Bishop (1967) whilst being at\nthe same time proof-theoretically very weak (due to the absence of set\ninduction). System B is in fact a conservative extension of\narithmetic (thus it is well below the limit of predicativity given the natural numbers\nbriefly recalled in section\n 1.3).\n Myhill and Friedman’s systems were\nsubsequently modified by Aczel, to obtain a system, CZF (Constructive\nZermelo-Fraenkel), that is fully compatible with the ZF language\n(Aczel 1978, 1982, 1986; Aczel and Rathjen 2001; 2010). CZF also\nincluded no choice principles. Aczel gave an interpretation of CZF in\nMartin-Löf type theory with the aim of corroborating the\nconstructive nature of the set theory. He also strengthened some of\nthe principles of Myhill’s system (namely, collection and\nexponentiation) on the ground that the stronger versions are still\nvalidated by the interpretation in type theory.", "\n\nOther foundational systems for\nBishop-style constructive mathematics were introduced in the early\n1970’s. For example: explicit mathematics by S. Feferman\n(Feferman 1975), and the already mentioned Intuitionistic Type\nTheory (Martin-Löf 1975; 1984). \nConstructive type theory is usually considered the \nmost satisfactory foundation for constructive mathematics Bishop-style. \nBoth type theory and explicit mathematics can be seen as expressing \nmore directly the computational \ncontent of constructive mathematics. Type theory, in particular, \ncan be read as a very general and expressive programming language. \nConstructive and intuitionistic set\ntheories display their computational\ncontent only indirectly through their semantic interpretations\n(see e.g. (Aczel 1977), (Lipton 1995) and the section on\n Semantic techniques)." ], "section_title": "2. Origins of Constructive and Intuitionistic Set Theories", "subsections": [] }, { "main_content": [ "\n\nFor a reader who is already familiar with ZF set theory, we now\nbriefly recall the axioms of the systems CZF and IZF. For a full list\nand an explanation of their axioms we refer instead to the\nsupplementary document:", "Axioms of CZF and IZF.", "\n\nCZF and IZF are formulated on the basis of\n intuitionistic first-order logic\nwith equality, having only \\(\\in\\) (membership) as an additional\nnon-logical binary predicate symbol. Their set-theoretic axioms are as\nfollows.", "\nNote that in IZF the schema of separation is unrestricted.\nIn CZF, Collection is strengthened to compensate for restricted separation.\nSubset collection is a strengthening of Myhill’s exponentiation axiom,\nthus substituting for ZF’s Powerset. " ], "section_title": "3. The Axioms Systems CZF and IZF", "subsections": [] }, { "main_content": [ "\n\nWhen discussing the role of classical set theory as a foundation for\nmathematics, one usually considers the theory ZFC, that is, the axiom\nsystem ZF plus the axiom of choice (AC). One might therefore wonder\nwhat is the status of the axiom of choice in intuitionistic\nsettings. The question is particularly significant because at its\nfirst appearance the axiom of choice was often seen as controversial\nand highly non-constructive. In constructive contexts, however, one\nwitnesses a peculiar phenomenon. The usual form of the axiom of choice\nis validated by theories of types such as Martin-Löf type theory,\nwhere the Curry-Howard correspondence holds\n(See Section 3.4\n of the entry on\n Constructive mathematics). \nOn the other hand, the assumption of the axiom of\nchoice gives rise to instances of the excluded middle\nin extensional contexts, where a form of separation is also\navailable. This is the case, for example, of constructive and\nintuitionistic ZF. (For the proof, see the supplementary document\non Set-theoretic Principles Incompatible with Intuitionistic Logic.) \nA proof of the\nincompatibility of AC with extensional set theories based on\nintuitionistic logic seems to have first appeared in (Diaconescu 1975)\nin a categorical context. Goodman and Myhill give an argument for set\ntheories based on intuitionistic logic (Goodman and Myhill 1978). ", "\n\nAlthough the axiom of choice is incompatible with both constructive\nand intuitionistic ZF, other choice principles may be added to the\nbasic systems without producing the same undesirable results. For\nexample one could add the principle of countable choice\n(AC\\(_0)\\) or that of dependent choice (DC). In fact, \nboth have been often\nemployed in the constructive mathematical practice. \n(For their exact formulation see the supplementary document on \nAxioms of CZF and IZF.)", "\nIn (Aczel 1978) the author also considered a choice principle called the Presentation\nAxiom, which asserts that every set is the\nsurjective image of a so-called base. A base is a set,\nsay \\(B\\), such that every relation with domain \\(B\\)\nextends a function with domain \\(B\\).", "\nThe compatibility of all these forms of choice with constructive set\ntheory has been proved by Aczel by extending his\ninterpretation of CZF in Martin-Löf type theory (Aczel\n1982). Rathjen (2006) has also considered various constructive choice\nprinciples and their mutual relations.", "\n\nA final remark: although constructive and intuitionistic set theories\nare compatible with the principles of choice just mentioned, the set\ntheories are often defined without any choice principles. This has\nthe aim of allowing for a “pluralistic” foundational\napproach. In particular, one would like to obtain a foundational\ntheory compatible with those contexts (e.g. categorical models\nof set theory) in which even these weaker principles of choice may not be\nvalidated. For similar ideas in the context of constructive type\ntheory, see (Maietti and Sambin 2005, Maietti 2009). We wish also to mention here\nRichman’s appeal for a constructive mathematics which makes no\nuse of choice principles (Richman 2000; 2001)." ], "section_title": "4. Constructive Choice Principles", "subsections": [] }, { "main_content": [ "\n\nIn considering a certain mathematical practice (or a theory used to\ncodify it) from a philosophical perspective, we need to clarify\nwith the greatest possible precision the assumptions which are made\nwithin it as well as the consequences which arise from those\nassumptions. This is particularly true when working with theories\nwhich are based on a weaker logic than the classical one, for which a\ndeeper, more precise insight is mandatory. Many technical tools are\navailable which can help us clarify those aspects. Among the available\ninstruments, there are proof-theoretic techniques, such as\nproof-theoretic interpretations, as well as semantic techniques, such\nas realisability, Kripke models, Heyting-valued semantics. In fact, in\nthe literature one often witnesses the interplay of proof-theoretic\nand semantic techniques. We here give a cursory look into some of\nthese topics and suggest further reading." ], "section_title": "5. Proof Theory and Semantics of Constructive and Intuitionistic ZF", "subsections": [ { "content": [ "\nA fundamental theme in proof theory (in particular in the branch of\nthis discipline known as ordinal analysis) is the classification of\ntheories by means of transfinite ordinals which measure their\n\"consistency strength\" and \"computational power\". These ordinals give\nan indication of how strong a theory is, and therefore offer a way of\ncomparing different theories. For example, the ordinal\n\\(\\varepsilon_0\\) is the proof-theoretic ordinal of Peano Arithmetic,\nand is much smaller than the ordinal \\(\\Gamma_0\\), usually referred to\nas \"the limit of predicativity\" \n (see section 1.3 above). \n This is indicative that there are predicatively acceptable theories\nwhich are much stronger than Peano Arithmetic. ", "\nAs discussed in section 1, the step\nfrom classical ZF to its intuitionistic variants requires us to choose\na suitable formulation for each set-theoretic axiom: one classical \naxiom may have a number of intuitionistic variants which turn out to be \nnon-equivalent to each other. This is sometimes reflected by the proof-theoretic\nstrength of the resulting theories, which may vary depending on which principles we choose. \nFor example, we already noted that \nin CZF we do not have full separation and power set, which are \nreplaced by the predicatively acceptable principles of bounded separation and \nsubset collection, respectively. However, if\nwe add to CZF either of these principles, we obtain impredicative\ntheories. The impredicativity of the resulting theories is witnessed \nby the fact that their proof-theoretic strenght far exceeds that of CZF.", "\nIt is not surprising that investigations on the proof-theoretic\nstrength of constructive and intutionistic set theories have been a\ncrucial meta-theoretical tool for understanding these theories and\ntheir relations with each other. Investigations on the\nproof-theoretic strength of a theory are rich and informative. In\nparticular, Feferman (1993) has argued that a proof-theoretic analysis\nmay help us establish whether a certain theory complies with a given\nphilosophical framework: for example, the analysis may reveal that a\ntheory is predicative or finitistic etc. Furthermore, as a by-product\nof the proof-theoretic analysis we sometimes obtain simple\nindependence proofs. In fact, we can show that a theory cannot prove a\nspecific principle because adding it to the theory would increase the\ntheory’s proof-theoretic strength. For example, CZF does not prove the\npowerset axiom, as the addition of powerset to CZF gives rise to a\nmuch stronger theory. Proof-theoretic interpretations have also been\nemployed to compare constructive and intuitionistic ZF set theories\namong each others, as well as with their classical counterparts, and\nalso with other foundational systems for constructive mathematics,\nsuch as constructive type theory and explicit mathematics (see\ne.g., Griffor and Rathjen 1994, Tupailo 2003). For a definition\nof the notion of proof-theoretic strength and for surveys on proof\ntheory see, for example, (Rathjen 1999, 2006b). ", "\n\nAlthough CZF and IZF are the most widely studied systems, numerous\nother systems for constructive and intuitionistic set theory have been\nconsidered in the literature so far. The proof-theoretic strength of a\nnumber of constructive and intuitionistic set theories has been\nestablished by a variety of tools, like, for example, an extension to\nset theory of the double negation interpretation (originated in\n(Friedman 1973a)), and a variety of other proof-theoretic\ninterpretations, often resulting from a careful combination of\nsemantic and proof theoretic techniques. In many cases the proof\ntheoretic strength of a system has been determined by a chain of\ninterpretations between constructive and classical systems, and by\nusing a variety of tools, from relisability to more \"traditional\"\nproof theoretic techniques, as ordinal analysis (see, for example,\nBeeson 1985; Griffor and Rathjen 1994; Rathjen 2012b). In particular,\nrealisability has turned out to be very useful, due to its\nflexibility. As to the outcomes of these investigations, some of the\nsystems analysed turn out to be as weak as arithmetic, as, for example,\nFriedman’s system B (Friedman 1977); other systems are as strong as\nfull classical ZF, as IZF (Friedman 1973a). There are also systems of\nintermediate strength, as CZF. The strength of the latter theory, in\nfact, equals that of a theory of one inductive definition known as\nID\\(_1\\). The fact that CZF has the same strength as\nID\\(_1\\) is taken to confirm the (generalised) predicativity of the set\ntheory, and to prove that it exceeds the limit of predicativity given \nthe natural numbers, since ID\\(_1\\)’s proof theoretic ordinal is well above \n\\(\\Gamma_0\\).", "\n\nAs a final remark: while the strength of CZF is well below that of \nsecond-order arithmetic, the simple addition of excluded middle to CZF\ngives us (full) ZF. This should be contrasted with IZF, which already\nhas the strength of ZF (Friedman 1973a). The limited \nproof theoretic strength of CZF compared with IZF has often been considered one of \nthe main advantages of constructive over intuitionistic set\ntheory. In a sense, it would seem that CZF makes the most of \nits use of intuitionistic logic, as it characterises a notion of \n(generalised) predicative set which is sufficiently strong for \nthe development of much of constructive mathematics but also \nweak enough to avoid impredicativity.\nInterestingly, when some large set axioms have been added to\nconstructive set theory, a similar pattern has emerged, as the\nstrength of the resulting theory is well below that of the\ncorresponding classical theory." ], "subsection_title": "5.1 Proof-theoretic strength" }, { "content": [ "\n\nA prominent area of research in classical set theory is that of large\ncardinals (see the entry on\n set theory). In constructive contexts, the ordinals are not linearly\nordered. (For the notion of constructive ordinal and a brief\ndiscussion of its properties, see the supplementary document on: \nSet-theoretic Principles Incompatible with Intuitionistic Logic.) \n As a consequence, cardinal numbers do not play the same role as in the classical\n setting.", "\n\nOne can nonetheless study the impact of “reflection\nprinciples” of the form of large set axioms.\nFor example, one can add to constructive and intuitionistic set theories \nan axiom asserting the existence of inaccessible \nsets.[2] \n The addition of large set axioms to intuitionistic ZF was first proposed\nby Friedman and Scedrov (Friedman and Scedrov 1984). One of their\naim was to shed light on the corresponding classical\nnotions; another was to study the impact of these principles on\nmetatheoretical properties of the original set theories. Friedman and\nScedrov have shown, for example, that the addition of large set axioms\ndoes not compromise the validity of the disjunction and numerical\nexistence properties for IZF.", "\n\nIn the context of constructive set theory, large sets have been\nintroduced by Aczel in the form of so-called regular sets to\nallow inductive definitions of sets (Aczel 1986). Rathjen and Crosilla\nhave considered inaccessible sets (Rathjen al. 1998; Crosilla and\nRathjen 2001) and Mahlo sets (Rathjen 2003a). Nevertheless, an\nobjection could be raised to extensions of constructive set theory by\nlarge set axioms. In classical set theory, large cardinals can be seen\nas an incarnation of higher infinity. How do we justify these\nprinciples constructively? The constructive justification of these\nnotions relies again on the type theoretic interpretation. The\naddition of these principles corresponds in fact to that of universes\nand \\(W\\)-types within constructive type theory. The\njustification of extensions by large sets is thus bound up with the\nquestion of the limits of Martin-Löf type theory (Rathjen\n2005). We also note that the addition of inacessible set axioms\n to a weak subsystem of CZF\n(with no set induction) produces a theory of strength\n\\(\\Gamma_0\\), the ordinal singled out by Feferman and\nSchütte as the limit of predicativity given the natural numbers (Crosilla and\nRathjen 2001; see also section 1.3). This is \nwitness to the fact that by working in a constructive, predicative\ncontext, we can tame traditionally strong set-theoretic notions.", "\nCrosilla and Rathjen’s set theory with inaccessible sets (but no set\ninduction) is proof theoretically rather weak, but mathematically\nquite expressive. For example, it has been used to verify that the\naddition of Voevodsky’s Univalence Axiom to Martin-Löf type\ntheory does not engender impredicativity (Rathjen 2017). The axiom of\nUnivalence was introduced by Voevodsky as part of his Univalent\nFoundations programme (Voevodsky 2015). (For Univalent Foundations,\nsee the entries on \n type theory \nand on\n intuitionistic type theory). \nVoevodsky gave a model of constructive type theory with\nthe Univalence Axiom which is based on Kan simplicial sets (see\nKapulkin & Lumsdaine 2012, Other Internet Resources). The\nsimplicial model of constructive type theory with univalence developed\nin the above article is carried out within an extension of ZFC with\ninaccessible cardinals. This prompted the question whether one could\ngive a more constructive model of this type theory, and, in\nparticular, whether the type theory is predicative. Bezem, Coquand and\nHuber (2014) have recently proposed a model of this type theory in\ncubical sets which is computational and “can be expressed in a\nconstructive metalogic”. Rathjen (2017) has verified that this new\nmodel can be codified in a suitable extension of CZF by inaccessible\nsets which is much weaker than classical set theory with inaccessible\ncardinals. In fact, it turns out that if we take as starting point a\nrelatively weak type theory, i.e. one without W-types, and extend it\nby the Univalence Axiom, the resulting theory has proof theoretic\nstrength \\(\\Gamma_0\\), the ordinal usually taken to represent the\nlimit of predicativity given the natural numbers (Rathjen 2017). To\nshow this, one proves that the cubical model by Bezem, Coquand and\nHuber can be carried out in an extension of the system introduced in\nCrosilla and Rathjen (2001) by (bounded) Relativized Dependent\nChoice. It follows from (Crosilla and Rathjen 2001) and (Rathjen 2003)\nthat the latter has proof theoretic ordinal \\(\\Gamma_0\\). " ], "subsection_title": "5.2 Large sets in constructive and intuitionistic ZF" }, { "content": [ "\n\nA variety of interpretations for\nintuitionistic logic have been\nextended to intuitionistic and constructive set theories, such as\nrealisability, Kripke models and Heyting-valued semantics. All these\ntechniques have been applied to obtain metamathematical results about\nthe set theories.", "\n\nSome intuitionistic set theories satisfy certain\n“hallmark” metamathematical properties, such as\nthe disjunction and the existence properties. They\ncan also be shown to be consistent with the addition of principles\nwhich go beyond what we most typically consider constructive. Among\nthese are, for example, Church Thesis and Markov’s\nprinciple. For a description of these principles in the context\nof intuitionistic logic, the reader may wish to consult sections 4.2\nand 5.2 of the entry on\nintuitionistic logic or\nTroelstra and van Dalen’s book Constructivism in Mathematics\n(Troelstra and van Dalen 1988).", "\n\nHere we recall the disjunction and existence properties, formulated for\na set theory \\(T\\). The informal motivation for the disjunction and \nthe existence properties is based on our understanding of\nthe constructive proofs of disjunctive and existential statements (respectively). \nIn fact, it seems reasonable to expect that if we constructively prove \na disjunction \\(\\phi \\vee \\psi\\), \nthen we should also be able to prove \\(\\phi\\) or prove \\(\\psi\\). \nSimilarly, if we prove an existential statement, then we should be \nable to prove that a witness to that statement is definable within our theory.", "Although such properties seem quite natural and are fairly\neasy to establish for arithmetical theories, they turn out to pose\nconsiderable technical challenges in the case of set theories, due to\ntheir transfinite hierarchies of sets and the extensionality axiom. In\nfact, prominent constructive and intuitionistic set theories turn out \nnot to possess the existence property, as discussed in the next section. ", "\n\nLet \\(T\\) be a theory whose language, \\(L(T)\\), encompasses the\nlanguage of set theory. Moreover, for simplicity, we shall assume that\n\\(L(T)\\) has a constant \\(\\omega\\) denoting the set of von Neumann\nnatural numbers and for each \\(n\\) a constant \\(c_n\\) denoting the\n\\(n\\)-th element of \\(\\omega\\).", "\n\nA theory \\(T\\) has the disjunction property\n(DP) if whenever \\(T\\) proves \\((\\phi \\vee \\psi)\\) for sentences\n\\(\\phi\\) and \\(\\psi\\) of \\(L(T)\\), then \\(T\\) proves \\(\\phi\\) or\n\\(T\\) proves \\(\\psi\\).", "\n\nThe existence property has two distinct\nversions in the context of set theory: the numerical\nexistence property (NEP) and the existence\nproperty (EP). Let \\(\\theta(x)\\) be a formula with\nat most \\(x\\) free. We say that:", "(1) \\(T\\) has the NEP if whenever \\(T\\) proves\n\\(\\exists x \\in \\omega \\theta(x)\\), then, for some natural\nnumber \\(n, T\\) proves \\(\\theta(c_n)\\).\n\n\n\n(2) \\(T\\) has the EP if whenever \\(T\\) proves\n\\(\\exists x\\theta\\)(x), then there is a formula \\(\\phi(x)\\)\nwith exactly \\(x\\) free, so that \\(T\\) proves\n\\(\\exists !x(\\phi(x) \\wedge \\theta(x))\\).\n", "\n\nAs realisability techniques have proved crucial in investigations on\nthe existence and disjunction properties for constructive and\nintuitionistic set theories, we discuss the outcomes of these studies\nin the next section.", "\n\nRealisability has been one of the first and principal tools in the\nresearch surrounding set theories based on intuitionistic logic,\nstarting from the early contributions by Friedman and Myhill (Friedman\n1973, Myhill 1973). Realisability semantics for intuitionistic\narithmetic were first proposed by Kleene (Kleene 1945) and extended to\nhigher order Heyting arithmetic by Kreisel and Troelstra (Kreisel and\nTroelstra 1970). For the definition of realisability for arithmetic\nsee section 5.2 of the entry\non intuitionistic logic. A\nrealisability similar to Kreisel and Troelstra was applied to systems\nof higher order arithmetic by Friedman (Friedman 1973). Myhill\nintroduced a variant of this realisability which resembles Kleene’s\nslash (Myhill 1973; Kleene 1962, 1963). He thus proved that a version\nof IZF with replacement in place of collection (called\nIZF\\(_{Rep})\\) has the DP, the NEP and the EP. These results were\nfurther extended in (Myhill 1975; Friedman and Scedrov 1983). While\nFriedman and Myhill gave realisability models for extensional set\ntheories, Beeson developed a notion of realisability for\nnon-extensional set theories. He then studied metatheoretical\nproperties of the extensional set theories via an interpretation in\ntheir non-extensional counterparts. He thus proved that IZF (with\ncollection) has the DP and NEP (Beeson 1985). Subsequently McCarty\nintroduced realisability for IZF directly for extensional set theory\n(McCarty 1984; 1986). Realisability semantics for variants of CZF have\nbeen considered, for example, in (Crosilla and Rathjen 2001; Rathjen\n2006a). The realisability in the latter article is inspired by\nMcCarty’s and has the important feature that, as McCarty’s for IZF, it\nis a self-validating semantics for CZF (that is, this notion of\nrealisability can be formalised in CZF and each theorem of CZF is\nrealised provably in CZF). Rathjen has made use of this notion of\nrealisability to show that CZF (and a number of extensions of it) have\nthe DP and the NEP (Rathjen 2005b).", "\nAnother kind of realisability that has proved very useful is Lifschitz\nrealisability. Lifschitz (1979) introduced a modification of Kleene’s\nrealizability for Heyting arithmetic which has the peculiarity of\nvalidating a weak form of Church’s Thesis (CT) with a uniqueness\ncondition, but not CT itself. Lifschitz realisability was extended to\nsecond order arithmetic by van Oosten (1990). It was subsequently\nextended to full IZF by Cheng and Rathjen, who employed it to obtain a\nnumber of independence results, as well as validating the so called\nLesser Limited Principle of Omniscience (LLPO) (for LLPO see the entry\non \n constructive mathematics).", "The question of which set theories satisfy the existence property turned out to be particularly difficult to solve. (Friedman and\nScedrov 1985) used Kripke models to show that IZF (that is, the system\nwith collection) does not have the EP, while as mentioned above, the\nsystem IZF\\(_{Rep}\\) (which has replacement in place of\ncollection) does have the EP. This prompted Beeson to pose the\nquestion [Beeson 1985, IX]:", "Does any reasonable set theory with collection have the existence property?", "A first answer to Beeson’s question came with (Rathjen 2012), where\nthe author introduced the notion of weak existence property:\nthe focus here is finding a provably definable\nset of witnesses for every existential theorem. He then\nintroduced a form of realizability based on general set recursive\nfunctions, where a realizer for an existential statement provides a\nset of witnesses for the existential quantifier, rather than\na single witness. Rathjen combined this notion of realizability with\ntruth to yield that a number of theories with collection do enjoy the\nweak existence property (while IZF does not). Among them, in\nparticular, the theory CZF without subset collection plus Myhill’s\nexponentiation axiom, CZF\\(_{Exp}\\). In fact, Rathjen claimed that\nby combining these results with further work he had carried out, he\ncould show that CZF\\(_{Exp}\\) (and a number of other theories) do\nhave the existence property. A striking observation is that these theories are formulated with collection; consequently the failure\nof the existence property in the case of IZF can not be attributed\nonly to collection, but to the interplay between this scheme and\nunrestricted separation.", "As to the prominent question of whether\nCZF itself has the existence property, this has been solved in the\nnegative by Swan (2014). There the author made use of three well\ndevised realisability models and embeddings between them, to show that\neven the weak existence property fails for CZF. In so doing he also\nshowed that CZF’s subset collection schema is the culprit. As clearly\nhighlighted in (Swan 2014) the fact that CZF does not have EP does not\nindicate some weakness in CZF as a constructive theory. Even if Swan\nproved essentially that CZF asserts the existence of mathematical\nobjects that it does not know how to construct, still CZF does have\nnatural interpretations in which these objects can be constructed,\nlike, for example, Aczel’s interpretation into type theory (Aczel\n1978).", "\nFor a survey of results in intuitionistic set theory see (Beeson 1985,\nChapter IX). For the corresponding developments in CZF, see (Rathjen\n2005b, 2006, 2012) and (Swan 2014).", "\n\nKripke models for intuitionistic set theories have been used \nin (Friedman and Scedrov 1985) to show that IZF does not have the EP (and\ncombining this with the results in (Myhill 1973) we have that\nIZF\\(_{Rep}\\) does not prove IZF). Kripke models have more\nrecently been applied to clarify the relation between the constructive\nsubstitutes of the power set axiom: Myhill’s exponentiation axiom and\nAczel’s subset collection schema. It is clear that the power set axiom\nimplies both of these principles, and that subset collection implies\nexponentiation. On the other hand, each of the latter two principles \ndoes not imply power set, as the theory CZF with power set in place of subset \ncollection is much stronger \nthan CZF and CZF\\(_{Exp}\\) (Rathjen 2012b). In fact, CZF and\nCZF\\(_{Exp}\\) have the same proof theoretic strength (Griffor and\nRathjen 1994); therefore to investigate the relation between \nsubset collection and exponentiation in constructive set theory \none needed to develop tools other then proof theoretic methods. \nLubarsky (2005) used Kripke models to\nshow that Myhill’s exponentiation axiom does not imply Aczel’s\nsubset collection (on the basis of CZF minus subset collection plus\nfull separtion). In (Lubarsky and Rathjen 2007) the authors applied the\ntechnique of Kripke models to show that also the consequences of the\ntheories CZF and CZF\\(_{Exp}\\) are different. Aczel and Rathjen\n(2001) had shown that the class of Dedekind real numbers forms a set in CZF, \nby using subset collection. Lubarsky and Rathjen (2007) showed that\nCZF\\(_{Exp}\\) does not suffice to prove the same statement. For\nfurther applications of Kripke models to separating crucial constructive \nnotions, see e.g. (Diener and Lubarsky 2013).", " \n\nHeyting-valued semantics for intuitionistic set theories were obtained\nby Grayson (Grayson 1979) as a counterpart for Boolean models for\nclassical set theory. They have been generalized especially via\ncategorical semantics (for an introduction see MacLane and Moerdijk 1992). \nHeyting-valued semantics \nhave found application to independence\nresults in (Scedrov 1981; 1982). A constructive treatment has been\ngiven in (Gambino 2006). See also (Lubarsky 2009). \nSee also Ziegler (2012) for a generalization of realisability and Heyting models for constructive set theory. ", "\n\nCategorical models of constructive and intuitionistic set theories\nhave flourished over the years. \nThe notions of topos and sheaf play an \nessential role here (see e.g. Fourman 1980 and Fourman and\nScott 1980). For an overview of the main concepts, see the entry on\n category theory and the references\nprovided there (see in particular the supplement\n Programmatic Reading Guide). \nFor recent developments that relate more\nspecifically to constructive set theories, see e.g. (Simpson\n2005) and (Awodey 2008), as well as the web page:\n algebraic set theory." ], "subsection_title": "5.3 Metamathematical properties of constructive and intuitionistic ZF and semantic techniques" } ] } ]

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Kritische Untersuchungen\nüber die Grundlagen der Analysis”, Veit, Leipzig.", "Ziegler, Albert, 2012, “Generalizing realizability and\nHeyting models for constructive set theory”, Annals of Pure\nand Applied Logic, 163 (2): 175–184.", "–––, 2014, “A cumulative hierarchy of sets\nfor constructive set theory”, Mathematical Logic\nQuarterly, 60 (1-2): 21–30." ]

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[ "\n\nThe independence results in arithmetic and set theory led to\na proliferation of mathematical systems. One very general way to\ninvestigate the space of possible mathematical systems is under the\nrelation of interpretability. Under this relation the space of\npossible mathematical systems forms an intricate hierarchy of\nincreasingly strong systems. Large cardinal axioms provide a\ncanonical means of climbing this hierarchy and they play a central role\nin comparing systems from conceptually distinct domains.", "\n\nThis article is an introduction to independence, interpretability,\nlarge cardinals and their interrelations. Section 1 surveys the\nclassic independence results in arithmetic and set theory. Section 2\nintroduces the interpretability hierarchy and describes some of its\nbasic features. Section 3 introduces the notion of a large cardinal\naxiom and discusses some of the central examples. Section 4 brings\ntogether the previous themes by discussing the manner in which large\ncardinal axioms provide a canonical means for climbing the hierarchy\nof interpretability and serve as an intermediary in the comparison of\nsystems from conceptually distinct domains. Section 5 briefly touches\non some philosophical considerations. " ]

[ { "content_title": "1. Independence", "sub_toc": [] }, { "content_title": "2. The Interpretability Hierarchy", "sub_toc": [] }, { "content_title": "3. Large Cardinal Axioms", "sub_toc": [] }, { "content_title": "4. Large Cardinal Axioms and the Interpretability Hierarchy", "sub_toc": [] }, { "content_title": "5. Some Philosophical Considerations", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nLet us begin with the notion of an axiom system. To motivate\nthis notion consider the manner in which justification traditionally\nproceeds in mathematics. In reasoning about a given domain of\nmathematics (or, in fact, any domain) the question of justification is\nsuccessively pushed back further and further until ultimately one\nreaches principles that do not admit more fundamental justification.\nThe statements at this terminal stage are elected as axioms\nand the subject is then organized in terms of derivability from the\nbase of axioms. In the case of arithmetic this led to the axiom\nsystem PA (Peano arithmetic) and in the case of set theory it led\nto the axiom system ZFC (Zermelo-Frankel set theory with the Axiom\nof Choice).", "\n\nTwo natural questions arise: (1) If the axioms do not admit of more\nfundamental justification then how does one justify them? (2) Is the\nbase of axioms sufficiently rich that one can settle every sentence on\nthis basis?", "\n\nThere are two traditional views concerning the epistemological status\nof axioms. On the first view the axioms do not admit further\njustification since they are self-evident. On the second\nview the axioms do not admit further justification since they\nare definitive of the subject matter. Each of these views\nconcerning our first question leads to an associated optimistic view\nconcerning our second question—according to the first optimistic\nview, all mathematical truths are derivable (in first-order logic)\nfrom self-evident truths, while according to the second optimistic\nview, all mathematical truths are derivable (in first-order logic)\nfrom statements that are definitive of the subject matter. Should\neither of these optimistic views turn out to be correct, then the\nquestion of justification in mathematics would take on a particularly\nsimple form: Either a statement would be an axiom (in which case it\nwould be self-evident or definitive of the subject matter (depending\non the view under consideration)) or it would be derivable in\nfirst-order logic from some such statements.", "\n\nUnfortunately, these optimistic views came to be challenged in 1931 by\nGödel's incompleteness theorems. Here is one version of the second\nincompleteness theorem:", "\n\nTheorem 1.1\n(Gödel, 1931). \nAssume that PA is consistent. Then\nPA does not prove Con(PA).\n", "\n\nHere Con(PA) is a statement of arithmetic that expresses the informal\nstatement that PA is consistent.[1]\nUnder slightly stronger assumptions (for\nexample, that PA is Σ01-sound[2]) one can\nstrengthen the conclusion by adding that PA does not prove\n¬Con(PA); in other words, under this stronger assumption,\nCon(PA) is independent of PA. Thus, we have here a\ncase of a statement of arithmetic (and, in fact, a very simple one)\nthat cannot be settled on the basis of the standard axioms. Moreover,\nthe theorem is completely general—it holds not just for PA but\nfor any sufficiently strong formal system T.", "\n\nThis raises a challenge for the two aforementioned optimistic views\nconcerning the nature of mathematical truth. To begin with it shows\nthat we cannot work with a fixed axiom system T. We will\nalways need to introduce new axioms. More importantly, it raises the\nquestion of how one is to justify these new axioms, for as one\ncontinues to add stronger and stronger axioms the claim that they are\neither self-evident or definitive of the subject matter will grow\nincreasingly more difficult to defend.", "\n\nAlready in 1931 Gödel pointed out a natural way to justify new\naxioms. He pointed out that if one moves beyond the natural numbers\nand climbs the hierarchy of types (the sets of natural numbers, the\nsets of sets of natural numbers, etc.) one arrives at axioms (the\naxioms of second-order arithmetic PA2, the axioms of third-order\narithmetic PA3, etc.) that settle the undecided statements that he\ndiscovered. The axiom system for the second level, PA2, settles\nthe statement left undecided at the first level, namely Con(PA);\nin fact, PA2 proves Con(PA), which is the desired result. But\nnow we have a problem at the second level. For the second\nincompleteness theorem shows that (under similar background\nassumptions to those above) PA2 does not settle Con(PA2).\nFortunately, the axiom system for the third level, PA3, settles\nthe statement left undecided at the second level, namely\nCon(PA2). This pattern continues. For every problem there is a\nsolution and for every solution there is a new problem. In this way,\nby climbing the hierarchy of types one arrives at systems that\nsuccessively settle the consistency statements that arise along the\nway.", "\n\nThe above hierarchy of types can be recast in the uniform setting of\nset theory. The set-theoretic hierarchy is defined inductively by\nstarting with the emptyset, taking the powerset at successor stages\nα+1, and taking the union at limit levels λ:", "\n\n \n V0\n = ∅\n\n \n Vα+1\n = P(Vα)\n\n \n Vλ\n = ∪α < λ Vα\n\n", "\n\nThe universe of sets V is the union of all such stages:\nV=∪α∈On Vα,\nwhere On is the class of ordinals. The first infinite level\nVω consists of all of the hereditarily finite sets[3]\nand this level satisfies ZFC-Infinity.\nThe sets at this level can be coded by natural numbers and in this way\none can show that PA and ZFC-Infinity are mutually\ninterpretable.[4]\nThe second infinite level Vω+1 is\nessentially P(ℕ) (or, equivalently, ℝ) and this\nlevel satisfies (a theory that is mutually interpretable with)\nPA2. The third infinite level\nVω+2 is essentially P(P(ℕ)) (or, equivalently,\nas the set of functions of real numbers) and this level satisfies (a\ntheory that is mutually interpretable with) PA3. The first three\ninfinite levels thus encompass arithmetic, analysis and functional\nanalysis and therewith most of standard mathematics. In this fashion,\nthe hierarchy of sets and associated set-theoretic systems encompasses\nthe objects and systems of standard mathematics.", "\n\nNow, should it turn out to be the case that the consistency sentences\n(and the other, related sentences discovered by Gödel in 1931) were\nthe only instances of undecidable statements, then the\nsequence of systems in the above hierarchy would catch every problem\nthat arises. And although we would never have a single system\nthat gave us a complete axiomatization of mathematical truth, we would\nhave a series of systems that collectively covered the\ntotality of mathematical truths.", "\n\nUnfortunately, matters were not to be so simple. The trouble is that\nwhen one climbs the hierarchy of sets in this fashion the greater\nexpressive resources that become available lead to more intractable\ninstances of undecidable sentences and this is true already of the\nsecond and third infinite levels. For example, at the second infinite\nlevel one can formulate the statement PM (that all projective sets\nare Lebesgue measurable) and at the third infinite level one can\nformulate CH (Cantor's continuum hypothesis).[5]\n These statements were intensively investigated during the early era\nof set theory but little progress was made. The explanation was\nultimately provided by the subsequent independence techniques of\nGödel and Cohen.", "\n\nGödel invented (in 1938) the method of inner models by\ndefining the minimal inner model L. This model is defined just as\nV is defined except that at successor stages instead of taking the\nfull powerset of the previous stage one takes the definable powerset of the previous stage, where for a given set\nX the definable powerset Def(X) of X is the set of all\nsubsets of X that are definable over X with parameters from X:", "\n\n \n L0\n = ∅\n \n Lα+1\n = Def(Lα)\n \n Lλ\n = ∪α < λ Lα\n \n", "\n\nThe inner model L is the union of all such stages:\nL\n= ∪α∈On Lα. Gödel\nshowed that L satisfies (arbitrarily large fragments of) ZFC\nalong with CH. It follows that ZFC cannot refute CH. Cohen\ncomplemented this result by inventing (in 1963) the method\nof forcing (or outer models). Given a complete\nBoolean algebra B he defined a model\nVB and showed that ¬CH holds in VB.[6]\nThis had the consequence that\nZFC could not prove CH. Thus, these results together showed\nthat CH is independent of ZFC. Similar results hold for PM\nand a host of other questions in set theory.", "\n\nThese instances of independence are more intractable in that no simple\niteration of the hierarchy of types leads to their resolution. They\nled to a more profound search for new axioms.", "\n\nOnce again Gödel provided the first steps in the search for new\naxioms. In 1946 he proposed as new axioms large cardinal\n axioms—axioms of infinity that assert that there are very large\nlevels of the hierarchy of types—and he went so far as\nto entertain a generalized completeness theorem for such axioms,\naccording to which all statements of set theory could be settled by\nsuch axioms (Gödel 1946, 151).", "\n\nThe purpose of the remainder of this entry is to describe the nature\nof independence (along with the hierarchy of interpretability) and the\nconnection between independence and large cardinal axioms. \n\n", "\n\nFurther Reading: For more on the incompleteness\ntheorems see Smoryński (1977), Buss (1998a), and\nLindström (2003). For more on the independence techniques in\nset theory see Jech (2003) and Kunen (1980)." ], "section_title": "1. Independence", "subsections": [] }, { "main_content": [ "\n\nOur aim is to investigate the space of mathematical theories\n(construed as recursively enumerable axiom systems). The ordering on\nthe space of such theories that we will consider is that\nof interpretability. The informal notion of interpretability\nis ubiquitous in mathematics; for example, Poincaré provided an\ninterpretation of two dimensional hyperbolic geometry in the Euclidean\ngeometry of the unit circle; Dedekind provided an interpretation of\nanalysis in set theory; and Gödel provided an interpretation of\nthe theory of formal syntax in arithmetic.", "\n\nWe shall use a precise formal regimentation of this informal notion.\nLet T1 and T2 be recursively enumerable axiom systems. We say\nthat T1 is interpretable in T2 (T1 ≤ T2) when,\nroughly speaking, there is a translation τ from the language of\nT1 to the language of T2 such that, for each sentence φ of\nthe language of T1, if T1⊢φ then\n T2⊢τ(φ).[7]\nWe shall write T1 < T2 when T1≤\nT2 and T2≰ T1 and we shall write T1≡ T2 when both\nT1≤ T2 and T2≤ T1. In the latter case, T1 and T2\nare said to be mutually interpretable. The equivalence class of\nall theories mutually interpretable with T is called the interpretability degree of T.", "\n\nFor ease of exposition we shall make three simplifying assumptions\nconcerning the theories under consideration. First, we shall assume\nthat all of our theories are couched in the language of set theory.\nThere is no loss of generality in this assumption since every theory\nis mutually interpretable with a theory in this language. For\nexample, as noted earlier, PA and ZFC-Infinity are mutually\ninterpretable. Second, we shall assume that all of our theories\ncontain ZFC-Infinity. Third, we shall assume that all of our\ntheories are Σ01-sound.", "\n\nThe interpretability hierarchy is the collection of all\ntheories (satisfying our three simplifying assumptions) ordered under\nthe relation ≤. We now turn to a discussion of the structure of\nthis hierarchy.", "\n\nTo begin with, there is a useful characterization of the relation\n≤. Let us write T1 ⊆ Π01 T2 to indicate that every\nΠ01-statement provable in T1 is also provable in T2. A\ncentral result in the theory of interpretability is that (granting our\nsimplifying assumptions) T1≤ T2 iff T1 ⊆ Π01 T2.\nIt follows from this characterization and the second incompleteness\ntheorem that for any theory T the theory T + Con(T) is strictly\nstronger than T, that is, \n T < T + Con(T). Moreover, it follows\nfrom the arithmetized completeness theorem that the theory\nT + ¬Con(T) is interpretable in T, hence,\nT ≡ T + ¬Con(T).", "\n\nIn terms of interpretability there are three possible ways in which a\nstatement φ can be independent of a theory T.", "\n\nIt turns out that each of these possibilities is realized. For the\nfirst it suffices to take the Π01-sentence Con(T). For the\nsecond it is easy to see that there is no example that is Π01;\nthe simplest possible complexity of such a sentence is Δ02\nand it turns out that there are such examples; examples of this type\nof independence are called Orey sentences. For the third kind\nof independence there are Π01 instances. (This is a corollary\nof Lemma 14 on pages 128–129 of Lindström (2003).)", "\n\nThese are all metamathematical examples, the kind of example that only\na logician would construct. It is natural to ask whether there are\n“natural” examples, roughly the sort of example occurring in the\nnormal course of mathematics. In the set theoretic case, such\nexamples are abundant for the first two cases. For example, PM is\nan example of the first kind of independence and CH is an example\nof the second kind of independence. There are no known “natural”\nexamples of the third kind of independence. In the arithmetical case,\nsuch examples are rare. There are examples of the first kind of\nindependence (the most famous of which is a classic example due to\nParis and Harrington) but none of the second or third kind of\nindependence.", "\n\nNotice that in the case of the third example the two theories above\nT are incomparable in the interpretability order. To construct a\npair of such Π01-statements one uses a reciprocal form of the\ndiagonal lemma to construct two Π01-statements that refer to one\nanother. Using such techniques can show that the interpretability\norder is quite complex. For example, for any two theories T1 and\nT2 such that T1 < T2 there is a third theory T such that\nT1 < T < T2. Thus, the order on the degrees of interpretability is\nneither linearly ordered nor well-founded. (See Feferman (1960).)", "\n\nRemarkably, it turns out that when one restricts to those theories\nthat “arise in nature” the interpretability ordering is quite\nsimple: There are no descending chains and there are no incomparable\nelements—the interpretability ordering on theories that “arise in\nnature” is a wellordering. In particular, although there are natural\nexamples of the first and second kind of independence (e.g. PM and\nCH, respectively, something to which we will return to below),\nthere are no known natural examples of the third kind of independence.", "\n\nSo, for theories that “arise in nature”, we have a wellordered\nhierarchy under the interpretability ordering. At the base of the\nordering one has the degree that is represented by our minimal theory\nZFC-Infinity and there is only one way to proceed, namely, upward\nin terms of strength.", "\n\nWe have already seen one way of climbing the hierarchy of the degrees\nof interpretability, namely, by adding consistency statements. There\nare two drawbacks to this approach. First, if one starts with a\ntheory that “arises in nature” and adds the consistency statement\none lands in a degree that has no known representative that “arises\nin nature”. Second, the consistency statement does not take one very\nfar up the hierarchy. Both of these drawbacks are remedied by a very\nnatural class of axioms—the large cardinal axioms.", "\n\nFurther Reading: For more on the structure of the\ninterpretability hierarchy see chapters 6–8 of Lindström\n(2003)." ], "section_title": "2. The Interpretability Hierarchy", "subsections": [] }, { "main_content": [ "\n\nLet Z0 be the theory ZFC-Infinity-Replacement. (This theory\nis logically equivalent to our base theory ZFC-Infinity.) We\nshall successively strengthen Z0 by reflectively adding axioms that\nassert certain levels of the universe of sets exist.", "\n\nThe standard model of Z0 is Vω. The Axiom of Infinity (in\none formulation) simply asserts that this set exists. So, when we add\nthe Axiom of Infinity, the resulting theory Z1 (known as Zermelo\nset theory with Choice) not only proves the consistency of Z0; it\nproves that there is a standard model of Z0. Now the standard\nmodel of Z1 is Vω+ω. The Axiom of Replacement\nimplies that this set exists. So, when we add the Axiom of\nReplacement, the resulting theory Z2 (known as ZFC), not only\nproves the consistency of Z1; it proves that there is a standard\nmodel of Z1.", "\n\nA standard model of Z2 has the\nform Vκ where κ is a regular cardinal\nsuch that for all α < κ, 2α <\nκ. Such a cardinal is called a\n(strongly) inaccessible cardinal. The next axiom in\nthe hierarchy under consideration is the statement asserting that such\na cardinal exists. The resulting theory \n ZFC + “There is a\nstrongly inaccessible cardinal” proves that there is a level of\nthe universe that satisfies ZFC. Continuing in this fashion one\narrives at stronger and stronger axioms that assert the existence of\nlarger and larger levels of the universe of sets. Before continuing\nwith an outline of such axioms let us first draw the connection with\nthe hierarchy of interpretability.", "\n\nRecall our classification of the three types of independence. We\nnoted that there are no known natural examples of the third kind of\nindependence but that there are natural examples of the first and\nsecond kind of independence.", "\n\nNatural examples of the second kind of independence are provided by\nthe dual method of inner and outer models. For example, these methods\nshow that the theories ZFC+CH and ZFC+ ¬CH are mutually\ninterpretable with ZFC, that is, all three theories lie in the same\ndegree. In other words, CH is an Orey sentence with respect to\nZFC. What about that other sentence we introduced: PM?", "\n\nUsing the method of inner models Gödel showed that ¬PM holds\nin L. It follows that ZFC+ ¬PM is mutually interpretable with\nZFC. But what about PM? To show that ZFC+PM is mutually\ninterpretable with ZFC a natural approach would be to follow the\napproach used for CH and build an outer model of ZFC that\nsatisfies PM. However, it is known that this cannot be done\nstarting with ZFC alone. For it turns out (by a result of\nShelah (1984)) that ZFC+PM implies the consistency of\nZFC and this implies, by the second incompleteness theorem, that\nZFC+PM is not interpretable in ZFC. In a sense we have here a\ncase of the independence of independence. More precisely, even if we\nassume that ZFC is consistent we cannot (in contrast to the case of\nCH) prove that PM is independent of ZFC. To establish the\nindependence of PM from ZFC we need to assume the consistency of\na stronger theory, namely, that of \n ZFC + “There is a strongly inaccessible\ncardinal”. For it turns out that ZFC+PM lies not in the\ninterpretability degree of ZFC but rather in that\nof ZFC + “There is a strongly\ninaccessible cardinal”. To summarize: While CH is a case of the\nsecond type independence, PM is a case of the first type independence;\nit is similar to Con(ZFC) in that it is a sentence φ such that\nonly one of φ or ¬φ leads to a jump in strength, only now\nthere are two differences; the jump lands in a degree that is much\nstronger and it is represented by a natural theory.", "\n\nIn general, the (known) sentences of set theory are either like CH\nor PM. Some are like CH in that both ZFC+φ and\nZFC+ ¬φ lie in the degree of ZFC. Others are like PM in\nthat one of ZFC+φ and ZFC+ ¬φ lies in the degree of\nZFC while the other lies in the degree of an extension of ZFC\nvia a large cardinal axiom.", "\n\nLet us now return to our overview of large cardinal axioms. After\nstrongly inaccessible cardinals there are Mahlo cardinals,\nindescribable cardinals, and ineffable cardinals. All of these large\ncardinal axioms can be derived in a uniform way using the traditional\nvariety of reflection principles (see Tait 2005) but there\nare limitations on how far this variety of reflection principles can\ntake one. For under a very general characterization of such\nprinciples it is known that they cannot yield the Erdős cardinal\nκ(ω). See Koellner (2009).", "\n\nThe large cardinals considered thus far (including κ(ω))\nare known as small large cardinals. A large cardinal is small if the associated large cardinal axiom can hold in\nGödel's constructible universe L, that is, if \n “V ⊨ κ is a\nφ-cardinal” is consistent, then \n “L ⊨ κ is a\nφ-cardinal” is consistent. Otherwise the large cardinal is large.", "\n\nThere is a simple template for formulating (large) large cardinal\naxioms is in terms of elementary embeddings. In general such an axiom\nasserts that there is a transitive class M and a non-trivial\nelementary embedding", "\nj : V → M.\n", "\n\nTo say that the embedding is non-trivial is just to say that it is not\nthe identity, in which case there must be a least ordinal that is\nmoved. This ordinal is called the critical point of j and\ndenoted crit(j). The critical point is (typically) the large\ncardinal associated with the embedding. A cardinal κ is said to be\nmeasurable iff it is the critical point of some such\nembedding.[8]\n", "\n\nIt is easy to see that for any such\nembedding Vκ+1⊆ M where\nκ = crit(j). This amount of agreement enables one to\nshow that κ is strongly inaccessible, Mahlo, indescribable,\nineffable, etc. To illustrate this let us assume that we have shown\nthat κ is strongly inaccessible and let us show that κ has\nmuch stronger large cardinal properties. Since κ is strongly\ninaccessible in V and since\n(Vκ+1)M\n=Vκ+1, M also thinks that κ\nis strongly inaccessible. In particular, M thinks that there\nis a strongly inaccessible cardinal (namely, κ)\nbelow j(κ). But then by the elementarity of\nj, V must think the same thing of the preimage of\nj(κ), namely, κ, that is, V must think that\nthere is a strongly inaccessible below κ. So κ cannot\nbe the least strongly inaccessible cardinal. Continuing in this\nmanner one can show that there are many strongly inaccessibles below\nκ and, in fact, that κ is Mahlo, indescribable,\nineffable, etc. So measurable cardinals subsume the small large\ncardinals.", "\n\nIn fact, Scott showed that (in contrast to the small large cardinals)\nmeasurable cardinals cannot exist in Gödel's constructible universe.\nLet us be precise about this. Let V=L be the statement that\nasserts that all sets are constructible. Then for each small large\ncardinal axiom φ (to be precise, those listed above) if the\ntheory ZFC+φ is consistent then so is the theory\nZFC+φ+V=L. In contrast, the theory ZFC + “There is a\nmeasurable cardinal” proves ¬V=L. This may seem somewhat\ncounterintuitive since L contains all of the ordinals and so if κ\nis a measurable cardinal then κ is an ordinal in L. The point is\nthat L cannot “recognize” that κ is a measurable cardinal since\nit is too “thin” to contain the ultrafilter that witnesses the\nmeasurability of κ.", "\n\nOne way to strengthen a large cardinal axiom based on the above\ntemplate is to demand greater agreement between M and V. For\nexample, if one demands that Vκ+2⊆ M then the fact that\nκ is measurable (something witnessed by a subset of P(κ))\ncan be recognized by M. And so, by exactly the same argument that\nwe used above, there must be a measurable cardinal below κ.", "\n\nThis leads to a progression of increasingly strong large cardinal\naxioms. It will be useful to discuss some of the major stepping\nstones in this hierarchy.", "\n\nIf κ is a cardinal and η>κ is an ordinal then\nκ is η-strong if there is a transitive\nclass M and a non-trivial elementary embedding\nj: V → M such that crit(j)=κ,\nj(κ)>η\nand Vη⊆ M. A cardinal κ\nis strong iff it is η-strong for all η>κ.\nOne can also demand that the embedding preserve certain classes:\nIf A is a class, κ is a cardinal, and η>κ\nis an ordinal then κ is η-A-strong if\nthere exists a j: V → M which witnesses that κ\nis η-strong and which has the additional feature that\nj(A ∩ Vκ)\n∩ Vη = A\n∩ Vη. The following large cardinal notion\nplays a central role in the search for new axioms.", "\n\nDefinition 3.1.\n\n A cardinal κ is a Woodin cardinal if κ is strongly\n inaccessible and for all A⊆ Vκ there is a cardinal\n κA < κ such that\n\n \n κA is η-A-strong,\n \n\nfor each η such that κA < η < κ.[9]\n", "\n\nOne can obtain stronger large cardinal axioms by forging a link\nbetween the embedding j and the amount of resemblance between M\nand V. For example, a cardinal κ is superstrong if there\nis a transitive class M and a non-trivial elementary embedding\nj: V → M such that crit(j)=κ and \n Vj(κ)⊆ M. If κ is\nsuperstrong then κ is a Woodin cardinal and there are arbitrarily\nlarge Woodin cardinals below κ. ", "\n\nOne can also obtain strong large cardinal axioms by placing closure\nconditions on the target model M. For example, letting γ ≥ κ a\ncardinal κ is γ-supercompact if there is a\ntransitive class M and a non-trivial elementary embedding j: V → M\nsuch that crit(j)=κ and γM⊆ M, that is, M is closed\nunder γ-sequences. (It is straightforward to see that if M is\nclosed under γ-sequences then H(γ+)⊆ M; so this approach\nsubsumes the previous approach.) A cardinal κ is supercompact if it is γ-supercompact for all γ ≥ κ. Now,\njust as in the previous approach, one can strengthen these axioms by\nforging a link between the embedding j and the closure conditions on\nthe target model. A cardinal κ is n-huge if there is\na transitive class M and a non-trivial elementary embedding j:V →\nM such that j n(κ)M ⊆ M, where κ=crit(j) and\nj i+1(κ) is defined to be j(j i(κ)). ", "\n\nOne can continue in this vein, demanding greater agreement between M\nand V. The ultimate axiom in this direction would, of course,\ndemand that M = V. This axiom was proposed by Reinhardt and shortly\nthereafter shown to be inconsistent (in ZFC) by Kunen. In fact,\nKunen showed that, assuming ZFC, there can be a transitive class\nM and a non-trivial elementary\nembedding j: V → M such that\nj ‘‘ λ ∈ M, where \n λ=supn < ω j n(κ) and\nκ=crit(j). In particular, there cannot exists such\nan M and\nj such that Vλ+1⊆ M. This placed a limit on the\namount of closure of the target model (in relation to the\nembedding).[10]\n", "\n\nNevertheless, there is a lot of room below the above upper bound. For\nexample, a very strong axiom is the statement that there is a\nnon-trivial elementary embedding j:Vλ+1→ Vλ+1. The\nstrongest large cardinal axiom in the current literature is the axiom\nasserting that there is a non-trivial elementary embedding\nj: L(Vλ+1)→ L(Vλ+1) such that crit(j)<λ. In recent\nwork, Woodin has discovered axioms much stronger than this.", "\n\nFurther Reading: For more on large cardinal axioms\nsee Kanamori (2003)." ], "section_title": "3. Large Cardinal Axioms", "subsections": [] }, { "main_content": [ "\n\nThe large cardinal axioms discussed above are naturally well-ordered\nin terms of strength.[11]\nThis provides a natural way of climbing the hierarchy of\ninterpretability. At the base we start with the theory\nZFC-Infinity and then we climb to ZFC and up through\nZFC+Φ for various large cardinal axioms Φ. Notice that for\ntwo large cardinal axioms Φ and Ψ, if Ψ is stronger\nthan Φ then Ψ implies that there is a standard model of\nΦ and so we have a natural interpretation of ZFC+Φ in\nZFC+Ψ.", "\n\nWe have already noted that ZFC+¬PM is mutually interpretable\nwith ZFC+LC where LC is the large cardinal axiom “There is a\nstrongly inaccessible cardinal” and that this is shown using the dual\ntechniques of inner and outer model theory. It is a remarkable\nempirical fact that for any “natural” statement in the\nlanguage of set theory φ one can generally find a large cardinal\naxiom Φ such that ZFC+φ and ZFC+Φ are mutually\ninterpretable. Again, this is established using the dual techniques\nof inner and outer model theory only now large cardinals enter the\nmix. To establish that ZFC+Φ interprets ZFC+φ one\ngenerally starts with a model of ZFC+Φ and uses forcing to\nconstruct a model of ZFC+φ. In many cases the forcing\nconstruction involves “collapsing” the large cardinal associated\nwith Φ and arranging the collapse in such a way that φ holds\nin the “rubble”. In the other direction, one generally starts with\na model of ZFC+φ and then constructs an inner model (a model\nresembling L but able to accommodate large cardinal axioms) that\ncontains the large cardinal asserted to exist by Φ. The branch of\nset theory known as inner model theory is devoted to the\nconstruction of such “L-like” models for stronger and stronger\nlarge cardinal axioms.", "\n\nIn this way the theories of the form ZFC+LC, where LC is a large\ncardinal axiom, provide a yardstick for measuring the strength of\ntheories. They also act as intermediaries for comparing theories\nfrom conceptually distinct domains: Given ZFC+φ and ZFC+ψ\none finds large cardinal axioms Φ and Ψ such that (using\nthe methods of inner and outer models) ZFC+φ and ZFC+Φ are\nmutually interpretable and ZFC+ψ and ZFC+Ψ are mutually\ninterpretable. One then compares ZFC+φ and ZFC+ψ (in terms\nof interpretability) by mediating through the natural interpretability\nrelationship between ZFC+Φ and ZFC+Ψ. So large\ncardinal axioms (in conjunction with the dual method of inner and outer\nmodels) lie at the heart of the remarkable empirical fact that\nnatural theories from completely distinct domains can be compared in\nterms of interpretability." ], "section_title": "4. Large Cardinal Axioms and the Interpretability Hierarchy", "subsections": [] }, { "main_content": [ "\n\nThe main question that arises in light of the independence results is\nwhether one can justify new axioms that settle the statements left\nundecided by the standard axioms. There are two views. On the first\nview, the answer is taken to be negative and one embraces a radical\nform of pluralism in which one has a plethora of equally legitimate\nextensions of the standard axioms. On the second view, the answer is\ntaken (at least in part) to be affirmative, and the results simply\nindicate that ZFC is too weak to capture the mathematical truths.\nThis topic is quite involved and lies outside the scope of the present\narticle. \n\n", "\n\nBut there are other philosophical questions more directly related to\nthe themes of this article. First, what is the significance of the\nempirical fact that the large cardinal axioms appear to be wellordered\nunder interpretability? Second, what is the significance of the\nempirical fact that large cardinal axioms play a central role in\ncomparing many theories from conceptually distinct domains? Let us\nconsider these two questions in turn.", "\n\nOne might try to argue that the fact that the large cardinal axioms\nare wellordered under interpretability is a consideration in their\nfavour. However, this would be a weak argument. For, as we have\nnoted above, all “natural” theories appear to be wellordered\nunder interpretability and this includes theories that are\nincompatible with one another. For example, it is straightforward to\nselect “natural” theories from higher and higher degrees of theories\nin the wellordered sequence that are incompatible with one another.\nIt follows that the feature of being wellordered under\ninterpretability, while remarkable, can not be a point in favour of\ntruth.", "\n\nBut large cardinal axioms have additional features that singles them\nout from the class of natural theories in the wellordered sequence of\ndegrees. To begin with they provide the most natural way to climb the\nhierarchy of interpretability—they are the simplest and most natural\nmanifestation of pure mathematical strength. But more important is\nthe second component mentioned above, namely, the large cardinal\naxioms act as intermediaries in comparing theories from conceptually\ndistinct domains. For recall how this works: Given ZFC+φ and\nZFC+ψ one finds large cardinal axioms Φ and Ψ such\nthat (using the methods of inner and outer models) ZFC+φ and\nZFC+Φ are mutually interpretable and ZFC+ψ and ZFC+Ψ\nare mutually interpretable. One then compares ZFC+φ and\nZFC+ψ (in terms of interpretability) by mediating through the\nnatural interpretability relationship between ZFC+Φ and\nZFC+Ψ.", "\n\nIt turns out that in many cases this is the only known way to\ncompare ZFC+φ and ZFC+ψ, that is, in many cases there is\nno direct interpretation in either direction, instead one must\n pass through the large cardinal axioms. Can this additional\nfeature be used to make a case for large cardinal axioms? The answer\nis unclear. However, what is clear is the absolute centrality of\nlarge cardinal axioms in set theory." ], "section_title": "5. Some Philosophical Considerations", "subsections": [] } ]

[ "Ackermann, Wilhelm, 1937, “Die Widerspruchsfreiheit der allgemeinen Mengenlehre,”\nMathematische Annalen, 114: 305–315.", "Barwise, Jon K., 1977, Handbook of Mathematical Logic\n(Studies in Logic and the Foundations of Mathematics: 90),\nAmsterdam: North-Holland.", "Buss, Samuel R., 1998a, “First-Order Proof Theory of Arithmetic,”\nin Buss 1998b, 79–147.", "–––, 1998b, Handbook of Proof Theory\n(Studies in Logic and the Foundations of Mathematics: 137), \nAmsterdam: North Holland.", "Feferman, Solomon, 1960, “Arithmetization of metamathematics\n in a general setting,” Fundamenta Mathematicae,\n 49: 35–92.", "Foreman, Matthew and Kanamori, Akihiro, 2009, Handbook of Set Theory,\nBerlin: Springer-Verlag.", "Gödel, Kurt, 1946, “Remarks before the Princeton\nbicentennial conference on problems in mathematics,” in\nGödel 1990, 150–153.", "–––, 1986, Collected Works I: Publications 1929–1936,\nS. Feferman, J. Dawson, S. Kleene, G. Moore, R. Solovay, and J. van Heijenoort (eds.),\nOxford: Oxford University Press.", "–––, 1990, Collected Works II: Publications 1938–1974,\nS. Feferman, J. Dawson, S. Kleene, G. Moore, R. Solovay, and J. van Heijenoort (eds.),\nOxford: Oxford University Press.", "Jech, Thomas J., 2003, Set Theory (Third Millennium Edition, Revised and Expanded),\nBerlin: Springer-Verlag.", "Kanamori, Akihiro, 2003, The Higher Infinite: Large Cardinals in Set Theory from their Beginnings\n(Springer Monographs in Mathematics), 2nd edition, Berlin: Springer.", "Koellner, Peter, 2009, “On Reflection Principles,”\nAnnals of Pure and Applied Logic, 157: 206–219.", "Kunen, Kenneth, 1980, Set theory: An Introduction to Independence Proofs\n(Studies in Logic and the Foundations of Mathematics: 102),\nAmsterdam: North-Holland.", "Lindström, Per, 2003, Aspects of Incompleteness\n(Lecture Notes in Logic: 10), 2nd edition, CITY: Association of\nSymbolic Logic.", "Shelah, Saharon, 1984, “Can you take Solovay's inaccessible away?,”\nIsrael Journal of Mathematics, 48(1): 1–47.", "Smoryński, Craig A., 1977, “The Incompleteness Theorems,”\nin Barwise 1977, 821–865.", "Tait, William W., 2005a, “Constructing cardinals from below,”\nin Tait 2005b, 133-154.", "–––, 2005b, The Provenance of Pure Reason:\n Essays in the Philosophy of Mathematics and Its History,\nOxford: Oxford University Press." ]

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[ "\n This entry is about two kinds of circularity: object\ncircularity, where an object is taken to be part of itself in\nsome sense; and definition circularity, where a collection is\ndefined in terms of itself. Instances of these two kinds of\ncircularity are sometimes problematic, and sometimes not. We are\nprimarily interested in object circularity in this entry, especially\ninstances which look problematic when one tries to model them in set\ntheory. But we shall also discuss circular definitions.", "\n The term non-wellfounded set refers to sets which contain\nthemselves as members, and more generally which are part of an\ninfinite sequence of sets each term of which is an element of the\npreceding set. So they exhibit object circularity in a blatant way.\nDiscussion of such sets is very old in the history of set theory, but\nnon-wellfounded sets are ruled out of Zermelo-Fraenkel set theory (the\nstandard theory) due to the Foundation Axiom (FA). As it happens,\nthere are alternatives to this axiom FA. This entry is especially\nconcerned with one of them, an axiom first formulated by Marco Forti\nand Furio Honsell in a 1983 paper. It is now standard to call this principle the\nAnti-Foundation Axiom (AFA), following its treatment in an\ninfluential book written by Peter Aczel in 1988.", "\n The attraction of using AFA is that it gives a set of tools for\nmodeling circular phenomena of various sorts. These tools are\nconnected to important circular definitions, as we shall see. We\nshall also be concerned with situating both the mathematics and the\nunderlying intuitions in a broader picture, one derived from work in\ncoalgebra.\nIncorporating concepts and results from category theory,\ncoalgebra leads us to concepts such as corecursion\nand coinduction; these are in a sense duals to the more\nstandard notions of recursion\nand induction.\n", "\n The topic of this entry also has connections to work in game theory\n(the universal Harsanyi type spaces), semantics (especially\nsituation-theoretic accounts, or others where a “world” is allowed\nto be part of itself), fractals sets and other self-similar sets, the\nanalysis of recursion, category theory, and the philosophical side of\nset theory." ]

[ { "content_title": "1. Circular Phenomena in Set Theory", "sub_toc": [ "1.1 Streams", "1.2 Infinite trees", "1.3 Hypersets" ] }, { "content_title": "2. The Foundation and Anti-Foundation Axioms", "sub_toc": [ "2.1 Background from set theory", "2.2 The Foundation Axiom", "2.3 The Anti-Foundation Axiom" ] }, { "content_title": "3. Using ", "sub_toc": [ "3.1 Bisimulation", "3.2 Doing without AFA", "3.3 Extended graphs", "3.4 Collection circularity in ZFA" ] }, { "content_title": " 4. Comparing Foundation and Anti-Foundation", "sub_toc": [ "4.1 The category of sets, the category of classes", "4.2 Algebras for a functor", "4.3 Coalgebras for a functor", "4.4 The axioms again", "4.5 Conceptual comparison" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n It is difficult to say in a general way what makes a definition\ncircular. In this entry we are concerned exclusively with\nmathematical definitions of various sorts. Consider the equation\nx = ½x + 1. Is this a circular\ndefinition of the number 2? In a sense, it is just that: a\nnumber has been defined in terms of itself. But there is nothing\nproblematic about this equation, and so one may wonder why this is in\nthe same class of equations as x = x + 1, or\nx = x. In the set theoretic setting, we often\nemploy circular definitions and characterizations of sets and classes.\nFor example, the collection HF of hereditarily\nfinite sets may be characterized by ", "\n \n (1) HF is the set of all x such that x is\na finite subset of HF.\n\n ", "\n With a bit of work, it can be shown that (1) defines a unique set in\nstandard set theory ZFC. (1) is more of a\ncharacterization than a textbook definition, however. In\nother words, if one were presented with (1) as a putative\ndefinition, then the first step in understanding it\n would be to “straighten out” the circularity by providing\na different definition D of a set, then to check that every\nset satisfying D satisfies the property defining HF,\nand vice-versa.", "\n It is easier to think about circular objects than circular\ndefinitions. Even so, it will be useful in reading this\nentry to keep circular definitions in mind. The most conspicuous form\nof object circularity would be a set having itself as an element; even\nworse would be a set x such that x = {x}.\nFor those with a background in standard set theory, such sets are\nruled out by the axioms in the first place, and in the second it is\nnot clear why one would want to change the axioms in order to admit\nthem. And if one does take the drastic step of altering the axioms of\na well-established theory, what changes? This entry is an extended\ndiscussion of this matter, and related ones." ], "section_title": "1. Circular Phenomena in Set Theory", "subsections": [ { "content": [ "\n Many of the ideas in this entry may be illustrated using\nstreams. A stream of numbers is an ordered pair\nwhose first coordinate is a number and whose second coordinate is\nagain a stream of numbers. The first coordinate is called the\nhead, and the second the tail. The tail of a given\nstream might be different from it, but again, it might be the very\nsame stream. For example, consider the stream s whose head\nis 0 and whose tail is s again. Thus the tail of the tail of\ns is s itself. We have s =\n〈0, s〉 , \n s = \n〈0, 〈0, s〉  〉 ,\n etc. This stream s exhibits object circularity. It is natural to\n“unravel” its definition as:", "\n (0,0,…,0,…)\n", "\nIt is natural to understand the\nunraveled form as an infinite sequence; standardly,\ninfinite sequences are taken to be functions whose domain is the set\nN of natural numbers. So we can take the unraveled form to\nbe the constant function with value 0. Whether we want to take the\nstream s described above to be this function is an\nissue we want to explore in a general way in this entry. Notice that\nsince we defined s to be an ordered pair, it follows from the\nway pairs are constructed in ordinary mathematics that s will\nnot itself be the constant sequence 0.", "\n One way to define streams is with systems of equations for them.\nFor example, here is such a system:", "\n\n\n(2)\nx ≈ \n〈0, y〉 \n\n\n\n\ny ≈ \n〈1, z〉 \n\n\n\n\nz ≈ \n〈2, x〉 \n\n\n", "\n We should comment on the ≈ notation here. We are concerned\nwith modeling various types of ordinary mathematical objects in set\ntheory, and one kind of object that we want to model will be that of a\nsystem of equations. This is an unusual thing to do. In\nanticipation of things to come, we use the ≈ sign for\nequations we would like to solve. So in our discussion of\nx = ½x + 1 above, we would prefer to write\nx ≈ ½x + 1. The point is that\n‘x’ here is a symbol, but whatever we take\nsymbols to be, it will almost never be the case that the symbol\nx is identical to the expression ‘½x +\n1’ or to anything related to it. For the solution to an\nequation or a system of them, we will use a “dagger” to\nrefer to the solution. Thus for this equation,\nx† = 2; the reason that 2 satisfies the\nequation is that 2 =\n½(2)+ 1 (and here we use = rather\nthan ≈).", "\n Returning to equation\n (2), we take it to define streams\nx†, y†, and\nz†. These satisfy equations:\n", "\n\n\n\n\nx† = \n〈0, y†〉 \n \n \n\n \n\n\n y† = \n〈1, z†〉 \n \n \n\n\n\n\nz† = \n〈2, x†〉 \n \n \n\n", "\n These\nstreams then have unraveled forms. For example, the unraveled form of\ny† is (1,2,0,1,2,0,…).", "\n There is a natural operation of “zipping” two streams.\nAlso called “merging”, it is defined by", "\n \n \n (3)\n zip(s, t) = \n〈 head(s),\n zip(t, \n tail(s)) 〉 \n \n\n", "\n So to zip two streams s and t one starts with the\nhead of s, and then begins the same process of zipping all\nover again, but this time with t first and the tail of\ns second. For example, if x†,\ny†, and z† are\nthe solutions to the system in equation (2) above, then we might wish to consider,\nfor example, \nzip(x†, y†). \n In unraveled form, this is ", "\n (0,1,1,2,2,0,0,1,1,2,2,0,…).\n", "\n But please note that our definition of \nzip\n does not work by recursion as one might expect; for one thing, there\nare no “base cases” of streams.", "\n We can even ask about solving systems of equations written in terms of \nzip.\n It is easy to see that an equation like x =\nzip(x, x)\n is satisfied by all and only the constant streams. One like\n ", "\n x =\nzip(head(x) + 1, x)\n ", "\n has no solutions whatsoever. But if we do things right, we can\ndefine very interesting streams. For example, consider", "\n\n\n(4)   \nx\n≈\n\n〈1,  zip(x, y)〉 \n\n\n\n\ny \n≈\n\n〈0, zip(y, x)〉 \n\n\n", "\n The system has a unique solution. The unraveled form of\nx† begins as", "\n (1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,…)\n ", "\n that of y† begins", "\n (0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,…).\n", "\n The first of these is a famous sequence, the Thue-Morse\nsequence t (actually x†\n= \ntail(t).)[1]", "\n We have been careful to emphasize the difference between streams as\nwe originally spoke of them and their unraveled form as functions on\nthe natural numbers. At this point we want to look at this matter\nmore closely.", "\n Before we turn to the details, let us consider the parallel matter of\nsequences construed as functions on the natural numbers.\nAnyone who teaches about (infinite) sequences of some sort, say\nsequences of integers or real numbers, may at some point need to say\nwhat a sequence actually is. Surely this is not done very often in\nelementary presentations: usually one would give examples instead of a\nformal definition, or illustrate what sequences are for by using them\nin some way or other. In any case, it happens that in the usual\nset-theoretic modeling of mathematics, sequences of real numbers would\nbe taken to be functions from the set of natural numbers to\nthe set of real numbers. So we have a reduction of one kind\nof object, sequences, to another, functions. Of course, functions are\nthen reduced to sets of ordered pairs, ordered pairs to sets of a\ncertain form, natural numbers to sets of yet another form, and real\nnumbers in their own way. Concerning this kind of reduction, we\nshould always ask whether it is necessary or silly, and whether it is\nuseful to those using the mathematical objects in the first place.\nAll of this is worth keeping in mind as we turn back to the sequences.", "\n Let N∞ be the set of streams of natural\nnumbers, and let NN be the set of\nfunctions from N to N. The reduction employs two\nfunctions", "\n\n\nφ\n:\nN∞\n→\nNN\n\n\n\nψ\n:\nNN\n→\nN∞\n\n\n", "\n defined as follows: For φ, we first take a stream s to a\nfunction fs : N\n→ N∞. This time we use recursion:", "\n\n\nfs(0)\n=\ns\n\n\n\nfs(n+1)\n=\ntail(fs(n))\n\n\n", "\n Then from f we get a function\nφ(s) : N → N by\ng(n) =\nhead(fs(n)).\n This defines φ, the precise definition of what we spoke of\nearlier by the name unraveling. In the other direction, we\nneed infinite systems of equations. Given a function\nf : N → N, consider", "\n\n\n(5)      \nx0\n = \n〈f(0), x1〉 \n\n\n\n\nx1\n = \n〈f(1), x2〉 \n\n\n\n\n\n…\n\n\n\n\n\nxn\n = \n〈f(n), xn+1〉 \n\n\n\n\n\n…\n\n\n\n", "\n Then this system has a solution, and we take ψ(f) =\nx0†. It is then possible to show\nthat the composition in one direction, ψ \n⋅\n φ ,\n is the identity on N∞ and the other composition\n φ\n⋅\n ψ is the identity on NN. In plainer\nterms, we can pass from streams to functions on\nnumbers, and we can also go the other way.", "\n At this point, we can ask questions about the reduction. The\nfirst question that comes to mind concerns the ontological status of\nthe entities:", "\n Let A be a collection of abstract objects (say functions\nfrom natural numbers to natural numbers), and suppose that\none believes that the objects in A exist. Let\nB be a different collection of abstract objects. Suppose\nthat A and B correspond in a natural way, and that\neverything one says about objects in B could well be said\nabout their correspondents in A, perhaps using different\nlanguage. Should one believe that the objects in B also\nexist?\n ", "\n Asking this about streams and functions on N is no different\nthan asking it for any other kind of reduction of mathematical\nobjects. Any discussion of it would take us to issues in the\nphilosophy of mathematics that go beyond our goals in this entry.\nHowever, there are two additional points to be made on this matter.", "\n First, the standard modeling of pairs in set\n theory[2]\n would have us believe that from the beginning of this section\nonwards, we have been talking about things which do not exist: as we\nhave literally defined them, there are no streams of numbers\nwhatsoever! We discuss this at length in Section 2.2.1, when we talk\nabout the Foundation Axiom of set theory. The point is is that this\naxiom forbids object-level circularity in a way that precludes streams\nin the exact form that we have them. Thus if one wants to model the\nintuitive notion of a stream as we have introduced it, one would need\nto say something like: “By a stream, we mean a function on\nnumbers. We adopt special notation to make it look like streams are\npairs of a certain sort, but deep down they are just functions on\nnumbers.”", "\n Continuing with questions about the reduction of streams to\nfunctions, we can ask whether there is any conceptual difference using\nstreams as opposed to functions. Certainly these represent different\npoints of view, and for this reason it should be useful to have both\navailable. To see the difference, let us return to the matter of\nzipping streams. Done in terms of functions\nf, g : N → N,\nthe zipped version would be", "\n\n\nzip(f, g)(n)\n = \n{\nf(n/2) \n g((n−1)/2))\nif n is even \n if n is odd\n\n\n", "\n It would be harder to use this to turn equation (4) into\nthe definition of two sequences by\n recursion.[3]\n The upshot is that we can start to see some kind of difference when\nwe use one kind of representation instead of another. And this brings\nus to our second point on the reduction of streams to functions:\nconceptual differences worth exploring may be hidden under the surface\nof such a reduction.", "\n At this point, we are done with our discussion of streams. Of course\nwe shall revisit them in later sections to illustrate various points.\nWe also broadly foreshadow the main points of this entry:" ], "subsection_title": "1.1 Streams" }, { "content": [ "\n We want to move from streams to a more complicated example, infinite\ntrees. Some of the points that we make will be closely related to\nwhat we have seen for streams, and some will raise new issues.", "\n Here is a class of objects which we shall call\n trees:[4]", "\n Trees may be specified by tree systems (of equations). Here\nis one such system:", "\n\n \n (6)\n \n \n \n \n s  \n ≈ \n \n \n \n \n \n *\n \n \n \n\n \n \n /\n \n \\\n \n \n \n \n t\n \n \n \n u\n \n \n \n \n \n\n\n\n \n \n t  \n ≈    \n •|s\n \n \n\n\n\n \n \n u  \n ≈ \n \n \n \n \n \n *\n \n \n \n \n \n \n /\n \n \\\n \n \n \n \n x\n \n \n \n y\n \n \n \n \n \n\n\n\n", "\n Again, we use the ≈ notation in variables for which we want to\nsolve, and we superscript variables with a dagger in the solution. In\nthis case, the one and only solution of this system might be pictured\nas", "\n\n \n\ns†    \n =  \n\n \n \n \n \n \n \n \n \n \n \n *\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n /\n \n \\\n \n \n \n \n \n \n \n \n \n \n \n \n •\n \n \n \n *\n \n \n \n \n \n \n \n \n \n \n /\n \n \n \n /\n \n \\\n \n \n \n \n \n \n \n \n *\n \n \n \n x\n \n \n \n y\n \n \n \n \n \n \n /\n \n \\\n \n \n \n \n \n \n \n \n\n \n \n \n •\n \n \n \n *\n \n \n \n \n \n \n \n \n \n \n /\n \n \n \n /\n \n \\\n \n \n \n \n \n \n \n \n …\n \n \n \n x\n \n \n \n y\n \n \n \n \n \n \n\n\n\n \n \n t†   \n = \n •|\n \n \n\n\n\n\n \n u†  \n = \n \n \n \n \n \n *\n \n \n \n \n \n \n /\n \n \\\n \n \n \n \n x\n \n \n \n y\n \n \n \n \n \n\n\n\n\n", "\n It will be useful to recast the definition of our trees in terms of\npairs and triples:", "\n Then our system above is", "\n\n\ns\n ≈ \n〈*, t, u〉 \n\n\n\nt\n ≈ \n〈•, s〉 \n\n\n\nu\n ≈ \n〈*, x, y〉 \n\n\n", "\n So now we have something that looks more like what we have seen with\nstreams. But with streams we had an unraveled form, and so we might\nwonder what the unraveled form of trees is. To some extent, it would\nbe the pictures that we have already seen. In particular, one could\ntake a tree as we have defined them and give a description of how one\nwould construct the picture. (The full construction would take forever,\nof course, but the same is true of our work on streams.) Conversely,\ngiven a picture, one could set down a tree system for it, where a\n“tree system” is a system of equations as in equation (6).\n(In general, the tree system would be infinite, but if you find a\nregular structure in the picture, then the system could be\nfinite.)", "\n On the other hand, pictures are not entirely respectable as standard\nmathematical objects, despite the work that has gone on and continues\nto go on to rehabilitate them. For work on trees, one would need a\nmore complicated set of definitions. We are not going to present any\nof this.", "\n More ‘cheating’. Let Tr be the\nset of trees that we have been discussing. Then our definition in\nterms of Tr would have:", "\n(7)   Tr   =  \n {x, y} ∪ ({•} × Tr) ∪\n ({*} × Tr × Tr).\n ", "\n Now again the standard modeling in set theory gives us a problem: one\ncan prove in ZF set theory that Tr has no solution whatsoever. \nAnd\nthis runs afoul of our pictures and intuition. The standard way out\nis to change the equals sign = in (7) to something else. For most\nmathematical work this is perfectly fine, but it is the kind of move\nwe explore in this entry." ], "subsection_title": "1.2 Infinite trees" }, { "content": [ "\n Let us turn from streams and trees to sets. Before presenting some\nanalogs to what we have just seen, at pictures of sets. To\nmake the discussion concrete, consider the set:", "\nx = {∅, {{∅}, ∅}}\n ", "\n Let us call this set x. We want to draw a picture of this\nset, so we start with a point which we think of as x itself.\nSince x has two elements, we draw add two children:", "\n\n\n\n\nx\n\n\n\n\n\n\n\n\n\n\n\n\n\ny\n\n\n\nz\n\n\n", "\n Again, we draw arrows on behalf of the members. We take y\nto be ∅ and z to be {{∅}, ∅}. We\ndo not add any children of y because it is empty. But we\nwant to add two children to z, one for w =\n{∅} and one for ∅. So we have", "\n\n\n\n\nx\n\n\n\n\n\n\n\n\n\n\n\n\n\ny\n\n←\n\nz\n\n\n\n\n\n\n\n↓\n\n\n\n\n\n\n\nw\n\n\n", "\n We conclude by putting an arrow from w to y, since\n∅ ∈ {∅}.", "\n\n\n\n\nx\n\n\n\n\n\n\n\n\n\n\n\n\n\ny\n\n←\n\nz\n\n\n\n\n\n\n\n↓\n\n\n\n\n\n\n\nw\n\n\n", "\n Now we want to forget the identity of the nodes. We could either\ntrade in the four sets that we used for numbers (to mention just one\nway), or else finesse the issue entirely. We would get one of the\npictures below:", "\n\n\n\n \n \n \n \n 1\n \n \n \n\n \n \n \n \n \n \n \n\n \n 2\n \n ←\n \n 3\n \n\n \n \n \n \n \n ↓\n \n\n \n \n \n \n \n 4\n \n \n\n\n\n \n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n\n \n \n \n ←\n \n \n \n\n \n \n \n \n \n ↓\n \n\n \n \n \n \n \n \n \n \n\n\n\n", "\n Incidentally, in building this graph, we allowed ourselves to share\nthe node y both times we came to ∅. It would be\npossible to avoid doing this, using different nodes. The end result\nwould be a tree:", "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n↓\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n", "\n A graph is a pair (G,→), where → is a\nrelation on G (a set of ordered pairs from G). The\nidea is that we want to think of a graphs as notations for\nsets, just as systems of equations were notation for streams.\nThis is explained by the concept of a decoration: A\ndecoration d of a graph G is a function whose domain\nis G and with the property that", "\n d(g) = {d(h) : g \n → h}.\n ", "\n For example, let us introduce names for the nodes in the tree-like\ngraph and then find its decoration:", "\n\n\n\n\n1\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n2\n\n\n\n3\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n4\n\n\n\n5\n\n\n\n\n\n↓\n\n\n\n\n\n\n\n\n\n6\n\n\n\n\n\n\n", "\n Since 6 has no children, d(6) must be ∅. Similarly,\nd(5) and d(2) are also ∅. d(4) =\n{d(6)} = {∅}. d(3) =\n{d(4), d(5)} =\n{ {∅}, ∅}. And d(1) =\n{d(2), d(3)} =\n{∅, { {∅}, ∅} }.\nNote this is the set x with which we started. This is no\naccident, and you are encouraged to think about why this is true. A\nrelated point: for a graph like the one in equation (8), where we use\nthe sets involved as the nodes of the graph, you should check that the\nidentity function is a decoration.", "\n However, things get more interesting with an example like the loop\ngraph", "\n \n \n x\n \n \n", "\n Let d be a decoration of this graph. Then we would have\nd(x) = {d(x)}. So writing Ω\nfor d(x), we have Ω = {Ω}. This set\nΩ is the most conspicuous example of object circularity: a set\nthat is a member of itself. (Indeed, Ω is its own only\nmember.)", "\n Finally, we want to consider an example that harks back to the stream\nsystem (2) in Section 1.1.", "\n \n ", "\n Let us try to understand what a decoration d of this graph\nwould be. In order to follow the discussion below, you should\nremember from set theory that the standard rendering of the first few\nnatural numbers is by", "\n\n\n0 = ∅, \n1 = {∅},\n2 = {0,1} = {∅, {∅}}\n\n\n", "\n and also that the standard definition of the ordered pair \n〈x, y〉 \n is as {{x},{x, y}}.", "\n Since x0 has no children,\nd(x0) must be ∅. Then it follows\nthat d(y0) =\n{d(x0)} = {∅} = 1. And now\n", "\nd(z0) =\n{d(x0),\nd(y0) } = {0,1} = 2. \n", "\n Furthermore,\nd(z1) = {2}. It follows now that", "\n\n\nd(x1) = {0},\nd(y1) = {1},\nd(z1) = {2}.\n\n\n", "\n And then ", "\n\n\nd(x2)\n = \n{d(y3),\n d(x1)}\n = \n{{0, d(y2)}, {0} }\n = \n〈0, d(y2)〉 \n\n\n\nd(y2)\n = \n{d(z3),\n d(y1)}\n = \n{{1, d(z2)}, {1} }\n = \n〈1, d(z2)〉 \n\n\n\nd(z2)\n = \n{d(x3),\n d(z1)}\n = \n{{2, d(x2)}, {2} }\n = \n〈2, d(x2)〉 \n\n\n", "\n The upshot is that we can go back to our original stream system in\nequation (2) and then solve it by putting down our big graph and\ndecorating it. The solution would be", "\n\n\nx† = d(x2),\ny† = d(y2),\nz† = d(z2).\n\n\n", "\n A hyperset or non-wellfounded set is a set that is\nobtained by decorating an arbitrary graph.", "\n Another way of thinking about hypersets is in terms of systems of\nset equations, as we have done it for streams and trees. By such\na system we mean a set X which we think of as variables (any\nset will do), and then a function e from X to its power set\n ℘X.\n That is, the value of e on each variable is again a set of\nvariables. Set systems and related concepts correspond to ones for\ngraphs in the following way:", "\n\n\nthe graph (G,→)\nthe system of set equations (X, e)\n\n\n\nthe nodes of G\nthe set X of variables\n\n\n\nthe relation → on the nodes\nthe function e : X \n →\n ℘X\n\n\n\nthe children of x in G\nthe set e(x) ∈ \n ℘X\n\n\n\na decoration of the graph\na solution of the system\n\n\n", "\n Every graph corresponds to a system of set equations, and vice-versa.\nFor example, corresponding to the picture in (9) we would take", "X = {x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3}", "\n So the way to go from the picture to the function is that each\nset e(v) is the set of children of v.\nIn terms of the kind of notation we have seen before, we prefer to\nwrite this system in a way that elides e:", "\n\n\nx0 ≈ ∅\nx1 ≈ {x0}\nx2 ≈ {x1,\n y3}\nx3 ≈ {z0,\n x2}\n\n\n\ny0 ≈ {x0}\ny1 ≈ {y0}\ny2 ≈ {y1,\n z3}\ny3 ≈ {x0,\n y2}\n\n\n\nz0 ≈ {x0,\n y0}\nz1 ≈ {z0}\nz2 ≈ {z1,\n x3}\nz3 ≈ {y0,\n z2}\n\n\n", "\n The study of non-wellfounded sets proposes to treat every\ngraph as a picture of a unique set. In order to make this work, some\nkind of change is needed in set theory. The reason is that sets like\nΩ = {Ω} do not exist in the most commonly-used set theory,\nZFC. This is due to the Foundation Axiom (FA):\nwe’ll discuss this issue further in Section 2 below. For now,\nFA implies that the only graphs with decorations are those\nwith no infinite sequence of points following the arrows. The change\nin set theory that we make is simply to replace this axiom FA\nwith a different one called AFA. The content of AFA\nis that every graph has a unique decoration (alternatively, every\nsystem of set equations has a unique solution).", "\n At the same time, there is a reduction of hypersets to ordinary sets.\nThis means that one could regard all talk of hypersets as merely\nabbreviatory. This reduction is fairly complicated, and we shall\npresent it in due course.", "\n Adopting AFA not only helps with circularly defined sets,\nbut it also helps with streams and trees. As we have mentioned, if\none uses FA, there are no streams or trees according to our\ndefinitions. That is, N∞ is literally the\nempty set with FA, as is Tr. But with AFA\nthese sets are non-empty. Moreover, one can prove that under\nAFA, N∞ and Tr have the\nproperties that one would want them to have. (For example, one can\nprove that N∞ corresponds to the function\nspace NN in the way we have discussed.)\nFinally, working out the resulting theory gives tools that are useful\nin studying collections of circularly-defined objects such as streams\nand trees. The point is that this one axiom AFA gives us all\nof this, and more.", "\n The Axiom AFA was first studied by Marco Forti and Furio\nHonsell in 1983. Their paper (Forti and Honsell 1983) studies a number\nof axioms which contradict the Foundation Axiom FA,\ncontinuing a much older line of work in set theory that deals with\nalternatives to FA. The one they call X1\nis equivalent to what has now come to be called AFA.", "\n Peter Aczel’s book (1988) treats many axioms that contradict\nFA, but it pays most attention to AFA. It also\nproved many of the important results in the subject, including ones\nmentioned in this entry. Aczel’s own entrance to the subject was an\narea of semantic modeling that he had been working on, concerning the\ncalculus of communicating systems (CCS). He found it natural to\npropose a set theoretic semantics, and yet the most obvious modeling\nseemed to run into problems with Foundation. It is always a bold step\nto recommend changing the axioms of set theory in order to make an\napplication of the subject. Usually it is a brash move. For the most\npart people resist the idea: when the proposal might well be cast in\nmore standard forms (as can be done with work using AFA),\npeople wonder why one wants to tamper with a standard theory; when it\ncannot be cast in a standard way, the reception is even worse.", "\n Aczel’s work became influential for two research areas. He visited\nStanford in 1985, where Jon Barwise was director of the Center for the\nStudy of Language and Information (and this author was a post-doc\nthere). Barwise recognized the value of the work, partly because he\nhad similar problems with Foundation in his own work on situation\nsemantics, and partly because he saw in the work an appealing\nconception of set that was at odds with the iterative conception that\nhad been received wisdom for him and\npractically everyone else raised in the mainstream tradition\nof mathematical \n logic.[5]\n He thought that non-wellfounded sets should be called by a\nname that reflected the change in conception, and he proposed calling\nthem hypersets in parallel to the hyperreal numbers\nof non-standard analysis. This terminology has for the most part not\nstuck, but it is not completely outdated, either. In this entry,\nwe’ll use both terms interchangeably.", "\nPerhaps the first serious application of the tools we are studying \nin this entry comes from this period. This is Barwise and Etchemendy’s\nbook The Liar (Barwise and Etchemendy 1987). \nIts proposals are contributions to the theory of truth. Since we are not\nprimarily interested in those applications of hypersets, we resist the temptation\nto discuss matters further. \n", "\n Aczel’s book was also immediately influential for people working on\nsemantic questions in theoretical computer science. This was not so\nmuch because it raised questions about set theory, but rather because\nit showed the value of using the categorical notion of a\ncoalgebra. The main use in the book is to organize certain\nconcepts into an elegant subject. But it quickly became apparent that\nthis notion of coalgebra could be studied on its own, that themes from\nthe book had a field of application much wider than pure set\ntheory.", "\n This entry reflects the influence of all of these sources. To be\nsure, we shall see the main results on the set theory obtained using\nAFA. Also, we present enough of the theory that someone who\nneeds to read papers that use it should be able to do start doing so.\nWe also emphasize the conceptual underpinnings of the subject, and\ncompare them to more standard foundational work. This is hardly ever\ndone in technical papers on the subject, but should be of interest to\npeople in several areas of philosophy. Finally, our work incorporates\nmany ideas and results coming from the coalgebra research community in\nthe years following the publication of Aczel 1988.", "\n We conclude this section with links to the two following\nsupplementary documents:", "\n Universal Harsanyi Type Spaces \n \n Self-similar Sets of Real Numbers \n ", "\n These contain introductory points on two issues that we shall revisit\n (again, in supplementary documents)\n at the end of this entry. The reason for the separation is that \n the issues discussed pertain to game theory and measure theory\n on the one hand, and fractals and metric spaces on the other.\n That is, the discussions are not entirely set theoretic. \n In addition, the mathematical prerequisites for all our supplements are\n greater than for the main body of this entry.\n They may be omitted without losing the main thread.\nHowever, we emphasize\n that the overall theory presented in this entry does treat all of these\n instances of circularity “under the same roof.”\n " ], "subsection_title": "1.3 Hypersets" } ] }, { "main_content": [ "\n\nThe set theoretic side of our story is connected to two axioms, the\nFoundation Axiom and the Anti-Foundation Axiom. We\npresent them here, and discuss some related conceptions of set." ], "section_title": "2. The Foundation and Anti-Foundation Axioms", "subsections": [ { "content": [ "\nWe start with a reminder of a few basic facts of set theory. One can\nfind more in any textbook on the subject, and also the entry on\n set theory, especially in its\nsupplementary document \n basic set theory.\n", "\nPower sets.\nFor any set s, the power set of s is the set of subsets of s.\nWe write this set as ℘(s)\nor just as ℘s.\n", "\nPairing.\nThe Kuratowski ordered pair \n〈a,b〉 \n of two sets a and \n b is {{a}, {a,b}}.\n[6]\nThe standard presentation of\nset theory defines and studies relations, functions, and the like\nin terms of this pairing operation.\nAll mathematical facts about these notions can then be proved in set theory.\n", "\nNatural numbers. One also defines versions of the\nnatural numbers by: 0 = ∅, 1 = {∅}, etc. Again, all facts\nabout numbers and functions on them can be proved in set theory. In\nfact, essentially all mathematical facts whatsoever can be stated\nformally and proved in set theory.\n", "\nUnion and transitive closure.\nFor any set a, ∪a\n is the set of elements of elements of a.\nA set is transitive if every element of it is also a subset of it.\nThe transitive closure of a is \n", "\na ∪ ∪a\n∪\n ∪∪a ….\n", " \nThis set is denoted tc(a). It is the smallest transitive set which \nincludes a as a subset.\n", "\n Theorem [Cantor].\n For all sets s, and all functions \n f   : s → \n ℘s,\nf is not surjective. In fact,\n{x ∈ s : x ∉ \n f(x)} is not in the image\nset f [s]. (Here, the image\nset f[s] =\n{f(x) : x ∈ s}.)\n", " \nProof.\nLet c = {x \n  ∈  s: x ∉  f(x)}. \nSuppose towards a contradiction that c ∈ \n f[s].\n Fix a  ∈  s\n such that c = f(a).\nThen a ∈ c iff \na ∉ \nf(a) iff \na ∉ c.\n\n", "\n\n Corollary.\n For all sets s, ℘s\n is not a subset of s.\n\n", " \n\nProof.\n If ℘s ⊆\n s, \nwe construct a function f from s onto \n℘s: \nlet ff(f) =\na\nif a ∈ s, and otherwise let \nff(f) = ∅.\nSo we cannot have ℘ s ⊆\ns, lest we contradict \nCantor’s Theorem.\n\n", "\nCorollary[Russell’s Paradox].. \nThere is no set R\n such that every set belongs to R.\n", " \nProof.\nSuch a set would have ℘s ⊆\n R\n for all sets s\nIn particular ℘ R ⊆\n R, contradicting our last result.\n", "\nWe call the last result Russell’s Paradox in view of\nits content. Neither our statement nor our proof are the most\nstandard ones.\n", "\nWell-ordered sets and ordinal numbers.\nWe need the concept of ordinal numbers at a few places.\n", "\nA well-ordered set is a pair W = (W, <),\n where < is a relation on the set W\nwhich is a strict linear order and with the property that every non-empty subset of\nW has a <-least element. For example, (N, < )\nis a well-order, where < is given by\n", "\n \n0 < 2 < 4 < … 1 < 3 < 5 < …\n\n", "\nOne can show using the Replacement Axiom that every well-ordered set W\nhas a unique decoration d. An ordinal number\n(or ordinal) is a set of the form\nd(w), for some well-ordered set \n(W,< ) and some w ∈ W.\n", "\nOne usually uses Greek letters such as α and β for ordinal numbers,\nand one also writes α < β if α ∈ β. There are a number of\nstandard facts about ordinal numbers, including the following:\n", "\nAn ordinal α is a successor ordinal if \nα = β ∪ {β} for some (other) ordinal β.\nOrdinals which are neither 0 nor\nsuccessor ordinals are called limit ordinals. The smallest\nlimit ordinal is ω; it is d(1) for the well-order we saw above,\n0 < 2 < 4 < … 1 < 3 < 5 < …\n", "\nThe cumulative hierarchy.\nThere is a unique operation \n taking ordinals α to \nsets Vα such that\n", "\n\n\nV0\n=\n∅\n\n\n\nVα+1\n=\n℘Vα\n\n\n\nVλ\n=\n∪β<λ\n Vβ for λ a limit ordinal \n\n\n", "\nThe ZFC axioms.\nWe are not going to state them here, but see \nthe entry on set theory.\n", "\nClasses.\nThe axioms of set theory are not about sets as much as they are about \nthe universe of sets. One of the intuitive\nprinciples of the theory is that arbitrary collections of mathematical objects\n“should be” sets. Due to paradoxes, this intuitive principle is not directly formalized\nin standard set theories. In a sense, the axioms one does have are intended to \ngive enough sets to constitute a mathematical universe while not having so many\nas to risk inconsistency. But \nit is natural in this connection to consider some collections of objects which\nare demonstrably not sets. These are called proper classes. The\nterm class informally refers to a collection of mathematical objects. \nClasses are usually not first-class objects in set theory. (Certainly they are not\nin the most standard set theory, ZFC. However, \nthe SEP entry\n on Alternative Axiomatic Set Theories\n does \nmention quite a few theories which treat classes as first-class objects.) \nInstead, a statement about classes\nis regarded as a paraphrase for some other (more complicated and usually less\nintuitive) statement about sets. This is probably not a good place to discuss\nthe details of the formalization; one \nuseful source is Chapter 1 of Azriel Levy (1979).\n", "\n For our purposes, classes may be taken as \n definable subcollections\nof the universe of sets. For example, if \na is any set, then the class of\n all sets which do not contain\na as an element is {x :a ∉ x}. \nIn specifying a class, one may use the first-order language with the \nmembership symbol and the rest of the syntax from logic, and one may \nalso use particular sets as parameters, as we have just done.\n", "\nThe class V of all sets is {x : x = x}.\nThe definability here is in the first-order logic with just a symbol ∈ for membership,\nand the quantifiers range over sets (not classes).\nAnother class of interest is WF, the class of all well-founded sets.\nThis is the same as ∪α\nVα, the sets that belong to\nVα for some ordinal α.\n", "\nIf C is a class, we define \nthe power class of C, ℘C,\nby \n", "\n℘C\n = {x : for all y, \n if y ∈ x, then φC(y)},\n", "\nwhere φC \nis the formula that defines the class C.\nIt is important that in this definition x ranges over sets and not classes;\nthe formal language used does not directly talk about classes in the first place.\nFor example, ℘V = V,\n and ℘(WF) = WF.\nWe also define the action of other operations on classes in the same general way.\nFor example, the finite power set ℘fin\n takes a class C to the class of\nfinite subsets of C.\n" ], "subsection_title": "2.1 Background from set theory" }, { "content": [ "\nThe Foundation Axiom (FA)\nmay be stated in different ways. \n Here are some formulations;\ntheir equivalence in the presence of the other axioms\n is a standard result of elementary set theory.\n", "\nThe first of these is probably the easiest to remember and think about.\nThe second is important because it is the one most easily expressed in first-order\nlogic. The third is a recursion principle; we shall consider a closely related \nprinciple in\nSection 4.4.\n\n", "\nAs we have seen, one formulation of FA says that every set belongs\nto some Vα. This is a mathematical formulation of the\niterative concept of set: sets are just what one gets by\niterating the power set operation on the well-ordered class of ordinal\nnumbers. We start with nothing, the empty set.[7]\nThis is V0. Then we form \nV1 = \n℘V0.\n Then \nV2 = \n℘V1.\nGoing on, when we come to the first limit ordinal ω, we take \nVω\nto be \nthe union of all the sets\nVn. \n Then we proceed to\nVω+ 1\n = ℘ Vω.\n We continue like this absolutely\nforever, going through “all the ordinal numbers”. The collection so\ndescribed is the universe V of sets.\n", "\nThis way of describing the iterative picture suggests that the ordinal numbers\nwere somehow present “before” all the iteration takes place, or at least\nthat they have a life apart from the rest of the sets. There is a different way\nof understanding the iterative conception, one that emphasizes the \nharmony between the iteration of the power set operation and the Replacement Axiom:\nas one iterates the power set axiom, more and more well-ordered sets appear.\nReplacement allows us to decorate these well-ordered sets, creating new ordinals\nin the process. Thus the whole picture is one of balance.\nIndeed, this point about balance can be phrased without reference to any\n“iteration” at all: there is an equilibrium in the set theoretic universe\nbetween the “sideways” push of the Power Set Axiom and the \n“upward” push of the Replacement\nAxiom.[8]\n", "\nUsing the Foundation Axiom.\nFA plays no role in the formalization of mathematics or in the study of infinity.\nIt is an “optional extra” for mathematics. FA is used\nto clarify our picture of sets, just as we have described. This often comes \nwith an implicit argument of roughly the following shape:\n", "\nAn argument.\nOne is tempted to justify FA along the following lines:\n", "\nThe rejoinder here is that there might be other intuitive pictures\nor conceptions of sets\n that also explain, or draw lessons from, the paradoxes. So they \n would be as sensible as FA in this regard.\n ", "\n Since FA plays a conceptual role but no mathematical role,\n it is not surprising that there are widely different views on \n whether it is an important part of standard set theory ZFC or not.\n For a collection of quotes on the role of FA, see\n Barwise and Moss (1991).\n", "\nThe Foundation Axiom and object circularity.\nWe mentioned in connection with streams that according to standard set theory,\nstreams of numbers do not exist. Here is the reasoning.\nRecall that we defined a stream to be a pair of a number and another stream.\n Suppose that a stream\ns exists, so that the set N∞\nof streams is non-empty.\n Recall that we have a function \nfs : N → N∞ \n by recursion:\n ", "\n\n\nfs(0)\n=\ns\n\n\n\nfs(n+1)\n=\ntail(fs(n))\n\n\n", "\nTo save on some notation at this point, let’s write hn for \nhead(fs(n))\nand \ntn\nfor\ntail(fs(n)).\nFor all n,\n", "\n\n fs(n) = \n〈 hn, tn 〉 \n = \n {{hn}, {{hn, tn}}}; \n\n", "\nthis is true of any pair whatsoever.\nNotice that \n", " \n\nfs(n+1) \n= tn\n∈\n{hn, tn}\n∈\nfs(n).\n\n", "\nSo we have\n", " \n\nfs(0)\n∋\n{h0, t0}\n∋\nfs(1)\n∋\n{h1, t1}\n∋\nfs(2)\n∋\n…\n\n", "\nThis is a descending sequence in the membership relation, something forbidden by FA.\n", "\nThe same kind of remark applies to infinite trees as we discussed them,\nand certainly to hypersets. The conclusion is that if one wants to work with such objects\nin a set theory with FA, then one must do so indirectly. \n" ], "subsection_title": "2.2 The Foundation Axiom" }, { "content": [ "\nThe Anti-Foundation Axiom AFA is stated as follows:\n", "\n Every graph has a unique decoration.\n", "\nThe theory ZFA is ZFC with FA replaced by AFA.\nIt includes the Axiom of Choice, even though there is no “C” in the \nacronym.\n", "\nThe coiterative conception of set.\nAFA gives rise to, or reflects, a conception of set that is at odds\nwith the iterative conception. For lack of a better name, we call it\nthe coiterative conception. According to this, a set is an abstract\nstructure obtained by taking a graph G \n(a set with a relation on it),\nand then associating to each node x in the graph a set in such a way that\nthe set associated to x is the set of sets associated to the children of x\nin G . This association is what we called decoration earlier.\n This association might be thought of procedurally, but it need not be\nso construed. One can instead posit a harmony between decoration\nand power sets.[9]", "\nWhat changes with AFA, and what does not change?. \n AFA gives us unique solutions to systems of set systems;\nthis is almost immediate from the axiom and the close relation of set systems\nand graphs. But it also gives us unique solutions for stream systems and tree systems.\nThe details of this are suggested by our work on the decoration of \n the graph related to streams and pairs which we saw\nearlier on.\n", "\nAll of the results in set theory which\ndo not use FA go through when one replaces it by AFA. In particular, \nthe following topics are unchanged: Russell’s Paradox and the Separation\n(Subset) Axioms;\nthe modeling of ordered pairs, relations and functions; \nthe natural numbers, real numbers, etc.; well-orderings and the ordinal numbers;\ntransfinite recursion on well-orders and well-founded relations;\nthe Axiom of Choice; problems and results concerning the sizes of infinite sets.\nThe only difference would be in modeling questions for circularly defined objects of various\nsorts,\nas we have been discussing\nthem. \n", "\nIn terms of modeling circularity, AFA gives several new concepts\nand techniques. These are described in our next section.\n" ], "subsection_title": "2.3 The Anti-Foundation Axiom" } ] }, { "main_content": [ "\nThis section offers\na quick introduction to the central parts of the theory\nnon-wellfounded sets: what one would need to know to use\nthe theory and to read papers on it.\n" ], "section_title": "3. Using AFA", "subsections": [ { "content": [ "\nThe topic of bisimulation is one of the earliest goals in a\ntreatment of non-wellfounded sets.\n", "\n Let (G,→) be a graph.\n A relation R on\nG is a bisimulation if the following holds:\nwhenever x R y, \n", "\nThese are sometimes called by the suggestive names\nzig and zag.\n", "\nBisimulation between graphs.\nBefore giving examples, we should clarify some usage.\nAt a few points, we’ll speak of bisimulation between two graphs\nG and H, rather than on a single graph.\n This can be defined in the same general way. Note also that one can\n take the disjoint union G + H\n of the graphs G and H, and then \n a bisimulation between G and H would be a \nbisimulation on G + H.\n", "\nReturning to bisimulation on a graph.\n For an example, let’s look at the following graph G:\n", "\n \n ", "\nAll of the 3-points have no children. \n(Point 3d is not reached from any other point, but\nthe arrows into a node are of no interest.)\n So every relation which\nonly relates 3-points is a bisimulation on G.\nConcretely, \n", "\n{(3a, 3b), (3c, 3a), (3d, 3d)}\n", "\nis easily seen to be a bisimulation.\n", "\nFor that matter, the empty relation is also a bisimulation on G.\n", "\nAnother bisimulation is\n", "{(2a, 2b), \n(2b, 2c), (2c, 2a),\n (3a, 3b), \n (3b, 3c), (3c, 3a)}. \n", "\nLet’s call this relation R.\nIt would take a lot of checking to actually verify\nthat R is a bisimulation.\nHere is just two items of it: We see that 2b R 2c.\nNow 2c → 2b. \nThus we need some node\nx so that x R 2b\n and 2b → x.\nFor this, we take 2a. For our second point \nof verification, again note that \n 2b R  2c . Since \n 2b → 3b, we need some\n node x so that 2c → x and 3b\n  R \n x.\n We take \n x = 3c for this.\n", "\n The largest bisimulation on our graph G is the \n relation that relates\n1\n to itself, all 2-points to\n all 2-points, and all 3-points\n to all 3-points.\n Note that this is an equivalence relation:\n reflexive, symmetric, and transitive.\n This is not an accident.\n", "\n Proposition For any graph H, there is a largest\n bisimulation on H. This relation is\n an equivalence relation denoted ≡b, \n and it is characterized by\n\nx ≡b\ny \niff there is a bisimulation on\n H \n relating x to y.\n\n", " This relation ≡b is\ncalled bisimilarity.\n", "\nWe can always form the quotient graph \n using the largest bisimulation.\nHere is how this works, using G\n from above\nas an example. In G/≡b,\nwe would have three nodes, corresponding to the\nthree equivalence classes under the largest bisimulation;\n let’s call these classes \n 1, 2 and 3. We put an arrow between\n two of these classes if some (every) element of the first has an\n arrow to some element of the second. In this way, we \n construct the quotient. \n Here is a picture of G\n again, along with its \n quotient G/≡b\nunder the largest bisimulation:\n", " \n           \n \n ", "\nThe map from G\n to G/≡b\n takes the 2-points to the point 2,\nand the 3-points to the point 3.\n", "\nUp until now, we have said what bisimulation is, but we did not describe \nits relation to anything else. To rectify matters, here is the main result.\n", "\n Theorem\nAssume AFA. Let G be a graph, let x and y \nbe nodes of G, and let d be the decoration of G.\nThen the following are equivalent:\n\n\n d(x) = d(y).\n\n There is a bisimulation relating x and y.\n\n\n", "\nWe are not going to prove this theorem in full here, but instead here\nare two hints. To prove that (1) implies (2), check that \nthe kernel relation of d, \n", "\n{(u, v) : d(u) = d(v)}\n", "\nis a bisimulation on G.\n", "\nIn the other direction, the idea is to turn a bisimulation into a graph\nitself, and then extract two decorations of it; by the uniqueness part\nof AFA these must coincide.\nHere is how this is done in a concrete example. \nWe saw above that \n", "\nR  =  \n {(2a, 2b), (2b, 2c), (2c, 2a),\n(3a, 3b), (3b, 3c), \n(3c, 3a)}. \n", "\nis a bisimulation. \nWe make it into a graph by taking the product relation.\nThis gives the following graph which we call H:\n", "\n\n", "\nLet d be a decoration (no, the decoration)\n of G.\nWe get two decorations of H, k and l defined by\n", "\nk(u, v) = d(u), \nand l(u, v) = d(v).\n ", "\n (It is good to check that these really are decorations of H.)\n But H can have only one decoration. So k = b.\n And then, corresponding to the fact that \n 2a R 2c,\n for example, \n we have\n", "\n d(2a) = k(2a,2b) \n= l(2a,2b)\n=\n d(2b).\n ", "\n This concludes our sketch. For more details, see Aczel (1988).\n" ], "subsection_title": "3.1 Bisimulation" }, { "content": [ "\nOur work on bisimulation above can be used to effect a \nreduction of the of non-wellfounded sets to that of ordinary sets,\nmuch in the spirit of what we saw for streams and functions in\nSection 1.1.\n There are several ways to \ndescribe such a reduction. \n", "\nA pointed graph is a triple (G,→, g) \n such that → is \na relation on G\n and g ∈  G.\n A bisimulation\n between pointed graphs (G,→, g) and \n (H,⇒, h) \nis a bisimulation R\n between (G,→) and \n (H,⇒) such that\ng   R   h. \n", "\nIn the remainder of this discussion, we let \np, q, … denote \npointed graphs. We write p ≡b\nq\n if there is a bisimulation\nbetween p and q. We write \np ε\nq\n if\nthere is a pointed graph (G,→, g)\n and some g → h\nin G\n so that\n", "\n\np ≡\n (G,→, h)      and  \nq ≡\n (G,→, g).\n\n", "\nSentences in the language of set theory talk about sets, and\nwe translate them to sentences about pointed graphs by \nrestricting all quantifiers to the class of pointed graphs, and then\ntranslating ∈ to ε, and ≡ for =. For\nexample, the Axiom of Extensionality", "\n\n∀x,y(x=y → \n ∀z(z ∈ x →\n z ∈ y)).\n\n", "\nwould translate to (where p, q, r range over\npointed graphs):\n", "\n\n∀p,q(p ≡ q →\n ∀r(r ε p →\n r ε q)).\n\n", "\nThis last sentence is then provable. (Hint: the union of any set\nof bisimulations on a graph is again a bisimulation on it.)\n", "\nIndeed, all of the axioms of ZFA are provable, including AFA.\nThis is a fairly long and tedious verification, but it is not so tricky. \n A version of it\n(for set theory with urelements, objects which are not sets)\nis the topic of a chapter in Barwise and Moss (1996).\n", "\nOne can also go further: instead of translating the identity relation\n = into something more complex, we may keep the language simple\nand complicate the interpretation. We would like to replace “pointed graph”\nby “≡-class of pointed graph”. Since these are not sets, we instead\nemploy Scott’s trick and instead use “set of \nwell-founded pointed graphs whose node sets are \n≡-equivalent\nand with the property that no pointed graph of smaller rank is \nalso ≡-equivalent to them.”\n", "\nDoing all of this leads to relative consistency result:\n", "\n Theorem.\nIf ZFC is consistent, then so is ZFA,\nand vice-versa.\n" ], "subsection_title": "3.2 Doing without AFA" }, { "content": [ "\nThe way we have presented graphs, decorations, and AFA is a \nvery “minimalist” presentation. \n If one would like some node of a graph G\nto be decorated by some set a\n the most obvious way would be to\nadd all the elements of tc({x})\n as fresh nodes in G, with\ny→ z iff z ∈ y. \nThis means that one must take new copies\nif some of the sets in tc({x})\n already happen to be nodes in G.\nThis is often cumbersome:\nwhen working with graphs and decorations, one might well want to \npre-specify as much as possible the value of the decoration on\na node. There are several ways to do this with AFA, and we’ll indicate\none here.\n", "\nTwo sets are disjoint if their intersection is\nempty. When one takes the union of two sets,\nsay a and b, it is sometimes\na good idea to make sure that no element occurs\nin both sets. The way to do this is to replace one or both\nof a and b by copies.\n", "\nThe disjoint union of sets a and b \n is a+ b, defined by\n", "\n a+b = (a  × {0})\n ∪ (b   × {1}).\n", "\nIt is easy to see that the two sets in the union are disjoint:\nthe elements of a+ b\n “wear on their sleeve” a mark of which\nset they come from.\n", "\nThe disjoint union comes with two natural functions:\n", "\ninl\n: a → a+ b\n  and  \ninr\n: b → a+ b\n", "\ndefined by inl(x) = \n〈x,0〉 \n and inr(x) = \n〈x,1〉 .\n[10]", "\nA graph extended with set parameters (or extended graph for short)\nis a set G\n together with a function \n e: G→ \n ℘G+V.\n If e(g) \n is of the form \n〈s,0〉 \n for some s ⊆ G, then \nwe intend it as a node just as in our earlier treatment. \n In particular, we want to decorate\nit with the set of decorations of its children. If e(g) = \n〈x,1〉 ,\n then\nwe want a decoration to be forced to have the value x on g. \n", "\nFormally, a decoration of an extended graph is a function d defined on G\nso that for all g ∈ G,\n", "\n\n\nd(g)\n = \n{\n \n{d(h) : g → h}\n \n x\n\nif e(g) = \n〈s,0〉 \n\n if e(g) = \n〈x,1〉 \n \n\n\n", "\nHere is an example: \nLet G be the extended graph with node set \n{w, x, y, z}\nand with e given by\n", "\n\n\ne(w) = \n\n〈{w, x, y}, 0〉 \n\n\n   \n\n \ne(y) = \n \n〈2,1〉 \n\n \n \n \n\n \n\n e(x) = \n \n \n〈{z}, 0〉 \n \n \n    \n \n\n e(z) =\n \n〈∅,0〉 \n\n\n\n", "\nThen a decoration d of this extended graph\n would satisfy the following conditions:\n ", "\n\n\n\nd(w) = \n{d(w),1,2} \n\n\n   \n\n \nd(y) = 2\n\n \n \n \n\n \n\n d(x) = {0} = 1\n \n \n    \n \n\n d(z) =\n∅ = 0\n\n\n\n", "\n Theorem\nAssume AFA. \n Then every extended graph has a unique decoration.\n", "\nThe point we are trying to make is that there is quite a bit of theory\naround to facilitate working in ZFA in order to do modeling of\nvarious forms of circular phenomena.\n" ], "subsection_title": "3.3 Extended graphs" }, { "content": [ "\n The fact that AFA allows us to solve various kinds of\nsystems of set equations is only the beginning. When we discussed\ninfinite trees in\n Section 1.2,\n we noted that the collection Tr of infinite trees\nshould satisfy (7), repeated below: ", "\nTr   =  \n {x, y} ∪ ({•} × Tr) ∪\n ({*} × Tr × Tr).\n ", "\nA similar equation should hold of streams from \nSection 1.1:\n", "\nN∞   =   N ×\nN∞ .\n ", "\nFor that matter, the universe V\nof sets should satisfy\n ", "\nV   =  ℘V\n", "\nAssuming the Power Set Axiom and the formulation of \n℘ as an operator\non classes, the universe \nV does satisfy this equation.\n", "\nWe are free to step back and think of these as equations which\nwe hope to solve. For example, we could take the set N as known,\nregard N∞ as a variable, and then consider an equation like\nX = N×X. \nHowever, the none of these is the kind of equation that we could hope to\nsolve in a perfectly general way using AFA: the right-hand sides are \nnot given in terms of sets of objects on the left.\nSolving more complicated systems takes special additional work.\nHere is what is known on this.\n", "\nFirst, under FA, \nthe first two of our three equations each have a unique\nsolution: the empty set. Under AFA, they have many solutions.\nFor example, for the stream equation, the set of streams corresponding to\nfunctions which are eventually 0 is a solution. \nHowever, the largest solutions are of special interest. \nFor these, one can prove that the largest solutions are in one-to-one correspondence\nwith what we have called the unraveled forms. And for other reasons which we\nshall see, there is a good reason to accept the claim that the largest solutions\nare good mathematical models of the intuitive concepts. \n", "\nUnder AFA, things are different. Here is the general picture:\nAn operator on sets F is monotone if whenever\na ⊆ b,\nthen also Fa ⊆ Fb.\n This is a very common feature\nfor operators on sets. The polynomial operators on sets\nare the smallest collection containing the constant operators, \nand closed under cartesian product, disjoint union, and functions from\na fixed set. For example, if A and B are fixed sets, then \nFs = (A × s) +\n B(s + A) is a polynomial operator on sets.\nIf one also allows the power set operator to occur, then we\nget the power polynomial operators. Every power polynomial operator\nis\nmonotone. And now, we have the following results due to Aczel:\n", "\n \n Proposition. Then \n every monotone operator F on\nsets has a least fixed point F* and a\n greatest fixed point F*. In particular, \n every polynomial operator on classes has least \n and greatest fixed points. On classes, the same is true for\n the larger collection of power polynomial operators.\n \n ", "\nAssuming FA, the fixed points are unique; frequently they are the \nempty set. \nWith AFA, the greatest fixed points usually have non-wellfounded \nmembers. We shall study this in more detail when we turn to coalgebra.\nFor now, we return to the last of the example equations\nat the top of this section, \nV   =  ℘V.\n This equation has no solutions\nin sets due to \nCantor’s Theorem.\nHowever, in terms of classes, this equation does have solutions, as we\nknow. The universal class V\n is a solution, as we have seen. \nAnd the class WF of well-founded sets is a solution. This is the \nsmallest solution ℘*, and \n V is the largest. Under FA, \n℘*\n = V\n = ℘*. Under AFA, \n ℘*\n and ℘* are\ndifferent: \n℘* = WF, and \n℘* = V\n and thus contains \nsets such as Ω= {Ω}.\n" ], "subsection_title": "3.4 Collection circularity in ZFA" } ] }, { "main_content": [ "\nThe purpose of this section is to compare FA and AFA in a \ntechnical way, using ideas from category theory. That is, the \nlanguage of category theory and especially its \nbuilt-in feature of duality are used to say something insightful\nabout the relation between FA and AFA. Further, the dual\nstatements about the axioms\n suggest a much more systematic and thoroughgoing \nduality about a host of other concepts. This deeper point is\nnot a strictly mathematical result but rather more of a research program,\nand so the final subsection here will detail some of what is known\nabout it.\n", "\nAs we said, our work here begins to use category theory.\nWe realize that not all readers will be familiar with that subject\nat all. \nSo we shall \ntry to make this section as accessible as possible.\nIn particular, we’ll \nonly present those notions from category theory that we actually\nneed in our work of this section. We also illustrate all of the \ndefinitions on a few categories which will be of interest. And as we go\non in future sections, we’ll develop only the background that we \nneed.[11]\n", "\nOur use of category theory is mainly for the terminology and intuition. \nWe know that there are philosophical issues connected with the use\nof category theory as a foundation for mathematics. This entry does not\ndeal with any of these issues in a head-on way.\n", "\nInitial and final objects.\n", "\nWe need a definition from category theory.\nFix a category C.\nAn object x is initial if for every object y\nthere is exactly one morphism \nf : x → y \nDually, an object x is final if for every object y\nthere is exactly one morphism\nf : y → x.\n", "\nIn Set, the empty set is an initial object; for every set y,\nthe empty function is the only function from ∅ to y.\nIn addition, the empty set is the only initial object.\n", "\nAs for final objects, every singleton {x} is a final object.\nFor every set y, the constant function with value x is the only\nfunction from y to x. And the singletons are the only final objects \nin the category.\n", "\n Proposition\nLet C be a category, and a\n and b\nbe initial objects.\nThen a and b are\nisomorphic objects: there are \nmorphisms\nf : a → b \nand \ng : b → a \nand \n such that\n g⋅f = ida\nand \n f⋅g = idb.\n", "\n Proof\nBy initiality, we get (unique) morphisms f and g as in our statement.\nNote that\ng⋅f is a morphism from\na to itself. And since \na is initial\nand ida\n is also such a morphism, we see that \n g⋅f \n = ida.\nSimilarly for b.\n" ], "section_title": "4. Comparing Foundation and Anti-Foundation", "subsections": [ { "content": [ "\nWe refer the reader to the entry on \n category theory\n for the definitions of category and functor.\n", "\nWe need to mention the objects and morphisms in the categories of sets\nand of classes, and also to spell out the functors of interest on\nthem.\n", "\nSet.\nThe objects are the sets, and the morphisms \n are triples \n〈x, y, f〉, where\nf : x → y. That is,\neach triple 〈 x, y, f〉 is a\nmorphism from x to y. The identity\nmorphism ida for a set a is\n〈a, a, f〉 , where f is\nthe identity function on a and the composition operation of\nmorphisms is given by:\n", "\n \n〈y, z, g〉 ⋅ \n〈x, y, f〉 = \n〈x, z, g ⋅ f〉 \n\n", "\nFunctors on Set.\nThe polynomial operators on sets extend to\n endofunctors on Set. The way that these operations are defined\n on morphisms is straightforward and may be found in any book\n on category theory. Here is a brief summary:\n For any set s, the constant functor with value s is a functor\non Set. \n It takes every function to ids.\nFor any two functors F and G,\nwe have a functor F×\nG\ndefined by (F×\nG)(a) = Fa ×\nGa; here we use the \ncartesian product on sets. If \nf : a → b, then \n", "\n(F×\n G)f(a, b) =\n(Ff(a), Gf(b)).\n", "\nWe also have a functor F+G defined by \n (F + G)(a) = Fa+ Ga\n using the coproduct on sets, that is, the disjoint union.\n Here the action on morphisms is by cases \n ", "\n \n (F + G)(f)\n (inl x) = Ff(x)\n \n \n \n (F + G)(f)\n (inr x) = Gf(x)\n \n ", "\nA special case is Fx = x + 1. That is, \nFx is the disjoint union of x\nwith a singleton. And if f : x → y,\n then \n Ff : Fx → Fy\nworks in much the same way, taking the new point in x to the new point in y,\nand otherwise behaving like f.\n", "\nThe power polynomial operators also extend to endofunctors on Set:\non morphisms\nf : x → y, \nthe function \n℘f:\n ℘x → \n ℘y\n takes each subset a ⊆\nx\nto its image \n", "\nf[a] = {f(z) : z   ∈  \n a}.\n", "\nClass.\nHere the objects are formulas in the language of set theory\nφ(x, y1,…, yn) together with n sets a1,…, \n an.\nWe think of this as \n", "\n\n{b : φ[b, a1,…, \n an]}.\n\n", "\nThe morphisms are then triples consisting of two \nformulas with parameters defining the domain and codomain,\nand a third one with two free parameters defining the action\nof the morphism.\n", "\nFunctors on Class.\nThe functors of interest are again the power polynomials.\nThey are defined on \n Class\n similarly to the way they are defined on Set.\nFor our purposes, the main difference between the two categories\n is that\nin \nSet we cannot solve \n℘(x) = x, while we can do so in \n Class.\n" ], "subsection_title": "4.1 The category of sets, the category of classes" }, { "content": [ "\nLet F be an endofunctor on a category \nC.\n An algebra for\nF is a pair (c, f),\nwhere c is an object of C, and\nf : Fc → c.\n", "\nHere is a basic example that illustrates why these are called \nalgebras. \nLet’s take the category Set\n of sets, and the functor\n", " Ha = (a × a) + \n(a × a). \n ", "\nFor the object N of natural numbers, HN is thus\ntwo copies of N×N.\n We’ll use colors to indicate\nthe different copies, with red for the first copy and blue for\nthe second. So we can view HN as\n", "\n\n\n\n\n\n(0,0)\n(0,1)\n(0,2)\n… \n\n\n(1,0)\n(1,1)\n(1,2)\n… \n\n\n(2,0)\n(2,1)\n(2,2)\n… \n\n\n…\n…\n…\n… \n\n\n\n\n\n\n(0,0)\n(0,1)\n(0,2)\n… \n\n\n(1,0)\n(1,1)\n(1,2)\n… \n\n\n(2,0)\n(2,1)\n(2,2)\n… \n\n\n…\n…\n…\n… \n\n\n\n\n\n", "\nOne example of an algebra for this functor\nis (N, α), \nwhere\nα(a, b)\n = a + b and \nα(a, b) \n= a ×\nb. In other words, α operates on the red pairs\nby adding and on the blue pairs by multiplying.\n", "\nGetting back to the terminology of “algebra”, the point is that \nthe function α does the work of the two tables. \nThe function “is” the tables.\n", "\nHere is another example of an algebra. \nThis time we are concerned on Set with \nFx = x +1, as defined above.\nThe algebra we have in mind is (N, s). Here\ns : N+1 → N \ntakes the natural number n to its successor n+1,\nand the new point in N+1 to the number 0.\n", "\nUp until now, we have merely given examples of algebras for\ndifferent functors.\nThe advantage of the categorical formulation is that the usual notions\nof a morphism of algebras turn out to be special case\nof a more general definition.\n", "\nLet \n (c, f) \n and \n (d, g) \nbe algebras for the same functor F on the category C.\nA morphism of algebras from\n (c, f) \nto\n (d, g) \n is\na morphism \nα : c → d\n so that\nthe diagram below commutes:\n", "\n\n\n\nFc\nf→\nc\n\n\n\n\nFα\n↓\n\n↓\nα\n\n\n\n\nFd\n→g\nd\n\n\n\n", "\n(This means that the two compositions, \nα ⋅ f and \n g⋅Fα,\n are the same function.)\n", "\nIt now is clear that we have a category of algebras for a given functor.\nAnd so we immediately have the concept of initial and final\nalgebras. There is no guarantee that these exist, but in many interesting cases \nthey do. The reason we are interested in initial algebras is their connection to\nrecursion. \n", "\nTo see this in detail, we return to the functor \nFx = x + 1\n on Set.\nWe saw the algebra (N, s) \n above. We claim that this is an initial algebra.\nWhat this means is that for any algebra \n (A, a), there is a unique algebra morphism\n h :  (N, s) → (N, s).\n That is, the diagram below commutes:\n", "\n\n\n\nN+1\ns→\nN\n\n\n\n\nh+1\n↓\n\n↓\nh\n\n\n\n\nA+1\n→a\nA\n\n\n\n", "\nThue function a from A+1 to A may be decomposed into \na map \n i : A → A \ntogether with\nan element b ∈ a.\n And to say that the diagram above commutes\nis the same thing as saying that \n h(0) = b, and for all n ∈ N,\n h(s(n)) = a(h(n)).\n", "\nStepping back, the purported initiality of (N, s) is the same as the following assertion:\n", "\nFor every set A, every b ∈ A,\n and every \n a : A → A,\n there is a unique\nfunction h : N → A \n such that \nh(0) = b, \nand for all \nn ∈ N,\n h(s(n)) = a(h(n)).\n", "\n This is the standard form of the Principle of Recursion on N.\nThe upshot is that this principle is equivalent to the assertion that \n (N, s) is an\ninitial algebra of the functor Fx = x +1. \n", "\nOne way to interpret this equivalence is that we can take the existence\nof an initial algebra for \nFx = \nx+ 1\n as an axiom of set theory,\nin place of the usual Axiom of Infinity. That axiom says that there is\nan algebra for the singleton functor \nSx = {x}\n on sets which contains\n∅ as an element and whose structure is the inclusion.\nThis principle is easier to state than the algebraic reformulation.\nIt takes a bit of work to use the simpler standard formulation to derive\nthe Recursion Principle, and this is one of the basic topics in any\ncourse on axiomatic set theory.\n", "\nTwo general facts: \nFirst, the structure map of an initial algebra on Set is always \na bijection. This follows from a very general result in category theory due to J. Lambek.\nAnd from this we see that ℘\n has no initial algebras on Set, by \n Cantor’s Theorem.\n", "\nInitial algebras for polynomial functors on Set.\n", "\nLet F :  Set → Set \n be a power polynomial functor. We know that F is \nmonotone (it preserves the subset relation on sets), and \nit is not hard to check a slightly stronger property: F preserves\ninclusion maps between classes: An inclusion\nis a map ia, b : a → b \n on classes which “doesn’t do anything”:\na must be a subset of b,\nand for all x ∈ a, \ni(x) = x. \nWe say that F is standard if it preserves inclusions in \nthe sense that \nFia, b = \niFa, Fb.\nOnce again, every power polynomial endofunctor on \nSet is standard.\n", "\nThe polynomial\noperations on sets (without power) are also continuous:\nthey preserve countable unions of sets. \n", "\nLet F :  Set → Set be a polynomial endofunctor.\nWe sketch the proof that the least fixed point F*\n carries the structure\nof an initial algebra, together with the identity on it. \n", "\nOne forms the increasing sequence\n", "\n0 ⊆ F0 ⊆ F(F0) ⊆ \nF(F(F0)) …\n", "\nWe write 0 for ∅.\nEach of the maps shown is an inclusion, by standardness.\nLet F* be the union of the increasing sequence \nFn0 of sets.\nThen F(F*) = F*\n by continuity. So (F*, id) is an algebra for F.\nTo check initiality, let \n(A, a)\nbe an algebra for F, \nso\n a : Fa → a.\nDefine maps\n gn : Fn(0)\n → A \n by recursion, with \n g0 : 0\n → A \n the empty function\n(this is what initiality of ∅ amounts to), and \n gn+1 = \n a ⋅ Fgn.\nCheck that we have an increasing sequence of functions\n", "\ng0 ⊆\ng1 ⊆\ng2 ⊆\n …\n ", "\nthen take the union to get \nφ  :  F* → A.\nOne checks that this φ is a morphism of F-algebras, and indeed\nis the only such.\n" ], "subsection_title": "4.2 Algebras for a functor" }, { "content": [ "\nWe now turn to coalgebras.\nAgain, let F be an endofunctor on a category C.\nA coalgebra for F is a pair (c, f), where \nc\nis an object of C, and \nf : c → Fc. Comparing\nthis to the definition of an algebra, we can see that a\ncoalgebra is the same kind of structure, except that the \ndirection of the arrow is reversed.\n", "\nFor example, every graph is a coalgebra of ℘ on \nF :  Set → Set.\nThat is, every graph (G,→) may be re-packaged \nas (G, e), with\ne : G →\n ℘ \n G \ngiven by\n e(x) = {y ∈ G :\n x→ y}. In words, we trade in the \nedge relation of a graph with the function that assigns to each\npoint its set of children. This re-packaging has an inverse,\nand so the notions of “graph as set with relation”\nand “graph as coalgebra of ℘” \nare in this sense\nnotational variants.[12]", "\nLet \n (c, f)\n and \n (e, g)\n be coalgebras for the same functor.\nA morphism of coalgebras from \n (c, f)\n to \n (d, g)\n is\na morphism \n α : c → d \n in the category C so that\nthe diagram below commutes:\n", "\n\n\n\nc\nf→\nFc\n\n\n\nα\n↓\n\n↓  Fα\n\n\n\n\nd\n→g\nFd\n\n\n", "\nA coalgebra (d, g) is a final (or terminal)\ncoalgebra if for every coalgebra (c, f), there is a \nunique morphism of coalgebras \nα : (c,f) → (d,g).\n", "\nHere is another example as we wind our way back\nto set theory.\nThese are based on discussions at the beginning of this entry,\nconcerning streams of numbers \n(Section 1.1).\nWe are dealing with the functor Fa = N×a. \nThen a \nsystem of stream equations is a coalgebra for F.\nTo see how this works in a concrete case, we return\nto equation (2), reiterated below:\n", "\n\n\n(2)\nx ≈ \n〈0, y〉 \n\n\n\n\ny ≈ \n〈1, z〉 \n\n\n\n\nz ≈ \n〈2, x〉 \n\n\n", "\nWe regard this system as a coalgebra (X, e), where \nX = {x, y, z},\ne(x) = \n〈0,y〉 , \n and similarly for e(y) and z(x) .\nSo now we have a concrete example of\na coalgebra for this F. Another\ncoalgebra for F uses the set N∞ of streams as its\ncarrier set. The coalgebra itself is \n", "\n(N∞, \n〈head,\n tail〉 ).\n ", "\nThis coalgebra is final. We shall not verify this here, but instead we\napply this point.\nBy finality, \n there is a unique \n e† : X → \n N∞\nsuch that the diagram\nbelow commutes:\n", "\n\n\n\n\n\nFc\nf→\nc\n\n\n\nFα\n↓\n\n↓    α\n\n\n\n\nN∞\n→〈 head,\n tail 〉\nN × N∞\n\n\n\n", "\nWe now follow the elements of X around the diagram\nboth ways.\nFor x, this tells us that \n", "\n〈head,\n tail〉 \n (e†(x))\n =\n 〈0, e†(y)〉 \n", "\nThat is, \ne†(x) is a stream whose\nfirst component is 0 and whose second component is \ne†(y).\nSimilar observations hold for\ne†(y)\nand e†(z), of course.\nThe upshot is that\nthe three streams\ne†(x),\ne†(y)\nand e†(z)\nare exactly the ones we are after.\n", "\nMuch the same applies to the tree example from\nSection 1.2.\n" ], "subsection_title": "4.3 Coalgebras for a functor" }, { "content": [ "\nAt this point we rephrase FA and AFA to make a comparison.\nRecall that V\n is the class of all sets, and that \n V = ℘V. This\nmeans that (trivially) the identity on the universe maps V onto\n℘V, and vice-versa. Despite this, we want to introduce notation\nfor these two maps that makes them different. We shall write\n", " i: \n ℘V → V\n", "\nThus i\ntakes a multiplicity (a set of sets) and\nregards it as a unity (a set).\nWe also have a map in the other direction\n", " j: V →℘V \n", "\nThis j takes a set and regards it as a set \nof sets.\n", "\nThe Foundation Axiom in Algebraic Form. Except for not being a set,\n(V, i)\n is an initial algebra for ℘:\nfor all sets a\n and all \n f : ℘\n a → a,\n there is a unique\n s : V → f\n such that\nm \n = \n f ⋅ ℘ m:\n ", "\n\n\n\n℘V\ni→\nV\n\n\n\n℘m\n↓\n\n↓  m\n\n\n\n\n℘a\n→f\na\n\n\n", "\nThe Anti-Foundation Axiom in Coalgebraic Form.\nExcept for not being a set,\n(V, j)\n is a final coalgebra for ℘:\nfor every set b\n and every \n e: b→ \n ℘b,\nthere exists a unique \ns : b → V\n such that\ns = ℘ s ⋅ e:\n", "\n\n\n\nb\ne→\n℘b\n\n\n\ns\n↓\n\n↓  ℘s\n\n\n\n\nV\n→i\n℘V\n\n\n", "\nThe map s is called the solution to the system\ne.\n ", "\nClass forms. We only mentioned forms of the axioms pertaining\nto sets. They are a little nicer when\nstated as axioms on Class:\n", "\nFA is equivalent to the assertion that \n(V, i)\n is an initial algebra for ℘\n on\nClass.\n", "\nAFA is equivalent to the assertion that \n(V, j)\n is a final coalgebra for ℘ on\nClass.\n" ], "subsection_title": "4.4 The axioms again" }, { "content": [ "\nA chart just below indicates a kind of conceptual comparison \nof iterative and coiterative ideas. \nThe entries towards the top are dualities in the categorical sense.\nMoving downwards, the rows in the chart are more like research directions\nthan actual results. So spelling out the details in the chart is more like\nan ongoing research project than a settled matter.\n", "\nFor many functors on Set, especially polynomial functors\nand the finite power set functor, \nthe initial algebra is the least fixed point together with the identity.\nFor the polynomial functors, this least fixed point is \nitself an algebra of terms. \n\n", "\n\n\nalgebra for a functor\ncoalgebra for a functor\n\n\n\ninitial algebra\nfinal coalgebra\n\n\n\nleast fixed point\ngreatest fixed point\n\n\n\ncongruence relation\nbisimulation equivalence relation\n\n\n\nequational logic\nmodal logic\n\n\n\nrecursion: map out of an initial algebra\ncorecursion: map into a final coalgebra\n\n\n\nFoundation Axiom \nAnti-Foundation Axiom \n\n\n\niterative conception\ncoiterative conception \n\n\n\nset with operations \n set with transitions and observations \n\n\n\nuseful in syntax \nuseful in semantics \n\n\n\nbottom-up \n top-down \n\n\n\n", "\nThe connection between greatest fixed points and final coalgebras is the\ncontent of the following result.\n", "\n Theorem [Aczel]\nFor every power polynomial F on \nClass, the greatest fixed point \ntogether with the identity on it, (F*, id),\n is a final coalgebra of F on \nClass.\nMoreover, if F is a polynomial functor, then \nF* is a set, and \n (F*, id)\nis a final coalgebra of F on Set.\n", "\nThe original result used much weaker hypotheses on F, \nusing notions which we did not define, so \nour statement is rather weaker than in Aczel’s book. Several papers\nhave gone on to weaken strengthen this Final Coalgebra Theorem.\n", "Bisimulation.\nWe have given the definition of bisimulation earlier,\nin Section 3.1.\nWe discussed it in connection with graphs, but the reader may also\nknow of a notion with the same name coming from modal logic.\nActually, the theory of coalgebra studies a more general notion,\nthat of bisimulation on a coalgebra for a given functor, defined first\nin Aczel and Mendler (1989).\nThis more general notion\nspecializes to several concepts which had been proposed in their own \nfields. In addition, it is (nearly) the dual concept of a congruence on\nan algebra; this explains our line in \nthe conceptual comparison chart.\n", "Equational logic and modal logic.\nA great deal of work has shown ways in which equational logic\nand modal logic are “dual”, but to spell this out in detail would\nrequire quite a bit more category theory than we need in the rest\nof this entry.\n", "\nThere is a growing field\nof coalgebraic generalizations of modal logic. For a survey of\nthis area, see Kurz (2006). \n", "\nThe final coalgebra\nof a functor may be regarded as a space of complete observations.\n(As with all our points in this section, this statement is mainly for functors on\nSet, and the notion of “complete observation”\nis, of course, merely suggestive.) For example, let \nAtProp be a set whose elements are\ncalled atomic propositions, and consider the functor\nF(a) = ℘fin(a) ×\n℘(AtProp ). A coalgebra for this is a set a\ntogether with one map of a into its finite subsets, and\nanother map into the collection of sets of atomic propositions.\nPutting the two maps together gives a finitely-branching\nKripke model: each point has finitely many children and some set of\natomic propositions. Now modal logic gives us a way of\n“observing” properties of points in coalgebras (Kripke\nmodels). And the record of everything that one could observe from a\npoint is the modal theory of that point. Further, one may take the\ncollection of all theories of all points in all finitely-branching\nKripke models and make this collection (it is a set) into the carrier\nof a final coalgebra for the functor. Indeed, this would be one way\nto construct a final coalgebra.\n", "\nCorecursion. Returning now to \nthe chart, we present an example of a corecursive\ndefinition.\n The equation for zip \ngiven above shows \n how the zip function on streams is\nto work. It should satisfy \n", "\nzip(s, t)   =   \n〈head(s), \n zip(t,\n tail(s))〉 \n ", "\nHere is how zip is uniquely defined via a corecursive definition.\nWrite N∞×\nN∞ as S in this discussion.\nWe want a map from S to N∞. \nWe are dealing with S as the final coalgebra of \n the functor Fa = N × a.\n And we’ll write the structure\n on the final coalgebra as\n〈 head, tail&thinsp;〉, just as we did it in\nSection 1.1.\nThe idea is to turn S into the carrier set\nof a coalgebra for, say (S, f). \nThen zip\nwill be the unique coalgebra morphism from \n (S, f) to \n (S,\n〈 head,tail 〉 ). \nIt remains to define f.\nLet \n", "\nf(s, t) =\n〈head(s),\n 〈t, tail(s)〉〉 .\n", "\nAs mentioned, by finality there is a unique \nzip : S → N∞ \n so that\nthe diagram below commutes:\n", "\n\n\n\n\nS\nf→\nFS\n\n\n\nzip\n↓\n\n↓    Fzip\n\n\n\n\nN∞\n→\n〈head,tail〉\nFN∞\n\n\n\n", "\nTo make sure that this works, we follow an arbitrary pair of streams,\nsay \n〈s,t〉 around the square, starting in the upper-left.\n Going down, we have the stream\n zip(s, t).\nFrom this, the structure takes this to\n〈head(zip(s, t)),\n tail(zip(s, t))〉\n ∈ FN∞.\nBut we could also take our \n〈s, t〉 across the top via f to get \n〈head(s), \n 〈t, tail(s)〉〉.\nNow Fzip applies to this pair, and\n this is where the action of F as a functor\nenters. We get \n〈head(s),\nzip(tail(t), s)〉.\nSo overall, we have \n", "\nzip(s, t))   =   \n head(s) \n ", "\n tail(zip(s, t)) \n   =   \n zip(tail(t), s)\n", "\njust as desired. It says: to zip two streams, start with the head of the first,\nand then repeat this very process on the second followed by the tail of the first.\n", "\nThe main point of this demonstration is that the principle of finality is \nsufficient to define and study corecursive definitions. There are many further\ndevelopments in this area.\n", "\nSets, again. We have already discussed at length the lines in the table concerning \nthe Foundation and Anti-Foundation Axioms, and their attendant \nconceptual backgrounds. The point of this section is to situate\nthat entire discussion inside of a larger one.\n", "\nExamples of final coalgebras and corecursive definitions. \nOur conceptual comparison makes the point that algebras embody \nsets with operations. This point is almost too easy: \nthe reason behind the terminology\nof “algebras” in category theory is that sets with operations may be modeled\nas algebras in the categorical sense. For coalgebras, it is harder to make the\ncase that they directly correspond to sets with either “transitions” or “observations”.\nHowever, we present a few examples that motivate this point.\n", "\nThe table above lists a few functors on Set \n or \nClass along with\nfinal coalgebras or other data from \nthe conceptual comparison chart.\n", "\nFirst, for any set S, the functor Fa = S×\n a. \nA coalgebra for this F is a stream system of equations\nas we saw it in \nSection 1.1,\n except that there\nwe made things concrete and took S to be the set of natural numbers.\nThe final coalgebra is the set S∞ = S ×\n S∞ of \nstreams over S.\n The logical language for this functor\nwould be a sentential (propositional) language \nwhose sentences are either true or of the form s : φ\n where s∈S.\nThe semantics would be the obvious one; for example\n", "\n(0, 1, 2, 3, … ) ⊨\n 0 : 1 : 2 : true.\n", "\nOne should note that carrier of the final coalgebra may be taken to be \ncertain theories in this language. These may be described extrinsically as\nthe theories of all points in all coalgebra. It is more informative, however, to \nset down a logical system and then consider the maximal consistent sets in the system.\nWith the right definition, the maximal consistent sets do turn out to be the carrier of a\nfinal coalgebra for the functor.\n", "\nSecond, we consider Fa = (S × a) + 1.\nHere 1 = {0} and + is the disjoint union operation. However, it is \nmore common for people to represent the one and only element of \n1 using a symbol like *.\nThe coalgebras are like stream systems of equations, except now an\nequation might ask for a stream to “stop” by having * on the right-hand \nside.\nSo an example of a coalgebra would be \nx ≈ \n〈s,y〉 ,\n y ≈ *.\nThen the solution would take \nx† to be the one-term sequence s.\nThe logic for this functor would be the same logic (HML) as before, except that\nnow we add an atomic sentence to detect the ends of finite sequences.\n ", "\nTurning to the last two lines, we already know that AFA is equivalent to\nthe assertion that (V, id)\n is a final coalgebra of ℘; also, even without \nAFA, we have a final coalgebra whose carrier set is the pointed graphs modulo\nbisimulation. The logic in this case is infinitary modal logic,\nactually, it is a fragment of this logic. It turns\nout that two points in a given coalgebra have the same infinitary modal theory\niff they are bisimilar.\n ", "\nThe line concerning ℘fin(a) ×\n ℘(AtProp) is the closest to \nthe Kripke semantics of modal logic. One might hope that the final coalgebra\nwould turn out to be the canonical model of the modal logic \nK, but this is not\nquite right. One needs to cut down to those maximal consistent sets which are\nrealized by some point in some finitely branching model.\n ", "As the reader may notice, we are being extremely vague about matters\nconcerning the logics: is there a principled explanation of where they come from?\nWhat, if anything,\nis the relation between the final coalgebras and canonical models\nas we find them in modal logic? The explanations here are too long and too\ninvolved for this entry. Once again,\none place to start reading about these matters is Kurz (2006).\n", "\nThe lines in at the bottom of the conceptual comparison chart\n are the most programmatic of all.\n ", "Doing without AFA: final coalgebras\nin ZF. We mentioned in note [2] that it is possible to alter the pairing\noperation in such a way that one may prove many of the results that\nour treatment obtains only by using ZFA. This points is\nmentioned in Forster (1994) and developed in detail in Paulson (1999)\n(and in other papers by Paulson). One replaces the Kuratowski pair\n〈x,y〉 with a variant,\n({0}× a)∪ ({1}× b). (This is the\nusual disjoint union operation, also called the coproduct on\nsets.) Then one defines variants of other notions: the cartesian\nproduct, functions, etc. And in terms of these one can indeed study\nstreams and infinite trees, and many other sets of interest in this\nentry. Even more, one can prove\nfinal coalgebra theorems, stating sufficient conditions\nfor the existence of a final coalgebra whose structure is the identity.\n(This is an important point for this line of work: in ZF we can \nshow the existence of final coalgebras for the same functors as in\nZFA, but in the latter theory we can get final coalgebras whose\nstructure maps are the identity.)\n", "\nOne might think that this move undermines much of the interest\nin AFA. For Paulson, the reduction is important since he wants\nto use an automatic theorem prover to work with assertions in set theory.\nIt makes sense to work out detailed reductions so as to avoid changing\nthe set theory. ", "\nOtthers may not find this conclusive, for two reasons. First, the\nmethod doesn’t apply to equations like x =\n{x}, or to collections like\nx = ℘fin(x). The latter kind of\nequation is especially useful in applications. But even more, what\nwill be of interest will be the whole assembly of what we might\ncall coalgebraic concepts: coinduction, corecursion, and\ntop-down treatments of various phenomena. Someone who is using these\nconcepts and is also worried about modeling in set theory would\nprobably find it convenient to work with AFA, even if many of\nthe end applications could be done in standard set theory.\n ", "\nTo put things differently, and to ask a question that surely belongs\nin this entry, why should one work with AFA instead\nof FA? Much depends on the purposes one brings to set\ntheoretic modeling in the first place. For most purposes, including\nmost of mathematics, it makes little or no difference. To model some\ncircular phenomena, it turns out to be convenient to work with final\ncoalgebras of various functors. It is especially nice with the\nstructure maps on those final coalgebras may be taken to be the\nidentity function. For example, this would allow us to say that a\nstream of numbers really and truly is an ordered pair of a number and\na stream. In this case, having AFA would be nice, but the\nresults above show that in many of the interesting cases, it is not\nactually needed. On the other hand, if one is content to work with\nisomorphisms, then having the structure map be the identity is a kind\nof “optional extra”. Further, the question of which axiom\nto adopt might appear to be besides the point.", "\n Interested readers may consult the following supplementary\ndocument for a discussion of how the more general ideas from coalgebra\nand closely related fields help with discussions of the kinds of\nmathematical circularity which we looked at previously. \n ", "\n Additional related modeling of circularity\n" ], "subsection_title": "4.5 Conceptual comparison" } ] }, { "main_content": [ "\n This entry has two major thrusts. First, it introduced\nnon-wellfounded sets and described some of the mathematics around\nthem. It was not comprehensive in this regard, and one should see\nPeter Aczel’s book (1988) for much more, including\ndiscussions of axioms besides AFA that we did not even mention.\nOne could also see Barwise and Moss (1996) for more on some of the\npoints that were touched on \nhere.[13]\n The presentation owes much to work in coalgebra that began\nshortly after these books appeared. So readers familiar with either\nof them would still find something new in the first sections of the\nentry.", "\n The other thrust had to do with the conceptual points made in\nSection 4.5.\nThe idea is to situate the\nmathematics of set theoretic circularity inside a larger topic,\ncoalgebra, and then to understand both points in terms of a larger\ndivision between “bottom-up” and “top-down”\nideas. This larger discussion is more programmatic than we would\nlike, and much remains to be done on it. Our hope is that it helps\nreaders understand set theoretic circularity, both how it\nworks, and also why it is attractive." ], "section_title": "Conclusion", "subsections": [] } ]

[ "Aczel, P., 1988, Non-Well-Founded Sets (CSLI Lecture\nNotes: Number 14), Stanford: CSLI Publications. ", "Aczel, P. and Mendler, N., 1989, ‘A final coalgebra\ntheorem,’ in D. H. Pitt et al. (eds.), Category Theory and\nComputer Science, Heidelberg: Springer-Verlag,\n357–365.", "Adámek, J., and Reitermann, J., 1994, ‘Banach’s\nFixed-Point Theorem as a Base for Data-Type Equations,’\nApplied Categorical Structures, 2: 77–90. ", "Alexandru Baltag, 2000, ‘STS: A Structural Theory of\nSets,’ in Michael Zakharyaschev, Krister Segerberg, Maarten de\nRijke & Heinrich Wansing (eds.), Advances in Modal Logic\n(Volume 2), Stanford: CSLI Publications,. 1–34.", "Barwise, J., and Etchemendy, J., 1987, \nThe Liar, Oxford: Oxford University Press.", "Barwise, J., and Moss, L., 1991, ‘Hypersets’,\nThe Mathematical Intelligencer, 13(4): 31–41.", "Barwise, J., and Moss, L., 1996, Vicious Circles (CSLI\nLecture Notes: Number 60), Stanford: CSLI Publications.", "Böge, W., and Eisele, T., 1979, ‘On solutions of\nBayesian games,’ International Journal of Game Theory,\n8(4): 193–215.", "Boolos, G., 1971, ‘The iterative conception of set,’\nThe Journal of Philosophy, 68: 215–231.", "Burgess, J., 1985, Reviews, Journal of Symbolic Logic, \n50(2): 544–547.", "Corfield, D., 2011, ‘Understanding the Infinite II:\nCoalgebra, Studies in History and Philosophy of Science (A),\n42: 571–579.", "Edalat, A., 1995, ‘Dynamical Systems, Measures and Fractals\nvia Domain Theory,’ Information and Computation,\n120(1): 32–48.", "Thomas Forster, 1994, ‘Why Set theory without the axiom of\nfoundation?’ Journal of Logic and Computation, 4(4):\n333–335.", "Forti, M. and Honsell, F., 1983, ‘Set theory with\nfree construction principles‘, Annali Scuola Normale Superiore\ndi Pisa, Classe di Scienze, 10: 493–522.", "Harsanyi, J. C., 1967, ‘Games with incomplete information\nplayed by ‘Bayesian’ players. I. The basic model,’\nManagement Science, 14: 159–182.", "Hayashi, S., 1985, ‘Self-similar sets as Tarski’s fixed\npoints,’, Publications of the Research Institute for\nMathematical Sciences, 21(5): 1059–1066.", "Heifetz, A., and Samet, D., 1998, ‘Topology-free typology of\nbeliefs,’ Journal of Economic Theory, 82(2):\n324–341.", "Incurvati, Luca, 2014, ‘The Graph Conception of Set,’\nJournal of Philosophical Logic, 43(1): 181–208.", "Jacobs, B. and Rutten, J., 1997, ‘A Tutorial on (Co)Algebras\nand (Co)Induction’, in Bulletin of the European Association\nfor Theoretical Computer Science, 62: 222–259. ", "Kurz, A., 2006, ‘Coalgebras and Their Logics’, ACM\nSIGACT News, 37(2): 57–77.", "Levy, A., 1979, Basic Set Theory, Berlin:\nSpringer-Verlag.", "Milius, S., 2005, ‘Completely iterative algebras and\ncompletely iterative monads,’ Information and\nComputation, 196: 1–41. ", "Moss, L., and Viglizzo, I., 2006, ‘Final coalgebras for\nfunctors on measurable spaces,’ Information and\nComputation, 204(4): 610–636.", "Parsons, C., 1975, ‘What is the iterative conception of\nset?’, in Hintikka and Butts (eds.), Logic, foundations of\nmathematics and computability theory (University of Western\nOntario Series in the Philosophy of Science, Volume 9: Proceedings of\nthe Fifth International Congress on Logic, Methodology and the\nPhilosophy of Science, University of Western Ontario, London, Ontario,\n1975), Dordrecht: Reidel, 1977, Part I, pp. 335–367. ", "Paulson, L., 1999, ‘Final coalgebras as greatest fixed\npoints in ZF set theory,’ Mathematical Structures in\nComputer Science, 9: 545–567.", "Pavlovic, D., and M. H. Escardo, 1998,\n‘Calculus in Coinductive Form,’ in \n13th Annual IEEE Symposium in Logic in Computer Science\n(LICS 98), Los Alamitos, CA: IEEE,\n408–417. doi:10.1109/LICS.1998.705675", "Rieger, A., 2000, ‘An argument for Finsler-Aczel set theory,’\nMind, 109(434): 241–253. doi:10.1093/mind/109.434.241", "Rutten, J., 2000, ‘Universal coalgebra: a theory of\nsystems,’ Theoretical Computer Science, 249(1):\n3–80.", "Turi, D., and Rutten, J., 1998, ‘On the foundations of final\nsemantics: non-standard sets, metric spaces, partial orders,’\nMathematical Structures in Computer Science, 8(5):\n481–540.", "Viglizzo, I., 2005, Coalgebras on measurable spaces,\nPh.D. Dissertation, Indiana University, Bloomington." ]

[ { "href": "../algebra/", "text": "algebra" }, { "href": "../category-theory/", "text": "category theory" }, { "href": "../set-theory/", "text": "set theory" }, { "href": "../settheory-alternative/", "text": "set theory: alternative axiomatic theories" } ]

[ "The first axiomatisation of set theory was given by Zermelo in his\n1908 paper “Untersuchungen über die Grundlagen der\nMengenlehre, I” (Zermelo 1908b), which became the basis for\nthe modern theory of sets. This entry focuses on the 1908\naxiomatisation; a further entry will consider later axiomatisations of\nset theory in the period 1920–1940, including Zermelo's second\naxiomatisation of 1930." ]

[ { "content_title": "1. The Axioms", "sub_toc": [] }, { "content_title": "2. The Background to Zermelo's Axiomatisation", "sub_toc": [ "2.1 Hilbert's Axiomatic Method", "2.2 The Well-Ordering Problem and the Well-Ordering Theorem" ] }, { "content_title": "3. The Major Problems with Zermelo's System", "sub_toc": [ "3.1 Separation", "3.2 Completeness" ] }, { "content_title": "4. Further reading", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "The introduction to Zermelo's paper makes it clear that set theory is regarded as a fundamental theory:", "\n Set theory is that branch of mathematics whose task is to\n investigate mathematically the fundamental notions\n “number”, “order”, and\n “function”, taking them in their pristine, simple form,\n and to develop thereby the logical foundations of all of arithmetic\n and analysis; thus it constitutes an indispensable component of the\n science of mathematics.\n (1908b: 261)[1]\n", "This is followed by an acknowledgment that it is necessary to\nreplace the central assumption that we can ‘assign to an\narbitrary logically definable notion a “set”, or\n“class”, as its “extension” ’\n(1908b: 261). Zermelo goes on:", "\n In solving the problem [this presents] we must, on the one hand,\nrestrict these principles [distilled from the actual operation with\nsets] sufficiently to exclude all contradictions and, on the other,\ntake them sufficiently wide to retain all that is valuable in this\ntheory. (1908b: 261)\n", "The ‘central assumption’ which Zermelo describes (let\nus call it the Comprehension Principle, or CP) had come to be seen by\nmany as the principle behind the derivation of the set-theoretic\ninconsistencies. Russell (1903: §104) says the following:", "\n Perhaps the best way to state the suggested solution [of the\n Russell-Zermelo contradiction] is to say that, if a collection of\n terms can only be defined by a variable propositional function,\n then, though a class as many may be admitted, a class as one must be\n denied. We took it as axiomatic that the class as one is to be found\n wherever there is a class as many; but this axiom need not be\n universally admitted, and appears to have been the source of the\n contradiction. By denying it, therefore, the whole difficulty will\n be overcome.\n", "But it is by no means clear that ‘the whole difficulty’\nis thereby ‘overcome’. Russell makes a clear\nidentification of the principle he cites (a version of CP) as the\nsource of error, but this does not in the least make it clear what is\nto take its \nplace.[2] \nIn his Grundgesetze (see e.g., Frege\n1903: §146–147) Frege recognises that his (in)famous Law V\nis based on a conversion principle which allows us to assume that for\nany concept (function), there is an object which contains precisely\nthose things which fall under that concept (or for which the function\nreturns the value ‘True’). Law V is then the principle\nwhich says that two such extension objects a, b stemming\nfrom two concepts F, G are the same if, and only\nif, F and G are extensionally equivalent. Frege clearly\nconsiders the ‘conversion’ of concepts to extensions as\nfundamental; he also regards it as widely used in mathematics (even if\nonly implicitly), and thus that he is not ‘doing anything\nnew’ by using such a principle of conversion and the attendant\n‘basic law of logic’, Law V. (The CP follows immediately\nfrom Law V.) Frege was made aware by Russell (1902) that his Law V is\ncontradictory, since Russell's paradox flows easily from it. In the\nAppendix to Grundgesetze (Frege 1903), Frege says this:", "\n Hardly anything more unwelcome can befall a scientific writer\n than to have one of the foundations of his edifice shaken after the\n work is finished. This is the position into which I was put by a\n letter from Mr Bertrand Russell as the printing of this volume was\n nearing completion. The matter concerns my Basic Law (V). I have\n never concealed from myself that it is not as obvious as the others\n nor as obvious as must properly be required of a logical\n law. Indeed, I pointed out this very weakness in the foreword to the\n first volume, p. VII. I would gladly have dispensed with this\n foundation if I had known of some substitute for it. Even now, I do\n not see how arithmetic can be founded scientifically, how the\n numbers can be apprehended as logical objects and brought under\n consideration, if it is not—at least\n conditionally—permissible to pass from a concept to its\n extension. May I always speak of the extension of a concept, of a\n class? And if not, how are the exceptions to be recognised? May one\n always infer from the extension of one concept's coinciding with\n that of a second that every object falling under the first concept\n also falls under the latter? These questions arise from Mr Russell's\n communication. …What is at stake here is not my approach to a\n foundation in particular, but rather the very possibility of any\n logical foundation of\n arithmetic. (p. 253)[3]\n", "The difficulty could hardly be summed up more succinctly. It was\nthe replacement of assumptions involving the unfettered conversion of\nconcepts to objects which was Zermelo's main task in his\naxiomatisation.", "Zermelo's system was based on the presupposition that", "\n Set theory is concerned with a “domain” 𝔅 of\n individuals, which we shall call simply “objects” and\n among which are the “sets”. If two symbols, a\n and b, denote the same object, we write a = b,\n otherwise\na ≠ b. We say of an\nobject a that it “exists” if it belongs to the\ndomain 𝔅; likewise we say of a class 𝔎 of objects that\n“there exist objects of the class 𝔎” if 𝔅\ncontains at least one individual of this class. (1908b: 262)\n", "Given this, the one fundamental relation is that of set membership,\n‘ε’ , which allows one to state that an\nobject a belongs to, or is in, a set b, written\n‘a ε \n b’.[4]\n Zermelo then laid down seven axioms which\ngive a partial description of what is to be found in B. These\ncan be described as follows:", "With the inclusion of this last, Zermelo explicitly rejects any\nattempt to prove the existence of an infinite collection from other\nprinciples, as we find in Dedekind (1888: §66), or in Frege via\nthe establishment of what is known as ‘Hume's Principle’.", "The four central axioms of Zermelo's system are the Axioms of\nInfinity and Power Set, which together show the existence of\nuncountable sets, the Axiom of Choice, to which we will devote some\nspace below, and the Axiom of Separation. This latter allows that any\n‘definite’ property φ does in fact give rise to a set,\nnamely the set of all those things which are already included in some\nset a and which have the property φ, in other words, gives\nrise to a certain subset of a, namely the subset of all the\nφ-things in a. Thus, it follows from this latter that there\nwill generally be many sets giving partial extensions of φ, namely\nthe φ-things in a, the φ-things in b, the\nφ-things in c, and so on. However, there will be no\nguarantee of the existence of a unique extension-set for φ, as, of\ncourse, there is under the CP, namely a = {x :\nφ(x)}.", "Zermelo shows that, on the basis of his system, the two central\nparadoxes, that of the greatest set and that of Russell, cannot\narise. In fact, Zermelo proves:", "\n Every set M possesses at least one\n subset M0 that is not an element\n of M. (1908b: 265)\n", "The proof is an easy modification of the argument for Russell's\nParadox, using the contradiction this time as a reductio. By\nSeparation, let M0 be the subset of M\nconsisting of those elements x of M such\nthat \nx ∉ x. Now either \nM0 ∈ M0\nor M0 ∉ M0. Assume\nthat \nM0 ∈ M0. Since \nM0 is a subset\nof M, this tells us that \nM0 ∈ M. But M0 is then a member of M\nwhich fails to satisfy the condition for belonging\nto M0, showing\nthat \nM0 ∉ M0, which is a\ncontradiction. Hence,\nnecessarily, \nM0 ∉ M0. But now\nif we suppose that M0 were in M,\nthen M0 itself is bound to be\nin M0 by the defining condition of this\nset. Hence, \nM0 ∉ M on pain of\ncontradiction. The argument for the Russell paradox is used here to\nconstructive effect: one person's contradiction is another person's\nreductio. Zermelo comments:", "\n It follows from the theorem that not all objects x of the\n domain 𝔅 can be elements of one and the same set; that is,\n the domain 𝔅 is not itself a set, and this disposes of the\n “Russell antinomy” so far as we are concerned. (1908b:\n 265) ", "For, in the absence of something like the CP, there is no\noverriding reason to think that there must be a universal\nset.[5]", "But although this deals with the Russell paradox and the paradox of\nthe universal set, it does not tackle the general consistency of the\nsystem. Zermelo was well aware of this, as is clear from the\nIntroduction to his paper:", "\n I have not yet even been able to prove rigorously that my axioms\n are “consistent”, though this is certainly very\n essential; instead I have had to confine myself to pointing out now\n and then that the “antinomies” discovered so far vanish\n one and all if the principles here proposed are adopted as a\n basis. But I hope to have done at least some useful spadework hereby\n for subsequent investigations in such deeper problems. (1908b:\n 262)\n", "It should be remarked in passing that Zermelo doesn't deal specifically with the\nBurali-Forti paradox either, for the simple reason that it cannot be properly\nformulated in his system, since it deals either with well-orderings\ngenerally or with the general concept of ordinal number. We will come\nback to this below. However, assuming that the known paradoxes can be\navoided, another question comes to the fore: if the Separation Axiom\nis to be the basic principle for the workaday creation of sets, is it\nadequate? This question, too, will be taken up later.", "There were attempts at the statement of axioms before Zermelo, both\npublicly and in private\n correspondence.[6] \nIn particular, Cantor, in correspondence\nwith Hilbert and Dedekind in the late 1890s, had endeavoured to\ndescribe some principles of set \nexistence[7] \nwhich he thought were legitimate, and would\nnot give rise to the construction of what he called\n‘inconsistent totalities’, totalities which engender\ncontradictions. (The best known of these totalities were the totality\nof all ordinals and the totality of all cardinals.) These principles\nincluded those of set union and a form of the replacement axiom, as\nwell as principles which seem to guarantee that every cardinal number\nis an aleph, which we call for short the ‘Aleph Hypothesis\n(AH)’.", "Despite this, there are reasons for calling Zermelo's system the\nfirst real axiomatisation of set theory. It is clear above all that\nZermelo's intention was to reveal the fundamental nature of the theory\nof sets and to preserve its achievements, while at the same time\nproviding a general replacement for the CP." ], "section_title": "1. The Axioms", "subsections": [] }, { "main_content": [], "section_title": "2. The Background to Zermelo's Axiomatisation", "subsections": [ { "content": [ "Hilbert's early work on the axiomatic method is an important part\nof the context of Zermelo's axiomatisation. Hilbert developed a\nparticular version of the axiomatic approach to fundamental\nmathematical theories in his work on geometry in the period\n1894–1904 (see Hallett and Majer 2004). This was to be seen as a\ndistinct alternative to what Hilbert called the ‘genetic\napproach’ to mathematics. (For a short, historically informed\ndescription, see Felgner 2010: 169–174.) Ebbinghaus's book on\nZermelo makes it very clear how embedded Zermelo was in the Hilbert\nfoundational circle in the early years of the\ncentury.[8]\n This is not meant to suggest that Zermelo adopted Hilbert's approach\nto the foundations of mathematics in all its aspects. Indeed, Zermelo\ndeveloped his own, distinctive approach to foundational matters which\nwas very different from Hilbert's, something which emerges quite\nclearly from his later work. Nevertheless, there are two elements of\nZermelo's procedure which fit very well with Hilbert's foundational\napproach in the early part of the century. The first element concerns\nwhat might be called the programmatic element of Hilbert's treatment\nof the foundations of mathematics as it emerged in the later 1890s,\nand especially with regard to the notion of mathematical\nexistence. And the second concerns proof analysis, a highly important\npart of Hilbert's work on Euclidean geometry and geometrical systems\ngenerally. These matters are intricate, and cannot be discussed\nadequately here (for fuller discussion, see both Hallett 2008 and\n2010a). But it is important for understanding Zermelo's work fully\nthat a rough account be given.", "First, Hilbert adopted the view that a mature presentation of a\nmathematical theory must be given axiomatically. This, he claims,\nrequires several things:", "For one thing, Hilbert was very clear (especially in his\nunpublished lectures on geometry: see Hallett and Majer 2004) that,\nalthough a domain is asserted to ‘exist’, all that is\nknown about the objects in the domain is what is given to us by the\naxioms and what can be derived from these through ‘finite\nproof’. In other words, while a domain is postulated, nothing is\ntaken to be known about the things in it independently of the axioms\nlaid down and what they entail. The basic example was given by\ngeometrical systems of points, lines and planes; although the\ngeometrical domain is made up of these things, nothing can be assumed\nknown about them (in particular no ‘intuitive’ geometrical\nknowledge from whatever source) other than what is given in the axioms\nor which can be derived from them by legitimate inference. (The axioms\nthemselves might sum up, or be derived from, ‘intuitive’\nknowledge, but that is a different matter. And even here it is\nimportant that we can detach the axioms from their intuitive\nmeanings.)", "Secondly, while ‘existence’ of the objects is just a\nmatter (as Zermelo says) of belonging to the domain (a fact which is\nestablished by the axioms or by proofs from those axioms), the\nmathematical existence of the domain itself, and (correspondingly) of\nthe system set out by the axioms, is established only by a consistency\nproof for the axioms. Thus, to take the prime example, the\n‘existence’ of Euclidean geometry (or more accurately\nEuclidean geometries) is shown by the consistency proofs given by\nmeans of analytic \n geometry.[9]\n Thus, the unit of consistency is not the\nconcept nor the individual propositions, but rather the system of\naxioms as a whole, and different systems necessarily give accounts of\ndifferent primitives. The expectation is that when a domain is\naxiomatised, attention will turn (at some point) to a consistency\nproof, and this will deal finally with the question of mathematical\nexistence. In any case, the task of showing existence is a\nmathematical one and there is no further ontological or metaphysical\nmystery to be solved once the axioms are laid down.", "Many aspects of Hilbert's position are summed up in this\npassage from his 1902 lectures on the foundations of geometry: the\naxioms ‘create’ the domains, and the consistency proofs\njustify their existence. As he puts it:", "\n The things with which mathematics is concerned are\ndefined through axioms, brought into life.\n\nThe axioms can be taken quite arbitrarily. However, if these axioms\ncontradict each other, then no logical consequences can be drawn from\nthem; the system defined then does not exist for the\nmathematician. (Hilbert 1902: 47 or Hallett and Majer 2004: 563)\n", "This notion of ‘definition through axioms’, what came\nto be known as the method of ‘implicit definition’, can be\nseen in various writings of Hilbert's from around 1900. His\nattitude to existence is illustrated in the following passage from his\nfamous paper on the axiomatisation of the reals:", "\n The objections which have been raised against the existence of\n the totality of all real numbers and infinite sets generally lose\n all their justification once one has adopted the view stated above\n [the axiomatic method]. By the set of the real numbers we do not\n have to imagine something like the totality of all possible laws\n governing the development of a fundamental series, but rather, as\n has been set out, a system of things whose mutual relations are\n given by the finite and closed systems of axioms I–IV [for\n complete ordered fields] given above, and about which statements\n only have validity in the case where one can derive them via a\n finite number of inferences from those axioms. (Hilbert 1900b:\n 184)[10]\n", "The parallels between this ‘axiomatic method’ of\nHilbert's and Zermelo's axiomatisation of set theory are\nreasonably clear, if not \n exact.[11]\nParticularly clear are the assumption of the existence of a\n‘domain’ 𝔅, the statement of a finite list of\naxioms governing its contents, and the recognition of the requirement\nof a general consistency proof. There's also implicit\nrecognition of the requirements of ‘finite proof’; this\nleads us to the second important aspect of the Hilbertian background,\nnamely proof analysis and the use of the Axiom of Choice.", "A great deal of Hilbert's work on geometry concerned the analysis\nof proofs, of what can, or cannot, be derived from what. Much of\nHilbert's novel work on geometry involved the clever use of\n(arithmetical) models for geometrical systems to demonstrate a\nsuccession of independence results, which, among other things, often\nshow how finely balanced various central assumptions\nare.[12]\nMoreover, a close reading of Hilbert's work makes it clear that the\ndevelopment of an appropriate axiom system itself goes hand-in-hand\nwith the reconstruction and analysis of proofs.", "One straightforward kind of proof analysis was designed to reveal\nwhat assumptions there are behind accepted ‘theorems’, and\nthis is clearly pertinent in the case of Zermelo's Axiom of Choice\n(his sixth axiom) and the WOT. What Zermelo's work showed, in effect,\nis that the ‘choice’ principle behind the Axiom is a\nnecessary and sufficient condition for WOT; and he shows this by\nfurnishing a Hilbertian style proof for the theorem, i.e., a\nconclusion which follows from (fairly) clear assumptions by means of a\nfinite number of inferential steps. Indeed, the Axiom is chosen so as\nto make the WOT provable, and it transpired subsequently that it also\nmade provable a vast array of results, mainly (but not solely) in set\ntheory and in set-theoretic algebra. To understand the importance of\nZermelo's work, it's necessary to appreciate the centrality of the the\nWOT." ], "subsection_title": "2.1 Hilbert's Axiomatic Method" }, { "content": [ "In one of the fundamental papers in the genesis of set theory,\nCantor (1883a) isolated the notion of a well-ordering on a collection\nas one of the central conceptual pillars on which number is\nbuilt. Cantor took the view that the notion of a counting number must\nbe based on an underlying ordering of the set of things being counted,\nan ordering in which there is a first element counted, and, following\nany collection of elements counted, there must be a next element\ncounted, assuming that there are elements still uncounted. This kind\nof ordering he called a ‘well-ordering’, which we now\ndefine as a total-ordering with an extra condition, namely that any\nsubset has a least element in the ordering. Cantor recognised that\neach distinct well-ordering of the elements gives rise to a distinct\ncounting number, what he originally called an ‘Anzahl\n[enumeral]’, later an ‘Ordnungszahl [ordinal\nnumber]’, numbers which are conceptually quite different from\ncardinal numbers or powers, meant to express just the size of\ncollections.[13]\nThis distinction is hard to perceive at first sight. Before Cantor and\nthe rise of the modern theory of transfinite numbers, the standard\ncounting numbers were the ordinary finite\nnumbers.[14]\nAnd, crucially, for finite collections, it turns out that any two\norderings of the same underlying elements, which are certainly\nwell-orderings in Cantor's sense, are order-isomorphic, i.e., not\nessentially\n distinct.[15] \nThis means that one can in effect\nidentify a number arrived at by counting (an ordinal number) with the\ncardinal number of the collection counted. Thus, the ordinary natural\nnumbers appear in two guises, and it is possible to determine the size\nof a finite collection directly by counting it. Cantor observed that\nthis ceases to be the case in rather dramatic fashion once one\nconsiders infinite collections; here, the same elements can give rise\nto a large variety of distinct well-orderings.", "Nevertheless, Cantor noticed that if one collects together all the\ncountable ordinal numbers, i.e., the numbers representing\nwell-orderings of the set of natural numbers, this collection, which\nCantor called the second number-class (the first being the set of\nnatural numbers), must be of greater cardinality than that of the\ncollection of natural numbers itself. Moreover, this size is the\ncardinal successor to the size of the natural numbers in the very\nclear sense that any infinite subset of the second number-class is\neither of the power of the natural numbers or of the power of the\nwhole class; thus, there can be no size which is strictly\nintermediate. The process generalises: collect together all the\nordinal numbers representing well-orderings of the second number-class\nto form the third number-class, and this must be the immediate\nsuccessor in size to that of the second number-class, and so on. In\nthis way, Cantor could use the ordinal numbers to generate an infinite\nsequence of cardinalities or powers. This sequence was later\n (Cantor 1895) called the aleph-sequence, ℵ0 (the\nsize of the natural numbers), ℵ1 (expressing the\nsize of the second number-class), ℵ2 (expressing the\nsize of the third number-class), and so on. Since the intention was\nthat ordinal numbers could be generated arbitrarily far, then so too,\nit seems, could the alephs.", "This raises the possibility of reinstating the centrality of the\nordinal numbers as the fundamental numbers even in the case of\ninfinite sets, thus making ordinality the foundation of cardinality\nfor all sets. In work after 1883, Cantor attempted to show that the\nalephs actually represent a scale of infinite cardinal number. For\ninstance, it is shown that the ordinal numbers are comparable, i.e.,\nfor any two ordinal numbers α, β, either \nα < β,\nα = β or \nα > β, a desirable, perhaps\nessential, property of counting numbers. Through this, comparability\ntherefore transfers to the alephs, and Cantor was able to give clear\nand appropriate arithmetical operations of addition, multiplication\nand exponentiation, generalising the corresponding notions for finite\ncollections, and the statement and proof of general laws concerning\nthese.", "In 1878, Cantor had put forward the hypothesis that there is no\ninfinite power between that of the natural numbers and the\ncontinuum. This became known as Cantor's Continuum Hypothesis\n(CH). With the adumbration of the number classes, CH takes on the form\nthat the continuum has the power of the second number-class, and with\nthe development of the aleph-scale, it assumes the form of a\nconjecture about the exponentiation operation in the generalised\ncardinal arithmetic, for it can be expressed in the form\n2ℵ0 =\nℵ1. The continuum problem more generally\nconstrued is really the problem of where the power of the continuum is\nin the scale of aleph numbers, and the generalised continuum\nhypothesis is the conjecture that taking the power set of an infinite\nset corresponds to moving up just one level in the aleph scale. For\nexample, in 1883, Cantor had assumed (without remark) that the set of\nall real functions has the size of the third number-class. Given the\nCH, this then becomes the conjecture that\n2ℵ1 = ℵ2.", "But adopting the aleph scale as a framework for infinite\ncardinality depends on significant assumptions. It is clear that any\ncollection in well-ordered form (given that it is represented by an\nordinal) must have an aleph-number representing its size, so clearly\nthe aleph-sequence represents the sizes (or powers as Cantor called\nthem) of all the well-ordered sets. However, can any set be put into\nwell-ordered form? A particular question of this form concerns the\ncontinuum itself: if the continuum is equivalent to the second\nnumber-class, then clearly it can be well-ordered, and indeed this is\na necessary condition for showing that the continuum is represented at\nall in the scale. But can it be well-ordered? More generally, to\nassume that any cardinality is represented in the scale of aleph\nnumbers is to assume in particular that any set can be\nwell-ordered. And to assume that the aleph-sequence is the scale of\ninfinite cardinal number is to assume at the very least that sets\ngenerally can be compared cardinally; i.e., that for any M, N, either\nM ≼ N or \nN ≼ M, COMP for short. But is this\ncorrect?", "When introducing the notion of well-ordering in 1883, Cantor\nexpressed his belief that the fact that any set\n(‘manifold’) can be well-ordered is ‘a law of\nthought [Denkgesetz]’, thus putting forward what for convenience\nwe can call the well-ordering hypothesis (WOH):", "\n The concept of well-ordered set reveals itself as\nfundamental for the theory of manifolds. That it is always possible to\narrange any well-defined set in the form of a well-ordered set is, it\nseems to me, a very basic law of thought, rich in consequences, and\nparticularly remarkable in virtue of its general validity. I will\nreturn to this in a later memoir. (Cantor 1883a or 1932: 169)\n", "Cantor says nothing about what it might mean to call the\nwell-ordering hypothesis a ‘law of thought’, and he never\ndid return to this question directly; however, in one form or another,\nthis claim is key. It could be that Cantor at this time considered the\nWOH as something like a logical\nprinciple.[16] This, however, is not\nparticularly clear, especially since the study of formal logic\nadequate for mathematical reasoning was only in its infancy, and the\nset concept itself was new and rather unclearly delimited. Another\nsuggestion is that well-orderability is intrinsic to the way that\n‘well-defined’ sets are either presented or conceived,\ne.g., that it is impossible to think of a collection's being a\nset without at the same time allowing that its elements can be\narranged ‘discretely’ in some way, or even that such\narrangement can be automatically deduced from the\n‘definition’. Thus, if one views sets as necessary for\nmathematics, and one holds that the concept of set itself necessarily\ninvolves the discrete arrangement of the elements of the set, then WOH\nmight appear necessary, too. But all of this is imprecise, not least\nbecause the notion of set itself was imprecise and imprecisely\nformulated. One clear implication of Cantor's remark is that he\nregards the WOH as something which does not require\nproof. Nonetheless, not long after he had stated this, Cantor clearly\nhad doubts both about the well-orderability of the continuum and about\ncardinal comparability (see Moore 1982: 44). All of\nthis suggested that the WOH, and the associated hypothesis that the\nalephs represent the scale of infinite cardinality, do require proof,\nand cannot just be taken as ‘definitional’. Thus, it\nseemed clear that the whole Cantorian project of erecting a scale of\ninfinite size depends at root on the correctness of the WOH.", "Work subsequent to 1884 suggests that Cantor felt the need to\nsupply arguments for well-ordering. For instance (Cantor 1895: 493) to\nshow that every infinite set T has a countable subset (and thus\nthat ℵ0 is the smallest cardinality), Cantor set\nout to prove the existence of a subset of T which is\nwell-ordered like the natural numbers. The key point to observe here\nis that Cantor felt it necessary to exhibit a well-ordered subset\nof T, and did not simply proceed by first assuming (by appeal\nto his ‘Denkgesetz’) that M can be\narranged in well-ordered form. He exhibits such a subset in the\nfollowing way:", "\n Proof. If one has removed from T a finite number of\n elements t1, t2,\n …, tν−1 according to some rule,\n then the possibility always remains of extracting a further\n element tν. The set {tν},\n in which ν denotes an arbitrary finite, cardinal number, is a\n subset of T with the cardinal number ℵ0,\n because {tν} ∼ {ν}. (Cantor 1895:\n 493)\n", "In 1932, Zermelo edited Cantor's collected papers (Cantor 1932),\nand commented on this particular proof as follows:", "\n The “proof” of Theorem A, which is purely intuitive\n and logically unsatisfactory, recalls the well-known primitive\n attempt to arrive at a well-ordering of a given set by successive\n removal of arbitrary elements. We arrive at a correct proof only\n when we start from an already well-ordered set, whose smallest\n transfinite initial segment in fact has the cardinal number\n ℵ0 sought. (Zermelo in Cantor 1932: 352)\n", "The second context in which an argument was given was an attempt\nby Cantor (in correspondence first with Hilbert and then Dedekind) to\nshow that every set must have an aleph-number as a\ncardinal.[17] What Cantor attempts to\nshow, in effect, is the following. Assume that Ω represents the\nsequence of all ordinal numbers, and assume (for a reductio argument)\nthat V is a ‘multiplicity’ which is not equivalent\nto any aleph. Then Cantor argues that Ω can be\n‘projected’ into V, in turn showing that V\nmust be what he calls an ‘inconsistent multiplicity’,\ni.e., not a legitimate set. It will follow that all sets have alephs\nas cardinals, since they will always be ‘exhausted’ by\nsuch a projection by some ordinal or other, in which case they will be\ncardinally equivalent to some ordinal\nnumber-class.[18] Zermelo's\ndismissal of this attempted proof is no surprise, given the comments\njust quoted. But he also comments further here exactly on this\n‘projection’:", "\n The weakness of the proof outlined lies precisely\nhere. It is not proved that the whole series of numbers Ω can be \n“projected into” any multiplicity V which does not\nhave an aleph as a cardinal number, but this is rather taken from a\nsomewhat vague “intuition”. Apparently Cantor imagines the\nnumbers of Ω successively and arbitrarily assigned to elements\nof V in such a way that every element of V is only used\nonce. Either this process must then come to an end, in that all\nelements of V are used up, in which case V would be then\nbe coordinated with an initial segment of the number series, and its\npower consequently an aleph, contrary to assumption; or V would\nremain inexhaustible and would then contain a component equivalent to\nthe whole of Ω, thus an inconsistent component. Here, the\nintuition of time [Zeitanschauung] is being applied to a process which\ngoes beyond all intuition, and a being [Wesen] supposed which can make\nsuccessive arbitrary choices and thereby define a subset V′\nof V which is not definable by the conditions given. (Zermelo in Cantor 1932:\n 451)[19]\n", "If it really is ‘successive’ selection which is relied\non, then it seems that one must be assuming a subset of instants of\ntime which is well-ordered and which forms a base ordering from which\nthe ‘successive’ selections are made. In short, what is\nreally presupposed is a well-ordered subset of temporal instants which\nacts as the basis for a recursive definition. Even in the case of\ncountable subsets, if the ‘process’ is actually to come to\na conclusion, the ‘being’ presupposed would presumably\nhave to be able to distinguish a (countably) infinite, discrete\nsequence of instants within a finite time, and this assumption is, as\nis well-known, a notoriously controversial one. In the general case,\nthe position is actually worse, for here the question of the\nwell-orderability of the given set depends at the very least on the\nexistence of a well-ordered subset of temporal instants of arbitrarily\nhigh infinite cardinality. This appears to go against the assumption\nthat time is an ordinary continuum, i.e., of cardinality\n2ℵ0, unless of course the power set of\nthe natural numbers itself is too ‘big’ to be counted by\nany ordinal, in which case much of the point of the argument would be\nlost, for one of its aims is presumably to show that the power of the\ncontinuum is somewhere in the\naleph-sequence.[20]", "Part of what is at issue here, at least implicitly, is what\nconstitutes a proof. It seems obvious that if a set is non-empty, then\nit must be possible to ‘choose’ an element from it (i.e.,\nthere must exist an element in it). Indeed, the obviousness of this is\nenshrined in the modern logical calculus by the way the inference\nprinciple of Existential Instantiation (EI) usually works: from\n∃xPx one assumes Pc, where\n‘c’ is a new constant, and reasons on that basis;\nwhatever can be inferred from\nP(c) (as long as it does not itself contain the new constant\n‘c’) is then taken to be inferable from ∃xPx\nalone. Furthermore, it is clear how this extends to finite sets (or\nfinite extensions) by stringing together successive inferential\nsteps. But how can such an inferential procedure be extended to\ninfinite sets, if at all?", "Some evidence of the centrality of WOH is provided by Problem 1 on\nHilbert's list of mathematical problems in his famous lecture to\nthe International Congress of Mathematicians in Paris in 1900. He\nnotes Cantor's conviction of the correctness of CH, and its\n‘great probability’, then goes on to mention another\n‘remarkable assertion’ of Cantor's, namely his\nbelief that the continuum, although not (in its natural order) in\nwell-ordered form, can be rearranged as a well-ordered set. However,\nRussell, writing at roughly the same time, expressed doubts about\nprecisely this:", "\n Cantor assumes as an axiom that every class is the field of some\n well-ordered series, and deduces that all cardinals can be\n correlated with ordinals …. This assumption seems to me\n unwarranted, especially in view of the fact that no one has yet\n succeeded in arranging a class of 2α0\n terms in a well-ordered series. (Russell 1903: 322–323)\n", "He goes on:", "\n We do not know that of any two different cardinal numbers one\nmust be the greater, and it may be that\n2α0 is neither greater nor less that\nα1 and α2 and their successors,\nwhich may be called well-ordered cardinals because they apply to\nwell-ordered series. (Russell 1903:\n 323)[21]\n", "And recall that, at the International Congress of Mathematicians in\nHeidelberg in 1904, König had given an apparently convincing\nproof that the continuum cannot be an aleph. König's\nargument, as we know, turned out to contain fatal flaws, but in any\ncase, the confusion it exhibits is\ninstructive.[22]", "In short, the clear impression in the immediate period leading up\nto Zermelo's work was both that only the WOH would provide a\nsolid foundation on which to build a reasonable notion of infinite\ncardinal number as a proper framework for tackling CH, and that WOH\nrequires justification, that it must become, in effect, the WOT, the\nWO-Theorem. In short, establishing the WOT was closely bound up with\nthe clarification of what it is to count as a set.", "Zermelo's approach to the well-ordering problem took place in\nthree stages. He published a proof of WOT in 1904 (Zermelo 1904, an\nextract from a letter to Hilbert), where he first introduced the\n‘choice’ principle, a principle designed (despite the name\nit has come to bear) to move away from the Cantorian\n‘choosing’ arguments which almost universally preceded\nZermelo's work, and which postulates that arbitrary\n‘choices’ have already been made. This paper produced an\noutcry, to which Zermelo responded by producing a new proof \n(1908a), which again uses the choice principle, but this time\nin a somewhat different form and expressed now explicitly as an\naxiom. The first three pages of this paper give the new proof; this\nwas then followed by seventeen pages which reply in great detail to\nmany of the objections raised against the first proof. These consisted\nin objections to the choice principle itself, and also objections to\nthe unclarity of the underlying assumptions about, and operation with,\nsets used in the proof. This paper was followed just two months later\nby Zermelo's official axiomatisation (1908b), an\naxiomatisation which to a large degree was prefigured in the paper\n(1908a).", "Zermelo's 1904 proof can be briefly described.", "As Zermelo points out (p. 516 of his paper), the WOT establishes a\nfirm foundation for the theory of infinite cardinality; in particular,\nit shows, he says, that every set (‘for which the totality of\nits subsets etc. has a sense’) can be considered as a\nwell-ordered set ‘and its power considered as an\naleph’. Later work of Hartogs (see Hartogs 1915) showed that,\nnot only does WOT imply COMP as Zermelo shows, but that COMP itself\nimplies WOT, and thus in turn Zermelo's choice principle. Thus,\nit is not just COMP which is necessary for a reasonable theory of\ninfinite cardinality, but WOT itself. Despite Zermelo's\nendorsement here, the correctness of the hypothesis that the scale of\naleph numbers represents all cardinals (AH, for short) is a more\ncomplicated matter, for it involves the claim that every set is\nactually equivalent to an initial segment of the ordinals, and not\njust well-orderable. In axiomatic frameworks for sets, therefore, the\ntruth of AH depends very much on which ordinals are present as sets in\nthe system.", "The subsequent work showing the independence of AC from the other\naxioms of set theory vindicates Zermelo's pioneering work; in\nthis respect, it puts Zermelo's revelation of the choice\nprinciple in a similar position as that which Hilbert ascribes to the\nParallel Postulate in Euclid's work. Hilbert claims that Euclid\nmust have realised that to establish certain ‘obvious’\nfacts about triangles, rectangles etc., an entirely new axiom\n(Euclid's Parallel Postulate) was necessary, and moreover that\nGauß was the first mathematician ‘for 2100 years’ to\nsee that Euclid had been right (see Hallett and Majer 2004:261–263 and 343–345).\nThis ‘pragmatic attitude’, which is on display in\nZermelo's second paper on well-ordering from 1908, became, in\neffect, the reigning attitude towards the choice principle: If certain\nproblems are to be solved, then the choice principle must be\nadopted. In 1908, Zermelo brings out this parallel explicitly:", "\n Banishing fundamental facts or problems from science merely\n because they cannot be dealt with by means of certain prescribed\n principles would be like forbidding the further extension of the\n theory of parallels in geometry because the axiom upon which this\n theory rests has been shown to be unprovable. (Zermelo 1908a:\n 115)\n", "Zermelo does not in 1904 call the choice principle an axiom; it\nis, rather, designated a ‘logical principle’. What Zermelo\nhas to say by way of an explanation is very short:", "\n This logical principle cannot, to be sure, be reduced to a still\n simpler one, but it is applied without hesitation everywhere in\n mathematical deduction. (Zermelo 1904: 516)\n", "It is not clear from this whether he thinks of the choice principle\nas a ‘law of thought’, as the term ‘logical\nprinciple’ might suggest, or whether he thinks it is just\nintrinsic to mathematical reasoning whenever sets are involved, a\nposition suggested by the reference to its application\n‘everywhere in mathematical deduction’. By the time of his\nsecond well-ordering paper of 1908, Zermelo seems to have moved away\nfrom the idea of AC as a ‘logical’ principle in the sense\nof a logical law, and appears to put the emphasis more on the view of\nit as intrinsic to the subject matter; there it appears as Axiom IV,\nand, as we saw, Axiom VI of Zermelo\n 1908b.[25]", "There were three central objections.", "Let us briefly deal with these. ", "(a) The objections to the choice principle were of two kinds. The\nmain objection was put forward by Borel in 1905 in\nthe Mathematische Annalen (Borel 1905), the journal which\npublished Zermelo's paper, and it is also widely discussed in\ncorrespondence between some leading French mathematicians, and also\npublished in that year in the same Journal (see Hadamard et\nal. 1905). The objection is basically that Zermelo's principle fails\nto specify a ‘law’ or ‘rule’ by which the\nchoices are effected; in other words, the covering used is not\nexplicitly defined, which means that the resulting well-ordering is\nnot explicitly defined either. In a letter to Borel, Hadamard makes it\nclear that the opposition in question is really that between the\nassumption of the existence of an object which is fully described, and\nof the existence of an object which is not fully described (see\nHadamard et al. 1905, esp. 262). In his reply, Zermelo remarks that\nthe inability to describe the choices is why the choice principle is\nin effect an axiom, which has to be added to the other principles. In\neffect, the position is that if one wants to do certain things which,\ne.g., rely on the WOT, then the choice principle is indispensable. His\nposition, to repeat, is like the one that Euclidean geometry takes\ntowards parallels. ", " (b) An objection to the choice principle was also put forward by\nPeano. This objection seems to be that since the choice principle\ncannot be proved ‘syllogistically’ (i.e., from the\nprinciples of Peano's Formulario), then it has to be rejected (see\nPeano 1906). (Peano does think, however, that finite versions of the\nchoice principle are provable, relying essentially on repeated\napplications of a version for classes of the basic logical principle\nEI mentioned above (§2.2.1).\nZermelo's reply is the following. Axiom systems like Peano's are\nconstructed so as to be adequate for mathematics; but how does one go\nabout selecting the ‘basic principles’ required? One\ncannot assemble a complete list of adequate principles, says Zermelo,\nwithout careful inspection of actual mathematics and thereby a careful\nassessment of what principles are actually necessary to such a list,\nand such inspection would show that the choice principle is surely one\nsuch; in other words, a selection of principles such as Peano's is\nvery much a post hoc procedure. The reply to Peano is of a piece with\nthe reply to Borel, and recalls strongly the invocation in Zermelo\n(1908b: 261), that it is necessary to distill principles from the\nactual operation with sets. He supports his claim that the choice\nprinciple is necessary by a list of seven problems which ‘in my\nopinion, could not be dealt with at all without the principle of\nchoice’ (Zermelo 1908a:\n 113).[26]\n In particular he points out that the\nprinciple is indispensable for any reasonable theory of infinite\ncardinality, for only it guarantees the right results for infinite\nunions/sums, and in addition is vital for making sense of the very\ndefinition of infinite product. That Peano cannot establish the choice\nprinciple from his principles, says Zermelo, strongly suggests that\nhis list of principles is not ‘complete’ (Zermelo 1908a:\n112). ", " (c) Another line of objection, represented in different ways by\nBernstein (Bernstein 1905), Jourdain (Jourdain 1904, 1905b) and Schoenflies (Schoenflies 1905), was that Zermelo's general\noperation with sets in his proof was dangerous and flirts with\nparadox. (See also Hallett 1984, 176–182.) In its imprecise form, the objection is that Zermelo is less\nthan explicit about the principles he uses in 1904, and that he\nemploys procedures which are reminiscent of those used crucially in\nthe generation of the Burali-Forti antinomy, e.g., in showing that if\nthe set\nLγ ≠ M, then it can be extended. \n(What if Lγ is already the collection W?) ", " Zermelo's reply is dismissive, but there is something to the\ncriticism. Certainly Zermelo's 1904 proof attempts to show that WOT\ncan be proved while by-passing the general abstract theory of\nwell-ordering and its association with the Cantorian ordinals, and\ntherefore also bypassing the ‘the set W’ (as it was\nwidely known) of all Cantorian ordinals (denoted ‘Ω’\nby Cantor), and consequently the Burali-Forti antinomy. However,\nwhatever Zermelo's intention, there is no explicit attempt to exclude\nthe possibility that Lγ = W and thus the\nsuggestion that antinomy might threaten. Of course, Zermelo, referring\nto critics who ‘base their objections upon the\n“Burali-Forti antinomy” ’, declares that this\nantinomy ‘is without significance for my point of view, since\nthe principles I employed exclude the existence of a set W [of\nall ordinals]’ (Zermelo 1908a: 128, with earlier hints on\n118–119) that the real problem is with the ‘more\nelementary’ Russell antinomy. It is also true that at the end of\nthe 1904 paper, Zermelo states that the argument holds for those\nsets M ‘for which the totality of subsets, and so on, is\nmeaningful’, which, in retrospect is clearly a hint at important\nrestrictions on set formation. Even so, Zermelo's attitude is\nunfair. It could be that the remark about ‘the totality of\nsubsets etc.’ is an indirect reference to difficulties with the\ncomprehension principle, but even so the principle is not repudiated\nexplicitly in the 1904 paper, neither does Zermelo put in its place\nanother principle for the conversion of properties to sets, which is\nwhat the Aussonderungsaxiom of the 1908 axiomatisation\ndoes. Moreover, he does not say that the existence principles on which\nthe proof is based are the only set existence principles, and he does\nnot divorce the proof of the theorem from the Cantorian assumptions\nabout well-ordering and ordinals. Indeed, Zermelo assumes that\n‘every set can be well-ordered’ is equivalent to the\nCantorian ‘every cardinality is an aleph’ (Zermelo 1904:\n141). And despite his later claim (Zermelo 1908a: 119), he does appear\nto use the ordinals and the informal theory of well-ordering in his\ndefinition of γ-sets, where a γ-set is ‘any\nwell-ordered Mγ…’, without any\nspecification of how ‘well-ordered set’ is to be\ndefined. What assurance is there that this can all be reduced to\nZermelo's principles? One important point here is that it had not yet\nbeen shown that all the usual apparatus of set-theoretic mathematics\n(relations, ordering relations, functions, cardinal equivalence\nfunctions, order-isomorphisms, etc.) could be reduced to a few simple\nprinciples of set existence. All of this was to come in the wake of\nZermelo's axiomatisation, and there is little doubt that this line of\ncriticism greatly influenced the shape of the second proof given in\n1908, of which a little more below. ", " (d) The last line of objection was to a general feature of the\n1904 proof, which was not changed in the second proof, namely the use\nof what became known as ‘impredicative definition’. An\nimpredicative definition is one which defines an object a by a\nproperty A which itself involves reference, either direct or\nindirect, to all the things with that property, and this must, of\ncourse, include a itself. There is a sense, then, in which the\ndefinition of a involves a circle. Both Russell and\nPoincaré became greatly exercised about this form of\ndefinition, and saw the circle involved as being\n‘vicious’, responsible for all the paradoxes. If one\nthinks of definitions as like construction principles, then indeed\nthey are illegitimate. But if one thinks of them rather as ways of\nsingling out things which are already taken to exist, then they are\nnot illegitimate. In this respect, Zermelo endorses Hilbert's view of\nexistence. To show that some particular thing ‘exists’ is\nto show that it is in 𝔅, i.e., to show by means of a finite\nproof from the axioms that it exists in 𝔅. What\n‘exists’, then, is really a matter of what the axioms,\ntaken as a whole, determine. If the separation, power set and choice\nprinciples are axioms, then for a given M in the domain, there\nwill be choice functions/sets on the subsets of M, consequently\nwell-orderings, and so forth; if these principles are not included as\naxioms, then such demonstrations of existence will not be\nforthcoming. From this point of view, defining within the language\ndeployed is much more like what Zermelo calls\n‘determination’, since definitions, although in a certain\nsense arbitrary, have to be supported by existence proofs, and of\ncourse in general it will turn out that a given extension can be\npicked out by several, distinct ‘determinations’. In\nshort, Zermelo's view is that definitions pick out (or determine)\nobjects from among the others in the domain being axiomatised; they\nare not themselves responsible for showing their existence. In\nthe end, the existence of a domain 𝔅 has to be guaranteed by a\nconsistency proof for the collection of axioms. Precisely this view\nabout impredicative definitions was put forward in Ramsey (1926:\n368–369) and then later in Gödel's 1944 essay on Russell's\nmathematical logic as part of his analysis of the various things which\ncould be meant by Russell's ambiguously stated Vicious Circle\nPrinciple. (See Gödel 1944: 136, 127–128 of the reprinting\nin Gödel 1990. See also Hadamard's letters in Hadamard et\nal. 1905.) To support his view, Zermelo points out that impredicative\ndefinitions are taken as standard in established mathematics,\nparticularly in the way that the least upper bound is defined; witness\nthe Cauchy proof of the Fundamental Theorem of Algebra. Once again,\nZermelo's reply is coloured by the principle of looking at the actual\npractice of mathematics.[27] ", "As mentioned, Zermelo published a second proof of the WOT,\nsubmitted to Mathematische Annalen just two weeks before the\nsubmission of his ‘official’ axiomatisation, and published\nin the same volume as that axiomatisation. This proof is too elaborate\nto be described here; a much fuller description can be found in\nHallett (2010b: 94–103), but some brief remarks about it must be\nmade nevertheless. Recall that the purpose of the proof was, in large\npart, to reply to (some of) the criticisms raised in objection to the\n1904 proof, and not least to clarify the status of the choice\nprinciple. ", " Suppose M is the set given, and suppose (using Zermelo's\nnotation) that 𝔘M is the set of its subsets\n(‘Untermengen’). The basic procedure in the 1904 proof was\nto single out certain subsets of M and to show that these can\nin effect be ‘chained’ together, starting from modest\nbeginnings (and using the choice function γ); thus we have\n{m1}, where \nm1 = γ(M), \n{m1, m2}, where\nagain \nm1 = γ(M)\nand \nm2 = γ(M −\n{m1}), and so on. In this way, the proof\nshows that one can ‘build up’ to the whole of M\nitself.[28] This\n‘build-up’ is one of the things which provoked scepticism,\nand particularly the step which shows that M itself must be\nembraced by it. In the 1908 proof, the basic idea is to start\nfrom M itself, and consider ‘cutting down’ by the\nelement ‘chosen’ by the choice principle, instead of\nbuilding up. Thus, if one accepts that if M is a legitimate\nset, then so is 𝔘M, and there is not the same danger of\nextending into inconsistent sets, not even the appearance of\ndanger. Again the key thing is to show that the sets defined are in\nfact ‘chained’ together and are in the right way\nexhaustive. ", " In the 1904 proof, there are points where it looks as if Zermelo\nis appealing to arbitrary well-orderings, and thus indirectly\narbitrary ordinals. This is avoided in the 1908 proof (as it could\nhave been in the 1904 proof) by focusing on the particular\n‘chain’ which the proof gives rise to. It is this chain\nitself which exhibits the well-ordering. ", " In the modern understanding of set theory, to show that there is a\nwell-ordering on M would be to show that there is a set of\nordered pairs of members of M which is a relation satisfying\nthe right properties of a well-ordering relation over M. It is\nwell to remember that Zermelo's task in 1908 was constrained in that he had to\nestablish the existence of a well-ordering using only the\nset-theoretical material available to him. This material did not\ninvolve the general notion of ordinal and cardinal numbers, not even\nthe general notions of relation and function. What Zermelo used,\ntherefore, was the particular relation\na ⊆ b of being a subset,\nand it is important to observe that the chain produced is\nordered by this relation. ", " Why would one expect this latter to work? Well, the chain produced\nis naturally a subset well-ordering, for it is both linear and also\nsuch that the intersection of arbitrary elements of members of the\nchain is itself a member of the chain, and thus there is a natural\nsubset-least element for each subset of members of the chain. But the\nwider explanation is hinted at towards the end of Zermelo's\nproof. Suppose a set M is (speaking informally) de facto\nwell-ordered by an ordering relation ≺. Call the set\nℜ≼(a) = {x\n∈ M : a ≼ x} the\n‘remainder [Rest]’ determined by a and the ordering\n≺. Consider now the set of ‘remainders’ given by\nthis ordering, i.e.,\n{ℜ≼(x) : x\n∈ M}. This set is in fact well-ordered by reverse\ninclusion, where the successor remainder to\nℜ≼(a) is just the remainder determined\nby a's successor a′ under ≺, and where\nintersections are taken at the limit elements (the intersection of a\nset of remainders is again a remainder). But not only is this set\nwell-ordered by reverse inclusion, the ordering is isomorphic to the\nordering ≺ on M, that is: ", "\na ≺ b if and only if\nℜ≼(b) ⊂\nℜ≼(a).\n", "Zermelo's 1908 construction is now meant to define a\n‘remainder set’ directly without detour through some\n≺; the resultant inclusion ordering is then\n‘mirrored’ on M. The key thing is to show that the\nchain of subsets of M picked out really matches M\nitself. But if there were some element a\n∈ M which did not correspond to a remainder\nℜ≼(a), then it must be possible to use\nthe choice function to ‘squeeze’ another remainder into\nthe chain, which would contradict the assumption that all the sets\nwith the appropriate definition are already in the\nchain.[29] We\nhave spoken of functions and relations here. But in fact Zermelo\navoids such talk. He defines M as being\n‘well-ordered’ when each element in M\n‘corresponds’ uniquely to such a ‘remainder’\n(Zermelo 1908a: 111). This shows, says Zermelo, that the theory of\nwell-ordering rests ‘exclusively upon the elementary notions of\nset theory’, and that ‘the uninformed are only too prone\nto look for some mystical meaning behind Cantor's relation\na ≺ b’ (Zermelo 1908a). ", " One can be considerably more precise about the relation between\norderings on M and ‘remainder inclusion orderings’\nin 𝔘M. Much of this was worked out in Hessenberg (1906), and\nwas therefore known to Zermelo (Zermelo and Hessenberg were in regular\ncontact), and simplified greatly by Kuratowski in the 1920s. We will\nhave reason to refer to Kuratowski briefly in the next\nsection.[30] ", " What about the choice principle? In 1904, this is framed in effect\nas a choice function, whose domain is the non-empty subsets\non M. But in 1908, Zermelo frames it differently: ", " Axiom IV. A set S that can be decomposed into a\nset of disjoint parts A, B, C, …, each\ncontaining at least one element, possesses at least one\nsubset S1 having exactly one element in common with\neach of the parts A, B, C, …\nconsidered. (Zermelo 1908a: 110)\n\n", "In other words, the choice principle is now cast in a set form, and\nnot in the function form of 1904. ", " In the 1908 axiomatisation, the axiom is stated in much the same\nway, but is called there (though not in the well-ordering paper) the\n‘Axiom of Choice’. However, the 1908 paper on WOT does say\nthat the axiom provides a set (the S1) of\n‘simultaneous choices’, to distinguish them from the\n‘successive choices’ used in the pre-Zermelo versions of\nwell-ordering. It is to be noted that in 1921, Zermelo wrote to\nFraenkel in partial repudiation of the designation ‘Axiom of\nChoice’, saying that ‘there is no sense in which my theory\ndeals with a real\n“choice” ’.[31]", "What axioms governing set-existence does Zermelo rely on in Zermelo\n(1908a)? At the start of the paper, Zermelo list two\n‘postulates’ that he explicitly depends on, a version of\nthe separation axiom, and the power set axiom. Later on he lists Axiom\nIV, which, as noted, asserts the existence of a choice set for any set\nof disjoint non-empty sets. In addition to this, Zermelo makes use of\nthe existence of various elementary sets, though he doesn't say\nexactly which principles he relies on. In the axiomatisation which\nfollows two weeks later, Zermelo adopts all these axioms, but adds\nclarification about the elementary sets. He also adds the Axiom of Infinity, to\nguarantee that there are infinite sets, and the Axiom of\nExtensionality, which codifies the assumption that sets are really\ndetermined by their members, and not by the accidental way in which\nthese members are selected. In addition, as we have noted,\nhe now calls the Axiom of Choice by this name. " ], "subsection_title": "2.2 The Well-Ordering Problem and the Well-Ordering Theorem" } ] }, { "main_content": [ "Zermelo's system, although it forms the root of all modern\naxiomatisations of set theory, initially faced various\ndifficulties. These were: ", "The problems concerning the Axiom of Choice were discussed above;\nwe now discuss the difficulties with the formulation of Separation and\nthose of ‘completeness’." ], "section_title": "3. The Major Problems with Zermelo's System", "subsections": [ { "content": [ "The problem with the Axiom of Separation is not with the\nobviousness of the principle; it seems straightforward to accept that\nif one has a set of objects, one can separate off a subclass of this\nset by specifying a property, and treat this in turn as a set. The\nquestion here is a subtler one, namely that of how to formulate this\nprinciple as an axiom. What means of ‘separating off’ are\nto be accepted? What are allowable as the properties? As a matter of\npractice, we use a language to state the properties, and in informal\nmathematics, this is a mixture of natural language and special\nmathematical language. The Richard Paradox (see Richard 1905 and also\nthe papers of Poincaré 1905, 1906a,b) makes it clear that one\nhas to be careful when defining properties, and that the unregulated\nuse of ‘ordinary language’ can lead to unexpected\ndifficulties.", "Zermelo's answer to this, in moving from the system of the second\nwell-ordering paper to the axiomatisation, is to try specifying what\nproperties are to be allowed. He calls the properties to be allowed\n‘definite properties’\n(‘Klassenaussagen’ or ‘propositional\nfunctions’), and states:", "\n A question or assertion 𝔈 is said to be\n“definite” if the fundamental relations of the domain, by\nmeans of the axioms and the universally valid laws of logic, determine\nwithout arbitrariness whether it holds or not. Likewise a\n“propositional function” 𝔈(x), in which the\nvariable term x ranges over all individuals of a\nclass 𝔎, is said to be “definite” if it is definite\nfor each single individual x of the class 𝔎. Thus the\nquestion whether\na ε b or not is always\ndefinite, as is the question whether M\n⊆ N or not.\n", "Zermelo asserts that this shows that paradoxes involving the\nnotions of definability (e.g., Richard's) or denotation (König's)\nare avoided, implying that what is crucial is the restriction to the\n‘fundamental relations of the domain’ (so, ε,\n=).", "The basic problem is that it is not explained by Zermelo what the\nprecise route is from the fundamental relations ε and = to a\ngiven ‘definite property’; it is this which gives rise to\na general doubt that the Separation Axiom is not, in fact, a safe\nreplacement for the comprehension principle (see Fraenkel 1927:\n104). This plays into the hands of those, who, like Poincaré,\nconsider adoption of the Separation Axiom as insufficiently radical in\nthe search for a solution to the paradoxes. Poincaré\nwrites:", "\n Mr. Zermelo does not allow himself to consider the set of all the\nobjects which satisfy a certain condition because it seems to him that\nthis set is never closed; that it will always be possible to introduce\nnew objects. On the other hand, he has no scruple in speaking of the\nset of objects which are part of a certain Menge M and which\nalso satisfy a certain condition. It seems to him that one cannot\npossess a Menge without possessing at the same time all its\nelements. Among these elements, he will choose those which satisfy a\ngiven condition, and will be able to make this choice very calmly,\nwithout fear of being disturbed by the introduction of new and\nunforeseen elements, since he already has all these elements in his\nhands. By positing beforehand this Menge M, he has erected an\nenclosing wall which keeps out the intruders who could come from\nwithout. But he does not query whether there could be intruders from\nwithin whom he enclosed inside his wall. (Poincaré 1909: 477;\np. 59 of the English translation)\n", "Here, Poincaré is referring indirectly to his view that the\nparadoxes are due to impredicative set formation, and this of course\nwill be still be possible even with the adoption of the Axiom of\nSeparation.", "The problem of the lack of clarity in Zermelo's account was\naddressed by Weyl in 1910 (Weyl 1910; see especially p. 113) and then\nagain by Skolem in 1922 (Skolem 1923, p. 139 of the reprint). What\nWeyl and Skolem both proposed, in effect, is that the question of what\n‘definite properties’ are can be solved by taking these to\nbe the properties expressed by 1-place predicate formulas in what we\nnow call first-order logic. In effect, we thus have a recursive\ndefinition which makes the definite properties completely transparent\nby giving each time the precise route from ε, = to the\ndefinite property in question. This does not deal with all aspects of\nPoincaré's worry, but it does make it quite clear what definite\nproperties are, and it does also accord with Zermelo's view that the\nrelations =, ε are at root the only ones\nused.[32]", "Fraenkel (1922 and later) took a different approach with a rather\ncomplicated direct axiomatisation of the notion of definite property,\nusing recursive generation from the basic properties giving a notion\nwhich appears to be a subset of the recursively defined first-order\nproperties.", "Zermelo accepted none of these approaches, for two reasons. First,\nhe thought that the recursive definitions involved make direct use of\nthe notion of finite number (a fact pointed out by Weyl 1910), which\nit ought to be the business of set theory to explain, not to\npresuppose. Secondly, he became aware that using essentially a\nfirst-order notion condemns the axiomatic system to countable models,\nthe fundamental fact pointed out in Skolem (1923). His own approach\nwas, first, to give a different kind of axiomatisation (see Zermelo\n1929), and then to use (in Zermelo 1930) an essentially second-order\nnotion in characterising the axiom of\nseparation.[33]" ], "subsection_title": "3.1 Separation" }, { "content": [ "There were also problems with the completeness of Zermelo's theory,\nsince there were important theoretical matters with which Zermelo does\nnot deal, either for want of appropriate definitions showing how\ncertain constructions can be represented in a pure theory of sets, or\nbecause the axioms set out in Zermelo's system are not strong\nenough.", "Zermelo gives no obvious way of representing much of\n‘ordinary mathematics’, yet it is clear from his opening\nremarks that he regards the task of the theory of sets to stand as the\nfundamental theory which should ‘investigate mathematically the\nfundamental notions “number”, “order”, and\n“function” ’. \n(See §1.)", "The first obvious question concerns the representation of the\nordinary number systems. The natural numbers are represented by\nZermelo as by ∅, {∅}, {{∅}}, …, and the Axiom\nof Infinity gives us a set of these. Moreover, it seems that, since\nboth the set of natural numbers and the power set axiom are available,\nthere are enough sets to represent the rationals and the reals,\nfunctions on reals etc. What are missing, though, are the details: how\nexactly does one represent the right equivalence classes, sequences\netc.? And assuming that one could define the real numbers, how does\none characterise the field operations on them? In addition, as\nmentioned previously, Zermelo has no natural way of representing\neither the general notions of relation or of function. This means that\nhis presentation of set theory has no natural way of representing\nthose parts of mathematics (like real analysis) in which the general\nnotion of function plays a fundamental part.", "A further difficulty is that the lack of the notion of function\nmakes the general theory of the comparison of sets by size (or indeed\nby order) cumbersome. Zermelo does develop a way of expressing, for\ndisjoint sets a, b, that a is of the same size\nas b, by first defining a ‘product’ of two disjoint\nsets, and then isolating a set of unordered pairs (a certain subset of\nthis product) which ‘maps’ one of the sets one-to-one onto\nthe other. But this is insufficiently general, and does not in any\ncase indicate any way to introduce ‘the’ size\nof a. Russell's method (defining the cardinality of M as\nthe set card(M) = {N : N\n∼ M} (where ‘∼’ means\n‘cardinally equivalent to’) is clearly inappropriate,\nsince with a set a = {b},\ncard(a) (which should be the cardinal number 1) is as big as\nthe universe, and the union set of 1 would indeed be the\nuniversal ‘set’. Over and above this, there is the more\nspecific problem of defining the aleph numbers.", "The second major difficulty is along the same lines, concerning,\nnot functions, but relations, and thus ordering relations and ordinal\nnumbers. As we have seen\n(in §2.2.4), Zermelo has the\nbeginnings of an answer to this in his second proof of the WOT, for\nthis uses a theory of subset-orderings to represent the underlying\nordering of a set. It turns out that the method given in this\nparticular case suggests the right way to capture the general\nnotion.", "Zermelo's idea (1908a) was pursued by Kuratowski in the 1920s,\nthereby generalising and systematising work, not just of Zermelo, but\nof Hessenberg and Hausdorff too, giving a simple set of necessary and\nsufficient conditions for a subset ordering to represent a linear\nordering. He also argues forcefully that it is in fact undesirable for\nset theory to go beyond this and present a general theory of ordinal\nnumbers:", "\n In reasoning with transfinite numbers one implicitly uses an\n axiom asserting their existence; but it is desirable both from the\n logical and mathematical point of view to pare down the system of\n axioms employed in demonstrations. Besides, this reduction will free\n such reasoning from a foreign element, which increases its\n æsthetic value. (Kuratowski 1922: 77)\n", "The assumption here is clearly that the (transfinite) numbers will\nhave to be added to set theory as new primitives. Kuratowski however\nundertakes to prove that the transfinite numbers can be dispensed with\nfor a significant class of \n applications.[34]\n Application of the ordinal numbers in\nanalysis, topology, etc. often focuses on some process of definition\nby transfinite recursion over these numbers. Kuratowski succeeds in\nshowing that in a significant class of cases of this kind, the\nordinals can be avoided by using purely set-theoretic methods which\nare reproducible in Zermelo's system. As he notes:", "\n From the viewpoint of Zermelo's axiomatic theory of sets, one can\nsay that the method explained here allows us to deduce theorems of a\ncertain well-determined general type directly from Zermelo's axioms,\nthat is to say, without the introduction of any independent,\nsupplementary axiom about the existence of transfinite\nnumbers. (Kuratowski 1922: \n 77)[35]\n", "It is in this reductionist context that Kuratowski develops his\nvery general theory of maximal inclusion orderings, which shows, in\neffect, that all orderings on a can really be represented as\ninclusion orderings on appropriate subsets of the power set\nof a, thus reducing ordering to Zermelo's primitive relation\nε.", "One immediate, and quite remarkable, result of this work is that it\nshows how one can define the general notions of relation and function\nin purely set-theoretic terms. It had long been recognised that\nrelations/functions can be conceived as sets of ordered pairs, and\nKuratowski's work now shows how to define the ordered pair\nprimitively. The ordered pair (a, b) can be considered\ninformally as the unordered pair M = {a, b},\ntogether with an ordering relation a < b. Suppose\nthis relation is treated now via the theory of inclusion chains. The\nonly maximal inclusion chains in the power set of M are\n{∅, {a}, {a, b}} and {∅,\n{b}, {a, b}}. Using\nKuratowski's definition of the ordering ‘<’ derived\nfrom a maximal inclusion chain, these chains must then correspond to\nthe orderings a < b and b < a\non {a, b} respectively. If\n∅ is ignored, the resulting chain {{a},\n{a, b}} is thus associated with the\nrelation a < b, and so with the ordered set (pair)\n(a, b). It is then quite natural to define\n(a, b) as {{a},\n{a, b}} (see Kuratowski 1921: 170–171). One\ncan now define the product a\n× b of a and b as the set of all\nordered pairs whose first member is in a and whose second\nmember is in b; relations on a can now be treated as\nsubsets of a × a, and\nfunctions from a to b as certain subsets\nof a × b. Thus, many of\nthe representational problems faced by Zermelo's theory are solved at\na stroke by Kuratowski's work, building as it does on Zermelo's\nown.", "But there was a problem concerning cardinality which is independent\nof the problem of definitional reduction. It was pointed out by both\nFraenkel and Skolem in the early 1920s that Zermelo's theory cannot\nprovide an adequate account of cardinality. The axiom of infinity and\nthe power set axiom together allow the creation of sets of\ncardinality ≥ ℵn\nfor each natural number n, but this (in the absence of a result\nshowing that 2ℵ0 >\nℵn for every natural number n) is not\nenough to guarantee a set whose power is ≥\nℵω, and a set of power\nℵω is a natural next step (in the Cantorian\ntheory) after those of power ℵn. Fraenkel\nproposed a remedy to this (as did Skolem independently) by proposing\nwhat was called the Ersetzungsaxiom, the Axiom of Replacement (see\nFraenkel 1922: 231 and Skolem 1923: 225–226). This says,\nroughly, that the ‘functional image’ of a set must itself\nbe a set, thus if a is a set,\nthen {F(x) : x\n∈ a} must also be a set, where\n‘F’ represents a functional correspondence. Such an\naxiom is certainly sufficient; assume that a0 is the\nset of natural numbers {0, 1, 2, …}, and now assume that to\neach number n is associated an an with\npower ℵn. Then according to the replacement\naxiom, a =\n{a0, a1, a2,\n…} must be a set, too. This set is countable, of course, but\n(assuming that the an are all disjoint) the union set of a must have cardinality at\nleast ℵω.", "The main difficulty with the Replacement Axiom is that of how to\nformulate the notion of a functional correspondence. This was not\nsolved satisfactorily by Fraenkel, but the Weyl/Skolem solution works\nhere, too: a functional correspondence is (in effect) just any\nfirst-order 2-place predicate ϕ(x, y) which\nsatisfies the condition of uniqueness,\ni.e., ∀x, y, z{[ϕ(x, y)\n∧ ϕ(x, z)] → y = z}.\nWith this solution, the Replacement Axiom will be (as required)\nstronger than Zermelo's original Separation Axiom and indeed can\nreplace it; however, in Fraenkel's system, one can prove his version\nof the Replacement Axiom from his version of the Separation Axiom,\nwhich shows that his separate definition of function is not\nsufficiently strong. (For details, see Hallett 1984:\n282–286.)", "Zermelo initially had doubts about the Replacement Axiom (see the\nletter to Fraenkel from 1922 published in Ebbinghaus 2007: 137), but\nhe eventually accepted it, and a form of it was included in his new\naxiomatisation published in 1930 (Zermelo 1930). Skolem's formulation\nis the one usually adopted, though it should be noted that von\nNeumann's own formulation is rather different and indeed\nstronger.[36]", "Although Kuratowski's work solved many of the representational\nproblems for Zermelo's theory, and the Replacement Axiom shows how the\nmost obvious cardinality gap can be closed, there still remained the\nissue (Kuratowski's view to one side) of representing accurately the\nfull extent of the theory which Cantor had developed, with the\ntransfinite numbers as fully fledged objects which\n‘mirror’ the size/ordering of sets. Once the ordinal\nnumber-classes are present, the representation of the alephs is not a\nsevere problem, which means that the representation of transfinite\nnumbers amounts to assuring the existence of sufficiently many\ntransfinite ordinal numbers. Indeed, as was stated above, the\nhypothesis that the scale of aleph numbers is sufficient amounts to\nthe claim that any set can be ‘counted’ by some\nordinal. There are then two interrelated problems for the\n‘pure’ theory of sets: one is to show how to define\nordinals as sets in such a way that the natural numbers generalise;\nthe other problem is to make sure that there are enough ordinals to\n‘count’ all the sets.", "The problem was fully solved by von Neumann in his work on\naxiomatic set theory from the early 1920s. Cantor's fundamental\ntheorems about ordinal numbers, showing that the ordinals are the\nrepresentatives of well-ordered sets, are the theorem that every\nwell-ordered set is order-isomorphic to an initial segment of the\nordinals, and that every ordinal is itself the order-type of the set\nof ordinals which precede it. These results prove crucial in the von\nNeumann treatment. Von Neumann's basic idea was explained by him as\nfollows:", "\n What we really wish to do is to take as the basis of our\nconsiderations the proposition: ‘Every ordinal is the type of\nthe set of all ordinals that precede it’. But in order to avoid\nthe vague notion ‘type’, we express it in the form:\n‘Every ordinal is the set of the ordinals that precede\nit’. (von Neumann 1923, p. 347 of the English translation)\n", "According to von Neumann's idea, 1 is just {0}, 2 is just {0, 1}, 3\nis just {0, 1, 2} and so on. On this conception, the first transfinite\nordinal ω is just {0, 1, 2, 3, …, n, …},\nand generally it's clear that the immediate successor of any ordinal\nα is just α ∪ {α}. If we\nidentify 0 with ∅, as Zermelo did, then we have available a\nreduction of the general notion of ordinal to pure set theory, where\nthe canonical well-ordering on the von Neumann ordinals is just the\nsubset relation, i.e., α < β just in case α ⊂\nβ, which von Neumann later shows is itself equivalent to saying\nα ∈ β. (See von Neumann 1928, p. 328 of the\nreprinting.) So again, inclusion orderings are fundamental.", "Von Neumann gives a general definition of his ordinals, namely that\na set α is an ordinal number if and only if it is a set ordered\nby inclusion, the inclusion ordering is a well-ordering, and each\nelement ξ in α equals the set of elements in the initial\nsegment of the ordering determined by ξ. This connects directly\nwith Kuratowski's work in the following way. Suppose M is a\nwell-ordered set which is then mirrored by an inclusion\nchain M in the power set of M. Then the first few\nelements of the inclusion chain will be the sets ∅, {a},\n{a, b}, {a, b, c}, …,\nwhere a, b, c, … are the first, second,\nthird …elements in the well-ordering of M. The von\nNeumann ordinal corresponding to M will also be an inclusion\nordering whose first elements will be", "∅, {∅}, {∅, {∅}}, {∅, {∅},\n {∅, {∅}}}, …", "(in other words, 0, 1, 2, 3…), and we have 0 ⊂ 1 ⊂ 2\n⊂ 3 ⊂… in mirror image of\n∅ ⊂ {a} ⊂ {a, b} \n⊂ {a, b, c}\n⊂ …", "These von Neumann ordinals had, in effect, been developed before\nvon Neumann's work. The fullest published theory, and closest to the\nmodern account, is to be found in Mirimanoff's work published in 1917\nand 1921 (see Mirimanoff 1917a,b, 1921), though he doesn't take the\nfinal step of identifying the sets he characterises with the ordinals\n(for an account of Mirimanoff's work, see Hallett 1984:\n273–275). It is also clear that Russell, Grelling and Hessenberg\nwere close to von Neumann's general set-theoretic definition of\nordinals. But crucially Zermelo himself developed the von Neumann\nconception of ordinals in the years 1913–1916, (for a full\naccount, see Hallett 1984: 277–280 and Ebbinghaus 2007:\n133–134). Zermelo's idea was evidently well-known to the\nGöttingen mathematicians, and there is an account of it in\nHilbert's lectures ‘Probleme der mathematischen\nLogik’ from 1920,\npp. 12–15.[37]", "Despite all these anticipations, it is still right to ascribe the\ntheory to von Neumann. For it was von Neumann who revealed the extent\nto which a full theory of the ordinals depends on the Axiom of\nReplacement. As he wrote later:", "\n A treatment of ordinal number closely related to mine was known\n to Zermelo in 1916, as I learned subsequently from a personal\n communication. Nevertheless, the fundamental theorem, according to\n which to each well-ordered set there is a similar ordinal, could not\n be rigorously proved because the replacement axiom was unknown. (von\n Neumann 1928: 374, n. 2)\n", "The theorem von Neumann states is the central result of Cantor's\nmentioned here in the second paragraph of this section. As von Neumann goes on to point out\nhere (also p. 374), it is the possibility of definition by transfinite\ninduction which is key, and a rigorous treatment of this requires\nbeing able to prove at each stage in a transfinite inductive process\nthat the collection of functional correlates to a set is itself a set\nwhich can thus act as a new argument at the next stage. It is just\nthis which the replacement axiom guarantees. Once justified,\ndefinition by transfinite induction can be used as the basis for\ncompletely general definitions of the arithmetic operations on ordinal\nnumbers, for the definition of the aleph numbers, and so on. It also\nallows a fairly direct transformation of Zermelo's first (1904) proof\nof the WOT into a proof that every set can be represented by (is\nequipollent with) an ordinal number, which shows that in the Zermelo\nsystem with the Axiom of Replacement added there are enough ordinal\nnumbers.[38]", "It is thus remarkable that von Neumann's work, designed to show how\nthe transfinite ordinals can be incorporated directly into a pure\ntheory of sets, builds on and coalesces with both Kuratowski's work,\ndesigned to show the dispensability of the theory of transfinite\nordinals, and also the axiomatic extension of Zermelo's theory\nsuggested by Fraenkel and Skolem." ], "subsection_title": "3.2 Completeness" } ] }, { "main_content": [ "For a summary of the Cantorian theory as it stood in the early\nyears of the twentieth century, see Young and Young (1906), and the\nmagisterial Hausdorff (1914); for further reading on the development\nof set theory, see the books Ferreiros 1999, Hallett 1984, Hawkins\n1970, and Moore 1982. See also the various papers on the history of\nset theory by Akihiro Kanamori (especially Kanamori 1996, 1997, 2003,\n2004, 2012) and the joint paper with Dreben (Dreben and Kanamori\n1997). For the place of set theory in the development of modern logic,\nsee Mancosu et al., 2009, especially pages 345–352.", "For an account of the various axiom systems and the role of the\ndifferent axioms, see Fraenkel et al. (1973). For a detailed summary\nof the role of the Axiom of Choice, and insight into the question of\nits status as a logical principle, see Bell (2009).", "This entry will be supplemented by a further entry on\naxiomatizations of set theory after Zermelo from 1920 to 1940." ], "section_title": "4. Further reading", "subsections": [] } ]

[ "Bell, J., 2009, The Axiom of Choice, London: College Publications.", "Benacerraf, P. and H. Putnam (eds.), 1964, Philosophy of Mathematics: Selected Readings, Oxford: Basil Blackwell.", "––– (eds.), 1983, Philosophy of Mathematics: Selected Readings, Second Edition, Cambridge: Cambridge University Press.", "Bernstein, F., 1905, “Über die Reihe der transfiniten Ordnungszahlen”, Mathematische Annalen 60: 187–193.", "Borel, E., 1905, “Quelque remarques sur les principes de la théorie des ensembles”, Mathematische Annalen 60: 194–195.", "Browder, F. (ed.), 1976, Mathematical Developments Arising from the Hilbert Problems, Volume 28 of Proceedings of Symposia in Pure Mathematics, Providence: American Mathematical Society.", "Cantor, G., 1883a, “Ueber unendliche, lineare Punktmannichfaltigkeiten” Mathematische Annalen 21: 545–591. Reprinted in Cantor 1883b and in Cantor 1932: 165–209. English translation in Ewald 1996, Volume 2.", "–––, 1883b, Grundlagen einer allegemeinen Mannigfaltichkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen, Leipzig: B. G. Teubner.", "–––, 1895, “Beiträge zur Begründung der transfiniten Mengenlehre, Erster Artikel”, Mathematische Annalen 46: 481–512. Reprinted in Cantor 1932: 282–311. English translation in Cantor 1915.", "–––, 1897, “Beiträge zur Begründung der transfiniten Mengenlehre, Zweiter Artikel”, Mathematische Annalen 49: 207–246. Reprinted in Cantor 1932: 312–351. English translation in Cantor 1915.", "–––, 1915, Contributions to the Founding of the Theory of Transfinite Numbers, La Salle: Open Court. English translation of Cantor 1895, 1897 by Philip E. B. Jourdain.", "–––, 1932, Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, mit eläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind herausgegeben von Ernst Zermelo, Berlin: Springer.", "–––, 1991, Georg Cantor: Briefe. Herausgegeben von Herbert Meschkowski, Berlin: Springer", "Dedekind, R., 1888, Was sind und was sollen die Zahlen?, Braunschweig: Vieweg und Sohn. Also reprinted in Dedekind 1932: 335–391; English translation in Ewald 1996: 787–833.", "–––, 1932, Gesammelte mathematische Werke. Band 3. Herausgegeben von Robert Fricke, Emmy Noether and Öystein Ore, Braunschweig: Friedrich Vieweg und Sohn. Reprinted with some omissions by Chelsea Publishing Co., New York, 1969.", "Dreben, B. and A. Kanamori, 1997, “Hilbert and set theory”, Synthese, 110: 77–125.", "Ebbinghaus, H.-D., 2007, Ernst Zermelo: An Approach to His Life and Work, Berlin: Springer.", "–––, 2010, “Introductory note to Über den Begriff von Definitheit in der Axiomatik [Zermelo 1929]”, in Zermelo 2010: 352–357.", "Ewald, W. (ed.), 1996, From Kant to Hilbert, Oxford: Oxford University Press.", "Ewald, W., W. Sieg, and M. Hallett (eds.), 2013, David Hilbert's Lectures on the Foundations of Logic and Arithmetic, 1917–1933, Volume 3 of Hilbert's Lectures on the Foundations of Mathematics and Physics, 1891–1933, Berlin: Springer.", "Felgner, U., 2010, “Introductory note to Untersuchungen über die Grundlagen der Mengenlehre, I [Zermelo 1908b]”, in Zermelo 2010: 160–188.", "Ferreiros, J., 1999, Labyrinth of Thought: A History of Set Theory and its Role in Modern Mathematics, Science Networks Historical Studies, Basel: Birkhäuser. Second Revised Edition, 2007", "Fraenkel, A., Y. Bar-Hillel, and A. Levy, 1973, Foundations of Set Theory. Amsterdam: North-Holland Publishing.", "Fraenkel, A. A., 1922, “Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre”, Mathematische Annalen 86: 230–237.", "–––, 1927, Zehn Vorlesungen über die Grundlegung der Mengenlehre, Leipzig: B. G. Teubner.", "Frege, G., 1879, Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle: Louis Nebert. Reprinted in Frege 1964, English\ntranslation in van Heijenoort 1967: 1–82.", "–––, 1893, Grundgesetze der Arithmetik, Band 1, Jena: Hermann Pohle. English translation by Philip Ebert and Marcus Rossberg, Frege, The Basic Laws of Arithmetic, Derived using Concept-Script, Oxford: Oxford University Press, forthcoming.", "–––, 1903, Grundgesetze der Arithmetik, Band II, Jena: Hermann Pohle. English translation by Philip Ebert and Marcus Rossberg, Frege, The Basic Laws of Arithmetic, Derived using Concept-Script, Oxford: Oxford University Press, forthcoming.", "–––, 1964, Begriffsschrift und andere Aufsätze. Mit E. Husserls und H. Scholz’ Anmerkungen herausgegeben von Ignacio Angelelli, Darmstadt: Wissenschaftliche Buchgesellschaft.", "Gödel, K., 1944, “Russell's mathematical logic”, in P. A. Schillp (ed.), The Philosophy of Bertrand Russell, pp. 125–153, La Salle: Open Court. \nReprinted in Benacerraf and Putnam 1964: 211–232; Benacerraf and Putnam 1983: 447–469; and in Gödel 1990: 119–141.", "–––, 1990, Kurt Gödel: Collected Works, Volume 2, edited by Solomon Feferman et al., Oxford: Oxford University Press.", "Haaparanta, L. (ed.), 2009, The Development of Modern Logic, Oxford: Oxford University Press.", "Hadamard, J. et al., 1905, “Cinq letters sur la théorie des ensembles”, Bulletin de la société mathématique de France, 33: 261–273. \nLetters between Baire, Borel, Lebesgue and Hadamard on objections to, and defense of, Zermelo's 1904 proof\nof the well-ordering theorem.", "Hallett, M., 1981, “Russell, Jourdain and ‘limitation of size’”, British Journal for the Philosophy of Science, 32: 381–399.", "–––, 1984, Cantorian Set Theory and Limitation of Size, Oxford: Clarendon Press.", "–––, 2008, “The ‘purity of method’ in Hilbert's Grundlagen der Geometrie”, in P. Mancosu (ed.), The Philosophy of Mathematical Practice, pp. 198–255, Oxford: Clarendon Press.", "–––, 2010a, “Frege and Hilbert”, in M. Potter and T. Ricketts (eds.), The Cambridge Companion to Frege, Cambridge: Cambridge University Press.", "–––, 2010b, “Introductory note to Zermelo's two papers on the well-ordering theorem”, in Zermelo 2010: 80–115.", "Hallett, M. and U. Majer (eds.), 2004, David Hilbert's Lectures on the Foundations of Geometry, 1891–1902, Volume 1 of Hilbert's Lectures on the Foundations of Mathematics and Physics, 1891–1933, Berlin: Springer.", "Hardy, G. H., 1904, “A theorem concerning the infinite cardinal numbers”, Quarterly Journal of Pure and Applied Mathematics 35: 87–94.", "Hartogs, F., 1915, “Über das Problem der Wohlordnung”, Mathematische Annalen, 76: 438–442.", "Harward, A. E., 1905, “On the transfinite numbers”, Philosophical Magazine 10(6): 439–460.", "Hausdorff, F., 1914, Grundzüge der Mengenlehre, Leipzig: Von Veit.", "Hawkins, T., 1970, Lebesgue's Theory of Integration. New York: Blaisdell.\nReprinted by the Chelsea Publishing Company, New York, 1979.", "van Heijenoort, J. (ed.), 1967, From Frege to Gödel: A Source Book in Mathematical Logic, Cambridge, Massachusetts: Harvard University Press.", "Heinzmann, G., 1986, Poincaré, Russell, Zermelo et Peano. Textes de la discusion (1906–1912) sur les fondements des mathématiques: des antinomies à la prédicativité, Paris: Albert Blanchard.", "Hessenberg, G., 1906, “Grundbegriffe der Mengenlehre”, Abhandlungen der neuen Fries'schen Schule (Neue Folge) 1: 479–706.", "Hilbert, D., 1899, “Grundlagen der Geometrie”, in Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen, Leipzig: B. G. Teubner.\nRepublished as Chapter 5 in Hallett and Majer 2004.", "–––, 1900a, “Mathematische Probleme”, Nachrichten von der königlichen Gesellschaft der Wissenschaften zu Göttingen, mathematisch-physikalische Klasse, pp. 253–296.\nEnglish translation by Mary Winston Newson, 1902, “Mathematical Problems” Bulletin of the American Mathematical Society 8: 437–479.", "–––, 1900b, “Über den Zahlbegriff”, Jahresbericht der deutschen Mathematiker-Vereinigung 8: 180–185.\nReprinted (with small modifications) in Second to Seventh Editions of Hilbert 1899.", "–––, 1902, “Grundlagen der Geometrie”. Ausarbeitung by August Adler for lectures in the Sommersemester of 1902 at the Georg-August Universität, Göttingen. Library of the Mathematisches Institut.\nPublished as Chapter 6 in Hallett and Majer 2004.", "–––, 1918, “Axiomatisches Denken”, Mathematische Annalen, 78: 405–415.\nReprinted in Hilbert 1935: 146–156; English translation in Ewald 1996: volume 2, pp. 1105–1115.", "–––, 1920, “Probleme der mathematischen Logik”, Lecture notes for a course held in the Wintersemester of 1920 at the Georg-August Universität, Göttingen, ausgearbeitet by Moses Schönfinkel and Paul Bernays. Library of the Mathematisches Institut, Universität Göttingen. Published in Ewald et al. 2013, Chapter 2.", "–––, 1935, Gesammelte Abhandlungen, Band 3. Berlin: Julius Springer.", "Jourdain, P. E. B., 1904, “On the transfinite cardinal numbers of well-ordered aggregates”, Philosophical Magazine 7(6): 61–75.", "–––, 1905a, “On a proof that every aggregate can be well-ordered”, Mathematische Annalen 60: 465–470.", "–––, 1905b, “On transfinite numbers of the exponential form”, Philosophical Magazine 9(6): 42–56.", "Kanamori, A., 1996, “The mathematical development of set theory from Cantor to Cohen”, Bulletin of Symbolic Logic 2: 1–71.", "–––, 1997, “The mathematical import of Zermelo's well-ordering theorem”, Bulletin of Symbolic Logic 3: 281–311.", "–––, 2003, “The empty set, the singleton, and the ordered pair”, Bulletin of Symbolic Logic 9: 273–298.", "–––, 2004, “Zermelo and set theory”, Bulletin of Symbolic Logic 10: 487–553.", "–––, 2012, “In praise of replacement”, Bulletin of Symbolic Logic, 18: 46–90.", "Kuratowski, C., 1921, “Sur la notion de l'ordre dans la théorie des ensembles”, Fundamenta Mathematicae 2: 161–171.", "–––, 1922, “Une méthode d'élimination des nombres transfini des raisonnements mathématiques”, Fundamenta Mathematicae 3: 76–108.", "Mancosu, P., 2009, “Measuring the size of infinite collections of natural numbers: was Cantor's theory of infinite number inevitable?”, Review of Symbolic Logic 2: 612–646.", "–––, 2010, The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900–1940. Oxford: Oxford University Press.", "Mancosu, P., R. Zach, and C. Badesa, 2009, “The development of mathematical logic from Russell to Tarski, 1900–1935”, in Haaparanta 2009: 318–470.\nReprinted in Mancosu 2010: 5–119.", "Mirimanoff, D., 1917a, “Les antinomies de Russell et de Burali-Forti et le problème fondamental de la théorie des ensembles”, L'enseignement mathématique 19: 37–52.", "–––, 1917b, “Remarques sur la théorie des ensembles et les antinomies Cantoriennes (I)”, L'enseignement mathématique 19: 208–217.", "–––, 1921, “Remarques sur la théorie des ensembles et les antinomies Cantoriennes (II)”, L'enseignement mathématique 21: 29–52.", "Moore, G., 1976, “Ernst Zemelo, A. E. Harward, and the axiomatisation of set theory”, Historia Mathematica 3: 206–209.", "–––, 1982, Zermelo's Axiom of Choice: Its Origins, Development and Influence. Berlin: Springer.", "Peano, G., 1906, “Additione”, Revista di mathematica 8: 143–157.\nReprinted in Heinzmann 1986: 106–120.", "Peckhaus, V., 1990, Hilbertprogramm und kritische Philosophie: das Göttinger Modell interdisziplinärer Zusammenarbeit zwischen Mathematik und Philosophie, Volume 7 of Studien zur Wissenschafts- Sozial- und Bildungsgeschichte, Göttingen: Vandenhoek and Ruprecht.", "Poincaré, H., 1905, “Les mathématiques et la logique”, Revue de métaphysique et de morale 13: 815–835.\nReprinted with alterations in Poincaré 1908: Part II, Chapter 3; and, with these alterations noted, in Heinzmann 1986: 11–34. English translation in Ewald 1996: 1021–1038.", "–––, 1906a, “Les mathématiques et la logique”, Revue de métaphysique et de morale 14: 17–34.\nReprinted with alterations in Poincaré 1908: Part II, Chapter 3; and, with these alterations noted, in Heinzmann 1986: 35–53. English translation in Ewald 1996: 1038–1052.", "–––, 1906b, “Les mathématiques et la logique”, Revue de métaphysique et de morale 14: 294–317.\nReprinted with alterations in Poincaré 1908: Part II, Chapter 5; and, with these alterations noted, in Heinzmann 1986: 35–53. English translation in Ewald 1996: 1052–1071.", "–––, 1908, Science et méthode, Paris: Ernst Flammarion.\nEnglish translation in Poincaré 1913b, and retranslated by Francis Maitland as Science and Method, New York: Dover Publications.", "–––, 1909, “Le logique de l'infini”, Revue de métaphysique et de morale 17: 462–482.\nReprinted in Poincaré 1913a: 7–31.", "–––, 1913a, Dernières Pensées, Paris: Ernest Flammarion.\nEnglish translation published in 1963 as Mathematics and Science: Last Essays, New York: Dover Publications.", "–––, 1913b, The Foundations of Science, New York: Science Press.\nPreface by Poincaré and an Introduction by Josiah Royce. Contains English translation by G. B. Halsted of Poincaré 1908.", "Ramsey, F. P., 1926, “The foundations of mathematics”, Proceedings of the London Mathematical Society 25 (Second Series): 338–384.\nReprinted in Ramsey 1931: 1–61, and Ramsey 1978: 152–212.", "–––, 1931, The Foundations of Mathematics and Other Logical Essays, R. B. Braithwaite (ed.), London: Routledge and Kegan Paul, London.", "–––, 1978, Foundations: Essays in Philosophy, Logic, Mathematics and Economics, D. H. Mellor (ed.), London: Routledge and Kegan Paul.", "Richard, J., 1905, “Les principes des mathématiques et le problème des ensembles”, Révue général des sciences pures et appliqués 16: 541.\nEnglish translation in van Heijenoort 1967: 142–144.", "Russell, B., 1902, Letter to Frege.\nIn Heijenoort 1967: 124–125.", "–––, 1903, The Principles of Mathematics, Volume 1, Cambridge: Cambridge University Press.", "Schoenflies, A., 1905, “Über wohlgeordnete Mengen”, Mathematische Annalen 60: 181–186.", "Skolem, T., 1923, “Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre”, Matimatikerkrongressen i Helsingfors den 4–7 Juli 1922, Den femte skandinaiska matematikerkongressen, redogörelse, 1923, pp. 217–232.\nReprinted in Skolem 1970: 137–152 which also preserves the original pagination. English translation in Heijenoort 1967: 290–301.", "–––, 1970, Selected Papers in Logic, Oslo: Universitetsforlaget. Edited by Jens Erik Fenstad.", "von Neumann, J., 1923, “Zur Einführung der transfiniten Zahlen”, Acta Litterarum ac Scientiarum Regiæ Universitatis Hungaricæ Francisco-Josephinæ. Sectio Scientiæ-Mathematicæ 1, pp. 199–208.\nReprinted in von Neumann 1961: 24–33. English translation in van Heijenoort 1967: 346–354.", "–––, 1928, “Über die Definition durch transfinite Induktion und verwandte Fragen der allgemeinen Mengenlehre”, Mathematische Annalen 99: 373–391.\nReprinted in von Neumann 1961: 320–338.", "–––, 1961, John von Neumann: Collected Works, Volume 1, Oxford: Pergamon Press.", "Weyl, H., 1910, “Über die Definitionen der mathematischen Grundbegriffe”, Mathematisch-naturwissenschaftliche Blätter 7, pp. 93–95, 109–113.\nReprinted in Weyl 1968, Volume 1, 298–304.", "–––, 1968, Gesammelte Abhandlungen, 4 Volumes, Berlin: Springer.", "Young, W. H. and G. C. Young, 1906, The Theory of Sets of Points, Cambridge: Cambridge University Press.", "Zermelo, E., 1904, “Beweis, daß jede Menge wohlgeordnet werden kann”, Mathematische Annalen 59: 514–516.\nReprinted in Zermelo 2010: 114–119, with a facing-page English translation, and an Introduction by Michael Hallett (2010b). English translation also in van Heijenoort 1967: 139–141.", "–––, 1908a, “Neuer Beweis für die Möglichkeit einer Wohlordnung”, Mathematische Annalen 65: 107–128.\nReprinted in Zermelo 2010: 120–159, with a facing-page English translation, and an Introduction by Michael Hallett (2010b). English translation also in van Heijenoort 1967: 183–198.", "–––, 1908b, “Untersuchungen über die Grundlagen der Mengenlehre, I”, Mathematische Annalen 65: 261–281.\nReprinted in Zermelo 2010: 189–228, with a facing-page English translation, and an Introduction by Ulrich Felgner (2010). English translation also in van Heijenoort 1967: 201–215.", "–––, 1929, “Über den Begriff von Definitheit in der Axiomatik”, Fundamenta Mathematicae 14: 339–344.\nReprinted with facing-page English translation in Zermelo 2010: 358–367, with an Introduction by Heinz-Dieter Ebbinghaus (2010).", "–––, 1930, “Über Grenzzahlen und Mengenbereiche: Neue Untersuchungen über die Grundlagen der Mengenlehre”, Fundamenta Mathematicae 16: 29–47.\nReprinted with facing-page English translation in Zermelo 2010: 400–431, with an Introduction by Akihiro Kanamori. English translation also in Ewald 1996, Volume 2, pp. 1219–1233.", "–––, 2010, Collected Works. Volume I: Set Theory, Miscellanea, H.-D. Ebbinghaus and A. Kanamori (eds.), Berlin: Springer." ]

[ { "href": "../russell-paradox/", "text": "Russell’s paradox" }, { "href": "../set-theory/", "text": "set theory" }, { "href": "../settheory-alternative/", "text": "set theory: alternative axiomatic theories" }, { "href": "../settheory-early/", "text": "set theory: early development" } ]

[ "\nSituation semantics was developed as an alternative to possible worlds\nsemantics. In situation semantics, linguistic expressions are\nevaluated with respect to partial, rather than complete, worlds. There\nis no consensus about what situations are, just as there is no\nconsensus about what possible worlds or events are. According to some,\nsituations are structured entities consisting of relations and\nindividuals standing in those relations. According to others,\nsituations are particulars. In spite of unresolved foundational\nissues, the partiality provided by situation semantics has led to some\ngenuinely new approaches to a variety of phenomena in natural language\nsemantics. In the way of illustration, this article includes\nrelatively detailed overviews of a few selected areas where situation\nsemantics has been successful: implicit quantifier domain\nrestrictions, donkey pronouns, and exhaustive interpretations. It\nmoreover addresses the question of how Davidsonian event semantics can\nbe embedded in a semantics based on situations. Other areas where a\nsituation semantics perspective has led to progress include attitude\nascriptions, questions, tense, aspect, nominalizations, implicit\narguments, point of view, counterfactual conditionals, and discourse\nrelations." ]

[ { "content_title": "1. Situations in direct perception reports", "sub_toc": [] }, { "content_title": "2. States of affairs, infons, and information content", "sub_toc": [] }, { "content_title": "3. Austinian topic situations", "sub_toc": [] }, { "content_title": "4. Situation semantics and implicit domain restrictions", "sub_toc": [] }, { "content_title": "5. Situation variables or unarticulated constituents?", "sub_toc": [] }, { "content_title": "6. Situations, minimality, and donkey sentences", "sub_toc": [] }, { "content_title": "7. Minimality and exemplification", "sub_toc": [] }, { "content_title": "8. Exemplification and exhaustive interpretations", "sub_toc": [] }, { "content_title": "9. Situation semantics and Davidsonian event semantics", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "References mentioned in the text", "References not mentioned in the text" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nSituations entered natural language semantics with Jon Barwise’s\npaper Scenes and Other Situations (Barwise 1981), followed by\nBarwise and Perry’s Situations and Attitudes (Barwise\n& Perry 1983). Scenes and Other Situations is about the\nmeaning of direct (or epistemically neutral) perception reports, a\nconstruction illustrated in (1):", "\nDirect perception reports contrast with indirect (or epistemically\npositive) perception reports, which typically have finite embedded\nclauses, as in (2):", "\nBoth (1) and (2) presuppose that Meryl fed the animals. But (1) and\n(2) still differ with respect to the interpretation of their embedded\ncomplements: the embedded complement in (1) can only be interpreted as\ntransparent, and this is not so for the embedded complement in (2).\nThe transparency of the embedded complement in (1) is shown by the\nvalidity of inferences like that in (3), for example:", "\nIn contrast to (3), the first sentence in (4) has an interpretation\nthat renders the inference in (4) invalid.", "\nA semantic analysis of direct perception reports has to explain what\nit is that forces their complements to be transparent. Barwise 1981\nproposes to analyze direct perception reports like (1) along the lines\nof (5):", "\nThe virtues of Barwise’s analysis can be appreciated even\nwithout seeing the exact details of how situations might support the\ntruth of sentences. In (5) the verb see semantically selects\nsituations rather than propositions as its first argument, and this\nhas the desirable effect that the truth value of those sentences does\nnot change when the description of the perceived situation is replaced\nby an extensionally equivalent one. If Meryl fed the animals just once\nin the actual world, and she fed them hay, then the set of actual\nsituations that support the truth of Meryl feed the animals\nis expected to be the same as the set of actual situations that\nsupport the truth of Meryl feed the animals hay. But then (5)\nand (6) must have the same actual truth-value, and Barwise’s\nanalysis predicts correctly that (1) and (7) must, too.", "\nThe publication of Barwise 1981 in the Journal of Philosophy\nwas followed by two papers providing commentary: Higginbotham 1983 in\nthe same journal, and Vlach 1983 in Synthese. The peer\nverdict on situations was that they were not needed for the semantics\nof direct perception reports: the facts could just as well be\nexplained by Davidsonian event semantics. (Davidson 1967a, 1980. See\nthe entries\n Donald Davidson\n and\n events.)\n In fact, Barwise’s argument showing that direct perception\nsee selects a situation is very much like Davidson’s\nargument showing that the verb cause expresses a relation\nbetween events (Davidson 1967b, 1980). Comparison with Davidsonian\nevent semantics has been an issue for situation semantics throughout\nits history. The relation between situation semantics and Davidsonian\nevent semantics will be taken up in section 9." ], "section_title": "1. Situations in direct perception reports", "subsections": [] }, { "main_content": [ "\nLater developments in situation semantics emphasized its role as a\ngeneral theory of information content. The key concept is the notion\nof a state-of-affair or “infon” (see the entry\n states of affairs).\n State-of-affairs are non-linguistic formal objects that come in\nvarious stages of complexity (see Gawron & Peters 1990 for a brief\noverview, Devlin 1991, 2006 for a more detailed exposition, and\nGinzburg & Sag 2000 for a system based on a richer ontology). The\nsimplest kinds of state-of-affairs consist of a relation, individuals\nrelated by the relation, and a polarity, and might be represented as\nin (8):", "\nArguments of a relation may be parameterized, as in (9):", "\nParameterized roles can be anchored to individuals. In (9), the\nparameterized botherer role may be anchored to Nina, for example, and\nin that case, the result is the unparameterized state-of-affairs in\n8(a). Parameterized states-of-affairs can be restricted by other\nparameterized state-of-affairs, as in (10), where the subject role for\nthe property of taking a shower is restricted to individuals who are\nsinging:", "\nProperties and relations can be produced from parameterized\nstates-of-affairs by absorbing parameters:", "\nParameter absorption is the situation theory analogue of\nλ-abstraction. (11) corresponds to the property of not\nbothering Stella. There are additional operations that build complex\nstates-of-affairs from simpler ones, including analogues of\nconjunction, disjunction, and existential and universal quantification\n(see Devlin 1991, 2006, and Ginzburg & Sag 2000). The ultimate\ngoal is to provide the necessary tools for a theory of information\ncontent (see the entry\n semantic conceptions of information).\n Barwise 1988 mentions a wide range of applications, including\n“a theory of information to account for the role information\npickup plays in the life of the frog, how the information it detects\nis related to the actions it takes, actions like flicking its tongue\nand hopping about” (Barwise 1988, 257). Other applications\nmentioned are theories of vision, databases, robot design,\nmathematical proofs, information exchange between speakers of\nparticular language, and cognitive science as a whole. Finally, the\ntheory should be able “to be turned on itself, and provide an\naccount of its own information content, or rather, of the statements\nmade by the theorist using the theory” (Barwise 1988, 258).", "\nWhen Barwise and Perry started their joint work, a new, more\nfine-grained, notion of information content seemed to be urgently\nneeded in natural language semantics, because of a known challenge\nfacing possible worlds semantics, which, under the influence of Lewis\n1972 and Montague 1974, was the framework of choice for most formal\nsemanticists at the time (see the entry on \n possible worlds). \n In possible\nworlds semantics, propositions are identified with the set of possible\nworlds where they are true (see the entry\n propositions).\n Consequently, propositions that are true in the same possible worlds\nare identical, and we seem to predict wrongly that a person who\nbelieves a proposition p should also believe any proposition\nthat is true in the same worlds as p (see the entry\n propositional attitude reports).\n To distinguish logically equivalent propositions, we seem to need a\nmore fine-grained notion of what the information content of a sentence\nis, and the state-of-affairs or infons of situation semantics were\nmarketed to provide just that.", "\nThe solution that situation semantics offered for the puzzle of\nlogically equivalents in attitude ascriptions encountered competition\nfrom the very start: state-of-affairs and infons looked suspiciously\nlike structured propositions (see the entry\n structured propositions).\n Intensional versions of structured propositions had already been\noffered as remedies for the attitude ascription problem by Carnap\n1947, Lewis 1972, Cresswell & von Stechow 1982, and were also\nappealed to for the analysis of information structure and intonational\nmeaning. The structured meanings of Carnap, Lewis, and Cresswell &\nvon Stechow are tree structures whose end nodes are intensions, rather\nthan lexical items. They are thus objects that are independent of the\nvocabularies of particular languages, but are nevertheless\nhierarchically structured in the way sentences are. Differences\nbetween structured propositions in various frameworks and the\nstate-of-affairs or infons of situation theory seem to largely boil\ndown to foundational matters regarding the status of possibilia (see\nthe entries on\n possible objects\n and possible worlds) and\nthe nature of properties and relations (see\n properties).", "\nThere is currently no consensus about the semantics of attitude\nascriptions, and it is not clear whether situation semantics has a\nprivileged place in the family of accounts that have been proposed.\nPerhaps more importantly, for most empirical generalizations in\nlinguistic semantics, propositions construed as sets of possible\nworlds or situations provide the right level of abstraction. There\nseems to be no need to posit unwieldy information contents in areas\nwhere simpler notions provide more elegant accounts. Since this\narticle is not about theories of information, the concern to provide a\ngeneral theory of information content will now have to be set aside,\neven though it is central to some areas in situation semantics and\nsituation theory (Devlin 1991, 2006; Ginzburg and Sag 2000; see also\nBarwise & Seligman 1997). The remainder of this article will\nreview situation-based accounts of selected topics that are currently\nunder active investigation in linguistics and philosophy: Austinian\ntopic situations, domain restrictions, donkey sentences, exhaustive\ninterpretations, and Davidsonian event predication. None of those\nphenomena requires a more fine-grained notion of information content.\nThe discussion will thus be cast within a possibilistic framework\n(Kratzer 1989, 2002, 2012; Elbourne 2005, 2013). Possibilistic\nversions of situation semantics are conservative extensions of\npossible worlds semantics that construe propositions as sets of world\nparts, rather than complete possible worlds (see Barwise 1988, chapter\n11, for an overview of the major branch points in situation\nsemantics). There are many areas that situation semantics has\ncontributed to that could not be reviewed here for reasons of space,\nincluding knowledge ascriptions, questions, discourse relations,\ncounterfactuals, viewpoint aspect, gerunds, and implicit arguments.\nStojanovich 2012 and Zucchi 2015 are recent general overviews of\nsituation semantics. Additional references to work on various\nphenomena within a situation-based semantics are given below under the\nheading references not mentioned in the text." ], "section_title": "2. States of affairs, infons, and information content", "subsections": [] }, { "main_content": [ "\nA core feature of many actual analyses of natural language phenomena\nwithin situation semantics is the idea attributed to John L. Austin\n1950 that utterances are about particular situations, with the actual\nworld being the limiting case (see the entry on \n John Langshaw Austin.)\nBarwise & Etchemendy 1987 illustrate the idea with an imagined\nutterance of sentence (12):", "\nWhether an utterance of (12) is true or false depends, among other\nthings, on what situation the utterance is about.", "\nWe might imagine, for example, that there are two card games going on,\none across town from the other: Max is playing cards with Emily and\nSophie, and Claire is playing cards with Dana. Suppose someone\nwatching the former game mistakes Emily for Claire, and claims that\nClaire has the three of clubs. She would be wrong on the Austinian\naccount, even if Claire had the three of clubs across town. (Barwise\nand Etchemendy 1987, p. 122)\n", "\nIf assertions are about particular situations, reports of assertions\nmight not be accurate unless they take into account the situations the\nassertions were about. And there are more repercussions of Austinian\nreasoning: if assertions are about particular situations, beliefs\nshould be, too, and this means that our belief ascriptions might not\nbe accurate unless they take into account the situations the beliefs\nare about. That those situations do indeed matter for belief\nascriptions is illustrated by the story of the Butler and the Judge\nfrom Kratzer 1998 (see Ogihara 1996, Kratzer 1990 (Other Internet\nResources), 2002, 2012; Portner 1992, Récanati 2000, for\nrelevant work on the role of topic situations in attitude ascriptions\nand other embedded constructions):", "\nThe judge was in financial trouble. He told his butler that he had\nbeen ready to commit suicide, when a wealthy man, who chose to remain\nanonymous, offered to pay off his debts. The butler suspected that\nMilford was the man who saved his master’s life by protecting\nhim from financial ruin and suicide. While the butler was away on a\nshort vacation, the judge fell into a ditch, drunk. Unconscious and\nclose to death, he was pulled out by a stranger and taken to the local\nhospital, where he recovered. When the butler returned to the village,\nhe ran into a group of women who were speculating about the identity\nof the stranger who saved the judge’s life by taking him to the\nhospital. One of the women said she thought that Milford saved the\njudge’s life. The butler, who hadn’t yet heard about the\naccident and thought the women were talking about the judge’s\nfinancial traumas, reacted with (13):", "\nThe next day, when discussion of the judge’s accident continued,\nsomebody said:", "\nGiven that the butler’s suspicion is not about the accident,\nthere is a sense in which this belief attribution is not true. It\nseems infelicitous, if not outright false. This suggests that our\nimagined assertion of (14) makes a claim about a particular situation\nthat the suspicion is about. In the context of the story, that\nsituation is the one everyone was talking about, and where the judge\nwas rescued from the ditch. Since the butler has no suspicion about\nsuch a situation, the person who uttered (14) said something\ninfelicitous or false. If (14) simply said that the butler suspected\nthat there was a situation where Milford saved the judge’s life,\nthe assertion would be true. There is support for the Austinian\nperspective on assertions and attitude ascriptions, then.", "\nAustinian topic situations (also referred to as “focus\nsituations”, “described situations”, or\n“reference situations” in the literature) are often\nnon-overt, but the tense of a sentence might give them away. A close\nlook at tenses tells us that topic situations do not always coincide\nwith the situations described by the main predication of a sentence.\nKlein (1994, 4) imagines a witness who is asked by a judge what she\nnoticed when she looked into the room. The witness answered with\n(15):", "\nIt is surprising that there is a past tense in the second sentence,\neven though the book must have still been in Russian when the witness\nwas called for testimony. Even more surprising is the fact that the\nwitness could not have said (16) instead of (15).", "\nTranslated into a situation semantics (Klein himself talks about topic\ntimes, rather than topic situations), Klein’s explanation is\nthat tense relates utterance situations to topic situations, which do\nnot necessarily coincide with the situations described by the main\npredication of a sentence. In Klein’s scenario, the topic\nsituation for the second part of the witness’s answer was the\npast situation that she saw when she looked into the room. Since the\ntopic situation was past, tense marking in the second sentence of (16)\nhas to be past, too. Via their temporal locations, topic situations\nplay an important role in the semantics of both tense and aspect (see\nthe entry on \n tense and aspect; \nalso Smith 1991, Kamp & Reyle 1993, and Cipria\n& Roberts 2000).", "\nIf Austinian topic situations play a role in the grammars of natural\nlanguages, there should be grammatical devices in at least some\nlanguages that track them. Recent work by Andrew McKenzie (McKenzie\n2012, 2015) has suggested that certain Switch Reference systems in a\nnumber of genetically unrelated languages seem to track Austinian\ntopic situations. For example, the North American language Kiowa\n(Tanoan, spoken in Oklahoma) uses different forms for certain\nsentential connectives (including conjunction), depending on whether\nthe topic situations of the conjoined conjuncts changes or stays the\nsame." ], "section_title": "3. Austinian topic situations", "subsections": [] }, { "main_content": [ "\nAmong the most innovative ideas in Barwise & Perry 1983 is the\nproposal to exploit the Austinian perspective on utterances to account\nfor implicit quantifier restrictions and so-called\n“incomplete” definite descriptions (see the entry\n descriptions):", "\nSuppose that I am in a room full of people, some of whom are sleeping,\nsome of whom are wide awake. If I say, “no one is\nsleeping,” have I told the truth or not? Again, it depends on\nwhich situation I am referring to. If I am referring to the whole\nsituation including all the people in the room, then what I have said\nis false. However, one can well imagine situations where I am clearly\nreferring only to a part of that situation. Imagine, for example, that\nI am conducting an experiment which requires an assistant to monitor\nsleeping people, and I look around the sleep lab to see if all of my\nassistants are awake and ready to go. Surely, then I may truly and\ninformatively say, “No one is asleep. Let’s begin.”\n…. The crucial insight needed goes back to Austin … As\nAustin put it, a statement is true when the actual situation to which\nit refers is of the type described by the statement. (Barwise &\nPerry 1983, 160)\n", "\nA similar example discusses incomplete definite descriptions:", "\nSuppose my wife and I collaborate on cooking for a party. And suppose\nthat at a certain point in the party I say, “I am the\ncook,” referring to l. Is what I said true or not?\n", "\nThe answer is, “It depends on which situation I am\ndescribing.” First, suppose someone comes up to me and says,\n“The food at this party is delicious! Who is the cook?” If\nI say “I am the cook,” I have clearly not described things\naccurately. I have claimed to be the person who did the\ncooking for the party. But suppose instead someone comes up to me\neating a piece of my famous cheesecake pastry and says, “Who\nmade this?” Then I may truly say that I am the cook. (Barwise\n& Perry 1983, 159)", "\nOn the Austinian perspective, at least certain kinds of implicit\nrestrictions for quantification domains are a direct consequence of\nthe fact that assertions are about particular actual situations, and\nthat those situations can be smaller or bigger parts of the actual\nworld.", "\nThe Austinian answer to implicit domain restrictions was endorsed and\ndeveloped in Récanati (1986/87, 1996, 2004a) and Cooper 1996.\nAn influential attack on the situation semantics approach to\n“incomplete” definite descriptions came from Soames 1986,\nwho concluded that “the analysis of definite descriptions is not\nfacilitated by the kind of partiality that situation semantics\nprovides” (Soames 1986, 368). Soames’ reservations against\nthe Austinian approach to domain restrictions come from two major\npotential counterarguments, both of which are directed against\nparticular implementations of the approach. One of the potential\nproblems discussed by Soames concerns attributive readings of definite\ndescriptions. However, as Soames is careful to note (Soames 1986,\n359), this problem does not necessarily affect possibilistic versions\nof situation semantics. Since Soames’ qualification is not\nelaborated in his article, it might be useful to look at a concrete\nexample illustrating his point. Suppose the two of us observe a bear\ncrossing the road one night in Glacier National Park. Since it is\ndark, we can’t see the bear very well, and I say to you:", "\nI am aware that the bear we see is not the only bear in the world, so\nmy assertion relies on an implicit domain restriction. On the\nAustinian view, my assertion is about a particular situation located\nsomewhere in Glacier National Park at a particular time in August\n2006. Call that situation “Bear Sighting”. Bear Sighting\nhas a particular bear in it, the bear we see. Call that bear\n“Bruno”. On the intended attributive reading, what I want\nto get across to you is not that Bruno may be a grizzly, but that our\nevidence about Bear Sighting is compatible with the assumption that\nthe bear there—whoever he is—is a grizzly. There is a\nlegitimate question whether we can get that reading on the Austinian\napproach to domain restrictions. If Bear Sighting has to give us the\nrestriction for bear, it seems that all it can do is restrict\nthe bears we are talking about to Bruno. But that wouldn’t\nproduce the attributive reading we are after. For that reading, so it\nmight seem, domain restrictions must be properties.", "\nThe above conclusion might look inevitable, but it is not. It is true\nthat on the Austinian view, my utterance of (17) is interpreted as a\nclaim about Bear Sighting. To see that we can nevertheless get the\ndesired interpretation, we need to look at technical details. 18(a)\ngives a plausible interpretation of the possibility modal in (17)\nwithin a possibilistic situation semantics. 18(b) is the\ninterpretation of the whole sentence (17) before the Austinian\ncomponent comes into play:", "\n(18) assumes an intensional semantics that is based on possible\nsituations. In possible situation semantics, propositions are sets of\npossible situations, or characteristic functions of such sets, and all\npredicates are evaluated with respect to a possible situation. 18(b)\nis the proposition expressed by (17) in context c. That\nproposition is a property that is true of a situation s iff\nthere is a situation s′ that is accessible from\ns and the unique bear in s′ is a grizzly in\ns′. The modal might introduces existential\nquantification over possible situations that are accessible from the\nevaluation situation s (see the entry\n modal logic).\n The kind of accessibility relation is determined by the lexical\nmeaning of the modal in interaction with properties of the utterance\ncontext c (see the entry\n indexicals).\n In our example, the modality is a particular kind of epistemic\nmodality that relates two situations s and s′\nin a context c just in case s and s′\nare equivalent with respect to the information available in\nc, that is, whatever evidence about s is available\nin c isn’t specific enough to distinguish between\ns and s′ (epistemic contextualism).\nEvidence that counts as available for epistemic modals might include\nthe distributed knowledge of the discourse participants (see von\nFintel & Gillies 2011), other available sources of information\nlike ship’s logs or computer printouts (Hacking 1967, von Fintel\n& Gillies 2011), but, interestingly, not necessarily information\nthat happens to be hidden from sight like test results in sealed\nenvelopes (de Rose 1991), babies in wombs (Teller 1972), weather\nconditions behind drawn curtains (Gillies 2001), or details of animals\nobscured by darkness. Suppose the actual bear in Bear Sighting is in\nfact a black bear, and not a grizzly. Since it is night and we\ncan’t see the bear very well, the evidence we have about Bear\nSighting when I utter (17) cannot distinguish the real situation from\nmany merely possible ones, including some where the bear is a grizzly\nand not a black bear. This is what makes my utterance of (17)\ntrue.", "\nWhen I uttered (17), I claimed that the proposition in 18(b) was true\nof Bear Sighting. Applying 18(b) to Bear Sighting yields the desired\nattributive interpretation. Bear Sighting is exploited to provide\nimplicit domain restrictions, but it doesn’t do so directly. We\nare considering epistemic alternatives of Bear Sighting. The epistemic\nalternatives are alternatives of Bear Sighting, hence are partial,\njust as Bear Sighting itself is. They have no more than a single bear\nin them. This suggests that the analysis of definite descriptions\nis facilitated by the kind of partiality that situation\nsemantics provides. Austinian topic situations can give us domain\nrestrictions for attributive definite descriptions.", "\nSoames’ second major objection against the Austinian approach to\ndomain restrictions relates to the fact that there are instances of\ndomain restrictions that can’t seem to come from Austinian topic\nsituations (see also Westerståhl 1985). One of Soames’\nexamples is (19) below (Soames 1986, 357), which is a variation of\nBarwise and Perry’s sleep lab example quoted above.", "\nIf all quantifier domains were provided by Austinian topic situations,\n(19) would seem to make contradictory demands on such a situation.\nAssuming that there is just a single topic situation for utterances of\n(19), we seem to predict that those utterances imply that the research\nassistants are among those who are asleep. But there is no such\nimplication. Soames is aware that proponents of the Austinian approach\nare not committed to the assumption that all domain\nrestrictions are directly provided by Austinian topic situations\n(Soames 1986, footnote 17, 371), and he therefore emphasizes that he\nis only commenting on the particular account of domain restrictions\noffered in Barwise and Perry (1983, 1985). Soames’ objection\ndoes not apply to Cooper 1996, for example, who allows quantifier\ndomains to be determined by different resource situations, which he\ndistinguishes from the Austinian topic situation (his “described\nsituation”). The objection also does not apply to possibilistic\nversions of situation semantics, where every predicate is necessarily\nevaluated with respect to an actual or possible situation. Different\npredicates in one and the same sentence can then be evaluated with\nrespect to different situations (Heim 1990, Percus 2000, Elbourne\n2002, 2005, 2013). A possible interpretation for (19) might be\n(20):", "\nWhen the doctor of the sleep lab utters (19), she claims that the\nproposition in (20) is true of a particular situation, call it\n“Sleep Lab”. Sleep Lab is the Austinian topic situation,\nbut it is not the situation that picks out the sleepers. The sleepers\nmight be recruited from a contextually salient (possibly scattered)\nsituation s′ that is related to Sleep Lab via the part\nrelation ≤p and functions as a resource\nsituation for the evaluation of the predicate person\nintroduced by the quantifier phrase everyone. This situation\ncould be the sum of the patients in the lab, for example.", "\nNeither topic nor resource situations have to be posited for the\nexclusive need of domain restriction. In a possibilistic situation\nsemantics resource situations are the kind of entities that the\nevaluation of any predicate routinely depends on. Topic situations,\ntoo, are independently needed: they are the situations that assertions\nand beliefs are about, and they are key players in the semantics of\ntense and aspect. This means that the contribution of topic and\nresource situations to domain restriction comes entirely for free.\nMany instances of domain restrictions can thus be explained without\npositing any special devices. Some of the remaining cases might also\nbe accounted for by independently attested mechanisms including\nsyntactic ellipsis, presupposition projection and conversational\nimplicatures. But there is also exaggeration, taboo related omissions,\nand some such. The implicit domain restriction in the following\nsentence, which appeared on a note posted in a bathroom in York\n(England), might very well fall in the last-mentioned category:", "\nIt is hard to see how any theory would want to literally prevent any\nkind of pragmatic enrichment processes (Récanati 1993, 2002,\n2004) from contributing to implicit quantifier restrictions, given\nthat humans are able to “interpret utterances replete with\nirony, metaphor, elision, anacoluthon, aposiopesis, and on top of all\nof this …identify what a speaker is implying as well\nas saying” (Neale 2004, 123). Implicit domain restrictions are\nlikely to be the byproducts of a number of independently attested\nmechanisms, then." ], "section_title": "4. Situation semantics and implicit domain restrictions", "subsections": [] }, { "main_content": [ "\nAn important question in situation semantics is how exactly situations\nenter the semantic interpretation process. Are they articulated via\nsyntactically represented variables, or are they “unarticulated\nconstituents” (Perry 1986, Récanati 2002), possibly mere\nindices of evaluation? The issue is well explored for times and\npossible worlds (see the entry on \n ontological commitment).\n Kripke’s semantics for modal logic allows quantification over\npossible worlds only in the metalanguage (see the entry\n modal logic),\n for example. Likewise, in Prior’s tense logic (see the entry\n Arthur Prior),\n quantification over times is confined to the metalanguage (see the\nentry\n time).", "\nMontague’s language of intensional logic (Montague 1974) was\ndeveloped in the tradition of Kripke and Prior, and does not have\nvariables ranging over times or worlds: tense and modal operators\nshift evaluation indices, as illustrated in (22), but do not bind\nvariables in the object language. Quantification over worlds and times\nis treated differently from quantification over individuals, then. The\ndistinction was made deliberately because it predicts differences that\nwere thought correct at the time. Once an evaluation index is shifted,\nit is gone for good, and can no longer be used for the evaluation of\nother expressions. This constrains temporal and modal anaphora. Until\nthe early seventies anaphoric reference to times and worlds in natural\nlanguages was believed to be constrained in precisely the way\npredicted by the evaluation index approach. The belief was challenged\nby work on temporal anaphora (Kamp 1971, Partee 1973, Vlach 1973, van\nBenthem 1977), however. Cresswell 1990 presented parallel arguments\nfor modal anaphora, and showed more generally that natural languages\nhave the full expressive power of object language quantification over\nworlds and times. Quantification over worlds or times is thus no\ndifferent from quantification over individuals, and should be\naccounted for in the same way.", "\nExact analogues of Cresswell’s examples can be constructed to\nshow that natural languages have the full expressive power of object\nlanguage quantification over situations. Here is a first taste of the\nkind of example we have to look at.", "\nSuppose (23) is uttered to make a claim about the town of Amherst\nduring the last 20 years. We are looking at the snowfalls during the\nrelevant period. For each of those actual snowfalls s, we are\nconsidering counterfactual situations r where it snowed much\nmore than it did in s. The claim is that each of those\ncounterfactual situations is part of a situation where the town plow\nremoved the snow for us. To formalize what was said, we have to be\nable to consider for each actual snowfall s a set of\ncounterfactual alternatives and compare the amount of snow in each of\nthem to the actual amount of snow in s. This means that we\nhave to be able to “go back” to the actual snowfall\nsituations after considering corresponding counterfactual situations.\nTo do so we have to keep track of the original situations. The\navailable bookkeeping tools are either evaluation indices, or else\nsituation variables and binding relations in the object language. If\nwe want to avoid possibly unpronounced situation variables, we need\ntwo shiftable evaluation indices for (23). In the long run, even two\nindices wouldn’t be enough, though. Here is an example that\nrequires three:", "\nIt is not hard to see that we can complicate such examples\nindefinitely, and that there would be no end to the number of\nevaluation indices needed. But that suggests that natural languages\nhave the full power of object language quantification over situations.\nQuantification over situations is no different from quantification\nover individuals, then, as far as expressive power is concerned. Since\nnatural languages have syntactically represented individual variables\nand it would be surprising if they used two different equally powerful\nquantification mechanisms, it seems to be at least a good bet that\nthere are syntactically represented situation variables in natural\nlanguages (but see Cresswell 1990 and Jacobson 1999 for dissenting\nopinions). But then the situations quantified over or referred to in\n(23), (24) and their kin do not necessarily correspond to\n“unarticulated constituents”. They are syntactically\nrepresented, even though they might happen to be unpronounced. The\nsyntactic representation of situation variables is investigated in\nPercus 2000, Keshet (2008, 2010), and F. Schwarz (2008, 2012)." ], "section_title": "5. Situation variables or unarticulated constituents?", "subsections": [] }, { "main_content": [ "\nOne of the most frequent uses of situation-based frameworks is in the\nanalysis of “donkey” pronouns, that is, anaphoric pronouns\nthat are interpreted as definite descriptions (see descriptive\ntheories of anaphora under the entry\n descriptions\n and the entry\n anaphora).", "\nThe pronoun it in 25(a) is an instance of a descriptive\npronoun that is interpreted like the corresponding definite\ndescription in 25(b). Suppose I use 25(a) or (b) to talk about a\nparticular situation, call it “Donkey Parade”. The\nsituations that whenever quantifies over are then all part of\nDonkey Parade. They are precisely those subsituations of Donkey Parade\nthat are minimal situations in which a donkey appeared. Those must\nthen be situations with a single donkey in them. The claim is that all\nthose situations are part of situations where the donkey was greeted\nenthusiastically. More formally, my claim about Donkey Parade is\n(26):", "\n(26) reflects the standard analysis of adverbs of quantification and\ndescriptive pronouns in a possibilistic situation semantics (Berman\n1987; Heim 1990; Portner 1992; von Fintel 1994, 2004b; Elbourne 2002,\n2005, 2013, 2016). All resource situations that are introduced in (26)\nare directly or indirectly related to the topic situation via the part\nrelation ≤p. The topic situation is the\nultimate anchor for all resource situations. It indirectly restricts\nthe donkeys being talked about to those that are present in Donkey\nParade. The antecedent of the conditional introduces a further\nrestriction: we are considering only those subsituations of Donkey\nParade that are minimal situations in which a donkey appeared. Those\nsituations have just one donkey in them, and they can thus be used as\nresource situations for the definite description the donkey\nor a corresponding descriptive pronoun.", "\nThe crucial feature of any analysis of donkey sentences within a\nsituation semantics is that quantification is over minimal situations\nsatisfying conditions imposed by the antecedent of the conditional.\nThe minimality condition is crucial for the analysis of descriptive\npronouns. Without it, we wouldn’t be able to analyze those\npronouns as definite descriptions:", "\nWe have to make sure that the situations or events quantified over\nhave just one man and just one donkey in them, because definite\ndescriptions have to be unique with respect to their resource\nsituations. The minimality condition is a source of potential trouble,\nhowever (Reinhart 1986, Dekker 2004; von Fintel 2004a,b). When the\nantecedent of a conditional contains a mass noun, negative\nquantifiers, or certain kinds of modified quantifier phrases,\nquantification over minimal situations or events seems to yield\nunwelcome results or isn’t possible at all:", "\n28(a) raises the question whether there ever are minimal situations or\nevents in which snow falls. But even if there are, we do not quantify\nover them in this case. We also do not seem to rely on discrete scales\nfor measuring portions of Super Supper. But even if we did, this would\nnot help with 28(b). This sentence does not necessarily quantify over\nsituations in which a cat eats just a little more than a can of Super\nSupper. Minimality also doesn’t seem to play a role for 28(c).\nIf 28(c) quantified over minimal situations that have between 20 and\n2000 wedding guests, it would quantify over situations or events with\nexactly 20 wedding guests, and might very well be true. 28(d) is even\nmore dramatic. What would a minimal situation or event look like in\nwhich nobody showed up? If any event- or situation-based analysis of\ndonkey sentences is to succeed, then, it must keep the events or\nsituations that are quantified over small enough to contain just one\nman and one donkey in cases like (27), but it has to accomplish this\nwithout minimizing the amount of snow, Super Supper, or wedding guests\nin cases like 28(a) to (c). And it should not mess with negative\nconstructions at all. When we are quantifying over situations in\ndonkey sentences, then, we need to relate possibly very complex\nsentences to exemplifying situations in a way that is responsive to\nthe different behavior of different kinds of antecedents illustrated\nby (27) and 28(a) to (d).", "\nThere are several proposals in the literature that elucidate the\nrelation between a sentence and the situations or events that\nexemplify it by positing a special recursive mechanism that relates\nsentences to the set of exemplifying events or situations (see Schein\n1993, chapters 9 and 10 for discussion of this issue). Possibilistic\nversions of situation semantics typically start out with a recursive\ntruth definition that relates utterances of sentences to the sets of\npossible situations in which the utterances are true, the propositions\nexpressed. The situations or events that exemplify a proposition can\nthen be defined as the “minimal” situations in which the\nproposition is true (see the entries on\n events,\n facts,\n states of affairs,\n and truthmakers). The\nchallenge presented by sentences (27) and 28(a) to (d) is that they\nsuggest that a naïve notion of minimality won’t do. A more\nflexible notion of minimality seems to be needed. The following\nsection will document in some detail how the desired notion of\nminimality might emerge from a simple definition of exemplification in\ninteraction with independently justified sentence denotations. The\nissue is under active investigation, however, and cannot be considered\nsettled before a wide range of different constructions has been looked\nat. Whatever the ultimate outcome may be, the following discussion\nwill provide the opportunity to illustrate how the shift from possible\nworlds to situations affects the denotations we might want to posit\nfor an expression. In a situation semantics, there are often several\nways of assigning denotations to an expression that are hard to\ndistinguish on truth-conditional grounds. Looking at the situations\nthat exemplify a sentence as well as its truth-conditions helps with\nthe choice." ], "section_title": "6. Situations, minimality, and donkey sentences", "subsections": [] }, { "main_content": [ "\nIn possibilistic versions of situation semantics, possible situations\nare parts of possible worlds. Some authors also assume that the parts\nof a possible world w form a join semi-lattice with maximal\nelement w (Bach 1986; Lasersohn 1988, 1990; Portner 1992; see\nalso the entry\n mereology).\n The part relation ≤p and the sum operation +\nare then related as usual: s ≤p\ns′ iff s + s′ =\ns′. Propositions are sets of possible situations or\ntheir characteristic functions (see the entry\n propositions).\n The notion of a situation that exemplifies a proposition might be\ndefined as in (29), which is a variation of a definition that appears\nin Kratzer 1990 (Other Internet Resources), 1998, 2002:", "\nIntuitively, a situation that exemplifies a proposition p is\none that does not contain anything that does not contribute to the\ntruth of p. The first part of (29) allows two possibilities\nfor a situation s to exemplify p. Either p\nis true in all subsituations of s or s is a minimal\nsituation in which p is true. The notion of minimality\nappealed to in (29) is the standard one: A situation is a minimal\nsituation in which a proposition p is true iff it has no\nproper parts in which p is true. The situation Mud (Case One\nbelow) gives a first illustration of what (29) does.", "\nCase One: Mud", "\nAssuming that Mud and all of its parts are mud, Mud and all of its\nparts exemplify the proposition in 30(b), since there are no parts of\nMud where there is no mud.", "\n30(b) is not exemplified by Mud & Moss (Case Two below),\nhowever:", "\nCase Two: Mud & Moss", "\nMud & Moss has parts where 30(b) is not true: the parts where\nthere is only moss. But Mud & Moss is not a minimal situation in\nwhich 30(b) is true.", "\nNext, consider (31):", "\n31(b) describes situations s that have at least three teapots\n(individuals that are teapots in the world of s) in them. The\nproposition in 31(b) seems to be exemplified by the situation Teapots\n(Case Three below).", "\nCase Three: Teapots", "\nThere is no proper subsituation of Teapots in which 31(b) is true.\nSince Teapots has nothing but three teapots in it, any proper\nsubsituation of Teapots would have to be one where a part of at least\none of the three teapots is missing. But 31(b) is true in Teapots\nitself, and Teapots is thus a minimal situation in which 31(b) is\ntrue.", "\nThere is a potential glitch in the above piece of reasoning. It\nassumes that when an individual is a teapot in a world, no proper part\nof that individual is also a teapot in that world. This assumption can\nbe questioned, however. Following Geach 1980 (p. 215; see entries\n identity,\n problem of many), we might reason as follows: My teapot would remain a\nteapot if we chipped off a tiny piece. Chipping off pieces from\nteapots doesn’t create new teapots, so there must have been\nsmaller teapots all along. We might feel that there is just a single\nteapot sitting on the table, but upon reflection we might have to\nacknowledge that there are in fact many overlapping entities that all\nhave legitimate claims to teapothood. The unexpected multitude of\nteapots is a source of headaches when it comes to counting. A\nfundamental principle of counting says that a domain for counting\ncannot contain non-identical overlapping individuals (Casati &\nVarzi 1999, 112):", "\n(32) implies that just one of the many overlapping teapots on the\ntable over there can be counted, and the question is which one. If we\nare that liberal with teapothood, we need a counting criterion that\ntells us which of the many teapots in our overpopulated inventory of\nteapots we are allowed to count.", "\nWith spatiotemporal objects like teapots, humans seem to rely on\ncounting criteria that privilege maximal self-connected entities\n(Spelke 1990, Casati & Varzi 1999). A self-connected teapot is one\nthat cannot be split into two parts that are not connected. In\ncontrast to parthood, which is a mereological concept, connectedness\nis a topological notion (see Casati and Varzi 1999 for discussion of\nvarious postulates for a “mereotopology”, a theory that\ncombines mereology and topology). The maximality requirement prevents\ncounting teapots that are proper parts of other teapots, and the\nself-connectedness requirement disqualifies sums of parts from\ndifferent teapots. Casati and Varzi point out that not all kinds of\nentities, not even all kinds of spatiotemporal entities, come with\ncounting criteria that involve topological self-connectedness. Obvious\ncounterexamples include bikinis, three-piece suits, and broken glasses\nthat are shattered all over the floor. We have to recognize a wider\nrange of counting criteria, then, that guarantee compliance with (32)\nin one way or other.", "\nAssuming counting criteria, the proposition expressed by 31(a) would\nstill be exemplified by Teapots, even if we grant that teapots can\nhave proper parts that are also teapots. The specification of\ndenotations for sentences with numerals would now have to make\nreference to teapots that can be counted, call them “numerical\nteapots”. Representations like 31(b) and its kin should then be\nunderstood along the lines of 33(b):", "\nIf Teapots contains nothing but three individuals that are numerical\nteapots in the actual world, 33(b) is true in Teapots. But then none\nof the proper subsituations of Teapots can contain three individuals\nthat are numerical teapots in the actual world. Any such situation\ncontains at least one teapot that is a proper part of one of the\nteapots in Teapots, hence can no longer contain three numerical\nteapots.", "\nIn contrast to Teapots, Teapots & Scissors (Case Four below) does\nnot exemplify 31(b). Teapots & Scissors has parts where 31(b) is\nnot true: take any part that has just the scissors or just a part of\nthe scissors in it, for example. But Teapots & Scissors is not a\nminimal situation in which 31(b) is true.", "\nCase Four: Teapots and Scissors", "\nDefinition (29) has the consequence that Teapots does not exemplify\nthe proposition 34(b) below, even though 34(b) is true in Teapots.", "\n34(b) is true in Teapots, since Teapots contains a plural individual\nthat contains exactly two teapots. However, 34(b) is not exemplified\nby Teapots. Teapots has parts in which 34(b) is not true without being\na minimal situation in which 34(b) is true. More generally, if\nsentences of the form there are n teapots denote propositions\nof the kind illustrated by 34(b), then those propositions can only be\nexemplified by situations that have exactly n teapots.\nLikewise, if there is a teapot is interpreted as in 35(b)\nbelow, the proposition it expresses can only be exemplified by\nsituations with exactly one teapot, even though it can be true in\nsituations with more teapots.", "\nThe predicted exemplification properties of sentences with numerals\nare welcome, since they suggest that (29) might indeed capture the\nrelation between propositions and situations that we are after: The\nsituations exemplifying the proposition expressed by there is a\nteapot are all situations that have a single teapot in them,\nhence are literally minimal situations containing a teapot. In\ncontrast, the situations exemplifying the proposition expressed by\nthere is mud are all situations that contain mud and nothing\nelse, hence do not have to be minimal situations containing mud.", "\nThe major consequence of (29) is that if a proposition has\nexemplifying situations at all, the set of its exemplifying situations\nmust be either homogeneous or quantized in the sense of Krifka 1992. A\nset of situations is quantized iff it doesn’t contain both a\nsituation s and a proper part of s. A set of\nsituations is homogeneous iff it is closed under the parthood\nrelation, that is, whenever it contains a situation s, it\nalso contains all parts of s. As argued in Krifka’s\nwork, algebraic notions like homogeneity and quantization might\ncapture linguistically important aspectual distinctions like that\nillustrated in (36) (see the entry on \n tense and aspect).", "\nThe proposition expressed by 36(a) seems to be exemplified by minimal\npast situations in which Josephine built an airplane, and this set of\nsituations is quantized. On the other hand, the proposition expressed\nby 36(b) seems to be exemplified by all past situations that contain\nairplane flying by Josephine and nothing else, and this set of\nsituations is homogeneous. Homogeneous sets cannot be used as counting\ndomains, however, and this requires adjustments with examples like\n37(b).", "\n37(b) cannot quantify over all situations that exemplify the\nproposition Josephine flew an airplane, since this would give\nus a quantification domain that violates the Counting Principle (32).\nWe have to impose a counting criterion, then, and the topological\nnotion of self-connectedness seems to be relevant here, too (see von\nFintel 2004a,b). As a result, 37(b) might quantify over maximal\nself-connected situations exemplifying the proposition expressed by\nJosephine flew an airplane.", "\nWe are now in a position to see how exemplification can be used for\nthe analysis of donkey sentences. Look again at (38) and (39):", "\n(38) and (39) quantify over parts of a contextually salient topic\nsituation. The antecedents of the conditionals tell us more about what\nthose parts are. In (38) quantification is over situations\nexemplifying the proposition expressed by a man saw a donkey,\nwhich are all situations that contain a single man and a single\ndonkey. Those situations can then be taken to be resource situations\nfor the definite descriptions the man and the donkey\nin the consequent of (38). (39) also quantifies over parts of the\ntopic situation that exemplify the antecedent proposition, but as in\nthe case of 37(b), considering all exemplifying situations would\nviolate the Counting Principle, and we therefore need a counting\ncriterion. (39) might then quantify over maximal self-connected\nsituations exemplifying the proposition expressed by snow falls\naround here. Those situations include complete snowfalls, then,\nand if it does indeed snow a lot around here whenever it snows, (39)\nmight very well wind up true.", "\nNot all propositions that look like perfectly acceptable candidates\nfor sentence denotations have exemplifying situations. Consider 40(b),\nfor example:", "\nWhenever there is a situation that has more than five tons of mud in\nit, there are parts that have just five tons or less. But none of\nthose parts can be part of any minimal situation with more than five\ntons of mud, since there are no such situations.", "\nIn a situation semantics, it often happens that there are several\noptions for assigning subtly different propositions to sentences, and\nsometimes the options are hard to distinguish on truth-conditional\ngrounds. Insisting on both adequate truth-conditions and adequate\nexemplification conditions might help narrow down the field of\ncandidates. 40(a) can also be paraphrased as saying that the total\namount of mud in some contextually salient resource situation weighs\nmore than five tons. The denotation of 40(a) could be (41), then,\nwhich includes a contextualized maximalization condition:", "\n(41) is true in a situation s if it contains all the mud of\nsome salient resource situation s′ (possibly the actual\nworld as a whole), and that mud weighs more than 5 tons. (41) is\nexemplified by the mud in s′, provided it weighs more\nthan five tons. Sentences may contain noun phrases that provide\nanchors for the maximalization condition. (42) is a case in\nquestion:", "\n42(b) is exemplified by the mud in this ditch, as long as it weighs\nmore than five tons.", "\nMaximalized interpretations for more than n and similar kinds\nof indefinites like at least n are discussed in Reinhart\n1986, Kadmon  (1987, 1990, 2001), Schein 1993, and Landman (2000,\n2004). Some of the original observations go back to Evans 1977. As\nnoted by Reinhart and Kadmon, more than n noun phrases\nproduce maximality effects of the kind illustrated in (43):", "\n(43) would be considered false in a situation where there was in fact\n7 tons of mud in this ditch, but only six tons were removed. This\njudgment can be accounted for by assuming that utterances of the\nsecond sentence in (43) are about a particular past situation that\nexemplifies the first sentence. This situation can then serve as a\nresource situation for the interpretation of the definite description\nthe mud. If sentences like 42(a) have maximalized\ninterpretations, it follows that the mud that was removed was all the\nmud in the ditch.", "\nThere are other numeral expressions that trigger maximalization. (44)\nis an example:", "\n44(c), too, would be considered false in situations where only some of\nthe teapots on the shelf are defective. Even simple numeral phrases\nlike four teapots can have maximalized interpretations.", "\nIntuitions for (45) are not so clear, but (46) brings out a sharp\ndifference between simple and complex numeral phrases.", "\nImagine that I sold exactly four teapots yesterday. 46(a) has an\ninterpretation where I am entitled to a $10 bonus. On this reading,\nour quantification domain is some set of non-overlapping situations\nthat are minimal situations in which I sold two teapots on the same\nday. Regardless of how we pair up yesterday’s four teapot sales\nto construct an acceptable counting domain, we always end up with\nexactly two bonus-qualifying situations. This shows that numeral\nexpressions like two teapots do not obligatorily have\nmaximalized interpretations. 46(a) contrasts with 46(b) and (c). 46(c)\nhas no interpretation where I qualify for a $10 bonus if I sold four\nteapots yesterday. And 46(b) has no interpretation where I get $10\ndollars if I sold six, for example. We can conclude, then, that\nnumeral expressions of the form more than n NP or between\nn and m NP trigger denotations that are obligatorily maximalized,\nbut this is not the case for simple numerals of the form n\nNP.", "\nReturning to the donkey sentences we looked at earlier, we now\nunderstand why 47(a) and (b) (repeated from above) do not simply\nquantify over minimal situations in a naïve sense:", "\nThe antecedents of 47(a) and (b) involve maximalization. For 47(a),\nfor example, the proposition expressed by the antecedent could be\n48(b):", "\n48(b) restricts the situations quantified over to those whose temporal\nextension is a day, which could be a calendar day, or, more plausibly,\na 24-hour period. The maximality condition can then pick out all the\nfood eaten during such a period by the relevant cats, regardless of\nwhether they ate just a little more than what comes in a can or much\nmore than that. There is no pressure to keep the portions small.\nHowever, Fox & Hackl (2006) have drawn attention to a class of\ncases where there is pressure to keep amounts small in\nsentences with more than n noun phrases. (49) below would be\nsuch a case:", "\n(49) suggests that candidates appeared on TV five minutes after it\nbecame clear that they had won the majority of votes. If 500 votes\nwere cast in all, for example, and the ballot count showed at 8:00 pm\nthat one of the candidates had won 251 votes, the winning candidate is\nclaimed to have appeared on TV at 8:05 pm. This judgment is expected\nif (49) quantifies over situations that exemplify the proposition\nexpressed by its antecedent. Factoring in maximalization triggered by\nmore than 50% of all votes, the antecedent can be paraphrased\nas (50):", "\nThe exemplifying situations for the proposition expressed by (50) are\nminimal ballot count situations that establish that one of the\ncandidates has carried the majority of votes. If there are 500 ballots\nin all, the exemplifying situations are all situations where 251\nballots have been counted.", "\nThe last case to discuss concerns negative quantifiers.", "\n51(b) is exemplified by the situations in which it is true. This makes\nthe situations exemplifying negative sentences a rather disparate\nbatch that do not resemble each other in any intuitive sense. If we\nwant to quantify over situations exemplifying the propositions\nexpressed by negative sentences, as we do in (52) below (repeated from\nabove), contextual restrictions for the topic situation must play a\nmajor role, including those contributed by the topic-focus\narticulation and presuppositions (Kratzer 1989, 2012; von Fintel 1994,\n2004a). Exemplification is not expected to make any contribution here,\nwhich is the result we want to derive.", "\nThis section discussed and tested a particular possibilistic account\nof the relation between a proposition and its exemplifying situations.\nThe test cases were conditionals that quantify over situations that\nare “minimal” in a way that is responsive to specific\nproperties of their antecedents: the presence of count nouns versus\nmass nouns, telic versus atelic verb phrases, modified versus\nunmodified numerals, negative versus positive quantifiers. The account\nshowed the right responsiveness in interaction with independently\nmotivated interpretations for the sentences involved. Interestingly,\nonce possible maximalizations are factored into sentence denotations,\nthe exemplification account spelled out in definition (29) coincides\nwith the naïve minimalization account in most cases. The only\nsystematic exceptions seem to be atelic antecedents, including those\ninvolving negation. Contrary to initial appearance, then, the\nnaïve minimalization accounts found in most existing analyses of\ndonkey sentences within a possibilistic situation semantics are close\nto correct (but see section 9 for discussion of another potentially\nproblematic case, example (61))." ], "section_title": "7. Minimality and exemplification", "subsections": [] }, { "main_content": [ "\nMinimal interpretations of sentences are a common phenomenon and are\nnot only found in the antecedents of donkey sentences. Among the most\nwidely discussed cases are exhaustive answers to questions, or more\ngenerally, exhaustive interpretations (Groenendijk & Stokhof 1984,\nBonomi & Casalegno 1993, Sevi 2005, Schulz and van Rooij 2006,\nSpector 2006, Fox (to appear), Fox & Hackl (to appear); see also\nthe entry\n implicature).\n Here is an illustration.", "\nWe tend to understand Beatrice’s answer as suggesting that Jason\nand Willie were the only ones who caught something. This is the\nexhaustive interpretation of Beatrice’s answer. Non-exhaustive\nor “mention some” answers are often marked with special\nintonation or particles, as in (54), for example:", "\nIn this case, Beatrice indicates that she does not mean her answer to\nbe understood exhaustively. In combination with Groenendijk and\nStokhof’s 1984 analysis of questions, the exemplification\nrelation allows a strikingly simple characterization of exhaustive and\nnon-exhaustive answers. If we import Groenendijk and Stokhof’s\nanalysis into a situation semantics, the extension of\nJosephine’s question in (54) is the proposition in (55):", "\n(55) describes possible situations in which the set of those who\ncaught something is the same as the set of those who caught something\nin the actual world. Since question extensions are propositions, they\ncan be exemplified. Suppose Jason, Willie, and Joseph are the only\nones who caught anything in the actual world. Then (55) is exemplified\nby all minimal situations in which Jason, Willie, and Joseph caught\nsomething. If nobody caught anything in the actual world, then any\nactual situation exemplifies (55). Bringing in the Austinian\nperspective, we can now say that answers to questions are always\nunderstood as claims about the actual situations that exemplify the\nquestion extension. Via their exemplifying situations, then, question\nextensions determine possibly multiple topic situations that answers\nare understood to make claims about. When an answer is interpreted as\nexhaustive, the proposition it expresses is understood as\nexemplified by the topic situations. When an answer is\ninterpreted as non-exhaustive, the proposition it expresses is\nunderstood as being merely true in the topic situations. We\nhave, then:", "\nThe proposition expressed by Beatrice’s exhaustive answer in\n(53) is understood as exemplified by the topic situations determined\nby Josephine’s question, and that implies that Jason and Willie\nwere the only ones who caught anything. In contrast, Beatrice’s\nnon-exhaustive answer in (54) is understood as being true in the topic\nsituations, and that allows for the possibility that there were others\nwho caught something.", "\nIt might be useful to consider a few more possible answers that\nBeatrice might have given in response to Josephine’s question\nand find out what the exemplification approach would predict if the\nanswers are understood exhaustively:", "\nThe proposition expressed by 57(a) is exemplified by minimal\nsituations in which two cats caught something. If the topic situations\nare of this kind, they, too, are minimal situations in which two cats\ncaught something. But then the only ones who caught anything in the\nactual world are two cats. Building in maximalization, the proposition\nexpressed by 57(b) is exemplified by minimal situations in which a\nbunch of two to five cats that consisted of all the cats that caught\nsomething in some salient resource situation caught something. If the\ntopic situations are of this kind, then only cats caught something,\nand there were between two and five of them. For 57(c), the set of\nsituations that exemplify the proposition it expresses coincides with\nthe set of situations in which it is true. Consequently, there is no\ndifference between an exhaustive and a non-exhaustive interpretation.\nThe topic situations include the actual world, and what is being\nclaimed about them is that nobody caught anything.", "\nThe examples discussed suggest that the notion of minimality that is\nneeded for the analysis of donkey conditionals also accounts for\nexhaustive interpretations of answers. A third area where what looks\nlike the same notion of minimality shows up is Davidsonian event\npredication." ], "section_title": "8. Exemplification and exhaustive interpretations", "subsections": [] }, { "main_content": [ "\nSituations and events seem to be the same kinds of things. If\nsituations are particulars, so are events. If situations are built\nfrom relations and individuals standing in those relations, so are\nevents. We don’t seem to need both of those things. We\ndon’t seem to need both situation semantics and Davidsonian\nevent semantics (see entries\n Donald Davidson\n and\n events).", "\nThe core of a Davidsonian event semantics are predications like the\nfollowing:", "\n(58) is the classical Davidsonian formalization of the tenseless\nsentence Ewan swim. The predication in (58) is standardly\nread as “e is a swim by Ewan”. Crucially, this\nformula is not understood as ‘e is an event that\ncontains a swim by Ewan’ or as “e is an event\nin which Ewan is swimming”. In other words, unlike the\nbasic predications in situation semantics, Davidsonian basic\npredications have a built-in minimality condition. This is a major\ndifference between situation semantics and Davidsonian event\nsemantics, maybe the difference. Without the minimality\ncondition, we couldn’t do many things we want to do with a\nDavidsonian semantics. As an illustration, consider the following\nexample:", "\nIf the simple predication swim(Ewan)(e) in 59(b) could be\nunderstood as “e is an event in which Ewan\nswims”, then 59(b) could describe an event where Ewan swam for\njust five minutes, but a lot of other things went on as well in that\nevent: He rode his bike, his sister slept, his mother harvested\nshallots, his father irrigated fields, and taken together, those\nactivities took a total of 10 hours. 59(a) doesn’t describe\nevents of this kind, hence 59(b) couldn’t be a formalization of\n59(a). The standard way of understanding 59(b) is as saying that there\nwas a swim by Ewan that took 10 hours.", "\nBut what is a swim by Ewan? A swim is typically a self-connected\nsituation in which someone is swimming, and which is\n“minimal” in a sense that it excludes other activities\nlike riding a bike, sleeping or farm work. It doesn’t exclude\nparts of the actual swimming, like movement of arms and legs. Most\nimportantly, a swim by Ewan doesn’t literally have to\nbe a minimal situation in which Ewan is swimming, which would be a\nvery short swim, if there are minimal swimming situations at all. The\nrelevant notion of minimality is by now familiar: a swim by Ewan is a\nsituation that exemplifies the proposition “Ewan is\nswimming”. This suggests that the exemplification relation can\nbe used to actually define basic Davidsonian event predications within\na situation semantics. The exemplification relation relates possibly\nvery complex sentences to their exemplifying situations. Davidsonian\nevent predications emerge as those special cases where the sentences\nthat are related to exemplifying situations are atomic.", "\nIf verbs have an event argument, as Davidson proposed, then simple\nsentences consisting of a verb and its arguments always involve\nDavidsonian event predication, and hence exemplification. Importing\nDavidsonian event semantics into situation semantics, the proposition\nexpressed by 59(a), for example, might be formalized as follows:", "\nThe formula in (60) incorporates the usual notation for Davidsonian\nevent predication. Within a situation semantics, this notation is just\na convenient way to convey that swim(Ewan)(e) is to be\ninterpreted in terms of exemplification: we are not talking about\nsituations in which Ewan swims, but about situations that exemplify\nthe proposition “Ewan swims”.", "\nIf Davidsonian event predication is part of the antecedent of a\nconditional, exemplification may come in more than once when\ndetermining the situations the conditional quantifies over. This is\ncrucial for examples like (61):", "\n(61) quantifies over situations that contain just one man and just one\ndonkey, but it does not seem to quantify over minimal donkey rides.\nThere is no pressure to keep the rides short and multiply the treats\naccordingly. A single shift from descriptions of merely verifying to\nexemplifying situations would not yield the correct quantification\ndomain for (61). If we tried to keep the situations small enough so as\nto contain no more than a single man and a single donkey we would have\nto keep the rides short as well. However, if the antecedent of (61)\ncontains Davidsonian event quantification, we can keep the situations\nquantified over small enough to prevent the presence of more than one\nman or donkey, but still big enough to contain complete donkey rides.\nThe proposition expressed by the antecedent of (61) would be (62):", "\nIf the domain for the event quantifier in (62) is established on the\nbasis of some suitable counting criterion, it could quantify over\nmaximal spatiotemporally connected donkey rides. The proposition in\n(62) can then be exemplified by minimal situations that contain a\nsingle man x and a single donkey y and a maximal\nspatiotemporally connected event of riding y by\nx.", "\nThe goal of bringing together situation semantics and Davidsonian\nevent semantics, at least in certain areas, is pursued in a number of\nworks, including Lasersohn (1988, 1990), Zucchi (1988), Portner\n(1992), Cooper (1997), and Kratzer (1998)." ], "section_title": "9. Situation semantics and Davidsonian event semantics", "subsections": [] } ]

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[ "\nSkepticism about moral responsibility, or what is more commonly\nreferred to as moral responsibility skepticism, refers to a\nfamily of views that all take seriously the possibility that human\nbeings are never morally responsible for their actions in a particular\nbut pervasive sense. This sense is typically set apart by the notion\nof basic desert and is defined in terms of the control in\naction needed for an agent to be truly deserving of blame and\npraise. Some moral responsibility skeptics wholly reject this notion\nof moral responsibility because they believe it to be incoherent or\nimpossible. Others maintain that, though possible, our best\nphilosophical and scientific theories about the world provide strong\nand compelling reasons for adopting skepticism about moral\nresponsibility. What all varieties of moral responsibility skepticism\nshare, however, is the belief that the justification needed to ground\nbasic desert moral responsibility and the practices associated with\nit—such as backward-looking praise and blame, punishment and\nreward (including retributive punishment), and the reactive attitudes\nof resentment and indignation—is not met. Versions of moral\nresponsibility skepticism have historically been defended by Spinoza,\nVoltaire, Diderot, d’Holbach, Priestley, Schopenhauer,\nNietzsche, Clarence Darrow, B.F. Skinner, and Paul Edwards, and more\nrecently by Galen Strawson, Derk Pereboom, Bruce Waller, Neil Levy,\nTamler Sommers, and Gregg D. Caruso. ", "\nCritics of these views tend to focus both on the arguments for\nskepticism about moral responsibility and on the implications\nof such views. They worry that adopting such a view would have dire\nconsequences for our interpersonal relationships, society, morality,\nmeaning, and the law. They fear, for instance, that relinquishing\nbelief in moral responsibility would undermine morality, leave us\nunable to adequately deal with criminal behavior, increase anti-social\nconduct, and destroy meaning in life. Optimistic skeptics,\nhowever, respond by arguing that life without free will and basic\ndesert moral responsibility would not be as destructive as many people\nbelieve. These optimistic skeptics argue that prospects of finding\nmeaning in life or of sustaining good interpersonal relationships, for\ninstance, would not be threatened. They further maintain that morality\nand moral judgments would remain intact. And although retributivism\nand severe punishment, such as the death penalty, would be ruled out,\nthey argue that the imposition of sanctions could serve purposes other\nthan the punishment of the guilty—e.g., it can also be justified\nby its role in incapacitating, rehabilitating, and deterring\noffenders." ]

[ { "content_title": "1. Moral Responsibility Skepticism and Basic Desert", "sub_toc": [] }, { "content_title": "2. Arguments for Moral Responsibility Skepticism", "sub_toc": [ "2.1 Hard Determinism", "2.2 Hard Incompatibilism", "2.3 Impossibility of Ultimate Responsibility", "2.4 Luck", "2.5 Scientific Challenges to Moral Responsibility" ] }, { "content_title": "3. Implications of Moral Responsibility Skepticism", "sub_toc": [ "3.1 Illusionism vs/ Disillusionism", "3.2 Reactive Attitudes", "3.3 Morality", "3.4 Criminal Punishment" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nTo begin, it is important to first get clear on what type of moral\nresponsibility is being doubted or denied by skeptics. Most moral\nresponsibility skeptics maintain that our best philosophical and\nscientific theories about the world indicate that what we do and the\nway we are is ultimately the result of factors beyond our control,\nwhether that be determinism, chance, or luck, and because of this\nagents are never morally responsible in the sense needed to justify\ncertain kinds of desert-based judgments, attitudes, or\ntreatments—such as resentment, indignation, moral anger,\nbackward-looking blame, and retributive punishment. This is not to say\nthat there are not other conceptions of responsibility that can be\nreconciled with determinism, chance, or luck. Nor is it to deny that\nthere may be good reasons to maintain certain systems of punishment\nand reward. Rather, it is to insist that to hold people truly\ndeserving of blame and praise, punishment and reward, would be to\nhold them responsible for the results of the morally arbitrary or for\nwhat is ultimately beyond their control, which is fundamentally unfair\nand unjust. Other skeptics defend the more moderate claim that in any\nparticular case in which we may be tempted to judge that an agent is\nmorally responsible in the desert-based sense, we lack the\nepistemic warrant to do so (e.g., Rosen 2004). ", "\nDerk Pereboom provides a very helpful definition of the kind of moral\nresponsibility being doubted by skeptics, which he calls basic\ndesert moral responsibility and defines as follows:", "\n\n\nFor an agent to be morally responsible for an action in this sense is\nfor it to be hers in such a way that she would deserve to be blamed if\nshe understood that it was morally wrong, and she would deserve to be\npraised if she understood that it was morally exemplary. The desert at\nissue here is basic in the sense that the agent would deserve to be\nblamed or praised just because she has performed the action, given an\nunderstanding of its moral status, and not, for example, merely by\nvirtue of consequentialist or contractualist considerations. (2014a:\n2)\n", "\nConsistent with this definition, other moral responsibility skeptics\nhave suggested that we understand basic desert moral responsibility in\nterms of whether it would ever be appropriate for a hypothetical\ndivine all-knowing judge (who didn’t necessarily create the\nagents in question) to administer differing kinds of treatment (i.e.,\ngreater or lesser rewards or punishments) to human agents on the basis\nof actions that these agents performed during their lifetime (see\nCaruso & Morris 2017; cf. G. Strawson 1986, 1994). The purpose of\ninvoking the notion of a divine judge in the afterlife is to instill\nthe idea that any rewards or punishments issued after death will have\nno further utility—be it positive or negative. Any differences\nin treatment to agents (however slight) would therefore seem warranted\nonly from a basic desert sense, and not a consequentialist\nperspective.", "\nMost moral responsibility skeptics distinguish between\nconsequentialist-based and desert-based approaches\nto blame and punishment (see, e.g., Nadelhoffer 2011; Pereboom 2001,\n2014a; Morris, forthcoming; cf. Vargas\n2012a, 2015 who rejects this distinction as too simplistic).\nConsequentialist-based approaches are forward-looking in the sense\nthat agents are considered proper targets of reprobation or punishment\nfor immoral actions on the grounds that such treatment will, say,\nprevent the agent (or other agents) from performing that type of\naction in the future. Desert-based responsibility, on the\nother hand, is considered to be backward-looking and retributivist in\nthe sense that any punitive attitudes or treatments that are deemed\nappropriate responses for an immoral act/decision are warranted simply\nby virtue of the action/decision itself, irrespective of whatever good\nor bad results might follow from the punitive responses (see Morris,\nforthcoming). Understood this way, basic desert moral responsibility\nrequires a kind of power or ability an agent must possess in order to\njustify certain kinds of desert-based judgments, attitudes, or\ntreatments in response to decisions or actions the agent performed or\nfailed to perform. These reactions would be justified on purely\nbackward-looking grounds and would not appeal to consequentialist or\nforward-looking considerations, such as future protection, future\nreconciliation, or future moral formation. It is this kind of moral\nresponsibility that is being denied by moral responsibility skeptics\n(e.g., Pereboom 2001, 2014a; G. Strawson 1986; N. Levy 2011; Waller\n2011, 2014; Caruso 2012; Vilhauer 2009a,b, 2012; Sommers 2009; Focquaert, Glenn, & Raine\nforthcoming).", "\nImportantly, moral responsibility skepticism, while doubting or\ndenying basic desert moral responsibility, is consistent with agents\nbeing responsible in others senses. For instance,\nattributability responsibility is about actions or attitudes\nbeing properly attributable to, or reflective of, an agent’s\nself. That is, we are responsible for our actions in the\nattributability sense only when those actions reflect our identity as\nmoral agents, i.e., when they are attributable to us. Since\nattributability makes no appeal to basic desert or backward-looking\npraise and blame, it remains independent of desert-based\naccountability (see Shoemaker 2011, 2015; Watson 1996; Eshleman 2014)\nand is consistent with moral responsibility skepticism.", "\nThe answerability sense of responsibility defended by Thomas\nScanlon (1998) and Hilary Bok (1998) is also claimed by some skeptics\nto be consistent with the rejection of basic desert (see Pereboom\n2012, 2014a; cf. Jeppsson 2016a). According to this\nconception of responsibility, someone is responsible for an action or\nattitude just in case it is connected to her capacity for evaluative\njudgment in a way that opens her up, in principle, to demands for\njustification from others (Scanlon 1998; Bok 1998; Pereboom 2014a).\nWhen we encounter apparently immoral behavior, for example, it is\nperfectly legitimate to ask the agent, “Why did you decide to do\nthat?” or “Do you think it was the right thing to\ndo?” If the reasons given in response to such questions are\nmorally unsatisfactory, we regard it as justified to invite the agent\nto evaluate critically what her actions indicate about her intentions\nand character, to demand an apology, or request reform.", "\nAccording to Derk Pereboom (2014a), a leading moral responsibility\nskeptic, engaging in such interactions is reasonable in light of the\nright of those harmed or threatened to protect themselves from immoral\nbehavior and its consequences. In addition, we might have a stake in\nreconciliation with the wrong doer, and calling her to account in this\nway can function as a step toward realizing this objective. We also\nhave an interest in her moral formation, and the address described\nfunctions as a stage in the process. On this forward-looking reading,\nanswerability responsibility is grounded, not in basic desert, but in\nthree non-desert invoking desiderata: future protection, future\nreconciliation, and future moral formation (see Pereboom 2014a).", "\nBasic desert moral responsibility has also been distinguished from\ntake charge responsibility (Waller 1989, 1990, 2004, 2011,\n2014). Bruce Waller, for instance, has argued: ", "\n\n\nJust deserts and moral responsibility require a godlike\npower—the existential power of choosing ourselves, the godlike\npower of making ourselves from scratch, the divine capacity to be an\nuncaused cause—that we do not have” (2011: 40). \n", "\nYet, he maintains, ", "\n\n\nyou [nevertheless] have take-charge responsibility for your own life,\nwhich is a responsibility you deeply value and enjoy\nexercising… (2011: 108). \n", "\nTaking responsibility is distinguished from being morally\nresponsible in that, if one takes responsibility for a particular\noutcome it does not follow that one is morally responsible for that\noutcome. One can take responsibility for many things, from the mundane\nto the vitally important. For example, one can take responsibility for\nteaching a course, organizing a conference, or throwing a birthday\nparty. The responsibility taken, however, is profoundly different from\nthe moral responsibility that would justify blame and punishment,\npraise and reward (Waller 2011: 105; Pereboom 2001: xxi).", "\nWhile some philosophers may claim (or assume) that taking\nresponsibility entails being morally responsible (e.g., Smilansky\n2012), this seems to conflate a very important distinction. To take\nresponsibility for, say, organizing a conference, is to agree to put\nforth the effort needed to achieve a certain set of goals or\ntasks—e.g., inviting speakers, putting out a CFP, reserving the\nspace, etc. If the conference were to fail for reasons completely\noutside the control of the agent—say there was a major snowstorm\nthat day and several of the speakers could not make it—it would\nremain a separate and open question whether the agent who took charge\nfor organizing the conference was deserving of blame for the failure.\nFor many, the intuition is rather strong that she is not, especially\nin cases where the reasons for failure are external to the agent\n(e.g., a snow storm, canceled flights, etc.). But skeptics would\ncontend that the same remains true when the failure is due to the\nagent’s own flaws (e.g., their laziness) since in a naturalistic\nworld devoid of miracles these too are the result of factors outside\nthe control of the agent (e.g., determinism, chance, or luck)." ], "section_title": "1. Moral Responsibility Skepticism and Basic Desert", "subsections": [] }, { "main_content": [ "\nNow that we understand the kind of moral responsibility being doubted\nor denied by skeptics, we can examine the arguments for moral\nresponsibility skepticism. Traditionally, the concept of moral\nresponsibility has been closely connected to the problem of free will.\nIn fact, many contemporary philosophers simply define free will in\nterms of the control in action needed for moral responsibility (though\nan epistemic condition for moral responsibility is generally also\nadded)—see, for example, Pereboom (2001, 2014a), G. Strawson\n(1986, 1994), Campbell (1957), Clarke (2005a), N. Levy (2011),\nRichards (2000), Caruso (2012), Nahmias (2012), Mele (2006), Sommers\n(2007b, 2009), Vargas (2013), Wolf (2011), Vilhauer (2009a), Callender\n(2010). According to these theorists, the concepts of free will and moral responsibility stand or fall together. And while there are a few notable exceptions to defining\nfree will in this way—namely John Martin Fischer’s\nsemi-compatibilism (Fischer & Ravizza 1998; Fischer 2007)\nand Bruce Waller’s reverse semi-compatibilism (2015)—even\nthese philosophers nevertheless acknowledge that moral responsibility,\nas an independent concept, can be threatened by the same kind of\nconcerns as free will (e.g., determinism, indeterminism, chance, and\nluck). I will examine each of these threats in turn. " ], "section_title": "2. Arguments for Moral Responsibility Skepticism", "subsections": [ { "content": [ "\nCausal determinism, as it is commonly understood, is roughly\nthe thesis that every event or action, including human action, is the\ninevitable result of preceding events and actions and the laws of\nnature. The traditional problem of free will and determinism\ncomes in trying to reconcile our intuitive sense of free will with the\nidea that impersonal forces over which we have no ultimate control may\ncausally determine our choices and actions. [I should note that a\nrelated problem arises with regard to God’s foreknowledge (see\nthe entry on\n foreknowledge and free will).]\n In the past, the standard view advancing moral responsibility\nskepticism was hard determinism: the view that causal\ndeterminism is true, and incompatible with free will and moral\nresponsibility—either because it precludes the ability to do\notherwise (leeway incompatibilism) or because it is inconsistent\nwith one’s being the “ultimate source” of action\n(source incompatibilism). For hard determinists, libertarian\nfree will is simply impossible because human actions are part of a\nfully deterministic world and compatibilism amounts to a\n“quagmire of evasion” (James 1884; see the entry on\n arguments for Incompatibilism).", "\nHard determinism had its classic statement in the time when Newtonian\nphysics reigned (see, Spinoza 1677 [1985]; d’Holbach 1770), but\nit has very few defenders today—largely because the standard\ninterpretation of quantum mechanics has been taken by many to\nundermine, or at least throw into doubt, the thesis of universal\ndeterminism. This is not to say that determinism has been refuted or\nfalsified by modern physics, because it has not. Determinism still has\nits modern defenders (e.g., Honderich 1988, 2002) and the final\ninterpretation of physics is not yet in (see, for example, the entry\non\n Bohmian mechanics).\n It is also important to keep in mind that even if we allow some\nindeterminacy to exist at the microlevel of our existence—the\nlevel studied by quantum mechanics—there would still likely\nremain determinism-where-it-matters (Honderich 2002: 5). That\nis, ", "\n\n\nAt the ordinary level of choices and actions, and even ordinary\nelectrochemical activity in our brains, causal laws govern what\nhappens. It’s all cause and effect in what you might call real\nlife. (Honderich 2002: 5) \n", "\nNonetheless, most contemporary skeptics tend to defend positions that\nare best seen as successors to traditional hard determinism." ], "subsection_title": "2.1 Hard Determinism" }, { "content": [ "\nOne of these positions is hard incompatibilism, which\nmaintains that whatever the fundamental nature of reality, whether it\nis deterministic or indeterministic, we lack basic desert\nmoral responsibility. Hard incompatibilism amounts to a rejection of\nboth compatibilism and libertarianism. It maintains that the sort of\nfree will required for basic desert moral responsibility is\nincompatible with causal determination by factors beyond the\nagent’s control and also with the kind of indeterminism\nin action required by the most plausible versions of libertarianism\n(see Pereboom 2001, 2014a).", "\nThe argument for hard incompatibilism can be sketched as follows:\nAgainst the view that free will is compatible with the causal\ndetermination of our actions by natural factors beyond our control\n(i.e., compatibilism), most hard incompatibilists maintain that there\nis no relevant difference between this prospect and our actions being\ncausally determined by manipulators (e.g., Pereboom 2001, 2014a). [For\nadditional arguments against compatibilism, see the entry on\n arguments for incompatibilism.]\n Against event-causal libertarianism, hard incompatibilists\ngenerally advance the “luck” or “disappearing\nagent” objection, according to which agents are left unable to\nsettle whether a decision/action occurs and hence cannot have\nthe control in action required for moral responsibility (Pereboom\n2001, 2014a; 2017c; Waller 1990, 2011, N. Levy 2008, 2011; for\nnon-skeptics who advance similar objections see Ekstrom 2000; Mele\n1999a, 2017; Haji 2001). The same problem, they contend, arises for\nnon-causal libertarian accounts since these too fail to\nprovide agents with the control in action needed for basic desert\n(Pereboom 2014a). While agent-causal libertarianism could, in\ntheory, supply this sort of control, hard incompatibilists argue that\nit cannot be reconciled with our best physical theories (Pereboom\n2001, 2014a; Waller 2011; Harris 2012; cf. N. Levy 2011)\nand faces additional problems accounting for mental causation. Since this exhausts the options for views on which we have the sort of free will needed for basic desert moral responsibility, hard incompatibilists conclude that moral responsibility skepticism is the\nonly remaining position.", "\nCritics of hard incompatibilism include both compatibilists and\nlibertarians. See, for example, the entries on\n compatibilism,\n incompatibilist (nondeterministic) theories of free will, and\n arguments for incompatibilism.\n I will here only briefly discuss one possible compatibilist\nreply—the attempt to block the conclusion of the manipulation\nargument, one of the main arguments employed by hard incompatibilists\nand other incompatibilists.", "\nMost manipulation arguments introduce various science-fiction-like\nscenarios, or manipulation cases, aimed to show that agents who meet\nall the various compatibilist conditions for moral responsibility can\nnevertheless be subject to responsibility-undermining manipulation.\nThese arguments further maintain that these manipulation cases\nresemble in the relevant ways agents in the normal (non-manipulated)\ndeterministic case. They go on to conclude that if agents fail to be\nmorally responsible in the manipulated cases they also fail to be\nmorally responsible in the normal deterministic case (see Pereboom\n1995, 2001, 2014a; Mele 2008; Todd 2013; for a less demanding version\nof the argument, one that aims to show only that the manipulation in\nquestion is mitigating with respect to moral responsibility,\nsee Todd 2011). ", "\nConsider, for example, Pereboom’s famous “four-case”\nargument. The argument sets out three examples of actions that involve\nmanipulation, the first of which features the most radical sort of\nmanipulation consistent with all the leading compatibilist conditions,\neach progressively more like the fourth, which is an ordinary case of\naction causally determined in a natural way. The challenge is for the\ncompatibilist to point out a relevant and principled difference\nbetween any two adjacent cases that would show why the agent might be\nmorally responsible in the latter example but not the former. Here,\nfor instance, is the second case:", "\n\n\nPlum is just like an ordinary human being, except that a team of\nneuroscientists programmed him at the beginning on his life so that\nhis reasoning is often but not always egoistic, and at times strongly\nso, with the intended consequence that in his current circumstances he\nis causally determined to engage in the egoistic reasons-responsive\nprocess of deliberation and to have the set of first and second-order\ndesires that result in his decision to kill White. Plum has the\ngeneral ability to regulate his actions by moral reasons, but in his\ncircumstances, due to the strongly egoistic nature of his deliberative\nreasoning, he is causally determined to make his decision to kill. Yet\nhe does not decide as he does because of an irresistible desire.\n(2014a: 77)\n", "\nIs Plum morally responsible in the basic desert sense for killing\nWhite? Defenders of manipulation arguments say “no.” They\nfurther argue that there is no relevant difference between this case\nand mere causal determinism. By comparing this case to the other three\ncases—the final case being just like the above except that\nnatural deterministic causes have taken the place of the\nneuroscientists—Pereboom and others argue that it is simply\nirrelevant whether Plum’s psychological states\nultimately trace back to intentional agents or non-intentional causes.\nWhat does matter, and what is responsibility-undermining, is that in\nall four cases the agent’s actions are ultimately the result of\nfactors beyond their control.", "\nIn response, compatibilists adopt either hard-line or\nsoft-line replies (see McKenna 2008). Hard-line replies grant\nthat there is no relevant difference between agents in the various\nmanipulated scenarios and ordinary (non-manipulated) agents in\ndeterministic settings, rather they attack the intuition that agents\nare not morally responsible in the manipulated cases. They maintain\nthat as long as the various compatibilist conditions for moral\nresponsibility are satisfied, manipulated agents are just as free and\nmorally responsible as determined agents—despite what might be\nour initial intuition. Soft-line replies, on the other hand, try to\ndifferentiate between the various cases. They search for relevant\ndifferences between the cases, differences that would account for why\nmanipulated agents are not free and morally responsible, but\nnon-manipulated and causally determined agents are. There are,\nhowever, problems with both types of replies.", "\nThe main worry people have with the hard-line approach is that it\nconflicts too deeply with our intuitions about the relevant class of\nmanipulation cases (Capes, forthcoming). Many people find it highly\nimplausible that someone like Plum could be morally responsible in the\nbasic desert sense for his behavior given how the behavior came about\n(cf. Fischer 2011, 2014; McKenna 2008, 2014, 2017; Sartorio 2016;\nTierney 2013, 2014; Capes 2013; Haji & Cuypers 2006). The main\nworry with the soft-line approach, on the other hand, is that any\ndifference identified as the relevant one between manipulated agents\nand ordinary determined agents may be a difference that applies only\nto current manipulation cases but not future cases. For example, most\nextant manipulation cases involve external agents who act as\nintentional manipulators, whereas this is missing in the normal case\nof natural determinism. Proponents of soft-line replies might\ntherefore be tempted to point to this as the relevant difference.\nSetting aside for the moment the potential question-begging nature of\nthis move, the reply also suffers from the fact that new manipulation\narguments have recently been devised that avoid external agents\naltogether.", "\nA similar problem confronts soft-line replies that point to\nresponsibility-conferring conditions not specified in a particular\nmanipulation case (Lycan 1987; Baker 2006; Feltz 2012; Murray &\nLombrozo 2017). That is, even if one could point to a relevant\ndifference between an agent in an extant manipulation case and an\nagent in the naturally-determined case, this may only serve as an\ninvitation for proponents of the manipulation argument to revise the\nvignette on which their argument is based so that the agent now\nsatisfies the relevant condition on which the soft-liner insists\n(Capes, forthcoming). The challenge, then, for defenders of the\nsoft-line approach is to show that there is some kind of requirement\nfor free action and moral responsibility that can be satisfied by\nagents in deterministic settings but which cannot (in principle) be\nsatisfied by agents in manipulation cases. [For a recent attempt at\nsatisfying this challenge, see Deery and Nahmias (2017); for a reply,\nsee Capes (forthcoming).] " ], "subsection_title": "2.2 Hard Incompatibilism" }, { "content": [ "\nAnother argument for moral responsibility skepticism, one that makes\nno appeal at all to determinism or indeterminism, was first introduced\nby Friedrich Nietzsche (1886 [1992]) and later revived and fleshed out\nby Galen Strawson (1994, 2011). This argument maintains that free will\nand ultimate moral responsibility are incoherent concepts, since to be\nfree in the sense required for ultimate moral responsibility we would\nhave to be causa sui (or “cause of oneself”) and\nthis is impossible. Nietzsche, for example, writes:", "\n\n\nThe causa sui is the best self-contradiction that has been\nconceived so far; it is a sort of rape and perversion of logic. But\nthe extravagant pride of man has managed to entangle itself profoundly\nand frightfully with just this nonsense. The desire for “freedom\nof the will” in the superlative metaphysical sense, which still\nholds sway, unfortunately, in the minds of the half-educated; the\ndesire to bear the entire and ultimate responsibility for one’s\nactions oneself, and to absolve God, the world, ancestors, chance, and\nsociety involves nothing less than to be precisely this causa\nsui and, with more than Baron Munchhausen’s audacity, to\npull oneself up into existence by the hair, out of the swamps of\nnothingness. (1886 [1992] sec. 21)\n", "\nGalen Strawson makes a similar case for the impossibility of moral\nresponsibility with his so-called Basic Argument (1986, 1994,\n2011). The central argument can be summarized as follows:", "\nThe expanded version of the argument runs as follows (Strawson\n2011):", "\nThis argument trades on some strong and commonsense intuitions.\nIt’s intuitive to think that one is initially the way one is as\na result of heredity and early experience—and it’s\nundeniable that these are factors for which one cannot be held in any\nway responsible (morally or otherwise). Yet, it also makes sense to\nthink that one cannot at any later stage of life hope to accede to\ntrue or ultimate moral responsibility for the way one is by trying to\nchange the way one already is as a result of one’s genetic\ninheritance and previous experience, since both the particular way in\nwhich one is moved to try to change oneself, and the degree of\none’s success in one’s attempt to change, will be\ndetermined by how one already is as a result of one’s genetic\ninheritance and previous experience. And any further changes that one\ncan bring about only after one has brought about certain initial\nchanges will in turn be determined, via the initial changes, by\none’s genetic inheritance and previous experience. Such is\nStrawson’s argument for the impossibility of moral\nresponsibility.", "\nWhile this argument is simple, eloquent, and rather intuitive, it has\nbeen widely criticized by compatibilists and libertarians alike (see,\ne.g., Hurley 2000; Clarke 2005a; Bernstein 2005; Fischer 2006; Kane\n2000; Coates 2017; for replies see Istvan 2011; Parks 2009). Some\ncritics question Strawson’s notion of ultimate\nresponsibility, which he defines as ", "\n\n\nresponsibility of such a kind that, if we have it, then it makes\nsense to suppose that it could be just to punish some of us with\n(eternal) torment in hell and reward others with (eternal) bliss in\nheaven. (2011: 43) \n", "\nOthers critics challenge the claim that in order to be responsible for\none’s actions, one has to be the cause of oneself. In the\nopposite direction, others try to escape from the regress of the\nargument by making sense of the possibility of self-creation\n(Bernstein 2005; see also Kane 1996; Lemos 2015; Roskies 2012). Others\nstill attack the claim that if what one does when one acts for a\nreason is to be up to one, then how one is mentally, in some respect,\nmust be up to one (Clarke 2005a). Finally, some simply suggest that accounts of free action\nare often meant to be accounts of precisely how it can be\nthat, even if it is not up to an agent how she is mentally, her action\ncan still be up to her, she can still have a choice about whether she\nperforms the action, even when she acts for reasons (Mele 1995:\n221–27).", "\nDefenders of the Basic Argument have attempted to counter these\nobjections in a number of ways. Some respond by arguing, contra\nFischer (2006), that the Basic Argument does not rely on the premise\nthat an agent can be responsible for an action only if she is\nresponsible for every factor contributing to that action (see\nIstvan 2011). Others argue, in response to Mele (1995) and Clarke\n(2005a), that it is highly counterintuitive to believe that an agent\ncan be morally responsible for an action when no factor contributing\nto that action is up to that agent (Istvan 2011). In response to the\nsuggestion that certain versions of agent-causal libertarianism can\nimmunize the agent to the Basic Argument (see Clarke 2005a), they\nargue that such accounts actually fail to do so (Istvan 2011). Lastly,\nsome defenders of the Basic Argument recast the argument in a form\nthat eliminates certain problems associated with Strawson’s\noriginal version and offer additional thought experiments to bolster\nits underlying assumptions (see Parks 2009)." ], "subsection_title": "2.3 Impossibility of Ultimate Responsibility" }, { "content": [ "\nAnother argument that maintains that regardless of the causal\nstructure of the universe we lack free will and moral responsibility\nholds that free will and basic desert moral responsibility are\nincompatible with the pervasiveness of luck (see N. Levy\n2009a, 2011; cf. Haji 2016). This argument is intended not only as an\nobjection to event-causal libertarianism, as the luck\nobjection is, but extends to compatibilism as well. At the heart\nof the argument is the following dilemma: either actions are subject\nto present luck (luck around the time of the action), or they\nare subject to what Thomas Nagel (1979) influentially named\nconstitutive luck (luck that causes relevant properties of\nagents, such as their desires, beliefs, and circumstances), or both\n(N. Levy 2011). Either way, luck undermines moral responsibility since\nit undermines responsibility-level control. This is what Neil Levy\ncalls the Luck Pincer and it can be summarized as follows\n(Levy 2011: 84–97; as summarized in Hartman 2017: 43):", "\n\n\nUniversal Luck Premise: Every morally significant act is\neither constitutively lucky, presently lucky, or both.\n\n\nResponsibility Negation Premise: Constitutive and present\nluck each negate moral responsibility.\n\n\nConclusion: An agent is not morally responsible for any\nmorally significant acts. \n", "\nLet us examine the argument in more detail, focusing first on what\nexactly is meant by “luck.”", "\nWhile there are several competing accounts of “luck” in\nthe literature, the Luck Pincer is couched in terms of a modal account\n(N. Levy 2011; cf. Pritchard 2005, 2014; Driver 2012; Hales 2015,\n2016; Latus 2000, 2003; Hartman 2017; Zimmerman 1987, 2002, 2009;\nCoffman 2015; see also entry on\n moral luck).\n The modal account, as developed by Levy (2011), defines luck by way\nof possible worlds without reference to indeterminism or determinism,\nand it classifies luck as either chancy or not\nchancy. An agent’s being chancy lucky is defined\nas follows: ", "\n\n\nAn event or state of affairs occurring in the actual world is chancy\nlucky for an agent if (i) that event or state of affairs is\nsignificant for that agent; (ii) the agent lacks direct control over\nthe event or state of affairs; and (iii) that event or state of\naffairs fails to occur in many nearby possible worlds; the proportion\nof nearby worlds that is large enough for the event to be chancy lucky\nis inverse to the significance of the event for the agent. (N. Levy\n2011: 36)\n", "\nOn the other hand:", "\n\n\nAn event or state of affairs occurring in the actual world that\naffects an agent’s psychological traits or dispositions is\nnon-chancy lucky for an agent if (i) that event or state of affairs is\nsignificant for that agent; (ii) the agent lacks direct control over\nthat event or state of affairs; (iii) events or states of affairs of\nthat kind vary across the relevant reference group, and…in a\nlarge enough proportion of cases that event or state of affairs fails\nto occur or be instantiated in the reference group in the way in which\nit occurred or was instantiated in the actual case. (N. Levy 2011:\n36)\n", "\nNote that the first two conditions are the same for an agent’s\nbeing chancy and non-chancy lucky—i.e., (i)\nsignificance, and (ii) lack of direct control. And\nwe can say that an event is significant for an agent if she\ncares about the event and it can have either good or bad significance\nfor her (N. Levy 2011: 13). It may, for instance, be chancy whether I\nhave an odd or even number of hairs on my head at 12 noon, but it\nwould be strange to say that this is a matter of luck since we\ngenerally reserve the appellation “luck” for events that\nmatter (N. Levy 2011: 13)—i.e., we do not generally\nspeak of entirely trivial events as lucky (i.e., as good or bad for an\nagent). With regard to the second condition, we can say that an agent\nhas direct control over an event if the agent is able (with\nhigh probability) to bring it about by intentionally performing a\nbasic action and if the agent realizes that this is the case (N. Levy\n2011: 19; cf. Coffman 2007).", "\nTo help understand how the third condition differs in the two\ndefinitions—i.e., the modal condition (chancy luck) and\nthe uncommon instantiation condition (non-chancy\nluck)—lets consider some examples. A paradigmatic example of a\nchancy lucky event is Louis’s winning the lottery. This is\nbecause (i) he lacks direct control over winning the lottery since\nthere is no basic action that he can perform to bring it about, (ii)\nthe event of his winning the lottery is also at least minimally\nsignificant, and (iii)—the modal condition—in most close\npossible worlds with a small divergence from the actual world, Louis\ndoes not win. On the other hand, Elaini may be non-chancy lucky for\nbeing a genius with a high IQ in comparison with her peers (Hartman\n2017: 44–46). This is because (i) Elaini lacks direct control\nover being a genius, (ii) it is significant for her, and\n(iii)—the uncommon instantiation condition—being a genius\nis not commonly instantiated in that reference group (assuming, of\ncourse, that most of her actual peers are not geniuses).", "\nTo these three conditions, we can now also add the distinction between\npresent luck and constitutive luck. We can say that\nan agent’s decision is the result of present luck if a\ncircumstantial factor outside of the agent’s control at or near\nthe time of action significantly influences the decision. Such\ncircumstantial factors could include the agent’s mood, what\nreasons happen to come to her, situational features of the\nenvironment, and the like. For instance: ", "\n\n\nOur mood may influence what occurs to us, and what weight we give to\nthe considerations that do cross our mind…Our attention may\nwander at just the wrong moment or just the right one, or our\ndeliberation may be primed by chance features of our environment. (N.\nLevy 2009a: 245; see also 2011: 90) \n", "\nIn contrast, we can say that an agent’s decision is the result\nof constitutive luck if that decision is partially settled by her\ndispositional endowment, which is outside of her control (N. Levy\n2011: 87). Finally, while present luck is limited to cases of chancy\nluck, constitutive luck can be a subspecies of both chancy and\nnon-chancy luck since it can refer to a disposition that an agent\npossesses in either a chancy or a non-chancy way (N. Levy 2011:\n87).", "\nWith these definitions in place we can now return to the Luck\nPincer and see how libertarian and compatibilist accounts fare\nagainst it. Libertarian accounts famously face the problem of\nexplaining how a decision or action can be free, given the libertarian\ndemand for indeterminacy immediately prior to directly free action.\nMoral responsibility skeptics and compatibilists alike have long\nargued that such indeterminacy makes the action unacceptably chancy,\nin a way that is responsibility-undermining (see, e.g., N. Levy 2009a,\n2011; Mele 1999a,b, 2006; Haji 2002, 2004, 2005, 2014; van Inwagen\n2000; Pereboom 2001, 2014a; for some replies see\nKane 1999; Clarke 2005b; Mele 2017). And it is argued that this\napplies to both event-causal and agent-causal versions of\nlibertarianism (see Mele 2006; Haji 2004, 2016; N. Levy 2011). The\nkind of luck that is problematic here is present chancy luck,\nsince the agent’s putatively “free” decision is\nchancy (i.e., the same decision would fail to occur in many nearby\npossible worlds), significant, and the circumstantial factor outside\nof the agent’s control (i.e., the indeterminate event(s)) occurs\njust prior to the decision. ", "\nPeter van Inwagen (2000) makes vivid the lack of control a libertarian\nagent has over genuinely undetermined events by considering what would\nhappen if God rolled back the relevant stretch of history to some\npoint prior to an undetermined event and then allowed it to unfold\nonce more (N. Levy 2009a: 238). Since events would not unfold in the\nsame way on the replay as they did the first time round, since these\nare genuinely undetermined, and nothing the agent does (or is) can\nensure which undetermined possibility is realized, the outcome of this\nsequence (in this case the agent’s decision) is a matter of\nluck. Such luck, skeptics argue, is responsibility-undermining.", "\nCompatibilist accounts of moral responsibility, on the other hand, are\nvulnerable to their own powerful luck objection (N. Levy 2009a, 2011;\nHaji 2003, 2016; cf. Vargas 2012b). We can divide compatibilist\naccounts into two main categories: historical and\nnon-historical. Historical accounts are sensitive to the\nmanner in which an agent comes to be the kind of person they are, in\nthe circumstances in which they find themselves (see Mele 1995, 2006;\nFischer & Ravizza 1998). If an agent, for instance, decides to\ndonate a large sum of money to Oxfam, historical accounts of moral\nresponsibility hold that it is important how the agent came to have\nsuch a generous nature and make the decision they did—for\nexample, did the agent have a normal history and acquire the\ndisposition to generosity naturally, or did a team of neuroscientists\n(say) engineer them to have a generous nature? Non-historical\naccounts, on the other hand, maintain that moral responsibility\ndepends instead on non-historical factors—like whether an agent\nidentifies with his/her own desires (Frankfurt 1971) or the quality of\nan agent’s will (Scanlon 1998).", "\nThe main problem with historical accounts is that they cannot\nsatisfactorily explain how agents can take responsibility for their\nconstitutive luck. The problem here is analogous to the problem raised\nby manipulation arguments (N. Levy 2009a, 2011). Manipulated agents\nare the victims of (very bad) luck: the manipulation is significant\nfor them, they lack control over its (non-) occurrence, and it is\nchancy, in as much as there are nearby possible worlds in which the\nmanipulation does not occur (N. Levy 2009a: 242). The problem of\nconstitutive luck is similar in that an agent’s\nendowments—i.e., traits and dispositions—likewise\nresult from factors beyond the agent’s control, are significant,\nand either chancy or non-chancy lucky. A historical compatibilist\ncould respond, as they often do to manipulations cases, that as long\nas an agent takes responsibility for her endowments,\ndispositions, and values, over time she will become morally\nresponsible for them. The problem with this reply, however, is that\nthe series of actions through which agents shape and modify their\nendowments, dispositions, and values are themselves significantly\nsubject to present luck—and, as Levy puts it, “we cannot\nundo the effects of luck with more luck” (2009a: 244). Hence,\nthe very actions to which history-sensitive compatibilists point, the\nactions whereby agents take responsibility for their endowment, either\nexpress that endowment (when they are explained by\nconstitutive luck) or reflect the agent’s present luck, or both\n(see N. Levy 2009a: 247, 2011).", "\nIf this argument is correct, present luck is not only a problem for\nlibertarianism it is also a problem for historical compatibilism. And\nwhile present luck may be a bigger problem for libertarians,\nsince they require the occurrence of undetermined events in the causal\nchain leading to free action, the problem it creates for historical\ncompatibilists is nonetheless significant. With compatibilism, we need\nto assess the implications of present luck in conjunction\nwith the implications of constitutive luck. When we do, we see that\nthough it might often be the case that the role played by present luck\nin the decisions and actions of compatibilist agents is relatively\nsmall, it is the agent’s endowment—directly, or as\nmodified by the effects of present luck, or both—which explains\nwhy this is so (N. Levy 2009a: 248). An agent’s pre-existing\nbackground of reasons, desires, attitudes, belief, and\nvalues—against which an agent deliberates—is the endowment\nfrom constitutive luck, inflected and modified, to be sure, but\ninflected and modified by decisions which either express\nconstitutive luck, or which were not settled by the endowment, and\ntherefore were subject to present luck (N. Levy 2009a: 248).\nHence, the Luck Pincer: actions are either the product of constitutive\nluck, present luck, or both. ", "\nNon-historical accounts, on the other hand, run into serious\ndifficulties of their own with the epistemic condition on control over\naction. The epistemic condition maintains that moral responsibility\nfor an action requires that the agent understands that, and how, the\naction is sensitive to her behavior, as well as appreciation of the\nsignificance of that action or culpable ignorance of these facts (N.\nLevy 2011: ch.5; cf. Rosen 2003, 2004, 2008; Zimmerman 1997, 2009;\nVargas 2005a). Because the epistemic condition on control is so\ndemanding and itself subject to the Luck Pincer, non-historical\naccounts of compatibilism (as well as other accounts that may survive\nthe above arguments) face a serious challenge (see N. Levy 2011,\n2009b). Consider cases of non-culpable ignorance. Imagine, for\ninstance, that a 16th century surgeon operates on a patient\nwithout washing his hands or sterilizing his equipment, and as a\nresult his patient gets an infection and dies. The surgeon would not\nbe blameworthy in this situation because he was non-culpably ignorant\nof the risks of non-sterilization, since germ theory was not\nestablished until much later. In this and other cases of non-culpable\nignorance, the fact that agents are ignorant of the relevant details\nis frequently a matter of luck—either present luck or\nconstitutive luck or both.", "\nWe can say that non-culpable ignorance is chancy lucky when an agent\nfails to know that p (where p is significant for\nher), lacks direct control over whether she knows that p, and\nin a large proportion of nearby possible worlds does know that\np. Lets say I drop my daughter Maya off at a friend’s\nhouse for a play date. She has a peanut allergy and I forget to inform\nthe other parent, Dolores, at the time of drop-off. When I get to the\ncoffee shop, I realize this and immediately text Dolores about the\nallergy, but because I’m in a “dead zone” the\nmessage does not go through. Not having received my text, Dolores\nproceeds to give the kids a snack with peanut butter in it, resulting\nin Maya having a near-fatal reaction. Dolores’ non-culpable\nignorance in this case is chancy lucky since in a large portion of\nnearby possible worlds she would have received the text. The\n16th century surgeon example, on the other hand, is better\nseen as an example of non-chancy luck, since his ignorance is the\nresult of bad luck inasmuch as beliefs about germs vary across agents\nin different historical periods (the relevant reference group here),\nrather than nearby possible worlds. ", "\nSince non-culpable ignorance is responsibility-undermining and much\nmore common than philosophers typically think, it gives additional\nforce to the Luck Pincer. Thanks to luck, distant or present, agents\nwho perform wrongful actions typically lack freedom-level\ncontrol over their actions because they fail to satisfy the epistemic\ncondition on such control (N. Levy 2011: 115–16). In cases of\nunwitting wrongdoing, there often is no plausible candidate for a\nculpable benighting action that could ground blameworthiness\n(N. Levy 2011: 131). Furthermore, it is often the case that we cannot\nreasonably demand of agents that they do not act in ways that express\ntheir epistemic vices (N. Levy 2011: 126). When an agent does not see\nthat she is managing her moral views badly, it would be unfair to\nblame her for doing wrong if she had no internal reasons for omitting\nher bad behavior. This is because, when an agent is managing her moral\nviews badly from the point of view of objective morality, it\nis often the case that her subjective moral values and\nbeliefs—which ex hypothesi she does not know are\nwrong—are governing herself in a perfectly rational and\nconsistent way. Since these internal moral values and beliefs are\nthemselves a matter of luck—either present, constitutive, or\nboth—we once again arrive at the Luck Pincer. It would seem,\nthen, that present luck, constitutive luck, or both, swallows all, and\nboth libertarian and compatibilist accounts fail to preserve moral\nresponsibility.", "\nFor some objections to the Luck Pincer, see Talbert (2013, 2016),\nHartman (2017), Hales (2016). For a different argument based on luck for the conclusion that agents are far less morally blameworthy than we have hitherto\npresumed, see Haji (2016). For a compatibilism that is responsive to\nconcerns of luck but that resists full-blown skepticism about free\nwill and moral responsibility, see Paul Russell’s free will\npessimism (2017). " ], "subsection_title": "2.4 Luck" }, { "content": [ "\nIn addition to these philosophical arguments, there have also been\nrecent developments in the behavioral, cognitive, and neurosciences\nthat have caused some to take moral responsibility skepticism\nseriously. Chief among them have been findings in neuroscience that\nputatively indicate that unconscious brain activity causally initiates\naction prior to the conscious awareness of the intention to act (see,\ne.g., Libet et al. 1983; Libet 1985, 1999; Soon et al. 2008; Wegner\n2002) and recent findings in psychology and social psychology on\nautomaticity, situationism, and the adaptive\nunconscious (see, e.g., Bargh 1997, 2008; Bargh & Chartrand\n1999; Bargh & Ferguson 2000; T. Wilson 2002; Doris 2002).", "\nThe neuroscientific threat to moral responsibility originates with the\npioneering work of Benjamin Libet and his colleagues. In their\ngroundbreaking study on the neuroscience of movement, Libet et al.\n(1983) investigated the timing of brain processes and compared them to\nthe timing of conscious will in relation to self-initiated voluntary\nacts. They found that the conscious intention to move (which they\nlabeled W) came 200 milliseconds before the motor act, but\n350-400 milliseconds after readiness potential (RP)—a\nramp-like buildup of electrical activity that occurs in the brain and\nprecedes actual movement. These findings lead Libet and others to\nconclude that the conscious intention or decision to move cannot be\nthe true cause of action because it comes too late in the\nneuropsychological sequence (see Libet 1985, 1999; Wegner 2002; Soon\net al. 2008; Pockett 2004; Obhi & Haggard 2004; Haggard &\nEimer 1999; Roediger, Goode, & Zaromb 2008). For some scientific\nskeptics, these and other findings (e.g., Soon et al. 2008) suggest\nthat the causal efficacy of the kind of willing required for free will\nand moral responsibility is an illusion (e.g., Wegner 2002).", "\nThere are, however, powerful objections to this interpretation of the\nneuroscientific findings. Some critics argue that there is no direct\nway to tell which conscious phenomena, if any, correspond to which\nneural events (Mele 2009). In particular, it is difficult to determine\nwhat the readiness potential corresponds to—is it, for instance,\nan intention formation or decision, or is it merely\nan urge of some sort? Al Mele (2009), for instance, has\nforcefully argued that the readiness potential (RP) that precedes\naction by a half-second or more need not be construed as the\ncause of the action but rather is best interpreted as the\nbeginning of forming an intention to act. On this reading,\nconscious intentions can still be causes. Other critics have pointed\nto the “impossible demand” of Libet-like experiments (N.\nLevy 2005), or the unusual nature of its experimental design (Nahmias\n2002, 2011), or to its irrelevance to moral responsibility (N. Levy\n2014a), or to alternative explanations that are less threatening\n(Rosenthal 2002; Dennett 2003). These objections have led many\ncontemporary philosophers (including many skeptics) to reject the\nneuroscientific argument for moral responsibility (see, e.g., Pereboom\n& Caruso forthcoming; N. Levy 2005, 2014a; Morris 2009). ", "\nThere are, however, other scientific threats to moral responsibility\nbesides those posed by neuroscience. Recent work in psychology and\nsocial psychology on automaticity, situationism, and\nthe adaptive unconscious, for instance, has shown that the\ncauses that move us are often less transparent to ourselves than we\nmight assume—diverging in many cases from the conscious reasons\nwe provide to explain and/or justify our actions (see, e.g., Nisbett\n& Wilson 1977; T. Wilson 2002; Doris 2002; Bargh 1997, 2008; Bargh\n& Chartrand 1999; Bargh & Ferguson 2000; Kahneman 2011). These\nfindings reveal just how wide open our internal psychological\nprocesses are to the influence of external stimuli and events in our\nimmediate environment, without knowledge or awareness of such\ninfluence. They also reveal the extent to which our decisions and\nbehaviors are driven by implicit biases (see, e.g., Uhlmann &\nCohen 2005; Greenwald, McGhee, & Schwartz 1998; Nosek et al. 2007)\nand other unconscious System-1 processes (Kahneman 2011). No longer is\nit believed that only “lower level” or “dumb”\nprocesses can be carried out non-consciously. We now know that the\nhigher mental processes that have traditionally served as\nquintessential examples of ‘free will’—such as\nevaluation and judgment, reasoning and problem solving, and\ninter-personal behavior—can and often do occur in the absence of\nconscious choice and guidance (Bargh & Ferguson 2000; T. Wilson\n2002; Kahneman 2011).", "\nWhile these findings may not be enough on their own to establish\nglobal skepticism about moral responsibility, they represent a\npotential threat to our everyday folk understanding of ourselves as\nconscious, rational, responsible agents, since they indicate that the\nconscious mind exercises less control over our behavior than we have\ntraditionally assumed. Even some compatibilists now admit that because\nof these findings “free will is at best an occasional\nphenomenon” (Baumeister 2008: 17; see also Nelkin 2005; Herdova\n2016). This is an important concession because it acknowledges that\nthe threat of shrinking agency (Nadelhoffer 2011) remains a\nserious one independent of the neuroscientific concerns discussed\nabove. The deflationary view of consciousness which emerges from these\nempirical findings, including the fact that we often lack transparent\nawareness of our true motivational states, is potentially agency\nundermining and could shrink the realm of morally responsible action\n(see N. Levy 2014a; Nadelhoffer 2011; King &\nCarruthers 2012; Sie & Wouters 2010, Brink 2013; Caruso 2015a; cf. Vargas 2013;\nK. Levy 2015; McKenna & Warmke forthcoming; Ciurria 2013; Mele\n& Shepherd 2013). A major point of disagreement, however, is over\nwhether consciousness is necessary for moral responsibility, and, if\nso, what role or function it must serve (cf. N. Levy 2014a; Shepherd 2012, 2015a,b,c; Searle 2000, 2001; Hodgson 2005, 2012; Sher 2009; Doris 2002, 2015; Nahmias 2002;\nSmith 2005, 2008; Sifferd 2016). ", "\nLastly, independent of the two more specific concerns mentioned above,\nthere is also the more general insight, more threatening to\nagent-causal libertarianism than compatibilism, that as the brain\nsciences progress and we better understand the mechanisms that\nundergird human behavior, the more it becomes obvious that we lack\nwhat some have called “soul control” (see Clark 2013).\nNaturalists about the mind argue that there is no longer any reason to\nbelieve in a non-physical self which controls action and is liberated\nfrom the deterministic laws of nature; a little uncaused\ncauser capable of exercising counter-causal free will. While most\ncontemporary philosophers, including most compatibilists, have long\ngiven up on the idea of soul control, eliminating such thinking from\nour folk psychological attitudes may not be so easy and may come at a\ncost for some. There is some evidence, for example, that we are\n“natural born” dualists (Bloom 2004) and that, at least in\nthe United States, a majority of adults continue to believe in a\nnon-physical soul that governs behavior (Demertzi et al. 2009;\nFahrenberg & Cheetham 2000; World Values Survey 1991–2004; Riekki et al. 2013). To whatever extent, then, such dualistic thinking is present in our folk psychological attitudes about free will and moral\nresponsibility (cf. Nadelhoffer 2014; Mele 2014), it is likely to come\nunder pressure and require some revision as the brain sciences advance\nand this information reaches the general public (see, e.g., Greene\n& Cohen 2004). Of course, how and in what direction this revision\nwill occur is an open empirical question—e.g., some may adopt a\nrevisionism about free will and moral responsibility\n(à la Vargas 2005b, 2009, 2007, 2012a) while other may opt for\na more eliminativist response (à la Pereboom 2001,\n2014a; Waller 1990, 2011; Strawson 1986; Caruso 2015b).", "\n[Note: While most anti-skeptical arguments focus on objections to the\nmanipulation argument, the luck objection, the Basic Argument, the\nLuck Pincer, etc., some recent anti-skeptical arguments have also\nfocused on the role of reference and alternative ways of thinking\nabout free will and moral responsibility. See, for example, the\narguments of Shaun Nichols (2013, 2015; Nichols et al. 2016) and \nOisín Deery (2015)\non reference and preservationism,\nKelly McCormick (2013, 2016) on anchoring reference in the context of\nresponsibility talk, and Manuel Vargas on preferring\nrevisionism to eliminativism (2005b, 2009, 2007,\n2012a).]" ], "subsection_title": "2.5 Scientific Challenges to Moral Responsibility" } ] }, { "main_content": [ "\nTurning now to the practical implications of moral responsibility\nskepticism, we can ask, what would happen if we came to accept this\nview? In recent years a small industry has grown up around precisely\nthis question. Since disbelief in moral responsibility would clearly\nhave profound consequences for our interpersonal relationships,\nsociety, morality, meaning, and the law, it’s important to\nquestion whether these consequences would be (on the whole) good or\nbad. Critics of moral responsibility skepticism fear that it would\nundermine morality, leave us unable to adequately deal with criminal\nbehavior, increase anti-social conduct, and/or destroy meaning in\nlife. Moral responsibility skeptics, on the other hand, offer up a\nnumber of different views—including illusionism\n(Smilansky 1999, 2000), disillusionism (Nadelhoffer 2011),\nand optimistic skepticism (e.g., Spinoza 1677 [1985];\nPereboom 1995, 2001, 2002b, 2009, 2011, 2013a, 2014a; Waller 1989,\n1990, 2004, 2006, 2011, 2014; Sommers 2007a,b; Caruso forthcoming-b; N.\nLevy 2011; Vilhauer 2009a,b, 2012, 2013a,b; Milam 2016, 2017; Smuts\n2014; Morris, forthcoming).", "\nIn recent years, empirical attempts have been made to test the\npractical implications of moral responsibility skepticism. One widely\ncited study found that diminishing belief in free will, which is\nostensibly related to moral responsibility, caused participants to\n“cheat” more on a problem solving task (Vohs &\nSchooler 2008). Another study found that participants who were asked\nto read anti-free will prompts behaved more aggressively than\nparticipants exposed to neutral or pro-free will prompts (Baumeister,\nMasicampo, & DeWall 2009). Another indicates that reduction in\nbelief in free will correlated with reduction in monitoring of errors\n(Rigoni, Pourtois, & Brass 2015). And two additional studies found\nthat diminishing free will belief impairs learning from negative\nemotions (Stillman & Baumeister 2010) and causes participants to\nexhibit more negative attitudes toward out-group members (Zhao, Liu,\nZhang, Shi, & Huang 2014). Such findings seem to suggest that\ndiminished belief in free will and moral responsibility would indeed\nhave negative consequences. Yet such a sweeping conclusion may be too\nhasty.", "\nFirst, some have criticized these studies on philosophical and\nmethodological grounds (see, e.g., Miles 2013; Caruso, forthcoming-b;\nMorris, forthcoming). The “cheating” study, for instance,\nhas failed to replicate on a number of occasions (Carey & Roston\n2015; Open Science Collaboration 2015; Zwaan 2013\n[see Other Internet Resources]) and the passages\nused to prompt anti-free will belief have been criticized for not\nbeing representative of what most free will and moral responsibility\nskeptics claim (Morris, forthcoming). There is also the question of\nwhether the negative effects tested in these studies indicate anything\nabout the long-term consequences of moral responsibility\nskepticism. Most of these effects are short-lived and temporary. But\nas people become more acquainted with the skeptical perspective, and\nas they come to understand what it does and does not maintain, it\nremains possible that these effects would fade over time. Lastly,\nthere is also a growing body of evidence in the opposite direction\nsuggesting that certain positive effects may follow from free\nwill and moral responsibility skepticism (Carey & Paulhus 2013;\nNadelhoffer & Tocchetto 2013; Krueger et al. 2014; Shariff et\nal. 2014; Caspar et al. 2017).", "\nA recent study by Shariff et al. (2014), for instance, found that\npeople with weaker belief in free will endorsed less retributive\nattitudes regarding punishment of criminals, yet their\nconsequentialist attitudes about punishment were unaffected. They also\nfound that learning about the neural bases of human behavior, either\nthrough reading popular science articles or taking an undergraduate\nneuroscience course, similarly reduced people’s support for\nretributive punishment. The same connection between belief in free\nwill and increased punitiveness has also been found in a number of\nother studies (see, e.g., Carey & Paulhus 2013; Clark et al. 2014;\nAspinwall, Brown, & Tabery 2012; Pizarro, Uhlmann, & Salovey\n2003). Additional studies have found that\nwhere belief in free will is strongest we find increased\nreligiosity and increased commitment to a cluster of\npotentially dangerous political beliefs and attitudes such as Just\nWorld Belief and Right Wing Authoritarianism (see Carey\n& Paulhus 2013; Nadelhoffer & Tocchetto 2013). The belief in a\njust world, for instance, is the belief that we live in a world where\npeople generally get what they deserve. But stronger commitment to\njust world belief is problematic since it correlates with the tendency\nto blame the victims of misfortunes for their own fate (see Lerner\n& Simmons 1966; Lerner 1965, 1980; Lerner & Miller 1978;\nWagstaff 1983; Furnham & Gunter 1984; Furnham 2003; Harper &\nManasse 1992; Montada 1998).", "\nGiven the mixed results of these empirical studies and the fact that\nthey tell us very little about any long-term consequences of adopting\nthe skeptical perspective, the real-life practical implications of\nmoral responsibility skepticism remain an open question. Perhaps, as\nthese studies indicate, it would have both good and bad\nconsequences. In which case, the practical question would shift to the\noverall balance—i.e., whether, on the whole, the\nconsequences would be good or bad. Or perhaps adopting the skeptical\nperspective would over time reduce or eliminate any initial\nnegative reactions—i.e., after an initial adjustment period,\npeople would come to terms with the new reality and their behavior\nwould normalize. An illustrative analogy might be made here with\nsimilar concerns voiced in the past about disbelief in God. It was\nlong argued (and perhaps still is argued in certain quarters of\nsociety) that if people were to come to disbelieve in God, the moral\nfiber of society would disintegrate and we would see a marked increase\nin anti-social behavior. These fears, however, have not materialized,\nas society has grown more secular over time.", "\nThe debate over the philosophical and practical implications of moral\nresponsibility skepticism nevertheless continues, and there is even\nsome debate among skeptics themselves." ], "section_title": "3. Implications of Moral Responsibility Skepticism", "subsections": [ { "content": [ "\nIllusionism is the view that while we lack free will and\nmoral responsibility, we should nonetheless promote belief in\nthese notions since to disbelieve in moral responsibility would have\ndire consequences for society and ourselves (see Smilansky 1999, 2000,\n2002, 2013). According to Saul Smilansky, one of the lead proponents\nof illusionism, most people not only believe in actual possibilities\nand the ability to transcend circumstances, but have ", "\n\n\ndistinct and strong beliefs that libertarian free will is a condition\nfor moral responsibility, which is in turn a condition for just reward\nand punishment (2000: 26–27; for more on the folk psychology of\nfree will and moral responsibility, cf. Nichols & Knobe 2007;\nNichols 2004; Deery et al. 2013; Sarkissian et al. 2010; Nahmias et\nal. 2005; Nahmias et al. 2007; Murray & Nahmias 2014). \n", "\nSmilansky and other proponents of illusionism go on to argue that\nwhile our commonplace beliefs in free will and desert-entailing moral\nresponsibility are illusions, if people were to accept this truth\nthere would be wide-reaching negative intrapersonal and interpersonal\nconsequences. It would be devastating, they warn, if we were to\ndestroy such beliefs since the difficulties caused by “the\nabsence of ultimate-level grounding” are likely to be great,\ngenerating “acute psychological discomfort” for many\npeople and “threatening morality” (Smilansky 2000: 166).\nTo avoid such deleterious social and personal consequences, and to\nprevent the unraveling of our moral fabric, illusionism contends that\npeople should be allowed their positive illusion of free will and\nmoral responsibility—i.e., we should not take these beliefs away\nfrom people, and for those of us who have already been disenchanted,\nwe ought simply to keep the truth to ourselves.", "\nIn direct contrast to illusionism, is disillusionism: the\nview that to the extent that folk intuitions and beliefs about the\nnature of human cognition and moral responsibility are mistaken,\nphilosophers and psychologists ought to do their part to educate the\npublic—especially when their mistaken beliefs arguably fuel a\nnumber of unhealthy emotions and attitudes such as revenge, hatred,\nintolerance, lack of empathy, etc. (Nadelhoffer 2011: 184). Proponents\nof disillusionism typically point to the benefits of a world without\nmoral responsibility. They cite the many instances in which moral\nresponsibility practices are counterproductive from a practical and\nhumanitarian standpoint—notably in how they stifle personal\ndevelopment, encourage punitive excess in criminal justice, and\nperpetuate social and economic inequalities (see Waller 2011; N. Levy\n2012, 2015; Morris, forthcoming). They maintain that if we abandon moral responsibility “we can look more clearly at the causes and more deeply into the systems that shape individuals and their behavior” (Waller 2011: 287), and this\nwill allow us to adopt more humane and effective interpersonal\nattitudes and approaches to education, criminal justice, and social\npolicy.", "\nA policy of disillusionism is present in the optimistic\nskepticisms of several leading moral responsibility skeptics\n(e.g., Spinoza, Pereboom, Waller, Levy, Caruso, Harris, Vilhauer,\nMilam, and Morris). These optimistic skeptics maintain that life\nwithout basic desert moral responsibility is not only possible, but\nalso preferable. Prospects of finding meaning in life or sustaining\ngood interpersonal relationships, for instance, would not be\nthreatened (see Pereboom 2001, 2014a; Waller 2011; Sommers 2007a; Milam 2016, 2017). They further maintain that morality and moral judgments would remain intact (see Pereboom 2001, 2014a; Waller 1990, 2004). And although retributivism and severe punishment, such as the death penalty, would\nbe ruled out, they argue that the imposition of sanctions could serves\npurposes other than the punishment of the guilty—e.g., it can\nalso be justified by its role in incapacitating, rehabilitating, and\ndeterring offenders (see Pereboom 2001, 2013b, 2014a; N. Levy 2012,\n2015; Caruso 2016, 2017, forthcoming-a; Pereboom & Caruso\nforthcoming; Corrado 2013, forthcoming-a; Vilhauer 2013a,b; Focquaert,\nGlenn, Raine 2013, forthcoming; Murtagh 2013)." ], "subsection_title": "3.1 Illusionism vs/ Disillusionism" }, { "content": [ "\nOne concern people have with moral responsibility skepticism is that\nit would threaten our personal relationships and the fulfillment in\nlife that they provide. P.F. Strawson (1962) famously argued that our\njustification for claims of blameworthiness and praiseworthiness is\ngrounded in the system of human reactive attitudes, such as\nmoral resentment, indignation, guilt, and\ngratitude. Strawson contends that because our moral\nresponsibility practices are grounded in this way, the truth or\nfalsity of causal determinism is not relevant to whether we\njustifiably hold each other and ourselves morally responsible.\nMoreover, if causal determinism were true and did threaten these\nattitudes, as some moral responsibility skeptics are apt to maintain,\nwe would face instead the prospect of the cold and calculating\nobjective attitude, a stance that relinquishes the reactive\nattitudes and treats individuals as objects to be manipulated and\nfixed for consequentialist ends. Strawson argues that adopting the\nobjective attitude would rule out the possibility of the meaningful\nsorts of personal relationships we value (see also Wolf 1981, 1990).\nSummarizing the Strawsonian concern, then, we can say that adopting\nglobal skepticism about moral responsibility, assuming it was\npsychologically possible, would undermine expressions of our\ninter-personal reactive attitudes essential to good personal\nrelationships, and would jeopardize our intra-personal reactive\nattitudes such as guilt and repentance, which are\ncrucial to personal moral development.", "\nMoral responsibility skeptics generally respond to this Strawsonian\nconcern in two ways. One response argues that, contra Strawson, it\nis possible to adopt the objective attitude in a way that\nrespects persons and does not hinder our personal relationships\n(Sommers 2007a). The second and more common response acknowledges that\nStrawson may be right about the objective attitude, but denies that\nskepticism about moral responsibility requires us to reject all the\nreactive attitudes (Pereboom 1995, 2001, 2014a; Waller 1990, 2006, 2011; Milam\n2016). This latter approach maintains that the attitudes we most want to retain either are not\nundermined by moral responsibility skepticism because they do not have\npresuppositions that conflict with this view, or else they have\nalternatives that are not under threat. And what remains does not\namount to Strawson’s objectivity of attitude and is sufficient\nto sustain the personal relationships we value.", "\nPerhaps no one has done more to develop this second line of reply than\nDerk Pereboom (see 1995, 2001, 2002a,b, 2009, 2012, 2013a, 2014a). He\nargues, for instance, that while certain kinds of moral anger, such as\nresentment and indignation, would be undercut if\nmoral responsibility skepticism is true, these attitudes are\nsuboptimal relative to alternative attitudes available to us, such as\nmoral concern, disappointment, sorrow, and\nresolve. The expression of these replacement attitudes can\nconvey the same relevant information as moral anger but in a way that\nis less harmful and consistent with the denial of basic desert moral\nresponsibility. Expression of resentment and indignation “often\nfails to contribute to the well being of those whom it is\ndirected” and is “apt to have harmful effects”\n(Pereboom 2014a: 180). Moral anger frequently is intended to cause\nphysical or emotional pain, and can give rise to “destructive\nresistance instead of reconciliation” (Pereboom 2014a: 180). As\na result it has the potential to damage or destroy relationships. It\nalso often leads to excessively punitive and counterproductive social\npractices and policies (see Waller 2011, 2014; Carey & Paulhus\n2013; Nadelhoffer & Tocchetto 2013; Shariff et al. 2014). [For\nadditional arguments against moral anger and the benefits of\nrelinquishing it, see Flanagan (2016) and Nussbaum (2016).] ", "\nGuilt also appears to be one of the reactive attitudes\nimperiled by moral responsibility skepticism since it involves the\nsupposition that one is blameworthy in the basic desert sense for an\nimmoral action one has performed. Strawsonians fear that absent guilt\nwe would not be motivated to moral improvement after acting badly, and\nwe would be kept from reconciliation in impaired relationships.\nFurthermore, because guilt is undermined by the skeptical view,\nrepentance is also ruled out, because feeling guilty is a\nprerequisite for a repentant attitude. It is unclear, though, whether\nguilt is really needed to perform the functions mentioned above.\nSuppose instead of guilt an agent acknowledges that she has acted\nimmorally and she feels deep sorrow for what she has done, and as a\nresult she is motivated to eradicate her disposition to behave in this\nbad way (see Waller 1990: 165–66). Such a reaction, skeptics\ncontend, can secure the good that guilt can also secure, and it is\nwholly compatible with the skeptical perspective (see Pereboom 2001,\n2014a; Waller 1990; cf. Bok 1998). Furthermore, since self-guilt can\noften be crippling and counterproductive for moral development, an\napproach that avoids guilt may actually be more successful in bring\nabout the desired change in agents (Sommers 2007a). ", "\nAnother reactive attitude that some think would be threatened by moral\nresponsibility skepticism is gratitude. Gratitude arguably\npresupposes that the person to whom one is grateful is praiseworthy in\nthe basic desert sense for a beneficial act (cf. Honderich 1988:\n518–19). But even if this is so, certain aspects of gratitude\nwould not be undercut, and these aspects would seem to provide what is\nrequired for the personal relationships we value (Pereboom 2001,\n2014a; Sommers 2007a). Gratitude involves being thankful toward the\nperson who has acted beneficially. This aspect of gratitude is in the\nclear—e.g., one can be thankful to a young child for some\nkindness without supposing that she is praiseworthy in the basic\ndesert sense. And while gratitude also often involves joy as a\nresponse to what someone has done, skepticism about moral\nresponsibility does not yield a challenge to being joyful and\nexpressing joy when others act beneficially, so this too is in the\nclear.", "\nOf course, some of the recommended transformations in emotional\nattitudes may not be possible for us. In certain situations refraining\nfrom resentment or moral anger may be beyond our power, and thus even\nthe committed skeptic might not be able to make the change the\nskeptical view suggests. Yet, a committed skeptic need not eliminate\nthese attitudes completely to accept the conclusion that agents are\nnever deserving of praise and blame, she must attempt instead not to\nengage or entertain them (Sommers 2007a: 328;\nRussell 1992: 296). Shaun Nichols (2007), for example, invokes the\ndistinction between narrow-profile emotional responses, e.g.,\nlocal or immediate emotional reactions to situations, and\nwide-profile responses, which are not immediate and involve\nrational reflection (see also Pereboom 2014a). We might expect to be\nunable to appreciably reduce narrow-profile moral anger as an\nimmediate reaction upon being deeply hurt in an intimate personal\nrelationship. In wide-profile cases, however, diminishing or even\neliminating moral anger is open—or, at least, we can disavow it\nin the sense of rejecting any force it may be assumed to have in\njustifying a harmful response to wrongdoing. This\nmodification of moral anger, skeptics contend, might well be\nadvantageous for our valuable personal relationships, and it has the\npotential to bring about the equanimity that Spinoza (1677 [1985])\nthought skepticism about free will and moral responsibility, more\ngenerally, would secure (see Pereboom 2001, 2014a; cf. Russell\n2004)." ], "subsection_title": "3.2 Reactive Attitudes" }, { "content": [ "\nSince moral responsibility skepticism would require us to reject our\nordinary view of ourselves as blameworthy and praiseworthy in the\nbasic desert sense, critics also fear that it would undermine\nmorality. Peter van Inwagen, for example, writes:", "\n\n\nI have listened to philosophers who deny the existence of moral\nresponsibility. I cannot take them seriously. I know a philosopher who\nhas written a paper in which he denies the reality of moral\nresponsibility. And yet this same philosopher, when certain of his\nbooks were stolen, said, “That was a shoddy thing to\ndo!” But no one can consistently say that a certain act was a\nshoddy thing to do and say that its agent was not morally\nresponsible when he performed it. (1983: 207)\n", "\nFellow libertarian C.A. Campbell agrees and asserts that denying moral\nresponsibility would destroy “the reality of the moral\nlife” (1957; quoted from Waller 2004: 427). The view that moral\nresponsibility is required for morality is not limited, however, to\nlibertarians. Susan Wolf also contends that if we deny moral\nresponsibility, then we must ", "\n\n\nstop thinking in terms of what ought not to be. We would have to stop\nthinking in terms that would allow the possibility that some lives and\nprojects are better than others. (1981: 386) \n", "\nAnd compatibilist W.T. Stace flatly states, “it is certain that\nif there is no free will [and basic desert moral responsibility] there\ncan be no morality” (1952). Similar remarks can be found\nthroughout the literature—see, e.g., Copleston (1965: 488),\nMurphy (1988: 400), Hintz (1958), Rychlak (1979), Babbitt (1999: 88),\nand Smilansky (2000, 2005).", "\nThe notion, though, that moral responsibility is a necessary condition\nfor morality may not be as clear as these philosophers contend and is\ndirectly challenged by most skeptics (see Pereboom 2001, 2014a; Waller\n1989, 2004, 2011, 2014; Sommers 2007a; see also Haji 1998, 2002). First, it’s unclear what exactly these critics mean when they say that ‘morality’\nwould be undermined by moral responsibility skepticism. Are they\nclaiming that axiological judgments about intrinsic good and evil,\naretaic judgments concerning virtue, deontic judgments about moral\nobligations, right and wrong, etc. are all undermined? If so,\nthat would be an extreme claim. Even if we came to hold that a serial\nkiller was not blameworthy due, lets say, to a degenerative brain\ndisease, skeptics contend that we could still justifiably agree that\nhis actions are morally bad (Pereboom 2001, 2014a; Waller 2004, 2011). Judgments of moral goodness and badness need not require an agent who is blameworthy or praiseworthy, they simply\nrequire grounds by which we can differentiate between the two types of\njudgments. If one were a Calvinist, for example, they could point the\ntranscendent moral law as a way to judge while simultaneously\nrejecting all moral responsibility (Waller 2004: 428). Less exalted\nmoral systems, such as utilitarianism or Kantianism, provide\nalternative ways of grounding moral judgments. Of course, if one were\nto adopt a Kantian test of universalizability while rejecting the rest\nof Kant’s moral views (which do presuppose agents are morally\nresponsible), it would hardly be an orthodox Kantian view. But, as\nseveral skeptics have noted, the denial of moral responsibility is not\ninconsistent with the principles of Kantian moral rationalism (see\nWaller 2004: 429; Vilhauer 2013a,b; Pereboom 2014a). It is arguable, then, that\naxiological judgments of moral goodness and badness would not be\naffected by moral responsibility skepticism (Haji 1998; Pereboom 2001,\n2014a), and this may be sufficient for moral practice.", "\nNonetheless, critics might question that if determinism precluded\nbasic desert blameworthiness, would it not also undercut judgments of\nmoral obligation? Kant famously argued that “ought implies\ncan,” and that if the moral law commands that we ought\nto perform some action, it “inescapably follows” that we\nmust be capable of performing that action (1793 [1998: 94];\n1781 [1998]: A548/B576). And G.E. Moore, following Kant, argues that\none “cannot say of anyone that he ought to do a certain thing,\nif it is a thing which it is physically impossible for him to\ndo” (1922: 317). But if ‘ought’ implies\n‘can,’ and if because determinism is true an agent could\nnot have avoided acting badly, it would be false that she ought to\nhave acted otherwise (see Nelkin 2011: 100–101; cf. Jeppsson\n2016b). Furthermore, if an action is wrong for an agent just in case\nshe is morally obligated not to perform it, determinism would also\nundermine judgments of moral wrongness (Haji 1998).", "\nThere are, however, a number of possible ways to respond to this\ncriticism. One is to argue, as Waller (2004, 2011) does, that while\nthe ‘ought implies ‘can’ principle (OIC for short)\nis widespread and deeply entrenched, it is nonetheless false (see also\nSinnott-Armstrong 1984; Ryan 2003; Graham 2011). In fact, recent work\nin experimental philosophy suggests that the principle may not be as\nintuitive as philosophers think. Buckwalter and Turri (2015), Mizrahi\n(2015a,b), Chituc et al. (2016), Henne et al. (2016), and Turri\n(2017) have all run experiments testing ordinary “folk”\nintuitions about the link between moral requirements and abilities.\nThey each independently found that commonsense morality rejects the\nOIC principle for moral requirements, and that judgments about moral\nobligations are made independently of considerations about ability. By\ncontrast, they also found that judgments of blame were highly\nsensitive to considerations about ability, which suggests that\ncommonsense morality might accept a “blame implies can”\nprinciple or that judgments of blame may play a modulatory role in\njudgments of obligation (see Buckwalter & Turri 2015; Chituc et\nal. 2016). These empirical findings support Waller’s claim that\nthe OIC principle is a philosopher’s invention infected by\nmistaken assumptions about moral responsibility (cf. Kurthy &\nLawford-Smith 2015; Kurthy et al. 2017; Cohen forthcoming; Graham\n2011; Zimmerman 1996).", "\nAnother option for skeptics is to accept the OIC principle but adopt\nan axiological understanding of ‘ought’ and an\nepistemic reading of ‘ought implies can’\n(Pereboom 2014a). On this reading of the principle, when we say that\nan agent ‘ought to x,’ we are simply making an axiological\njudgment about x and recommending that the agent perform x at some\nfuture time. When we say ‘ought implies can,’ on the other\nhand, we mean that it is epistemically open to the agent that\nshe will develop the requisite motivation to x, and in this sense\ncan perform x. Furthermore, the axiological and epistemic\ncomponents are connected in that the recommendation made by the\naxiological judgment may itself contribute causally to producing the\nmotivation (Pereboom 2014a: 140). Of course, this is not the\n‘ought’ of obligation Kant and others may have had in\nmind, since given the assumption of determinism and that determinism\nprecludes alternatives, when one tells an agent that she ought to\nrefrain from performing an action of some type in the future,\nit’s not the ‘ought’ of specific action demand, but\nrather the ‘ought’ of axiological evaluation that is\nlegitimately invoked (Pereboom 2014a: 141). Pereboom calls this the\n‘ought’ of axiological recommendation (2014a:\n141), and it should not be understood as presupposing a route actually\nassessable to an agent, via reasons for action, to her acting in some\nrelevant way. All that is required for the legitimate use of\n‘ought,’ on this account, is that one be unsure\nepistemically about whether such a route is accessible, and in most\nreal-life cases this requirement is satisfied since we lack certainty\nabout the future (cf. Nelkin 2014; for reply see Pereboom 2014b). ", "\nFrom the skeptical perspective, then, morality is not about\nbackward-looking assessments of blameworthiness and praiseworthiness,\nsince these are rejected. Rather, morality is forward-looking and\nfunctions by invoking the ‘ought’ of axiological\nrecommendation, the epistemic sense of the notion of\n‘can,’ and (at least in the case of Pereboom (2014a,\n2017b)) a forward-looking notion of blame grounded in the goods of\nprotection, reconciliation, and moral formation. While critics may\nfear this is still not enough since morality must be capable of\ngrounding backward-looking judgments of blameworthiness and\npraiseworthiness, the skeptic’s conception of morality may\nnevertheless be sufficient for the vast majority of our moral\npractices. [Cf. Fischer 2004; Athanassoulis 2005; Edmundson 2007;\nRosen 2004; Moya 2010; Morris 2015]" ], "subsection_title": "3.3 Morality" } ] } ]

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[ "\nOverarching surveys of the history of philosophy often leave the\nimpression that philosophical skepticism—roughly, the position\nthat nothing can be known—had many adherents in the Ancient and\nHellenistic Periods, disappeared completely as a topic of intellectual\ninterest during the Middle Ages, and returned as a viable position in\nthe Renaissance and Early Modern Periods.", "\nAs a survey, this is quite understandable, since no thinker from the\nMiddle Ages professed an active allegiance to a systematic\nphilosophical skepticism. But a closer examination of Medieval\nPhilosophy shows that despite skepticism’s disappearance as an\novert philosophical movement, it continued to swirl in the thoughts of\nmany of the best philosophers of the period. A very few, including\nmost prominently Augustine and Al-Ghazali, claimed to have been\nsystematic skeptics at some points in their pasts. Many others held\nskeptical views about localized issues such as one’s ability to\nknow an efficient cause. And even more discussed and attempted to\nrefute commonplace skeptical arguments in defense of their own,\nanti-skeptical positions.", "\nChronologically speaking, skeptical issues were most prominently\nconsidered in works from both the leading and tail ends of the Middle\nAges. Augustine’s 4th and 5th century attacks against the\nAcademic Skeptics mark the beginning of such discussions, and a\nsmattering of treatments of skeptical issues appears periodically\nthroughout the next 800 years. From the late 13th century onwards,\nhowever, skeptical issues began to exert a dominant and wide influence\non epistemological discussions, as seen in the works of such important\nfigures as Henry of Ghent, John Duns Scotus, William of Ockham, Peter\nAuriol, John Buridan, and Nicholas of Autrecourt.", "\nThough medieval discussions of skepticism are often found buried\nwithin larger, formulaic discussions of theological topics, these\ntreatments had influence beyond the academic circles within which they\nwere originally created and considered. Among Early Modern\nphilosophers, Descartes in particular owes a debt to these earlier\naccounts of skepticism: versions of both his cogito and Evil\nDemon arguments may be found in the works of medieval\nphilosophers.", "\nIn what follows we will briefly examine the relevant views of a few\nrepresentative figures from each tradition and era. Though none claims\nto be inclusive of the entire Middle Ages, the best scholarly\noverviews of important aspects of the medieval epistemological\ntradition are Tachau (1988), Pasnau (1997), Perler (2006), and\nLagerlund (2010a)." ]

[ { "content_title": "1. Ancient and Hellenistic Sources", "sub_toc": [ "1.1 Pyrrhonian Skepticism", "1.2 Academic Skepticism" ] }, { "content_title": "2. Skepticism in Pre-Scholastic Christian Philosophy", "sub_toc": [ "2.1 Augustine", "2.2 Other Pre-Scholastics" ] }, { "content_title": "3. Skepticism in Islamic and Jewish Philosophy", "sub_toc": [ "3.1 Islamic Philosophy", "3.2 Jewish Philosophy" ] }, { "content_title": "4. Scholasticism and Skepticism", "sub_toc": [ "4.1 Thirteenth Century", "4.2 Fourteenth Century" ] }, { "content_title": "5. Concluding Remarks", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Primary Texts and Translations", "Secondary Sources" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThere were many varieties of skepticism extant during the Ancient and\nHellenistic periods, but two were particularly important to the later\nhistory of topic: Pyrrhonian Skepticism, especially as presented by\nSextus Empiricus, and the Academic Skepticism of Cicero.", "\nPre-medieval adherents of both types of skepticism not only held\nparticular skeptical positions, but also participated in a skeptical\nway of life, taking their arguments and positions as part of an\noverarching ethical worldview. Skeptics took their radical views of\nknowledge as means to the end of reaching the state of tranquility. By\nusing common argumentative moves called tropes, skeptics sought to\nelevate themselves and others to a state of suspension of belief\n(epochê). And once this was reached, they held,\none’s worries about philosophical matters would dissolve in\ntranquility.", "\nBecause of these ethical excellences, skeptics held themselves up as\nwise men. The more radical Pyrrhonian Skeptics, who doubted the truth\nof all claims, quickly ran afoul of the following objection, which has\nbeen given in various forms throughout the history of philosophy: a\nthoroughgoing skeptic, it seems, cannot live his or her skepticism. If\none doubts (and thus fails to act) on the truth of such claims as\n“Food is necessary for human life”, it would follow that\none could not live at all. Academic Skeptics attempted to avoid this\nobjection by arguing that though skepticism precluded living by the\ntruth, since the truth could not be known, nevertheless one could live\nby the truthlike or plausible. Hence theirs was a more practical\nversion of skepticism." ], "section_title": "1. Ancient and Hellenistic Sources", "subsections": [ { "content": [ "\nPyrrhonian Skepticism, which was to play such an central role in the\nRenaissance and Early Modern Philosophy, had no significant, direct\ninfluence on later medieval thinkers, since texts exploring the\nposition (primarily the works of Sextus Empiricus, and to a much\nlesser extent, Diogenes Laertius) were not in wide circulation.\nFloridi (2002) and Wittwer (2016) explore the textual transmission of\nSextus’s works; Floridi notes that there are only seven known\nLatin manuscripts from the period, though Wittwer has found further\nevidence to supplement this.", "\nA few scattered references to Pyrrhonian skepticism have been found in\nthe Latin West, in the works of Bede (early 8th century), Rabanus\nMaurus (9th century), and Peter of Auvergne (late 13th century). More\nwas known of it to Byzantine and Islamic philosophers, since knowledge\nof Greek was preserved in their intellectual communities, and since\nthey had access to a greater range of ancient texts that addressed the\ntopic." ], "subsection_title": "1.1 Pyrrhonian Skepticism" }, { "content": [ "\nAcademic Skepticism, so-called because of its birth among scholars\nworking in Plato’s Academy, was the type most known to the\nmedievals. Academic skepticism was presented through the sympathetic\nworks of Cicero (De Natura Deorum and Academica,\nprimarily), and especially through many of Augustine’s\nanti-skeptical arguments, such as those found in his Contra\nAcademicos. In fact, for most of the Middle Ages—at least\nup through the 1430s—the term scepticus wasn’t\nused in the Latin tradition; academicus was the most common\nterm for the skeptic. Further complicating matters, the medievals\nfailed to recognize the distinction between Academic and Pyrrhonian\nSkepticism. See Floridi (2002) and Schmitt (1972).", "\nSchmitt’s (1972) study of the textual transmission of\nCicero’s skeptical works brings out many interesting aspects of\nits history. As was the case with Sextus, there were few manuscripts\nof Cicero’s Academica extant in the Middle Ages. In\naddition, there were two versions of it in circulation, and the\nmedievals had only parts of each. And yet another problem for those\nwho had access to the texts was that Cicero’s position was often\nconfused with that of one of his interlocutors in the work,\nLucullus.", "\nHenry of Ghent (late 13th C.) is the first medieval philosopher both\nto have obvious knowledge of the Academica, and to have made\na serious philosophical attempt to come to grips with the views\nexpressed there. When John Duns Scotus critiques Henry’s\nepistemology, he shows no evidence of knowing Cicero’s text. And\nfor the most part, later medievals were equally ignorant of it. Their\ndiscussions of skepticism seem not to have been based on an\nexamination of or engagement with skepticism as presented by ancient\nauthors; it was a skepticism of its own sort, as will be detailed\nbelow." ], "subsection_title": "1.2 Academic Skepticism" } ] }, { "main_content": [], "section_title": "2. Skepticism in Pre-Scholastic Christian Philosophy", "subsections": [ { "content": [ "\nAugustine of Hippo (354–430) was a classically trained\nrhetorician who explored many different schools of thought (Platonism,\nManicheanism, and Skepticism) before converting to Christianity. After\nhis conversion, he began to write philosophical and theological works\naddressing some of the views from these schools. The most important\nanti-skeptical work was his Contra Academicos (Against\nthe Academicians), which has been discussed by Matthews (1977 and\n1992), Burnyeat (1982), King (1995), Curley (1997), O’Daly\n(2001), Bolyard (2006), and Dutton (2016).", "\nIn Contra Academicos, Augustine targets a few key Academic\nclaims: (a) that appealing to truthlikeness or plausibility is\ncoherent; (b) that skeptics are wise; (c) that nothing can be known;\nand finally (d) that skepticism leads to tranquility.", "\nAccording to Augustine, three of the four claims can be relatively\nquickly dispatched. The first claim, concerning truthlikeness, cannot\nfunction alone as a standard, since one cannot know that something is\nlike the truth without also knowing the truth itself. Second,\nskeptics cannot be wise, since wisdom requires knowledge of some sort.\nThird, skepticism leads away from tranquility, rather than towards it,\nsince it puts one at odds with the morals of the rest of society,\nwhich in turn is likely to lead to strife.", "\nThe most important claim for the epistemological history of the\nproblem is the third: that nothing whatsoever can be known. Augustine\ntreats of it in some detail.", "\nHe casts the issue as follows. The skeptic argues that a wise man must\nretreat to skepticism since nothing can be known. This inability is\ndue to the fact that knowledge of a truth—at least as understood\nby certain Stoics—is only possible if that truth could not\npossibly be caused to appear mentally by something different than what\nit is in fact caused by. For example, if an internal mental image or\nconcept of a tree’s being beside a house could be\ncaused by a dream, then the tree’s being beside the house cannot\nbe known, even if the tree is in fact beside the house. With\nthese stringent causal requirements, it is unsurprising to find that\nAcademic Skeptics take the line they do: since no appearance meets\nthis strict standard, they argue, it follows that nothing at all can\nbe known.", "\nAugustine thinks this standard can be met, however, at least in some\ncases. Augustine aims to uncover propositions about which doubt is an\nutter impossibility. He soon finds the following four disjunctive\nstatements:", "\nI still know something about physics. For I am certain that (1) there\nis either one world or not. And (2) if there is not just one, the\nnumber of them is either finite or infinite… In the same way, I\nknow that (3) our world is disposed as it is either by the nature of\nbodies or by some plan. And I know that (4) (a) either it always did\nexist and always will, or (b) it started to exist and will never stop,\nor (c) it did not start in time but will have an end, or (d) it\nstarted and will not last forever…These truths are [logical]\ndisjunctions, and no one can confuse a likeness of something false\nwith them. (Contra Academicos 3.10.23)\n", "\nIn short, Augustine challenges the skeptic to convince him that such\nexhaustive, disjunctive propositions can be confused with, or have a\nlikeness of, what is false.", "\nAt this point that the skeptic counters with external world\nskepticism: “How do you know this world exists…if the\nsenses are fallible?” In other words, the skeptic argues, these\ndisjunctive statements about the external, physical world all assume\nthe existence of an external world, and thus they cannot be known to\nbe true if the external world itself cannot be known to exist. If\nexternal world skepticism can be maintained, it follows that\nAugustine’s disjunctions can be mistaken for what is\nfalse, and thus this particular argument against global skepticism\nwill fail.", "\nAugustine’s primary response to the external-world skeptic is\nAugustine’s claim that things “seem” to him, and\nthat these seemings constitute the world. He supports this view by\narguing that seemings are required in order for error to\noccur—otherwise, what would we be mistaken about? And since the\npossibility of error is the main impetus for skeptical doubt,\nskepticism requires the admission that things seem. In other words,\nfor Augustine, one cannot doubt that one has mental content, even if\none might have doubt about whether this content corresponds to\nanything external to the mind.", "\nAugustine gives further, more central arguments against global\nskepticism as Contra Academicos continues, claiming\nmathematical truths (e.g., “2 + 3 = 5”) and logical truths\n(e.g., “nothing both is and is not”) to be undoubtedly\ntrue. As with the physical disjunctions, such truths can be known\nwithout knowing external objects with any determinacy.", "\nBeyond his discussions in the Contra Academicos, Augustine\nfrequently tackles epistemological topics in other works. Most\nfamously, Augustine makes proto-Cartesian moves frequently, arguing\nthat the mere fact that he doubts and has various other mental\nhappenings proves his own existence:", "\n…who would doubt that he lives, remembers, understands, wills,\nthinks, knows, and judges? For even if he doubts, he lives; if he\ndoubts, he remembers why he doubts; if he doubts, he understands that\nhe doubts; if he doubts, he wishes to be certain; if he doubts, he\nthinks; if he doubts, he knows that he does not know; if he doubts, he\njudges that he ought not to consent rashly. Whoever then doubts about\nanything else ought never to doubt about all of these… (On\nthe Trinity 10.10.14)\n", "\nLater, Augustine will draw on his theory of illumination to provide\nthe grounds for certainty. According to this theory, God’s\nDivine Ideas serve as the guarantors of certainty, and they function\nin much the way that Plato’s Forms do. Augustine first presents\nthis view in De Magistro (On the Teacher), and he\nmakes other references to it in later works. Augustinian Illumination\nhas been widely discussed in the secondary literature, and Nash (1969)\nstill remains one of the best introductions to the position." ], "subsection_title": "2.1 Augustine" }, { "content": [ "\nThere is little interest in skepticism exhibited in Christian\nphilosophy until the rise of the Universities in the 13th century.\nHadoardus (9th C.) includes many quotations from the\nAcademica in his compilation of Cicero’s views\ngenerally, but he did no philosophical work with these quotations.\nJohn of Salisbury (12th C.) discusses Academic Skepticism to some\ndegree in his Policraticus, but there’s no evidence\nthat he had direct access to Cicero’s text; he most likely got\nthe information either from Augustine or from some other secondary\nsource." ], "subsection_title": "2.2 Other Pre-Scholastics" } ] }, { "main_content": [], "section_title": "3. Skepticism in Islamic and Jewish Philosophy", "subsections": [ { "content": [ "\nTwo Islamic thinkers are particularly important to the history of\nmedieval skepticism. Al-Ghazali (Algazel to the Latin-speaking world)\n(ca. 1058–1111) travelled throughout the Middle East, but spent\nmost of his time in what are now Iran and Iraq. Al-Haytham (= Alhazen)\n(965–1039), who was born in what is now Basra, Iraq, wrote\nwidely on various scientific and mathematical subjects. In addition,\nwhile the Persian philosophers Rāzī (1149–1210) and\nṬūsī (1201–1274) are not skeptics, their\nconcerns with global skepticism and the knowledge of first principles\nlead them to have extended discussions of skeptical arguments. For\nmore on Rāzī and Ṭūsī, see Fatoorchi\n(2013).", "\nAl-Haytham’s Kitab al-Manazir (Book of Optics)\nwas of particular importance for the later history of skepticism.\nBeyond his Arabic-speaking audience, it widely read in the Latin West\nunder the title Perspectiva or De aspectibus,\nbeginning with such philosophers as Roger Bacon (ca. 1214–1294).\nHis views about the perceptual process had a wide influence throughout\nthe later Middle Ages.", "\nAl-Haytham held that many perceptions are inferential, and he explains\nhis views in II.3 of the Optics. Rather than always grasping\nsensed things in an unmediated way, he argues, we sometimes grasp them\nthrough sudden, “imperceptible” inferences. These\ninferences proceed so rapidly as to seem immediate, and thus we\nusually don’t notice that they are occurring at all. Al-Haytham\neven argues that seemingly self-evident propositions such as\n“the whole is greater than its [proper] part” are\ninferential. Given this inferential process, cognitive error becomes a\nmore reasonable possibility.", "\nHe catalogued a number of optical illusions as well (Optics\nIII.7), examining such problems as the way the moon when low on the\nhorizon appears larger than it does when higher in the sky, and the\nway that when one is in a boat floating down a river, the trees on the\nshore appear to be moving. Though Al-Haytham was not a skeptic\nhimself, these illusory experiences provided fertile material for\nlater thinkers to consider. Tachau (1988) discusses his wide influence\non the scholastic tradition.", "\nAl-Ghazali sounds surprisingly Cartesian in an important section of\nhis Munkidh min al-Dalal (Deliverance from Error).\nHe begins by declaring his desire to reach certain knowledge, which he\nexplains as “that in which what is known is laid bare in such a\nway as to leave no room for doubt, and is unaccompanied by the\npossibility of error or illusion, to the point that the mind cannot\neven conceive it.” (Deliverance 82)", "\nHe gives a (by now) familiar list of reasons for doubting the\ncertainty of things. First, disagreement among competing theories\ngives some initial doubt. Second, a few cases of sensory skepticism\n(e.g., a shadow cast by the sun appearing to remain still, when in\nfact it is slowly moving as the day passes; the apparently small size\nof celestial bodies) lead him to lose confidence in all of his sensory\nbeliefs. This distrust of his senses also suggests, third, that\nanother of his faculties—reason itself—may be faulty, and\nhe wonders whether even apparent logical truths might be false. And\nfinally, he concludes by invoking dream skepticism. After setting up\nthese doubts, he says the following:", "\nWhen these notions occurred to me and made an impression on my mind, I\nsought a cure but found none. For they could only be rebutted with a\nproof, and a proof can only be constructed by combining the first\n[principles of] knowledge. If these are not given, then it is\nimpossible to arrange a proof. This disease defied all cure and lasted\nfor almost two months, during which I embraced the [skeptical] creed\nin actual fact, though not in speech or expression. Eventually, God\ncured me of this disease and my mind was restored to health and\nbalance. The rational necessary beliefs were once again accepted and\ntrusted, both securely and certainly. This did not come about by\ncomposing a proof or by an arrangement of words, but rather by a light\nthat God almighty cast into my breast, which is the key to the greater\npart of cognizance. Whoever supposes that enlightenment depends upon\nexplicit proofs has narrowed the expanse of God’s mercy.\n(Deliverance 86)\n", "\nBeyond this, Ghazali also questions the nature of causation in his\nIncoherence of the Philosophers (Tahafut\nal-falasifa). Though he ultimately holds that all causation can\nbe traced to God, he argues that our observations of so-called natural\ncauses are not sufficient for proving a direct causal link between the\napparent cause and that which is caused. This Humean-leaning position\nhas been discussed widely in the secondary literature. See, e.g.,\nHalevi (2002) for a recent treatment. For another recent account that\ndoes much to situate Ghazali’s discussion of skepticism within a\nbroader Islamic intellectual conversation about the subject, and\ndownplays the supposed connections between Ghazali and the Early\nModerns, see Kukkonen (2010)." ], "subsection_title": "3.1 Islamic Philosophy" }, { "content": [ "\nThere is no strong evidence of any significant skeptical tendencies or\ninterests among medieval Jewish philosophers. Judah Halevi (ca.\n1075–1141) discuses skepticism briefly in his Kuzari\nI.4–8; in this passage, a character in the poem professes\nskepticism about religious truths, and presents his requirements for\nwhat would count as knowledge. See Kogan (2003).", "\nThere has also been limited discussion of Maimonides as a skeptic.\nSome of it focuses, e.g., on his claims in the Guide for the\nPerplexed 2.24 that humans cannot have knowledge of heavenly\nthings. To take this to imply either a thoroughgoing skepticism or a\nthoroughgoing concern with skepticism, however, is probably too strong\nan inference. For more on this issue, see Ivry (2008) and\nHaliva (2018)." ], "subsection_title": "3.2 Jewish Philosophy" } ] }, { "main_content": [], "section_title": "4. Scholasticism and Skepticism", "subsections": [ { "content": [ "\nThe thirteenth century saw the birth of Scholasticism in the Latin\nWest. As Universities began to develop in such important centers of\nlearning as Paris and Oxford, so too did highly formalized and\nargumentative styles of debate and writing. At the same time, some of\nthe intellectual consequences of the Crusades came to play an\nimportant role in the history of skepticism: Muslim and Jewish\nscholars and writings came to the attention of Christians working on\nsimilar topics. Of particular importance was the translation of all of\nAristotle’s works into Latin, along with many commentaries on\nthem (as well as original works) by Ibn-Rushd (Averroes) and Ibn-Sina\n(Avicenna).", "\nWith these texts came others (such as Al-Haytham’s\nOptics), and Christian scholars such as Roger Bacon began to\ninvestigate the cognitive process more thoroughly in their own\nwritings. The dominant Augustinian theory of knowledge began to come\nunder attack as the wealth of new accounts were contrasted, rejected,\nor synthesized. And as Augustine was reinterpreted, so too was his\nrejection of skepticism.", "\nThomas Aquinas (ca. 1225–1274) and Siger of Brabant (ca.\n1240–ca. 1282) were philosophers of vastly different reputations\n(the first was declared a saint and holds a preeminent place in\nCatholic theology; the second was accused of heresy and died under\nmysterious circumstances). Yet they both shared a deep commitment to\nsynthesizing the new Aristotelian texts into their respective\nviews.", "\nAquinas, as with Aristotle, exhibits no serious concerns with\nskepticism or with skeptical arguments. He occasionally makes\nreferences to sensory illusions, e.g., but he sees them as no\nepistemological threat. Baertschi (1986) and Pasnau (1997) treat of\nthis issue briefly. Indeed, most of the secondary literature on\nAquinas focuses on the question of why he has no such\ninterest in skepticism. Varying accounts are given, and among them is\nAquinas’s Aristotelian belief that the cognitive process is\nfundamentally a reliable one. For the most part, Aquinas and most\nlater medievals aim to explain the processes by which knowledge is\nacquired, rather than aiming to justify knowledge.", "\nFurthermore, many scholars argue that the Aristotelian doctrine of the\nformal identity of knower and known plays a significant role for\nAquinas in particular. If (on this interpretation) the knower quite\nliterally takes on the form of the known object, and thus becomes\nidentical to the known object in this formal way, then there is no\nchance for error. The knower is not at a remove from the known object\nat all, on this account. There is considerable disagreement about\nAquinas’s motivations here; for a few representative views, see\nGilson (1986), MacDonald (1993), Pasnau (1997), Jenkins (1997), and\nHibbs (1999).", "\nSiger of Brabant, on the other hand, dealt directly with skepticism\nand skeptical arguments in his Impossibile 2 and his\nQuestions on the Metaphysics. Though, as Côté\n(2006) argues, he also declines to take skepticism to be a serious\nthreat, he does take the time to address it. Most notably, Siger\nraises the following question for consideration in\nImpossibile 2: “everything that appears to us are\nillusions and similar to dreams, so that we are not certain of the\nexistence of anything.” Siger has various responses in his\ndiscussions, but his most important claims are (a) that a failure of\nthe senses in some cases does not automatically imply failure in all\ncases; and (b) that if a sense report is not contradicted by another,\nmore reliable sense report, then it itself is reliable. Furthermore,\nSiger gives a rather unconvincing reductio, arguing that if\nthe senses are unreliable, no knowledge at all is possible. Taking\nthis as a reductio of skepticism obviously would do little to\nassuage the worries of the committed skeptic.", "\nSiger’s responses, though somewhat unsatisfying, do indicate the\nbeginning of a growing interest in skeptical problems. Henry of Ghent\nshows this interest even more starkly.", "\nHenry of Ghent (ca. 1217–1293) was one of the most important\ntheological masters of his day, and he was a contemporary of both\nAquinas and Siger. Beyond his own philosophical work, Henry was a\ncentral figure in one of the crucial events in medieval intellectual\nhistory: the Condemnation of 1277, which will be discussed at the end\nof this section. Brown (1973), Marrone (1985), Pasnau (1995), and\nAdams (1987) discuss Henry’s views in some detail.", "\nHenry’s most concentrated attention to skeptical issues occurs\nin the first two questions of his Summa Quaestionum\nOrdinariarum (Ordinary Questions). Henry’s\ndiscussion of skepticism stands out when placed alongside other works\nfrom the same period. Though Augustine’s Contra\nAcademicos was extant, and though Augustine’s De\nTrinitate echoed many of the anti-skeptical arguments from his\nown earlier work, the vast majority of Henry’s scholastic\ncontemporaries (including Aquinas) took no serious interest in\nskepticism. Various explanations of this general attitude can be\ngiven. Perhaps Augustine’s self-proclaimed refutation of\nAcademic skepticism was taken to be the final word on the subject;\nAristotle’s dismissive attitude towards skepticism would have\nreinforced this idea. But for whatever reason, Henry thought the issue\nof skepticism important enough to raise it in the opening question of\nhis own most important theological work.", "\nHenry lists a number of different skeptical arguments, drawing from\nthe critical accounts of Aristotle, Cicero, Augustine, and Averroes,\nand mentioning the support skepticism garners from the views of\nHeraclitus, Zeno, Protagoras, and Democritus, and Plato. He gives no\nevidence here of having direct access to any of the texts of the\nlatter five thinkers, though he knows of their views through the works\nof others.", "\nHe begins by listing preliminary arguments both for and against the\npossibility of knowledge. On the skeptic’s side, Henry discusses\ncases of sensory relativism (what seems sweet to one person does not\nseem sweet to another, e.g.); the changeable nature of the sensory\nworld; and the Learner’s Paradox from the Meno. Among\nthe anti-skeptical arguments is Aristotle’s view\n(Metaphysics IV) that in denying knowledge, one is thereby\nclaiming certainty that one does not know, and thus the skeptic must\nadmit to knowing something. He also pulls from Augustine’s\noft-repeated claim that in doubting, one knows that one doubts (De\nvera religione xxxix.73).", "\nHenry then argues in a number of different ways that knowledge is in\nfact possible. First, he draws from Augustine and Cicero. His weakest\nclaim here is that we can rely upon the testimony of others;\notherwise, he says, knowledge of the distant past, or of places that\none has never visited, would be impossible. He also explains that one\ncan trust the veracity of a given sense experience provided it\nhasn’t been contradicted by a more reliable sense experience. In\naddition, he says that even if one is dreaming, one still knows that\none lives. As with many who follow him, Henry cites the certainty of\nthe law of non-contradiction as well.", "\nIn the final section of the question, Henry replies directly to the\nskeptical arguments he outlined in the beginning. Though he gives too\nmany responses to detail here, Henry’s core idea is that though\nthe senses grasp only changeable things, one has the ability to\nabstract what he calls the “created exemplar” from the\nobjects of the senses; from this created exemplar, we can obtain a\nlow-level knowledge of external objects (he calls this knowledge of\nthe “true” or of the “truth”). Knowledge in\nthe full sense—that is, knowledge of the “pure\ntruth”—requires knowledge of the “uncreated\nexemplar”, or Divine Idea. Because the created exemplar is\nmutable in itself, it is only by seeing how it accords with the\nuncreated exemplar in God’s mind that full and certain knowledge\nis possible. In short, Henry follows Augustine in spirit, even if not\nin detail: for both philosophers, knowledge is impossible without\nDivine Illumination.", "\nIn the second question of his Summa, Henry explores\nIllumination in more detail. As he begins to explain things, it sounds\nas if God’s general background influence is sufficient to\nexplain human knowledge. Later, however, Henry limits his optimistic\noutlook. First, he argues that God illuminates each person", "\naccording to his condition and capacity, unless someone by displaying\ngreat malice merits that it be taken away from him altogether. Such a\nperson, as a result, would not see any truth at all…but would\ndissipate into the error that he deserves. (Summa I.2.134)\n", "\nEchoing some of Augustine’s remarks in the De Magistro,\nHenry here seems to restrict epistemic certainty to those who are\nmorally worthy. Second, Henry diverges even further from his initial\nargument, saying that God offers the “rules of the eternal\nlight”—that is, the Divine Ideas—", "\nto whomever he wants and takes them away from whomever he\nwants… Thus God sometimes bestows the eternal rules on bad\npeople, with the result that in these rules they see many truths that\nthe good cannot see… Sometimes, too, God takes these same rules\naway from such people and allows them to fall into error… [God]\nbestows [pure truth] through free will, on whomever he wants.\n(Summa I.2.131–132)\n", "\nIn short, according to this second argument, our ability to know with\ncertainty is entirely dependent upon God’s whim. We will know\nonly in cases in which God wants us to. This emphasis on God’s\nrole in the knowing process is of a piece with the emphasis on Divine\nOmnipotence one finds in the Condemnation of 1277, with which Henry\nwas intimately involved.", "\nAs the newly rediscovered Aristotelian texts began to find their way\ninto university curricula in the thirteenth century, more conservative\nfaculty reacted. Bonaventure and Henry were among the latter, and each\nargued against those who sought to replace the reigning Augustinianism\nwith too many new Aristotelian elements. Aquinas, Siger of Brabant,\nand others sought to synthesize Aristotle and Christianity in a much\nmore thoroughgoing way than Henry thought acceptable. And as part of\nthe commission organized at the Pope’s request, Henry helped\ncreate a list of 219 propositions—some held by Aquinas\nhimself—that were condemned as heretical to the Catholic faith\nin 1277 by Bishop Etienne Tempier.", "\nIf there were ever an instance of philosophical irony in the Middle\nAges, this would be it. Despite Henry’s strong aversion to\nskepticism, and despite his arguments against it, the most important\npractical effect of the Condemnation of 1277 was to introduce an\nentirely new level of skeptical doubt. The Condemnation emphasized\nGod’s omnipotence, and declared views that denied this to be\nheretical. As a result, the realm of the possible was expanded\ndramatically in medieval discussions. This concern quickly spreads\nthroughout most Christian epistemological discussions, up through the\nend of the Middle Ages. If God is omnipotent, according to this\nconcern, couldn’t he be deceiving us either in particular cases,\nor perhaps even globally? For a fascinating discussion of the variety\nof responses one finds in the 13th and 14th century treatments of this\nproblem, see Perler (2010)." ], "subsection_title": "4.1 Thirteenth Century" }, { "content": [ "\nAfter the Condemnation of 1277, Christian philosophers became even\nmore focused on epistemology. Debates often centered on the medieval\ndistinction between intuitive cognition and abstractive\ncognition—roughly, the distinction between knowing something as\npresent and existent, and knowing something from a remove (e.g.,\nthrough memory, or through an inference). In addition, many\nphilosophers began to explore the nature of sensory illusions in more\ndetail. And of course, the Evil Demon hypothesis loomed ever larger as\nthe notion of Divine Omnipotence was explored more fully.", "\nJohn Duns Scotus (1265–1308) worked in Oxford, Paris, and\nCologne. Living roughly a generation before Ockham, Scotus was a\nfollower of Aristotle, and as with many of his time, Avicenna too had\na profound impact on the development of his thought. As far as\nskepticism is concerned, Scotus is unconvinced by Henry’s\nanti-skeptical arguments, but he thinks the threat of skepticism\ndangerous enough that he devotes considerable attention to arguing\nagainst the problem. Adams (1987) and Pickavé (2010) discuss\nhis position in connection with skepticism.", "\nIn his Ordinatio I.3.1.4, Scotus finds Henry’s created\nexemplar/uncreated exemplar distinction insufficient for defeating\nskepticism. Scotus’ critique of Henry has two main foci:\nHenry’s appeal to mutability, and Henry’s need for an\nuncreated exemplar. First, Scotus finds numerous problems with\nHenry’s worries about change, and he argues that change as such\ndoes not prevent knowledge, and that even if it did, much of what we\nknow is sufficiently stable to support our knowledge claims. In\ndefense of his initial claim he argues, e.g., that our own mutability\nwould make knowledge utterly impossible, if Henry’s views are\ncorrect. His second claim about change also receives support in\nvarious ways, most notably by his appeal to what he calls a nature\n(natura), which is (roughly) the essence of a thing. Here, he\nargues that since natures in themselves are immutable, and since each\ncan have what Scotus calls an immutable relation to something else, we\nhave sufficient grounds for stability-based certainty.", "\nHenry’s appeal to an uncreated exemplar to ground knowledge and\ncertainty is also problematic, according to Scotus. If we understand\nthe created exemplar as a species (roughly, an image or intentional\nobject) formed in the soul during an act of cognition, then we are\noften unsure whether that created exemplar existing in the soul truly\ncorresponds to an extramental object. Thus,", "\n…if it cannot be judged when such a species represents itself\nas such and when it represents itself as an object, then [no matter]\nwhat else concurs with such a species, one cannot have [any] certitude\nby which the true may be distinguished from the truthlike.\n(Ordinatio I.3.1.4.104)\n", "\nIn other words, showing that the species in the soul corresponds to an\nuncreated exemplar—that is, a Divine Idea—does\nnothing to help us determine whether that species corresponds to\nsomething in the sensory world.", "\nAccording to Scotus, God has created the world in such a way that\nknowledge is possible by means of his general, background\nillumination, which amounts, in Scotus’ view, to a natural\nprocess. With this in mind, we may now turn to an examination of\nScotus’ positive view and its relation to skepticism.", "\nScotus holds that we have “necessary certitude” about four\nkinds of knowledge. The first type is knowledge of self-evident\npropositions (propositions per se notae)—such as\n‘a whole is greater than its parts’—as well as\nknowledge of propositions derived syllogistically from them. This type\nof knowledge amounts to necessary, analytic truths, in his view: once\none knows the terms that enter into such a proposition, and once those\nterms are combined into the proposition, one cannot help but assent.\nScotus’ second type of knowledge is knowledge of our own\ncontingent acts, including such propositions as ‘I am\nawake’ and ‘I am alive’. Scotus follows Augustine in\nholding that such knowledge is immune to skeptical attack because even\nif the senses are deceived, once these terms are grasped, we can know\nthe truth about them in such propositional contexts.", "\nThough much can be said about these types of knowledge, the most\nrelevant discussions for our purposes deal with the remaining types.\nOur certitude here depends crucially on the following claim:", "\nWhatever happens frequently through something that is not free, has\nthis something as its natural per se cause.\n(Ordinatio I.3.1.4.106)\n", "\nIn other words, Scotus suggests a general inductive principle:\nwhenever something occurs frequently over time, such repeatability\ncannot be due to chance. God has ordained that such regularities will\noccur, and thus we can reach a general principle based on those\ninitial cases. Such regularities amount to natural occurrences, and\nthus require no appeal to special illumination.", "\nGiven this, his third type of certainty is discussed: what Scotus\ncalls things knowable “through experience”—e.g.,\nthat “a certain species of herb is hot”. Such general\nclaims, derived through our experience of numerous instances of the\nhotness of such herbs, are certain in virtue of the “non-free\ncause” principle above. Recognizing, however, that inductions\ndon’t hold the same level of assurance that he is claiming for\nfirst two types of knowledge, Scotus backs off of his claim a bit\nlater, calling it “the lowest degree of scientific\nknowledge”, and admitting that such inductions may only tell us\nthat such regularities are “aptitudes”, not certainties\n(Ordinatio I.3.1.4.110–111).", "\nWhen Scotus begins discussing his fourth type of\ncertainty—particular knowledge claims about the external world,\nknown through the senses—he ignores this weakened conception of\nour senses’ reliability. Though later thinkers will be clearer\nin their indebtedness to the Condemnation of 1277 here, Scotus gives\nminimal notice of this. Instead, appealing again to his non-free cause\nclaim, he gives explanations of two main types of such experience.", "\nFirst, because it is often the case that different sense modalities\nagree in their judgment about an external object—e.g., when we\ncan both touch and see the size of a ball—we have an induction\nof sorts running here, and thus we can infer that this regularity is\nenough to give us certainty regarding the object under\nconsideration.", "\nSecond, in cases in which the sense modalities are not in\nagreement—either because one modality yields a different result\nthan another modality, or because a single modality yields different\nresults at different times—we can appeal to the intellect to\nadjudicate among them. Using his example, we know that a stick in\nwater that appears broken cannot really be broken, because our\nintellect knows the truth of the claim ‘the harder object is not\nbroken by the touch of something soft that gives way before it’\n(Ordinatio I.3.1.4.114–115). Thus, in such a case, we\ncan discount the testimony of sight. Scotus makes a similar move\nregarding the apparent deception that occurs in dreams. In his view,\n“a person can tell when his faculty is disposed and when it is\nnot”, and thus he can tell whether he is asleep or dreaming\n(Ordinatio I.3.1.4.118–120).", "\nPeter Auriol (1280–1322) and William of Ockham (1285–1347)\nwere contemporaries, though they took different paths both\nphilosophically and ecclesiastically. Auriol spent most of his time at\nthe University of Paris, and eventually became an Archbishop before\nhis untimely death. Ockham studied and taught at Oxford before being\nbrought up on charges of heresy by the papal court in Avignon; he\nspent the last years of his life excommunicated from the Church, after\nhaving fled to Munich. Though there is no evidence of the two having\never met, Ockham often argues against Auriol’s views in some\ndetail. Adam Wodeham (ca. 1300–1358), who commented on both of\ntheir views, was the personal secretary of Ockham for a time, and\nworked at Oxford.", "\nAuriol’s role in the history of skepticism is twofold, and he\nhas been discussed in this connection most recently by Tachau (1988),\nPerler (1994), and Denery (1998). First, he develops an account of\nintuitive cognition that raises the possibility of sensory illusion;\nsecond, he discusses particular cases of sensory illusion in some\ndetail in his Scriptum (prologue, q. 2 and d. 3, q. 14).", "\nHe begins by diverging from Scotus’s account of cognition.\nScotus suggests that cognition of God, and cognition generally, can\noccur in one of two ways: either abstractively or intuitively.\nIntuitive cognition is meant to include a human’s more-or-less\ndirect sensory experience of the external world. Abstractive\ncognition, on the other hand, is knowledge from a distance; it\nabstracts from the presence and existence of the thing, as when we\nremember a deceased acquaintance or perform astronomical calculations\nin a windowless room.", "\nAuriol agrees with much of Scotus’s account of intuitive and\nabstractive cognition. Yet he imbues it with a psychological character\nthat is absent in the latter’s work. For Auriol an intuitive\ncognition is had when one has the experience of something\nas if it is present and existent. It is even possible, in\nAuriol’s view, to have such a cognition when the thing itself is\nabsent or non-existent. Auriol’s abstractive cognition, on the\nother hand, does not involve this experience or feeling of\nsomething’s presence and existence, even if the thing\nis both present and existent. For any given state of the\nextramental world, both abstractive and intuitive cognitions can\noccur. As a result, his position leaves him open to skeptical\nattack.", "\nHe realizes this possibility, and discusses many illusory experiences\nbefore developing a response. These illusory experiences include such\nstock examples as dreams, hallucinations, mirror images, the\nafter-images of the sun, the bent appearance of a straight stick that\nis immersed in water, and the apparent motion of trees experienced by\nthose traveling down a river. He also mentions such cases as the\ndouble image of a candle that appears when one’s eyes are\ndistorted, the shimmering, changing appearance of colors on a\ndove’s neck, and most interestingly, the fiery circle that\nappears when a burning stick is whirled rapidly through the air.\nThough Auriol’s discussion stresses some experiences more than\nothers, his basic point is that failing to identify such events as\nintuitive cognitions amounts to the assertion that “all things\nthat appear, are” (Scriptum 3.14.697).", "\nAuriol responds to these challenges by distinguishing between real\nbeing (esse reale) and apparent being (esse\napparens). This distinction has perplexed most readers of Auriol,\nand there is considerable disagreement about how to interpret it. Even\nso, it is generally agreed that real being is what the object has\nindependently of any perceiver, and also that whatever it is that is\nmeant by esse apparens, it is to be identified with a mental\nor sensory appearance of some sort. Some scholars (e.g., Tachau) read\nAuriol as a representationalist, which of course does little to solve\nthe skeptical problem; others (e.g., Perler) see him as a direct\nrealist. Whatever the answer in this particular case, Auriol is no\nskeptic. Not only does he believe that we can know external objects;\nwe also know many self-evident propositions with certainty (logical\ntruths, e.g.). For more on this aspect of Auriol’s thought, see\nBolyard (2000).", "\nWilliam of Ockham considers Auriol’s perceptual problems, but he\nconcludes that they are not a serious threat. On his view, our\nperceptual process (which occurs by means of intuitive cognitions) is\nsuch that it is infallible: for any such intuitive cognition, if it is\nof a thing that exists, we will know this fact, and if it is not, we\nwill know this as well. He holds this view even given the possibility\nthat God is deceiving us about such perceptions (e.g., by destroying\nthe object while maintaining the perception of it).", "\nAdam Wodeham disagrees with Ockham on this point; for him, there is no\nclear mark by which we can distinguish a true perception from a false\none in the case of a deceptive God. Nevertheless, he holds that our\nperceptual process is generally reliable despite these problems. For\nmore on Ockham and Wodeham, see especially Karger (2004), Panaccio and\nPiché (2010), and Wood (2003); Adams (1987) and Tachau (1988)\nalso discuss their skeptical and anti-skeptical views.", "\nWilliam Crathorn (fl. 1330) was not considered by his contemporaries\nor later medieval commentators to be of the stature of such thinkers\nas Aquinas, Henry of Ghent, Scotus, or Ockham; still, his views give a\nwindow into some of the skeptical worries extant at the time. He\nworked at Oxford, flourishing in the generation after Scotus, and\nduring the time of Ockham. Tachau (1988) and Pasnau (1997) discuss his\nviews.", "\nIn his Questions on the First Book of Lombard’s\nSentences, q.1, the Condemnation-inspired acknowledgment of\nGod’s omnipotence generates and reinforces many skeptical\nproblems for Crathorn. In response, Crathorn uses God to bring himself\nback from the skeptical abyss. Though not as rhetorically compelling\nas Descartes’ analogous moves in the Meditations, the\nphilosophical similarities among the two are striking.", "\nCrathorn also makes frequent appeal to God’s omnipotence and\npower to deceive us—nearly every page makes reference, directly\nor obliquely, to this possibility. A favorite non-epistemological\nexample he uses concerns heat and fire: God, he repeatedly says, has\nthe power to separate the heat from the fire that normally produces\nit. He also extends such divine powers to sensory cases. God, it\nseems, could maintain the vision of something even after that thing\nceases to exist. And as he tells us later, God’s power to do\nthis is vast. Here, his example is that of the lighted, fiery circle\nwe see when a torch is rapidly twirled through the air at night:", "\n…if God were to preserve in your head for a whole year that\ncircular color or another like it while no color existed externally,\nit would appear to you seeing that circular shape that you were seeing\nfor the whole year a flaming circle and the color of a circular shape\nexisting outside you—when nevertheless there was no such thing.\n(Questions I.98–99)\n", "\nSimilar examples are used to show that we can be deceived in other\nways as well. Afterimages of colors can remain briefly after\nwe’ve turned away from that which caused the initial color\nsensation. And it is within God’s power both to preserve a\nsensible species of color after destroying the thing, and even to\ncreate such a sensible species even when no extramental thing ever\nexisted. And finally, he mentions dream skepticism. Unlike Scotus and\nmost others who discuss this problem, Crathorn explains a case in\nwhich one who is awake thinks he is dreaming.", "\nIt is here that Crathorn begins to move us out of our skeptical\nposition, by putting limits on God’s power to deceive. First, he\nshows us cases in which God’s power cannot extend to the\nlogically contradictory: even God, Crathorn says, cannot make a stone\nthink. Second, he agrees with Scotus that seeming claims (e.g.,\n‘I feel hot’) and standard self-evident propositions\n(e.g., ‘the whole is greater than its part’) cannot be\ndoubted. Furthermore, he follows Augustine in arguing that this\ninference cannot be doubted: ‘I doubt that I exist; therefore, I\nexist’.", "\nFor more standard sensory skepticism, however, he combines the\napproaches offered by Henry and Scotus. By appealing to a self-evident\nproposition concerning God’s goodness, Crathorn tells us, we can\nshow that external world skepticism is incoherent. A benevolent God\nwould not systematically deceive us in this way.", "\nNicholas of Autrecourt (ca. 1300–ca. 1350) and John Buridan (ca.\n1295–1361) were contemporaries at the University of Paris. While\nBuridan maintained a good relationship with his ecclesiastical\nsuperiors, Nicholas did not: the latter’s works were condemned\nand publicly burned. Of particular interest in what survives are two\nof his Letters to Bernard of Arezzo. Recent discussions of\nAutrecourt’s views may be found in Beuchot (2003), Zupko (2003),\nand Grellard (2007).", "\nIn his First Letter, Autrecourt argues that Bernard’s\nviews lead to an extreme form of skepticism. As he interprets the\nview, it would follow that intuitive cognitions cannot guarantee their\nown certitude: sensory illusions and the possibility of a deceptive\nGod preclude this. But he goes further. As he explains, “you\nmust say that you are not certain of your own acts, for example, that\nyou are seeing or hearing”. Furthermore, “you are not\ncertain whether anything appears to you at all” (First\nLetter 11). In short, one cannot be certain about any aspect of\nthe external world, including even its very existence. And as he goes\non to say, the existence of the past is equally uncertain, as is the\nvery existence of one’s own mind.", "\nAutrecourt’s Second Letter seeks to temper this\nskepticism, but only to a degree. According to him, the only things of\nwhich we can be certain are the principle of non-contradiction (i.e.,\n“nothing both is and is not”) and other propositions that\ncan be derived from this principle. He maintains a causal,\nproto-Humean skepticism about existential inferences: “From the\nfact that some thing is known to be, it cannot be inferred evidently,\nby evidentness reduced to the first principle, or to the certitude of\nthe first principle, that there is some other thing” (Second\nLetter 11). As he continues, he says that the only substance of\nwhich we can possess evident knowledge is his own soul", "\nNicholas of Autrecourt espoused the most radical form of skepticism\nfound at any point during the Middle Ages, and he was punished for it.\nBuridan, however, argues specifically against Autrecourt in his own\nworks.", "\nIn his Questions on Aristotle’s Metaphysics II.1, for\ninstance, Buridan discusses various skeptical challenges, including\nsensory illusion, dream skepticism, skepticism about induction, and\nAutrecourt’s causal skepticism. Again, the deceptive\npossibilities of an omnipotent God play a large role in his worries\nhere.", "\nIn response, Buridan takes a few different approaches. First, as with\nAutrecourt, Buridan holds the principle of non-contradiction to be\nundeniable, as is every proposition that can be derived from it. But\nhe also says that there is a “virtual infinity of self-evident\nprinciples through the senses, or through experience, or through the\ninclusion of terms without having to be proved by means of the first\nprinciple [i.e., non-contradiction]” (Questions\nII.1.147, Klima trans.). In addition, Buridan drops his\nepistemological standards for sensory knowledge in general: because of\nthe possibility of God’s deceptiveness, at best we are capable\nof “conditional evidentness”. Similar reductions in\nstandards occur in cases of induction, causation, etc. As he says,\nmathematical certainty is not expected in every subject. For more on\nBuridan and his broader intellectual context, see Zupko (2003),\nGrellard (2007), Lagerlund (2010b), and Karger (2010)." ], "subsection_title": "4.2 Fourteenth Century" } ] }, { "main_content": [ "\nMedieval Skepticism was not a movement. Rather, it was a series of\n(sometimes isolated) worries and responses to such skeptical problems\nas those outlined above. While some impetus for later discussions was\ngained from classical skeptical sources, for the most part medieval\nskepticism took its own path. Among the distinctly medieval additions\nto the debate were an emphasis on the certainty of self-knowledge, and\nespecially on a widespread recognition across traditions that\nGod’s omnipotence, and thus the possibility of Divine deceit on\nthese grounds, provides a special challenge to the epistemology of\nanyone who holds a theistic worldview.", "\nThe fate of skepticism in the Renaissance and Early Modern Periods has\nbeen discussed widely, but connections between these later versions\nand those of their medieval antecedents have been less thoroughly\nstudied. Heider (2016) explores skeptical themes in the “Second\nScholasticism” of the 16th and 17th centuries. Thinkers such as\nFrancisco Suárez, John Poinsot, and Francisco de Oviedo\ncontinue to treat the Scotistic/Auriolian/Ockhamist issue of the\nintuitive cognition of non-existent objects. They do not consider\nglobal skepticism a live threat, as Descartes does, and their accounts\nare thus closer to those of 13th and 14th century philosophers.", "\nFor an overview of the later history of the skepticism, with a focus\non canonical Early Modern philosophers, see Popkin (2003)." ], "section_title": "5. Concluding Remarks", "subsections": [] } ]

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Malik (ed.), Beirut: American University of Beirut,\npp. 83–98.", "Wittwer, R., 2016, “Sextus Empiricus’ Outlines of\nPyrrhonism in the Middle Ages,” Vivarium, 54(4):\n255–285.", "Wolfson, H. A., 1969, “Nicolaus of Autrecourt and\nGhazali’s Argument against Causality,” Speculum,\n44: 234–238.", "Wood, R., 2003, “Adam of Wodeham,” in A Companion\nto Philosophy in the Middle Ages, J. E. Gracia and T. B. Noone\n(eds.), Oxford: Blackwell, pp. 77–85.", "Zupko, J., 1993, “Buridan and Skepticism,” Journal\nof the History of Philosophy, 31: 191–221.", "–––, 2003, John Buridan: Portrait of a\nFourteenth-Century Arts Master, Notre Dame: University of Notre\nDame Press." ]

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[ "\nAdam Smith developed a comprehensive and unusual version of moral\nsentimentalism in his Theory of Moral Sentiments (1759, TMS).\nHe did not expressly lay out a political philosophy in similar detail,\nbut a distinctive set of views on politics can be extrapolated from\nelements of both TMS and his Wealth of Nations (1776, WN);\nstudent notes from his lectures on jurisprudence (1762–1763, LJ)\nhave also helped flesh out his thoughts on governance. A central\nthread running through his work is an unusually strong commitment to\nthe soundness of the ordinary human being’s judgments, and a\nconcern to fend off attempts, by philosophers and policy-makers, to\nreplace those judgments with the supposedly better\n“systems” invented by intellectuals. In his “History\nof Astronomy”, he characterizes philosophy as a discipline that\nattempts to connect and regularize the data of everyday experience\n(Smith 1795: 44–7); in TMS, he tries to develop moral theory out\nof ordinary moral judgments, rather than beginning from a\nphilosophical vantage point above those judgments; and a central\npolemic of WN is directed against the notion that government officials\nneed to guide the economic decisions of ordinary people. Perhaps\ntaking a cue from David Hume’s skepticism about the capacity of\nphilosophy to replace the judgments of common life, Smith is\nsuspicious of philosophy as conducted from a foundationalist\nstandpoint, outside the modes of thought and practice it examines.\nInstead, he maps common life from within, correcting it where\nnecessary with its own tools rather than trying either to justify or\nto criticize it from an external standpoint. He aims indeed to break\ndown the distinction between theoretical and ordinary thought. This\nintellectual project is not unconnected with his political interest in\nguaranteeing to ordinary individuals the “natural liberty”\nto act in accordance with their own judgments." ]

[ { "content_title": "1. Methodology", "sub_toc": [] }, { "content_title": "2. Summary of Smith’s Moral Philosophy", "sub_toc": [] }, { "content_title": "3. Advantages of Smith’s Moral Philosophy", "sub_toc": [] }, { "content_title": "4. Objections to Smith’s Moral Philosophy", "sub_toc": [] }, { "content_title": "5. Smith’s Political Philosophy", "sub_toc": [] }, { "content_title": "6. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Primary Sources", "Secondary Sources", "Other Selected Secondary Literature" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nSmith’s Theory of Moral Sentiments (TMS) tends to\narouse sharply divergent reactions among the philosophers who pick it\nup. Kant is said to have considered it his favorite among Scottish\nmoral sense theories (Fleischacker 1991), but others have dismissed it\nas devoid of systematic argument, or derivative, in its theoretical\naspirations, of Hume. What explains these disparate reactions is one\nand the same feature of the book: that it consists largely of what\nSmith himself calls “illustrations” of the workings of the\nmoral sentiments (TMS, “Advertisement”)—short\nvignettes, elegantly described, that attempt to show what frightens us\nabout death, what we find interesting and what dull or distasteful\nabout other people’s love affairs, how moral luck factors into\nour assessment of various actions (Garrett 2005; Hankins 2016), or how\nand why we deceive ourselves. To some, this provides the detail and\npsychological acuity that they find lacking in most moral philosophy;\nto others, it seems something more properly taken up by novelists or\nempirical psychologists, not the business of a philosopher. Indeed,\none prominent view of TMS is that it is a work in descriptive\npsychology or sociology, not a contribution to normative moral theory\n(Campbell 1971; Raphael 2007). This reading is hard to square with\nthe many normative judgments in TMS (see Hanley 2009, chapter 2 and\nOtteson 2002, chapter 6). It also misses the force of Smith’s\ninsistence that the proper way to make normative judgments is to\nconsider the details of a phenomenon from an impartial perspective: to\njudge the workings of our moral faculties, then, we need to consider\nthem, and their uses, in appropriate detail. Laying out in\ndetail how they work can help us see how they can be corrupted, and\ntherefore to avoid that corruption, at least to some extent (see TMS\n61–6, 92–104). If this was Smith’s goal—and it\nfits the text of TMS very well—then he was engaged not in the\nsociology or psychology but the phenomenology of morals,\ndescribing the workings of our modes of moral judgment as carefully as\npossible from within, and believing that the comprehensive view that\nresults can itself help guide us in moral judgment. Moral\nphenomenology is normative moral theory, for him, and there\nis no more foundational theory—no set of general\nprinciples—of which we might avail ourselves. Justification for\nhow we make moral judgments can only be found within the way we\nactually do make moral judgments; both moral justification and moral\ncritique must be immanent to, not transcendent of, our moral practice\n(compare TMS 313–4).", "\nA few implications of this approach. First, Smith is an\nanti-reductionist. He does not think morality can be reduced to a set\nof natural or divine laws, nor that it is simply a means for producing\n“the greatest happiness for the greatest number of\npeople,” in the phrase coined by his teacher, Frances Hutcheson.\nHe indeed says explicitly, against the proto-utilitarianism of\nHutcheson and Hume, that philosophers in his day have paid too much\nattention to the consequences of actions, and he wants to focus\ninstead on their propriety: the relation they bear to the motive that\ninspires them (18–19). At the same time, he argues that the\nmoral systems proposed by Samuel Clarke, William Wollaston, and Lord\nShaftesbury overstress propriety, which is just one “essential\ningredient” in virtuous action (294; see also 265 and 326). His\nown view attempts to take account of all the essential ingredients in\nvirtue and moral judgment, and to resist the temptation to reduce\nthose ingredients to a single principle (see 326–7).", "\nSecond, and relatedly, Smith’s way of approaching virtue often\nresembles Aristotle’s—who has also sometimes been seen as\ntoo fond of the description of virtue, and who tried to acknowledge\nthe many diverse elements of virtue, and the judgment of virtue,\nrather than to reduce them to a single principle. Smith says at the\nend of TMS that his system corresponds “pretty exactly”\nwith Aristotle’s (271). The attentive reader of TMS will have\nnoticed this earlier: when he characterizes propriety as lying between\nthe excess and defect of passion (27), for instance, or when he\ndistinguishes the restraint of appetite out of self-interest from the\nvirtue of temperance (28), or when he emphasizes habit (152, 324), or\nthe superiority of friendships of virtue over friendships of pleasure\n(224–5).", "\nFinally, Smith’s phenomenological method is interwoven\nwith his strong leanings toward particularism. He insists that general\nmoral rules are “founded upon experience of what, in particular\ninstances, our moral faculties, our natural sense of merit and\npropriety, approve, or disapprove of” (159; see also 160 and\n320), and that our notions of right and wrong bottom out in these\nreactions to particular cases (320; see also 187 and Gill 2014). His\naccount of virtue as depending on our attempts to adjust ourselves as\nclosely as possible to the feelings of the particular others we\nencounter also suggests that what is virtuous in one set of\ncircumstances may not be so in different circumstances. These\ncommitments entail that moral theorists will give us little moral\nguidance if they present just the general structure of right and wrong\n(and Smith thinks that moral theory should help guide moral practice:\nTMS 293, 315). A fine-grained phenomenology of how we carry out\nvarious kinds of moral judgment, and the errors or infelicities to\nwhich we are prone in this process, will be far more helpful." ], "section_title": "1. Methodology", "subsections": [] }, { "main_content": [ "\nWith these methodological points in mind, let’s proceed to the\ncontents of TMS. Smith begins the book with an account of sympathy,\nwhich he describes as arising when we imagine how we would feel in the\ncircumstances of others. (A rich discussion of Smith on sympathy can\nbe found in Griswold 1999, ch.2; see also Fleischacker 2019, chapter\n2.) This is somewhat different from Hume’s account, on which\nsympathy normally consists in feeling what others actually\nfeel in their circumstances. Hume’s may be called a\n“contagion” account of sympathy, while Smith’s is a\n“projective” account (see Fleischacker 2012 and\n2019). Smith’s projective account opens up the possibility that\nour feelings on another person’s behalf may often not match the\nfeelings she herself has. Indeed to some extent they will never match,\nsince imagining oneself into a set of circumstances will always lack\nthe intensity of actually experiencing those circumstances (TMS\n21–2). This difference is of great importance to Smith, since he\nmaintains that trying to share the feelings of others as closely as\npossible is one of our main drives in life. We make constant efforts\nto adjust our feelings, as spectators, to those of the people\n“principally concerned” in a set of circumstances\n(importantly, these include people acted upon as well as agents), and\nto adjust our feelings as people principally concerned to a level with\nwhich sympathetic spectators can go along (110–13,\n135–6). It is this process of mutual emotional adjustment that\ngives rise to virtue: the “awful” virtues of\nself-restraint, insofar as the people principally concerned keep\nthemselves from feeling, or at least expressing, the full flood of\ntheir grief or joy, and the “amiable” virtues of\ncompassion and humanity, insofar as the spectators strive to\nparticipate in the joys and sufferings of others (23–5).", "\nNeither the feelings we seek to have nor the standards\nby which we judge feelings need be identical with the feelings\nand standards that are actually current in our society. We know that\nmany actual spectators misjudge our situations out of ignorance or\ninterest, so we seek to judge, and act on, just the feelings that a\nwell-informed and impartial spectator would have (TMS 129,\n135). Smith thinks that to sympathize with another’s feelings is\nto approve of those feelings (17), and to sympathize as we think an\nimpartial spectator would is to approve morally of\nthose feelings. Moral norms thus express the feelings of an impartial\nspectator. A feeling, whether on the part of a person motivated to\ntake an action or on the part of a person who has been acted upon by\nothers, is worthy of moral approval if and only if an impartial\nspectator would sympathize with that feeling. (Again, people acted\nupon are subject to moral judgment as well as agents; reactions can be\njudged as well as actions.) When achieving a morally right feeling is\ndifficult, we call that achievement “virtuous”; otherwise,\nwe describe people as acting or failing to act within the bounds of\n“propriety” (25). Thus do moral norms and ideals, and the\njudgments by which we guide ourselves towards those norms and ideals,\narise out of the process by which we try to achieve mutual\nsympathy.", "\nSmith distinguishes two kinds of normative guides to action: rules and\nvirtues. Moral rules, formed on the basis of our reactions to specific\ninstances (we say to ourselves, “I’ll never do\nthat”), bar certain especially egregious kinds of\nbehavior—murder, rape, theft—and provide a framework of\nshared expectations for society (156–66). They are essential to\njustice, especially, without which societies could not survive. They\nalso enable people who are not fully virtuous to behave with a minimum\nof decorum and decency (162–3), and help all of us cut through\nthe “veil of self-delusion” (158) by which we misrepresent\nour situations to ourselves. Virtue requires more than simply\nfollowing moral rules, however. Our emotional dispositions need to be\nre-configured so that we do not merely “affect” the\nsentiments of the impartial spectator but “adopt” those\nsentiments: identify ourselves with, become, the impartial spectator,\ninsofar as that is possible (147). If we are truly virtuous, a\nsubmission to certain rules will constrain everything we do, but\nwithin that framework we will operate without rules, trying instead to\nmold ourselves with the know-how by which an artist molds his clay,\nsuch that we develop dispositions to proper gratitude, kindness,\ncourage, patience, and endurance.", "\nThis is a picture that owes a great deal to Hume and Joseph Butler,\nbut gets worked out by Smith in much greater detail. It has been\nhailed by some as an especially sensible recognition of the kind and\ndegree of virtue appropriate to modern liberal politics and commercial\nsociety (Berry 1992; McCloskey 2006). Others see a darker, more\npessimistic attitude towards virtue in Smith, echoing the kinds of\nworries to be found in Rousseau about the corruption wrought by\ncommerce (Dwyer 1987, chapter 7). Still others argue that\nSmith’s account of virtue re-works but to a remarkable degree\nalso retains the highest ideals of both the Christian and the ancient\nGreco-Roman traditions, suggesting that his willingness to uphold such\nan ideal of character even in modern commercial societies should be\nunderstand as a critique rather than an endorsement of Rousseau\n(Hanley 2009).", "\nIn any case, Smith gives us more a virtue ethics than a rule-based\nmoral system along the lines proposed by Kant and the utilitarians.\nNevertheless, he tries to incorporate some of the intuitions that\ngenerated these other systems. As we have seen, he thinks that we need\nto submit to general rules, and his reasons for supposing that relying\non sentiment alone can feed our self-deceit anticipate Kant’s\ncritique of moral sentimentalism in the Groundwork (see\nFleischacker 1991). Smith also acknowledges that we in fact judge\nactions by their effects as well as their intentions, and thinks this\nsort of judgment is appropriate as long as we look at effects\nas they are intended, and not just as they happen to occur.\nThe “merit” of actions, he says in Book II of TMS, depends\non their consequences, even if their propriety is independent of\nconsequences; the point, for him, is just that these are two\ndifferent elements of moral judgment and the first is of\ngreater importance than the second (188). Having insisted on this, he\ngrants that in some cases the consequences of an action—where\nthey threaten the very survival of our society, for instance—may\ntrump all other considerations (90–91).", "\nIn line with his concern for accurate moral phenomenology, Smith also\ntries to make sense of the role that religion and culture play in our\nmoral lives. He handles the first of these by explaining why people\nwho come to believe in higher powers will naturally attribute virtues,\nand a concern for our virtue, to those powers (163–6). He also\nsays that it adds to the sacredness we attribute to moral rules to see\nthem as laws of the Deity, and to the importance of morality as a\nwhole to see it as a way of “co-operat[ing] with the\nDeity” in the governance of the universe (166). And he shows how\na belief in an afterlife may be necessary if we are to see the\nuniverse as just, which in turn is important if we are to maintain our\ncommitment to the value of acting morally (168–70). In all these\nways, but especially the last, he anticipates Kant’s moral\nargument for belief in God, without ever quite saying that there\nis a God. At the same time, he makes clear that any religion\nthat gives priority to ritual or creed over morality is baleful, and\nposes grave dangers to a decent and peaceful society\n(TMS 176–7; cf. WN 802–3).", "\nSmith handles the importance of culture under the heading of\n“custom and fashion.” Book V of TMS takes up this topic,\nacknowledging the influence of prevailing opinions in each society\nover all sorts of value judgments, and granting that what is regarded\nas virtuous will vary to some extent in accordance with this\ninfluence. The French value politeness more than the Russians, and the\nDutch value frugality more than the Poles (TMS 204). The leisured\nclasses in every country tend to be less strict about sexual mores\nthan the working classes (WN 794). These are easily explicable\ndifferences, and not worrisome ones: they are matters of emphasis, and\ncannot affect “the general style of conduct or behaviour”\nof a society. That general style of conduct cannot vary in its\nessentials. No society could survive otherwise (TMS 209, 211).", "\nPart VI of TMS, added in the last edition, presents the virtues of\nprudence, benevolence and self-command by way of a series of elegant\ncharacter portraits, and part VII offers a short history of moral\nphilosophy, which stresses the contributions of Plato, Aristotle, and\nthe Stoics. This way of concluding the book reinforces the emphasis on\nvirtuous character, as opposed to a decision-procedure for specific\nactions, and indicates that we might gain by returning to the ancient\nschools of moral philosophy that shared this emphasis. Smith does not\nendorse any ancient moral theorist uncritically, but—like\nShaftesbury and Hume—he seems to look forward to a revival of\nancient Greek ethics, a modern retrieval and re-working of the\ncharacter ideals on which those schools had focused." ], "section_title": "2. Summary of Smith’s Moral Philosophy", "subsections": [] }, { "main_content": [ "\nSmith’s version of moral sentimentalism has a number of\nadvantages over those of his contemporaries. His approach yields moral\njudgments closer to those we already normally make, and makes better\nsense of the complexity and richness of both virtue and the judgment\nof virtue. He is expressly concerned to do justice to this complexity,\ncriticizing Hutcheson for reducing virtue too single-mindedly to\nbenevolence, and Hume for putting too much emphasis on utility.", "\nIn addition, none of Smith’s predecessors had developed such an\nessentially social conception of the self. Hutcheson and Hume both see\nhuman beings as having a natural disposition to care about\nthe good of their society, but for Smith, all our feelings, whether\nself-interested or benevolent, are constituted by a\nprocess of socialization. Smith conceives of humanity as less capable\nof solipsism than Hume does, less capable of the thoroughgoing egoism\nthat Hume, in his famous discussion of the sensible knave, finds it so\ndifficult to refute (Hume 1777, 81–2). At the same time, Smith\nreconciles his social conception of the self with a deep respect for\nthe importance of each individual self, and the capacity of each self\nfor independent choice. Ethical self-transformation, for Smith, is\ninspired and guided by social pressures but ultimately carried out by\nthe individual for him or herself. The “impartial\nspectator” begins as a product and expression of society, but\nbecomes, once internalized, a source of moral evaluation that enables\nthe individual to stand apart from, and criticize, his or her society.\nIndividually free action and the social construction of the self are\ncompatible, for Smith, even dependent on one another.", "\nWe can more fully appreciate what is distinctive in Smith by comparing\nhim with Hume. Smith’s thought circles around Hume’s:\nthere is virtually nothing in either TMS or WN without some sort of\nsource or anticipation in Hume, although there is also almost no\nrespect in which Smith agrees entirely with Hume. Take their accounts\nof sympathy, for example. When Hume describes the workings of\nsympathy, he says that emotions “readily pass from one person to\nanother,” like the motion of a string equally wound up with\nother strings, “communicat[ing] itself to the rest” (Hume\n1739–40, p. 576; see also pp. 317, 605). He then explains that\nwe obtain our idea of the other person’s feelings by\ninference—from the effects (smiles, frowns) or causes of those\nfeelings. In both cases, the other’s feeling, once inferred,\ncommunicates itself directly to us, and our imaginations only\nintensify our idea of that feeling so as to raise it to the level of\nan impression (Hume 1739–40, pp. 576, 319–20). For Smith,\nby contrast, we place ourselves in the other’s situation and\nimagine what we would feel if we were there. Imagination is essential\nto the production even of the “idea” of another’s\nfeelings, and sympathetic feelings are no longer ones that the other\nperson need actually have. (Smith points out that this explains how we\nsympathize with some people, like gravely ill infants or the insane,\nwho do not actually experience the suffering we feel on their behalf\n[TMS 12–13]). This account allows for us to judge other\npeople’s feelings against the background of our sympathetic\nfeelings for them. Sympathy is thus not just a way of sharing\nfeelings with others; it also opens a gap between their\nfeelings and ours. And that gap gives us a grip on the\nnotion—crucial to Smith’s theory—that certain\nfeelings are appropriate to a situation, while others are not.", "\nThese seemingly slight shifts from Hume—understanding sympathy\nas 1) produced by the imagination and 2) a response to situations\nrather than something passed on, causally, from one person to\nanother—have immense implications for the shape of Smith’s\nthought. The first of them leads him to give a central place to works\nof the imagination in moral development. He frequently brings in\nexamples from poetry and drama to explain or give evidence for his\npoints (e.g., TMS 30, 32–3, 34, 177, 227), twice recommends\nwriters like Voltaire as great “instructors” in certain\nvirtues (TMS 143, 177), and seems to see moral philosophy itself as a\nwork of the imagination, a project that needs to draw on imaginative\nresources and that properly aims at extending and enriching the moral\nimaginations of its readers (compare Griswold 1999, chapter 1). It is\ntherefore for him a project to which clarity, vivacity and elegance\nare as important as good argument, and Smith was in fact very\nconcerned with finding the appropriate rhetoric—the appropriate\nappeal to the imagination—for his works (see Griswold 1999;\nMuller 1993; Brown 1994). Both of his books are beautifully written,\nand filled with vivid, memorable examples.", "\nThe second of the shifts enables Smith to be more of a moral realist\nthan Hume. Smith finds an ingenious way of importing Samuel\nClarke’s concern with “fitnesses” (Clarke 1703) into\nmoral sentimentalism. On his view, we aim to have, and act on, just\nthose feelings that an impartial spectator would have in our\nsituations; the feelings we attribute to such a spectator are then the\nones fitted to that situation. So our feelings have something to aim\nat, by which they can be judged or measured. This allows Smith to\ntalk, as he does throughout TMS, of “fitness” (e.g., 149,\n159, 165, 305, 311), of feelings being “suitable to their\nobjects” (16–20, 40, 70, 73, 102), and, by extension, of\npeople being suited to the approval or disapproval bestowed upon them\n(58, 114, 118, 126). He thereby restores a meaning to our ordinary\nview of value judgments as correct or incorrect, and not merely as\nfostering or discouraging actions and qualities that may be useful to\nsociety. Relatedly, he sees our sentiments as more flexible than Hume\ndoes, and more responsive to criticism. As socialized human beings, we\ndo not simply desire certain objects but desire to have just\nthose desires of which an impartial spectator would approve. What are\ntoday called “second-order desires” accompany and shape\nall our first-order desires (110–11; compare Frankfurt 1971). This\ngives our emotions the internal structure they need to be able to\nchange in response to norms.", "\nAccordingly, it makes much more sense for Smith than for Hume that we\nought to assess our sentiments critically. Hume grants that we correct\nour sympathy for partiality by adopting in imagination a “steady\nand general point of view” (Hume 1739–40, p. 581), but for\nSmith this concession comes too late. Smith sees sympathy as building\nan aspiration to make one’s sentiments harmonize with the\nsentiments of others into those sentiments themselves. If\nthey did not already have such an aspiration, we would have neither\nmotivation nor reason to take up the “steady and general point\nof view.” It makes little sense to treat our sentiments as\nbaldly given natural reactions, impervious to reason, but then add\nthat they may need “correction.” If sentiments are bald\nnatural reactions, they can be neither correct nor incorrect; if they\nare impervious to reason, then we can have reason, at most, to\nappear to have sentiments other than the ones we happen to\nhave, not truly to change those sentiments. For Smith, the\naspiration to be worthy of approval belongs to our sentiments from the\nbeginning, and we have, accordingly, both motivation and reason to\nchange our sentiments if they keep us from this aspiration. ", "\nRelatedly, for Smith but not for Hume there is a lot to learn about\nwhat sentiments we should have. In neither the Treatise nor\nthe second Enquiry does Hume spend any significant time on\nhow we might learn to acquire new sentiments or alter the ones we\nhave. By contrast, the first five parts of TMS—almost two-thirds\nof the text—are devoted to a delineation of the various ways in\nwhich we learn to assess our sentiments, and in which learning to\nassess them enables us both to express them with propriety, and to\nchange them.", "\nThere is also for Smith, far more than for Hume, a place for moral\nhistory. Smith’s deep interweaving of individuals with their\nsociety, and of socialization with moral development, alerts him to\nthe many ways in which moral norms and ideals are indexed to\nhistorical circumstances (see Schliesser 2006). This comes out in the\ndetailed accounts he gives, in his lectures on jurisprudence, of how\nnotions of property, contract, marriage, and punishment have arisen\nand changed in various societies. The idea of a history of morals\nopens up here, and Smith—via his student John Millar, who\nattended the lectures on jurisprudence—was an important source\nof later sociological and anthropological accounts of normative\nchange.", "\nFinally, Smith is further from utilitarianism than Hume. Both the\nnotion of sentiments as having or lacking an intrinsic propriety\nindependently of their effects, and the arguments, in Books II and IV,\nagainst reducing our interest in justice and beauty to our interest in\ntheir useful effects, are meant to counteract the utilitarian\ntendencies in Hume. Smith’s particularist conception of moral\njudgment, and his playing down of the effects of actions in favor of\ntheir motivations, keep him far from consequentialism. He believes\nthat our faculties of moral evaluation are always directed toward the\nmotivations and well-being of particular individuals in particular\nsituations, not to goods that might be possessed jointly by groups of\nhuman beings, and he rejects the idea that our assessments or\ndecisions should aim at the greatest happiness for the greatest number\nof people (TMS 237). In addition, he sees happiness as so shaped by\nthe possession of morally appropriate dispositions that it cannot\nserve as a nonmoral goal that might help us define those dispositions.\nIt is essential to the hedonic calculus that happiness be defined\nindependently of morality, so that it can bestow content on moral\nclaims (see McDowell 1998a). That is impossible, for Smith. Smith sees\nmeeting the demands of the impartial spectator as intrinsic to\nhappiness; there is no happiness independent of morality." ], "section_title": "3. Advantages of Smith’s Moral Philosophy", "subsections": [] }, { "main_content": [ "\nSmith’s moral theory has been accused of three major failings.\nFirst, it offers us no clear procedure for deciding which actions we\nshould take in specific circumstances, no guidelines for how we can\ntell, in specific cases, what the impartial spectator has to say.\nSecond, the impartial spectator seems too enmeshed in the attitudes\nand interests of the society in which it develops for it to be free of\nthat society’s biases, or to help us care impartially for all\nhuman beings. And third, even if Smith’s analysis of moral\nclaims is correct, even if it is true that moral judgments in ordinary\nlife consist in attempts to express how an impartial spectator would\nfeel about our conduct, it remains unclear what justifies these\njudgments. Why should we heed the demands of the impartial\nspectator?", "\nSmith would probably dismiss the first of these objections, as based\non an erroneous notion of what moral philosophy ought to do. Moral\nphilosophy can deepen our love for virtue, refine our understanding of\nthe virtues, and enrich our understanding of ourselves, all of which\ncan conduce to a firmer moral disposition and to a wiser, more careful\napproach to moral decisions, but it cannot and should not replace the\ncommon-life processes by which we actually make those decisions.\nPhilosophy is an abstract, intellectual, and solitary activity, while\nmoral decision-making is and should be concrete, driven by emotion as\nmuch as by the intellect, and shaped by our interactions with the\npeople affected by our actions.", "\nThe second and third objections constitute what we might call a\ntribalist or relativist and a skeptical challenge. The tribalist sees\nno reason to extend moral sentiments or modes of judgment to people\noutside his society, and no reason to criticize the basic structures\nof moral sentiment in his society. He thereby seems to miss a basic\nfeature of moral demands. But where is the room for a universalist\nmorality in Smith’s account? Since we construct the impartial\nspectator within us out of attitudes in the society around us, how can\nthat spectator reach beyond our society sufficiently to achieve a\nsensitive and impartial concern for members of other societies, and to\nrecognize where our society’s sentiments are biased or\ncorrupt?", "\nThe skeptic represents a yet deeper problem. Smith says that when we\nissue a moral judgment, of others or of ourselves, we express the\nrelationship of one set of sentiments—the cooler, more\nreflective sentiments characteristic of a spectator—to another.\nThis seems a plausible account of what we actually do, when judging\nmorally; it captures nicely the “feel” of ordinary moral\njudgments. But does it give us reason to heed such judgments? Does it\nexplain the normativity of moral judgments, our sense that we ought to\nlisten to them?", "\nSmith clearly rejects any tribal limit to the reach of moral demands.\nHe adopts the Stoic view that each person is “first and\nprincipally recommended [by nature] to his own care” (TMS 219),\nand that we similarly care more about members of our own society than\nabout people far away from us (139–40, 227–8). At the same\ntime, however—also like the Stoics—he thinks that our\nmoral feelings extend, if to a lesser degree, to all rational and\nsensible beings: “our good-will is circumscribed by no boundary,\nbut may embrace the immensity of the universe” (235). Indeed, he\nregards accepting harm to one’s local community, if that is\nnecessary for the good of the universe, as a mark of the highest\nwisdom and virtue (235–6). As Amartya Sen has stressed, Smith\nalso wants us to evaluate our conduct from the perspective of any\nhuman being anywhere, not just a member of our own society. Sen quotes\na passage in TMS in which Smith says that we “endeavour to\nexamine our own conduct as we imagine any other fair and\nimpartial spectator would imagine it” (110), arguing that it\nimplies we should seek to be informed by the views of people far\noutside our cultural communities. “The need to invoke how things\nwould look to ‘any other fair and impartial\nspectator,’” says Sen, “is a requirement that can\nbring in judgments that would be made by disinterested people from\nother societies as well” (Sen 2009: 125). And Smith certainly\ndid aspire to provide such a standard of moral judgment, a structure\nfor morality that reaches out across national and cultural\nborders.", "\nBut is Smith’s impartial spectator capable of doing this?\nConsider two of its features. First, it uses sentiments rather than\nreason as the basis of its judgments. It is not like Roderick\nFirth’s ideal observer, dispassionately watching people from\nabove the emotional fray (Firth 1952). Rather, Smith follows Hutcheson\nand Hume in tracing moral judgment, ultimately, to feelings. The\nimpartial spectator is supposed to be free of partial\nfeelings—feelings that depend on a stake it might have\nin a dispute, or on blind favoritism or dislike for one party or the\nother—but it is not supposed to be free of feelings altogether,\nnor to reach for a principle it might derive from reason alone,\nindependent of feeling (see Raphael 2007, chapter 6). But our feelings\nare notoriously shaped by our societies, and it is not clear how a\ndevice that depends on feelings could correct for biases built into\nthem. ", "\nSecond, the impartial spectator develops within us as part of our\nefforts to align our feelings with those of the people immediately\naround us. The “chief part of human happiness,” for Smith,\ncomes from the consciousness that we are “beloved” (TMS\n41), but that is not possible unless our feelings, and the actions we\ntake on those feelings, meet with other people’s approval. The\nsearch for feelings we can share—for mutual sympathy—is a\nbasic human drive, and it leads among other things to the rise of\nmorality. Of course, that eventually means that we correct the modes\nof approval of people around us for bias and misinformation; we seek\nthe judgment of an impartial spectator within rather than partial\nspectators without. But Smith never suggests that this impartial\nspectator uses different methods of judging, appeals to\ndifferent sorts of norms, than our neighbors do. It arises out of the\nactual process of moral judgment around us, and we heed it as part of\nour drive to find a harmony of feelings with our actual neighbors. It\nis very unlikely, then, to use a method of judging radically unlike\nthose of our actual neighbors, or perceive, let alone correct for, a\nsystematic bias in the sentiments of our society. If sentiments of\ncondescension or dislike toward poor people, or black people, or gay\npeople, pervade our society, then there is every reason to expect that\nmany of us, especially in privileged groups, will build an impartial\nspectator within ourselves that shares those biases rather than rising\nabove them. ", "\nThese are the sorts of considerations that led Smith himself to worry\nabout the danger that “established custom” can distort\nmoral judgment (TMS 210), and that nature may lead people, foolishly\nand unjustly, to admire the rich and despise the poor (50–62).\nSmith also worried that political faction and religious fanaticism can\n“pervert” our moral feelings (155–6, 176–7),\nand did not suggest ways to correct for that danger. It is unclear how\nhis moral theory might supply such a corrective.", "\nMoreover, much that is attractive about Smith’s theory is bound\nup with this limitation; his relativistic tendencies are not a mere\nmistake but a consequence of the structure of his theory. The absence\nof transcendental principles in favor of judgments rooted in our\neveryday sentiments, the view of individuals as aiming, by way of\nmorality, for emotional harmony with their neighbors, the\npsychological insight of his view of moral development—all these\nthings go together with a picture on which we are deeply shaped by our\nlocal societies in the way we make moral judgments, and can turn those\njudgments on our society only with difficulty. It has been suggested\nthat Smith thought better information about the lives of poor people\ncould help well-off people judge the poor more favorably (Fleischacker\n2004, chapter 10), and perhaps he thought that slavery and other\ninjustices could likewise be overturned by better information:\ninformation enabling people to project themselves into the lives of\nslaves, and other victims of injustice, and thereby to sympathize with\nthem. Sometimes Smith also drops proto-Kantian hints that a concern\nfor the equal worth of every human being lies at the basis of all\nmoral sentiments (TMS 90, 107, 137), and Stephen Darwall and Remy\nDebes have brought out a latent egalitarianism in the structure of\nSmith’s moral theory that could be turned against inegalitarian\nsocial institutions (Darwall 1999; Debes 2012). But even a commitment\nto the equal worth of every human being can be interpreted in ways\nthat support local biases—Kant, notoriously, maintained racist\nand sexist views long after coming up with his arguments for equal\nworth—and Smith in any case says little to justify his\negalitarian tendencies. So it must be admitted that the tribalist\nchallenge brings out a weakness in Smith’s theory, and cannot\neasily be answered without sacrificing some of its central elements.\n(For more on these issues, see Forman-Barzilai 2010).", "\nSmith does better with the skeptical challenge. To the person who\nasks, “why be moral?,” Smith essentially provides what\nChristine Korsgaard calls a “reflective endorsement”\nargument (Korsgaard 1996: 19, 49–89). Reflective endorsement\ntheorists—Korsgaard gives Hume and Butler as\nexamples—substitute the question, “are the claims of our\nmoral nature good for human life?” for the question, “are\nmoral claims true?” They identify a certain faculty for approval\nor disapproval as giving force to moral claims, and then ask whether,\non reflection, we can approve of that faculty of approval itself. This\ntest requires in the first instance that the faculty of moral approval\napprove of its own workings. It then looks to whether our other\nfaculties of approval can approve of the moral one: we seek a\ncomprehensive endorsement, by all our modes of approval, of moral\napproval in particular. The second part of the test asks above all\nwhether the faculty for prudential approval—the faculty by which\nwe applaud or condemn things in accordance with\nself-interest—can applaud the moral faculty, since the latter\noften requires us to override our self-interest.", "\nWe should not assume that the first part of the test is trivial.\nKorsgaard quotes Hume’s declaration that our sense for\nmorals", "\n\n\nmust certainly acquire new force, when reflecting on itself, it\napproves of those principles, from whence it is deriv’d, and\nfinds nothing but what is great and good in its rise and origin, (Hume\n1739–40, pp. 267–8) \n", "\nand contrasts this with Hume’s earlier demonstration that the\nunderstanding, when reflecting on its own procedures, undermines\nitself (Korsgaard 1996, p. 62). So a faculty can fail a purely\nreflexive test: it can fail to live up to its own standards for\nevaluation. But the moral sense, for Hume, and the impartial\nspectator, for Smith, pass their own tests. Indeed, a good way to read\nTMS is to see Smith as demonstrating, to an impartial spectator in a\nmoment of reflection, that the impartial spectator we use in the\ncourse of action operates in a reasonable and noble way—that, in\nparticular, it is not just a tool of our self-interest.", "\nAt the same time, to meet the full reflective endorsement test, Smith\nneeds to show that heeding the impartial spectator does not, overall,\nconflict with our self-interest. In order to show this he\ntries, like many ancient ethicists, to get us to re-think the nature\nof self-interest. If we consider our real interests, Smith maintains,\nwe will see that the very question, “why should I be\nmoral?,” with its implicit supposition that being moral is\nsomething I might want to avoid, is based on a misconception of\nself-interest. “The chief part of human happiness arises from\nthe consciousness of being beloved” (TMS 41), Smith says, and\nbeing beloved normally requires acting in accordance with the demands\nof the impartial spectator. Violating those demands will also normally\nbring on internal unease—fear of discovery, pangs of conscience,\nand other disturbances—making it difficult to achieve the\ntranquility that Smith takes to be a prime component of happiness (TMS\n149). Finally, if one fully incorporates the impartial spectator into\noneself, one will discover that moral self-approbation is itself a\ngreat source of happiness. But if happiness consists so centrally in\nthe approbation of others, and in self-approbation, there can be no\nreasonable conflict between pursuing happiness and pursuing morality.\nSo the demands of our moral sentiments are justified, capable both of\nendorsing themselves and of being endorsed by our nonmoral\nsentiments.", "\nIt should be clear that this argument does not involve any reduction\nof morality to self-interest. For Smith, the agent who supposes that\nself-interest can be defined independently of morality, and morality\nthen reduced to it, misunderstands the nature of self-interest. Such\nan agent lacks a well-developed impartial spectator within herself,\nand therefore fails to realize that acting in accordance with moral\ndemands is essential to her own happiness. She will gain a better\nunderstanding of happiness only once she starts to engage in the\npursuit of virtue. Smith explicitly says that the virtuous agent sees\nthings that others do not (TMS 115–7, 146–8). Like the\ncontemporary philosopher John McDowell, he thus suggests that the\nvirtuous agent can properly see the point of virtue, and how virtue\nhelps constitute happiness, only from a perspective within the actual\npractice of virtue. But, as McDowell says, there is no reason to think\none can find better arguments, or indeed any arguments, for seeking\nvirtue from a perspective outside of such practice (McDowell 1998a,b).\nThere may therefore be a certain circularity to Smith’s defense\nof morality, as some of his critics have alleged, but the circularity\nis not a vicious one, and an entirely nonmoral defense of morality,\nwhich the critics seem to want, may be impossible.", "\nSmith himself does not clearly spell out the responses proposed here\nto the philosophical problems that his theory raises. His strengths as\na moral philosopher lie elsewhere. Moral philosophers need not be\nconcerned solely with the grounds of morality. Displaying, clarifying,\nand showing the internal connections in the way we think about virtue\nis already a philosophical task, even if we set aside the question of\nwhether that way of thinking is justified. There are indeed\nphilosophers who reject the idea that philosophy is well-suited to\noffer justifications. Smith’s work fits in with the view of Iris\nMurdoch, who understood moral philosophy as consisting in the attempt\n“to fill in a systematic explanatory background to our ordinary\nmoral life” (Murdoch 1970, p. 45). His astute and nuanced\nanalysis of what goes into moral approval—of the sorts of\nfactors the impartial spectator considers, of how it can deceive\nitself or otherwise go wrong, of how it develops and how it judges\ndifferent virtues in different ways—is accomplishment enough,\nregardless of whether he adequately justifies the fact that we engage\nin such approval at all. " ], "section_title": "4. Objections to Smith’s Moral Philosophy", "subsections": [] }, { "main_content": [ "\nIt is clear from the end of TMS that Smith intended to complement it\nwith a system of political philosophy, and it is clear from the\nAdvertisement to the last edition of TMS that WN represents the\npartial but not complete fulfillment of that plan. Strikingly, what\ngot left out was the part of political philosophy that most concerned\nSmith at the end of TMS, and that has most concerned other moral\nphilosophers who turn to politics: a systematic account of justice.\nSmith’s lectures on jurisprudence dealt with this topic, and\nfrom the notes we have on those lectures, he seems to have hoped to\nbuild a comprehensive, universally-applicable theory of justice out of\nimpartial-spectator judgments about property, contract, punishment,\netc. But the manuscript drawn from these lectures was never finished,\nand he had it burned at his death. Some scholars speculate that the\nfailure of this project was fore-ordained: the moral theory of TMS is\ntoo particularist to sustain a universally-applicable theory of\njustice (see Griswold 1999, pp. 256–8 and Fleischacker 2004,\nchapter 8). Others have tried to re-construct such a theory for Smith\n(see Haakonssen 1981 and 1996).", "\nIn any case, Smith concluded his lectures on jurisprudence with some\nextended remarks on “police”—public policy\n—and this he did, of course, work up into a book of its own. It\nis unclear, however, how much WN has to do with his philosophical\nconcerns. Smith became increasingly interested in political economy\nafter completing TMS, and WN can be seen as the fruition simply of a\nnew direction in his research, unconnected to his moral system. He did\ncome to a comprehensive, one might say philosophical, view of\npolitical economy: from his understanding of the workings of\neconomics, he thought that states could foster the productiveness of\ntheir economies only by the rule of law, accompanied by a few\nlimitations on banking practices, and should otherwise lift measures\nthat restrict or encourage particular enterprises. The practical point\nof his treatise on economics was to urge this restrained, modest\napproach to economic intervention on governing officials. Smith did\nnot favor as hands-off an approach as some of his\nself-proclaimed followers do today—he believed that states could\nand should re-distribute wealth to some degree, and defend the poor\nand disadvantaged against those who wield power over them in the\nprivate sector (see Fleischacker 2004, § 57)—but he\ncertainly wanted the state to end all policies, common in his\nmercantilist day, designed to favor industry over agriculture, or some\nindustries over others. Smith believed strongly in the importance of\nlocal knowledge to economic decision-making, and consequently thought\nthat business should be left to businesspeople, who understand the\nparticular situations in which they work far better than any\ngovernment official (on this Hayek understood Smith well: see Hayek\n1978 [1976] and C. Smith 2013). By the same token, governance should be kept\nout of the hands of businesspeople, since they are likely to\nuse it to promote their particular interests, and not be concerned for\nthe well-being of the citizenry as a whole: Smith’s opposition\nto the East India Company is based on this principle (see Muthu\n2008).", "\nSmith’s political views tend more generally towards a minimalist\nstate. He did not want the state to micro-manage the economy, and he\nalso did not want it to promote religion or virtue. He was suspicious\nof the motives and skills of politicians, and their ability, even when\nwell-meaning, to change society (see Fleischacker 2004, chapter 11).\nAnd he did not believe that the political life was the crown of the\nmoral life, or that law or political institutions can help people\ndevelop virtue.", "\nOne might therefore wonder whether there is any connection between his\npolitics and his moral philosophy. Aside from the construction of\ntheories of justice—which, as we have noted, Smith wound up\nnot doing—there are three main reasons why moral\nphilosophers write political theories. Some, like Aristotle, see\nmorality as the cultivation of virtuous character and believe that the\nstate can help people with this cultivation. Others, like Jeremy\nBentham, see morality as maximizing human pleasure and believe that\nlegal and political reform can contribute significantly toward that\nend. And still others, like Hegel, see morality as the expression of\nfreedom and believe that states can embody the highest expression of\nfreedom. But Smith believes none of these things. His conception of\nmorality is quite Aristotelian, but for him the state can do little to\nhelp people achieve virtuous character. He shares neither\nBentham’s reduction of the good life to the pleasurable life nor\nBentham’s optimism about the likely effectiveness, for moral or\nhedonic purposes, of even much-reformed governments. And he never\ndescribes the state as an expression of freedom.", "\nThat leaves us with the possibility that Smith tries in WN precisely\nto try to cure his readers of the illusion that states have a moral\nfunction. There is a strong Stoic component to TMS, and we might say,\nin Stoic vein, that in WN Smith wants to help us see how much the\nsociety around us is out of our control. WN shows us the great degree\nto which social institutions and policies have unintended\nconsequences, the central role, in particular, of unforeseeable\nfactors in the workings of the market, and the fact that uncontrolled\nmarkets on the whole do well by all their participants. This allows us\nto become reconciled to allowing markets, and other social\ninstitutions, to run unfettered.", "\nSmith is more of an Enlightenment progressive than this reading\nsuggests, more of a believer that an enlightened understanding of\ntheir circumstances can help people improve those circumstances, but\nhe had less faith in this notion than did most of his contemporaries.\nThere are deep roots in his thought for a sceptical attitude towards\nprogressivism. His belief in local knowledge leads him to be\nsuspicious of large-scale plans for the reform of society. He also\nprovides a number of reasons for doubting whether we can successfully\nset for ourselves clear goals for such reform. For most enlightenment\nthinkers, including Smith’s predecessors Hutcheson and Hume,\nwhat human beings desire seemed fairly obvious. For Smith, this is not\nso obvious. Smith believes that it is very difficult for us to know\nour true intentions (TMS 156–9), and that our desires are\nheavily shaped by social interaction. He also casts doubt on the\ndegree to which we seek things that are truly useful to our ends. In a\nfamous passage, he says that we are more interested in a thing’s\napparent conduciveness to utility than in its actual\nutility (179–80). This observation serves as the jumping-off\npoint for his first foray into economics. The “poor man’s\nson, whom heaven in its anger has visited with ambition” pursues\nwealth without knowing what it is really like, because it\nseems—falsely—to be useful (181–3). In\nseveral ways, then, Smith pictures human desires and aims as more\nopaque than do most other Enlightenment thinkers. This picture informs\nhis distinctive account of society and history, moreover, according to\nwhich unintended consequences tend to be more important than intended\nones and the course of history is correspondingly unknowable in\nadvance. On such a view, it is futile for politicians to try to\ndetermine the future development of their societies. They do better\nrestricting their activities to protecting individual liberty against\nviolence—to defense and the administration of justice.", "\nWe might call this the libertarian reading of Smith, and it certainly\ncaptures an important element of his political philosophy. Smith gives\njustice priority over the other virtues in TMS (86), he begins his\nlectures on jurisprudence by saying that the maintenance of justice is\n“the first and chief design of every system of government”\n(Smith 1978, p. 5), and he brings in justice as a constraint on\neconomic activity many times in WN (e.g., WN 157, 539, 687). But he\ndoes not say that the enforcement of justice is the sole job of\ngovernment. The third of the tasks he gives to government in WN\nconsists in “maintaining and erecting” a broad range of\n“publick works and … publick institutions” for the\ngood of the whole society (WN 687–8). In TMS, the chapter often\nquoted as claiming that justice is the only virtue that may be\nenforced actually maintains only that “kindness or beneficence,\n… cannot, among equals, be extorted by force”\n(TMS 81). In a state “antecedent to the institution of civil\ngovernment,” Smith says, no impartial spectator would approve of\none person’s using force to make another act beneficently. But\nonce civil government has been established, people may legitimately be\nforced to carry out at least the greatest and most obvious duties of\nbeneficence. Smith says that", "\n\n\n[t]he civil magistrate is entrusted with the power not only of\n… restraining injustice, but of promoting the prosperity of the\ncommonwealth, by establishing good discipline, and by\ndiscouraging every sort of vice and impropriety; he may prescribe\nrules, therefore, which not only prohibit mutual injuries among\nfellow-citizens, but command mutual good offices to a certain degree.\n(81, emphasis added)\n", "\nSmith warns against taking this license for a general promotion of\nvirtue too far—that, he says, would be “destructive of all\nliberty, security, and justice”—but he also says that\nneglecting it will lead “to many gross disorders and shocking\nenormities” (TMS 81). These enormities may well include the\nmisery of the poor, a central concern of Smith’s in WN. Smith\nhad no principled objections to government power being used to help\nthe poor, and indeed proposed a number of policies with that in mind.\nIt should be remembered that the idea that governments might massively\nre-distribute wealth out of fairness to the poor was not on the agenda\nin Smith’s time. Only in the 1790s, after Smith died, did Jeremy\nBentham and Tom Paine offer their groundbreaking poverty programs; the\nsocialism of Robert Owen and Charles Fourier lay another generation in\nthe future. Until the late eighteenth century, most writers on the\nrole of government vis-à-vis the poor maintained that\ngovernments should keep the poor in poverty, so that they show proper\nrespect to their superiors and not waste money on drink. Smith had\nmore influence than anyone else in changing this attitude—he was\none of the earliest and most fervent champions of the rights and\nvirtues of the poor, arguing against wage caps and other constraints\nthat kept the poor from rising socially and economically (see Baugh\n1983 and Fleischacker 2004, chapter 10).", "\nSmith also had a more restricted conception of individual rights than\ndo contemporary libertarians. Taxation does not count as any sort of\nthreat to property rights, for him—he indeed describes paying\ntaxes as “a badge … of liberty” (WN 857)—nor\ndoes the government’s mere support for certain ideas and values\ncount as an infringement of the right to conscience. Although it may\nbe inefficient and otherwise unwise, it is not unjust for the\ngovernment to intervene in the economy on behalf of one or another\ncommercial interest, to spread propaganda for one or another\nconception of virtue, or even to establish a religion. Smith of course\nopposes economic intervention of this kind and thinks it better if\ngovernments do not establish religions, but his views on these issues\nstem from concerns other than justice. Moreover, he favors militia\ntraining to instill courage in people, state incentives urging people\nto study science and philosophy, and state encouragement for secular\namusements—the latter two as an “antidote to the poison of\n[religious] enthusiasm and superstition.” (WN 796) So\nSmith’s state is not a neutral one, in the modern sense, and it\nis not wholly uninterested in the promotion of virtue.", "\nWhy, then, does Smith recommend such a minimal state? The\ninterventions just listed are practically the only ones he urges in\nWN, and even in those cases, Smith calls for limited state action. Why\nallow governments to go so far, and no farther?", "\nThe first answer to that is that Smith did not think government\nofficials were competent to handle much beside the needs of defense\nand the administration of justice. Smith’s writings are\npermeated by a lack of respect for the sorts of people who go into\npolitics: for the vanity that leads them to seek fame and power, for\nthe presumption by which they regard themselves as morally superior to\nothers, and for the arrogance by which they think they know the\npeople’s interests and needs better than the people do\nthemselves. He also believes that politicians tend to be manipulated\nby the preaching of merchants who do not have the good of the nation\nas a whole at heart (WN 266–7), and that they can rarely know\nenough to guide large numbers of people. Correlatively, Smith has a\ngreat respect for the competence and virtue of common people. He shows\nno trace of the thought, common at the time and strongly held by\nHutcheson, that a class of wise and virtuous people ought to rule over\nthe common herd.", "\nIn addition, Smith holds that social sanctions can do a better job at\nmany tasks that other thinkers expected of political sanctions. His\nrich account in TMS of the way that spectators around us shape us\nmorally enables him to hold that governments need not teach\nvirtue. Society, independent of governmental power, will do that on\nits own. Thus sumptuary laws are unnecessary because the desire to\nmaintain or increase one’s social status will keep most people\nprudent and frugal (WN 341–6). Thus religious groups that\nspontaneously arise without government assistance do a better job of\ninculcating virtues than their government-supported counterparts (WN\n792–6). And thus—implicitly—the civic republican\nobsession with a citizen militia is overwrought because the habits of\nself-command inculcated by military service can also be achieved, for\nmost people, by the social interactions of the market (see\nFleischacker 1999, pp. 153–6, 169–72).", "\nFinally, Smith limits the activities of governments because he\nconsiders it crucial to the development of virtue that people have\nplenty of room to act, and shape their feelings, on their own.\nBecoming a good human being is ultimately a task that each individual\nmust take up for him or herself. People develop better moral judgment\nby actually making moral judgments (WN 782–3, 788), and virtue\nrequires the practice of virtue (TMS 324); we cannot achieve these\nthings simply by following the say-so of an authority. So exercises of\npower tend to be inimical to moral development, and governments should\nuse their power mostly to minimize the degree to which power gets\nexercised elsewhere. ", "\nIndeed, for Smith, governments can best encourage virtue precisely by\nrefraining from encouraging virtue. In TMS, the person who\nmerely tries to appear virtuous, whether out of fear of the law or out\nof fear of social disapproval, is not really virtuous. But there is a\nsliding scale here. One who acts virtuously out of concern for the\npraise and blame of her neighbors is not as virtuous as one who is\nconcerned to be praise-worthy in the eyes of an impartial spectator,\nbut one who acts virtuously out of concern for legal sanctions is\nworse than either of the other two. As long as neighbors know each\nother reasonably well, their approval and disapproval will normally\ntake into account the particular circumstances, the peculiar history\nand psychology, of the individuals they judge—their judgments\nwill reflect, say, the difference in gratitude due to a loudly\nself-pitying parent as opposed to a truly long-suffering one. Legal\nsanctions are blunt instruments that cannot attend to such subtleties.\nSo social approval is more likely than legal approval to pick out the\nright sort of actions to mark for moral worth. Furthermore, since\nsocial sanctions are milder than legal sanctions—it is much\neasier to ignore a neighbor’s disapproval than a threat of\nimprisonment—people who care about social sanctions display\nbetter character than people who can be motivated to good action only\nby the law. The pressure of social sanctions is more like, and more\nlikely to draw one towards, the pressure of conscience. Even if\nconcern for social approval is not the ideal motivation for moral\naction, therefore, it is at least some sign of good character, and a\nstep along the way to the motivations of the fully virtuous person.\nLegal sanctions by contrast affect our physical well-being and social\nstanding so severely that they drive out all thought of the sanctions\nof conscience. A government concerned to foster virtue in its citizens\nshould therefore aim as much as possible to remove its own sanctions\nfrom the pursuit of virtue. Governments foster virtue best where they\nrefuse, directly, to foster virtue at all: just as they protect\neconomic development best where they refuse, directly, to protect that\ndevelopment. This ironic conception of government power runs through\nSmith’s political thinking. Accordingly, his main\npolitical object in writing WN is to instill modesty in policy-makers,\nto urge them to take on only very limited, well-defined tasks, and to\nrecognize that the flourishing of their society does not, on the\nwhole, much depend on them.", "\nIn sum, if Smith’s political philosophy looks like\nlibertarianism, it is a libertarianism aimed at different ends, and\ngrounded in different moral views, than that of most contemporary\nlibertarians. Today, many libertarians are suspicious of the notion\nthat individuals ought to develop virtues expected of them by others:\nbeyond, at least, those virtues that are needed for the functioning of\nthe market and the liberal state themselves. Smith does not share this\nattitude. He is far from an agnostic about what a good human life\nlooks like, let alone an enthusiast for a conception of the good life\nthat eschews virtue in favor of preference-satisfaction. He is not a\npositivist sceptical of the significance of moral argument, like\nMilton Friedman, nor a hedonist, like Bentham and his followers, nor a\nradical individualist, like the followers of Ayn Rand. Any decent\nhuman life, he believes, requires certain virtues, and depends on a\nrespect and love of individuals for the people around them. If he\nencourages governments, nevertheless, to refrain from promoting\nvirtue, that is because he thinks that social forces can effectively\nachieve that end without government help, and that legal sanctions are\nin any case useless or counter-productive for the promotion of virtue.\nSo he may arrive at some libertarian conclusions, but not in the way\nthat most libertarians do." ], "section_title": "5. Smith’s Political Philosophy", "subsections": [] }, { "main_content": [ "\nSmith has an account of the nature of moral judgment, and its\ndevelopment, that is richer and subtler than Hume’s; he offers a\nprototype for modern Aristotelianism in morality; he brings out the\nimportance of the imagination to moral development as few other\nphilosophers have done; he is an early and forceful promoter of the\nnotion that history is guided largely by unintended consequences; and\nhe derives from these views an unusual variant of liberal politics.\nFew of these contributions are spelled out with the clarity and tight\nargumentation that contemporary philosophers demand of their canonical\nfigures, but Smith compensates for this weakness by the humanity and\nthoughtfulness of his views, by their detachment from metaphysical\ncommitments, and by an abundance of historical and imaginative detail.\nThe richness of his ideas, and their quiet plausibility, earn him a\nplace among the most important of modern moral and political\nphilosophers." ], "section_title": "6. Conclusion", "subsections": [] } ]

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Bryce (eds.), Oxford: Oxford\nUniversity Press, 1980.", "–––, Lectures on Rhetoric and Belles\nLettres, J.C. Bryce (ed.), Oxford: Oxford University Press,\n1983.", "–––, Correspondence of Adam Smith,\nE.C. Mossner and I.S. Ross (eds.), Oxford: Oxford University Press,\n1987.", "Baugh, Daniel A., 1983, “Poverty, Protestantism, and\nPolitical Economy: English Attitudes Toward the Poor,\n1660–1800,” in S. Baxter (ed.), England’s rise\nto greatness, Berkeley: University of California Press, pp.\n63–107", "Berry, Christopher, 1992, “Smith and the Virtues of\nCommerce,” in NOMOS XXXIV: Virtue, New York: New York\nUniversity Press, pp. 69–88.", "Brown, Vivienne, 1994, Adam Smith’s Discourse,\nLondon: Routledge.", "Campbell, T.D., 1971, Adam Smith’s science of\nmorals, Totowa, NJ: Rowman & Littlefield.", "Darwall, Stephen, 1998, “Empathy, Sympathy, Care,”\nPhilosophical Studies, 89 (2–3): 261–282.", "–––, 1999, “Sympathetic Liberalism: Recent\nWork on Adam Smith,” Philosophy and Public Affairs, 28\n(2): 139–64.", "Debes, Remy, 2012, “Adam Smith on dignity and\nequality,” British Journal for the History of\nPhilosophy, 20 (1): 109–40.", "Dwyer, John, 1987, Virtuous Discourse: Sensibility and\nCommunity in Late Eighteenth Century Scotland, Edinburgh: John\nDonald Publishers.", "Firth, Roderick, 1952, “Ethical absolutism and the ideal\nobserver,” Philosophy and Phenomenological Research, 12\n(3): 317–45.", "Fleischacker, Samuel, 1991, “Philosophy in Moral Practice:\nKant and Adam Smith,” Kant-Studien, 82 (3):\n249–69.", "–––, 1999, A Third Concept of Liberty:\nJudgment and Freedom in Kant and Adam Smith, Princeton: Princeton\nUniversity Press.", "–––, 2004, On Adam Smith’s Wealth of\nNations: A Philosophical Companion, Princeton: Princeton\nUniversity Press.", "––– 2012, “Sympathy in Hume and\nSmith,” in Intersubjectivity and Objectivity in Husserl and\nAdam Smith, C. Fricke and D. Føllesdal (eds.), Frankfurt:\nOntos Verlag, pp. 273–311.", "–––, 2019, Being Me Being You: Adam Smith\nand Empathy, Chicago: University of Chicago University\nPress.", "Forman-Barzilai, Fonna, 2010, Adam Smith and the Circles of\nSympathy, Cambridge: Cambridge University Press.", "Frankfurt, Harry, 1971, “Freedom of the Will and the Concept\nof a Person,” Journal of Philosophy, 68 (1):\n5–20.", "Garrett, Aaron, 2005, “Adam Smith and Moral Luck,” in\nFricke and Schütt (eds.), Adam Smith als Moralphilosoph,\nBerlin: de Gruyter.", "Gill, Michael, 2014, “Moral Pluralism in Smith and His\nContemporaries,” Revue internationale de philosophie,\n269 (3): 275–306.", "Griswold, Charles, 1999, Adam Smith and the Virtues of\nEnlightenment, Cambridge: Cambridge University Press.", "Haakonssen, Knud, 1981, The Science of the Legislator,\nCambridge: Cambridge University Press.", "–––, 1996, Natural Law and Moral\nPhilosophy, Cambridge: Cambridge University Press.", "Hankins, Keith, 2016, “Adam Smith’s Intriguing\nSolution to the Problem of Moral Luck,” Ethics, 126\n(3): 711–746.", "Hanley, Ryan, 2009, Adam Smith and the Character of\nVirtue, Cambridge: Cambridge University Press.", "Hayek, Friedrich, 1978 [1976], “Adam Smith’s Message\nin Today’s Language,” in F. Hayek, New Studies in\nPhilosophy, Politics, Economics and the History of Ideas,\nChicago: University of Chicago Press, pp. 267–9; originally\npublished, Daily Telegraph, London, March 9, 1976.", "Korsgaard, Christine, 1996, Sources of Normativity,\nCambridge: Cambridge University Press.", "McCloskey, Deirdre, 2006, The Bourgeois Virtues, Chicago:\nUniversity of Chicago Press.", "McDowell, John, 1998a, “The role of eudaimonia in\nAristotle’s ethics,” in McDowell, Mind, value, and\nreality, Cambridge, MA: Harvard University Press, pp.\n3–22.", "–––, 1998b, “Virtue and reason,” in\nMcDowell, Mind, value, and reality. Cambridge: Harvard\nUniversity Press, pp. 50–73.", "Montes, Leonidas, 2004, Adam Smith in Context, London:\nPalgrave Macmillan.", "Muller, Jerry, 1993, Adam Smith in his Time and Ours,\nPrinceton: Princeton University Press.", "Murdoch, Iris, 1970, The Sovereignty of Good, London:\nRoutledge.", "Muthu, Sankar, 2008, “Adam Smith’s Critique of\nInternational Trading Companies: Theorizing\n‘Globalization’ in the Age of Enlightenment,”\nPolitical Theory, 36 (2): 185–212.", "Otteson, James, 2002, Adam Smith’s Marketplace of\nLife, Cambridge: Cambridge University Press.", "Raphael, D.D., 2007, The Impartial Spectator, Oxford:\nClarendon Press.", "Rothschild, Emma, 2001, Economic Sentiments,\nCambridge: Harvard University Press", "Schliesser, Eric, 2006, “Articulating Practices as\nReasons,” The Adam Smith Review, 2: 69–97.", "Sen, Amartya, 2009, The Idea of Justice, Cambridge:\nHarvard University Press.", "Smith, Craig, 2013, “Adam Smith and the New Right,” in\nThe Oxford Handbook of Adam Smith, C. J. Berry, M. Paganelli\n& C. Smith (eds.), Oxford: Oxford University Press, pp.\n539–558.", "Winch, Donald, 1978, Adam Smith’s Politics,\nCambridge: Cambridge University Press.", "Berry, Christopher, Maria Paganelli, & Craig Smith (eds.),\n2013, The Oxford Handbook of Adam Smith, Oxford: Oxford\nUniversity Press.", "Brown, Vivienne and Samuel Fleischacker (eds.), 2010, The\nPhilosophy of Adam Smith, London: Routledge.", "Fricke, Christel and Hans-Peter Schütt (eds.), 2005, Adam\nSmith als Moralphilosoph, Berlin: de Gruyter.", "Griswold, Charles, 2018, Jean-Jacques Rousseau and Adam Smith:\nA Philosophical Encounter, London: Routledge.", "Hanley, Ryan (ed.), 2016, Adam Smith: His Life, Thought, and\nLegacy, Princeton: Princeton University Press.", "Herzog, Lisa, 2013, Inventing the Market: Smith, Hegel, and\nPolitical Theory, Oxford: Oxford University Press.", "Hont, Istvan and Michael Ignatieff (eds.), 1985, Wealth and\nVirtue, Cambridge: Cambridge University Press.", "Jones, Peter and Andrew Skinner (eds.), 1992, Adam Smith\nReviewed, Edinburgh: Edinburgh University Press.", "Montes, Leonidas, 2004, Adam Smith in Context, London:\nPalgrave Macmillan.", "Rasmussen, Dennis, 2009, The Problems and Promise of\nCommercial Society: Adam Smith’s Response to Rousseau,\nUniversity Park: Penn State University Press.", "–––, 2017, The Infidel and The Professor:\nDavid Hume, Adam Smith, and the Friendship that Shaped Modern\nThought, Princeton: Princeton University Press.", "Schliesser, Eric, 2017, Adam Smith: Systematic Philosopher and\nPublic Thinker, Oxford: Oxford University Press.", "Smith, Craig, 2006, Adam Smith’s Political\nPhilosophy, London: Routledge.", "Winch, Donald, 1978, Adam Smith’s Politics,\nCambridge: Cambridge University Press.", "Vivenza, Gloria, 2001, Adam Smith and the Classics,\nOxford: Oxford University Press." ]

[ { "href": "../scottish-18th/", "text": "Scottish Philosophy: in the 18th Century" } ]

[ "\nSocial “construction,” “constructionism” and\n“constructivism” are terms in wide use in the humanities\nand social sciences, and are applied to a diverse range of objects\nincluding the emotions, gender, race, sex, homo- and hetero-sexuality,\nmental illness, technology, quarks, facts, reality, and truth. This\nsort of terminology plays a number of different roles in different\ndiscourses, only some of which are philosophically interesting, and\nfewer of which admit of a “naturalistic” approach—an\napproach that treats science as a central and successful (if sometimes\nfallible) source of knowledge about the world. If there is any core\nidea of social constructionism, it is that some object or objects are\ncaused or controlled by social or cultural factors rather than natural\nfactors, and if there is any core motivation of such research, it is\nthe aim of showing that such objects are or were under our control:\nthey could be, or might have been, otherwise.", "\nDetermination of our representations of the world (including our\nideas, concepts, beliefs, and theories of the world) by factors other\nthan the way the world is may undermine our faith that any independent\nphenomena are represented or tracked, undermining the idea that there\nis a fact of the matter about which way of representing is correct.\nAnd determination of the non-representational facts of the world by\nour theories seems to reverse the “direction of fit”\nbetween representation and reality presupposed by our idea of\nsuccessful epistemic activity. For both of these reasons, proponents\nand opponents of constructionist thought have held it to embody a\nchallenge to the naturalism endemic in contemporary philosophy. But\nsocial constructionist themes can be and have been picked up by\nnaturalists who hope to accommodate the interesting and important\ncultural phenomena documented by constructionist authors while denying\nmore radical anti-scientific and anti-realist theses widely associated\nwith social constructionism.", "\nI begin by discussing social constructionism, and I then discuss some\nthreads of contemporary naturalism. I go on to consider two different\nsorts of objects of social construction—representations and\nhuman traits—and discuss naturalistic, constructionist\napproaches to them." ]

[ { "content_title": "1. What is Social Construction?", "sub_toc": [ "1.1 What Constructs?", "1.2 What is Constructed?", "1.3 What is it to Construct?" ] }, { "content_title": "2. Naturalism and Social Construction", "sub_toc": [] }, { "content_title": "3. Naturalizing Social Construction", "sub_toc": [ "3.1 The Social Construction of Representations", "3.2 Construction, Human Kinds and Human Traits" ] }, { "content_title": "4. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nWhile constructionist claims often take the passive form of a\ndeclaration that “Y is socially constructed,” it\nis more useful to think of social constructionist claims as having the\nform of a two-part relation:", "\nX socially constructs Y.\n", "\nWe can then think of different accounts of social construction as\ndiffering in their accounts either of the relation itself, or of one\nor both relata." ], "section_title": "1. What is Social Construction?", "subsections": [ { "content": [ "\nWhile philosophers have carefully engaged various constructionist\nclaims over the last several decades, much of the attention has been\npaid to various objects of construction (e.g., ideas? knowledge?\nfacts? human nature?). In contrast, comparatively little attention has\nbeen paid to distinguishing different sorts of agents of construction.\nMany of the agents in social constructionist claims can be neatly\ndivided into two groups: those that view the agents as primarily\nimpersonal agents, and those that view the agents as\npersonal agents (i.e., persons or groups).", "\nWork in the first group emphasizes a causal role for impersonal causes\nlike cultures, conventions, or institutions in producing some\nphenomenon. For example, the claim that what we perceive is determined\nby our background theories emphasizes an impersonal causal\nagent—culture—in determining some phenomena. Perhaps the\nmost influential version of this claim came in Thomas Kuhn’s\nsuggestion that, “what a man sees depends both upon what he\nlooks at and also upon what his previous visual-conceptual experience\nhas taught him to see” (1962/1970, 113), a suggestion with some\nfoundation in “New Look ” psychology (e.g. Briner,\nPostman, and Rodrigues 1951). This view was subsequently taken up by a\nrange of other authors across disciplines. For example, the historian\nThomas Laqueur writes that, “powerful prior notions of\ndifference or sameness determine what one sees and reports about the\nbody” (1990,\n 21).[1]\n Provocative claims like Kuhn’s and Laqueur’s suggest that\nperception is so dependent upon the background theories that the\nobservational data becomes compromised as an independent constraint on\nempirical inquiry. Impersonal cultural accounts of construction are\nalso found in explanations of nonrepresentational phenomena, for\nexample, of sex-differentiated behavior. Here a core claim might admit\nthat there is sex difference, but claim that the cause of difference\nis rooted in different conceptions of sex (and the practices caused by\nthose conceptions) rather than biological facts (see\n Feminist Perspectives on Sex and Gender).", "\nA second group of constructionist claims emphasizes personal\nsocial agents that construct through their choices. For example,\nAndrew Pickering’s (1984) influential work Constructing\nQuarks emphasizes the role of scientists’ judgments in a\nvariety of roles in scientific process including, e.g., theory\nselection, experiment evaluation, assessments of research fecundity,\nand so forth, and such an emphasis on apparently highly contingent\nchoices by researchers and scientific institutions is a mainstay of\nthe social studies of knowledge literature. In emphasizing personal\nchoices, some constructionist work (including some of\nPickering’s) seems primarily aimed at emphasizing the\ncontingency of the scientific theory that we come to accept (cf.\nHacking\n 1999).[2]\n Other constructionists—those we might call critical\nconstructionists—emphasize personal choices not just to\nestablish the contingency of the acceptance of some representation as\nto emphasize the role of an agent’s interests or power relations\nin determining the content of an accepted representation. For example,\nCharles Mills suggests that the borders of American racial categories\nwere determined in such a way as to “establish and maintain the\nprivileges of different groups. So, for example, the motivation for\nusing the one-drop rule to determine black racial membership is to\nmaintain the subordination of the products of\n‘miscegenation’” (1998, 48). And a range of\nconstructionist research, especially research on human classifications\nlike “race” and “gender,” documents shifts in\nhuman classification in response to shifts of interests or power." ], "subsection_title": "1.1 What Constructs?" }, { "content": [ "\nSocial constructionist claims are made about so many different objects\nthat it is perhaps not surprising to find that such claims have\ndifferent implications depending upon the different objects at which\nthey are directed. Most uses of “construction”-talk (and\nrelated talk to the effect that that objects are, surprisingly,\n“invented” or “made up”) are directed at three\nvery different sorts of entities: representations (e.g. ideas,\ntheories, concepts, accounts, taxonomies, and so forth),\n(non-representational) facts quite generally, and a special sort of\nnon-representational fact: facts about human traits.", "\nMost philosophical discussion of social constructionism has been\nconcerned with the so-called “science wars” which means\nthat they have been concerned with evaluating the inference from the\nnumerous and complex social influences operating in the production of\nscientific theories to the social construction of the facts those\ntheories purport to represent, or to the failure of accounts of\nscientific rationality, or scientific realism, or scientific process\n(e.g. Laudan 1981, Nelson 1994, Fine 1996, Kukla 2000).", "\nBut “construction” talk has a more or less independent,\nbut equally contentious life in the “human nature wars”\nwhere it labels the position that human traits (for example the\nemotions) or human kinds (which we can think of categories whose\nmembers share traits or clusters of traits, including, especially,\ndispositions to think and behave) are produced by culture rather than\nby biology or nature. ", "\nThis kind constructionist view contrasts with the view that\nhuman kinds or traits are to be explained in terms of non-cultural\nmechanisms – especially internal, biological or natural states of the\norganism. The most pronounced disputes are prima facie concerned with\nwhether the clustering of traits in, for example, sex difference,\nemotional behavior, or mental illness, are caused by a cultural\npractice of differentiating persons or are instead caused by natural\nprocesses operating in relative independence from culture.", "\nBut this kind constructionist view has also (especially in the\nphilosophy of race) come to contrast with the skeptical view that a\nkind does not exist. In the context of race, constructionism amounts\nto the positive assertion that race is real even though it is not\nconstituted by, or grounded in, biological facts such as genetic\ndifference. (See, e.g., Haslanger 2012, Taylor 2013, Sundstrom 2002,\nOutlaw 1995, and the section “Race: Do Races Exist? Contemporary\nPhilosophical Debates” in the entry on\n race.)", "\nWe consider naturalistic approaches to the construction of\nrepresentations and human traits in more detail below, but it is\nuseful to first distinguish global constructionist claims\nthat hold that every fact is a social construction, from\nlocal constructionist claims that hold that only particular\nfacts\n are.[3]\n Because of their provocative nature, many philosophers associate the\nterm “social construction” with a global thesis, and a\nstandard argument against global constructionism concerns whether such\na program is sustainable in the face of the regress such a global\nthesis engenders regarding the thesis of constructionism itself (e.g.\nBoghossian 2006, Kukla 2000). Philosophers may have focused on these\nmore radical claims in part because of the recognition that, relying\non something like the general idea of construction sketched above,\nclaims that are relatively global in scope are quite provocative and\nsurprising while claims that would count as locally socially\nconstructionist are quite familiar in many areas of philosophy,\nperhaps most importantly in meta-ethics, aesthetics, and social\nontology. The domain of social ontology is especially interesting\nbecause here many facts are widely recognized as social constructions:\nfor example, facts about being a U.S. Senator or a\nlicensed dog are social\n constructions.[4]\n Call such constructions overt\n constructions.[5]", "\nBut even local constructionist claims can be interesting to the extent\nthat they try to show some object may be produced by unacknowledged\nsocial practices—when they are covert constructions.\nThis is the role that they play in the philosophy of psychiatry\n(Hacking 1995a, Scheff 1984, Showalter 1996, cf. Murphy 2006), the\nphilosophy of the emotions (Averill 1980a, 1980b, Armon-Jones 1986,\nHarré 1986, cf. Griffiths 1997), the philosophy of race (e.g.\nOutlaw 1990, 1995; Mills 1998; Taylor 2013), and the philosophy of\ngender (see\n Feminist Theories of Sex and Gender: Gender as Socially Constructed).\n Here the local claim that some kind (for example mental\nillness, emotion, race, or gender) is\nexplained by received culture or practice retains its interest because\nit offers a metaphysical alternative to other explanations\n(biological, religious, etc.) of the differential features of the kind\nmembers as well as an alternative to skepticism about the reality of\nthe\n kind.[6]" ], "subsection_title": "1.2 What is Constructed?" }, { "content": [ "\nWe have already suggested that the core idea of constructionism is\nthat some social agent produces or controls some object. Of course,\n“construction” talk is meant to evoke a variety of\nconnotations that attend more paradigmatic construction: intentional\nactivity, engaged in step-by step fashion, producing a designed,\nartifactual product. While different objects lead constructionist talk\nto be interpreted in different ways, we can distinguish two different\nsorts of relationship: causal or\n constitutive.[7]\n On the first, X constructs Y if Y is\ncaused to come to exist, to continue to exist, or to have the\nproperties that it does by X. On the second, Y is\nconstructed if it is constituted by X’s\nconceptual or social activity (perhaps even independently of\nX’s causal influence on Y).", "\nThe first, and more straightforward idea is causal\nconstruction:", "\nX causally constructs Y if and only if\nX causes Y to exist or to persist or X\ncontrols the kind-typical properties of\n Y.[8]\n ", "\nThere is no special problem posed by the claim that human social and\nlinguistic activities cause certain things to exist or persist, or\ncause certain facts to be. More obscure is the idea that\nX’s construction of Y is some sort of\nconstitutive relationship. Many constructionist claims seem\nto involve the idea that the world is itself “made up” by\nsocial and cultural activities in ways that suggest our\nsocio-linguistic behaviors are at least necessary to the object in\nquestion. This suggests a relationship such as:", "\nX constitutively constructs Y if and only\nif X’s conceptual or social activity regarding an\nindividual y is metaphysically necessary for y to be\na Y.\n", "\nConsider the ways in which causal and constitutive claims might pull\napart in a case of a socially produced artifact. Representations\nexpressing the concept watch are normally causally necessary\nfor some materials to come to have the intrinsic features of a watch,\nbut they are not metaphysically necessary. It is metaphysically\npossible, however unlikely, that we could walk across a heath and find\n(something with the intrinsic features of) a watch that had\n“always been there.”", "\nIn contrast, the best candidates for constitutive construction are\nsocial facts:", "\nFor social facts, the attitude that we take toward the phenomenon is\npartly constitutive of the phenomenon … Part of being a\ncocktail party is being thought to be a cocktail party; part of being\na war is being thought to be a war. This is a remarkable feature of\nsocial facts; it has no analogue among physical facts. (Searle 1995,\n33–34)\n", "\nOn Searle’s view, a particular gathering of persons can be a\ncocktail party only with the conceptual and social recognition of\nthose gathered. A similar idea has been influential in constructionist\ndiscussions. For example, the provocative claims that there were no\nhomosexuals before the concept homosexual came to be\nexpressed in Western culture in the nineteenth century (e.g. Foucault\n1978, Halperin 1990) or that race is a modern invention (e.g Taylor\n2004) seem to make sense if we see sexual or racial kinds as in part\nconstituted by our concepts of them.", "\nBut Searle is right that there is something remarkable here, at least\nin the case of social facts: somehow our conceptual scheme or practice\nare necessary to make it true that some event instantiates\ncocktail party or war. What is wanted is, at a\nminimum, a model of this production—a model of exactly how the\nconceptual practice constitutes the fact. Perhaps the most obvious\nmodel to explain such constitutive claims is to hold that the relevant\nnecessity is analytic, it holds in virtue of the meaning of\nthe relevant term or concept. It is a fact about the meaning of\n“cocktail party” and perhaps “homosexual” and\n“race”) that it does not apply to a thing unless it is\nrecognized to do so.", "\nWhether any such meaning claims can be accommodated has been\na contentious question since Quine (1953), but it is a question we can\nput aside for now (see\n The Analytic/Synthetic Distinction).\n Instead, we should ask whether such model of constitutivity as\nanalyticity is plausible for objects of social construction.", "\nOn the one hand, if Searle’s general account of social facts is\ncorrect, there may be many terms that operate like “cocktail\nparty” in that the participants produce them only when they\nshare certain intentional states about what they are doing. On the\nother hand, this does not seem plausible for the objects of many\nsocial constructionist claims. Remember, it is a mainstay of\nconstructionist research to claim that social influence is exercised\nin surprising and provocative ways, especially on objects that we take\nto be produced naturally. But just this feature suggests that it\ncannot be part of our ordinary concepts of covertly constructed kinds\nthat instances require our social-conceptual imprimatur to be members\nof these kinds (Machery 2014, Mallon 2017). This point is highlighted\nin a more general way by Paul Boghossian’s query:", "\nisn’t it part of the very concept of an electron, or of\na mountain, that these things were not constructed by us?\nTake electrons, for example. Is it not part of the very purpose of\nhaving such a concept that it is to designate things that are\nindependent of us? (2006, 39)\n", "\nIf this is right, constructionists who view construction as a\nconstitutive relation need another account of the necessity of our\nconceptual practice: it is implausible and inconsistent to claim that\nthe necessity arises out of concept or word meanings in cases of\ncovert construction.", "\nThere is a different model of necessity for the constructionist,\nhowever, which is to hold that the necessity in question is revealed\na posteriori by our investigations of the phenomenon in\nquestion. Saul Kripke (1980), Hilary Putnam (1975) and others defended\na causal theory of reference on which some terms (notably natural kind\nterms) referred to some sort of stuff or essence underlying the\ncentral uses of the term (see\n Reference: Causal Theories).\n Crucially, however, because the reference relation is external,\ncompetent users of a term can be radically mistaken about what the\nterm refers to and still successfully refer. In the case of water, for\nexample, Putnam suggests that “water” picks out the sort\nof stuff that bears the appropriate causal-historical relation to\nparadigmatic instances in our own causal history (viz.\nH2O), and this was true even when we did not know what sort\nof stuff that was (i.e. before we knew the chemical structure).\nKripke, Putnam, and others emphasized that claims such as\n“water=H2O” express necessary though a\nposteriori truths.", "\nWhile the causal theory of reference (and its correct interpretation)\nremains controversial, in many quarters of philosophy it has become\naccepted wisdom. It is thus an option for interpreters of social\nconstructionism to claim that certain terms—for example,\n“race”—actually refer to a kind that is produced by\nour socio-linguistic behavior, even if that fact is revealed only\na\n posteriori.[9]\n Such a constitutive constructionist could grant, then, that it is\npart of our ordinary conception of the concept (e.g. of race) that –\nlike electron – it refers to an independent, natural fact about the\nworld, but such a constructionist would insist that further\nexploration of the world reveals that conventional features of our\npractice produce the object of our study. As with the case of\n“water” before modern chemistry, the conception widely\nassociated with “race” (viz. that it is a biological kind)\nis wrong, but the term successfully refers all the same. Ideally, for\nsuch an approach to work, the constitutive constructionist would like\nan independent characterization of the sorts of social objects that\ninvestigation reveals to be identical with the kinds in question (e.g.\nÁsta 2016; Bach 2012; Mallon 2003, 2016), but they also need to\nfend off critics of applying the causal theory of reference in the\ncontext of reference to socially produced objects (e.g. Thomasson\n2003) as well as more general critiques of employing theories of\nreference as premises in arguments with philosophically significant\nconclusions (Mallon et al. 2009, Mallon 2007b). Still, if it can be\nmade to work, this strategy would make sense of constitutive\nconstructionist claims while respecting Boghossian’s idea (one\nthat is also central to constructionism) that these kinds are\nordinarily believed to be natural and independent of us. For this\nreason, this strategy has been suggested in the case of race, gender,\nand other human kinds (Haslanger 2003, 2005; Mallon 2003, 2016), and\nmore generally for scientific facts (Boyd 1992). ", "\nOf course, there may well be other models of necessity available. For\nexample, it is sometimes suggested that a neo-Kantian interpretation\nof social constructionism is possible, an interpretation on which our\nsocio-linguistic activities could provide a transcendental basis for\nany knowledge of the world. Such an interpretation might allow certain\napparently radical constitutive claims, but the challenge would remain\nto reconcile the view with a naturalistic conception of ourselves,\nsomething such a proposal may fail to do (e.g. Boyd 1992, Rosen\n1994)." ], "subsection_title": "1.3 What is it to Construct?" } ] }, { "main_content": [ "\nAny discussion of naturalistic approaches to social construction is\ncomplicated by the fact that “naturalism” itself has no\nvery widespread and uniform understanding (see\n Naturalism).\n Still, the prospect seems provocative, in part, because social\nconstruction has come to be associated with a critical anti-realist\nattitude towards science.", "\nAbove, we identified naturalism with a certain attitude towards\nscience, and for present purposes, we develop this idea by identifying\nthree naturalistic attitudes toward science that have been picked up\nby naturalists addressing social constructionist themes.", "\nThese features characterize substantial threads of contemporary\nnaturalist thought—threads that arise repeatedly in discussions\nof constructionism. Still, it is worth noting that something may be\nnaturalistic in one sense but not another, and that the various\nthreads we have characterized may sometimes be at odds. For example,\nrational choice explanations in economics might count as naturalist in\nthat they attempt to reduce complex macro-level phenomena to simple,\nmicro-level phenomena at the level of individuals (exhibiting some\nvariety of metaphysical fundamentalism), and in the sense that they\nemploy idealized causal modeling to do so (as in 1c). But they seem\nnonnaturalist insofar as they offer a highly idealized account of\nhuman behavior, one that seems frequently contradicted by the\npsychological facts about human reasoning (see, e.g., Nisbett and Ross\n1980, Tversky and Kahneman, 1974) (against, perhaps, 1a and b, and\n3).", "\nWe now review various naturalistic approaches to social construction,\nconsidering different sorts of entities in turn." ], "section_title": "2. Naturalism and Social Construction", "subsections": [] }, { "main_content": [ "\nAs we noted above, the production of facts by social agents poses no\nspecial problem for the naturalist where that production is understood\ncausally, though naturalists of many stripes may want to produce\ncausal models to show how the macro-level social phenomena of interest\nto many social theorists and social scientists are causally realized\ngiven what we know about, e.g. human nature or the causal structure of\nthe universe. In contrast, constitutive claims of construction seem\ndifficult to make sense of (except on an account of construction on\nwhich social activity involving a representation comes to produce and\ncausally sustain an object that is referred to by that\nrepresentation).", "\nIn recognition of this state of affairs, many naturalist approaches to\nconstructed phenomena have involved attempts to causally model matters\nof interest to constructionists in ways that engage more or less\ncompletely with existing scientific knowledge. By way of illustrating\nsuch naturalistic approaches, I’ll discuss the social\nconstruction of representations and of human nature in more\ndetail." ], "section_title": "3. Naturalizing Social Construction", "subsections": [ { "content": [ "\nIn talking about the construction of representations, we address the\nrange of mental states, group beliefs, scientific theories, and other\nrepresentations that express concepts or propositions. Such\nrepresentations are, among other things, the vehicles of our thought\nas well as the means by which we store, organize, and further our\nknowledge of the world, and we do this in virtue of their role as\nbearers of meaning. A number of commentators have noted that many\nprovocative constructionist claims are, in the first instance, claims\nthat some sort of representation is constructed (e.g. Andreasen 1998,\nHacking 1999, Haslanger 2012, Mallon 2004). Specifically, these are\nclaims that social causes produce or control the selection of some\nrepresentations with some meanings rather than others: for example,\nwhen Pickering (1984) writes of the construction of quarks or Laqueur\n(1990) suggests that sex is “made up,” they seem to be\nmost directly addressing the process by which the theories of\nthe quark or theories of sex are produced, viz. they are\nshowing how a theory with one meaning was selected or endorsed rather\nthan another theory or no theory at all. Where we limit the objects of\nconstructionist claims to representations (such as theories), the\nclaims cease to be particularly metaphysically provocative though\ndetailed constructionist accounts of how certain representations came\nto be selected may still teach us much about science (e.g. Latour and\nWoolgar 1979l Collins and Pinch 2012).", "\nIn light of this, philosophers may be wont to diagnose some\nconstructionist talk as a careless (or even an intentionally\nprovocative) error of talking about the object of construction\nusing a representation when one should be mentioning\nit (thereby expressing a view about the referent of the representation\nrather than the representation itself). When Claudius Ptolemy offered\na geo-centric theory of the universe in the second century CE, he\nthereby contributed to the social construction of something: namely,\na geocentric theory of the universe. We can talk about how\nand when that theory arose, and how it changed over time, but in doing\nso we are simply talking about a representation (or perhaps a lineage\nof related representations). It would be a mistake simply to slip from\nthose claims into saying that in constructing this theory he thereby\nconstructed a geocentric universe. Hence, charity in\ninterpretation alone may suggest attributing only the weaker claim to\na constructionist\n author.[10]", "\nStill some constructionists endorse a stronger claim as\nwell—that in constructing the theories, the facts described by\nthose theories are thereby made to be. But if we leave at least the\nglobal versions of these additional claims aside as impossible to\nreconcile with naturalism, the distinctive feature of social\nconstructionist explanations of representations is that they explain\nhow we came to have those representations not by reference to the\nfacts in the world they represent (as in realism), nor by reference to\nassociations among our sensations (as in some forms of empiricism),\nnor by reference to innate knowledge or concepts (as in rationalism),\nnor by reference to the conditions of our thought or experience (as in\ntranscendental arguments) but rather by reference to social and\ncultural background facts.", "\nNaturalist work on constructionist approaches to representations can\nbe grouped according to the debate the naturalist is addressing.\nNaturalists addressing the challenge posed by social construction to\nthe authority of science have attempted to respond to this challenge\nin a variety of ways that pit various versions of realism and\nempiricism against constructionism (e.g. Boyd 1992; see\n Social Dimensions of Scientific Knowledge).\n Because naturalists are typically committed to science as a central,\nif fallible, avenue of knowledge about the world (i.e. some variety of\nepistemic fundamentalism), naturalists will want to explain how this\ncan be if, as social constructionists about scientific representations\nnote, empirical observation is theory-laden and scientific theories\nare themselves subject to massive social influences.", "\nFor example, Jerry Fodor’s account of the modularity of\nperception (e.g. 1983, 1984, 1988) is, in part, a response to the\nimplication that perception is so theory-laden that it lacks the\nindependence required to constrain belief (see above for this\nimplication in such diverse thinkers as Kuhn 1962/1970 and Laqueur\n1990). Fodor suggests that sensory perception is modular by which he\nmeans (in part) “mandatory” and “informationally\nencapsulated” in its operations—i.e., it operates\nindependently of our will and of our background theories and\nexpectations. Fodor illustrates this effect by pointing to cases of\noptical illusions like the Muller-Lyer illusion (Fodor 1984). Here,\ntwo parallel line segments continue to appear to be different lengths\neven when one knows them be the same length, suggesting the\nindependence of the process that produces sensory phenomena from\none’s background theoretical beliefs. And while some\nphilosophers (e.g. Churchland 1988, cf. Fodor 1988) have resisted this\nconclusion, some social scientists of knowledge have attempted to\nrestate a constructionist view in ways that allow that Fodor may be\ncorrect. Barry Barnes, David Bloor and John Henry, for example, shift\nfrom emphasis on the determination of perceptual experience by culture\nto an emphasis on the underdetermination of belief by perceptual\nexperience (a view which leaves room for cultural determination of\nbelief) (1996, Ch. 1). More generally, epistemologists and\nphilosophers of science have taken up the project of accommodating\nsocial influence in the production of knowledge, and this project is\nwell underway in contemporary social epistemology and philosophy of\nscience (e.g. Boyd 1992; Kitcher 1993, 2001). These issues are taken\nup elsewhere\n (Social Epistemology)\n so we address them no further here. Instead, I focus on attempts by\nnaturalists to accommodate the cultural and personal processes at the\nheart of constructionist phenomena in naturalistic terms.", "\nIn contrast to naturalistic responses to the threat of scientific\nanti-realism, naturalistic responses to constructionist claims about\nrepresentations (including beliefs) understood as human traits have\nbeen far more sympathetic to constructionist approaches. Indeed, an\nemphasis on the cultural and social causes of belief is quite amenable\nto range of naturalists, and naturalistic approaches to these causes\nare well represented in constructionist precursors, including such\nluminaries as Karl Marx, Friedrich Nietzsche (see the section on the\ncritique of the descriptive component of MPS in\n Nietzsche’s Moral and Political Philosophy),\n and Karl Mannheim (1936). In contemporary naturalistic philosophy of\nscience and psychology, the naturalistic explanation of culturally\nproduced cognition is picked up by at least three distinct strands of\nwork taking up constructionist themes of culture. The first is\ncentered on the idea that culture can be understood by analogy with\npopulation genetics, and that cultural items might be understood to be\nmore or less successful based upon their success in spreading in a\npopulation. Various versions of this sentiment find expression in such\ndiverse thinkers as Robert Boyd and Peter Richerson (1985, 2005a,\n2005b), D.T. Campbell (1960), Luca Cavalli-Sforza and Marcus Feldman\n(1981), David Hull (1988), Jesse Prinz (2007, Ch. 6), Daniel Sperber\n(1996), and one version of it has a substantial popular following\n(Richard Dawkins’s (1976) widely read discussion of\n“memes”). While only some of these thinkers link the\nproject to the understanding of constructionist research themes, the\nproject in every case is to formally model cultural processes,\nunderstanding these complex processes as depending on simpler ones\n(See also\n Cultural Evolution.)\n ", "\nThe second, overlapping strand of naturalistic inquiry also views\nculture as a system of representations upon which selection acts, but\nattempts to integrate this idea with the idea, common in evolutionary\ncognitive psychology, that the mind is comprised of a great many\ndomain-specific mental mechanisms, and uses these as the selective\nmechanisms that act as a primary mechanism of selection (so called\n“massive modularity”; see\n Evolutionary Psychology: Massive Modularity;\n cf. Carruthers 2006), and it is most firmly represented among\ncognitive anthropologists and psychologists like Scott Atran (1998),\nPascal Boyer (1994, 2001), Laurence Hirschfeld (1996), and Daniel\nSperber (1996). Such an approach represents naturalism in most (or\nperhaps all) of the above senses, and it is finding its way into the\nwork of naturalist philosophers of science and psychology (Machery and\nFaucher 2005, Mallon 2013, Nichols 2002, Prinz 2007, Sripada 2006,\nSterelny 2003).", "\nA third, philosophically underdeveloped strand naturalizes crucial\nelements of critical constructionist approaches by suggesting\nthe influence of sometimes implicit evaluations on judgments and\ntheoretical activities. For example, a growing body of empirical\nevidence on so-called “motivated cognition” (cf. Kunda\n1999) suggests mechanisms for (and some empirical validation of) the\ncritical social constructionist tradition of explaining the content of\naccepted theories in part by appeal to the interests of the theorists.\n" ], "subsection_title": "3.1 The Social Construction of Representations" }, { "content": [ "\nAny sort of human trait could be an object of social construction, but\nmany of the most interesting and contested cases are ones in which\nclusters of traits—traits that comprise human kinds—are\npurported to co-occur and to correlate with mental states, including\ndispositions to think and behave in particular\n ways.[11]\n ", "\nBecause discussion of kinds of persons with dispositions to think and\nbehave quickly gives rise to other questions about freedom of the will\nand social regulation, debates over constructionism about kinds are\ncentral to social and political debates regarding human\ncategorization, including debates over sex and gender, race, emotions,\nhetero- and homo-sexuality, mental illness, and disability. Since the\nconstructionist strategy explains a trait by appeal to highly\ncontingent factors (including culture), partisans of these debates\noften come inquire whether a trait or cluster of traits is culturally\nspecific, or can be found across cultures.", "\nThese issues can quickly come to generate more heat than light, and so\none role that philosophers in general, and naturalists in particular,\nhave played is to carefully analyze constructionist positions and\ntheir alternatives. For example, in reflecting on debates over\ncultural specificity or universality, a number of commentators have\nnoted that constructionist claims of cultural specificity often hinge\nnot on genuine empirical disagreement about what is or is not found\nthrough history and across cultures, but also on a strategy of\nindividuating the phenomena in question in ways that do or do\nnot involve contextual features that vary across cultures (Mallon and\nStich 2000; Boghossian 2006, 28; Pinker 2003, 38).", "\nPhilosophers have also distinguished claims of social construction\nfrom the possibility of cultural control (Mallon 2007a, Stein 1999),\ndisentangled claims of social construction from claims of\nvoluntariness and nonessentialism (Stein 1999), set out alternate\nforms of constructionism or anti-constructionism (Griffiths 1997,\nMallon 2007c, Andreasen 1998), disentangled questions regarding the\nneural basis of a human kind from the innate/constructed dichotomy\n(Murphy 2006, Ch. 7) and so forth.", "\nThis conceptual project is a philosophical project par\nexcellence, and it has contributed a great deal to clarifying\njust what conceptual and empirical issues are at stake in\nconstructionist work.", "\nNaturalist interpretations of constructionism have also taken up the\ndistinct, open-ended, empirical project of defending substantive\nclaims regarding the development and distribution of human traits via\nthe suggestions that human socio-linguistic behaviors shape human\ntraits (including behavior) via different avenues, both developmental\nand situational.", "\nOne “social role” family of theories emphasizes the way\nthat our socio-linguistic practices produce social roles that\nstructure and shape human life and behavior. Perhaps the most\ninfluential philosophical project in this area has been Ian\nHacking’s work on “making up people” (1986, 1992,\n1995a, 1995b, 1998). In a series of papers and books, Hacking argues\nthat the creation and promulgation of bureaucratic, technical, and\nmedical classifications like “child abuse,”\n“multiple personality disorder,” and “fugue”\ncreate “new ways to be a person” (1995b, p. 239). The idea\nis that the conception of a certain kind of person shapes both a\nwidespread social response (e.g. one that exculpates and perhaps\nencourages kind-typical behaviors), while at the same time, the\nconception shapes individual “performances” of the\nbehavior in question (by suggesting highly specific avenues of\nbehavior). On Hacking’s model, one he calls “the looping\neffect of human kinds,” the conception of the behavior may be\npart of an epistemic project of understanding a human kind that in\nturn gives rise to the clusters of traits that the theory represents\n(thereby providing epistemic support for the\n conception).[12]\n Much of Hacking’s own recent work has been aimed at providing\ndetailed historical and cultural evidence that suggests that looping\neffects really are a feature of (at least modern) human social life,\ne.g. for the American epidemic of multiple personality disorder that\nstarted in the 1980s (Hacking 1995) or the European epidemic of fugue\nin the late nineteenth century (Hacking 1998). Hacking makes further\nclaims about the “looping effect,” for example, that\nlooping effects mark “a cardinal difference between the\ntraditional natural and social sciences” because “the\ntargets of the natural sciences are stationary” while “the\ntargets of the social sciences are on the move” (1999, 108)\n),claims that themselves have spurred lively discussions over the\nnature of looping effects (e.g. Cooper 2004, Laimann forthcoming) and of their\nmechanisms in human groups (e.g. Mallon 2016, Kuorikoski and\nPöyhönen 2012).", "\nOthers have drawn on Hacking’s account to offer similar accounts\nof constructed kinds of person, including K. Anthony Appiah (1996) on\nracial identities, and Paul Griffiths (1997) on performed emotional\nsyndromes. Together with Hacking’s work, these accounts provide\npartial, causal interpretation of even quite radical claims about\nkinds of person. For example, Judith Butler has provocatively claimed\nthat the sex-differentiated behavior is a performance, writing,\n“That the gendered body is performative suggests that it has no\nontological status apart from the various acts which constitute its\nreality. … In other words, acts and gestures, articulated and\nenacted desires create the illusion of an interior and organizing\ngender core…” (1990, 136). Following on the work of\nHacking, Appiah, Griffiths, and others, we can naturalistically\n(re)interpret Butler’s claim as one that explains gender\ndifferences in actions, gestures, desires, and so on by reference to\nthe social role that a person occupies. Such a causal model of the way\nin which social roles might shape behavior is at least arguably\nnaturalistic in all of the above senses.", "\nThis “social role project” amounts to only one way of\ndeveloping constructionist ideas in the service of explaining the\ndevelopment of human kinds, traits, or behaviors. For example,\nconstructionist ideas find diverse manifestations in the theory of\nemotions (e.g. Armon-Jones 1986, Barrett 2017, Harré 1986, cf.\nGriffiths 1997 and Prinz 2004 for discussion). Because social\nconstructionism offers a general set of explanatory approaches,\nconstructionist approaches can be expected to reemerge in a variety of\nways in the attempt to explain a wide range of human phenomena. ", "\nStill a different way of developing naturalistic constructionist\naccounts of kinds involves using various formal methods to model such\nkinds. Among recent work in social ontology, Francesco Guala has\ndistinguished “rules-based” approaches to social\ninstitutions from “equilibrium-based” approaches (2016,\nxxv). The former attempts to understand social structure as emerging\nfrom the collective adoption of rules, while the latter sees it as\nemerging along with various solutions to coordination and cooperation\nproblems. As an example of the former, Searle (1995) influentially\nargues that we can understand social institutions as brought into\nbeing by collective endorsement of rules of the form:", "\nX counts as Y in C.\n", "\nHere, “X” is a specification of the individual or\ntype to which the status “Y” applies. And\n“C” specifies the context in which this imposition\noccurs. For instance, it might specify that tokens of a certain type\nproduced by the U.S. mint count as money in the United States. Such\nstatuses obtain in virtue of collective acceptance of one or more\nstatus functions. (See the entry on\n social ontology.)\n ", "\nIn contrast, the latter family of approaches attempts to understand\nsocial structure by using the tools of economic and evolutionary game\ntheory to understand culture (e.g. Bicchieri 2006, 2016; Guala 2016;\nO’Connor 2017). Here, norms, behaviors, and social regularities\nare seen as produced and stabilized by the preferences of individual\nactors making decisions in a social context of other actors. For\nexample, Richard McElreath, Robert Boyd, and Peter Richerson (2003)\nhave argued that ethnic-group based “markers” (e.g. things\nlike styles of dress or other indicators of membership in an ethnic\ngroup) culturally evolved because they allowed actors to\ndifferentially interact with those who shared common norms, thus\nreaping the benefits of coordination and cooperation with greater\nefficiency.", "\nWhile rules-based approaches have been much discussed across a range\nof philosophical fields (including metaphysics, social philosophy,\nempirically-informed philosophy of mind), equilibrium-based approaches\nhave so far received comparatively little philosophical attention.", "\nMany constructionist projects concerning human kinds are, or are\npursued as part of, normative projects. Thinkers interested in gender,\nrace, mental illness and disability, are often motivated not only by\nconcern with the metaphysics of these categories, but with questions\nof social morality and justice that connect with them. For instance,\nSally Haslanger’s work on the construction of gender and race\n(Haslanger 2012), or Elizabeth Barnes’s (2016) constructionist\naccount of disability seem to essentially incorporate normative\nconcepts. This connection, in turn, raises a number of further\nquestions about why they are connected, and how we ought to understand\ntheir relationship.", "\nOne answer to these questions is simply that, once we understand the\nconstructed nature of some category or phenomena, different normative\nconclusions will follow. For instance, some have emphasized that\nbecause constructionist explanations highlight the role of agents in\nthe production or the sustenance of phenomena, they make those agents\nsubject to moral evaluation (Kukla 2000; Mallon 2016,\nforthcoming).", "\nA different approach might be that normative considerations ought to\ndrive us towards certain metaphysical explanations. For instance, Esa\nDiaz-Leon (2015) has argued that constitutive constructionist\nexplanations are politically better than causal constructionist ones,\non the grounds that constitutive constructions are more tightly\nconnected to our socio-conceptual practices:", "\nrevealing the constitutive connections between instantiating a certain\ncategory and standing in a certain relation to certain social\npractices, opens a clear path for social change: just change those\nsocial practices, and social change will automatically follow. (2015,\n1145)\n", "\nIn contrast, Theresa Marques (2017) has argued that a focus on causal\nsocial construction is more relevant to projects of social justice.\nBut if we see constructionism as a kind of explanation, then this\ndebate can seem to put the cart before the horse. The correctness of\nan explanation is given by some facts in the world. Deciding what we\nwould like those facts to be, given our aims, seems to fail to\nappreciate the reality of our socio-conceptual practices and their\nconsequences.", "\nMore generally, while normative constructionist projects can be deeply\nengaged with our best scientific understanding, many naturalists will\nbe tempted to attempt to distinguish descriptive and normative\nelements in order to engage them separately.", "\nAt the same time, ongoing naturalist work on human cooperation and\ncoordination suggests the future possibility of more thoroughgoing\nnaturalist approaches to construction that integrate naturalistic\napproaches to norms and normativity (e.g., Bicchieri 2016, Sripada\n2006, and the entry on\n social norms)\n with accounts of the human kinds that our socio-conceptual behaviors\nstructure and shape." ], "subsection_title": "3.2 Construction, Human Kinds and Human Traits" } ] }, { "main_content": [ "\nThe metaphor of “social construction” has proven\nremarkably supple in labeling and prompting a range of research across\nthe social sciences and humanities, and the themes of personal and\ncultural causation taken up in this research are themselves of central\nconcern. While most philosophical effort has gone towards the\ninterpretation and refutation of provocative accounts of social\nconstruction arising especially out of studies in the history and\nsociology of science, social constructionist themes emerge across a\nhost of other contexts, offering philosophical naturalists a range of\nalternate ways of engaging constructionist themes. Philosophical\nnaturalists as well as working scientists have begun to take up this\nopportunity in ways that use the methods of philosophy and science to\nboth state and evaluate social constructionist hypotheses (though not\nalways under that label). Because of the powerful and central role\nculture plays in shaping human social environments, behaviors,\nidentities and development, there is ample room for continuing and\neven expanding the pursuit of social constructionist themes within a\nnaturalistic framework." ], "section_title": "4. Conclusion", "subsections": [] } ]

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[ "\nThe idea of the social contract goes back at least to Protagoras and\nEpicurus. In its recognizably modern form, however, the idea is\nrevived by Thomas Hobbes and was later developed, in different ways,\nby John Locke, Jean-Jacques Rousseau, and Immanuel Kant. After Kant,\nthe idea fell out of favor with political philosophers until it was\nresurrected by John Rawls. It is now at the heart of the work of a\nnumber of moral and political philosophers.", "\nThe basic idea seems simple: in some way, the agreement of all\nindividuals subject to collectively enforced social arrangements shows\nthat those arrangements have some normative property (they are\nlegitimate, just, obligating, etc.). Even this basic idea, though, is\nanything but simple, and even this abstract rendering is objectionable\nin many ways.", "\nTo explicate the idea of the social contract we analyze contractual\napproaches into five elements: (1) the role of the social contract (2)\nthe parties (3) agreement (4) the object of agreement (5) what the\nagreement is supposed to show." ]

[ { "content_title": "1. The Role of the Social Contract", "sub_toc": [ "1.1 The Distinctiveness of the Social Contract Approach", "1.2 The Social Contract as a Model" ] }, { "content_title": "2. Modeling the Parties", "sub_toc": [ "2.1 Reductionist vs. Non-Reductionist ", "2.2 Idealization vs. Identification", "2.3 Homogeneity vs. Heterogeneity ", "2.4 Doxastic vs. Evaluative " ] }, { "content_title": "3. Modeling Agreement", "sub_toc": [ "3.1 Consent ", "3.2 Bargaining", "3.3 Aggregation", "3.4 Equilibrium" ] }, { "content_title": "4. The Object of Agreement", "sub_toc": [] }, { "content_title": "5. What Does the Contract Show?", "sub_toc": [] }, { "content_title": "6. Conclusion: The Social Contract and Public Justification", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. The Role of the Social Contract", "subsections": [ { "content": [ "\nThe aim of a social contract theory is to show that members of some\nsociety have reason to endorse and comply with the fundamental social\nrules, laws, institutions, and/or principles of that society. Put\nsimply, it is concerned with public justification, i.e., “of\ndetermining whether or not a given regime is legitimate and therefore\nworthy of loyalty” (D’Agostino 1996, 23). The ultimate\ngoal of state-focused social contract theories is to show that some\npolitical system can meet the challenge Alexander Hamilton raised in\nFederalist no. 1 of whether “men are really capable or\nnot of establishing good government from reflection and choice, or\nwhether they are forever destined to depend for their political\nconstitutions on accident and force” (Hamilton 1788). Going\nfurther, David Gauthier argues that any system of moral constraints\nmust be justified to those to whom it is meant to apply. “What\ntheory of morals,” Gauthier asks, “can ever serve any\nuseful purpose unless it can show that all the duties it recommends\nare truly endorsed in each individual’s reason?” (1986,\n1).", "\nThe ultimate goal, then, of social contract theories is to show, in\nthe most general sense, that social (moral, political, legal, etc.)\nrules can be rationally justified. This alone does not, however,\ndistinguish the social contract from other approaches in moral and\npolitical philosophy, all of which attempt to show that moral and\npolitical rules are rationally justifiable in some sense. The true\ndistinctiveness of the social contract approach is that justification\ndoes not rely, for its foundation, on some exogenous reason or truth.\nJustification is generated endogenously by rational agreement (or lack\nof rejection in T. M. Scanlon’s version). That is, the fact that\neveryone in a society, given their individual reasoning, would agree\nto a certain rule or principle is the critical justification for that\nrule or principle.", "\nAlthough contract theorists differ in their account of the reasons of\nindividuals, with some being attracted to more objectivist accounts\n(Scanlon 2013), most follow Hobbes in modeling individual reasons as\nsubjective, motivationally internal, or at least agent-relative. This\nmay be because of skepticism about moral reasons generally (Harman\n1975, Gauthier 1986, Binmore 1998), a conviction about the\noverwhelming importance of self-interest to the social order (Hobbes\n1651, Buchanan 2000 [1975], Brennan and Buchanan 1985), a concern to\ntake seriously the disagreement of individual view in modern society\n(Gaus 2011a, 2016; Muldoon 2017; Moehler 2014, 2015, 2018) or because\nthis approach is consistent with the most well-developed theories of\nrational choice in the social sciences (Binmore 2005, Buchanan 2000\n[1975]). In any case, the reasons individuals have for agreeing to\nsome rules or principles are importantly their own reasons, not\n“good reasons” from the impartial perspective. Of course,\nthose same individuals may care about what they perceive to be the\nimpartial good or some other non-individualistic notion—they\nneed not be egoists—but what they care about, and so their\nreasons will differ from one another. This point, as Rawls highlights\nin his later work, is crucial to understanding political justification\nin a diverse society where members of a society cannot reasonably be\nexpected to have similar conceptions of the good (Rawls 1996). Recent\ncontractarian accounts put even greater weight on heterogeneity\n(Southwood 2010, Gaus 2016, Muldoon 2017, Moehler 2018, Sugden\n2018)." ], "subsection_title": "1.1 Distinctiveness of the Social Contract Approach " }, { "content": [ "\nThe social contract is a model of rational justification that\ntransforms the problem of justification (what reasons individuals\nhave) into a problem of deliberation (what rules they will agree to).\nAs Rawls argues:", "\n[T]he question of justification is settled by working out a problem of\ndeliberation: we have to ascertain which principles it would be\nrational to adopt given the contractual situation. This connects the\ntheory of justice with the theory of rational choice (Rawls 1999, 16).\n", "\nJustification is not a “mere proof” (Rawls 1999a 508), nor\nis it reasoning from given or generally accepted premises to\nconclusions about political legitimacy or morality (Rawls 1980, p.\n518). Rather, the contractual model makes explicit the reasoning that\nconnects our standpoint as persons with determinate interests and\ngoals to our standpoint as citizens.", "\nAt the simplest level, models take something complex and make it\nsimpler. Along these lines, both the economist Ariel Rubinstein (2012)\nand the philosopher Nancy Cartwright (1991) compare models to fables.\nFables are stories that communicate some important lesson in a simple,\neasy-to-understand fashion. Fables, like models, communicate important\ngeneral rules through particular, though fictional, cases.", "\nModels involve abstraction and idealization, but they do more than\nthat: they help us see what our key assumptions are, identify the\nfactors that we see as relevant (Gaus 2016, xv-xvii). Models, as\ntechniques of idealization, do more than abstract (Weisberg 2007a,\n2013). Consider the periodic table of the elements. It is an\nabstraction, but not a model according to Michael Weisberg. He calls\nabstractions like the periodic table abstract direct\nrepresentations to distinguish them from models (2007b). Modeling\nseeks to isolate the important features of the target phenomena,\nallowing the modeler to understand and manipulate important elements\nof the phenomena in simulations. John Rawls’s representatives to\nthe original position, for instance, are not only abstractions of real\npersons. They are idealizations that isolate particular aspects of\npersons that are relevant to justification as a choice, specifically\ntheir thin theory of rationality, and their values (in the form of\nprimary goods). Isolating these features is important for modeling the\nagreement procedure in Rawls’s theory.", "\nGiven this, we can think of social contract theories as having a\ngeneral schematic form. Social contract theories are models of\njustification with several general parameters that are set differently\nin different theories. What distinguishes contractarian theories is\nhow they specify these general parameters (Thrasher 2019). The goal of\nthe model is to represent our reasons for endorsing and complying with\nsome set of social rules, principles, or norms. This is done by\nshowing that our representatives in the model would agree to a given\nset of these rules, principles, or norms in a suitably constructed\nchoice situation. What “suitably constructed” means here\nwill depend on the other parameters in the model.", "\nCritically, there are two sets of relevant individuals (N and\nN*). The first set is the representative choosers\n(N) constructed in the “device of representation”\nsuch as the original position (Rawls 1996, 27). The second set\n(N*) is composed of real individuals whose terms of\ninteraction are to be guided by the contract/agreement. If the\ndeliberations of the contractors (N) are to be relevant to\nthe actual participants (N*), the reasoning of the former\nmust, in some way, be shared by the latter. There is, however,\nconsiderable debate about what it means for reasons to be shared in\nthis sense (see\n Public Reason\n and\n Public Justification).\n The other main parameter in the model is the deliberative setting\n(M), in which the model choosers (N) endorse some\nrules, principles, or norms (R).", "\nGiven all of this, we can identify a general model of social contract\ntheories:", "\nGeneral Model of the Social Contract: N\nchooses R in M and this gives N* reason to\nendorse and comply with R in the real world insofar as the\nreasons N has for choosing R in M can be\nshared by N*.", "\nEach of these parameters (N,M,R,N*) can be specified in any\nnumber of ways. The shape of a particular contractual theory depends\non the precise way these parameters are set in the theory." ], "subsection_title": "1.2 The Social Contract as a Model" } ] }, { "main_content": [], "section_title": "2. Modeling the Parties", "subsections": [ { "content": [ "\nHow contract theorists model the representative choosers (N)\nis determined by our (actual) justificatory problem and what\nis relevant to solving it. A major divide among contemporary social\ncontract theories thus involves defining the justificatory problem. A\ndistinction is often drawn between the Hobbesian/Lockean\n (“contractarian”)\n and Rousseavian/Kantian\n (“contractualist”)\n interpretations of the justificatory problem. These categories are\nimprecise, and there is often as much difference within these two\napproaches as between them, yet, nevertheless, the distinction can be\nuseful for isolating some key disputes in contemporary social contract\ntheory.", "\nAmong those “contractarians” who—very\nroughly—can be called followers of Hobbes and/or Locke, the\ncrucial justificatory task is, as Gauthier (1991, 16) puts it, to\nresolve the “foundational crisis” of morality:", "\nFrom the standpoint of the agent, moral considerations present\nthemselves as constraining his choices and action, in ways independent\nof his desires, aims, and interests…. And so we ask, what\nreason can a person have for recognizing and accepting a constraint\nthat is independent of his desires and interests? … [W]hat\njustifies paying attention to morality, rather than dismissing it as\nan appendage of outworn beliefs?\n", "\nIf our justificatory problem is not simply to understand what morality\nrequires, but whether morality ought to be paid attention to, or\ninstead dismissed as a superstition based on outmoded metaphysical\ntheories, then obviously the parties to the agreement must not employ\nmoral judgments in their reasoning. Another version of this concern is\nGregory Kavka’s (1984) description of the project to reconcile\nmorality with prudence. On both these accounts, the aim of the\ncontract is to show that commitment to morality is an effective way to\nfurther one’s non-moral aims and interests, answering the\nquestion “why be moral?” The political version of this\nproject, is similar, though the target of justification is a set of\npolitical rules or constitution rather than morality generally\n(Buchanan 2000[1975], Coleman 1985, Kavka 1986, Sugden 2018). This\n“contractarian” project is reductionist in a pretty\nstraightforward sense: it derives moral or political reasons from\nnon-moral ones. Or, to use Rawls’s terminology, it attempts to\ngenerate the reasonable out of the rational (1996, 53).", "\nThe reductionist approach is appealing for several reasons. First,\ninsofar as we doubt the normative basis of moral reasons, such a\nreductionist strategy promises to ground morality—or at least a\nvery basic version of it—on the prosaic normativity of the basic\nrequirements of instrumentalist practical rationality (Moehler 2018).\nThe justificatory question “why be moral?” is transformed\ninto the less troubling question “why be rational?”\nSecond, even if we recognize that moral reasons are, in some sense,\ngenuine, contractarians like Kavka also want to show that prudent\nindividuals, not independently motivated by morality would have reason\nto reflectively endorse morality. Furthermore, if we have reason to\nsuspect that some segment of the population is, in fact, knavish then\nwe have good defensive reasons based on stability to build our social\ninstitutions and morality so as to restrain those who are only\nmotivated by prudence, even if we suspect that most persons are not so\nmotivated. Geoffrey Brennan and James Buchanan argue that a version of\nGresham’s law holds in political and social institutions that\n“bad behavior drives out good and that all persons will be led\nthemselves by even the presence of a few self-seekers to adopt\nself-interested behavior” (2008 [1985], 68). We need not think\npeople are mostly self-seeking to think that social institutions and\nmorality should be justified to and restrain those who are.", "\nOn the other hand, “contractualists,” such as Rawls, John\nHarsanyi (1977), Thomas Scanlon (1998), Stephen Darwall (2006),\nNicholas Southwood (2010) and Gerald Gaus (2011) attribute ethical or\npolitical values to the deliberative parties, as well as a much more\nsubstantive, non-instrumentalist form of practical reasoning. The\nkinds of surrogates that model the justificatory problem are already\nso situated that their deliberations will be framed by\nethico-political considerations. The agents’ deliberations are\nnot, as with the Hobbesian theorists, carried out in purely prudential\nor instrumentalist terms, but they are subject to the ‘veil of\nignorance’ or other substantive conditions. Here the core\njustificatory problem is not whether the very idea of moral and\npolitical constraints makes sense, but what sorts of moral or\npolitical principles meet certain basic moral demands, such as\ntreating all as free and equal moral persons, or not subjecting any\nperson to the will or judgment of another (Reiman 1990, chap. 1). This\napproach, then, is non-reductionist in the sense that justification is\nnot derived from the non-moral.", "\nA benefit of the non-reductive approach is that the choosers in the\ncontractual procedure (N) share many of the normative\nconcerns of their actual counterparts (N*). This should\nensure a closer normative link between the two parties and allow for\nthe contract to generate a thicker, more substantive morality,\npresumably closer to that already held by N*. Whether this is\nso, however, depends on how closely the non-reductionist model of\nrationality is to the reasoning of actual individuals.", "\nAt this point, the debate seems to be centered on two positions, which\nwe might call the robustness and sensitivity\npositions. According to the proponents of robustness, whatever else\nmoral agents may disagree about, we can safely assume that they would\nall be committed to basic standards of rationality (Moehler 2013,\n2017, 2018). We should thus suppose this same basic, shared conception\nof rationality and agency: when people fall short of more moralistic\nideals and virtue, the contract will still function. It will be\nrobust. According to this view, we are better off following Hume\n(1741) in assuming every person to be a knave, even though that maxim\nis false in fact.", "\nThe sensitivity position rejects this, holding that, if, in fact,\nindividuals in N* are not resolutely self-interested, the\nproblems of N, resolutely self-interested individuals, and\ntheir contractual solutions, will be inappropriate to N*.\nPerhaps whereas N* can count on social trust, the\nself-interested contractors will find it elusive and arrive at\nsecond-best alternatives that trusting folks would find silly and\ninefficient. Indeed, the sensitivity theorist may insist that even if\nthe self-interested agents can talk themselves into acting as moral\nagents they do so for the wrong sort of reasons (Gaus 2011,\n185ff)." ], "subsection_title": "2.1 Reductionist vs. Non-Reductionist" }, { "content": [ "\nThe core idea of social contract theories, we have been stressing, is\nthat the deliberation of the parties is supposed to model the\njustificatory problem of ordinary moral agents and citizens. Now this\npulls social contract theories in two opposing directions. On the one\nhand, if the deliberations of the hypothetical parties are to model\nour problem and their conclusions are to be of relevance to\nus, the parties must be similar to us. The closer the parties are to\n“you and me” the better their deliberations will model you\nand me, and be of relevance to us. On the other hand, the point of\ncontract theories is to make headway on our justificatory problem by\nconstructing parties that are models of you and me, suggesting that\nsome idealization is necessary and salutary in constructing a model of\njustification. To recognize that some forms of idealization are\nproblematic does not imply that we should embrace what Gaus has called\n“justificatory populism” that every person in society must\nactually assent to the social and moral institutions in question (Gaus\n1996, 130–131). Such a standard would take us back to the older\nsocial contract tradition based on direct consent and as we argue in\n§3, modern contract theories are concerned with appeals to our\nreason, not our self-binding power of consent.", "\nDespite possible problems, there are two important motivations behind\nidealization in the modeling of the deliberative parties. First, you\nand I, as we now are, may be confused about what considerations are\nrelevant to our justificatory problem. We have biases and false\nbeliefs; to make progress on solving our problem of justification we\nwish, as far as possible, to see what the result would be if we only\nreasoned correctly from sound and relevant premises. So in\nconstructing the hypothetical parties we wish to idealize them in this\nway. Ideal deliberation theorists like Jürgen Habermas (1985) and\nSouthwood (2010), in their different ways, are deeply concerned with\nthis reason for idealization. On the face of it, such idealization\ndoes not seem especially troublesome, since our ultimate concern is\nwith what is justified, and so we want the deliberations of the\nparties to track good reasons. But if we idealize too far from\nindividuals and citizens as they presently are (e.g., suppose we posit\nthat they are fully rational in the sense that they know all the\nimplications of all their beliefs and have perfect information) their\ndeliberations may not help much in solving our justificatory problems.\nWe will not be able to identify with their solutions (Suikkanen 2014,\nSouthwood 2019). For example, suppose that hyper-rational and\nperfectly informed parties would have no religious beliefs, so they\nwould not be concerned with freedom of religion or the role of\nreligion of political decision making. But our problem is that among\ntolerably reasonable but far from perfectly rational citizens,\npluralism of religious belief is inescapable. Consequently, to gain\ninsight into the justificatory problem among citizens of limited\nrationality, the parties must model our imperfect rationality." ], "subsection_title": "2.2 Idealization and Identification " }, { "content": [ "\nSocial contract theories model representative choosers (N) so\nas to render the choice situation determinate. This goal of\ndeterminacy, however, can have the effect of eliminating the pluralism\nof the parties that was the original impetus for contracting in the\nfirst place. In his Lectures on the History of Political\nPhilosophy Rawls tells us that “a normalization of\ninterests attributed to the parties” is “common to social\ncontract doctrines” and it is necessary to unify the\nperspectives of the different parties so as to construct a\n“shared point of view” (2007, 226). Here Rawls seems to be\nsuggesting that to achieve determinacy in the contract procedure it is\nnecessary to “normalize” the perspectives of the\nparties.", "\nThe problem is this. Suppose that the parties to the contract closely\nmodel real agents, and so they have diverse bases for their\ndeliberations—religious, secular, perfectionist, and so on. In\nthis case, it is hard to see how the contract theorist can get a\ndeterminate result. Just as you and I disagree, so will the parties.\nRawls (1999, 121) acknowledges that his restrictions on particular\ninformation in the original position are necessary to achieve a\ndeterminate result. If we exclude “knowledge of those\ncontingencies which set men at odds …. ” then since\n“everyone is equally rational and similarly situated, each is\nconvinced by the same arguments”(Rawls 1999, 17, 120). Gaus\n(2011a, 36–47) has argued that a determinative result can only\nbe generated by an implausibly high degree of abstraction, in which\nthe basic pluralism of evaluative standards—the core of our\njustificatory problem—is abstracted away. Thus, on Gaus’s\nview, modelings of the parties that make them anything approaching\nrepresentations of real people will only be able to generate a\nnon-singleton set of eligible social contracts. The parties might\nagree that some social contracts are better than none, but they will\ndisagree on their ordering of possible social contracts. This\nconclusion, refined and developed in (Gaus 2011a, Part Two) connects\nthe traditional problem of indeterminacy in the contract procedure\n(see also Hardin 2003) with the contemporary, technical problem of\nequilibrium selection in games (see Vanderschraaf 2005). A topic we\nwill explore more in §3 below.", "\nIt is possible, however, that determinacy may actually require\ndiversity in the perspective of the deliberative parties in a way that\nRawls and others like Harsanyi didn’t expect. The reason for\nthis is simple, though the proof is somewhat complex. Normalizing the\nperspectives of the parties assumes that there is one stable point of\nview that has all of the relevant information necessary for generating\na stable and determinate set of social rules. There is no reason,\nantecedently, to think that such a perspective can be found, however.\nInstead, if we recognize that there are epistemic gains to be had from\na “division of cognitive labor” there is good reason to\nprefer a diverse rather than normalized idealization of the parties to\nthe contract (see: Weisberg and Muldoon 2009, Gaus 2016, Muldoon 2017,\nMuldoon 2017a, Muldoon 2018). There is reason to conclude that if we\nwish to discover social contracts that best achieve a set of\ninterrelated normative desiderata (e.g., liberty, equality, welfare,\netc.), a deliberative process that draws on a diversity of\nperspectives will outperform one based on a strict normalization of\nperspectives (Gaus 2011b, 2016; Thrasher 2020)." ], "subsection_title": "2.3 Homogeneity vs. Heterogeneity " }, { "content": [ "\nAny representation of the reasoning of the parties will have two\nelements that need to be specified: 1) doxastic and 2) evaluative.\nThese elements, when combined, create a complete model that will\nspecify how and why representatives in the contractual model choose or\nagree to some set of social rules. The first (doxastic) is the\nspecification of everything the representatives in the original\nposition know or at least believe. Choice in the contractual model in\nthe broadest sense, is an attempt by the parties to choose a set of\nrules that they expect will be better than in some baseline condition,\nsuch as “generalized egoism” (Rawls, 1999: 127) a\n“state of nature” (Hobbes 1651) or the rules that they\ncurrently have (Binmore, 2005; Buchanan 2000 [1975]). To do this, they\nneed representations of the baseline and of state of the world under\ncandidate set of rules). Without either of these doxastic\nrepresentations, the choice problem would be indeterminate. Rawls\nfamously imposes severe doxastic constraints on his parties to the\nsocial contract by imposing a thick veil of ignorance that eliminates\ninformation about the specific details of each individual and the\nworld they live in. James Buchanan imposes a similar, but less\nrestrictive “veil of uncertainty” on his representative\nchoosers (Buchanan and Tullock 1965 [1962]; Buchanan 1975; see also\nRawls, 1958).", "\nIn addition to specifying what the representatives believe to be the\ncase about the world and the results of their agreement, there must\nalso be some standard by which the representative parties can evaluate\ndifferent contractual possibilities. They must be able to rank the\noptions on the basis of their values, whatever those may be. Rawls\nmodels parties to the contractual situation as, at least initially,\nhaving only one metric of value: primary goods. They choose the\nconception of justice they do insofar as they believe it will likely\ngenerate the most primary goods for them and their descendants. This\nspecification of the evaluative parameter is uniform across choosers\nand therefore, choice in the original position can be modeled as the\nchoice of one individual. Insofar as there is evaluative diversity\nbetween the representatives, more complex models of agreement will be\nneeded (see §3). If we think in terms of decision theory, the\ndoxastic specification individuates the initial state of affairs and\nthe outcomes of the contractual model, while the specification of the\nevaluative elements gives each representative party a ranking of the\noutcomes expected to result from the choice of any given set of rules.\nOnce these elements are specified, we have a model of the parties to\nthe contract." ], "subsection_title": "2.4 Doxastic vs. Evaluative " } ] }, { "main_content": [ "\nSocial contract theories fundamentally differ in whether the parties\nreason differently or the same. As we have seen (§2.3) in\nRawls’s Original Position, everyone reasons the same: the\ncollective choice problem is reduced to the choice of one individual.\nAny one person’s decision is a proxy for everyone else. In\nsocial contracts of this sort, the description of the parties (their\nmotivation, the conditions under which they choose) does all the work:\nonce we have fully specified the reasoning of one party, the contract\nhas been identified.", "\nThe alternative view is that, even after we have specified the parties\n(including their rationality, values and information), they continue\nto disagree in their rankings of possible social contracts. On this\nview, the contract only has a determinate result if there is some way\nto commensurate the different rankings of each individual to yield an\nagreement (D’Agostino 2003). We can distinguish four basic\nagreement mechanisms of doing this." ], "section_title": "3. Modeling Agreement", "subsections": [ { "content": [ "\nThe traditional social contract views of Hobbes, Locke, and Rousseau\ncrucially relied on the idea of consent. For Locke only “consent\nof Free-men” could make them members of the government (Locke\n1689, §117). In the hands of these theorists—and in much\nordinary discourse—the idea of “consent” implies a\nnormative power to bind oneself. When one reaches “the age of\nconsent” one is empowered to make certain sorts of binding\nagreements—contracts. By putting consent at the center of their\ncontracts these early modern contract theorists (1) were clearly\nsupposing that individuals had basic normative powers over themselves\n(e.g. self-ownership) before they entered into the social contract (a\npoint that Hume (1748) stressed), and (2) brought the question of\npolitical obligation to the fore. If the parties have the power to\nbind themselves by exercising this normative power, then the upshot of\nthe social contract was obligation. As Hobbes (1651, 81 [chap\nxiv,¶7) insisted, covenants bind; that is why they are\n“artificial chains” (1651, 138 [chap. xxi, ¶5).", "\nBoth of these considerations have come under attack in contemporary\nsocial contract theories, especially the second. According to\nBuchanan, the key development of recent social contract theory has\nbeen to distinguish the question of what generates political\nobligation (the key concern of the consent tradition in\nsocial contract thought) from the question of what constitutional\norders or social institutions are mutually beneficial and stable over\ntime (1965). The nature of a person’s duty to abide by\nthe law or social rules is a matter of morality as it pertains to\nindividuals (Rawls 1999, 293ff), while the design and justification of\npolitical and social institutions is a question of public or social\nmorality. Thus, in Buchanan’s view, a crucial feature of more\nrecent contractual thought has been to refocus political philosophy on\npublic or social morality rather than individual obligation. In most\nmodern social contract theories, including Rawls’s, consent and\nobligation play almost no role whatsoever.", "\nAlthough contemporary social contract theorists still sometimes employ\nthe language of consent, the core idea of contemporary social contract\ntheory is agreement. “Social contract views work from\nthe intuitive idea of agreement” (Freeman 2007a, 17). One can\nendorse or agree to a principle without that act of endorsement in any\nway binding one to obey. Social contract theorists as diverse as\nSamuel Freeman and Jan Narveson (1988, 148) see the act of agreement\nas indicating what reasons we have; agreement is a “test”\nor a heuristic (see §5). The “role of unanimous collective\nagreement” is in showing “what we have reasons to do in\nour social and political relations” (Freeman 2007, 19). Thus\nunderstood, the agreement is not itself a binding act—it is not\na performative that somehow creates obligation—but is\nreason-revealing (Lessnoff 1986). If individuals are rational, what\nthey agree to reflects the reasons they have. In contemporary contract\ntheories such as Rawls’s, the problem of justification takes\ncenter stage. Rawls’s revival of social contract theory in A\nTheory of Justice thus did not base obligations on consent,\nthough the apparatus of an “original agreement” persisted.\nRecall that for Rawls (1999, 16) the aim is to settle “the\nquestion of justification … by working out a problem of\ndeliberation.”", "\nGiven that the problem of justification has taken center stage, the\nsecond aspect of contemporary social contract thinking appears to fall\ninto place: its reliance on models of counterfactual agreement. The\naim is to model the reasons of citizens, and so we ask what they would\nagree to under conditions in which their agreements would be expected\nto track their reasons. Contemporary contract theory is,\ncharacteristically, doubly counterfactual. Certainly, no\nprominent theorist thinks that questions of justification are settled\nby an actual survey of attitudes towards existing social arrangements,\nand are not settled until such a survey has been carried out. The\nquestion, then, is not “Are these arrangements\npresently the object of an actual agreement among citizens?” (If\nthis were the question, the answer would typically be\n“No”.) The question, rather, is “Would\nthese arrangements be the object of an agreement if citizens were\nsurveyed?” Although both of the questions are, in some sense,\nsusceptible to an empirical reading, only the latter is in play in\npresent-day theorizing. The contract nowadays is always counterfactual\nin at least this first sense.", "\nThere is a reading of the (first-order) counterfactual question,\n“Would R be the object of agreement if___” which,\nas indicated, is still resolutely empirical in some sense. This is the\nreading where what is required of the theorist is that she try to\ndetermine what an actual survey of actual citizens would reveal about\ntheir actual attitudes towards their system of social arrangements.\n(This is seldom done, of course; the theorist does it in her\nimagination. See, though, Klosko 2000). But there is another\ninterpretation that is more widely accepted in the contemporary\ncontext. On this reading, the question is no longer a counterfactual\nquestion about actual reactions; it is, rather, a\ncounterfactual question about counterfactual\nreactions—it is, as we have said, doubly\ncounterfactual. Framing the question is the first\ncounterfactual element: “Would R be the object of\nagreement if they were surveyed?” Framed by this\nquestion is the second counterfactual element, one which involves the\ncitizens, who are no longer treated empirically, i.e. taken as given,\nbut are, instead, themselves considered from a counterfactual point of\nview—as they would be if (typically) they were better informed\nor more impartial, etc. The question for most contemporary contract\ntheorists, then, is, roughly: “If we surveyed the idealized\nsurrogates of the actual citizens in this polity, what social\narrangements would be the object of an agreement among\nthem?”", "\nFamously, Ronald Dworkin (1975) has objected that a (doubly)\nhypothetical agreement cannot bind any actual person. For the\nhypothetical analysis to make sense, it must be shown that\nhypothetical persons in the contract can agree to endorse and comply\nwith some principle regulating social arrangements. Suppose that it\ncould be shown that your surrogate (a better informed, more impartial\nversion of you) would agree to a principle. What has that to do with\nyou? Where this second-stage hypothetical analysis is employed, it\nseems to be proposed that you can be bound by agreements that\nothers, different from you, would have made. While it might\n(though it needn’t) be reasonable to suppose that you\ncan be bound by agreements that you would yourself have entered into\nif, given the opportunity, it seems crazy to think that you can be\nbound by agreements that, demonstrably, you wouldn’t have made\neven if you had been asked.", "\nThis criticism is decisive, however, only if the hypothetical social\ncontract is supposed to invoke your normative power to self-bind via\nconsent. That your surrogate employs her power to self-bind would not\nmean that you had employed your power. Again, though, the power to\nobligate oneself is not typically invoked in the contemporary social\ncontract: the problem of deliberation is supposed to help us make\nheadway on the problem of justification. So the question for\ncontemporary hypothetical contract theories is whether the\nhypothetical agreement of your surrogate tracks your reasons to accept\nsocial arrangements, a very different issue (Stark 2000).", "\nThis argument has been revived by Jussi Suikkanen (2014) as the claim\nthat certain forms of contract theory, most notably Southwood’s\n(2010) “deliberative” contractualism, commit the\nconditional fallacy. The conditional fallacy is a specific version of\nthe problem we are considering here, namely that a conditional with\ncounterfactual agents, will not necessarily apply if the\ncounterfactual agents are sufficiently different from the real ones it\nis meant to apply to. In response, Southwood (2019) develops what he\ncalls an “advice model” of contractualism wherein we take\nthe counterfactual contractors to generate reasons that should appeal\nto us as advice from a more thoughtful, idealized version of\nourselves, along lines similar to Michael Smith’s (1994) ideal\nadvisor theory of moral reasons. Thrasher (2019) raises a different\nbut related concern that segmented choice in the model of agreement\ncan create outcomes that are not rationalizable to the parties, since\nthey are the result of path-dependent processes.", "\nAs we have argued, contemporary social contract theory rely on\nhypothetical or counterfactual agreement, rather than actual\nagreement. In one sense this is certainly the case. However, in many\nways the “hypothetical/actual” divide is artificial: the\ncounterfactual agreement is meant to model, and provide the basis for,\nactual agreement. All models are counterfactual Understanding\ncontemporary social contract theory is best achieved, not through\ninsisting on the distinction between actual and hypothetical\ncontracts, but by grasping the interplay of the counterfactual and the\nactual in the model of agreement.", "\nRawls (1995) is especially clear on this point in his explication of\nhis model of agreement in response to Habermas. There he distinguishes\nbetween three different perspectives relevant to the assessment of the\nmodel (1996, 28):", "\nThe agreement of the parties in the deliberative model is certainly\ncounterfactual in the two-fold sense we have analyzed: a\ncounterfactual agreement among counterfactual parties. But the point\nof the deliberative model is to help us (i.e., “you and\nme”) solve our justificatory problem—what social\narrangements we can all accept as “free persons who have no\nauthority over one another” (Rawls 1958, 33). The parties’\ndeliberations and the conditions under which they deliberate, then,\nmodel our actual convictions about justice and justification. As Rawls\nsays (1999, 514), the reasoning of the counterfactual parties matters\nto us because “the conditions embodied in the description of\nthis situation are ones that we do in fact accept.” Unless the\ncounterfactual models the actual, the upshot of the agreement could\nnot provide us with reasons. Gaus describes this process as a\n“testing conception” of the social contract (2011a, 425).\nWe use the counterfactual deliberative device of the contract to\n“test” our social institutions. In this way, the\ncontemporary social contract is meant to be a model of the\njustificatory situation that all individuals face. The counterfactual\nand abstracted (see §2) nature of the contract is needed to\nhighlight the relevant features of the parties to show what reasons\nthey have.", "\nSamuel Freeman has recently stressed the way in which focusing on the\nthird perspective—of citizens in a well-ordered\nsociety—also shows the importance of counterfactual agreement in\nRawls’s contract theory. On Freeman’s interpretation, the\nsocial contract must meet the condition of publicity. He\n(2007b:15) writes:", "\nRawls distinguishes three levels of publicity: first, the publicity of\nprinciples of justice; second, the publicity of the general beliefs in\nlight of which first principles of justice can be accepted\n(“that is, the theory of human nature and of social institutions\ngenerally)”; and, third, the publicity of the complete\njustification of the public conception of justice as it would be on\nits own terms. All three levels, Rawls contends, are exemplified in a\nwell-ordered society. This is the “full publicity”\ncondition.\n", "\nA justified contract must meet the full publicity condition: its\ncomplete justification must be capable of being actually accepted by\nmembers of a well-ordered society. The counterfactual agreement itself\nprovides only what Rawls (1996, 386) calls a “pro\ntanto” or “so far as it goes” justification of\nthe principles of justice. “Full justification” is\nachieved only when actual “people endorse and will liberal\njustice for the particular (and often conflicting) reasons implicit in\nthe reasonable comprehensive doctrines they hold” (Freeman\n2007b, 19). Thus understood, Rawls’s concern with the stability\nof justice as fairness, which motivated the move to political\nliberalism, is itself a question of justification (Weithman, 2010).\nOnly if the principles of justice are stable in this way are they\nfully justified. Rawls’s concern with stability and publicity is\nnot, however, idiosyncratic and is shared by all contemporary contract\ntheorists. It is significant that even theorists such as Buchanan\n(2000 [1975], 26–27), Gauthier (1986, 348), and Binmore (2005,\n5–7)—who are so different from Rawls in other\nrespects—share his concern with stability." ], "subsection_title": "3.1 Consent " }, { "content": [ "\nIt is perhaps no surprise that the renaissance in contemporary contact\ntheory occurred at the same time as game-theoretic tools and\nespecially bargaining theory began to be applied to philosophical\nproblems. Bargaining theory, as it was developed by John Nash (1950)\nand John Harsanyi (1977) is a rigorous approach to modeling how\nrational individuals would agree to divide some good or surplus. In\nits most general form, the bargaining model of agreement specifies\nsome set of individuals who have individual utility functions that can\nbe represented in relation to one other without requiring\ninterpersonal comparisons of utility directly. Some surplus is\nspecified and if the individuals involved can agree on how to divide\nthe good in question, they will get that division. If, however, they\ncannot agree they will instead get their disagreement result. This may\nbe what they brought to the table or it could be some other specified\namount. One example is a simple demand game where two people must\nwrite down how much of given pot of money they want. If the two\n“bids” amount to equal or less than the pot, each will get\nwhat he or she wrote down, otherwise each will get nothing.", "\nAs Rawls recognized in his 1958 essay “Justice as\nFairness” one way for parties to resolve their disagreements is\nto employ bargaining solutions, such as that proposed by R.B.\nBraithwaite (1955). Rawls himself rejected bargaining solutions to the\nsocial contract since, in his opinion, such solutions rely on\n“threat advantage” (i.e., disagreement result) and\n“to each according to his threat advantage is hardly a principle\nof fairness” (Rawls 1958, 58n). In addition to Rawls’s\nconcern about threat advantage, a drawback of all such approaches is\nthe multiplicity of bargaining solutions, which can significantly\ndiffer. Although the Nash solution is most favored today, it can have\ncounter-intuitive implications. Furthermore, there are many who argue\nthat bargaining solutions are inherently indeterminate and so the only\nway to achieve determinacy is to introduce unrealistic or\ncontroversial assumptions (Sugden, 1990, 1991; Thrasher 2014). Similar\nproblems also exist for equilibrium selection in games (see\nVanderschraaf 2005 and Harsanyi and Selten 1988).", "\nGauthier famously pursued the bargaining approach, building his Morals\nby Agreement on his bargaining solution, minimax relative concession,\nwhich is equivalent to the Kalai-Smorodinsky bargaining solution in\nthe two-person case (see also Gaus 1990, Ch. IX). Binmore (2005) has\nrecently advanced a version of social contract theory that relies on\nthe Nash bargaining solution, as does Ryan Muldoon (2017) while\nMoehler (2018) relies on a “stabilized” Nash bargaining\nsolution. In later work, Gauthier (1993) shifted from minimax relative\nconcession to the Nash solution. Gauthier has since adopted a less\nformal approach to bargaining that is, nevertheless, closer to his\noriginal solution than to the Nash Solution (2013).", "\nMany of the recent developments in bargaining theory and the social\ncontract have adopted dynamic (Muldoon 2017, Vanderschraaf 2018) or\neven evolutionary approaches to modeling bargaining (Alexander and\nSkyrms 1999, Skyrms 2014). This highlights a general divide in\nbargaining models between what we can call axiomatic and\nprocess models. The traditional, axiomatic, approach to the\nbargaining problem going back to John Nash, codified by John Harsanyi,\nand popularized by R. Duncan Luce and Howard Raiffa (1957). Out of\nthis tradition has come several core bargaining solutions. Each uses a\nslightly different set of axioms to generate a unique and generally\napplicable way to divide a surplus. These include, most notably, the\negalitarian (Raiffa 1953), the Nash (1950), the stabilized Nash\n(Moehler 2010), the Kalai-Smorodinsky (1975), and Gauthier’s\nminimax relative concession (1986). The main point of contention among\nthese theories is whether to employ Nash’s independence axiom or\nto use a monotonicity axiom (as the egalitarian, Kalai-Smorodinsky,\nand minimax relative concession do), although, to one degree or\nanother all of the axioms have been contested.", "\nThe other approach is what we can call a process model.\nInstead of using various axioms to generate a uniquely rational\nsolution, these theorists rely on some procedure that will generate a\ndeterminate, though not always unique result. Process approaches use\nsome mechanism to generate agreement. An example is an auction. There\nare many types of auctions (e.g., English, Dutch, Vickrey, etc.), each\nhas a way of generating bids on some good and then deciding on a\nprice. Posted price selling, like one often sees in consumer markets,\nare also a kind of bargain, though an extremely asymmetric one where\nthe the seller has offered a “take or leave it” ask.\nDouble-auctions are more symmetrical and have a clearer link to the\ninitial bargaining model. Although auctions are not typically used to\nsolve pure division problems, there are some examples of auction\nmechanisms being used to solve public goods problems in interesting\nways that guarantee unanimity (Smith 1977). Dworkin also uses a kind\nof auction mechanism in his work on equality, though he doesn’t\ndevelop his approach for more general application (Dworkin 1981, Heath\n2004). Despite its promise, however, auction theory and its potential\napplication to social contract theory have largely gone\nunexploited.", "\nThe main process approach to bargaining derives from the influential\nwork of Rubinstein (1982) and his proof that it is possible to show\nthat an alternating offer bargaining process will generate the same\nresult as Nash’s axiomatic solution in certain cases. This\nresult added life to Nash’s (1950) early observation that\nbargaining and the rules of bargaining must be the result of some\nnon-cooperative game, with the idea being that it might be possible to\nunify bargaining theory and game theory. This approach, called the\nNash Program, is most notably championed by Binmore (1998), whose\nevolutionary approach to the social contract relies on biological\nevolution (the game of life) to generate the background conditions of\nbargaining (the game of morals). Both can be modeled as\nnon-cooperative games and the later can be modeled as a bargaining\nproblem. By using this approach, Binmore (1998, 2005) claims to be\nable to show, in a robust and non-question-begging way, that something\nvery much like Rawls’s “justice as fairness” will be\nthe result of this evolutionary bargaining process.", "\nA more empirically minded approach follows Schelling’s (1960)\nearly work on bargaining and game theory by looking at the way actual\npeople bargain and reach agreement. The pioneers of experimental\neconomics used laboratory experiments to look at how subjects behaved\nin division problems (Hoffman et. al. 2000, Smith 2003). Some of the\nmost interesting results came, perhaps surprisingly, from asymmetric\nbargaining games like the ultimatum game (Smith 1982). Since these\nearly experiments, considerable experimental work has been done on\nbargaining problems and cooperative agreement in economics. Much of\nthe most philosophically relevant work involves the importance of\nsocial norms and conventions in determining the result (Bicchieri\n2016, Vanderschraaf 2018).", "\nAlthough appealing to a bargaining solution can give determinacy to a\nsocial contract, it does so at the cost of appealing to a\ncontroversial commensuration mechanism in the case of axiomatic\nbargaining or of moving to process approaches that must ultimately\nrely on the empirically contingent outcome of social and biological\nevolution. Although the importance of bargaining in the social\ncontract has been moribund for some time, recent work is changing that\n(see Alexander 2007, Thrasher 2014, Thoma 2015, Muldoon 2017, Moehler\n2018, Vanderschraaf 2018, Bruner 2020)." ], "subsection_title": "3.2 Bargaining" }, { "content": [ "\nWe can distinguish bargaining from aggregation models of agreement.\nRather than seeking an outcome that (as, roughly, the\nKalai-Smorodinsky solution does) splits the difference between various\nclaims, we might seek to aggregate the individual rankings into an\noverall social choice. Arrow’s theorem and related problems with\nsocial choice rules casts doubt on any claim that one specific way of\naggregating is uniquely rational: all have their shortcomings (Gaus\nand Thrasher 2021, chap. 8). Harsanyi (1977, chaps. 1 and 2; 1982)\ndevelops a contractual theory much like Rawls’s using this\napproach. In Harsanyi’s approach, reasoning behind a veil of\nignorance in which people do not know their post-contract identities,\nhe supposes that rational contractors will assume it is equally\nprobable that they will be any specific person. Moreover, he argues\nthat contractors can agree on interpersonal utility comparisons, and\nso they will opt for a contract that aggregates utility at the highest\naverage (see also Mueller 2003, chap. 26). This, of course, depends on\nthe supposition that there is a non-controversial metric that allows\nus to aggregate the parties’ utility functions. Binmore (2005)\nfollows Harsanyi and Amartya Sen (2009, Chap. 13) in arguing that\ninterpersonal comparisons can be made for the purposes of aggregation,\nat least some of the time. John Broome (1995) develops something like\nHarsanyi’s approach that relies on making interpersonal\ncomparisons.", "\nOne of the problems with this approach, however, is that if the\ninterpersonal comparisons are incomplete they will not be able to\nproduce a complete social ordering. As Sen points out, this will lead\nto a maximal set of alternatives where no alternative is dominated by\nany other within the set but also where no particular alternative is\noptimal (Sen, 1997). Instead of solving the aggregation problem, then,\ninterpersonal comparisons may only be able to reduce the set of\nalternatives without being able to complete the ordering of\nalternatives.", "\nBecause of the problems with indeterminacy, many theorists have\nrejected the aggregation approach as being either unworkable or as\nbeing incomplete in some way. Gaus (2011), for instance, uses an\nevolutionary mechanism to generate determinacy in his aggregation\nmodel. Brian Kogelmann (2017) argues, however, that under reasonable\nassumptions about the preferences of the representative agents,\naggregation alone is sufficient to generate determinacy." ], "subsection_title": "3.3 Aggregation" }, { "content": [ "\nThere is a long tradition of thinking of the social contract as a kind\nof equilibrium. Within this tradition, however, the tendency is to see\nthe social contract as some kind of equilibrium solution to a\nprisoner’s dilemma type situation (see Gauthier, 1986 and\nBuchanan, 2000 [1975]). Brian Skyrms (1996, 2004) suggests a different\napproach. Suppose that we have a contractual negotiation in which\nthere are two parties, ordering four possible “social\ncontracts”:", "\nLet 3 be the best outcome, and let 1 be the worst in each\nperson’s ranking (Alf’s ranking is first in each pair). We\nthus get Figure 1", "\nThe Stag Hunt, Skyrms argues, “should be a focal point for\nsocial contract theory” (2004, 4). The issue in the Stag Hunt is\nnot whether we fight or not, but whether we cooperate and gain, or\neach go our separate ways. There are two Nash equilibria in this game:\nboth hunting stag and both hunting hare. Alf and Betty, should they\nfind themselves at one of these equilibria, will stick to it if each\nconsults only his or her own ranking of options. In a Nash\nequilibrium, no individual has a reason to defect. Of course, the\ncontract in which they both hunt stag is a better contract: it is\nPareto superior to that in which they both hunt hare. The Hare\nequilibrium is, however, risk superior in that it is a safer bet.\nSkyrms argues that the theory of iterated games can show not simply\nthat our parties will arrive at a social contract, but how they can\ncome to arrive at the cooperative, mutually beneficial contract. If we\nhave a chance to play repeated games, Skyrms holds, we can learn from\nHume about the “shadow of the future”: “I learn to\ndo a service to another, without bearing him any real kindness;\nbecause I foresee, that he will return my service, in expectation of\nanother of the same kind, and in order to maintain the same\ncorrespondence of good offices with me and with others” (Skyrms\n2004, 5). Sugden, along different lines, also suggests that repeated\ninteractions, what he calls “experience” is essential to\nthe determination of which norms of social interaction actually hold\nover time (1986).", "\nThe problem with equilibrium solutions is that, as in the stag hunt\ngame, many games have multiple equilibria. The problem then becomes\nhow to select one unique equilibrium from a set of possible ones. The\nproblem is compounded by the controversies over equilibrium refinement\nconcepts (see Harsanyi and Selten 1988). Many refinements have been\nsuggested but, as in bargaining theory, all are controversial to one\ndegree or another. One of the interesting developments in social\ncontract theory spurred by game theorists such as Skyrms and Binmore\nis the appeal to evolutionary game theory as a way to solve the\ncommensuration and equilibrium selection problem (Vanderschraaf 2005).\nWhat cannot be solved by appeal to reason (because there simply is no\ndeterminate solution) may be solved by repeated interactions among\nrational parties. The work of theorists such as Skyrms and Binmore\nalso blurs the line between justification and explanation. Their\nanalyses shed light both on the justificatory problem—what are\nthe characteristics of a cooperative social order that people freely\nfollow?—while also explaining how such orders may come\nabout.", "\nThe use of evolutionary game theory and evolutionary techniques is a\nburgeoning and exciting area of contract theory. One of the many\nquestions that arise, however, is that of why, and if so under what\ncircumstances, we should endorse the output of evolutionary\nprocedures. Should one equilibrium be preferred to another merely\nbecause it was the output of an evolutionary procedure? Surely we\nwould want reasons independent of history for reflectively endorsing\nsome equilibrium. This problem highlights the concern that social\ncontracts that are the product of evolutionary procedures will not\nmeet the publicity condition in the right kind of way. If the\npublicity condition seems harder to meet, the evolutionary approach\nprovides a powerful and dynamic way to understand stability. Following\nMaynard Smith (1982), we can see stability as being an evolutionarily\nstable strategy equilibrium or an ESS. Basically, this is the idea\nthat an equilibrium in an evolutionary game where successful\nstrategies replicate at higher rates is stable if the equilibrium\ncomposition of the population in terms of strategies is not\nsusceptible to invasion by a mutant strategy. An ESS is an application\nof the Nash equilibrium concept to populations. A population is\nevolutionarily stable when a mutant strategy is not a better response\nto the population than the current mix of strategies in the\npopulation. This gives a formal interpretation of Rawls’s\nconception of “inherent stability” and to Buchanan’s\nnotion that social contracts should be able to withstand subversion by\na sub-population of knaves. This new conception of stability combined\nwith the dynamic nature of evolutionary games provides interesting new\nways for the social contract theorist to model the output of the\ncontract." ], "subsection_title": "3.4 Equilibrium" } ] }, { "main_content": [ "\nSocial contract theories differ about the object of the contract. In\nthe traditional contract theories of Hobbes and Locke, the contract\nwas about the terms of political association. In particular, the\nproblem was the grounds and limits of citizen’s obligation to\nobey the state. In his early formulation, Rawls’s parties\ndeliberated about “common practices” (1958). In his later\nstatement of his view, Rawls took the object of agreement to be\nprinciples of justice to regulate “the basic\nstructure:”", "\nThe basic structure is understood as the way in which the major social\ninstitutions fit together into one system, and how they assign\nfundamental rights and duties and shape the division of advantages\nthat arises through social cooperation. Thus the political\nconstitution, the legally enforced forms of property, and the\norganization of the economy, and the nature of the family, all belong\nto the basic structure. (Rawls 1996, 258)\n", "\nFor Rawls, as for most contemporary contract theorists, the object of\nagreement is not, at least directly, the grounds of political\nobligation, but the principles of justice that regulate the basic\ninstitutions of society. Freeman (2007a: 23), focuses on “the\nsocial role of norms in public life.” Buchanan is concerned with\njustifying constitutional orders of social and political institutions\n(2000 [1975]). Gauthier (1986), Scanlon (1998), Darwall (2006),\nSouthwood (2010), and Gaus (2011a) employ the contract device to\njustify social moral norms or rules.", "\nThe level at which the object of the contract is described is apt to\naffect the outcome of the agreement. “A striking feature of\nHobbes’ view,” Russell Hardin points out, “is that\nit is a relative assessment of whole states of affairs. Life under one\nform of government versus life under anarchy” (2003, 43). Hobbes\ncould plausibly argue that everyone would agree to the social contract\nbecause “life under government” is, from the perspective\nof everyone, better than “life under anarchy” (the\nbaseline condition). However, if a Hobbesian sought to divide the\ncontract up into, say, more fine-grained agreements about the various\nfunctions of government, she is apt to find that agreement would not\nbe forthcoming on many functions. As we “zoom in” (Lister,\n2010) on more fine-grained functions of government, the contract is\napt to become more limited. If the parties are simply considering\nwhether government is better than anarchy, they will opt for just\nabout any government (including, say, one that funds the arts); if\nthey are considering whether to have a government that funds the arts\nor one that doesn’t, it is easy to see how they may not agree on\nthe former. In a similar way, if the parties are deliberating about\nentire moral codes, there may be wide agreement that all the moral\ncodes, overall, are in everyone’s interests; if we “zoom\nin” in specific rights and duties, we are apt to get a very\ndifferent answer.", "\nIn multi-level contract theories such as we find in the work of\nBuchanan’s (2000 [1975], Moehler’s (2018), or Thrasher\n(2020), each stage or level has its own unique object. In\nBuchanan’s theory, the object of the constitutional stage is a\nsystem of constraints that will allow individuals to peacefully\nco-exist, what Buchanan calls the “protective state” (2000\n[1975]). On his view, the state of nature is characterized by both\npredation and defense. One’s ability to engage in productive\nenterprises is decreased because of the need to defend the fruits of\nthose enterprises against those who would rely on predation rather\nthan production. We all have reason to contract, according to\nBuchanan, in order to increase the overall ability of everyone to\nproduce by limiting the need for defense by constraining the ability\nto engage in predation. Once the solution to the predation-production\nconflict has been solved by the constitutional contract, members of\nsociety also realize that if all contributed to the production of\nvarious public goods, the productive possibility of society would be\nsimilarly increased. This second, post-constitutional stage, involves\nwhat Buchanan calls the “productive state.” Each stage is\nlogically distinct though there are causal relationships between\nchanges made at one stage and the efficacy and stability of the\nsolution at the later stage. The distinction between the two stages is\nanalogous to the traditional distinction between commutative and\ndistributive justice. Although these two are often bound up together\nin contemporary contract theory, one of Buchanan’s novel\ncontributions is to suggest that there are theoretical gains to\nseparating these distinct objects of agreement.", "\nMoehler’s (2017) “multi-level” contract has several\naspects. First, drawing on their pluralistic moral commitments\nindividuals seek to agree on social-moral rules that all can endorse\nas a common morality. This object of this agreement is similar to that\nof Darwall’s, Gaus’s and Southwood’s models. The\nsecond-level agreement is appropriate to circumstances in which\npluralism is so deep and wide no common morality can be forged. Rather\nthan moral agents, the parties are reconceived as instrumentally\nrational prudential agents: the object of this second level is rules\nof cooperation that advance the interests of all when a deeper moral\nbasis cannot be uncovered." ], "section_title": "4. The Object of Agreement", "subsections": [] }, { "main_content": [ "\nSuppose, then, that we have arrived at some social contract. Depending\non the initial justificatory problem, it will yield an outcome\nR (principles, rules, etc. that have some normative property\nL—such as justice, morality, authority, obligation,\nlegitimacy, mutual benefit, and so on. But, supposing that the\ncontract has generated a principle, rule, etc. with the relevant\nnormative property, precisely what is shown by the fact that this\nprinciple or rule was generated through the contractual device?", "\nThroughout we have been distinguishing the justificatory problem from\nthe deliberative model. Now the strongest that could be claimed for a\ncontractual argument is that the outcome of the deliberative model is\nconstitutive of both the correct solution of the\njustificatory problem and the conclusion that “R has\nL.” On this “constructivist” reading of the\noutcome of the deliberative model, there is no independent and\ndeterminate external justification that R has L,\nwhich the contractual device is intended to approximate, but, rather,\nthat R is the outcome of the deliberative model is the\ntruth-maker for “R has L”.", "\nRawls, along with Gauthier and Buchanan, was sometimes attracted to\nsuch a reading. Rawls (1999, 104) describes the argument from the\noriginal position as invoking “pure procedural\njustice”—the deliberative situation is so set up that\nwhatever principles it generates are, by the fact of their\ngeneration, just. But, his considered position is that the outcome of\nthe deliberative model is indicative (not constitutive) of\nthe correct solution to “the question of justification”\n(1999, 16).", "\nWe might say that the deliberative model is evidence of the\nproper answer to the question of justification. However, this is still\nconsistent with Rawls’s “constructivism” because the\nanswer to the justificatory problem is constitutive of\nR’s having L. So we might say that\nRawls’s two principles are just—simply because they are in\nreflective equilibrium with the considered judgments of you and me and\nthat they would be chosen in the original position is indicative of\nthis.", "\nThe weakest interpretation of the contract is that the contractual\nresult is simply indicative of the correct answer to the\njustificatory problem, which itself is simply indicative of the fact\nthat R has L. One could be a “realist,”\nmaintaining that whether R has L is a fact that\nholds whether or not the contract device generates R has\nL, and independently of whether the correct answer to our\njustificatory problem (i.e., what we can justify to each other) is\nthat R has L. There is still logical space for a\ntype of contractualism here, but an indicative contractualism of this\nsort would not be a form of “constructivism.” Some, for\nexample, have argued that Scanlon’s theory is actually based on\na sort of natural rights theory, where these rights are prior to the\ncontract (Mack 2007). Even if this is correct, Scanlon can be a sort\nof social contract theorist. The diversity of possible approaches\nwithin social contract theory indicates the variety of different uses\nto which social contract theory can be applied." ], "section_title": "5. What Does the Contract Show?", "subsections": [] }, { "main_content": [ "\nThe social contract theories of Hobbes, Locke, and Rousseau all\nstressed that the justification of the state depends on showing that\neveryone would, in some way, consent to it. By relying on consent,\nsocial contract theory seemed to suppose a voluntarist conception of\npolitical justice and obligation: what counts as “justice”\nof “obligation” depends on what people agree\nto—whatever that might be. Only in Kant (1797) does it become\nclear that consent is not fundamental to a social contract view: we\nhave a duty to agree to act according to the idea of the\n“original contract.” Rawls’s revival of social\ncontract theory in A Theory of Justice did not base\nobligations on consent, though the apparatus of an “original\nagreement” persisted as a way to help solve the problem of\njustification. As the question of public justification takes center\nstage, it becomes clear that posing the problem of justification in\nterms of a deliberative or a bargaining problem is a heuristic: the\nreal issue is “the problem of justification”—what\nprinciples can be justified to all reasonable citizens or persons." ], "section_title": "6. Conclusion: The Social Contract and Justification", "subsections": [] } ]

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[ "\nSince antiquity, natural philosophers have struggled to comprehend the\nnature of three tightly interconnected concepts: space, time, and\nmotion. A proper understanding of motion, in particular, has been seen\nto be crucial for deciding questions about the natures of space and\ntime, and their interconnections. Since the time of Newton and\nLeibniz, philosophers’ struggles to comprehend these concepts\nhave often appeared to take the form of a dispute between\nabsolute conceptions of space, time and motion, and\nrelational conceptions. This article guides the reader\nthrough some of the history of these philosophical struggles. Rather\nthan taking sides in the (alleged) ongoing debates, or reproducing the\nstandard dialectic recounted in most introductory texts, we have\nchosen to scrutinize carefully the history of the thinking of the\ncanonical participants in these debates – principally Descartes,\nNewton, Leibniz, Mach and Einstein. Readers interested in following up\neither the historical questions or current debates about the natures\nof space, time and motion will find ample links and references\nscattered through the discussion and in the\n Other Internet Resources\n section below." ]

[ { "content_title": "1. Introduction", "sub_toc": [] }, { "content_title": "2. Aristotle", "sub_toc": [] }, { "content_title": "3. Descartes", "sub_toc": [ "3.1 The Nature of Motion", "3.2 Motion and Dynamics" ] }, { "content_title": "4. Newton", "sub_toc": [ "4.1 Newton Against the Cartesian Account of Motion – The Bucket", "4.2 Absolute Space and Motion" ] }, { "content_title": "5. Newtonian Absolute Space in the Twentieth Century", "sub_toc": [ "5.1 The Spacetime Approach", "5.2 Substantivalism" ] }, { "content_title": "6. Leibniz", "sub_toc": [ "6.1 The Ideality of Space", "6.2 Force and the Nature of Motion", "6.3 Motion and Dynamics", "6.4 Where Did the Folk Go Wrong?", "6.5 Leibniz’s Response to Newton’s Scholium" ] }, { "content_title": "7. ‘Not-Newton’ versus ‘Be-Leibniz’", "sub_toc": [ "7.1 Non Sequiturs Mistakenly Attributed to Newton", "7.2 The Best Explanation Argument Mistakenly Attributed to Newton", "7.3 Substantivalism and The Best Explanation Argument" ] }, { "content_title": "8. Beyond Newton", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Works cited in text", "Notable Philosophical Discussions of the Absolute-Relative Debates" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThings change. This is a platitude but still a crucial feature of the\nworld, and one which causes many philosophical perplexities –\nsee for instance the entry on\n Zeno’s paradoxes.\n For Aristotle, motion (he would have called it\n‘locomotion’) was just one kind of change, like\ngeneration, growth, decay, fabrication and so on. The atomists held on\nthe contrary that all change was in reality the motion of atoms into\nnew configurations, an idea that was not to begin to realize its full\npotential until the Seventeenth Century, particularly in the work of\nDescartes. (Of course, modern physics seems to show that the physical\nstate of a system goes well beyond the geometrical configuration of\nbodies. Fields, while perhaps determined by the states of bodies, are\nnot themselves configurations of bodies if interpreted literally, and\nin quantum mechanics bodies have ‘internal states’ such as\nparticle spin.)", "\nNot all changes seem to be merely the (loco)motions of bodies in\nphysical space. Yet since antiquity, in the western tradition, this\nkind of motion has been absolutely central to the understanding of\nchange. And since motion is a crucial concept in physical theories,\none is forced to address the question of what exactly it is. The\nquestion might seem trivial, for surely what is usually meant by\nsaying that something is moving is that it is moving relative\nto something, often tacitly understood between speakers. For instance:\nthe car is moving at 60mph (relative to the road and things along it),\nthe plane is flying (relative) to London, the rocket is lifting off\n(the ground), or the passenger is moving (to the front of the speeding\ntrain). Typically the relative reference body is either the\nsurroundings of the speakers, or the Earth, but this is not always the\ncase. For instance, it seems to make sense to ask whether the Earth\nrotates about its axis West-East diurnally or whether it is instead\nthe heavens that rotate East-West; but if all motions are to be\nreckoned relative to the Earth, then its rotation seems\nimpossible.", "\nBut if the Earth does not offer a unique frame of reference for the\ndescription of motion, then we may wonder whether any arbitrary object\ncan be used for the definition of motions: are all such motions on a\npar, none privileged over any other? It is unclear whether anyone has\nreally consistently espoused this view: Aristotle, perhaps, in the\nMetaphysics. Descartes and Leibniz are often thought to have\ndone so; however, as we’ll see, those claims are suspect.\nPossibly Huygens, though the most recent and thorough reconstruction\nof his position (Stan 2016) indicates not. Mach at some moments\nperhaps. If this view were correct, then the question of whether the\nEarth or heavens rotate would be ill-formed, those alternatives being\nmerely different but equivalent expressions of the facts.", "\nHowever, suppose that, like Aristotle, you take ordinary language\naccurately to reflect the structure of the world. Then you could\nrecognize systematic everyday uses of ‘up’ and\n‘down’ that require some privileged standards – uses\nthat treat things closer to a point at the center of the Earth as more\n‘down’ and motions towards that point as\n‘downwards’. Of course we would likely explain this usage\nin terms of the fact that we and our language evolved in a very\nnoticeable gravitational field directed towards the center of the\nEarth; but for Aristotle, as we shall see, this usage helped identify\nan important structural feature of the universe, which itself was\nrequired for the explanation of weight. Now a further question arises:\nhow should a structure, such as a preferred point in the universe,\nwhich privileges certain motions, be understood? What makes that point\nprivileged? One might expect that Aristotle simply identified it with\nthe center of the Earth, and so relative to that particular body;\nhowever, we shall soon see that he did not adopt that tacit convention\nas fundamental. So the question arises of whether the preferred point\nis somewhere picked out in some other way by the bodies in the\nuniverse – the center of the heavens perhaps? Or is it picked\nout quite independently of the arrangements of matter?", "\nThe issues that arise in this simple theory help to frame the debates\nbetween later physicists and philosophers concerning the nature of\nmotion; in this article, we will focus on the theories of Descartes,\nLeibniz, and Newton. In the companion entry on\n absolute and relational space and motion: post-Newtonian theories,\n we study the approaches followed by Mach, Einstein, and certain\ncontemporary researchers. We will see that similar concerns pervade\nall these works: is there any kind of privileged sense of motion: a\nsense in which things can be said to move or not, not just relative to\nthis or that reference body, but ‘truly’? If so, can this\ntrue motion be analyzed in terms of motions relative to other bodies\n– to some special body, or to the entire universe perhaps? (And\nin relativity, in which distances, times and measures of relative\nmotion are frame-dependent, what relations are relevant?) If not, then\nhow is the privileged kind of motion to be understood, as relative to\nspace itself – something physical but non-material –\nperhaps? Or can some kinds of motion be best understood as not being\nspatial changes – changes of relative location or of place\n– at all?" ], "section_title": "1. Introduction", "subsections": [] }, { "main_content": [ "\nTo see that the problem of the interpretation of spatiotemporal\nquantities as absolute or relative is endemic to almost any kind of\nmechanics one can imagine, we can look to one of the simplest theories\n– Aristotle’s account of natural motion (e.g., On the\nHeavens I.2). According to this theory it is because of their\nnatures, and not because of ‘unnatural’ forces, that that\nheavy bodies move down, and ‘light’ things (air and fire)\nmove up; it is their natures, or ‘forms’, that constitute\nthe gravity or weight of the former and the levity of the latter. This\naccount only makes sense if ‘up’ and ‘down’\ncan be unequivocally determined for each body. According to Aristotle,\nup and down are fixed by the position of the body in question relative\nto the center of the universe, a point coincident with the center of\nthe Earth. That is, the theory holds that heavy bodies naturally move\ntowards the center, while light bodies naturally move away.", "\nDoes this theory involve absolute or merely relative quantities? It\ndepends on the nature of the center. If the center were identified\nwith the center of the Earth, then the theory could be taken to eschew\nabsolute quantities: it would simply hold that the natural motions of\nany body depend on its position relative to another, namely the Earth.\nBut Aristotle is explicit that the center of the universe is not\nidentical with, but merely coincident with the center of the Earth\n(e.g., On the Heavens II.14): since the Earth itself is\nheavy, if it were not at the center it would move there! So the center\nis not identified with any body, and so perhaps direction-to-center is\nan absolute quantity in the theory, not understood fundamentally as\ndirection to some body (merely contingently as such if some body\nhappens to occupy the center). But this conclusion is not clear\neither. In On the Heavens II.13, admittedly in response to a\ndifferent issue, Aristotle suggests that the center itself is\n‘determined’ by the outer spherical shell of the universe\n(the aetherial region of the fixed stars). If this is what he intends,\nthen the natural law prescribes motion relative to another body after\nall – namely up or down with respect to the mathematical center\nof the stars.", "\nIt would be to push Aristotle’s writings too hard to suggest\nthat he was consciously wrestling with the issue of whether mechanics\nrequired absolute or relative quantities of motion, but what is clear\nis that these questions arise in his physics and his remarks impinge\non them. His theory also gives a simple model of how they arise: a\nphysical theory of motion will say that ‘under such-and-such\ncircumstances, motion of so-and-so a kind will occur’ –\nand the question of whether that kind of motion makes sense in terms\nof the relations between bodies alone arises automatically. Aristotle\nmay not have recognized the question explicitly, but we see it as one\nissue in the background of his discussion of the center of the\nuniverse." ], "section_title": "2. Aristotle", "subsections": [] }, { "main_content": [ "\nThe issues are, however, far more explicit in the entry on\n Descartes’ physics;\n and since the form of his theory is different, the ‘kinds of\nmotion’ in question are quite different – as they change\nwith all the different theories that we discuss. For Descartes argued\nin his 1644 Principles of Philosophy (see Book II) that the\nessence of matter is extension (i.e., size and shape), because any\nother attribute of bodies could be imagined away without imagining\naway matter itself. But he also held that extension constitutes the\nnature of space, and hence he concluded that space and matter are one\nand the same thing. An immediate consequence of the identification is\nthe impossibility of the vacuum; if every region of space is a region\nof matter, then there can be no space without matter. Thus\nDescartes’ universe is ‘hydrodynamical’ –\ncompletely full of mobile matter of different sized pieces in motion,\nrather like a bucket full of water and lumps of ice of different\nsizes, which has been stirred around. Since fundamentally the pieces\nof matter are nothing but extension, the universe is in fact nothing\nbut a system of geometric bodies in motion without any\n gaps.[1]" ], "section_title": "3. Descartes", "subsections": [ { "content": [ "\nThe identification of space and matter poses a puzzle about motion: if\nthe space that a body occupies literally is the matter of the body,\nthen when the body – i.e., the matter – moves, so does the\nspace that it occupies. Thus it doesn’t change place, which is\nto say that it doesn’t move after all! Descartes resolved this\ndifficulty by taking all motion to be the motion of bodies relative to\none another, not a literal change of space.", "\nNow, a body has as many relative motions as there are bodies, but it\ndoes not follow that all are equally significant. Indeed, Descartes\nuses several different concepts of relational motion. First there is\n‘change of place’, which is nothing but motion relative to\nthis or that arbitrary reference body (II.13). In this sense no motion\nof a body is privileged, since the speed, direction, and even curve of\na trajectory depends on the reference body, and none is singled out.\nNext, he discusses motion in ‘the ordinary sense’ (II.24).\nThis is often conflated with mere change of arbitrary place, but\nstrictly it differs because according to the rules of ordinary speech\none correctly attributes motion only to bodies whose motion is caused\nby some action, not to arbitrary relative motion. (For\ninstance, a person sitting on a speeding boat is ordinarily said to be\nat rest, since ‘he feels no action in himself’.) This\ndistinction is important in some passages, but arguably not in those\nthat we discuss. Finally, he defined motion ‘properly\nspeaking’ (II.25) to be ‘the transference of one part of\nmatter or of one body, from the vicinity of those bodies immediately\ncontiguous to it and considered as at rest, into the vicinity of\n[some]\n others.’[2]\n Since a body can only be touching one set of surroundings, Descartes\nargued (questionably) that this standard of motion was unique.", "\nWhat we see here is that Descartes, despite holding motion to be the\nmotion of bodies relative to one another, also held there to be a\nprivileged sense of motion; in a terminology sometimes employed by\nwriters of the period (see Rynasiewicz 2019, §3), he held there\nto be a sense of ‘true motion’, over and above the merely\nrelative motions. In logical terms we can make the point this way:\nwhile moves-relative-to is a two-place predicate,\nmoves-properly-speaking is a one-place predicate. (And this,\neven though it is defined in terms of relative motion: let\ncontiguous-surroundings be a function from bodies to their\ncontiguous surroundings, then x\nmoves-properly-speaking is defined as x\nmoves-relative-to-contiguous-surroundings(x).)", "\nThis example illustrates why it is crucial to keep two questions\ndistinct: on the one hand, is motion to be understood in terms of\nrelations between bodies or by invoking something additional,\nsomething absolute; on the other hand, are all relative motions\nequally significant, or is there some ‘true’, privileged\nnotion of motion? Descartes’ views show that eschewing absolute\nmotion is logically compatible with accepting true motion; which is of\ncourse not to say that his definitions of motion are themselves\ntenable." ], "subsection_title": "3.1 The Nature of Motion" }, { "content": [ "\nThere is an interpretational tradition which holds that Descartes only\ntook the first, ‘ordinary’ sense of motion seriously, and\nintroduced the second notion to avoid conflict with the Catholic\nChurch. Such conflict was a real concern, since the censure of\nGalileo’s Copernicanism took place only 11 years before\npublication of the Principles, and had in fact dissuaded\nDescartes from publishing an earlier work, The World. Indeed,\nin the Principles (III.28) he is at pains to explain how\n‘properly speaking’ the Earth does not move, because it is\nswept around the Sun in a giant vortex of matter – the Earth\ndoes not move relative to its surroundings in the vortex.", "\nThe difficulty with the reading, aside from the imputation of\ncowardice to the old soldier, is that it makes nonsense of\nDescartes’ mechanics, a theory of collisions. For instance,\naccording to his laws of collision if two equal bodies strike each\nother at equal and opposite velocities then they will bounce off at\nequal and opposite velocities (Rule I). On the other hand, if the very\nsame bodies approach each other with the very same relative\nspeed, but at different speeds then they will move off together in the\ndirection of the faster one (Rule III). But if the operative meaning\nof motion in the Rules is the ordinary sense, then these two\nsituations are just the same situation, differing only in the choice\nof reference frame, and so could not have different outcomes –\nbouncing apart versus moving off together. It seems\ninconceivable that Descartes could have been confused in such a\ntrivial\n way.[3]", "\nThus Garber (1992, Chapter 6–8) proposes that Descartes actually\ntook the unequivocal notion of motion properly speaking to be the\ncorrect sense of motion in mechanics. Then Rule I covers the case in\nwhich the two bodies have equal and opposite motions relative to\ntheir contiguous surroundings, while Rule VI covers the case in\nwhich the bodies have different motions relative to those\nsurroundings – one is perhaps at rest in its surroundings.\nThat is, exactly what is needed to make the rules consistent is the\nkind of privileged, true, sense of motion provided by Descartes’\nsecond definition. Insurmountable problems with the rules remain, but\nrejecting the traditional interpretation and taking motion properly\nspeaking seriously in Descartes’ philosophy clearly gives a more\ncharitable reading." ], "subsection_title": "3.2 Motion and Dynamics" } ] }, { "main_content": [ "\nNewton articulated a clearer, more coherent, and more physically\nplausible account of motion that any that had come before. Still, as\nwe will see, there have been a number of widely held misunderstandings\nof Newton’s views, and it is not completely clear how best to\nunderstand the absolute space that he postulated." ], "section_title": "4. Newton", "subsections": [ { "content": [ "\nIn an unpublished essay – De Gravitatione (Newton,\n2004) – and in a Scholium to the definitions given in\nhis 1687 Mathematical Principles of Natural Philosophy,\nNewton attacked both of Descartes’ notions of motion as\ncandidates for the operative notion in mechanics. (Newton’s\ncritique is studied in more detail in the entry\n Newton’s views on space, time, and motion.)[4]", "\nThe most famous argument invokes the so-called ‘Newton’s\nbucket’ experiment. Stripped to its basic elements one\ncompares:", "\nAs is familiar from any rotating system, there will be a tendency for\nthe water to recede from the axis of rotation in the latter case: in\n(i) the surface of the water will be flat (because of the\nEarth’s gravitational field) while in (ii) it will be concave.\nThe analysis of such ‘inertial effects’ due to rotation\nwas a major topic of enquiry of ‘natural philosophers’ of\nthe time, including Descartes and his followers, and they would\ncertainly have agreed with Newton that the concave surface of the\nwater in the second case demonstrated that the water was moving in a\nmechanically significant sense. There is thus an immediate problem for\nthe claim that proper motion is the correct mechanical sense of\nmotion: in (i) and (ii) proper motion is anti-correlated with\nthe mechanically significant motion revealed by the surface of the\nwater. That is, the water is flat in (i) when it is in motion relative\nto its immediate surroundings – the inner sides of the bucket\n– but curved in (ii) when it is at rest relative to its\nimmediate surroundings. Thus the mechanically relevant meaning of\nrotation is not that of proper motion. (You may have noticed a small\nlacuna in Newton’s argument: in (i) the water is at rest and in\n(ii) in motion relative to that part of its surroundings constituted\nby the air above it. It’s not hard to imagine small\nmodifications to the example to fill this gap.)", "\nNewton also points out that the height that the water climbs up the\ninside of the bucket provides a measure of the rate of rotation of\nbucket and water: the higher the water rises up the sides, the greater\nthe tendency to recede must be, and so the faster the water must be\nrotating in the mechanically significant sense. But suppose, very\nplausibly, that the measure is unique, that any particular height\nindicates a particular rate of rotation. Then the unique height that\nthe water reaches at any moment implies a unique rate of rotation in a\nmechanically significant sense. And thus motion in the sense of motion\nrelative to an arbitrary reference body is not the mechanical sense,\nsince that kind of rotation is not unique at all, but depends on the\nmotion of the reference body. And so Descartes’ change of place\n(and for similar reasons, motion in the ordinary sense) is not the\nmechanically significant sense of motion." ], "subsection_title": "4.1 Newton Against the Cartesian Account of Motion – The Bucket" }, { "content": [ "\nIn our discussion of Descartes we called the sense of motion operative\nin the science of mechanics ‘true motion’, and the phrase\nis used in this way by Newton in the Scholium. Thus\nNewton’s bucket shows that true (rotational) motion is\nanti-correlated with, and so not identical with, proper motion (as\nDescartes proposed according to the Garber reading); and Newton\nfurther argues that the rate of true (rotational) motion is unique,\nand so not identical with change of place, which is multiple. Newton\nproposed instead that true motion is motion relative to a temporally\nenduring, rigid, 3-dimensional Euclidean space, which he dubbed\n‘absolute space’. Of course, Descartes also defined motion\nas relative to an enduring 3-dimensional Euclidean space; the\ndifference is that Descartes’ space was divided into parts (his\nspace was identical with a plenum of corpuscles) in motion, not a\nrigid structure in which (mobile) material bodies are\nembedded. So according to Newton, the rate of true rotation of the\nbucket (and water) is the rate at which it rotates relative to\nabsolute space. Or put another way, Newton effectively defines the\n1-place predicate x moves-absolutely as x\nmoves-relative-to absolute space; both Newton and Descartes offer\ncompeting 1-place predicates as analyses of x\nmoves-truly.", "\nNewton’s proposal for understanding motion solves the problems\nthat he posed for Descartes, and provides an interpretation of the\nconcepts of constant motion and acceleration that appear in his laws\nof motion. However, it suffers from two notable interpretational\nproblems, both of which were pressed forcefully by Leibniz (in the\nLeibniz-Clarke Correspondence, 1715–1716) – which is not\nto say that Leibniz himself offered a superior account of motion (see\n below).[5]\n First, according to this account, absolute velocity is a well-defined\nquantity: more simply, the absolute speed of a body is the rate of\nchange of its position relative to an arbitrary point of absolute\nspace. But the Galilean relativity of Newton’s laws (see the\nentry on\n space and time: inertial frames)\n means that the evolution of a closed system would have been identical\nif it had been moving at a different (constant) overall velocity: as\nGalileo noted in his (see the entry on\n Galileo Galilei),\n an experimenter cannot determine from observations inside his cabin\nwhether his ship is at rest in harbor or sailing smoothly. Put another\nway, according to Newtonian mechanics, in principle Newton’s\nabsolute velocity cannot be experimentally determined.", "\nSo in this regard absolute velocity is quite unlike acceleration\n(including rotation). Newtonian acceleration is understood in absolute\nspace as the rate of change of absolute velocity, and is, according to\nNewtonian mechanics, generally measurable; for instance by measuring\nthe height that the water ascends the sides of the\n bucket.[6]\n Leibniz argued (rather inconsistently, as we shall see) that since\ndifferences in absolute velocity are unobservable, they are not be\ngenuine differences at all; and hence that Newton’s absolute\nspace, whose existence would entail the reality of such differences,\nmust also be a fiction. Few philosophers today would immediately\nreject a quantity as unreal simply because it was not experimentally\ndeterminable, but this fact does justify genuine doubts about the\nreality of absolute velocity, and hence of absolute space.", "\nThe second problem concerns the nature of absolute space. Newton quite\nclearly distinguished his account from Descartes’ – in\nparticular with regards to absolute space’s rigidity versus\nDescartes’ ‘hydrodynamical’ space, and the\npossibility of the vacuum in absolute space. Thus absolute space is\ndefinitely not material. On the other hand, presumably it is supposed\nto be part of the physical, not mental, realm. In De\nGravitatione, Newton rejected both the traditional philosophical\ncategories of substance and attribute as suitable characterizations.\nAbsolute space is not a substance for it lacks causal powers and does\nnot have a fully independent existence, and yet it is not an attribute\nsince it would exist even in a vacuum, which by definition is a place\nwhere there are no bodies in which it might inhere. Newton proposes\nthat space is what we might call a ‘pseudo-substance’,\nmore like a substance than property, yet not quite a\n substance.[7]\n In fact, Newton accepted the principle that everything that exists,\nexists somewhere – i.e., in absolute space. Thus he viewed\nabsolute space as a necessary consequence of the existence of\nanything, and of God’s existence in particular – hence\nspace’s ontological dependence. Leibniz was presumably unaware\nof the unpublished De Gravitatione in which these particular\nideas were developed, but as we shall see, his later works are\ncharacterized by a robust rejection of any notion of space as a real\nthing rather than an ideal, purely mental entity. This is a view that\nattracts even fewer contemporary adherents, but there is something\ndeeply peculiar about a non-material but physical entity, a worry that\nhas influenced many philosophical opponents of absolute\n space.[8]" ], "subsection_title": "4.2 Absolute Space and Motion" } ] }, { "main_content": [ "\nThis article is largely a historical survey of prominent views.\nHowever, it is hard to fully understand those debates without knowing\nsomething about scientific and mathematical developments have changed\nrecent understanding of the issues. In particular, a spacetime\napproach can clarify the situation with which the interlocutors were\nwrestling, and help clarify their arguments. This is a point widely\nrecognized in the secondary literature, and indeed colors much of what\nis said there (for good and bad, as we shall touch on later). So a\nshort digression into these matters is important for engaging the\nliterature responsibly; that said, while §7 presupposes this\nsection, the reader only interested in §6 could skip this\nsection." ], "section_title": "5. Newtonian Absolute Space in the Twentieth Century", "subsections": [ { "content": [ "\nAfter the development of relativity theory (a topic that we address in\nthe companion article), and its interpretation as a spacetime\ntheory, it was realized that the notion of spacetime had applicability\nto a range of theories of mechanics, classical as well as\nrelativistic. In particular, there is a spacetime geometry –\n‘Galilean’ or ‘neo-Newtonian’ spacetime (the\nterms are interchangeable) – for Newtonian mechanics that solves\nthe problem of absolute velocity; an idea exploited by a number of\nphilosophers from the late 1960s onwards (e.g., Stein 1968, Earman\n1970, Sklar 1974, and Friedman 1983). For details the reader is\nreferred to the entry on\n spacetime: inertial frames,\n but the general idea is that although a spatial distance is\nwell-defined between any two simultaneous points of this spacetime,\nonly the temporal interval is well-defined between non-simultaneous\npoints. Thus things are rather unlike Newton’s absolute space,\nwhose points persist through time and maintain their distances: in\nabsolute space the distance between p-now and q-then\n(where p and q are points) is just the distance\nbetween p-now and q-now. However, Galilean spacetime\nhas an ‘affine connection’ which effectively specifies for\nevery point of every continuous curve, the rate at which the curve is\nchanging from straightness at that point; for instance, the straight\nlines are picked out as those curves whose rate of change from\nstraightness is zero at every\n point.[9]", "\nSince the trajectories of bodies are curves in spacetime, the affine\nconnection determines the rate of change from straightness at every\npoint of every possible trajectory. The straight trajectories thus\ndefined can be interpreted as the trajectories of bodies moving\ninertially (i.e., without forces), and the rate of change from\nstraightness of any trajectory can be interpreted as the acceleration\nof a body following that trajectory. That is, Newton’s First Law\ncan be given a geometric formulation as ‘bodies on which no net\nforces act follow straight lines in spacetime’; similarly, the\nSecond Law can be formulated as ‘the rate of change from\nstraightness of a body’s trajectory is equal to the forces\nacting on the body divided by its mass’. The significance of\nthis geometry is that while acceleration is well-defined, velocity is\nnot – in accordance with the empirical determinability of\nacceleration (generally though not universally) but not of velocity,\naccording to Newtonian mechanics. Thus Galilean spacetime gives a very\nnice interpretation of the choice that nature makes when it decides\nthat the laws of mechanics should be formulated in terms of\naccelerations not velocities. (In fact, there are complications here:\nin light of Newton’s Corollary VI mentioned above, one might\nwonder whether even Galilean spacetime is the appropriate spacetime\nstructure for Newtonian mechanics. Saunders (2013), for example,\nargues that in fact only a yet more impoverished spacetime structure\n– ‘Newton-Huygens spacetime’ – is needed.)" ], "subsection_title": "5.1 The Spacetime Approach" }, { "content": [ "\nPut another way, one can define the predicate x accelerates\nas trajectory(x)\nhas-non-zero-rate-of-change-from-straightness, where\ntrajectory maps bodies onto their trajectories in Galilean\nspacetime. And this predicate, defined this way, applies to the water\nin Newton’s bucket if and only if it is rotating, according to\nNewtonian mechanics formulated in terms of the geometry of Galilean\nspacetime; it is the mechanically relevant sense of\naccelerate in this theory. But this theoretical formulation\nand definition have been given in terms of the geometry of spacetime,\nnot in terms of the relations between bodies; acceleration is\n‘absolute’ in the sense that there is a preferred (true)\nsense of acceleration in mechanics and which is not defined in terms\nof the motions of bodies relative to one another. Note that this sense\nof ‘absolute’ is broader than that of motion relative to\nabsolute space, which we defined earlier. In the remainder of this\narticle we will use it in this new broader sense. The reader should be\naware that the term is used in many ways in the literature, and such\nequivocation often leads to significant misunderstanding.", "\nIf any of this analysis of motion is taken literally then one arrives\nat a position regarding the ontology of spacetime rather like that of\nNewton’s regarding space: it is some kind of\n‘substantial’ (or maybe pseudo-substantial) thing\nwith the geometry of Galilean spacetime, just as absolute space\npossessed Euclidean geometry. This view regarding the ontology of\nspacetime is usually called ‘substantivalism’ (Sklar,\n1974). The Galilean substantivalist usually sees themselves as\nadopting a more sophisticated geometry than Newton but sharing his\nsubstantivalism (though there is plenty of room for debate on\nNewton’s exact ontological views; see DiSalle, 2002, and Slowik\n2016). The advantage of the more sophisticated geometry is that\nalthough it allows the absolute sense of acceleration apparently\nrequired by Newtonian mechanics to be defined, it does not allow one\nto define a similar absolute speed or velocity – x\naccelerates can be defined as a 1-place predicate in terms of\nthe geometry of Galilean spacetime, but not x moves in\ngeneral – and so the first of Leibniz’s problems is\nresolved. Of course we see that the solution depends on a crucial\nshift from speed and velocity to acceleration as the relevant senses\nof ‘motion’: from the rate of change of position to the\nrate of rate of change.", "\nWhile this proposal solves the first kind of problem posed by Leibniz,\nit seems just as vulnerable to the second. While it is true that it\ninvolves the rejection of absolute space as Newton conceived it, and\nwith it the need to explicate the nature of an enduring space, the\npostulation of Galilean spacetime poses the parallel question of the\nnature of spacetime. Again, it is a physical but non-material\nsomething, the points of which may be coincident with material bodies.\nWhat kind of thing is it? Could we do without it? As we shall see\nbelow, some contemporary philosophers believe so." ], "subsection_title": "5.2 Substantivalism" } ] }, { "main_content": [ "\nThere is a ‘folk-reading’ of Leibniz that one often finds\neither explicitly or implicitly in the philosophy of physics\nliterature which takes account of only some of his remarks on space\nand motion. For instance, the quantities captured by Earman’s\n(1999) ‘Leibnizian spacetime’ do not do justice to\nLeibniz’s view of motion (as Earman acknowledges). But it is\nperhaps most obvious in introductory texts (e.g., Huggett 2000).\nAccording to this view, the only quantities of motion are relative\nquantities, relative velocity, acceleration and so on, and all\nrelative motions are equal, so there is no true sense of motion.\nHowever, Leibniz is explicit that other quantities are also\n‘real’, and his mechanics implicitly – but obviously\n– depends on yet others. The length of this section is a\nmeasure, not so much of the importance of Leibniz’s actual\nviews, but the importance of showing what the prevalent folk view\nleaves out regarding Leibniz’s views on the metaphysics of\nmotion and interpretation of mechanics. (For further elaboration of\nthe following points the reader is referred to the entry on\n Leibniz’s philosophy of physics.)", "\nThat said, we shall also see that no one has yet discovered a fully\nsatisfactory way of reconciling the numerous conflicting things that\nLeibniz says about motion. Some of these tensions can be put down\nsimply to his changing his mind (see Cover and Hartz 1988 or Arthur\n2013 for explications of how Leibniz’s views on space\ndeveloped). However, we will concentrate on the fairly short period in\nthe mid 1680–90s during which Leibniz developed his theory of\nmechanics, and was most concerned with its interpretation. We will\nsupplement this discussion with the important remarks that he made in\nhis Correspondence with\n Samuel Clarke\n around 30 years later (1715–1716); this discussion is broadly\nin line with the earlier period, and the intervening period is one in\nwhich he turned to other matters, rather than one in which his views\non space were evolving dramatically." ], "section_title": "6. Leibniz", "subsections": [ { "content": [ "\nArguably, Leibniz’s views concerning space and motion do not\nhave a completely linear logic, starting from some logically\nsufficient basic premises, but instead form a collection of mutually\nsupporting doctrines. If one starts questioning why Leibniz held\ncertain views – concerning the ideality of space, for instance\n– one is apt to be led in a circle. Still, exposition requires\nstarting somewhere, and Leibniz’s argument for the ideality of\nspace in the Correspondence with Clarke is a good place to\nbegin. But bear in mind the caveats made here – this argument\nwas made later than a number of other relevant writings, and its\nlogical relation to Leibniz’s views on motion is complex.", "\nLeibniz (LV.47 – this notation means Leibniz’s Fifth\nletter, section 47, and so on) says that (i) a body comes to have the\n‘same place’ as another once did, when it comes to stand\nin the same relations to bodies we ‘suppose’ to be\nunchanged (more on this later); (ii) that we can define ‘a\nplace’ to be that which any such two bodies have in common (here\nhe claims an analogy with the Euclidean/Eudoxan definition of a\nrational number in terms of an identity relation between ratios); and\nfinally that (iii) space is all such places taken together. However,\nhe also holds that properties are particular, incapable of\nbeing instantiated by more than one individual, even at different\ntimes; hence it is impossible for the two bodies to be in\nliterally the same relations to the unchanged bodies. Thus the thing\nthat we take to be the same for the two bodies – the place\n– is something added by our minds to the situation, and only\nideal. As a result, space, which is constructed from these ideal\nplaces, is itself ideal: ‘a certain order, wherein the mind\nconceives the application of relations’.", "\nContrast this view of space with those of Descartes and of Newton.\nBoth Descartes and Newton claim that space is a real, mind-independent\nentity; for Descartes it is matter, and for Newton a\n‘pseudo-substance’, distinct from matter. And of course\nfor both, these views are intimately tied up with their accounts of\nmotion. Leibniz simply denies the mind-independent reality of space,\nand this too is bound up with his views concerning\n motion.[10]" ], "subsection_title": "6.1 The Ideality of Space" }, { "content": [ "\nSo far (apart from that remark about ‘unchanged’ bodies)\nwe have not seen Leibniz introduce anything more than relations of\ndistance between bodies, which is certainly consistent with the folk\nview of his philosophy. However, Leibniz sought to provide a\nfoundation for the Cartesian/mechanical philosophy in terms of the\nAristotelian/scholastic metaphysics of substantial forms (here we\ndiscuss the views laid out in Sections 17–22 of the 1686\nDiscourse on Metaphysics and the 1695 Specimen of\nDynamics, both in Garber and Ariew 1989). In particular, he\nidentifies primary matter with what he calls its ‘primitive\npassive force’ of resistance to changes in motion and to\npenetration, and the substantial form of a body with its\n‘primitive active force’. It is important to realize that\nthese forces are not mere properties of matter, but actually\nconstitute it in some sense, and further that they are not themselves\nquantifiable. However, because of the collisions of bodies with one\nanother, these forces ‘suffer limitation’, and\n‘derivative’ passive and active forces\n result.[11]\n Derivative passive force shows up in the different degrees of\nresistance to change of different kinds of matter (of ‘secondary\nmatter’ in scholastic terms), and apparently is measurable.\nDerivative active force, however, is considerably more problematic for\nLeibniz. On the one hand, it is fundamental to his account of motion\nand theory of mechanics – motion fundamentally is\npossession of force. But on the other hand, Leibniz endorses the\nmechanical philosophy, which precisely sought to abolish Aristotelian\nsubstantial form, which active force represents. Leibniz’s goal\nwas to reconcile the two philosophies, by providing an Aristotelian\nmetaphysical foundation for modern mechanical science; as we shall\nsee, it is ultimately an open question exactly how Leibniz intended to\ndeal with the inherent tensions in such a view.", "\nThe texts are sufficiently ambiguous to permit dissent, but arguably\nLeibniz intends that one manifestation of derivative active force is\nwhat he calls vis viva – ‘living force’.\nLeibniz had a famous argument with the Cartesians over the correct\ndefinition of this quantity. Descartes defined it as size\ntimes speed – effectively as the magnitude of the\nmomentum of a body. Leibniz gave a brilliant argument (repeated in a\nnumber of places, for instance Section 17 of the Discourse on\nMetaphysics) that it was size times\nspeed2 – so (proportional to) kinetic\nenergy. If the proposed identification is correct then kinetic energy\nquantifies derivative active force according to Leibniz; or looked at\nthe other way, the quantity of virtus (another term used by\nLeibniz for active force) associated with a body determines its\nkinetic energy and hence its speed. As far as the authors know,\nLeibniz never explicitly says anything conclusive about the relativity\nof virtus, but it is certainly consistent to read him (as\nRoberts 2003 does) to claim that there is a unique quantity of\nvirtus and hence ‘true’ (as we have been using\nthe term) speed associated with each body. At the very least, Leibniz\ndoes say that there is a real difference between possession and\nnon-possession of vis viva (e.g., in Section 18 of the\nDiscourse) and it is a small step from there to true, privileged\nspeed. Indeed, for Leibniz, mere change of relative position is not\n‘entirely real’ (as we saw for instance in the\nCorrespondence) and only when it has vis viva as its\nimmediate cause is there some reality to\n it.[12]\n An alternative interpretation to the one suggested here might say\nthat Leibniz intends that while there is a difference between\nmotion/virtus and no motion/virtus, there is somehow\nno difference between any strictly positive values of those\nquantities.", "\nIt is important to emphasize two points about the preceding account of\nmotion in Leibniz’s philosophy. First, motion in the everyday\nsense – motion relative to something else – is\nnot real. Fundamentally motion is possession of virtus,\nsomething that is ultimately non-spatial (modulo its interpretation as\nprimitive force limited by collision). If this reading is right\n– and something along these lines seems necessary if we\naren’t simply to ignore important statements by Leibniz on\nmotion – then Leibniz is offering an interpretation of motion\nthat is radically different from the obvious understanding. One might\neven say that for Leibniz motion is not movement at all! (We will\nleave to one side the question of whether his account is ultimately\ncoherent.) The second point is that however we should understand\nLeibniz, the folk reading simply does not and cannot take account of\nhis clearly and repeatedly stated view that what is real in motion is\nforce not relative motion, for the folk reading allows\nLeibniz only relative motion (and of course additionally,\nmotion in the sense of force is a variety of true motion, again\ncontrary to the folk reading)." ], "subsection_title": "6.2 Force and the Nature of Motion" }, { "content": [ "\nHowever, from what has been said so far it is still possible that the\nfolk reading is accurate when it comes to Leibniz’s views on the\nphenomena of motion, the subject of his theory of mechanics. The case\nfor the folk reading is in fact supported by Leibniz’s\nresolution of the tension that we mentioned earlier, between the\nfundamental role of force/virtus (which we will now take to\nmean mass times speed2) and its\nassociation with Aristotelian form. Leibniz’s way out (e.g.,\nSpecimen of Dynamics) is to require that while considerations\nof force must somehow determine the form of the laws of motion, the\nlaws themselves should be such as not to allow one to determine the\nvalue of the force (and hence true speed). One might conclude that in\nthis case Leibniz held that the only quantities which can be\ndetermined are those of relative position and motion, as the folk\nreading says. But even in this circumscribed context, it is at best\nquestionable whether the interpretation is correct.", "\nConsider first Leibniz’s mechanics. Since his laws are what is\nnow (ironically) often called ‘Newtonian’ elastic\ncollision theory, it seems that they satisfy both of his requirements.\nThe laws include conservation of kinetic energy (which we identify\nwith virtus), but they hold in all inertial frames, so the\nkinetic energy of any arbitrary body can be set to any initial value.\nBut they do not permit the kinetic energy of a body to take on any\nvalues throughout a process. The laws are only Galilean relativistic,\nand so are not true in every frame. Furthermore, according to the laws\nof collision, in an inertial frame, if a body does not collide then\nits Leibnizian force is conserved while if (except in special cases)\nit does collide then its force changes. According to Leibniz’s\nlaws one cannot determine initial kinetic energies, but one certainly\ncan tell when they change. At the very least, there are quantities of\nmotion implicit in Leibniz’s mechanics – change in force\nand true speed – that are not merely relative; the folk reading\nis committed to Leibniz simply missing this obvious fact.", "\nThat said, when Leibniz discusses the relativity of motion –\nwhich he calls the ‘equivalence of hypotheses’ about the\nstates of motion of bodies – some of his statements do suggest\nthat he was confused in this way. For another way of stating the\nproblem for the folk reading is that the claim that relative motions\nalone suffice for mechanics and that all relative motions are on a par\nis a principle of general relativity, and could Leibniz – a\nmathematical genius – really have failed to notice that his laws\nhold only in special frames? Well, just maybe. On the one hand, when\nhe explicitly articulates the principle of the equivalence of\nhypotheses (for instance in Specimen of Dynamics) he tends to\nsay only that one cannot assign initial velocities on the\nbasis of the outcome of a collision, which requires only Galilean\nrelativity. However, he confusingly also claimed (On Copernicanism\nand the Relativity of Motion, also in Garber and Ariew 1989) that\nthe Tychonic and Copernican hypotheses were equivalent. But if the\nEarth orbits the Sun in an inertial frame (Copernicus), then there is\nno inertial frame according to which the Sun orbits the Earth (Tycho\nBrahe), and vice versa: these hypotheses are simply not Galilean\nequivalent (something else Leibniz could hardly have failed to\nrealize). So there is some textual support for Leibniz endorsing\ngeneral relativity for the phenomena, as the folk reading\nmaintains.", "\nA number of commentators have suggested solutions to the puzzle of the\nconflicting pronouncements that Leibniz makes on the subject: Stein\n1977 argues for general relativity, thereby imputing a\nmisunderstanding of his own laws to Leibniz; Roberts 2003 argues for\nGalilean relativity, thereby discounting Leibniz’s apparent\nstatements to the contrary. Jauernig 2004 and 2008 points out that in\nthe Specimen, Leibniz claims that all motions are composed of\nuniform rectilinear motions: an apparently curvilinear motion is\nactually a series of uniform motions, punctuated by discontinuous\ncollisions. This observation allows one to restrict the scope of\nclaims of the kind ‘no motions can be attributed on the basis of\nphenomena’ to inertial motions, and so helps read Leibniz as\nmore consistently advocating Galilean relativity, the reading Jauernig\nfavors (see also Huggett’s 2006 ‘Can Spacetime Help Settle\nAny Issues in Modern Philosophy?’, in the Other Internet\nResources, which was inspired by Jauernig’s work). Note that\neven in a pure collision dynamics the phenomena distinguish a body in\nuniform rectilinear motion over time, from one that undergoes\ncollisions changing its uniform rectilinear motion over time: the laws\nwill hold in the frame of the former, but not in the frame of the\nlatter. That is, apparently contrary to what Jauernig says,\nLeibniz’s account of curvilinear motion does not collapse\nGalilean relativity into general relativity. In that case,\nLeibniz’s specific claims of the phenomenal equivalence of\nCopernican and Tychonic hypotheses still need to be accommodated." ], "subsection_title": "6.3 Motion and Dynamics" }, { "content": [ "\nSo the folk reading simply ignores Leibniz’s metaphysics of\nmotion, it commits Leibniz to a mathematical howler regarding his\nlaws, and it is arguable whether it is the best rendering of his\npronouncements concerning relativity; it certainly cannot be accepted\nunquestioningly. However, it is not hard to understand the temptation\nof the folk reading. In his Correspondence with Clarke,\nLeibniz says that he believes space to be “something merely\nrelative, as time is, … an order of coexistences, as time is an\norder of successions” (LIII.4), which is naturally taken to mean\nthat space is at base nothing but the distance and temporal relations\nbetween bodies. (Though even this passage has its subtleties, because\nof the ideality of space discussed above, and because in\nLeibniz’s conception space determines what sets of relations are\npossible.) And if relative distances and times exhaust the\nspatiotemporal in this way, then shouldn’t all\nquantities of motion be defined in terms of those relations?", "\nWe have seen two ways in which this would be the wrong conclusion to\ndraw. Force seems to involve a notion of speed that is not\nidentified with any relative speed. And (unless the equivalence of\nhypotheses is after all a principle of general relativity), the laws\npick out a standard of constant motion that need not be any constant\nrelative motion. Of course, it is hard to reconcile these quantities\nwith the view of space and time that Leibniz proposes – what is\nspeed in size times speed2 or\nconstant speed if not speed relative to some body or to\nabsolute space? Given Leibniz’s view that space is literally\nideal (and indeed that even relative motion is not ‘entirely\nreal’) perhaps the best answer is that he took force\nand hence motion in its real sense not to be determined by\nmotion in a relative sense at all, but to be primitive monadic\nquantities. That is, he took x moves to be a 1-place\npredicate, but he believed that it could be fully analyzed in terms of\nstrictly monadic predicates: x moves iff x\npossesses-non-zero-derivative-active-force. And this reading\nexplains just what Leibniz took us to be supposing when we\n‘supposed certain bodies to be unchanged’ in the\nconstruction of the idea of space: that they had no force, nothing\ncausing, or making real any motion." ], "subsection_title": "6.4 Where Did the Folk Go Wrong?" }, { "content": [ "\nIt’s again helpful to compare Leibniz with Descartes and Newton,\nthis time regarding motion. Commentators often express frustration at\nLeibniz’s response to Newton’s arguments for absolute\nspace: “I find nothing … in the Scholium that\nproves or can prove the reality of space in itself. However, I grant\nthat there is a difference between an absolute true motion of a body\nand a mere relative change …” (LV.53). Not only does\nLeibniz apparently fail to take the argument seriously, he then goes\non to concede the step in the argument that seems to require absolute\nspace! But with our understanding of Newton and Leibniz, we can see\nthat what he says makes perfect sense (or at least that it is not as\ndisingenuous as it is often taken to be).", "\nNewton argues in the Scholium that true motion cannot be\nidentified with the kinds of motion that Descartes considers; but both\nof these are purely relative motions, and Leibniz is in complete\nagreement that merely relative motions are not true (i.e.,\n‘entirely real’). Leibniz’s ‘concession’\nmerely registers his agreement with Newton against Descartes on the\ndifference between true and relative motion; he surely understood who\nand what Newton was refuting, and it was a position that he had\nhimself, in different terms, publicly argued against at length. But as\nwe have seen, Leibniz had a very different analysis of the difference\nto Newton’s; true motion was not, for him, a matter of motion\nrelative to absolute space, but the possession of quantity of force,\nontologically prior to any spatiotemporal quantities at all. There is\nindeed nothing in the Scholium explicitly directed against\nthat view, and since it does potentially offer an alternative way of\nunderstanding true motion, it is not unreasonable for Leibniz to claim\nthat there is no deductive inference from true motion to absolute\nspace." ], "subsection_title": "6.5 Leibniz’s Response to Newton’s Scholium" } ] }, { "main_content": [], "section_title": "7. ‘Not-Newton’ versus ‘Be-Leibniz’", "subsections": [ { "content": [ "\nThe folk reading which belies Leibniz has it that he sought a theory\nof mechanics formulated in terms only of the relations between bodies.\nAs we’ll see in the companion article, in the Nineteenth\nCentury, Ernst Mach indeed proposed such an approach, but Leibniz\nclearly did not; though certain similarities between Leibniz and Mach\n– especially the rejection of absolute space –\nsurely helps explain the confusion between the two. But not only is\nLeibniz often misunderstood, there are influential misreadings of\nNewton’s arguments in the Scholium, influenced by the\nidea that he is addressing Leibniz in some way. Of course the\nPrincipia was written 30 years before the\nCorrespondence, and the arguments of the Scholium\nwere not written with Leibniz in mind, but Clarke himself suggests\n(CIV.13) that those arguments – specifically those concerning\nthe bucket – are telling against Leibniz. That argument is\nindeed devastating to the parity of all relative motions, but we have\nseen that it is highly questionable whether Leibniz’s\nequivalence of hypotheses amounts to such a view. That said, his\nstatements in the first four letters of the Correspondence\ncould understandably mislead Clarke on this point – it is in\nreply to Clarke’s challenge that Leibniz explicitly denies the\nparity of relative motions. But, interestingly, Clarke does not\npresent a true version of Newton’s argument – despite some\ninvolvement of Newton in writing the replies. Instead of the argument\nfrom the uniqueness of the rate of rotation, he argues that systems\nwith different velocities must be different because the effects\nobserved if they were brought to rest would be different.\nThis argument is of course utterly question begging against a view\nthat holds that there is no privileged standard of rest (the view\nClarke mistakenly attributes to Leibniz)!", "\nAs we discuss further in the companion article, Mach attributed to\nNewton the fallacious argument that because the surface of the water\ncurved even when it was not in motion relative to the bucket, it must\nbe rotating relative to absolute space. Our discussion of Newton\nshowed how misleading such a reading is. In the first place he also\nargues that there must be some privileged sense of rotation, and hence\nnot all relative motions are equal. Second, the argument is ad\nhominem against Descartes, in which context a disjunctive\nsyllogism – motion is either proper or ordinary or relative to\nabsolute space – is argumentatively legitimate. On the other\nhand, Mach is quite correct that Newton’s argument in the\nScholium leaves open the logical possibility that the\nprivileged, true sense of rotation (and acceleration more generally)\nis some species of relative motion; if not motion properly speaking,\nthen relative to the fixed stars perhaps. (In fact Newton rejects this\npossibility in De Gravitatione (1962) on the grounds that it\nwould involve an odious action at a distance; an ironic position given\nhis theory of universal gravity.)" ], "subsection_title": "7.1 Non Sequiturs Mistakenly Attributed to Newton" }, { "content": [ "\nThe kind of folk-reading of Newton that underlies much of the\ncontemporary literature replaces Mach’s interpretation with a\nmore charitable one: for instance, Dasgupta 2015, is a recent\ninfluential presentation of the following dialectic, and its relation\nto\n symmetry\n arguments. According to this reading, Newton’s point is that\nhis mechanics – unlike Descartes’ [special\ncharacter:mdash] could explain why the surface of the\nrotating water is curved, that his explanation involves a privileged\nsense of rotation, and that absent an alternative hypothesis about its\nrelative nature, we should accept absolute space. But our discussion\nof Newton’s argument showed that it simply does not have an\n‘abductive[special character:rsquo], ‘best\nexplanation’ form, but shows deductively, from Cartesian\npremises, that rotation is neither proper nor ordinary motion.", "\nThat is not to say that Newton had no understanding of how such\neffects would be explained in his mechanics. For instance, in\nCorollaries V and VI to the Definitions of the Principles he\nstates in general terms the conditions under which different states of\nmotion are not – and so by implication are –\ndiscernible according to his laws of mechanics. Nor is it to say that\nNewton’s contemporaries weren’t seriously concerned with\nexplaining inertial effects. Leibniz, for instance, analyzed a\nrotating body (in the Specimen). In short, parts of a\nrotating system collide with the surrounding matter and are\ncontinuously deflected, into a series of linear motions that form a\ncurved path. (Though the system as Leibniz envisions it –\ncomprised of a plenum of elastic particles of matter – is far\ntoo complex for him to offer any quantitative model based on this\nqualitative picture. So he had no serious alternative explanation of\ninertial effects.)" ], "subsection_title": "7.2 The Best Explanation Argument Mistakenly Attributed to Newton" }, { "content": [ "\nAlthough the argument is then not Newton’s, it is still an\nimportant response to the kind of relationism proposed by the\nfolk-Leibniz, especially when it is extended by bringing in a further\nexample from Newton’s Scholium. Newton considered a\npair of identical spheres, connected by a cord, too far from any\nbodies to observe any relative motions; he pointed out that their rate\nand direction of rotation could still be experimentally determined by\nmeasuring the tension in the cord, and by pushing on opposite faces of\nthe two globes to see whether the tension increased or decreased. He\nintended this simple example to demonstrate that the project he\nintended in the Principia, of determining the absolute\naccelerations and hence gravitational forces on the planets from their\nrelative motions, was possible. However, if we further specify that\nthe spheres and cord are rigid and that they are the only\nthings in their universe, then the example can be used to point out\nthat there are infinitely many different rates of rotation all of\nwhich agree on the relations between bodies. Since there are no\ndifferences in the relations between bodies in the different\nsituations, it follows that the observable differences\nbetween the states of rotation cannot be explained in terms of the\nrelations between bodies. Therefore, a theory of the kind attributed\nto the folk’s Leibniz cannot explain all the phenomena of\nNewtonian mechanics, and again we can argue abductively for absolute\n space.[13]", "\nThis argument is not Newton’s, neither the premises nor\nconclusion, and must not be taken as a historically accurate reading,\nHowever, that is not to say that the argument is fallacious, and\nindeed many have found it attractive, particularly as a defense not of\nNewton’s absolute space, but of Galilean spacetime. That is,\nNewtonian mechanics with Galilean spacetime can explain the phenomena\nassociated with rotation, while theories of the kind proposed by Mach\ncannot explain the differences between situations allowed by Newtonian\nmechanics; but these explanations rely on the geometric structure of\nGalilean spacetime – particularly its affine connection, to\ninterpret acceleration. And thus – the argument goes –\nthose explanations commit us to the reality of spacetime: a manifold\nof points whose properties include the appropriate geometric ones.\nThis final doctrine, of the reality of spacetime with its component\npoints or regions, distinct from matter, with geometric properties, is\nwhat we earlier identified as ‘substantivalism’.", "\nThere are two points to make about this line of argument. First, the\nrelationist could reply that they need not explain all situations\nwhich are possible according to Newtonian mechanics, because that\ntheory is to be rejected in favor of one which invokes only distance\nand time relations between bodies, but which approximates to\nNewton’s if matter is distributed suitably. Such a relationist\nwould be following Mach’s proposal, which we will discuss in the\nsequel article. Such a position would be satisfactory only to the\nextent that a suitable concrete replacement theory to Newton’s\ntheory is developed; Mach never offered such a theory, but recently\nmore progress has been made (again, see the companion article for\ndiscussion).", "\nSecond, one must be careful in understanding just how the argument\nworks, for it is tempting to gloss it by saying that in Newtonian\nmechanics the affine connection is a crucial part of the explanation\nof the surface of the water in the bucket, and if the spacetime which\ncarries the connection is denied, then the explanation fails too. But\nthis gloss tacitly assumes that Newtonian mechanics can only be\nunderstood in a substantial Galilean spacetime; if an interpretation\nof Newtonian mechanics that does not assume substantivalism can be\nconstructed, then all Newtonian explanations can be given without\npostulating a connection in an ontologically significant sense. Both\nSklar (1974) and van Fraassen (1970) have made proposals along these\nlines.", "\nSklar proposes interpreting ‘true’ acceleration as a\nprimitive quantity not defined in terms of motion relative to\nanything, be it absolute space, a connection or other bodies. (Ray\n1991 points out the family resemblance between this proposal and\nLeibniz’s suggestion that vis viva addresses\nNewton’s Scholium arguments.) Van Fraassen proposes\nformulating mechanics as ‘Newton’s Laws hold in\nsome frame’, so that the form of the laws and the\ncontingent relative motions of bodies – not absolute space or a\nconnection, or even any instantaneous relations – pick out a\nstandard of true motion, namely with respect to such an\n‘inertial frame’. These proposals aim to keep the full\nexplanatory resources of Newtonian mechanics, and hence admit\n‘true acceleration’, but deny any relations between bodies\nand spacetime itself. Like the actual Leibniz, they allow absolute\nquantities of motion, but claim that space and time themselves are\nnothing but the relations between bodies.", "\nSome may question how the laws can be such as to privilege frames\nwithout prior spacetime geometry. In reply, Huggett 2006 proposes that\nthe laws be understood as a Humean ‘best system’ (see the\nentry on\n laws of nature)\n for a world of bodies and their relations; the laws don’t\nreflect prior geometric structure, but systematic regularities in\npatterns of relative motions. For obvious reasons, this proposal is\ncalled ‘regularity relationism’. (Several authors have\ndeveloped a similar approach to a variety of physical theories: for\ninstance, Vassallo & Esfeld 2016.) This approach is committed to\nthe idea that in some sense Newton’s laws are capable of\nexplaining all the phenomena without recourse to spacetime geometry;\nthat the connection and the metrical properties are explanatorily\nredundant. This idea is also at the core of the ‘Dynamical\nApproach’, discussed in the companion article.", "\nAnother approach is to consider fully spatiotemporal relations. For\ninstance, Maudlin 1993 discusses the possibility of a ‘Newtonian\nrelationism’ which adds cross-temporal distance\nrelations, i.e., distances between bodies at distinct moments of time.\nWith such distances, relationists can capture (almost) the full\nstructure of Newtonian space, and time, including the affine structure\nrequired for Newton’s first and second laws." ], "subsection_title": "7.3 Substantivalism and The Best Explanation Argument" } ] }, { "main_content": [ "\nIn sum: we have seen how historical authors, from Aristotle through to\nNewtonian and Leibniz, tackled the puzzles of motion and change in\nphysical theorising. In a sequel entry on\n absolute and relational space and motion: post-Newtonian theories,\n we will see how post-Newtonian authors, from Mach through to Einstein\nand other contemporary physicists and philosophers, have brought new\nconceptual and technical resources to bear on (arguably) the selfsame\nissues. The sequel also includes a longer conclusion, reflecting on\nthe themes running through both articles.", "\nFor now we will just note that we have focussed on authors who made\ncontributions to the science of mechanics, and so a significant\nphilosophical lacuna is a discussion of Kant’s views on space\nand motion. For recent treatments, see Friedman 2013 and Stan\n2015." ], "section_title": "8. Beyond Newton", "subsections": [] } ]

[ "Aristotle, 1984, The Complete Works of Aristotle: The Revised\nOxford Translation, J. Barnes (ed.), Princeton: Princeton\nUniversity Press.", "Arthur, R.T., 2013, “Leibniz’s theory of space,”\nFoundations of Science, 18(3), pp.499–528.", "Biener, Z., 2017, “De Gravitatione Reconsidered: The\nChanging Significance of Experimental Evidence for Newton’s\nMetaphysics of Space,” Journal of the History of\nPhilosophy, 55(4), pp.583–608.", "Brill, D. R. and Cohen, J., 1966, “Rotating Masses and their\neffects on inertial frames,” Physical Review 143:\n1011–1015.", "Dasgupta, S., 2015, “Substantivalism vs relationalism about\nspace in classical physics,” Philosophy Compass, 10(9),\npp.601–624.", "Descartes, R., 1983, Principles of Philosophy, R. P.\nMiller and V. R. Miller (trans.), Dordrecht: D. Reidel.", "Earman, J., 1970, “Who’s Afraid of Absolute\nSpace?,” Australasian Journal of Philosophy, 48:\n287–319.", "Friedman, M., 2013, Space in Kantian idealism. Space: A\nHistory (Oxford Philosophical Concepts), A. Janiak (ed.), New\nYork: Oxford University Press.", "–––, 1983, Foundations of Space-Time\nTheories: Relativistic Physics and Philosophy of Science,\nPrinceton: Princeton University Press.", "Garber, D., 1992, Descartes’ Metaphysical Physics,\nChicago: University of Chicago Press.", "Garber, D. and J. B. Rauzy, 2004, “Leibniz on Body, Matter\nand Extension,” The Aristotelian Society (Supplementary\nVolume), 78: 23–40.", "Hartz, G. A. and J. A. Cover, 1988, “Space and Time in the\nLeibnizian Metaphysic,” Noûs, 22:\n493–519.", "Huggett, N., 2012, “What Did Newton Mean by ‘Absolute\nMotion’,” in Interpreting Newton: Critical\nEssays, A. Janiak and E. Schliesser (eds.), Cambridge: Cambridge\nUniv Press, 196–218.", "–––, 2006, “The Regularity Account of\nRelational Spacetime,” Mind, 115: 41–74.", "–––, 2000, “Space from Zeno to Einstein:\nClassic Readings with a Contemporary Commentary,”\nInternational Studies in the Philosophy of Science, 14:\n327–329.", "Janiak, A., 2015, Space and motion in nature and Scripture:\nGalileo, Descartes, Newton. Studies in History and Philosophy of\nScience Part A, 51, pp.89–99.", "Jauernig, A., 2008, “Leibniz on Motion and the Equivalence\nof Hypotheses,” The Leibniz Review, 18:\n1–40.", "–––, 2004, Leibniz Freed of Every Flaw: A\nKantian Reads Leibnizian Metaphysics, Ph.D. Dissertation,\nPrinceton University.", "Leibniz, G. W., 1989, Philosophical Essays, R. Ariew and\nD. Garber (trans.), Indianapolis: Hackett Pub. Co.", "Leibniz, G. W., and Samuel Clarke, 1715–1716,\n“Correspondence”, in The Leibniz-Clarke\nCorrespondence, Together with Extracts from Newton’s\n“Principia” and “Opticks”, H. G.\nAlexander (ed.), Manchester: Manchester University Press, 1956.", "Maudlin, T., 1993, “Buckets of Water and Waves of Space: Why\nSpace-Time is Probably a Substance,” Philosophy of\nScience, 60: 183–203.", "Newton, I. and I. B. Cohen, 1999, The Principia: Mathematical\nPrinciples of Natural Philosophy, I. B. Cohen and A. M. Whitman\n(trans.), Berkeley: University of California Press.", "Pooley, O., 2002, The Reality of Spacetime, D. Phil.\nthesis, Oxford: Oxford University.", "Ray, C., 1991, Time, Space and Philosophy, New York:\nRoutledge.", "Roberts, J. T., 2003, “Leibniz on Force and Absolute\nMotion,” Philosophy of Science, 70: 553–573.", "Rynasiewicz, R., 2019, “Newton’s Scholium on Time,\nSpace, Place and Motion,” in The Oxford Handbook of\nNewton, E. Schliesser and C. Smeenk (eds.), published online 8\nJanuary 2019. doi:10.1093/oxfordhb/9780199930418.013.28\n [Preprint available online]", "–––, 1995, “By their Properties, Causes,\nand Effects: Newton’s Scholium on Time, Space, Place, and Motion\n– I. The Text,” Studies in History and Philosophy of\nScience, 26: 133–153.", "Sklar, L., 1974, Space, Time and Spacetime, Berkeley:\nUniversity of California Press.", "Slowik, E., 2016, Deep Metaphysics of Space, Cham,\nSwitzerland: Springer.", "Stan, M., 2015, “Absolute Space and the Riddle of Rotation:\nKant’s Response to Newton”. Oxford Studies in Early\nModern Philosophy, vol. 7, Daniel Garber and Donald Rutherford\n(eds.), pp. 257–308. Oxford: Oxford University Press.", "Stan, M., 2016, “Huygens on Inertial Structure and\nRelativity,” Philosophy of Science, 83(2),\npp.277-298.", "Stein, H., 1977, “Some Philosophical Prehistory of General\nRelativity,” in Minnesota Studies in the Philosophy of\nScience 8: Foundations of Space-Time Theories, J. Earman, C.\nGlymour and J. Stachel (eds.), Minneapolis: University of Minnesota\nPress.", "–––, 1967, “Newtonian Space-Time,”\nTexas Quarterly, 10: 174–200.", "Van Fraassen, B. C., 1970, An introduction to the philosophy\nof time and space, New York: Columbia University Press.", "Vassallo, A. and M. Esfeld, 2016, “Leibnizian relationalism\nfor general relativistic physics,” Studies in History and\nPhilosophy of Science Part B: Studies in History and Philosophy of\nModern Physics, 55. pp. 101–107.", "Barbour, J. B., 1982, “Relational Concepts of Space and\nTime,” British Journal for the Philosophy of Science,\n33: 251–274.", "Belot, G., 2000, “Geometry and Motion,” British\nJournal for the Philosophy of Science, 51: 561–595.", "Butterfield, J., 1984, “Relationism and Possible\nWorlds,” British Journal for the Philosophy of Science,\n35: 101–112.", "Callender, C., 2002, “Philosophy of Space-Time\nPhysics,” in The Blackwell Guide to the Philosophy of\nScience, P. Machamer (ed.), Cambridge: Blackwell, pp.\n173–198.", "Carrier, M., 1992, “Kant’s Relational Theory of\nAbsolute Space,” Kant Studien, 83: 399–416.", "Dasgupta, S., 2015, “Substantivalism vs Relationalism About\nSpace in Classical Physics”, Philosophy Compass 10, pp.\n601–624.", "Dieks, D., 2001, “Space-Time Relationism in Newtonian and\nRelativistic Physics,” International Studies in the\nPhilosophy of Science, 15: 5–17.", "DiSalle, R., 2006, Understanding Space-Time, Cambridge:\nCambridge University Press.", "Disalle, R., 1995, “Spacetime Theory as Physical\nGeometry,” Erkenntnis, 42: 317–337.", "Earman, J., 1986, “Why Space is Not a Substance (at Least\nNot to First Degree),” Pacific Philosophical Quarterly,\n67: 225–244.", "–––, 1970, “Who’s Afraid of Absolute\nSpace?,” Australasian Journal of Philosophy, 48:\n287–319.", "Earman, J. and J. Norton, 1987, “What Price Spacetime\nSubstantivalism: The Hole Story,” British Journal for the\nPhilosophy of Science, 38: 515–525.", "Hoefer, C., 2000, “Kant’s Hands and Earman’s\nPions: Chirality Arguments for Substantival Space,”\nInternational Studies in the Philosophy of Science, 14:\n237–256.", "–––, 1998, “Absolute Versus Relational\nSpacetime: For Better Or Worse, the Debate Goes on,” British\nJournal for the Philosophy of Science, 49: 451–467.", "–––, 1996, “The Metaphysics of Space-Time\nSubstantialism,” Journal of Philosophy, 93:\n5–27.", "Huggett, N., 2000, “Reflections on Parity\nNonconservation,” Philosophy of Science, 67:\n219–241.", "Le Poidevin, R., 2004, “Space, Supervenience and\nSubstantivalism,” Analysis, 64: 191–198.", "Malament, D., 1985, “Discussion: A Modest Remark about\nReichenbach, Rotation, and General Relativity,” Philosophy\nof Science, 52: 615–620.", "Maudlin, T., 1993, “Buckets of Water and Waves of Space: Why\nSpace-Time is Probably a Substance,” Philosophy of\nScience, 60: 183–203.", "–––, 1990, “Substances and Space-Time:\nWhat Aristotle would have Said to Einstein,” Studies in\nHistory and Philosophy of Science, 21(4): 531–561.", "Maudlin, T., 2012, Philosophy of Physics: Space and Time,\nPrinceton, NJ: Princeton University Press.", "Mundy, B., 1992, “Space-Time and Isomorphism,”\nProceedings of the Biennial Meetings of the Philosophy of Science\nAssociation, 1: 515–527.", "–––, 1983, “Relational Theories of\nEuclidean Space and Minkowski Space-Time,” Philosophy of\nScience, 50: 205–226.", "Nerlich, G., 2003, “Space-Time Substantivalism,” in\nThe Oxford Handbook of Metaphysics, M. J. Loux (ed.), Oxford:\nOxford Univ Press, 281–314.", "–––, 1996, “What Spacetime\nExplains,” Philosophical Quarterly, 46:\n127–131.", "–––, 1994, What Spacetime Explains:\nMetaphysical Essays on Space and Time, New York: Cambridge\nUniversity Press.", "–––, 1973, “Hands, Knees, and Absolute\nSpace,” Journal of Philosophy, 70: 337–351.", "Pooley, O., 2013 “Substantivalism and Relationalism About\nSpace and Time”, in R. Batterman (ed.), The Oxford Handbook\nof Philosophy of Physics, OUP.", "Rynasiewicz, R., 2000, “On the Distinction between Absolute\nand Relative Motion,” Philosophy of Science, 67:\n70–93.", "–––, 1996, “Absolute Versus Relational\nSpace-Time: An Outmoded Debate?,” Journal of\nPhilosophy, 93: 279–306.", "Teller, P., 1991, “Substance, Relations, and Arguments about\nthe Nature of Space-Time,” Philosophical Review,\n363–397.", "Torretti, R., 2000, “Spacetime Models for the World,”\nStudies in History and Philosophy of Modern Physics (Part B),\n31(2): 171–186." ]

[ { "href": "../descartes-physics/", "text": "Descartes, René: physics" }, { "href": "../genrel-early/", "text": "general relativity: early philosophical interpretations of" }, { "href": "../newton-stm/", "text": "Newton, Isaac: views on space, time, and motion" }, { "href": "../spacetime-theories/", "text": "space and time: absolute and relational space and motion, post-Newtonian theories" }, { "href": "../spacetime-holearg/", "text": "space and time: the hole argument" }, { "href": "../paradox-zeno/", "text": "Zeno of Elea: Zeno’s paradoxes" } ]

[ "\nWhat is the nature of motion in physical theories and theorising, and\nis there any significance to the distinction between\n‘absolute’ and ‘relative’ motion? In the\ncompanion article, on\n absolute and relational space and motion: classical theories,\n we discussed how such questions were addressed in the history of\nphysics from Aristotle through to Newton and Leibniz. In this article,\nwe explore the ways in which the selfsame issues have been taken up by\ncontemporary authors, beginning with Mach, moving on to Einstein, and\nconcluding with a discussion of two highly relevant modern research\nprogrammes: shape dynamics and the so-called ‘dynamical\napproach’ to spacetime. Readers interested in following up\neither the historical or the current debates about the natures of\nspace, time and motion will find ample links and references scattered\nthrough the discussion and in the\n Other Internet Resources\n section below.", "\nThe reader should note at the outset that this article presupposes\nfamiliarity with some of the basic concepts of relativity theory; in\naddition, section 3 presupposes familiarity with some relativity\nstandard machinery from theoretical physics (e.g., Lagrangian\nmechanics). It would not be appropriate, in this philosophical\narticle, to explain all of the background details here from the ground\nup. In lieu of doing so, we have (a) provided extensive references to\nliterature in which the relevant concepts are explained further, (b)\nhighlighted more technical subsections of this article which can be\nskipped on first reading, and (c) provided throughout non-technical\nsummaries of the relevant conceptual points. " ]

[ { "content_title": "1. Mach", "sub_toc": [ "1.1 Two Interpretations of Mach on Inertia", "1.2 Implementing Mach-heavy", "1.3 Mach-lite versus Mach-heavy" ] }, { "content_title": "2. Einstein", "sub_toc": [ "2.1 Relations Determine State of Motion?", "2.2 The Relationist Roots of STR and GTR", "2.3 From Special Relativity to General Relativity", "2.4 General Relativity and Relativity of Motion" ] }, { "content_title": "3. Shape Dynamics", "sub_toc": [ "3.1. Configuration Space", "3.2. Emergent Temporality", "3.3. Best Matching", "3.4. Relativistic Best Matching", "3.5. Conceptual Matters" ] }, { "content_title": "4. The Dynamical Approach", "sub_toc": [ "4.1 The Dynamical Approach and Regularity Relationism", "4.2 Space-time and Explanation on the Dynamical Approach", "4.3 The Dynamical Approach and General Relativity" ] }, { "content_title": "5. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Works cited in text", "Notable Philosophical Discussions of the Absolute-Relative Debates" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nBetween the time of Newton and Leibniz and the 20th century,\nNewton’s mechanics and gravitation theory reigned essentially\nunchallenged, and with that long period of dominance, Newton’s\nabsolute space came to be widely accepted. At least, no natural\nphilosopher or physicist offered a serious challenge to Newton’s\nabsolute space, in the sense of offering a rival theory that dispenses\nwith it. But like the action at a distance in Newtonian gravity,\nabsolute space continued to provoke philosophical unease. Seeking a\nreplacement for the unobservable Newtonian space, Neumann (1870) and\nLange (1885) developed more concrete definitions of the reference\nframes in which Newton’s laws \n hold.[1]\n In these and a few other works, the concept of the set of\ninertial frames (those in which material bodies obey Newton’s\nthree laws of motion) was first clearly expressed, though it was\nimplicit in both remarks and procedures found in Newton’s\nPrincipia. (See the entries on\n space and time: inertial frames\n and\n Newton’s views on space, time, and motion)\n The most sustained, comprehensive, and influential attack on absolute\nspace was made by Ernst Mach in his Science of Mechanics\n(1883).", "\nIn a lengthy discussion of Newton’s Scholium on\nabsolute space, Mach accuses Newton of violating his own\nmethodological precepts by going well beyond what the observational\nfacts teach us concerning motion and acceleration. Mach at least\npartly misinterpreted Newton’s aims in the Scholium,\nand inaugurated a reading of Newton’s bucket argument (and by\nextension the globes argument) that has largely persisted in the\nliterature since. (See\n absolute and relational space and motion: classical theories,\n section 4, for discussion of Newton’s bucket argument.) Mach viewed\nthe argument as directed against a ‘strict’ or\n‘general-relativity’ form of relationism, and as an\nattempt to establish the existence of absolute space. (Strict\nrelationism denies that there is any such thing as an absolute motion;\nall motion is merely relative, i.e., is nothing more than changes of\nlocation relative to some arbitrarily chosen reference frame.) Mach\npoints out the obvious gap in the argument when so construed: the\nexperiment only establishes that acceleration (rotation) of the water\nwith respect to the Earth, or the frame of the fixed stars,\nproduces the tendency to recede from the center; it does not prove\nthat a strict relationist theory cannot account for the bucket\nphenomena, much less the existence of absolute space.", "\nThe reader of the entry on\n absolute and relational space and motion: classical theories\n will recall that Newton’s actual aim was simply to show that\nDescartes’ two kinds of motion are not adequate to account for\nrotational phenomena. Newton’s bucket argument showed that the\neffects of rotational motion could not be accounted for by means of\nthe motion of the water relative to its immediate surroundings (the\nbucket walls); Newton’s thought experiment with two globes\nconnected by a cord was meant to show that one can determine whether\nthey are rotating about their common center (and if so, in which\ndirection) without needing any reference to anything external. By\npushing on opposite faces of the two globes and checking for an\nincrease or decrease in the tension in the cord, one can determine in\nwhich sense the spheres are in rotation, if they are rotating at\nall.", "\nAlthough Mach does not mention the globes thought experiment\nspecifically, it is easy to read an implicit response to it in the\nthings he does say: nobody is competent to say what would happen, or\nwhat would be possible, in a universe devoid of matter other than two\nglobes. In other words, Mach would question Newton’s starting\npremise that the cord connecting the two globes in an otherwise empty\nuniverse might be under tension, and indeed under a wide range of\ndifferent quantities of tension. So, for Mach, neither the bucket nor\nthe globes can establish the existence of absolute space." ], "section_title": "1. Mach", "subsections": [ { "content": [ "\nBoth in Mach’s interpretations of Newton’s arguments and\nin his replies, one can already see two anti-absolute space viewpoints\nemerge, though Mach himself never fully kept them apart. The first\nstrain, which we may call ‘Mach-lite’, criticizes\nNewton’s postulation of absolute space as a metaphysical leap\nthat is neither justified by actual experiments, nor methodologically\nsound. The remedy offered by Mach-lite is simple: we should retain\nNewton’s mechanics and use it just as we already do, but\neliminate the unnecessary posit of absolute space. In its place we\nneed only substitute the reference frame of the fixed stars, as is the\npractice in astronomy in any case. If we find the incorporation of a\nreference to contingent circumstances (the existence of a single\nreference frame in which the stars are more or less stationary) in the\nfundamental laws of nature problematic (which Mach need not, given his\nofficial positivist account of scientific laws), then Mach suggests\nthat we replace the 1st law with an empirically equivalent\nmathematical rival, such as this one:", "\nMach’s Equation (1960, 287)\n\n\n\\[ \\frac{d^2 (\\frac{\\Sigma mr}{\\Sigma m})}{dt^2} = 0 \\]", "\nIn this equation the sums are to be taken over all massive bodies in\nthe universe. Since the top sum is weighted by distance, distant\nmasses count much more than near ones. In a world with a (reasonably)\nstatic distribution of heavy distant bodies, such as we appear to live\nin, the equation entails that the velocity of a free body will be\nconstant (to an extremely good approximation) in precisely those\nframes that we already consider to be ‘inertial’ frames.\nThe upshot of this equation is that the frame of the fixed stars plays\nthe role of absolute space in the statement of the 1st law. This\nproposal does not, by itself, offer an alternative to Newtonian\nmechanics, and as Mach himself pointed out, the law is not\nwell-behaved in an infinite universe filled with stars; but the same\ncan perhaps be said of Newton’s law of gravitation (see Malament\n1995, and Norton 1993). But Mach did not offer this equation as a\nproposed law valid in any circumstances; he avers, “it is\nimpossible to say whether the new expression would still represent the\ntrue condition of things if the stars were to perform rapid movements\namong one another.” (p. 289)", "\nIt is not clear whether Mach offered this revised first law as a first\nstep toward a theory that would replace Newton’s mechanics,\nderiving inertial effects from only relative motions, as Leibniz\ndesired. But many other remarks made by Mach in his chapter\ncriticizing absolute space point in this direction, and they have\ngiven birth to the Mach-heavy view, later to be christened\n“Mach’s Principle” by Albert\n Einstein.[2]\n The Mach-heavy viewpoint calls for a new mechanics that invokes only\nrelative distances and (perhaps) their 1st and 2nd time derivatives,\nand thus is ‘generally relativistic’ in the sense\nsometimes read into Leibniz’s remarks about motion (see\n absolute and relational space and motion: classical theories,\n section 6). Mach wished to eliminate absolute time from physics too,\nso he would have wanted a proper relationist reduction of these\nderivatives also. The Barbour-Bertotti theories, discussed below,\nprovide this.", "\nMach-heavy apparently involves the prediction of novel effects due to\n‘merely’ relative accelerations. Mach hints at such\neffects in his criticism of Newton’s bucket:", "\nNewton’s experiment with the rotating vessel of water simply\ninforms us that the relative rotation of the water with respect to the\nsides of the vessel produces no noticeable centrifugal forces, but\nthat such forces are produced by its relative rotation with respect to\nthe mass of the earth and the other celestial bodies. No one is\ncompetent to say how the experiment would turn out if the sides of the\nvessel [were] increased until they were ultimately several leagues\nthick. (1883, 284.)\n", "\nThe suggestion here seems to be that the relative rotation in stage\n(i) of the experiment might immediately generate an outward force\n(before any rotation is communicated to the water), if the sides of\nthe bucket were massive enough. (Note that this response could not\nhave been made by Leibniz – even if he had wanted to defend\nMachian relationism – because it involves action at a distance\nbetween the water and the parts of the bucket, something he regarded\nas a metaphysical absurdity.)", "\nMore generally, Mach-heavy involves the view that all inertial effects\nshould be derived from the motions of the body in question relative to\nall other massive bodies in the universe. The water in Newton’s\nbucket feels an outward pull due (mainly) to the relative rotation of\nall the fixed stars around it. Mach-heavy is a speculation that an\neffect something like electromagnetic induction should be built into\ngravity theory. (Such an effect does exist according to the General\nTheory of Relativity, and is called ‘gravitomagnetic\ninduction’. The Gravity Probe B mission was designed to measure\na gravitomagnetic induction effect on orbiting gyroscopes due to the\nEarth’s rotation.) Its specific form must fall off with distance\nmuch more slowly than \\(1/r^2\\), if the theory is to be\nempirically similar to Newtonian physics; but it will certainly\npredict experimentally testable novel behaviors. A theory that\nsatisfies all the goals of Mach-heavy would appear to be ideal for the\nvindication of strict relationism and the elimination of absolute\nquantities of motion from mechanics." ], "subsection_title": "1.1 Two Interpretations of Mach on Inertia" }, { "content": [ "\nDirect assault on the problem of satisfying Mach-heavy in a classical\nframework proved unsuccessful for a long time, despite the efforts of\nothers besides Mach – for example, Friedländer (1896),\nFöpl (1904), and Reissner (1914, 1915). (Between the late 19th\ncentury and the 1970s, there was of course one extremely important\nattempt to satisfy Mach-heavy: the work of Einstein that led to the\nGeneral Theory of Relativity. Since Einstein’s efforts took\nplace in a non-classical (Lorentz/Einstein/Minkowski) spacetime\nsetting, we discuss them in the next section.) One very influential\napproach to implementing Mach-heavy was promulgated in the work of\nBarbour and Bertotti (1977); this has since developed into the\nresearch programme of ‘shape dynamics’, and will be\ndiscussed in more detail in section 3 below." ], "subsection_title": "1.2 Implementing Mach-heavy" }, { "content": [ "\nMach-lite, like the relational interpretations of Newtonian physics\nreviewed in the entry on\n absolute and relational space and motion: classical theories,\n section 5, offers us a way of understanding Newtonian physics without\naccepting absolute position, velocity or acceleration. But it does so\nin a way that lacks theoretical clarity and elegance, since it does\nnot delimit a clear set of cosmological models. We know that Mach-lite\nmakes the same predictions as Newtonian physics for worlds in which\nthere is a static frame associated with the stars and galaxies; but if\nasked about how things will behave in a world with no frame of fixed\nstars, or in which the stars are far from ‘fixed’, it\nshrugs and refuses to answer. (Recall that Mach-lite simply says:\n“Newton’s laws hold in the frame of reference of the fixed\nstars.”) This is perfectly acceptable according to Mach’s\nphilosophy of science, since the job of mechanics is simply to\nsummarize observable facts in an economical way. But it is\nunsatisfying to those with stronger realist intuitions about laws of\nnature.", "\nIf there is, in fact, a distinguishable privileged frame of reference\nin which the laws of mechanics take on a specially simple form,\nwithout that frame being determined in any way by relation to the\nmatter distribution, a realist will find it hard to resist the\ntemptation to view motions described in that frame as the\n‘true’ or ‘absolute’ motions. If there is a\nfamily of such frames, disagreeing about velocity but all agreeing\nabout acceleration, then the realist will feel a temptation to think\nof at least acceleration as ‘true’ or\n‘absolute’. If such a realist believes motion to be by\nnature a relation rather than a property (and not all philosophers\naccept this; see the entry on\n absolute and relational space and motion: classical theories,\n section 1) then they will feel obliged to accord some sort of\nexistence or reality to the structure – e.g., the structure of\nGalilean spacetime – in relation to which these motions are\ndefined. For philosophers with such realist inclinations, the ideal\nrelational account of motion would therefore be some version of\nMach-heavy." ], "subsection_title": "1.3 Mach-lite versus Mach-heavy" } ] }, { "main_content": [ "\nEinstein’s Special Theory of Relativity (STR) is notionally\nbased on a principle of relativity of motion; but that principle is\n‘special’ – meaning, restricted. The relativity\nprinciple built into STR is in fact nothing other than the Galilean\nprinciple of relativity, which is built into Newtonian\n physics.[3]\n In other words, while there is no privileged standard of velocity,\nthere is nevertheless a determinate fact of the matter about whether a\nbody has accelerated or non-accelerated (i.e., inertial) motion. In\nthis regard, the spacetime of STR is exactly like Galilean spacetime\n(discussed in the entry on\n absolute and relational space and motion: classical theories,\n section 5). In terms of the question of whether all motion can be\nconsidered purely relative, one could argue that there is nothing new\nbrought to the table by the introduction of Einstein’s STR\n– at least, as far as mechanics is concerned. (See the entry on\n space and time: inertial frames\n for a more detailed discussion.)" ], "section_title": "2. Einstein", "subsections": [ { "content": [ "\nIn this subsection we will discuss an interesting sense in which, in\nSTR, the letter (if not the spirit) of classical relationism can be\nconsidered vindicated: the spatio-temporal relations between material\nthings are, on their own, sufficient to fully determine the state of\nmotion of a body. The discussion here presupposes acquaintance with\nSTR and its basic mathematics, and will be hard to follow for readers\nlacking that background; such readers should feel free to skip this\nsubsection, which is not necessary for following the material in the\nrest of section 2. ", "\nAs Dorling (1978) first pointed out, there is a sense in which the\nstandard absolutist arguments against ‘strict’ relationism\nusing rotating objects (buckets or globes) fail in the context of STR.\nMaudlin (1993) used the same considerations to show that there is a\nway of recasting relationism in STR that appears to be successful. STR\nincorporates certain novelties concerning the nature of time and\nspace, and how they mesh together; perhaps the best-known examples are\nthe phenomena of ‘length contraction’, ‘time\ndilation’, and the ‘relativity of\n simultaneity.’[4]\n In STR both spatial distances and time intervals between\nevents – when measured in the standard ways – are\nframe-relative (observers in different states of motion, i.e. at rest\nin different reference frames, will ‘disagree’ about their\nsizes). The standard classical relationist starting point – the\nconfiguration of relative distances between the existing bodies at\na moment of time – does not exist, at least not as an\nobjective, observer- or frame-independent set of facts. Because of\nthis, when considering what spatial or temporal relations a\nrelationist should postulate as fundamental, it is arguably most\nnatural to restrict oneself to the frame-invariant spatiotemporal\n‘distance’ between events in spacetime. This is given by the\ninterval between two points: \n\\([\\Delta x^2 + \\Delta y^2 + \\Delta z^2 - \\Delta t^2]\\)\n– the four-dimensional analog of\nthe Pythagorean theorem, for spacetime distances. If one regards the\nspacetime interval relations between point-masses-at-times as\none’s basis, on which spacetime is built up as an ideal entity\n(analogously to how Leibniz thought of 3-d space as an ideal entity\nabstracted from spatial distance relations), then with only mild\ncaveats relationism works: the spacetime interval relations suffice to\nuniquely fix how the material systems can be embedded (up to\nisomorphism) in the ‘Minkowski’ spacetime of STR. The\nmodern variants of Newton’s bucket and globes arguments no\nlonger stymie the relationist because (for example) the spacetime\ninterval relations among bits of matter in Newton’s bucket at\nrest are quite different from the spacetime interval relations found\namong those same bits of matter after the bucket is rotating. For\nexample, the spacetime interval relation between a bit of\nwater near the side of the bucket, at one time, and itself (say) a\nsecond later is smaller than the interval relation between a\ncenter-bucket bit of water and itself one second later (times referred\nto inertial-frame clocks). The upshot is that, unlike the situation in\nclassical physics, a non-rotating body cannot have all the same\nspatiotemporal relations among its parts as a similar body in\nrotation. We cannot put a body or system into a state of rotation (or\nother acceleration) without thereby changing the spacetime interval\nrelations between the various bits of matter at different moments of\ntime, compared to what they would have been if the body had remained\nnon-accelerated or non-rotated. The facts about rotation and\nacceleration, thus, supervene on spacetime interval\nrelations.[5]\n", "\nIt is worth pausing to consider to what extent this victory for (some\nform of) relationism satisfies the classical ‘strict’\nrelationism traditionally ascribed to Mach and Leibniz. The\nspatiotemporal relations that save the day against the bucket and\nglobes are, so to speak, mixed spatial and temporal distances. They\nare thus quite different from the spatial-distances-at-a-time\npresupposed by classical relationists; moreover they do not correspond\nto relative velocities (-at-a-time) either. Their oddity is forcefully\ncaptured by noticing that if we choose appropriate bits of matter at\n‘times’ eight minutes apart, I-now am at zero\ndistance from the surface of the sun (of eight minutes\n‘past’, since it took 8 minutes for light from the sun to\nreach me-now). So we are by no means dealing here with an innocuous,\n‘natural’ translation of classical relationist quantities\ninto the STR setting. On the other hand, in light of the relativity of\nsimultaneity (see footnote 5), \n it can be argued that the absolute simultaneity presupposed by\nclassical relationists and absolutists alike was, in fact, something\nthat relationists should always have regarded with misgivings. From\nthis perspective, instantaneous relational configurations –\nprecisely what one starts with in the theories of Barbour and Bertotti\ndiscussed below – would be the things that should be treated\nwith suspicion.", "\nIf we now return to our questions about motions – about the\nnature of velocities and accelerations – we find, as noted\nabove, that matters in the interval-relational interpretation of STR\nare much the same as in Newtonian mechanics in Galilean spacetime.\nThere are no well-defined absolute velocities, but there are indeed\nwell-defined absolute accelerations and rotations. In fact, the\ndifference between an accelerating body (e.g., a rocket) and an\ninertially moving body is codified directly in the cross-temporal\ninterval relations of the body with itself. So we are very\nfar from being able to conclude that all motion is relative motion of\na body with respect to other bodies. It is true that the\nabsolute motions are in 1–1 correlation with patterns of\nspacetime interval relations, but it is not at all correct to say that\nthey are, for that reason, eliminable in favor of merely relative\nmotions. Rather we should simply say that no absolute acceleration can\nfail to have an effect on the material body or bodies accelerated. But\nthis was already true in classical physics if matter is modeled\nrealistically: the cord connecting the globes does not merely tense,\nbut also stretches; and so does the bucket, even if imperceptibly,\ni.e., the spatial relations change.", "\nMaudlin does not claim this version of relationism to be victorious\nover an absolutist or substantivalist conception of Minkowski\nspacetime, when it comes time to make judgments about the\ntheory’s ontology. There may be more to vindicating relationism\nthan merely establishing a 1–1 correlation between absolute\nmotions and patterns of spatiotemporal relations." ], "subsection_title": "2.1 Relations Determine State of Motion?" }, { "content": [ "\nThe simple comparison made above between STR and Newtonian physics in\nGalilean spacetime is somewhat deceptive. For one thing, Galilean\nspacetime is a mathematical innovation posterior to\nEinstein’s 1905 theory; before then, Galilean spacetime had not\nbeen conceived, and full acceptance of Newtonian mechanics implied\naccepting absolute velocities and, arguably, absolute positions, just\nas laid down in the Scholium. So Einstein’s elimination\nof absolute velocity was a genuine conceptual advance. Moreover, the\nScholium was not the only reason for supposing that there\nexisted a privileged reference frame of ‘rest’: the\nworking assumption of almost all physicists in the latter half of the\n19th century was that, in order to understand the wave theory of\nlight, one had to postulate an aetherial medium filling all space,\nwave-like disturbances in which constituted electromagnetic radiation.\nIt was assumed that the aether rest frame would be an inertial\nreference frame; and physicists felt some temptation to equate its\nframe with the absolute rest frame, though this was not necessary.\nRegardless of this equation of the aether with absolute space, it was\nassumed by all 19th century physicists that the equations of\nelectrodynamic theory would have to look different in a reference\nframe moving with respect to the aether than they did in the\naether’s rest frame (where they presumably take their canonical\nform, i.e., Maxwell’s equations and the Lorentz force law). So\nwhile theoreticians labored to find plausible transformation rules for\nthe electrodynamics of moving bodies, experimentalists tried to detect\nthe Earth’s motion in the aether. Experiment and theory played\ncollaborative roles, with experimental results ruling out certain\ntheoretical moves and suggesting new ones, while theoretical advances\ncalled for new experimental tests for their confirmation or – as\nit happened – disconfirmation.", "\nAs is well known, attempts to detect the Earth’s velocity in the\naether were unsuccessful. On the theory side, attempts to formulate\nthe transformation laws for electrodynamics in moving frames –\nin such a way as to be compatible with experimental results –\nwere complicated and\n inelegant.[6]\n A simplified way of seeing how Einstein swept away a host of problems\nat a stroke is this: he proposed that the Galilean principle of\nrelativity holds for Maxwell’s theory, not just for mechanics.\nThe canonical (‘rest-frame’) form of Maxwell’s\nequations should be their form in any inertial reference\nframe. Since the Maxwell equations dictate the velocity c of\nelectromagnetic radiation (light), this entails that any inertial\nobserver, no matter how fast she is moving, will measure the velocity\nof a light ray as c – no matter what the relative\nvelocity of its emitter may be. Einstein worked out logically the\nconsequences of this application of the special relativity principle,\nand discovered that space and time must be rather different from how\nNewton described them. STR undermined Newton’s absolute time\njust as decisively as it undermined his absolute space." ], "subsection_title": "2.2 The Relationist Roots of STR and GTR" }, { "content": [ "\nEinstein’s STR was the first clear and empirically successful\nphysical theory to overtly eliminate the concepts of absolute rest and\nabsolute velocity while recovering most of the successes of\nclassical mechanics and 19th century electrodynamics. It therefore\ndeserves to be considered the first highly successful theory to\nexplicitly relativize motion, albeit only partially. But STR only\nrecovered most of the successes of classical physics: crucially, it\nleft out gravity. And there was certainly reason to be concerned that\nNewtonian gravity and STR would prove incompatible: classical gravity\nacted instantaneously at a distance, while STR eliminated the\nprivileged absolute simultaneity that this instantaneous action\npresupposes.", "\nSeveral ways of modifying Newtonian gravity to make it compatible with\nthe spacetime structure of STR suggested themselves to physicists in\nthe years 1905–1912, and a number of interesting\nLorentz-covariant theories were proposed (i.e., theories compatible\nwith the spacetime of STR, which is called ‘Minkowski spacetime’\nbecause Hermann Minkowski first revealed the spacetime structure that\nEinstein’s postulates in STR entail). Einstein rejected these proposed\ntheories one and all, for violating either empirical facts or\ntheoretical desiderata. But Einstein’s chief reason for not\npursuing the reconciliation of gravitation with STR’s spacetime\nappears to have been his desire, beginning in 1907, to replace STR\nwith a theory in which not only velocity could be considered merely\nrelative, but also acceleration. That is to say, Einstein wanted if\npossible to completely eliminate all absolute quantities of motion\nfrom physics, thus realizing a theory that satisfies at least one kind\nof ‘strict’ relationism. (Regarding Einstein’s\nrejection of Lorentz-covariant gravity theories, see Norton 1992;\nregarding Einstein’s quest to fully relativize motion, see\nHoefer 1994.)", "\nEinstein began to see this complete relativization as possible in\n1907, thanks to his discovery of the Equivalence Principle (cf.\nLehmkuhl forthcoming). Imagine we are far out in space, in a\nrocket ship accelerating at a constant rate \n\\(g = 9.81 m/s^2.\\) Things will feel just like they do\non the surface of the Earth; we will feel a clear up-down direction,\nbodies will fall to the floor when released, etc. Indeed, due to the\nwell-known empirical fact that gravity affects all bodies by imparting\na force proportional to their matter (and energy) content, independent\nof their internal constitution, we know that any experiment performed\non this rocket will give the same results that the same experiment\nwould give if performed on the Earth. Now, Newtonian theory teaches us\nto consider the apparent downward, gravity-like forces in the rocket\nship as ‘pseudo-forces’ or ‘inertial forces’,\nand insists that they are to be explained by the fact that the ship is\naccelerating in absolute space. But Einstein asked whether there is\nany way for the person in the rocket to regard him/herself as being\n‘at rest’ rather than in absolute (accelerated) motion?\nAnd the answer he gave is: Yes. The rocket traveler may regard\nhim/herself as being ‘at rest’ in a homogeneous and\nuniform gravitational field. Such a field would entail an accelerative\nforce “downward” on every body that is equal in magnitude and\ndirection everywhere in space. This is unlike the Earth’s\ngravitational field, which varies depending on distance from the\nEarth’s center and points in different directions at different\nlocations. Positing the existence of such a field will explain all the\nobservational facts just as well as the supposition that he/she is\naccelerating relative to absolute space (or, absolutely accelerating\nin Minkowski spacetime). But is it not clear that the latter is the\ntruth, while the former is a fiction? By no means; if there\nwere a uniform gravitational field filling all space, then it\nwould affect all the other bodies in the world – the Earth, the\nstars, etc, – imparting to them a downward acceleration away\nfrom the rocket; and that is exactly what the traveler observes.", "\nIn 1907 Einstein published his first gravitation theory (Einstein\n1907), treating the gravitational field as a scalar field that also\nrepresented the (now variable and frame-dependent) speed of light.\nEinstein viewed the theory as only a first step on the road to\neliminating absolute motion. In the 1907 theory, the theory’s\nequations take the same form in any inertial or uniformly\naccelerating frame of reference. One might say that this theory\nreduces the class of absolute motions, leaving only rotation and other\nnon-uniform accelerations as absolute. But, Einstein reasoned, if\nuniform acceleration can be regarded as equivalent to being at rest in\na constant gravitational field, why should it not be possible also to\nregard inertial effects from these other, non-uniform motions as\nsimilarly equivalent to “being at rest in a (variable)\ngravitational field”? Thus Einstein set himself the goal of\nexpanding the principle of equivalence to embrace all forms of\n‘accelerated’ motion.", "\nEinstein thought that the key to achieving this aim lay in further\nexpanding the range of reference frames in which the laws of physics\ntake their canonical form, to include frames adapted to any arbitrary\nmotions. More specifically, since the class of all continuous and\ndifferentiable coordinate systems includes as a proper subclass the\ncoordinate systems adapted to any such frame of reference, if he could\nachieve a theory of gravitation, electromagnetism and mechanics that\nwas generally covariant – its equations taking the same\nform in any coordinate system from this general class – then the\ncomplete relativity of motion would be achieved. If there are no\nspecial frames of reference in which the laws take on a simpler\ncanonical form, there is no physical reason to consider any particular\nstate or states of motion as privileged, nor deviations from those as\nrepresenting ‘absolute motion’. (Here we are just laying\nout Einstein’s train of thought; later we will see reasons to\nquestion the last step.) And in 1915, Einstein achieved his aim in the\nGeneral Theory of Relativity (GTR)." ], "subsection_title": "2.3 From Special Relativity to General Relativity" }, { "content": [ "\nThere is one key element left out of this success story, however, and\nit is crucial to understanding why most physicists reject\nEinstein’s claim to have eliminated absolute states of motion in\nGTR. Going back to our accelerating rocket, we accepted\nEinstein’s claim that we could regard the ship as hovering at\nrest in a universe-filling gravitational field. But a gravitational\nfield, we usually suppose, is generated by matter. How is this\nuniverse-filling field linked to generating matter? The answer may be\nsupplied by Mach-heavy. Regarding the ‘accelerating’\nrocket which we decide to regard as ‘at rest’ in a\ngravitational field, the Machian says: all those stars and galaxies,\netc., jointly accelerating downward (relative to the rocket),\n‘produce’ that gravitational field. The mathematical\nspecifics of how this field is generated will have to be different\nfrom Newton’s law of gravity, of course; but it should give\nessentially the same results when applied to low-mass, slow-moving\nproblems such as the orbits of the planets, so as to capture the\nempirical successes of Newtonian gravity. Einstein thought, in 1916 at\nleast, that the field equations of GTR are precisely this mathematical\nreplacement for Newton’s law of gravity, and that they fully\nsatisfied the desiderata of Mach-heavy relationism. But it was not so.\n(See the entry on\n early philosophical interpretations of general relativity.)", "\nIn GTR, spacetime is locally very much like STR’s flat Minkowski\nspacetime. There is no absolute velocity locally, but there are clear\nlocal standards of accelerated vs non-accelerated motion, i.e., local\ninertial frames. In these ‘freely falling’ frames bodies\nobey the usual rules for non-gravitational physics familiar from STR,\nalbeit only approximately (this is sometimes called the ‘strong\nequivalence principle’, and is discussed further in section 4\nbelow). But overall spacetime is curved, and local inertial frames may\ntip, bend and twist as we move from one region to another. The\nstructure of curved spacetime is encoded in the metric field tensor\ngab, with the curvature encoding gravity\nat the same time: gravitational forces are so to speak ‘built\ninto’ the metric field, geometrized away. Since the spacetime\nstructure encodes gravity and inertia, and in a Mach-heavy theory\nthese phenomena should be completely determined by the relational\ndistribution of matter (and relative motions), Einstein wished to see\nthe metric as entirely determined by the distribution of matter and\nenergy. But what the GTR field equations entail is, in general, only a\npartial-determination relation.", "\nWe cannot go into the mathematical details necessary for a full\ndiscussion of the successes and failures of Mach-heavy in the GTR\ncontext. But one can see why the Machian interpretation Einstein hoped\nhe could give to the curved spacetimes of his theory fails to be\nplausible, by considering a few simple ‘worlds’ permitted\nby GTR. In the first place, for our hovering rocket ship, if we are to\nattribute the gravity field it feels to matter, there has got to\nbe all this other matter in the universe. But if we regard\nthe rocket as a mere ‘test body’ (not itself substantially\naffecting the gravity present or absent in the universe), then we can\nnote that according to GTR, if we remove all the stars, galaxies,\nplanets etc. from the world, the gravitational field does not\ndisappear. On the contrary, it stays basically the same locally, and\nglobally, in the simplest solution of the field equations, it takes\nthe form of empty Minkowski spacetime – precisely the\nquasi-absolute structure Einstein was hoping to eliminate. Solutions\nof the GTR field equations for arbitrary realistic configurations of\nmatter (e.g., a rocket ship ejecting a stream of particles to push\nitself forward) are hard to come by, and in fact a realistic two-body\nexact solution has yet to be discovered. But numerical methods can be\napplied for many purposes, and physicists do not doubt that something\nlike our accelerating rocket – in otherwise empty space –\nis possible according to the\n theory.[7]\n We see clearly, then, that GTR fails to satisfy Einstein’s own\nunderstanding of Mach’s Principle, according to which, in the\nabsence of matter, space itself should not be able to exist.", "\nA second example: GTR allows us to model a single rotating\nobject in an otherwise empty universe (e.g., a neutron star).\nRelationism of the Machian variety says that such rotation is\nimpossible, since it can only be understood as rotation relative to\nsome sort of absolute space. In the case of GTR, this is indeed the\nnatural way to understand such a model: the rotation is best\nunderstood as rotation relative to a ‘background’\nspacetime that is identical to the Minkowski spacetime of STR, only\n‘curved’ by the presence of matter in the region of the\nstar.", "\nOn the other hand, there is one charge of failure-to-relativize-motion\nsometimes leveled at GTR that is unfair. It is sometimes asserted that\nthe simple fact that the metric field (or the connection it\ndetermines) distinguishes, at every location, motions that are\n‘absolutely’ accelerated and/or ‘absolutely\nrotating’ from those that are not, by itself entails that GTR\nfails to embody a folk-Leibniz style general relativity of motion\n(e.g. Earman (1989), ch. 5). We think this is incorrect, and leads to\nunfairly harsh judgments about confusion on Einstein’s part. The\nlocal inertial structure encoded in the metric would not be\n‘absolute’ in any meaningful sense, if that structure were\nin some clear sense fully determined by the relationally specified\nmatter-energy distribution. Einstein was not simply confused\nwhen he named his gravity theory. (Just what is to be understood by\n“the relationally specified matter-energy distribution” is\na further, thorny issue, which we cannot enter into here.)", "\nGTR does not fulfill all the goals of Mach-heavy, at least as\nunderstood by Einstein, and he recognized this fact by 1918 (Einstein\n1918). And yet … GTR comes tantalizingly close to achieving\nthose goals, in certain striking ways (cf. Hoefer 2014). For one\nthing, GTR does predict Mach-heavy effects, known as\n‘frame-dragging’: if we could model Mach’s\nthick-walled bucket in GTR, it seems clear that it would pull the\nwater slightly outward, and give it a slight tendency to begin\nrotating in the same sense as the bucket (even if the big\nbucket’s walls were not actually touching the water). While GTR\ndoes permit us to model a lone rotating object, if we model the object\nas a shell of mass (instead of a solid sphere) and let the size of the\nshell increase (to model the ‘sphere of the fixed stars’\nwe see around us), then as Brill & Cohen (1966) showed, the\nframe-dragging becomes complete inside the shell. In other words: our\noriginal Minkowski background structure effectively disappears, and\ninertia becomes wholly determined by the shell of matter, just as Mach\nposited was the case. This complete determination of inertia by the\nglobal matter distribution appears to be a feature of other models,\nincluding the Friedman-Lemâitre-Robertson-Walker Big Bang models\nthat best match observations of our universe.", "\nFinally, it is important to recognize that GTR is generally covariant\nin a very special sense: unlike all other prior theories (and unlike\nmany subsequent quantum theories), it postulates no fixed\n‘prior’ or ‘background’ spacetime structure.\nAs mathematicians and physicists realized early on, other theories,\ne.g., Newtonian mechanics and STR, can be put into a generally\ncovariant form. But when this is done, there are inevitably\nmathematical objects postulated as part of the formalism, whose role\nis to represent absolute elements of spacetime structure (see Friedman\n1983, Pooley 2017). What is unique about GTR is that it was the first,\nand is still the only ‘core’ physical theory, to have no\nsuch absolute elements in its covariant equations. (Whether these\nclaims are exactly correct is a matter of ongoing debate, relating to\nthe question of the ‘background independence’ of GTR: for\ndiscussion, see e.g. Belot (2011), Pitts (2006), Read (2016), and\nPooley (2017).) The spacetime structure in GTR, represented by the\nmetric field, is at least partly ‘shaped’ by the\ndistribution of matter and energy. And in certain models of the\ntheory, such as the Big Bang cosmological models, some authors have\nclaimed that the local standards of inertial motion – the local\n‘gravitational field’ of Einstein’s equivalence\nprinciple – are entirely fixed by the matter distribution\nthroughout space and time, just as Mach-heavy requires (see, for\nexample, Wheeler and Cuifollini 1995).", "\nAbsolutists and relationists are thus left in a frustrating and\nperplexing quandary by GTR. Considering its anti-Machian models, we\nare inclined to say that motions such as rotation and acceleration\nremain absolute, or nearly-totally-absolute, according to the theory.\nOn the other hand, considering its most Mach-friendly models, which\ninclude all the models taken to be good candidates for representing\nthe actual universe, we may be inclined to say: motion in our\nworld is entirely relative; the inertial effects normally used to\nargue for absolute motion are all understandable as effects of\nrotations and accelerations relative to the cosmic matter, just as\nMach hoped. But even if we agree that motions in our world are in fact\nall relative in this sense, this does not automatically settle the\ntraditional relationist/absolutist debate, much less the\nrelationist/substantivalist debate. Many philosophers (including, we\nsuspect, Nerlich 1994 and Earman 1989) would be happy to acknowledge\nthe Mach-friendly status of our spacetime, and argue nevertheless that\nwe should understand that spacetime as a real thing, more like a\nsubstance than a mere ideal construct of the mind as Leibniz insisted.\nBy contrast, other philosophers (e.g., Rynasiewicz 1995) argue that\ndue to the conceptual and mathematical novelties introduced in GTR,\nthe traditional absolute vs. relational motion debate simply fails to\nmake sense any more (on this question, see also Hoefer 1998)." ], "subsection_title": "2.4 General Relativity and Relativity of Motion" } ] }, { "main_content": [ "\nWe turn now to a modern-day attempt to implement Mach-heavy known as\n‘shape dynamics’. (In fact, shape dynamics is just one\ntheory within this tradition, as we will see below.) This approach was\ninitiated – albeit not under that name – by Barbour and\nBertotti (1977, 1982). In tackling the problem of implementing\nMach-heavy, rather than formulating a revised law of gravity/inertia\nusing relative quantities, Barbour and Bertotti used the framework of\nLagrangian mechanics, replacing elements of the mathematics referring\nto absolute quantities of motion with new terms invoking only relative\ndistances, velocities, etc. In this section, we presuppose a basic\nfamiliarity with the Lagrangian framework. For a non-technical\nintroduction to shape dynamics, see Barbour (1999); for an up-to-date\nreview of recent work in the field, see Mercati (2018).", "\nIn this section, we survey the results and motivations of the shape\ndynamics research program, focussing first on the above-mentioned\ntheory of Barbour and Bertotti (which recovers a subsection of the\nsolution space of Newtonian particle theory), before turning to the\nMachian alternative to general relativity developed by Barbour and\ncollaborators: it is this latter theory which is shape dynamics\n‘proper’. Readers uninterested in the technical details of\nthis work can skip to section 3.5, in which its conceptual upshots are\ndiscussed." ], "section_title": "3. Shape Dynamics", "subsections": [ { "content": [ "\nFor a given physical system, define its ‘configuration\nspace’ to be the space of possible instantaneous states of that\nsystem. (For example, the space of possible distributions of N\nparticles in Euclidean space, according to a Cartesian coordinate\nsystem laid down on that space.) As the system evolves, the point in\nconfiguration space representing the system’s instantaneous\nstate traces out a continuous curve. On this picture, metaphysically\npossible worlds are represented by (rising) curves in the product\nspace formed from configuration space and a one-dimensional space\nrepresenting time. Nomologically possible worlds are represented by\nthose curves that are allowed by the dynamics. For example, in the\nLagrangian formalism, the nomologically possible worlds are\nrepresented by those curves which extremize the action: a particular\nfunctional of such curves.", "\nConsider now, for the sake of concreteness, two Newtonian worlds which\ndiffer by either a static or a kinematic Leibniz shift: that is,\nconstant translations or velocity boosts of the material content of\nthe universe (see the companion entry on\n absolute and relational space and motion: classical theories,\n for further discussion of such shifts). These two worlds will be\nrepresented by distinct curves in configuration space. However, given\na configuration space, one can construct a ‘reduced’\nconfiguration space, in which certain such histories are\nmathematically identified, or ‘quotiented’, such that they\nare mapped to the same unique history in reduced configuration space.\nSpecifically, proponents of this approach define two such reduced\nconfiguration spaces:", "\n(Two points here. First, recall that a ‘dilatation’ is a\nscale transformation. Second, in what follows we will refer to the\ngroup which consists of the union of translations, rotations and\ndilatations as the ‘similarity group’.) If these Machian\ntheorists are able to formulate a dynamics on shape space (i.e., a\ndynamics which identifies the curves in shape space which represent\nnomologically possible worlds), then that dynamics will, in light of\nthe above reduction, not bring with it a meaningful notion of absolute\nposition, or absolute velocity, or absolute scales. Barbour and\ncollaborators take such a dynamics to realize Mach-heavy: the\nundetectable spacetime structure associated with such quantities has\nbeen expunged. Below, we will see how this can be done in the concrete\ncontexts of Newtonian particle dynamics and general relativity." ], "subsection_title": "3.1. Configuration Space" }, { "content": [ "\nThe Machian ambitions of Barbour and collaborators do not end there,\nfor these authors also seek to excise primitive temporal structure.\nInitially, one might distinguish histories that correspond to a single\ncurve in configuration space being traced out at different rates with\nrespect to the primitive temporal parameter. Those working in this\ntradition, however, view each curve in configuration space as\ncorresponding to exactly one possible history. They therefore elect to\ndispose of the auxiliary one-dimensional space representing a\nprimitive absolute time which was introduced above. Instead, they seek\nto construct an ‘emergent’ notion of temporality from\ndynamics defined on configuration space alone. By way of a procedure\nknown as ‘Jacobi’s principle’, the Machian\nrelationist selects a unique temporal parameter which maximally\nsimplifies this dynamics defined on configuration space. For the\ndetails of Jacobi’s principle, see Pooley (2013)." ], "subsection_title": "3.2. Emergent Temporality" }, { "content": [ "\nIt is all well and good speaking of a dynamics defined on relative\nconfiguration space, or shape space. However, it remains incumbent on\nour Machian theorists to construct explicit dynamics appropriate for\nthese spaces: i.e., dynamics which do not recognise solutions related\nby the action of the similarity group (viz., translations, rotations,\nand dilatations) as being distinct. Given a dynamics on configuration\nspace, one can indeed achieve this task. The procedure which\nimplements this is known as ‘best matching’, and was\ndeveloped in the seminal work of Barbour and Bertotti (1982), in which\na version of Newtonian particle mechanics with dynamics formulated on\nrelative configuration space was first constructed. The extension to\nshape space was undertaken in (Barbour 2003).", "\nInformally, the goal of best matching is to use the similarity group\nto minimize the intrinsic difference between successive points along a\nhistory in configuration space. To take a simple example drawn from\nBarbour (1999), consider the history of a particular triangle: the\ntriangle may, along that history, rotate, dilate, alter its internal\nangles, and so on. However, at each point best matching allows one to\nact on the triangle with similarity transformations; thereby,\ntriangles which at successive points along a history differ merely by\na translation, rotation or dilatation will be regarded as being\nidentical after best matching. In this way, a ‘best matched’ history\nis selected, in which the intrinsic differences between successive\nstates of the system under consideration (in the above example, the\ntriangle) are minimised. While a metric on configuration space will in\ngeneral assign a different length to histories differing by the action\nof the similarity group, the length of the best matched history,\nconstructed via the above procedure, will induce a unique length of\npaths, and therefore metric, on shape space.", "\nA little more formally, the best matching procedure works as follows.\nConsider a class of paths in configuration space, all corresponding to\nthe same path in shape space (i.e., consider a class of paths in\nconfiguration space related by the action of the similarity group). As\nmentioned above, a given metric on configuration space will in general\nassign to each path in that space a different length; as a result, the\nlength of the associated path in shape space will be underdetermined.\nHowever, starting from any given point p in configuration space, one\ncan use the action of the similarity group on configuration space to\ndefine a unique curve, by shifting the points of any curve through p\nalong the corresponding orbits of the similarity group (think of these\n‘orbits’ as contour lines in configuration space, relating\npoints which differ only by the action of the similarity group) so as\nto extremize the length assigned to the curve (relative to the metric\nunder consideration). It is this extremized length which is assigned\nto the unique curve in shape space. With each curve in shape space\nassigned a unique length, one can then, as usual, specify a principle\nwhich selects some such curves as representing nomologically possible\nworlds, based upon their lengths. (Recall again, for example, that in\nLagrangian mechanics it is those curves which extremize an action\nwhich are regarded as being dynamically possible.)" ], "subsection_title": "3.3. Best Matching" }, { "content": [ "\nThe best matching prescription can be applied not only to Newtonian\nparticle theories, but also to other spacetime theories, including\nGTR. (There is no reason why best matching cannot be applied to\nNewtonian field theories, or to special relativistic particle\ndynamics, but these steps are usually skipped by Machian relationists\nfollowing in the tradition of Barbour and Bertotti, who proceed at\nthis stage straight to GTR.)", "\nTo see how best matching works in the case of GTR, first note that a\ncertain subclass of solutions of that theory (namely, those which are\nglobally hyperbolic) can be formulated in terms of the ‘3+1\nformalism’, according to which the state of the universe at a\nparticular time is represented by a determinate 3-manifold with\nassociated Riemannian metric; dynamical equations then determine how\nsuch 3-geometries evolve in time. (For a summary of the 3+1 formalism,\nsee e.g. Gourgoulhon (2012).) The Machian relationists working in the\nshape dynamics research program take this 3+1 approach to GTR as their\nstarting point. They thus assume that instantaneous spaces which are\nthe points in configuration space have the determinate topology of\nsome closed 3-manifold without boundary. Configuration space is the\nspace of Riemannian 3-metrics on that 3-manifold. The natural analogue\nof relative configuration space is, then, this space of Riemannian\n3-metrics quotiented by diffeomorphisms, which are the generalisations\nof Leibniz shifts appropriate to GTR (see the entry on\n the hole argument).\n The analogue of shape space in this case is the space of Riemannian\n3-metrics, but quotiented in addition by local dilatations (by\n‘local’, we mean here a transformation which can vary from\npoint to point).", "\nHaving constructed shape space in the relativistic case, one may then\nbest match in order to construct one’s relational theory\nimplementing Mach-heavy (the metric on configuration space is defined\nfrom the 3+1 dynamics of GTR): conceptually, the approach here is the\nsame as that presented in the previous section. Moreover, one can\nagain apply Jacobi’s principle, in order to eliminate a\ncommitment to primitive temporal structure. In this case, the\nresulting theory is known as ‘shape dynamics’, which\ninvolves a commitment only to primitive conformal structure (i.e.,\nfacts about angles between objects) on the 3-geometries: all other\nabsolute quantities, the claim goes, have been excised. One way to\nunderstand the relationship between GTR and shape dynamics is that one\ntrades the relativity of simultaneity but absoluteness of scales in\nthe former theory, for absolute simultaneity but the relativity of\nscales in the latter." ], "subsection_title": "3.4. Relativistic Best Matching" }, { "content": [ "\nThere are important differences between the relationship between\n‘standard’ Newtonian particle mechanics and its\nbest-matched alternative on the one hand, and the relationship between\nGTR and shape dynamics on the other. In the former case, the class of\nsolutions of the best-matched theory is a proper subset of the\nsolutions of Newtonian mechanics: for example, it includes only the\nsector of the solution space of Newtonian mechanics which ascribes\nzero angular momentum to the entire universe. Sometimes, this is\nmarketed as an advantage of the latter theory: the best-matched theory\npredicts what was, in the Newtonian case, an unexplained coincidence.\n(For discussion, see Pooley & Brown 2002.) In the latter case, by\ncontrast, it has been discovered that one can ‘glue’\nsolutions of shape dynamics to construct new solutions, which are not\nassociated with any particular solution of GTR (in the sense that they\nare not the best matched equivalents of any solution of GTR): see\n(Mercati 2018). Thus, the solution spaces of GTR and shape dynamics\noverlap, but the latter is not a proper subset of the former. Given\nthis, it is no longer clear that shape dynamics can be presented as a\n‘more predictive’ alternative to GTR.", "\nA second conceptual point to make regarding the Machian relationism of\nBarbour and collaborators pertains to its motivations. Barbour claims,\nas we have already seen above, that only spatial angles – and\nnot spatial scales, or a temporal timescale, or absolute velocities or\npositions – are directly empirically observable. Thus, the\nthought goes that an empiricist of good standing should favour (say)\nshape dynamics over GTR, for the former theory, unlike the latter,\nrenders only such ‘directly observable’ quantities\nmeaningful; it does not commit to any absolute quantities which are\nnot ‘directly observable’. There are, however, two central\npoints at which this reasoning could be questioned. First: one could\nrepudiate Barbour’s empiricist motivations. Second: one could\ndeny that only angles are directly observable, or, indeed, that this\nstructure is directly observable at all (see Pooley 2013, p. 47). As\nPooley points out, these are not the strongest grounds on which to\nmotivate Barbour’s project. Rather, a better motivation is this:\nbest-matched theories have the merit of ontological parsimony, as\ncompared with the theories such as Newtonian particle mechanics or\ngeneral relativity, to which the best-matching procedure is applied. A\nsecond motivation has to do with the potential of this research\nprogramme to present new avenues for exploration in the quest for a\nquantum theory of gravity.", "\nOur third and final point is this. Although it is possible to couple\nshape dynamics to matter (see e.g. (Gomes 2012)), in this theory, just\nas in GTR as discussed in the previous section, one also has vacuum\nsolutions, with primitive conformal structure on the 3-geometries.\nGiven the existence of these vacuum solutions, as with GTR, it is far\nfrom clear that the theory makes good on the ambitions of Mach and the\nearly Einstein to construct a theory in which all spatiotemporal\nnotions are reduced to facts about matter. That said, it is worth\nnoting that, unlike in GTR, in shape dynamics one cannot have\na solution consisting of a single rotating body: the overall angular\nmomentum of the universe must vanish." ], "subsection_title": "3.5. Conceptual Matters" } ] }, { "main_content": [ "\nSince 2000, a new ‘dynamical’ approach to spacetime structure has\nemerged in the works of Robert DiSalle (2006) and especially Oliver\nPooley and Harvey Brown (2001, 2006). This approach is to be situated\nagainst an opposing, supposedly orthodox ‘geometrical’ approach to\nspacetime structure, as encapsulated in the works of e.g. Janssen\n(2009) and Maudlin (2012). (This is not to say that either the\ndynamical view or the opposing geometrical view is a unified edifice,\nas we will see below.) The dynamical-geometrical debate has many\nfacets, but one can take the central bone of contention to pertain to\nthe arrow of explanation: is it the case that the geometrical\nstructures of spacetime explain why material bodies behave as they do\n(as the geometrical view would have it), or is it rather the case that\nthe geometrical structure of spacetime is explained by facts about the\nbehaviour of material bodies (as the dynamical view would have it)?\nAlthough this debate connects with historical debates between\nsubstantivalists and relationists, it should be regarded as a distinct\ndispute, for reasons to which we will come.", "\nWhile it is important to keep in mind the above disagreement regarding\nthe arrow of explanation when one is considering the\ndynamical-geometrical debate, it will be helpful in this article to\nhone in on two more specific claims of the dynamical approach, as\npresented by Brown (2005), consistent with the above claim that it is\nfacts about the dynamics of material bodies which explain facts about\nspatiotemporal structure, rather than vice versa. These two claims are\nthe following (Read 2020a):", "\nOn the first of these two points: proponents of the dynamical approach\nmaintain that the spacetime structure of our world is what it is\nbecause of the dynamical laws of nature and their symmetries.\nThat is, the dynamical laws are (at least, relative to spacetime)\nfundamental, and spacetime structure is derivative; in this sense, the\nview is (at least in some cases) a modern-day form of relationism\n(Pooley 2013, §6.3.2) – albeit of a very different kind\nfrom the relationist approaches considered up to this point. (Note,\nthough, that this relationism is a corollary of the above\nexplanatory contention of the dynamical approach; moreover, it is one\nwhich is applicable only to theories which fixed spacetime structure\nsuch as Newtonian mechanics or STR – and therefore not\nto theories with dynamical spacetime structure, such as GTR. For this\nreason, as already indicated above, proponents of the dynamical view\nare not to be identified naïvely with relationists.)", "\nOn the second of these two points: the idea – what Butterfield\n(2007) calls ‘Brown’s moral’ – is that one cannot simply posit a\npiece of geometrical structure in one’s theory, e.g. a Minkowski\nmetric field in STR, and know ab initio that material bodies\n(in particular rods and clocks) will read off intervals of that\nstructure; rather, whether this is the case or not will depend upon\nthe constitution of, and dynamics governing, those material bodies. We\nwill see below specific theories in which any such assumption seems to\nfail. Note that this second point is again consistent with the\nexplanatory contention taken above to be characteristic of the\ndynamical approach: a given piece of structure inherits its\noperational significance as spacetime by dint of the behaviour of\nmaterial bodies.", "\nBefore addressing the second of these two points, we should consider\nthe first in greater detail. The claim that fixed spatiotemporal\nstructure is to be ontologically reduced to facts about material\nbodies invites many questions, chief among which is perhaps the\nfollowing: to what could this ontological reduction possibly amount?\nIn the following section, we will see one particular metaphysical\nprogramme which promises to make good on this claim." ], "section_title": "4. The Dynamical Approach", "subsections": [ { "content": [ "\nThere is arguably a tight relationship between the geometrical\nsymmetries of a spacetime and the symmetries of a theory that\ndescribes the physics of matter (in a broad sense, including fields)\nin it. (Theories such as GTR, in which space-time has its own dynamics\nare more complicated, and will be discussed later; for further\ndiscussion of symmetries in physics, see the entry on\n symmetry and symmetry breaking.)\n Each symmetry is a set of transformations, with a rule of\ncomposition: formally a ‘group’. For instance, the group\nof rotations in the plane has a distinct element for every angle in\nthe range 0–360 degrees; the composition of two rotations is the\nsingle rotation through the sum of their angles. Spacetime symmetries\nare those transformations which leave invariant a piece of spacetime\nstructure (e.g., the symmetries of Minkowski spacetime are\ntranslations, spatial rotations and Lorentz boosts: together, the\nso-called Poincaré transformations); dynamical symmetries are\nthose transformations which leave invariant a set of dynamical\nequations (e.g., the symmetries of Maxwell’s equations of\nelectromagnetism are again the Poincaré transformations). There\nare good reasons to hold that the symmetry groups of theory and\nspacetime must agree. First, since the theory describes matter, and\nhence (arguably) what is measurable, any theoretical symmetries not\nreflected in the postulated spacetime structure indicate unmeasurable\ngeometry: for instance, if an absolute present were postulated in\nrelativistic physics. While in the other direction, if there were\nextra spacetime symmetries beyond those found in the dynamics, then\nper impossible one could measure nonexistent geometric\nquantities: for instance, a theory that depends on absolute velocities\ncannot be formulated in Galilean spacetime (see the entry on\n absolute and relational space and motion: classical theories\n for further discussion of these Newtonian spacetime structures).\nFamously, Earman (1989, ch. 3) declares that the matching of\nspace-time and dynamical symmetries is, thus, an ‘adequacy\ncondition’ on a physical theory.", "\nGiven this ‘adequacy condition’, a given geometry for\nspacetime formally constrains the allowable theories to those with the\njust the right symmetries: not too many, and not too few. It was an\nassumption of many substantivalists (the views of whom are discussed\nbelow) that this constraint was not merely formal, but ontological:\nthat the geometry is more fundamental than the laws, or that geometry\noffers a ‘real’ explanation of the form of the laws\n– such authors would, by the above categorization, qualify as\nproponents of a geometrical view. However, that the symmetries should\nagree does not specify any direction of dependence, and it could be\nreversed, so that the geometric symmetries are ontologically\ndetermined by those of the laws of the theory: hence the geometry\nitself is an expression of the (symmetry properties of the) dynamics\nof matter – transparently, this is consistent with the first of\nthe two specific commitments of the dynamical view discussed above. In\nthe words of Brown and Pooley (2006) (making these points about STR):\n“… space-time’s Minkowskian structure cannot be\ntaken to explain the Lorentz covariance of the dynamical laws. From\nour perspective … the direction of explanation goes the other\nway around. It is the Lorentz covariance of the laws that underwrites\nthe fact that the geometry of space-time is Minkowskian.”", "\nOf the opposing geometrical approach to spacetime, Brown and Pooley\n(2006, p. 84) question the mechanism by which autonomous\nspacetime structure is supposed to explain or constrain the behaviour\nof material bodies. Although we will keep our attention focussed on\nthe dynamical view in this subsection, rather than upon its opponents\n(see the following subsection for more on the explanatory capacities\nof spacetime), one might, however, ask at this point: does the\ndynamical view really do better in this regard? How is it that\ndynamical symmetries are supposed to explain, or account for,\nspacetime structure? In the context of theories with fixed spacetime\nstructure, this question is answered by proponents of the dynamical\nview via an ontological reduction of spatiotemporal structure\nto symmetries of dynamical equations governing matter fields, as\nindicated in (1) above. (In fact, this ‘reduction’ is\nbetter described as a form of elimination, as we will see.)\nBut this, in turn, invites yet more questions: how, metaphysically, is\nthis ontological reduction operating? Can one in fact state dynamical\nlaws, or understand them as “holding” or\n“governing”, without presupposing facts about\nspacetime structure?", "\nTake, for example, Newton’s laws of motion. The 1st law asserts\nthat bodies not acted upon by an external force will move with\nconstant velocity; similarly for the 2nd law and acceleration. These\nlaws seem to presuppose that these are meaningful terms, but in\nspacetime terms their meaning is given by geometric structures: for\ninstance, constant velocity in Galilean spacetime means having a\nstraight spacetime trajectory. And the problem is not restricted to\nNewtonian physics; the same point can be made regarding theories that\npresuppose the Minkowski background spacetime structure, e.g., the\nquantum field theories of the Standard Model.", "\nIt is increasingly well-appreciated that one suitable metaphysical\nprogram to which the dynamical approach can appeal here is\nHuggett’s (2006) regularity relationism: see (Huggett 2009;\nPooley 2013; Stevens 2020). The idea is to consider the dynamical laws\nas regularities that systematize and describe the patterns of events\nconcerning an underlying ontology/ideology that involves or\npresupposes only very limited spatiotemporal features. To illustrate\nhow this approach might go, consider Pooley’s (2013, §6.3)\nproposal that the dynamical approach to STR might postulate only\nR4 topological spatiotemporal structure, which could be\n(for example) attributed to a massive scalar field. Suppose we are\ngiven a full 4D field description of such a field, in terms of some\narbitrary coordinate system. This would describe a simple\n‘Humean mosaic’, to use David Lewis’ term for\none’s basic spatiotemporal and material commitments (see article\n David Lewis\n for further discussion). Now, smooth coordinate changes applied to\nsuch a description will generate distinct mathematical representations\nof that Humean mosaic, given using distinct coordinatizations of the\nfield-stuff. It might happen that, among all such representations,\nthere is a subclass of coordinate systems which are such that (i) when\nthe scalar field is described using a member of the class, it turns\nout that its values at spacetime points satisfy some simple/elegant\nmathematical equation; and moreover, (ii) the members of the class are\nrelated by a nicely-specifiable symmetry group. If this is so, then\nthe simple/elegant equation can be taken as expressing a dynamical law\nfor the world of this mosaic (understood as a statement: “There\nare frames in which …”), and the symmetry group of the\nlaw can be seen as capturing the derivative, not intrinsic,\nspacetime structure of the world. If the symmetry group is the\nPoincaré group, for example, then the field behaves ‘as\nif’ it were embedded in a spacetime with Minkowski geometry. But\nall this means is that the dynamics is representationally equivalent\nto a theory with an autonomous Minkowski geometry. From the point of\nview of the dynamical approach, such a theory is merely an\ninteresting, and perhaps useful, representation of the real facts: and\nit’s a mistake to take every feature of a representation to\ncorrespond to something in reality (Brown & Read 2020,\n§5).", "\nEven granting that this regularity relationist understanding of the\ndynamical approach goes through, three outstanding issues for the\ndynamical approach deserve to be mentioned. First: given that the\nproponent of the view seeks to excise metrical (more generally:\ngeometrical) spacetime structure, one might ask: why stop there? Is\nthere not something unnatural about excising fixed metric structure,\nwhile taking topological structure to be primitive? Such a concern was\nraised by Norton (2008), to which two responses have been offered in\nthe literature: (I) In direct response to Norton, Pooley points out\nthat “the project was to reduce chronogeometric facts to\nsymmetries, not to recover the entire spatiotemporal nature of the\nworld from no spatiotemporal assumptions whatsoever” (2013, p.\n57). (II) Menon (2019) has argued that the machinery of\n‘algebraic fields’ can be deployed in order to reduce\ntopological structure to facts about matter, thereby, if successful,\nmeeting Norton’s challenge head-on. Second: how is one to extend\nthe dynamical approach, understood as a form of Huggett’s\nregularity relationism, to theories of dynamical space-time such as\nGTR? Here, the lack of spacetime symmetries in the theory has posed\nproblems for the successful implementation of any such account\n(Stevens 2014), although arguably initial progress in this regard has\nbeen made by Vassallo and Esfeld (2016). Third: to which symmetries of\nthe laws is the dynamical approach supposed to be sensitive? In the\nphilosophy of physics, it is common to draw a distinction between\n‘internal’ and ‘external’ symmetries: examples\nof the former include U(1) gauge transformations in electromagnetism;\nexamples of the latter are coordinate transformations, such as\nGalilean boosts in Newtonian mechanics. But there are many questions\nhere, such as: (i) how, precisely, is the distinction between internal\nand external symmetries to be drawn? (ii) why should the proponent of\nthe dynamical approach stop at external symmetries? For discussion of\nthese questions, see (Dewar 2020)." ], "subsection_title": "4.1 The Dynamical Approach and Regularity Relationism" }, { "content": [ "\nWe have already seen how the dynamical approach, qua\nprogramme of ontological reduction, is supposed to play out in the\ncontext of theories with fixed spacetime structure, including both\nNewtonian theories and STR. We have also witnessed Brown and\nPooley’s concerns about the ability of a substantival spacetime\nto explain facts about the behavior of matter. These concerns are\nmotivated by apparent problem cases, in which the symmetries of a\nsubstantival spacetime seem to come apart from those of the dynamical\nlaws governing matter. Such cases include: (i) Newtonian mechanics set\nin Newtonian spacetime (Read 2020a); (ii) the Jacobson-Mattingly\ntheory (Jacobson & Mattingly 2001), in which dynamical symmetries\nare a subset of spacetime symmetries, as a result of the presence of\nan additional (dynamical) symmetry-breaking vector field (Read, Brown\n& Lehmkuhl 2018).", "\nIt is not obvious that these critiques are fair to proponents of a\ngeometrical view. One might take their position not to be that a\ncertain piece of geometrical structure (e.g., the Minkowski metric of\nSTR) invariably constrains matter, whenever it is present in a theory,\nto manifest its symmetries (a claim which seems to be false, in light\nof the above cases). Instead, one might take their claim to be\nconditional: if one has matter which couples to this piece of\ngeometrical structure in such-and-such a way, then that\ngeometrical structure can explain why the laws have the such-and-such\nsymmetries. In (Read, 2020a), the (arguably) straw man version of a\ngeometrical view critiqued by Brown and Pooley is dubbed the\n‘unqualified geometrical approach’, in contrast with this\nmore nuanced and defensible version of the view, which is dubbed the\n‘qualified geometrical approach’. (Brown might still\nreject the qualified geometrical approach on the grounds that it makes\nexplanatory appeal to objects which violate the ‘action-reaction\nprinciple’, which states that every entity physical should both\nact on, and react to, other physical entities (Brown 2005, p. 140). If\nso, that this is the real reason for the rejection deserves to be\nflagged; moreover, it remains open whether the objection succeeds\nagainst the non-substantivalist versions of the geometrical view which\nare discussed below.)", "\nFocussing on the qualified geometrical approach, there are also\nquestions regarding the particular sense in which spacetime structure\ncan be said to be explanatory of dynamical symmetries. One notion of\nexplanation discussed in this literature is that of a\n‘constructive explanation’.This is derivative on\nEinstein’s distinction between ‘principle theories’\nand ‘constructive theories’ (Einstein 1919): for detailed\ndiscussion, see (Brown 2005, §5.2). In brief, a constructive\nexplanation is one in which phenomenological effects are explained by\nreference to real (but possibly unobservable) physical bodies. (For\nfurther discussion of how to understand constructive theories and\nexplanations, see (Frisch 2011).) With the idea of a constructive\nexplanation in mind, one can say this: if a proponent of a geometrical\nview hypostatizes spacetime, then they can give constructive\nexplanations of certain physical effects by appeal to that spacetime\nstructure; otherwise, they cannot. That said, even if one does not\nhypostatise spacetime, and so concedes that spacetime cannot offer\nconstructive explanations of the behaviour of matter, it is not\nobvious that spacetime cannot still facilitate other kinds of\nexplanation. For discussions of these issues, see (Acuña 2016;\nDorato & Felline 2010; Frisch 2011; Read 2020b)." ], "subsection_title": "4.2 Space-time and Explanation on the Dynamical Approach" }, { "content": [ "\nAs we have already seen in section 2, spacetime in GTR is dynamical.\nThis leads Brown to maintain that there is no substantial conceptual\ndistinction between the metric field of GTR and matter fields:\n“Gravity is different from the other interactions, but this\ndoesn’t mean that it is categorically distinct from,\nsay, the electromagnetic field” (Brown 2005, p. 159). In this\nsense, Brown is a relationist about GTR, and counts authors such as\n(Rovelli, 1997) as allies. However, much caution is needed concerning\nthis use of the term ‘relationism’. In particular, in the\ncontext of GTR – and in significant contrast with his approach\nto theories such as STR – Brown makes no claim that the metric\nfield should be ontologically reduced to properties of (the laws\ngoverning) matter fields; rather, in light of its dynamical status,\nthe metric field of GTR “cries out for reification”\n(Brown, personal communication). Indeed, even if Brown did not\nmaintain this, we have already registered above that there are\ntechnical problems with attempting to apply the dynamical approach,\nunderstood as a version of regularity relationism, to theories such as\nGTR.", "\nIn light of these issues, when considering GTR, Brown (2005, ch. 9)\nfocuses entirely on thesis (2), presented in the introduction to this\nsection: no piece of geometrical structure has its\n‘chronogeometric significance’ of necessity – that\nis, no piece of geometrical structure is necessarily surveyed by\nphysical bodies; rather, in order to ascertain whether such is the\ncase, one must pay detailed attention to the dynamics of the matter\nfields constituting those physical bodies. This, indeed, should\nalready be evident in light of the examples discussed in the previous\nsubsection, such as the Jacobson-Mattingly theory, in which matter\ndoes not ‘advert’ to the designated piece of spacetime\nstructure.", "\nThis thesis (2) should be uncontroversial. There are, however,\nconcerns that the thesis is so uncontroversial that any\ndistinction between the dynamical approach and its opponents in the\ncontext of theories such as GTR (and, in particular, without the\nregularity relationist approach to ontological reduction applied in\nthe case of theories with fixed spacetime structure) has been effaced\n(Pooley 2013; Read 2020a). Even setting this aside, there are also\ndisagreements regarding how exactly a piece of structure in a given\ntheory is to acquire its ‘chronogeometric\nsignificance’ – that is, for the intervals which it\ndetermines to be accessible operationally to physical bodies and\nmeasuring devices. Brown’s preferred answer to this question\n(Brown 2005, ch. 9) makes appeal to the ‘strong equivalence\nprinciple’. There are a great many subtleties and technical\ndifficulties which need to be overcome in order to attain a clear\nunderstanding of this principle (Read, Brown & Lehmkuhl 2018;\nWeatherall 2020), but, roughly speaking, it states that, in local\nregions in GTR, matter fields can be understood to obey Lorentz\ncovariant dynamical equations, just as in STR (we have already seen\nsomething of this in section 2 above). Absent further details,\npace Brown, it is not clear why this is sufficient to secure\nthe ‘chronogeometric significance’ of the metric field in\nGTR. Even setting this aside, there are questions regarding whether\nthe strong equivalence principle is necessary for\nchronogeometric significance. For example, an alternative approach\nmight make appeal to the results of (Ehlers, Pirani & Schild,\n1972), in which the authors demonstrate that the trajectories of\nmassive and massless bodies are sufficient to reconstruct the metric\nfield in GTR (cf. (Malament 2012, §2.1)). These issues are raised\nin (Read 2020a), but much work remains to be done in uncovering the\nfull range of ways in which a given piece of structure might come to\nhave chronogeometric significance." ], "subsection_title": "4.3 The Dynamical Approach and General Relativity" } ] }, { "main_content": [ "\nThis entry, and its companion on\n classical theories,\n have been concerned with tracing the history and philosophy of\n‘absolute’ and ‘relative’ theories of space\nand motion. Along the way we have been at pains to introduce some\nclear terminology for various different concepts (e.g.,\n‘true’ motion, ‘substantivalism’,\n‘absolute space’), but what we have not really done is say\nwhat the difference between absolute and relative space and\nmotion is: just what is at stake? Rynasiewicz (2000) argued that there\nsimply are no constant issues running through the history from\nantiquity through general relativity theory; that there is no stable\nmeaning for either ‘absolute motion’ or ‘relative\nmotion’ (or ‘substantival space’ vs\n‘relational space’). While we agree to a certain extent,\nwe think that nevertheless there are a series of issues that have\nmotivated thinkers again and again. Rynasiewicz is probably right that\nthe issues cannot be expressed in formally precise terms, but that\ndoes not mean that there are no looser philosophical affinities that\nshed useful light on the history and on current theorizing.", "\nOur discussion has revealed several different issues, of which we will\nhighlight three as components of the ‘absolute-relative\ndebate’. (i) There is the question of whether all motions and\nall possible descriptions of motions are equal, or whether some are\n‘real’ – what we have called, in Seventeenth Century\nparlance, ‘true’. There is a natural temptation for those\nwho hold that there is ‘nothing but the relative positions and\nmotions between bodies’ to add ‘and all such motions are\nequal’, thus denying the existence of true motion. However,\narguably – perhaps surprisingly – no one we have discussed\nhas unreservedly held this view (at least not consistently): Descartes\nconsidered motion ‘properly speaking’ to be privileged,\nLeibniz introduced ‘active force’ to ground motion\n(arguably in his mechanics as well as metaphysically), and\nMach’s view seems to be that the distribution of matter in the\nuniverse determines a preferred standard of inertial motion. In\ngeneral relativity there is a well-defined distinction between\ninertial and accelerated motion, given by the spacetime metric, but\nEinstein initially hoped that the metric itself would be determined in\nturn by relative locations and motions of the matter distribution in\nspacetime.", "\nThat is, relationists can allow ‘true’ motions if they\noffer an analysis of them in terms of the relations between bodies.\nGiven this logical point, we are led to the second question: (ii) is\ntrue motion definable in terms of relations or not? (And if one hopes\nto give an affirmative answer, what kinds of relations are acceptable\nto use in the reductive definition?) It seems reasonable to call this\nthe issue of whether motion is absolute or relative.\nDescartes and Mach were relationists about motion in this sense, while\nNewton was an absolutist. In the case of Einstein and GTR we linked\nrelational motion to the satisfaction of Mach’s Principle, just\nas Einstein did in the early years of the theory. Despite some\npromising features displayed by GTR, and certain of its models, we saw\nthat Mach’s Principle is certainly not fully satisfied in GTR as\na whole. We also noted that in the absence of absolute simultaneity,\nit becomes an open question what relations are to be permitted in the\ndefinition (or supervience base) – spacetime interval relations?\nInstantaneous spatial distances and velocities on a 3-d hypersurface?\nThe shape dynamics program comes at this question from a new\nperspective, starting with momentary slices of space (with or without\nmatter contents) which are given a strongly relational – as\nopposed to absolute – interpretation. However, we argued that it\nultimately remains unclear whether this approach vindicates\nMach’s Principle.", "\nThe final issue we have discussed in this article is that of (iii)\nwhether spacetime structures are substantial entities in their own\nright, metaphysically speaking not grounded on facts about dynamical\nlaws, or whether instead it is best to think of the reality of\nspacetime structures as dependent upon, and explained by, facts about\nthe world’s dynamical laws, as advocates of the dynamical\napproach maintain. The debate here is not the same as that between\nclassical relationism and substantivalism, although there are clear\naffinities between the dynamical approach and classical relationism.\nWe explored how this issue takes quite different forms in the context\nof special relativistic (Lorentz covariant) physical theories and in\nthe context of general relativistic theories." ], "section_title": "5. Conclusion", "subsections": [] } ]

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[ "\n\nIn his first paper on the special theory of relativity, Einstein\nindicated that the question of whether or not two spatially separated\nevents were simultaneous did not necessarily have a definite answer,\nbut instead depended on the adoption of a convention for its\nresolution. Some later writers have argued that Einstein’s choice of a\nconvention is, in fact, the only possible choice within the framework\nof special relativistic physics, while others have maintained that\nalternative choices, although perhaps less convenient, are indeed\npossible." ]

[ { "content_title": "1. The Conventionality Thesis", "sub_toc": [] }, { "content_title": "2. Phenomenological Counterarguments", "sub_toc": [] }, { "content_title": "3. Malament’s Theorem", "sub_toc": [] }, { "content_title": "4. Other Considerations", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nThe debate about the conventionality of simultaneity is usually\ncarried on within the framework of the special theory of relativity.\nEven prior to the advent of that theory, however, questions had been\nraised (see, e.g., Poincaré 1898) as to whether simultaneity\nwas absolute; i.e., whether there was a unique event at location A\nthat was simultaneous with a given event at location B. In his first\npaper on relativity, Einstein (1905) asserted that it was necessary to\nmake an assumption in order to be able to compare the times of\noccurrence of events at spatially separated locations (Einstein 1905,\n38–40 of the Dover translation or 125–127 of the Princeton\ntranslation; but note Scribner 1963, for correction of an error in the\nDover translation). His assumption, which defined what is usually\ncalled standard synchrony, can be described in terms of the following\nidealized thought experiment, where the spatial locations A\nand B are fixed locations in some particular, but arbitrary,\ninertial (i.e., unaccelerated) frame of reference: Let a light ray,\ntraveling in vacuum, leave A at time t1\n(as measured by a clock at rest there), and arrive at B\ncoincident with the event E at B. Let the ray be\ninstantaneously reflected back to A, arriving at time\nt2. Then standard synchrony is defined by saying\nthat E is simultaneous with the event at A that\noccurred at time (t1 +\nt2)/2. This definition is equivalent to the\nrequirement that the one-way speeds of the ray be the same on the two\nsegments of its round-trip journey between A and\nB.", "\n\nIt is interesting to note (as pointed out by Jammer (2006, 49), in his\ncomprehensive survey of virtually all aspects of simultaneity) that\nsomething closely analogous to Einstein’s definition of standard\nsimultaneity was used more than 1500 years earlier by St. Augustine in\nhis Confessions (written in 397 CE). He was arguing against\nastrology by telling a story of two women, one rich and one poor, who\ngave birth simultaneously but whose children had quite different lives\nin spite of having identical horoscopes. His method of determining\nthat the births, at different locations, were simultaneous was to have\na messenger leave each birth site at the moment of birth and travel to\nthe other, presumably with equal speeds. Since the messengers met at\nthe midpoint, the births must have been simultaneous. Jammer comments\nthat this “may well be regarded as probably the earliest\nrecorded example of an operational definition of distant\nsimultaneity.”", "\n\nThe thesis that the choice of standard synchrony is a convention,\nrather than one necessitated by facts about the physical universe\n(within the framework of the special theory of relativity), has been\nargued particularly by Reichenbach (see, for example, Reichenbach\n1958, 123–135) and Grünbaum (see, for example,\nGrünbaum 1973, 342–368). They argue that the only\nnonconventional basis for claiming that two distinct events are not\nsimultaneous would be the possibility of a causal influence connecting\nthe events. In the pre-Einsteinian view of the universe, there was no\nreason to rule out the possibility of arbitrarily fast causal\ninfluences, which would then be able to single out a unique event\nat A that would be simultaneous with E. In an\nEinsteinian universe, however, no causal influence can travel faster\nthan the speed of light in vacuum, so from the point of view of\nReichenbach and Grünbaum, any event at A whose time of\noccurrence is in the open interval between t1 and\nt2 could be defined to be simultaneous\nwith E. In terms of the ε-notation introduced by\nReichenbach, any event at A occurring at a\ntime t1 + ε(t2 −\nt1), where 0 < ε < 1, could be\nsimultaneous with E. That is, the conventionality thesis\nasserts that any particular choice of ε within its stated\nrange is a matter of convention, including the choice ε=1/2\n(which corresponds to standard synchrony). If ε differs from\n1/2, the one-way speeds of a light ray would differ (in an\nε-dependent fashion) on the two segments of its round-trip\njourney between A and B. If, more generally, we\nconsider light traveling on an arbitrary closed path in\nthree-dimensional space, then (as shown by Minguzzi 2002,\n155–156) the freedom of choice in the one-way speeds of light\namounts to the choice of an arbitrary scalar field (although two\nscalar fields that differ only by an additive constant would give the\nsame assignment of one-way speeds).", "\n\n It might be argued that the definition of\nstandard synchrony makes use only of the relation of equality (of the\none-way speeds of light in different directions), so that simplicity\ndictates its choice rather than a choice that requires the\nspecification of a particular value for a parameter. Grünbaum\n(1973, 356) rejects this argument on the grounds that, since the\nequality of the one-way speeds of light is a convention, this choice\ndoes not simplify the postulational basis of the theory but only gives\na symbolically simpler representation." ], "section_title": "1. The Conventionality Thesis", "subsections": [] }, { "main_content": [ "\n\nMany of the arguments against the conventionality thesis make use of\nparticular physical phenomena, together with the laws of physics, to\nestablish simultaneity (or, equivalently, to measure the one-way speed\nof light). Salmon (1977), for example, discusses a number of such\nschemes and argues that each makes use of a nontrivial convention. For\ninstance, one such scheme uses the law of conservation of momentum to\nconclude that two particles of equal mass, initially located halfway\nbetween A and B and then separated by an explosion,\nmust arrive at A and B\nsimultaneously. Salmon (1977, 273) argues,\nhowever, that the standard formulation of the law of conservation of\nmomentum makes use of the concept of one-way velocities, which cannot\nbe measured without the use of (something equivalent to) synchronized\nclocks at the two ends of the spatial interval that is traversed;\nthus, it is a circular argument to use conservation of momentum to\ndefine simultaneity.", "\n\nIt has been argued (see, for example, Janis 1983, 103–105, and\nNorton 1986, 119) that all such schemes for establishing\nconvention-free synchrony must fail. The argument can be summarized as\nfollows: Suppose that clocks are set in standard synchrony, and\nconsider the detailed space-time description of the proposed\nsynchronization procedure that would be obtained with the use of such\nclocks. Next suppose that the clocks are reset in some nonstandard\nfashion (consistent with the causal order of events), and consider the\ndescription of the same sequence of events that would be obtained with\nthe use of the reset clocks. In such a description, familiar laws may\ntake unfamiliar forms, as in the case of the law of conservation of\nmomentum in the example mentioned above. Indeed, all of special\nrelativity has been reformulated (in an unfamiliar form) in terms of\nnonstandard synchronies (Winnie 1970a and 1970b). Since the proposed\nsynchronization procedure can itself be described in terms of a\nnonstandard synchrony, the scheme cannot describe a sequence of events\nthat is incompatible with nonstandard synchrony. A comparison of the\ntwo descriptions makes clear what hidden assumptions in the scheme are\nequivalent to standard synchrony. Nevertheless, editors of respected\njournals continue to accept, from time to time, papers purporting to\nmeasure one-way light speeds; see, for example, Greaves et\nal. (2009). Application of the procedure just described shows\nwhere their errors lie." ], "section_title": "2. Phenomenological Counterarguments", "subsections": [] }, { "main_content": [ "\n\nFor a discussion of various proposals to establish synchrony, see the\nsupplementary document:", "\n Transport of Clocks\n ", "\nThe only currently discussed proposal is based on a theorem of\nMalament (1977), who argues that standard synchrony is the only\nsimultaneity relation that can be defined, relative to a given\ninertial frame, from the relation of (symmetric) causal\nconnectibility. Let this relation be represented by κ, let the\nstatement that events p and q are simultaneous be represented\nby S(p,q), and let the given inertial frame\nbe specified by the world line, O, of some inertial\nobserver. Then Malament’s uniqueness theorem shows that if\nS is definable from κ and O, if it is an\nequivalence relation, if points p on O and\nq not on O exist such that\nS(p,q) holds, and if S is not the\nuniversal relation (which holds for all points), then S is\nthe relation of standard synchrony.", "\n\nSome commentators have taken Malament’s theorem to have settled\nthe debate on the side of nonconventionality. For example, Torretti\n(1983, 229) says, “Malament proved that simultaneity by standard\nsynchronism in an inertial frame F is the only\nnon-universal equivalence between events at different points\nof F that is definable (‘in any sense of\n“definable” no matter how weak’) in terms of causal\nconnectibility alone, for a given F”; and Norton\n(Salmon et al. 1992, 222) says, “Contrary to most\nexpectations, [Malament] was able to prove that the central claim\nabout simultaneity of the causal theorists of time was false. He\nshowed that the standard simultaneity relation was the only nontrivial\nsimultaneity relation definable in terms of the causal structure of a\nMinkowski spacetime of special relativity.”", "\n\nOther commentators disagree with such arguments, however.\nGrünbaum (2010) has written a detailed critique of Malament’s\npaper. He first cites Malament’s need to postulate that S is an\nequivalence relation as a weakness in the argument, a view also\nendorsed by Redhead (1993, 114). Grünbaum’s main argument,\nhowever, is based on an earlier argument by Janis (1983,\n107–109) that Malament’s theorem leads to a unique (but\ndifferent) synchrony relative to any inertial observer, that this\nlatitude is the same as that in introducing Reichenbach’s ε,\nand thus Malament’s theorem should carry neither more nor less weight\nagainst the conventionality thesis than the argument\n(mentioned above in the last paragraph of the\nfirst section of this article) that standard synchrony is the simplest\nchoice. Grünbaum concludes “that Malament’s remarkable\nproof has not undermined my thesis that, in the STR, relative\nsimultaneity is conventional, as contrasted with its\nnon-conventionality in the Newtonian world, which I have articulated!\nThus, I do not need to retract the actual claim I made in\n1963…” Somewhat similar arguments are given by Redhead\n(1993, 114) and by Debs and Redhead (2007, 87–92).", "\nFor further discussion, see the supplement document:", "\nFurther Discussion of Malament’s Theorem\n " ], "section_title": "3. Malament’s Theorem", "subsections": [] }, { "main_content": [ "\n\nSince the conventionality thesis rests upon the existence of a fastest\ncausal signal, the existence of arbitrarily fast causal signals would\nundermine the thesis. If we leave aside the question of causality, for\nthe moment, the possibility of particles (called tachyons) moving with\narbitrarily high velocities is consistent with the mathematical\nformalism of special relativity (see, for example, Feinberg 1967).\nJust as the speed of light in vacuum is an upper limit to the possible\nspeeds of ordinary particles (sometimes called bradyons), it would be\na lower limit to the speeds of tachyons. When a transformation is made\nto a different inertial frame of reference, the speeds of both\nbradyons and tachyons change (the speed of light in vacuum being the\nonly invariant speed). At any instant, the speed of a bradyon can be\ntransformed to zero and the speed of a tachyon can be transformed to\nan infinite value. The statement that a bradyon is moving forward in\ntime remains true in every inertial frame (if it is true in one), but\nthis is not so for tachyons. Feinberg (1967) argues that this does not\nlead to violations of causality through the exchange of tachyons\nbetween two uniformly moving observers because of ambiguities in the\ninterpretation of the behavior of tachyon emitters and absorbers,\nwhose roles can change from one to the other under the transformation\nbetween inertial frames. He claims to resolve putative causal\nanomalies by adopting the convention that each observer describes the\nmotion of each tachyon interacting with that observer’s apparatus in\nsuch a way as to make the tachyon move forward in time. However, all\nof Feinberg’s examples involve motion in only one spatial\ndimension. Pirani (1970) has given an explicit two-dimensional example\nin which Feinberg’s convention is satisfied but a tachyon signal is\nemitted by an observer and returned to that observer at an earlier\ntime, thus leading to possible causal anomalies.", "\n\nA claim that no value of ε other than 1/2 is mathematically\npossible has been put forward by Zangari (1994). He argues that\nspin-1/2 particles (e.g., electrons) must be represented\nmathematically by what are known as complex spinors, and that the\ntransformation properties of these spinors are not consistent with the\nintroduction of nonstandard coordinates (corresponding to values of\nε other than 1/2). Gunn and Vetharaniam (1995), however,\npresent a derivation of the Dirac equation (the fundamental equation\ndescribing spin-1/2 particles) using coordinates that are consistent\nwith arbitrary synchrony. They argue that Zangari mistakenly required\na particular representation of space-time points as the only one\nconsistent with the spinorial description of spin-1/2 particles.", "\n\nAnother argument for standard synchrony has been given by Ohanian (2004),\nwho bases his considerations on the laws of dynamics. He argues that a\nnonstandard choice of synchrony introduces pseudoforces into Newton’s\nsecond law, which must hold in the low-velocity limit of special\nrelativity; that is, it is only with standard synchrony that net force\nand acceleration will be proportional. Macdonald (2005) defends the\nconventionality thesis against this argument in a fashion analagous to\nthe argument used by Salmon (mentioned above in\nthe first paragraph of the second section of this article) against the\nuse of the law of conservation of momentum to define simultaneity:\nMacdonald says, in effect, that it is a convention to require Newton’s\nlaws to take their standard form.", "\n\nMany of the arguments against conventionality involve viewing the\npreferred simultaneity relation as an equivalence relation that is\ninvariant under an appropriate transformation group. Mamone Capria\n(2012) has examined the interpretation of simultaneity as an invariant\nequivalence relation in great detail, and argues that it does not have\nany bearing on the question of whether or not simultaneity is\nconventional in special relativity.", "\n\nA vigorous defense of conventionality has been offered by Rynasiewicz\n(2012). He argues that his approach “has the merit of nailing\nthe exact sense in which simultaneity is conventional. It is\nconventional in precisely the same sense in which the gauge freedom\nthat arises in the general theory of relativity makes the choice\nbetween diffeomorphically related models conventional.” He\nbegins by showing that any choice of a simultaneity relation is\nequivalent to a choice of a velocity in the equation for local time in\nH.A. Lorentz’s Versuch theory (Lorentz 1895). Then, beginning\nwith Minkowski space with the standard Minkowski metric, he introduces\na diffeomorphism in which each point is mapped to a point with the\nsame spatial coordinates, but the temporal coordinate is that of a\nLorentzian local time expressed in terms of the velocity as a\nparameter. This mapping is not an isometry, for the light cones are\ntilted, which corresponds to anisotropic light propagation. He\nproceeds to argue, using the hole argument (see, for example, Earman\nand Norton 1987) as an analogy, that this parametric freedom is just\nlike the gauge freedom of general relativity. As the tilting of the\nlight cones, if projected into a single spatial dimension, would be\nequivalent to a choice of Reichenbach’s ε, it seems that\nRynasiewicz’s argument is a generalization and more completely argued\nversion of the argument given by Janis that is mentioned above in the\nthird paragraph of Section 3.", "\n\nThe debate about conventionality of simultaneity seems far from\nsettled, although some proponents on both sides of the argument might\ndisagree with that statement. The reader wishing to pursue the matter\nfurther should consult the sources listed below as well as additional\nreferences cited in those sources." ], "section_title": "4. Other Considerations", "subsections": [] } ]

[ "Anderson, R., I. Vetharaniam, and G. Stedman, 1998.\n“Conventionality of Synchronisation, Gauge Dependence and Test\nTheories of Relativity,” Physics Reports, 295: 93–180.", "Augustine, St., Confessions, translated by E.J. Sheed,\nIndianapolis: Hackett Publishing Co., 2nd edition, 2006.", "Ben-Yami, H., 2006. “Causality and Temporal Order in Special\nRelativity,” British Journal for the Philosophy of\nScience, 57: 459–479.", "Brehme, R., 1985. “Response to ‘The Conventionality of\nSynchronization’,” American Journal of Physics, 53:\n56–59.", "Brehme, R., 1988. “On the Physical Reality of the Isotropic Speed\nof Light,” American Journal of Physics, 56:\n811–813.", "Bridgman, P., 1962. A Sophisticate’s Primer of Relativity.\nMiddletown: Wesleyan University Press.", "Debs, T. and M. Redhead, 2007. Objectivity, Invariance, and\nConvention: Symmetry in Physical Science, Cambridge, MA and\nLondon: Harvard University Press.", "Earman, J. and J. Norton, 1987. “What Price Spacetime\nSubstantivalism? The Hole Story,” British Journal for the\nPhilosophy of Science, 38: 515–525.", "Eddington, A., 1924. The Mathematical Theory of Relativity,\n2nd edition, Cambridge: Cambridge University Press.", "Einstein, A., 1905. “Zur Elektrodynamik bewegter\nKörper,” Annalen der Physik, 17: 891–921. English\ntranslations in The Principle of Relativity, New York: Dover,\n1952, pp. 35–65; and in J. Stachel (ed.), Einstein’s Miraculous\nYear, Princeton: Princeton University Press, 1998,\npp. 123–160.", "Ellis, B. and P. Bowman, 1967. “Conventionality in Distant\nSimultaneity,” Philosophy of Science, 34:\n116–136.", "Feinberg, G., 1967. “Possibility of Faster-Than-Light Particles,”\nPhysical Review, 159: 1089–1105.", "Giulini, D., 2001. “Uniqueness of Simultaneity,” British\nJournal for the Philosophy of Science, 52: 651–670.", "Greaves, E., A. Rodriguez, and J. Ruiz-Camaro, 2009. “A One-Way\nSpeed of Light Experiment,” American Journal of Physics, 77:\n894–896.", "Grünbaum, A., 1973. Philosophical Problems of Space and\nTime (Boston Studies in the Philosophy of Science,\nVolume 12), 2nd enlarged edition, Dordrecht/Boston: D. Reidel.", "Grünbaum, A., 2010. “David Malament and the\nConventionality of Simultaneity: A Reply,” Foundations of\nPhysics, 40: 1285–1297.", "Grünbaum, A., W. Salmon, B. van Fraassen, and A. Janis,\n1969. “A Panel Discussion of Simultaneity by Slow Clock Transport in\nthe Special and General Theories of Relativity,” Philosophy of\nScience, 36: 1–81.", "Gunn, D. and I. Vetharaniam, 1995. “Relativistic Quantum Mechanics\nand the Conventionality of Simultaneity,” Philosophy of\nScience, 62: 599–608.", "Havas, P., 1987. “Simultaneity, Conventionalism, General Covariance,\nand the Special Theory of Relativity,” General Relativity and\nGravitation, 19: 435–453.", "Jammer, M., 2006. Concepts of Simultaneity: From Antiquity to\nEinstein and Beyond, Baltimore: Johns Hopkins University\nPress.", "Janis, A., 1983. “Simultaneity and Conventionality,” in R. Cohen\nand L. Laudan (eds.), Physics, Philosophy and Psychoanalysis\n(Boston Studies in the Philosophy of Science, Volume 76),\nDordrecht/Boston: D. Reidel, pp. 101–110.", "Lorentz, H., 1895. Versuch einer Theorie der electrischen und\noptischen Erscheinungen in bewegter Körpern, Leiden:\nE.J. Brill.", "Macdonald, A., 2005. “Comment on ‘The Role of Dynamics\nin the Synchronization Problem,’ by Hans C. Ohanion,”\nAmerican Journal of Physics, 73: 454–455.", "Malament, D., 1977. “Causal Theories of Time and the\nConventionality of Simultaniety,” Noûs, 11:\n293–300.", "Mamone Capria, M., 2001. “On the Conventionality of Simultaneity\nin Special Relativity,” Foundations of Physics, 31:\n775–818.", "Mamone Capria, M., 2012. “Simultaneity as an Invariant\nEquivalence Relation,” Foundations of Physics, 42:\n1365–1383.", "Minguzzi, E., 2002. “On the Conventionality of Simultaneity,”\nFoundations of Physics Letters, 15: 153–169.", "Norton, J., 1986. “The Quest for the One Way Velocity of Light,”\nBritish Journal for the Philosophy of Science,\n37: 118–120.", "Ohanian, H., 2004. “The Role of Dynamics in the\nSynchronization Problem,” American Journal of Physics,\n72: 141–148.", "Pirani, F., 1970. “Noncausal Behavior of Classical\nTachyons,” Physical Review, D1: 3224–3225.", "Poincaré, H., 1898. “La Mesure du Temps,” Revue de\nMétaphysique et de Morale, 6: 1–13. English translation\nin The Foundations of Science, New York: Science Press, 1913,\npp. 223–234.", "Redhead, M., 1993. “The Conventionality of Simultaneity,” in J.\nEarman, A. Janis, G. Massey, and N. Rescher (eds.), Philosophical\nProblems of the Internal and External Worlds, Pittsburgh:\nUniversity of Pittsburgh Press, pp. 103–128.", "Reichenbach H., 1958. The Philosophy of Space & Time,\nNew York: Dover.", "Rynasiewicz, R., 2012. “Simultaneity, Convention, and Gauge\nFreedom,” Studies in History and Philosophy of Modern\nPhysics, 43: 90–94.", "Salmon, M., J. Earman, C. Glymour, J. Lennox, P. Machamer,\nJ. McGuire, J. Norton, W. Salmon, and K. Schaffner,\n1992. Introduction to the Philosophy of Science, Englewood\nCliffs: Prentice Hall.", "Salmon, W., 1977. “The Philosophical Significance of the One-Way\nSpeed of Light,” Noûs, 11: 253–292.", "Sarkar, S. and J. Stachel, 1999. “Did Malament Prove the\nNon-Conventionality of Simultaneity in the Special Theory of\nRelativity?” Philosophy of Science, 66:\n208–220.", "Scribner, C., 1963. “Mistranslation of a Passage in Einstein’s\nOriginal Paper on Relativity,” American Journal of Physics,\n31: 398.", "Spirtes, P., 1981. Conventionalism and the Philosophy of Henri\nPoincaré, Ph.D. Dissertation, University of\nPittsburgh.", "Stein, H., 1991. “On Relativity Theory and Openness of the\nFuture,” Philosophy of Science, 58: 147–167.", "Torretti, R., 1983. Relativity and Geometry, Oxford, New\nYork: Pergamon.", "Winnie, J., 1970a. “Special Relativity Without One-Way Velocity\nAssumptions: Part I,” Philosophy of Science,\n37: 81–99.", "Winnie, J., 1970b. “Special Relativity Without One-Way Velocity\nAssumptions: Part II,” Philosophy of Science,\n37: 223–238.", "Zangari, M., 1994. “A New Twist in the Conventionality of\nSimultaneity Debate,” Philosophy of Science,\n61: 267–275." ]

[ { "href": "../einstein-philscience/", "text": "Einstein, Albert: philosophy of science" }, { "href": "../reichenbach/", "text": "Reichenbach, Hans" }, { "href": "../wesley-salmon/", "text": "Salmon, Wesley" } ]

[ "\nA spacetime singularity is a breakdown in spacetime, either in its\ngeometry or in some other basic physical structure. It is a topic of\nongoing physical and philosophical research to clarify both the nature\nand significance of such pathologies. When it is the fundamental\ngeometry that breaks down, spacetime singularities are often viewed as\nan end, or “edge”, of spacetime itself. Numerous\ndifficulties, however, arise when one tries to make this notion more\nprecise. Breakdowns in other physical structures pose other problems,\njust as difficult. Our current theory of spacetime, general\nrelativity, not only allows for singularities, but tells us that they\nare unavoidable in some real-world circumstances. Thus we apparently\nneed to understand the ontology of singularities if we are to grasp\nthe nature of space and time in the actual universe. The possibility\nof singularities also carries potentially important implications for\nthe issues of physical determinism and the scope of physical laws.\n", "\nBlack holes are regions of spacetime from which nothing, not even\nlight, can escape. A typical black hole is the result of the\ngravitational force becoming so strong that one would have to travel\nfaster than light to escape its pull. Such black holes generically\ncontain a spacetime singularity at their center; thus we cannot fully\nunderstand a black hole without also understanding the nature of\nsingularities. Black holes, however, raise several additional\nconceptual problems and questions on their own. When quantum effects\nare taken into account, black holes, although they are nothing more\nthan regions of spacetime, appear to become thermodynamical entities,\nwith a temperature and an entropy. This seems to point to a deep and\nhitherto unsuspected connection among our three most fundamental\ntheories, general relativity, quantum field theory and thermodynamics.\nIt is far from clear, however, what it may mean to attribute\nthermodynamical properties to black holes. At the same time, some of\nthese thermodynamical properties of black holes now seem amenable to\ndirect testing in terrestrial laboratories by observing the behavior\nof “analogue” systems composed of ordinary material. This\nall raises problems about inter-theory relations, in particular about\nrelations between the “same” quantity as it appears in\ndifferent theories. It also bears on the meaning and status of the\nSecond Law of thermodynamics, with possible implications for\ncharacterizing a cosmological arrow of time. ", "\nFinally, the evolution of black holes is apparently in conflict with\nstandard quantum evolution, for such evolution rules out the sort of\nincrease in entropy that seems to be required when black holes are\npresent. Indeed, as purely gravitational entities with striking\nquantum properties, what we know about black holes lies at the heart\nof and guides many attempts to formulate a theory of quantum gravity.\nThis has led to a debate over what seemingly fundamental physical\nprinciples are likely to be preserved in, or violated by, a full\nquantum theory of gravity. ", "\nBecause so few philosophers have worked on these issues, many\nquestions and problems of great possible interest have not been\ninvestigated philosophically at all; others have had only the barest\nstarts made on them; consequently, several sections discussed in this\narticle merely raise questions and point to problems that deserve\nphilosophical attention. The field is wide open for expansive and\nintensive exploration. ", "\nAll the technical material required to delve more deeply into the\nsubject of this entry can be found in any of a number of excellent\nclassic and recent sources, including: Hawking and Ellis (1973);\nGeroch and Horowitz (1979); Wald (1984, 1994); Brout et\nal (1995); Malament (2007, 2012); and Manchak (2013). The\nreader unfamiliar with general relativity may find it helpful to\nreview the Hole Argument entry's\n Beginner's Guide to Modern Spacetime Theories,\n which presents a brief and accessible introduction to the concepts of\na spacetime manifold, a metric, and a worldline. " ]

[ { "content_title": "1. Spacetime Singularities", "sub_toc": [ "1.1. Path Incompleteness", "1.2. Boundary Constructions", "1.3. Curvature Pathology", "1.4. Non-Standard Singularities" ] }, { "content_title": "2. The Significance of Singularities", "sub_toc": [ "2.1. Definitions and Existence of Singularities", "2.2. The Breakdown of General Relativity?" ] }, { "content_title": "3. Black Holes", "sub_toc": [ "3.1. Standard Definition and Properties", "3.2. The Most Perfect Objects in the Cosmos", "3.3. Quasi-Local Black Holes", "3.4. Different Definitions of Black Holes" ] }, { "content_title": "4. Naked Singularities, the Cosmic Censorship Hypothesis, and Indeterminism", "sub_toc": [] }, { "content_title": "5. Black Holes and Thermodynamics", "sub_toc": [ "5.1. The Classical Laws of Black Holes", "5.2. Black Hole Thermodynamics", "5.3. What Is Black Hole Entropy?", "5.4. The Generalized Second Law of Thermodynamics", "5.5. General Gravitational Entropy" ] }, { "content_title": "6. Black Holes and Quantum Theory", "sub_toc": [ "6.1. Hawking Radiation", "6.2. Information Loss Paradox", "6.3. A Path to Quantum Gravity?" ] }, { "content_title": "7. Cosmology and the Arrow of Time", "sub_toc": [] }, { "content_title": "8. Analogue Black Holes and Hawking Radiation", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Bibliography: Philosophy", "Bibliography: Physics", "Bibliography: Philosophy Reference", "Bibliography: Physics Reference" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nGeneral relativity, Einstein's theory of space, time, and gravity,\nallows for the existence of singularities. Everyone agrees on this.\nWhen it comes to the question of how, precisely, singularities are to\nbe defined, however, there is widespread disagreement. Singularities\nin some way signal a breakdown of the geometry of spacetime itself,\nbut this presents an obvious difficulty in referring to a singularity\nas a “thing” that resides at some location in\nspacetime: without a well-behaved geometry, there can be no location.\nFor this reason, some philosophers and physicists have suggested that\nwe should not speak of “singularities” at all, but rather\nof “singular spacetimes”. In this entry, the two\nformulations will generally be treated as equivalent, but the\ndistinction will be highlighted when it becomes significant. ", "\nSingularities are often conceived of metaphorically as akin to a tear\nin the fabric of spacetime. The most common attempts to define\nsingularities center on one of two core ideas that this image readily\nsuggests. The first is that a spacetime has a singularity if it\ncontains an incomplete path, one that cannot be continued\nindefinitely, but draws up short, as it were, with no possibility of\nextension. (“Where is the path supposed to go after it runs into\nthe tear? Where did it come from when it emerged from the\ntear?”) The second is that a spacetime is singular just in case\nthere are points “missing from it”. (“Where are the\nspacetime points that should be where the tear is?”) ", "\nAnother common thought, often adverted to in discussion of the two\nprimary notions, is that singular structure, whether in the form of\nmissing points or incomplete paths, must be related to pathological\nbehavior of some sort in the singular spacetime's curvature, that is,\nthe fundamental deformation of spacetime that manifests itself as\n“the gravitational field”. For example, some measure of\nthe intensity of the curvature (“the strength of the\ngravitational field”) may increase without bound as one\ntraverses the incomplete path. ", "\nIn recent years it was realized that there is another kind of singular\nbehavior that spacetimes may manifest, distinct conceptually and\nphysically from the idea that singularities come in the form of\nincomplete curves or missing points. These are known as ‘sudden\nsingularities’, and are particularly important in cosmological\ncontexts. Besides their intrinsic interest, they also call into\nquestion much of the standard, traditional conceptions and claims made\nabout singular structure in general relativity. ", "\nFinally, there is considerable disagreement over the significance of\nsingularities. Many eminent physicists believe that general\nrelativity's prediction of singular structure signals a serious\ndeficiency in the theory: singularities are an indication that the\ndescription offered by general relativity is breaking down. Others\nbelieve that singularities represent an exciting new possibility for\nphysicists to explore in astrophysics and cosmology, holding out the\npromise of physical phenomena differing so radically from any that we\nhave yet experienced as to signal, in our attempt to observe, quantify\nand understand them, a profound advance in our comprehension of the\nphysical world. ", "\nEach of these issues will be considered in turn below. ", "\nThe history of singular structure in general relativity is\nfascinating, with debate over it dating back to the earliest days of\nthe theory, but discussion of it is beyond the scope of this article;\nthe interested reader should consult Earman (1999), Earman and\nEisenstaedt (1999), Senovilla and Garfinkle (2015), and references\ntherein. " ], "section_title": "1. Spacetime Singularities", "subsections": [ { "content": [ "\nWhile there are competing definitions of spacetime singularities, the\nmost central and widely accepted criterion rests on the possibility\nthat some spacetimes contain incomplete, inextendible paths. Indeed,\nthe rival definitions (in terms of missing points or curvature\npathology), as we will see, rely on the notion of path incompleteness.\n", "\nA path in spacetime is a continuous chain of events through space and\ntime. If I snap my fingers continually, without pause, then the\ncollection of snaps forms a path. The paths used in the most important\nsingularity theorems represent possible trajectories of particles and\nobservers. Such paths are known as world-lines; they consist of the\ncontinuous sequence of events instantiated by an object's existence at\neach instant of its lifetime. That the paths be incomplete and\ninextendible means, roughly speaking, that, after a finite amount of\ntime, a particle or observer following that path would “run out\nof world”, as it were—it would hurtle into the tear in the\nfabric of spacetime and vanish. (See\n Figure 1.)\n Alternatively, a particle or observer could leap out of the tear to\nfollow such a path. While there is no logical or physical\ncontradiction in any of this, it appears on the face of it physically\nsuspect for an observer or a particle to be allowed to pop in or out\nof existence right in the middle of spacetime, so to speak—if\nthat does not suffice for concluding that the spacetime is singular,\nit is difficult to imagine what else would. At the same time as this\ncriterion for singularities was first proposed, the ground-breaking\nwork predicting the existence of such pathological paths (Penrose\n1965, 1968; Hawking 1965, 1966a, 1966b, 1966c, 1966d; Geroch 1966,\n1967, 1968b, 1970; Hawking and Penrose 1970) produced no consensus on\nwhat ought to count as a necessary condition for singular structure\naccording to this criterion, and thus no consensus on a fixed\ndefinition for it. ", "\nIn this context, an incomplete path in spacetime is one that is both\ninextendible and of finite proper length, which means that any\nparticle or observer traversing the path would experience only a\nfinite interval of existence that in principle cannot be continued any\nlonger. For this criterion to do the work we want it to, however, we\nwill need to limit the class of spacetimes under discussion.\nSpecifically, we shall be concerned with spacetimes that are maximally\nextended (or just ‘maximal’, for short). In effect, this\ncondition says that one's representation of spacetime is “as big\nas it possibly can be”. There is, from the mathematical point of\nview, no way to treat the spacetime as being a proper subset of a\nlarger, more extensive spacetime. (See\n figure 2.)\n ", "\nIf there is an incomplete path in a spacetime, goes the thinking\nbehind the requirement, then perhaps the path is incomplete only\nbecause one has not made one's model of spacetime big enough. If one\nwere to extend the spacetime manifold maximally, then perhaps the\npreviously incomplete path could be extended into the new portions of\nthe larger spacetime, indicating that no physical pathology underlay\nthe incompleteness of the path. The inadequacy would merely have\nresided in the incomplete physical model we had been using to\nrepresent spacetime. ", "\nAn example of a non-maximally extended spacetime can be easily had,\nalong with a sense of why they intuitively seem in some way or other\ndeficient. For the moment, imagine spacetime is only two-dimensional,\nand flat, like an endless sheet of paper. Now, excise from somewhere\non this plane a closed set shaped like Ingrid Bergman. Any path that\nhad passed through one of the points in the removed set is now\nincomplete. ", "\nIn this case, the maximal extension of the resulting spacetime is\nobvious, and does indeed fix the problem of all such incomplete paths:\nre-incorporate the previously excised set. (See\n Figure 3.)\n The seemingly artificial and contrived nature of such examples, along\nwith the ease of rectifying them, seems to militate in favor of\nrequiring spacetimes to be maximal. Also, inextendibility is sometimes\nargued for on the grounds that there is no known physical process that\ncould cause spacetime to draw up short, as it were, and not continue\non as it could have, were it to have an extension (Clarke 1975; Ellis\nand Schmidt 1977). ", "\nIn recent important work, Manchak has questioned the need and even the\nreasonableness of requiring spacetimes to be maximal (i.e.,\ninextendible), pointing out problems with the condition's epistemic\nstatus (Manchak 2011), its conceptual cogency (Manchak 2016a), and its\nmetaphysical character (Manchak 2016b). Because inextendibility is the\nmost common assumption made in the physics literature when singular\nstructure is discussed, however, we will continue to assume it for the\npurposes of this discussion, Manchak's interesting arguments\nnotwithstanding. (Manchak's arguments will be discussed further in\n section 4\n below.) ", "\nOnce we have established that we are interested in maximal spacetimes,\nthe next issue is what sort of path incompleteness is relevant for\nsingularities. Here we find a good deal of controversy. Criteria of\nincompleteness typically look at how some parameter naturally\nassociated with the path (such as its proper length) grows. One\ngenerally also places further restrictions on the paths that one\nconsiders—for example, one may rule out paths that could be\ntraversed only by particles undergoing unbounded acceleration in a\nfinite period of time. A spacetime, then, is said to be\nsingular if it possesses a path such that the specified\nparameter associated with that path cannot increase without bound as\none traverses the entirety of the maximally extended path. The idea is\nthat the parameter at issue will serve as a marker for some manifestly\nphysical property, such as the time experienced by a particle or\nobserver, and so, if the value of that parameter remains finite along\nthe whole path, then we have run out of path in a finite amount of\ntime, as it were. We have hit an edge or a “tear” in\nspacetime. ", "\nFor a path that is everywhere timelike, i.e., that does not\ninvolve speeds at or above that of light, it is natural to take as the\nparameter the proper time a particle or observer would experience\nalong the path, that is, the time measured along the path by a natural\nclock, such as one based on the vibrational frequency of an atom.\n(There are also natural choices that one can make for spacelike paths,\ne.g., those that consist of points at a single\n“time”, and for null paths, those followed by light\nsignals; however, because the spacelike and null cases add yet another\nlevel of technical complexity, we shall not discuss them here.) The\nphysical interpretation of this sort of incompleteness for timelike\npaths is more or less straightforward: a timelike path incomplete with\nrespect to proper time in the future direction would represent the\npossible trajectory of a massive body that would never age beyond a\ncertain point in its existence. (An analogous statement can be made,\nmutatis mutandis, if the path were incomplete in the past\ndirection.) ", "\nWe cannot, however, simply stipulate that a maximal spacetime is\nsingular just in case it contains paths of finite proper time that\ncannot be extended. Such a criterion would imply that even the flat\nspacetime described by special relativity is singular, which is surely\nunacceptable. This would follow because, even in flat spacetime, there\nare timelike paths with unbounded acceleration that have only a finite\nproper time and are also inextendible. ", "\nThe most obvious option is to define a spacetime as singular if and\nonly if it contains incomplete, inextendible timelike geodesics,\ni.e., paths representing the possible trajectories of\ninertial observers, those in free-fall. This criterion, however, seems\ntoo permissive, in that it would count as non-singular some spacetimes\nwhose geometry seems otherwise pathological. For example, Geroch\n(1968c) describes a spacetime that is geodesically complete and yet\npossesses an incomplete timelike path of bounded total\nacceleration—that is to say, an inextendible path in spacetime\ntraversable by a rocket with a finite amount of fuel, along which an\nobserver could experience only a finite amount of proper time. Surely\nthe intrepid astronaut in such a rocket, who would never age beyond a\ncertain point, but who also would never necessarily die or cease to\nexist, would have just cause to complain that something was singular\nabout this spacetime. ", "\nWhen deciding whether a spacetime is singular, therefore, we want a\ndefinition that is not restricted to geodesics. We need, however, some\nway of overcoming the fact that non-singular spacetimes include\ninextendible paths of finite proper length that are not prima\nfacie pathological (e.g., flat spacetimes with\ninextendible paths of unbounded total acceleration). The most widely\naccepted solution to this problem makes use of a slightly different,\ntechnically complex notion of length, known as ‘generalized\naffine length’ (Schmidt\n 1971).[1]\n Unlike proper time, this generalized affine length depends on some\narbitrary choices. (Roughly speaking, the length will vary depending\non the coordinates one chooses to compute it; see\n note 1.)\n If the length is infinite for one such choice, however, it will be\ninfinite for all other choices. Thus the question of whether a path\nhas a finite or infinite generalized affine length is a well-defined\nquestion, and that is all we will need. ", "\nThe definition that has won the most widespread\nacceptance—leading Earman (1995, p. 36) to dub this the\nsemiofficial definition of singularities—is the\nfollowing: ", "\nA spacetime is singular if and only if it is maximal and\ncontains an inextendible path of finite generalized affine length.\n", "\nTo say that a spacetime is singular then is to say that there is at\nleast one maximally extended path that has a bounded (generalized\naffine) length. To put it another way, a spacetime is nonsingular when\nit is complete in the sense that the only reason any given path might\nnot be extendible is that it's already infinitely long (in this\ntechnical sense). ", "\nThe chief problem facing this definition of singularities is that the\nphysical significance of generalized affine length is opaque, and thus\nit is unclear what the physical relevance of singularities, defined in\nthis way, might be. It does nothing, for example, to clarify the\nphysical status of the spacetime described by Geroch (geodesically\ncomplete but containing incomplete paths of bounded total\nacceleration), which it classifies as non-singular, as the\ncurve at issue indeed has infinite generalized affine length, even\nthough it has only a finite total proper time (to the future). The new\ncriterion does nothing more than sweep the troubling aspects of such\nexamples under the rug. It does not explain why we ought not to take\nsuch prima facie puzzling and troubling examples as\nphysically pathological; it merely declares by fiat that they are not.\n", "\nRecently, Manchak (2014a) proposed a condition spacetimes may satisfy,\nmanifestly relevant to the issue of what characterizes singular\nbehavior, which he calls ‘effective completeness’. The\nidea is to try to give what may be thought of as a quasi-local\ncharacterization of path\n incompleteness.[2]\n Manchak (2014a, p. 1071) describes the intended physical significance\nas follows: “If a space-time fails to be effectively complete,\nthen there is a freely falling observer who never records some\nparticular watch reading but who ‘could have’ in the sense\nthat nothing in her vicinity precludes it.” This condition has\nthe pleasant property of being logically intermediate between the\ncondition of geodesic incompleteness for spacetime, on the one hand,\ngenerally conceded to be too strong to capture the general idea of\nsingular behavior (because of examples such that of Geroch 1968c,\ndiscussed above), and, on the other hand, the condition of being\nextendible, generally conceded to be too weak, for effective\ncompleteness is implied by geodesic completeness and in turn implies\ninextendibility. While this new condition appears promising as a clear\nand useful characterization of singular structure (in the sense of\npath incompleteness), and does so in a way that avoids the problems of\nphysical opacity plaguing the semi-official definition, it is too new\nand unexplored for definitive judgments to be made about it. One wants\nto know, among other things, whether it can be used to prove novel\ntheorems with the same physical depth and reach as the standard\nsingularity theorems (Penrose 1965, 1968; Hawking 1965, 1966a, 1966b,\n1966c, 1966d; Geroch 1966, 1967, 1968b, 1970; Hawking and Penrose\n1970), and whether it can shed real light on the philosophical issues\ndiscussed below in\n section 2.\n ", "\nSo where does all this leave us? The consensus seems to be that, while\nit is easy in specific examples to conclude that incomplete paths of\nvarious sorts represent singular structure, no entirely satisfactory,\nstrict definition of singular structure in their terms has yet been\nformulated (Joshi 2014). As we will see in\n section 1.4\n below, moreover, spacetimes can evince entirely different kinds of\nbehavior that manifestly are singular in an important sense, and yet\nwhich are independent of path incompleteness. For a philosopher, the\nissues offer deep and rich veins for those contemplating, among other\nmatters, the role of explanatory power in the determination of the\nadequacy of physical theories, the role of metaphysics and intuition\nin the same, questions about the nature of the existence attributable\nto physical entities in spacetime and to spacetime itself, and the\nstatus of mathematical models of physical systems in the determination\nof our understanding of those systems as opposed to the mere\nrepresentation of our knowledge of them. All of these issues will be\ntouched upon in the following. " ], "subsection_title": "1.1. Path Incompleteness" }, { "content": [ "\nWe have seen that one runs into difficulties if one tries to define\nsingularities as “things” that have locations, and how\nsome of those difficulties can be avoided by defining singular\nspacetimes using the idea of incomplete paths. It would be desirable\nfor many reasons, however, to have a characterization of a spacetime\nsingularity in general relativity as, in some sense or other, a\nspatiotemporal “place”. If one had a precise\ncharacterization of a singularity based on points that are missing\nfrom spacetime, one might then be able to analyze the structure of the\nspacetime “locally at the singularity”, instead of taking\ntroublesome, perhaps ill-defined, limits along incomplete paths. Many\ndiscussions of singular structure in relativistic spacetimes,\ntherefore, are premised on the idea that a singularity represents a\npoint or set of points that in some sense or other is missing from the\nspacetime manifold, that spacetime has a “hole” or\n“tear” in it that we could fill in, or patch, by attaching\na boundary to it. ", "\nIn trying to determine whether an ordinary web of cloth has a hole in\nit, for example, one would naturally rely on the fact that the web\nexists in space and time. In this case one can point to a hole in the\ncloth by specifying points of space at a particular moment of time not\ncurrently occupied by any of the cloth, but which would complete the\ncloth were they so occupied. When trying to conceive of a singular\nspacetime, however, one does not have the luxury of imagining it\nembedded in a larger space with respect to which one can say there are\npoints missing from it. In any event, the demand that the spacetime be\nmaximal rules out the possibility of embedding the spacetime manifold\nin any larger spacetime manifold of any ordinary sort. It would seem,\nthen, that making precise the idea that a singularity is a marker of\nmissing points ought to involve some idea of intrinsic structural\nincompleteness in the spacetime manifold rather than extrinsic\nincompleteness with respect to an external structure. ", "\nThe most obvious route, especially in light of the previous\ndiscussion, and the one most often followed, is to define a spacetime\nto have points missing from it if and only if it contains incomplete,\ninextendible paths, and then try to use these incomplete paths to\nconstruct in some fashion or other new, properly situated points for\nthe spacetime, the addition of which will make the previously\ninextendible paths extendible. These constructed points would then be\nour candidate singularities. Missing points on this view would\ncorrespond to a boundary for a singular spacetime—actual points\nof a (non-standard) extended spacetime at which paths incomplete in\nthe original spacetime would terminate. (We will, therefore, alternate\nbetween speaking of missing points and speaking of\nboundary points, with no difference of sense intended.) The\ngoal then is to construct this extended space using the incomplete\npaths as one's guide. ", "\nNow, in trivial examples of spacetimes with missing points such as the\none offered before, flat spacetime with a closed set in the shape of\nIngrid Bergman excised from it, one does not need any technical\nmachinery to add the missing points back in. One can do it by hand.\nMany spacetimes with incomplete paths, however, do not allow missing\npoints to be attached in any obvious way by hand, as that example\ndoes. For this program to be viable, which is to say, in order to give\nsubstance to the idea that there really are points that in some sense\nought to have been included in the spacetime in the first place, we\nrequire a physically natural completion procedure that can be applied\nto incomplete paths in arbitrary spacetimes. There are several\nproposals for such a construction (Hawking 1966c, Geroch 1968a,\nSchmidt\n 1971).[3]\n ", "\nSeveral problems with this kind of program make themselves felt\nimmediately. Consider, for example, a spacetime representing the final\nstate of the complete gravitational collapse of a spherically\nsymmetric body resulting in a black hole. (See\n section 3\n below for a description of black holes in general, and\n Figure 4\n for a representation of a body collapsing to form a black hole.) In\nthis spacetime, any timelike path entering the black hole will\nnecessarily be extendible for only a finite amount of proper\ntime—it then “runs into the singularity” at the\ncenter of the black hole. In its usual presentation, however, there\nare no obvious points missing from the spacetime at all. By any\nstandard measure, as a manifold in its own right it is as complete as\nthe Cartesian plane, excepting only the existence of incomplete\ncurves, no class of which indicates by itself a place in the manifold\nat which to add a point so as to make the paths in the class complete.\nLikewise, in our own spacetime every inextendible, past-directed\ntimelike path is incomplete (and our spacetime is singular): they all\nrun into the Big Bang. Insofar as there is no moment of time at which\nthe Big Bang occurred (no moment of time at which time began, so to\nspeak), there is no point to serve as the past endpoint of such a\npath. We can speak of the cosmic epoch, the time after the big bang.\nThat makes it easy to imagine that cosmic time zero is some initial\nevent. That, however, is an illusion of our labeling. Cosmic time\n“zero” is a label attached to no event. If instead we had\nlabeled epochs with the logarithm of cosmic time, then the imaginary\nmoment of the big bang would be assigned the label of minus infinity\nand its fictional character would be easier to accept. (One can make\nthe point a little more precise: the global structure of our universe,\nas modeled by our best cosmological theories, is essentially the same\nas a well known mathematical space, either ℝ4 or\n𝕊3 x ℝ, which are both complete and\ninextendible as manifolds independent of any spacetime metrical\nstructure, in every reasonable sense of those terms.) ", "\nEven more troublesome examples are given by topologically compact\nregions of spacetimes containing incomplete, inextendible paths, as in\na simple example due to Misner (1967). In a sense that can be made\nprecise, compact sets, from a topological point of view,\n“contain every point they could possibly be expected to\ncontain”, one manifestation of which is that a compact manifold\ncannot be embedded as an open submanifold of any other manifold, a\nnecessary pre-requisite for attaching a boundary to a singular\nspacetime. It is not only with regard to the attachment of a boundary,\nhowever, that compact sets already contain all points they possibly\ncould: every sequence of points in a compact set has a subsequence\nthat converges to a point in the set. Non-convergence of sequences is\nthe standard way that one probes geometrical spaces for\n“missing” points that one can add in by hand, as it were,\nto complete the space; thus, compact sets, in this natural sense,\ncannot have any missing points. ", "\nPerhaps the most serious problem facing all the proposals for\nattaching boundary points to singular spacetimes, however, is that the\nboundaries necessarily end up having physically pathological\nproperties (Geroch et al. 1982): in a sense one can make\nprecise, the boundary points end up being arbitrarily\n“near” to every point in the interior of the spacetime.\nAttaching boundary points to our own universe, therefore, to make the\nBig Bang into a real “place”, ends up making the Big Bang\narbitrarily close to every neuron in my brain. Far from making\ntractable the idea of localizing singular structure in a physically\nfruitful way, then, all the proposals only seem to end up making the\nproblems worse. ", "\nThe reaction to the problems faced by these boundary constructions is\nvaried, to say the least, ranging from blithe acceptance of the\npathology (Clarke 1993), to the attitude that there is no satisfying\nboundary construction currently available while leaving open the\npossibility of better ones in the future (Wald 1984), to not even\nmentioning the possibility of boundary constructions when discussing\nsingular structure (Joshi 1993, 2007b, 2014), to rejection of the need\nfor such constructions at all (Geroch et al. 1982; Curiel\n1999). ", "\nNonetheless, many eminent physicists seem convinced that general\nrelativity stands in need of such a construction, and have exerted\nextraordinary efforts in trying to devise one. This fact raises\nseveral philosophical problems. Though physicists sometimes offer as\nstrong motivation the possibility of gaining the ability to analyze\nsingular phenomena locally in a mathematically well-defined manner,\nthey more often speak in terms that strongly suggest they suffer a\nmetaphysical itch that can be scratched only by the sharp point of a\nlocalizable, spatiotemporal entity serving as the locus of their\ntheorizing. Even were such a construction forthcoming, however, what\nsort of physical and theoretical status could accrue to these missing\npoints? They would not be idealizations of a physical system in any\nordinary sense of the term, since they would not represent a\nsimplified model of a system formed by ignoring various of its\nphysical features, as, for example, one may idealize the modeling of a\nfluid by ignoring its viscosity. Neither would they seem necessarily\nto be only convenient mathematical fictions, as, for example, are the\nphysically impossible dynamical evolutions of a system one integrates\nover in the variational derivation of the Euler-Lagrange equations. To\nthe contrary, as we have remarked, many physicists and philosophers\nseem eager to find such a construction for the purpose of bestowing\nsubstantive and clear ontic status on singular structure. What sorts\nof theoretical entities, then, could they be, and how could they serve\nin physical theory? ", "\nWhile the point of this project may seem at bottom identical to the\npath-incompleteness account discussed in\n section 1.1,\n insofar as singular structure will be defined by the presence of\nincomplete, inextendible paths, there is a crucial conceptual and\nlogical difference between the two. Here, the existence of the\nincomplete path does not constitute the singular structure, but rather\nserves only as a marker for the presence of singular structure in the\nsense of missing points: the incomplete path is incomplete because it\n“runs into a hole” in the spacetime that, were it filled,\nwould allow the path to be continued; this hole is the singular\nstructure, and the points constructed to fill it constitute its locus.\nIndeed, every known boundary construction relies on the existence of\nincomplete paths to “probe” the spacetime, as it were,\nlooking for “places” where boundary points should be\nappended to the spacetime; the characterization of singular structure\nby incomplete paths seems, therefore, logically, perhaps even\nconceptually, prior to that by boundary points, at least, again, for\nall known constructions of boundary points. ", "\nCurrently, there seems to be even less consensus on how (and whether)\none should define singular structure based on the idea of missing\npoints than there is regarding definitions based on path\nincompleteness. Moreover, this project also faces even more technical\nand philosophical problems. For these reasons, path incompleteness is\ngenerally considered the default definition of singularities. For the\nremainder of this article, therefore, singular structure will be\nassumed to be characterized by incomplete, inextendible paths, with\nthe exception of the discussion of\n section 1.4\n below. ", "\nThere is, however, one special case in which it seems a boundary can\nbe placed on singular spacetimes in such a way as to localize the\nsingularity in a physically meaningful way: for so-called conformal\nsingularities. Their properties are discussed at the end of\n section 1.3,\n and their physical and philosophical significance explored in more\ndetail in\n section 7.\n " ], "subsection_title": "1.2. Boundary Constructions" }, { "content": [ "\nWhile path incompleteness seems to capture an important aspect of the\nintuitive picture of singular structure, it completely ignores another\nseemingly integral aspect of it: curvature pathology. If there are\nincomplete paths in a spacetime, it seems that there should be a\nreason that the path cannot go further. The most obvious candidate\nexplanation of this sort is that something going wrong with the\ndynamical structure of the geometry of spacetime, which is to say,\nwith the curvature of the spacetime. This suggestion is bolstered by\nthe fact that local measures of curvature do in fact blow up as one\napproaches the singularity of a standard black hole or the Big Bang\nsingularity. There is, however, one problem with this line of thought:\nno species of curvature pathology we know how to define is either\nnecessary or sufficient for the existence of incomplete paths. (For a\ndiscussion of foundational problems attendant on attempts to define\nsingularities based on curvature pathology, see Curiel 1999; for a\nrecent survey of technical issues, see Joshi 2014.) ", "\nTo make the notion of curvature pathology more precise, we will use\nthe manifestly physical idea of tidal force. Tidal force is generated\nby the difference in intensity of the gravitational field at\nneighboring points of spacetime. For example, when you stand, your\nhead is farther from the center of the Earth than your feet, so it\nfeels a (practically negligible) smaller pull downward than your feet.\n\n Tidal forces are a physical manifestation of spacetime curvature, and\none gets direct observational access to curvature by measuring the\nresultant relative difference in accelerations of neighboring test\nbodies. For our purposes, it is important that in regions of extreme\ncurvature tidal forces can grow without bound. ", "\nIt is perhaps surprising that the state of motion of an object as it\ntraverses an incomplete path (e.g., whether it is\naccelerating or spinning) can be decisive in determining its physical\nresponse to curvature pathology. Whether an object is spinning or not,\nfor example, or accelerating slightly in the direction of motion, may\ndetermine whether the object gets crushed to zero volume along such a\npath or whether it survives (roughly) intact all the way along it, as\nshown by examples offered by Ellis and Schmidt (1977). Indeed, the\neffect of the observer's state of motion on his or her experience of\ntidal forces can be even more pronounced than this. There are examples\nof spacetimes in which an observer cruising along a certain kind of\npath would experience unbounded tidal forces and so be torn apart,\nwhile another observer, in a certain technical sense approaching the\nsame limiting point as the first observer, accelerating and\ndecelerating in just the proper way, would experience a perfectly\nwell-behaved tidal force, though she would approach as near as she\nlikes to the other fellow who is in the midst of being ripped to\n shreds.[4]\n ", "\nThings can get stranger still. There are examples of incomplete\ngeodesics contained entirely within a well-defined, bounded region of\na spacetime, each having as its limiting point an honest-to-goodness\npoint of spacetime, such that an observer freely falling along such a\npath would be torn apart by unbounded tidal forces; it can easily be\narranged in such cases, however, that a separate observer, who\nactually travels through the limiting point, will experience perfectly\nwell-behaved tidal\n forces.[5]\n Here we have an example of an observer being ripped apart by\nunbounded tidal forces right in the middle of spacetime, as it were,\nwhile other observers cruising peacefully by could reach out to touch\nhim or her in solace during the final throes of agony. This example\nalso provides a nice illustration of the inevitable difficulties\nattendant on attempts to localize singular structure in the senses\ndiscussed in\n section 1.2.\n ", "\nIt would seem, then, that curvature pathology as characterized based\non the behavior of tidal forces is not in any physical sense a\nwell-defined property of a region of spacetime simpliciter.\nWhen we consider the physical manifestations of the curvature of\nspacetime, the motion of the device that we use to probe a region (as\nwell as the nature of the device) becomes crucially important for the\nquestion of whether pathological behavior manifests itself. This fact\nraises questions about the nature of quantitative measures of\nproperties of entities in general relativity, and what ought to count\nas observable, in the sense of reflecting the underlying physical\nstructure of spacetime. Because apparently pathological phenomena may\noccur or not depending on the types of measurements one is performing,\nit seems that purely geometrical pathology does not necessarily\nreflect anything about the state of spacetime itself, or at least not\nin any localizable way. What then does it reflect, if anything? Much\nwork remains to be done by both physicists and by philosophers in this\narea, i.e., the determination of the nature of physical\nquantities in general relativity and what ought to count as an\nobservable with intrinsic physical significance. See Bertotti (1962),\nBergmann (1977), Rovelli (1991, 2001 in\n Other Internet Resources, henceforth OIR,\n 2002), Curiel (1999) and Manchak (2009a) for discussion of many\ndifferent topics in this area, approached from several different\nperspectives. ", "\nThere is, however, one form of curvature pathology associated with a\nparticular form of an apparently important class of singularities that\nrecently has been clearly characterized and analyzed, that associated\nwith so-called conformal singularities, also sometimes called\nisotropic singularities (Goode and Wainright 1985; Newman 1993a,\n1993b; Tod 2002). The curvature pathology of this class of\nsingularities can be precisely pinpointed: it occurs solely in the\nconformal part of the curvature; thus, what is singular in one\nspacetime will not necessarily be so in a conformally equivalent\n spacetime.[6]\n This property allows for a boundary to be attached to the singular\nspacetime in a way that seems to be physically meaningful (Newman\n1993a, 1993b; Tod 2002). Many physicists hold that, in a sense that\ncan be made precise, all “purely gravitational degrees of\nfreedom” in general relativity are encoded in the conformal\nstructure (Penrose 1979; Gomes et al. 2011). These\nproperties, along with the fact that the Big Bang singularity almost\ncertainly seems to be of this form, make conformal singularities\nparticularly important for the understanding and investigation of many\nissues of physical and philosophical interest in contemporary\ncosmology, as discussed below in\n section 7.\n " ], "subsection_title": "1.3. Curvature Pathology" }, { "content": [ "\nIn 2004, it was discovered that general relativity admits even more\nkinds of singularities than those known before, so-called\n‘sudden singularities’ (Barrow 2004a, 2004b). The\ncharacterization of this kind of singularity has, so far, been\nconfined to the context of cosmological models, including essentially\nall spacetimes whose matter content consists of homogeneous perfect\nfluids and a very wide class of spacetimes consisting of inhomogeneous\nfluids. The dynamics of those cosmological models is largely governed\nby the behavior of the cosmological expansion factor, a measure of the\nrelative sizes of local regions of space (not spacetime) at different\ncosmological times. In an expanding spacetime, such as the one we\nbelieve ourselves to live in, the expansion factor continually\nincreases, having “started from zero at the Big Bang”. If\nthe universe's expansion stops, and the net gravitational effect on\ncosmological scales results in the universe's collapsing in on itself,\nthis would be marked by a continual decrease in the expansion factor,\neventuating in a Big Crunch singularity as the expansion factor\nasymptotically approached zero. The remaining dynamics of these\ncosmological models is encoded in the behavior of the Hubble\nparameter, a natural measure of the rate of change of the expansion\nfactor. A sudden singularity, then, is defined by the divergence of a\ntime derivative of the expansion factor or the Hubble parameter,\nthough the factor or parameter itself remains finite. ", "\nBecause important physical quantities, such as spatial pressure of the\ncosmological fluid, are proportional to such time derivatives, the\nphysical interpretation of sudden singularities is often, in at least\none sense, perspicuous: depending on the time derivative that\ndiverges, a sudden singularity can mark the divergence of a physically\nimportant quantity such as pressure, within a finite interval of\nproper time (Cattoën and Visser 2005; Cotsakis and Klaoudatou\n2005; Fernández-Jambrina 2014; Jiménez et\nal. 2016). In such cases, it may happen that the mass-density\nof the fluid itself, the expansion factor and its first derivative,\nand even the Hubble parameter and its first derivative, all remain\nfinite: only the pressure (and so the second derivative of the\nexpansion factor) diverges. Because the physical significance of\nquantities such as pressure is thought to be unambiguous, this feature\nof sudden singularities stands in marked contrast to the problems of\nphysical interpretation that plague the standard type of singularity,\ndiscussed in\n section 1.3.\n ", "\nOf most interest, however, is the way that sudden singularities may\ndiffer in an even more fundamental way from standard singularities:\nthere need be no path-incompleteness associated with them\n(Fernández-Jambrina and Lazkoz 2004, 2007). In effect, although\nthe values of some physically important quantities diverge, the metric\nitself remains well defined, allowing curves “running\ninto” the pathological point to continue through it. Indeed,\npoint particles passing through the sudden singularity would not even\nnotice the pathology, as only tidal forces may diverge (and not even\nall sudden singularities involve divergence of those): point\nparticles, having no extension, cannot experience tidal force. If one\nwants to count sudden singularities as true singularities—and\nthere seems every reason to do so—then this would put the nail\nin the coffin for the idea that singularities always can or should be\nassociated with “missing\n points”.[7]\n ", "\nAlthough the discovery of sudden singularities has reinvigorated the\nstudy of singular spacetimes in the physics community (Cotsakis 2007),\nthey remain so far almost entirely unexamined by the philosophy\ncommunity. Nonetheless, they raise questions of manifest philosophical\ninterest and import. The fact that they are such radically different\nstructures from all other previously known kinds of singularity, for\nexample, raises methodological questions about how to understand the\nmeaning of terms in physical theories when those terms refer to\nstructurally quite different but obviously still intimately related\nphenomena—the reasons for thinking of them as singularities are\ncompelling, even though they violate essentially every standard\ncondition known for characterizing singularities. ", "\nAnother unusual kind of singularity characterized only recently\ncharacterized deserves mention here, because of its possible\nimportance in cosmology. The physical processes that seem to eventuate\nin most known kinds of singular structure involve the unlimited\nclumping together of matter, as in collapse singularities associated\nwith black holes, and the Big Bang and Big Crunch singularities of\nstandard cosmological models. A big rip, contrarily, occurs\nwhen the expansion of matter increasingly accelerates without bound in\na finite amount of proper time (Caldwell 2002; Caldwell et\nal. 2003; Chimento and Lazkov 2004; Dabrowski 2006;\nFernández-Jambrina 2014). Rather than the volume of spacetime\nshrinking to zero, its volume increases without bound—spacetime\nliterally tears itself apart, not even fundamental particles being\nable to maintain their structural unity and integrity (Chimento and\nLazkoz 2004; Fernández-Jambrina 2014). Again, standard concepts\nand arguments about singularities characterized as incomplete paths do\nnot seem easily applicable here. Although big rips do have incomplete\npaths associated with them as well as curvature pathology, they are of\nsuch radically different kinds as to prima facie warrant\nseparate analysis. ", "\nRecent work, codified by Harada et al. (2018), shows just how\ndifferent such cosmological singularities can be. For homogeneous\ncosmological models filled with perfect fluids with a linear equation\nof state—the standard cosmological model—certain values of\nthe barotropic index yield past, future, or past and future big rips\nthat are such that every timelike geodesic runs into them, but every\nnull geodesic avoids them. (See\n note 7\n for an explanation of the barotropic index.) In other words, any body\ntraveling more slowly than light will run into the singularity, but\nevery light ray will escape to infinity. This is not a situation that\nlends itself to easy and perspicuous physical interpretation. " ], "subsection_title": "1.4. Non-Standard Singularities" } ] }, { "main_content": [ "\nWhen considering the implications of spacetime singularities, it is\nimportant to note that we have good reasons to believe that the\nspacetime of our universe is singular. In the late 1960s, Penrose,\nGeroch, and Hawking proved several singularity theorems, using path\nincompleteness as a criterion (Penrose 1965, 1968; Hawking 1965,\n1966b, 1966c, 1966d; Geroch 1966, 1967, 1968b, 1970; Hawking and\nPenrose 1970). These theorems showed that if certain physically\nreasonable premises were satisfied, then in certain circumstances\nsingularities could not be avoided. Notable among these conditions is\nthe positive energy condition, which captures the idea that energy is\nnever negative. These theorems indicate that our universe began with\nan initial singularity, the Big Bang, approximately 14 billion years\nago. They also indicate that in certain circumstances (discussed\nbelow) collapsing matter will form a black hole with a central\nsingularity. According to our best current cosmological theories,\nmoreover, two of the likeliest scenarios for the end of the universe\nis either a global collapse of everything into a Big Crunch\nsingularity, or the complete and utter diremption of everything, down\nto the smallest fundamental particles, in a Big Rip singularity. (See\nJoshi 2014 for a recent survey of singularities in general, and Berger\n2014 for a recent survey of the different kinds of singularities that\ncan occur in cosmological models.) ", "\nShould these results lead us to believe that singularities are real?\nMany physicists and philosophers resist this conclusion. Some argue\nthat singularities are too repugnant to be real. Others argue that the\nsingular behavior at the center of black holes and at the beginning\n(and possibly the end) of time indicates the limit of the domain of\napplicability of general relativity. Some are inclined to take general\nrelativity at its word, however, and simply accept its prediction of\nsingularities as a surprising but perfectly consistent account of the\npossible features of the geometry of our world. (See Curiel 1999 and\nEarman 1995, 1996 for discussion and comparison of these opposing\npoints of view.) In this section, we review these and related problems\nand the possible responses to them. " ], "section_title": "2. The Significance of Singularities", "subsections": [ { "content": [ "\nLet us summarize the results of\n section 1:\n there is no commonly accepted, strict definition of singularity;\nthere is no physically reasonable characterization of missing points;\nthere is no necessary connection between singular structure, at least\nas characterized by the presence of incomplete paths, and the presence\nof curvature pathology; and there is no necessary connection between\nother kinds of physical pathology (such as divergence of pressure) and\npath incompleteness. ", "\nWhat conclusions should be drawn from this state of affairs? There\nseem to be two basic kinds of response, illustrated by the views of of\nClarke (1993) and Earman (1995) on the one hand, and those of Geroch\net al. (1982) and Curiel (1999) on the other. The former\nholds that the mettle of physics and philosophy demands that we find a\nprecise, rigorous and univocal definition of singularity. On this\nview, the host of philosophical and physical questions surrounding\ngeneral relativity's prediction of singular structure would best be\naddressed with such a definition in hand, so as better to frame and\nanswer these questions with precision, and thus perhaps find other,\neven better questions to pose and attempt to answer. The latter view\nis perhaps best summarized by a remark of Geroch et al.\n(1982): “The purpose of a construction [of ‘singular\npoints’], after all, is merely to clarify the discussion of\nvarious physical issues involving singular space-times: general\nrelativity as it stands is fully viable with no precise notion of\n‘singular points’.” On this view, the specific\nphysics under investigation in any particular situation should dictate\nwhich definition of singularity to use in that situation if, indeed,\nany at all. ", "\nIn sum, the question becomes the following: is there a need for a\nsingle, blanket definition of singularity or does the urge for one\nbetray only an old Aristotelian, essentialist prejudice? This question\nhas obvious connections to the broader question of natural kinds in\nscience. One sees debates similar to those canvassed above when one\ntries to find, for example, a strict definition of biological species.\nClearly, part of the motivation for searching for a single\nexceptionless definition is the impression that there is some real\nfeature of the world (or at least of our spacetime models) that we can\nhope to capture precisely. Further, we might hope that our attempts to\nfind a rigorous and exceptionless definition will help us to better\nunderstand the feature itself. Nonetheless, it is not clear why we\nshould not be happy with a variety of types of singular structure,\ntaking the permissive attitude that none should be considered the\n“right” definition of singularities, but each has its\nappropriate use in context. ", "\nEven without an accepted, strict definition of singularity for\nrelativistic spacetimes, the question can be posed: what would it mean\nto ascribe existence to singular structure under any of the available\nopen possibilities? It is not far-fetched to think that answers to\nthis question may bear on the larger question of the existence of\nspacetime points in general (Curiel 1999, 2016; Lam 2007). (See the\nentries\n The Hole Argument\n and\n Absolute and Relational Theories of Space and Motion\n for discussions of the question of the existence of spacetime\nitself.) ", "\nIt would be difficult to argue that an incomplete path in a maximal\nrelativistic spacetime does not exist in at least some sense of the\nterm. It is not hard to convince oneself, however, that the\nincompleteness of the path does not exist at any particular\npoint of the spacetime in the same way, say, as this glass of beer\nexists at this point of spacetime. If there were a point on the\nmanifold where the incompleteness of the path could be localized,\nsurely that would be the point at which the incomplete path\nterminated. But if there were such a point, then the path could be\nextended by having it pass through that point. It is perhaps this fact\nthat lies behind much of the urgency surrounding the attempt to define\nsingular structure as missing points. ", "\nThe demand that singular structure be localized at a particular place\nbespeaks an old Aristotelian substantivalism that invokes the maxim,\n“To exist is to exist in space and time” (Earman 1995, p.\n28). Aristotelian substantivalism here refers to the idea\ncontained in Aristotle's contention that everything that exists is a\nsubstance and that all substances can be qualified by the Aristotelian\ncategories, two of which are location in time and location in space.\nSuch a criterion, however, may be inappropriate for features and\nproperties of spacetime itself. Indeed, one need not consider anything\nso outré as incomplete, inextendible paths in order to\nproduce examples of entities that seem undeniably to exist in some\nsense of the term or other, and yet which cannot have any even vaguely\ndetermined location in time and space predicated of them. Several\nessential features of a relativistic spacetime, singular or not,\ncannot be localized in the way that an Aristotelian substantivalist\nwould demand. For example, the Euclidean (or non-Euclidean) nature of\na space is not something with a precise location. (See Butterfield\n2006 for discussion of these issues.) Likewise, various spacetime\ngeometrical structures (such as the metric, the affine structure, the\ntopology, etc.) cannot be localized in the way that the Aristotelian\nwould demand, whether that demand be for localization at a point,\nlocalization in a precisely determinate region, or even just\nlocalization in a vaguely demarcated region. The existential status of\nsuch entities vis-à-vis more traditionally considered\nobjects is an open and largely ignored issue (Curiel 1999, 2016;\nButterfield 2006). Because of the way the issue of singular structure\nin relativistic spacetimes ramifies into almost every major open\nquestion in relativistic physics today, both physical and\nphilosophical, it provides a peculiarly rich and attractive focus for\nthese sorts of questions. ", "\nAn interesting point of comparison, in this regard, would be the\nnature of singularities in other theories of gravity besides general\nrelativity. Weatherall's (2014) characterization of singularities in\ngeometrized Newtonian gravitational theory, therefore, and his proof\nthat the theory accommodates their prediction, may serve as a possible\ntesting ground for ideas and arguments on these issues. ", "\nMany of these questions, in the end, turn upon the issue of what\nconstitutes “physically reasonable” spacetime structure.\nGeneral relativity admits spacetimes exhibiting a vast and variegated\nmenagerie of structures and behaviors, even over and above\nsingularities, that most physicists and philosophers would consider,\nin some sense or other, not reasonable possibilities for physical\nmanifestation in the actual world. But what is to count as\n“reasonable” here: who is to decide, and on what basis\n(Curiel 1999)? Manchak (2011) has argued that there cannot be purely\nempirical grounds for ruling out the seemingly unpalatable structures,\nfor there always exist spacetimes that are, in a precise sense,\nobservationally indistinguishable from our own (Malament 1977; Manchak\n2009a) that have essentially any set of properties one may stipulate.\nNorton (2011) argues that this constitutes a necessary failure of\ninductive reasoning in cosmology, no matter what one's account of\ninduction. Butterfield (2012) discusses the relation of Manchak's\nresults to standard philosophical arguments about under-determination\nof theory by data. ", "\nThe philosopher of science interested in the definition and status of\ntheoretical terms in scientific theories has at hand here a rich\npossible case-study, enlivened by the opportunity to watch eminent\nscientists engaged in fierce, ongoing debate over the definition of a\nterm—indeed, over the feasibility of and even need for defining\nit—that lies at the center of attempts to unify our most\nfundamental physical theories, general relativity and quantum field\ntheory. " ], "subsection_title": "2.1. Definitions and Existence of Singularities" }, { "content": [ "\nAt the heart of all of our conceptions of a spacetime singularity is\nthe notion of some sort of failure: a path that disappears, points\nthat are torn out, spacetime curvature or some other physical quantity\nsuch as pressure whose behavior becomes pathological. Perhaps the\nfailure, though, lies not in the spacetime of the actual world (or of\nany physically possible world), but rather in our theoretical\ndescription of the spacetime. That is, perhaps we should not think\nthat general relativity is accurately describing the world when it\nposits singular structure—it is the theory that breaks down, not\nthe physical structure of the world. ", "\nIndeed, in most scientific arenas, singular behavior is viewed as an\nindication that the theory being used is deficient, at least in the\nsense that it is not adequate for modeling systems in the regime where\nsuch behavior is predicted (Berry 1992). It is therefore common to\nclaim that general relativity, in predicting that spacetime is\nsingular, is predicting its own demise, and that classical\ndescriptions of space and time break down at black hole singularities\nand the Big Bang, and all the rest (Hawking and Ellis 1973; Hawking\nand Penrose 1996). Such a view denies that singularities are real\nfeatures of the actual world, and rather asserts that they are merely\nartifacts of our current, inevitably limited, physical theories,\nmarking the regime where the representational capacities of the theory\nat issue breaks down. This attitude is widely adopted with regard to\nmany important cases, e.g., the divergence of the Newtonian\ngravitational potential for point particles, the singularities in the\nequations of motion of classical electromagnetism for point electrons,\nthe singular caustics in geometrical optics, and so on. No one\nseriously believes that singular behavior in such models in those\nclassical theories represents truly singular behavior in the physical\nworld. We should, the thought goes, treat singularities in general\nrelativity in the same way. ", "\nOne of the most common arguments that incomplete paths and non-maximal\nspacetimes are physically unacceptable, and perhaps the most\ninteresting one, coming as it does from physicists rather than from\nphilosophers, invokes something very like the Principle of Sufficient\nReason: if whatever creative force responsible for spacetime could\nhave continued on to create more of it, what possible reason could\nthere have been for it to have stopped at any particular point\n(Penrose 1969; Geroch\n 1970)?[8]\n An opponent of this view could respond that it implicitly relies on a\ncertain picture of physics that may not sit comfortably with general\nrelativity, that of the dynamical evolution of a system. An advocate\nof this viewpoint would argue that, from a point of view natural for\ngeneral relativity, spacetime does not evolve at all. It just sits\nthere, once and for all, as it were, a so-called block universe\n(Putnam 1967; the entries\n Time Machines,\n Time Travel and\n Being and Becoming in Modern Physics).\n If it happens to sit there non-maximally, well, so be it. This kind\nof response, however, has problems of its own, such as with the\nrepresentation of our subjective experience, which seems inextricably\ntied up with ideas of evolution and change. Those sorts of problem,\nhowever, do not seem peculiar to this dispute, but arise from the\ncharacter of general relativity itself: “dynamical\nevolution” and “time” are subtle and problematic\nconcepts in the theory no matter what viewpoint one takes (Stein 1968,\n1970, 1991). ", "\nOne can produce other metaphysical arguments against the view that\nspacetime must be maximal. To demand maximality may lead to Buridan's\nAss problems, for it can happen that global extensions exist in which\none of a given set of incomplete curves is extendible, but no global\nextension exists in which every curve in the set is\nextendible (Ellis and Schmidt 1977). Also, there may exist several\nphysically quite different global extensions: the spacetime covered by\nthe usual Schwarzschild coordinates outside the Schwarzschild radius,\nfor instance, can be extended analytically to Kruskal-Schwarzschild\nspacetime with a spacetime “tunnel” or\n“bridge” to an otherwise disconnected part of the universe\n(Hawking and Ellis 1973, sec. 5.5), or it can be extended to a\nsolution representing the interior of a massive spherical body. It is,\nin any event, difficult to know what to make of the invocation of such\novertly metaphysical considerations in arguments in this most hard of\nall hard sciences. See Curiel (1999) and Earman (1996) for critical\nsurvey of such arguments, and Doboszewski (2017) for a recent\ncomprehensive survey of all these issues, including discussion of the\nmost recent technical results. ", "\nA common hope is that when quantum effects are taken into account in\nthe vicinity of such extreme conditions of curvature where\nsingularities are predicted by the classical theory, the singular\nnature of the spacetime geometry will be suppressed, leaving only well\nbehaved spacetime structure. Advocates of various programs of quantum\ngravity also argue that in such a complete, full theory, singularities\nof the kinds discussed here will not appear. Recent important work by\nWall (2013a, 2013b) shows that these hopes face serious problems. We\npick up these issues below, in\n section 5.4.4\n and\n section 6.3\n respectively, for it is in those contexts that many of the explicit\ndebates play out over the limits of general relativity. ", "\nIn any event, it is well to keep in mind that, even if singularities\nare observed one day, and we are able to detect regularity in their\nbehavior of a sort that lends itself to formulation as physical law,\nit seems likely that this law will not be a consequence of general\nrelativity but will rather go beyond its bounds in radical ways, for,\nas we have seen, general relativity by itself does not have any\nmechanism for constraining the possible behavior that singular\nstructure of various types may manifest. It is perhaps just this\npossibility that excites a frisson of pleasure in those of the\nlibertine persuasion at the same time as it makes the prudish shudder\nwith revulsion. ", "\nFor a philosopher, the issues mooted here offer deep and rich veins\nfor those contemplating, among other matters: the role of explanatory\npower in the assessment of physical theories; the interplay among\nobservation, mathematical models, physical intuition and metaphysical\npredilection in the genesis of scientific knowledge; questions about\nthe nature of the existence attributable to physical entities in\nspacetime and to spacetime itself; and the role of mathematical models\nof physical systems in our understanding of those systems, as opposed\nto their role in the mere representation of our knowledge of them.\n" ], "subsection_title": "2.2. The Breakdown of General Relativity?" } ] }, { "main_content": [], "section_title": "3. Black Holes", "subsections": [ { "content": [ "\nThe simplest picture of a black hole is that of a system whose gravity\nis so strong that nothing, not even light, can escape from it. Systems\nof this type are already possible in the familiar Newtonian theory of\ngravity. The escape velocity of a body is the velocity at which an\nobject would have to begin to travel to escape the gravitational pull\nof the body and continue flying out to infinity, without further\nacceleration. Because the escape velocity is measured from the surface\nof an object, it becomes higher if a body contracts and becomes more\ndense. (Under such contraction, the mass of the body remains the same,\nbut its surface gets closer to its center of mass; thus the\ngravitational force at the surface increases.) If the object were to\nbecome sufficiently dense, the escape velocity could therefore exceed\nthe speed of light, and light itself would be unable to escape. ", "\nThis much of the argument makes no appeal to relativistic physics, and\nthe possibility of such Newtonian black holes was noted in the late\n18th Century by Michell (1784) and Laplace (1796, part ii,\np. 305). These Newtonian\nobjects, however, do not precipitate the same sense of crisis as do\nrelativistic black holes. Although light emitted at the surface of the\ncollapsed body cannot escape, a rocket with powerful enough motors\nfiring could still push itself free. It just needs to keep firing its\nrocket engines so that the thrust is equal to or slightly greater than\nthe gravitational force. Since in Newtonian physics there is no upper\nbound on possible velocities, moreover, one could escape simply by\nbeing fired off at an initial velocity greater than that of light.\n", "\nTaking relativistic considerations into account, however, we find that\nblack holes are far more exotic entities. Given the usual\nunderstanding that relativity theory rules out any physical process\npropagating faster than light, we conclude that not only is light\nunable to escape from such a body: nothing would be able to\nescape this gravitational force. That includes the powerful rocket\nthat could escape a Newtonian black hole. Further, once the body has\ncollapsed down to the point where its escape velocity is the speed of\nlight, no physical force whatsoever could prevent the body from\ncontinuing to collapse further, for that would be equivalent to\naccelerating something to speeds beyond that of light. Thus once this\ncritical point of collapse is reached, the body will get ever smaller,\nmore and more dense, without limit. It has formed a relativistic black\nhole. Here is where the intimate connection between black holes and\nsingularities appears, for general relativity predicts that, under\nphysically reasonable and generic conditions, a spacetime singularity\nwill form from the collapsing matter once the critical point of\nblack-hole formation is reached (Penrose 1965; Schoen and Yau 1983;\nWald 1984). ", "\nFor any given body, this critical stage of unavoidable collapse occurs\nwhen the object has collapsed to within its so-called Schwarzschild\nradius, which is proportional to the mass of the body. Our sun has a\nSchwarzschild radius of approximately three kilometers; the Earth's\nSchwarzschild radius is a little less than a centimeter; the\nSchwarzschild radius of your body is about 10-27\ncm—ten times smaller than a neutrino and 1010 times\nsmaller than the scale characteristic of quark interactions. This\nmeans that if you could collapse all the Earth's matter down to a\nsphere the size of a pea, it would form a black hole. ", "\nIt is worth noting, however, that one does not need an extremely high\ndensity of matter to form a black hole if one has enough mass. If all\nthe stars in the Milky Way gradually aggregate towards the galactic\ncenter while keeping their proportionate distances from each other,\nthey will all fall within their joint Schwarzschild radius and so form\na black hole long before they are forced to collide. Or if one has a\ncouple hundred million solar masses of water at its standard density\n(1 gm/cm3)—so occupying in total a region of about\n1027 cubic kilometers, the approximate size of the smallest\nsphere containing the orbit of Uranus—it will be contained\nwithin its Schwarzschild radius. (In this case, of course, the water\nwould indeed eventually collapse on itself to arbitrarily high\ndensities.) Some supermassive black holes at the centers of galaxies\nare thought to be even more massive than the example of the water, at\nseveral billion solar masses, though in these cases the initial\ndensity of the matter thought to have formed the black holes was\nextraordinarily high. ", "\nAccording to the standard definition (Hawking and Ellis 1973; Wald\n1984), the event horizon of a black hole is the surface formed by the\npoints of no return. That is, it is the boundary of the collection of\nall events in the spacetime closest to the singularity at which a\nlight signal can still escape to the external universe. Everything\nincluding and inside the event horizon is the black hole itself. (See\n section 3.4\n for a discussion of different ways to define a black hole, and the\nproblems these competing definitions raise.) For a standard\n(uncharged, non-rotating) black hole, the event horizon lies at the\nSchwarzschild radius. A flash of light that originates at an event\ninside the black hole will not be able to escape, but will instead end\nup in the central singularity of the black hole. A light flash\noriginating at an event outside of the event horizon will escape\n(unless it is initially pointed towards the black hole), but it will\nbe red-shifted strongly to the extent that it started near the\nhorizon. An outgoing beam of light that originates at an event on the\nevent horizon itself, by definition, remains on the event horizon\nuntil the temporal end of the universe. ", "\nGeneral relativity tells us that clocks running at different locations\nin a gravitational field will, in a sense that can be made precise,\ngenerally not agree with one another. In the case of a black hole,\nthis manifests itself in the following way. Imagine someone falls into\na black hole, and, while falling, she flashes a light signal to us\nevery time her watch hand ticks. Observing from a safe distance\noutside the black hole, we would find the times between the arrival of\nsuccessive light signals to grow larger without limit, because it\ntakes longer for the light to escape the black hole's gravitational\npotential well the closer to the event horizon the light is emitted.\n(This is the red-shifting of light close to the event horizon.) That\nis, it would appear to us that time were slowing down for the falling\nperson as she approached the event horizon. The ticking of her watch\n(and every other process as well) would seem to go ever more slowly as\nshe approached ever more closely to the event horizon. We would never\nactually see the light signals she emits when she crosses the event\nhorizon; instead, she would seem to be eternally “frozen”\njust above the horizon. (This talk of seeing the person is somewhat\nmisleading, because the light coming from the person would rapidly\nbecome severely red-shifted, and soon would not be practically\ndetectable.) ", "\nFrom the perspective of the infalling person, however, nothing unusual\nhappens at the event horizon. She would experience no slowing of\nclocks, nor see any evidence that she is passing through the event\nhorizon of a black hole. Her passing the event horizon is simply the\nlast moment in her history at which a light signal she emits would be\nable to escape from the black hole. The concept of an event horizon is\na global one that depends on the overall structure of the\nspacetime, and in particular on how processes physically evolve into\nthe indefinite future. Locally there is nothing noteworthy about the\npoints on the event horizon. In particular, locating the event horizon\nby any combination of strictly local measurements is impossible in\nprinciple, no matter how ingeniously the instruments are arranged\nand precisely the measurements made. The presence of an event horizon\nin this global sense is a strictly unverifiable hypothesis. One need\nnot be a verificationist about scientific knowledge to be troubled by\nthis state of affairs (Curiel 2019). Indeed, the global nature of the\nevent horizon manifests in an even more striking way: they are\n“prescient”, in the sense that where the event horizon\nhorizon is located today depends on what I will throw in the black\nhole tomorrow. How should a good empiricist feel about all of this?\n", "\nThe global and geometrical nature of black holes also raises\ninteresting questions about the sense in which one may or should think\nof them as physical objects or systems (Curiel 2019). A black hole is\nsimply a geometrically characterized surface in spacetime, with no\nordinary matter at the event horizon, and no other local feature that\nwould allow one to detect it. The same questions as with singularities\n (section 2.1),\n therefore, force themselves on us here: in what sense, if any, should\nwe attribute existence to black holes, in so far as, considered\nlocally, they are an undistinguished region of spacetime whose\nphysically important properties manifest only as global structure?\n", "\nBecause of the peculiar nature of black holes as physical systems, the\nattempt to observe them also raises interesting epistemic problems\nabout, inter alia, under-determination of theoretical models\nby data, the way that theoretical assumptions play ineliminable roles\nin the interpretation of data, and what it means at all to\n“observe” a physical system that is, in principle, able to\nemit no signal directly. Eckart et al. (2017) provides a\ncomprehensive survey of the issues; see also Collmar et al.\n(1998) for the record of a round-table discussion on these questions\nby a group of eminent theoreticians and observational astronomers. In\nlight of the recent epoch-making detection by LIGO of gravitational\nwaves with a signature indicating they were generated by a binary\nblack-hole system coalescing (Abbott et al. 2016), these\nissues become even more urgent for philosophers to explore. " ], "subsection_title": "3.1. Standard Definition and Properties" }, { "content": [ "\nOne of the most remarkable features of relativistic black holes is\nthat they are purely gravitational entities: all the standard\nblack-hole spacetime models (Schwarzschild, Reissner-Nordström,\nKerr, Kerr-Newman) contain no matter whatsoever. They are vacuum\nsolutions to the Einstein field equations, which just means a solution\nin which the matter density is everywhere zero. (Of course, one can\nalso consider a black hole with matter present, as standard\nastrophysical models do for the supermassive black holes that are\nbelieved to live at the center of most galaxies, which are thought to\nbe surrounded by strong magnetic fields and accretion disks of\nsuper-heated matter.) In pre-relativistic physics we think of gravity\nas a force produced by the mass associated with some matter. In the\ncontext of general relativity, however, we do away with gravitational\nforce, and instead postulate a curved spacetime geometry that produces\nall the effects we standardly attribute to gravity. One of the most\ncharacteristic features of general relativity that sets it apart from\nNewtonian gravitational theory is that it admits the possibility of\nsuch curvature (“gravitational effects”) in the absence of\nmatter, such as at the boundary of a black hole. Thus a black hole is\nnot a thing in spacetime; it is instead a feature of\nspacetime itself. ", "\nA careful definition of a relativistic black hole will therefore rely\nonly on the geometrical features of spacetime. We will need to be a\nlittle more precise about what it means to be “a region from\nwhich nothing, not even light, can escape”. First, there will\nhave to be someplace to escape to if our definition is to\nmake sense. The most common method of making this idea precise and\nrigorous employs the notion of escaping to infinity. The idea is that\nif a particle or light ray cannot travel arbitrarily far from a\ndefinite, bounded region in the interior of spacetime but must remain\nalways in the region, then that region is one of no escape, and is\nthus a black hole. The boundary of the region is the event horizon.\nOnce a physical entity crosses the event horizon into the black hole,\nit never crosses it again. ", "\nSecond, we will need a clear notion of the kind of geometry that\nallows for escape, or makes such escape impossible. For this, we need\nthe notion of the causal structure of spacetime. At any event in the\nspacetime, the possible trajectories of all light signals form a cone\n(or, more precisely, the four-dimensional analogue of the boundary of\na cone). Since light travels at the fastest speed allowed in the\nspacetime, these cones map out the boundaries of the propagation of\npossible causal processes in the spacetime. If an occurrence at an\nevent A is able to causally affect another occurrence at event\nB, there must be a continuous trajectory in spacetime from\nevent A to event B such that the trajectory lies in or\non the light cones of every event along it. (For more discussion, see\nthe Supplementary Document:\n Light Cones and Causal Structure.)\n ", "\n\n Figure 4\n is a spacetime diagram of a sphere of matter collapsing to form a\nblack hole. The curvature of the spacetime is represented by the\ntilting of the light cones away from 45 degrees. Notice that the light\ncones tilt inwards more and more as one approaches the center of the\nblack hole. The jagged line running vertically up the center of the\ndiagram depicts the central singularity inside the black hole. As we\nemphasized in Section 1, this is not actually part of the spacetime,\nbut might be thought of as the “place” where the structure\nof spacetime breaks down. Thus, one should not imagine the possibility\nof traveling through the singularity; this would be as nonsensical as\nsomething's leaving the diagram (i.e., the spacetime)\naltogether. ", "\nWhat makes this a black hole spacetime is the fact that it contains a\nregion from which it is impossible to exit while traveling at or below\nthe speed of light. This region is marked off by the events at which\nthe outside edge of the forward light cone points straight upward. As\none moves inward from these events, the light cone tilts so much that\none is always forced to move inward toward the central singularity.\nThis set of points of no return is, of course, the event horizon; and\nthe spacetime region inside it is the black hole. In this region, one\ninevitably moves towards the singularity; the impossibility of\navoiding the singularity is just the impossibility of preventing\nourselves from moving forward in time. (Again, see\n section 3.4\n for a discussion of other ways to define a black hole.) ", "\nNotice that, as represented in\n Figure 4, the matter of the collapsing\n star eventually disappears into the black hole singularity. All the\n details of the matter are then completely lost; all that is left is\n the geometrical properties of the black hole. Astonishingly, those\n properties can be identified with a small, fixed set of physical\n quantities. Indeed, the remarkable No-Hair Theorems (Israel 1967,\n 1968; Carter 1971, 1973, 1997 [Other Internet Resources]; Robinson\n 1975; Mazur 1982; Heusler 1996; Chruściel et al. 2012)\n make rigorous the idea that a black hole in equilibrium is entirely\n characterized by just three numbers, viz., its mass, its\n angular momentum, and its electric\n charge.[9] This\n has the remarkable consequence that no matter what the particulars\n may be of any body that collapses to form a black hole—it may\n be as intricate, complicated and Rococo as one likes, composed of the\n most exotic materials—the final result after the system has\n settled down to equilibrium will be identical in every respect to a\n black hole that formed from the collapse of any other body\n having the same total mass, angular momentum and electric charge\n (Carter 1997 [Other Internet Resources]). Because of this extremity\n of simplicity, Chandrasekhar (1983, Prologue,\n p. xxiii) called black\n holes “the most perfect macroscopic objects … in the\n universe.” (The fact that their physical state is entirely\n characterized by only three numbers plays an important role in the\n ascription of thermodynamical properties to black holes, discussed in\n 5.2\n below.) ", "\nRemarkably, not only are black holes in and of themselves objects of\nthe utmost simplicity. They enforce simplicity on all else in the\nuniverse as well, no matter how far away from themselves. In a sense\nthat can be made precise, one of the most basic structures of the\nspacetime manifold itself, its topology, is as simple as possible\neverywhere outside a well behaved black\n hole.[10]\n This is known as the Topological Censorship Theorem (Friedman et\nal. 1983; Chruściel and Wald 1994; Galloway 1995). As its\nname suggests, it bears on the larger question of the Cosmic\nCensorship Hypothesis (Galloway and Woolgar 1997), discussed in\n section 4\n below. In itself, though, it raises fascinating questions about the\nrelation of topological to metrical structure in a spacetime,\nquestions almost completely unexplored by philosophers. (See Geroch\nand Horowitz 1979 for a long list of conceptual and technical problems\nand questions about this relation.) For a philosopher interested in\nthe nature of spacetime, however, the way that its different\nstructures relate to and constrain each other must be of fundamental\nimportance. " ], "subsection_title": "3.2. The Most Perfect Objects in the Cosmos" }, { "content": [ "\nFor the reasons discussed in\n section 3.1,\n the standard definition of a black hole, based on the idea of a\nglobal event horizon, has limited application to the modeling of real\nastrophysical systems (except in so far as one can idealize them as\nessentially isolated). In an attempt to rectify this situation,\nHayward (1994b) offered a generalized definition of a black hole, not\nrequiring any of the special global structures that the traditional\ndefinition relies on. Hayward defines a black hole based on what he\ncalls a trapping horizon. This is, roughly speaking, a surface on\nwhich all inward-directed light rays are converging, and to which all\noutward-directed light rays are tangent. This definition tries to\ncapture the idea that a black hole is a surface at which the\ngravitational intensity is such that not even light can escape: any\nlight ray incident on the surface the smallest bit inward will get\nsucked in; otherwise, light rays can be only tangent to the surface.\nThe surface does not admit incident light rays traveling away from its\ninterior. This definition has the virtue that the boundary of the\nblack hole now has clear, local physical significance in principle: an\nobserver could determine when she crossed it by making only local\nmeasurements. (More precisely, a team of synchronized observers, whose\ncombined instrumental reach encompasses the entire surface at a given\nmoment of time, could jointly make this determination, with enough\nbackground knowledge of the spacetime geometry outside the boundary.)\nPerhaps one of the most intriguing aspects of Hayward's definition is\nthat a black hole would not necessarily be a region of no escape: in\nsome black holes so defined, an observer entering the trapped region\ncould later escape it (Hayward 1994a, in OIR).\n ", "\nAshtekar et al. (1999, 2000) offer a different, related\ngeneralization of the idea of a black hole, based on what they call\nisolated horizons. This definition is somewhat more restrictive than\nHayward's in so far as, as the name suggests, it requires that no\nstress-energy cross such a horizon. Subsequent work by Ashtekar and\nKrishnan (2003), Ashtekar (2007) and Hayward (2006, in OIR,\n 2009) clarified the relationship between the two, showing that the\nisolated horizon can be considered, in a sense, a special case of the\ntrapping horizon. (See Hayward 2013 for a recent comprehensive review,\nand Faraoni 2013 for one with special attention to its relevance to\ncosmology.) For lack of a better term, we shall call black holes\ndefined by trapping or isolated horizons “quasi-local black\nholes”. (‘Local’ because they are not global objects\nin the sense that black holes as tradionally defined are, and\n‘quasi’ because they still can extend arbitrarily far\nthroughout spacetime.) ", "\nThe status of these competing definitions of a quasi-local black hole\nand of the differences among them, and what their respective virtues\nand demerits may be, appear to be open questions, though both Hayward\nand Ashtekar et al., in the works just cited, go some way\ntowards answering some of them by using their respective definitions\nto prove generalizations of the so-called laws of black hole mechanics\n (section 5.1\n below). Hayward also demonstrates that analogues to some of the\nclassical singularity theorems hold for his definition as well. Still,\nmany questions remain open. To take one example, it is not clear\nwhether or not the new definitions coincide with the traditional\ndefinition in those spacetimes in which the traditional definition can\nbe formulated, or whether collateral conditions must be met for the\ntwo to coincide. It is also not clear whether the analogues to the\nclassical No Hair Theorems hold using the new definitions or even what\nthose analogues may be. ", "\nPerhaps the most fascinating feature of quasi-local black holes is the\nfact that, in a sense that can be made precise, they are\n“clairvoyant”: they are aware of and respond to changes in\nthe geometry in spacetime regions that they cannot be in causal\ncontact with (Bengtsson and Senovilla 2011). Indeed, they can\nencompass regions whose entire causal past is flat! This subject\nexemplifies the exuberant weirdness that causal structure in general\nrelativity can manifest. " ], "subsection_title": "3.3. Quasi-Local Black Holes" }, { "content": [ "\nBesides the standard definition of a black hole based on the presence\nof a global event horizon, and the quasi-local definitions just\ndiscussed, there is an enormous and greatly variegated menagerie of\ndifferent definitions and conceptions of a black hole that physicists\nin different fields (and sometimes those in the same field) use in\ntheir day to day work, none agreeing with the standard or quasi-local\ndefinitions, many of them manifestly inconsistent with each other\n(Curiel 2019). However one views this situation, it is clear, as a\nbrute fact about the practice of physics today, that there is no\nsingle definition of “black hole” that will serve all\ninvestigative purposes in all fields in which black holes are objects\nof study.\n Table 1\n lists the core concepts most commonly used in definitions and\ncharacterizations of black holes across several different fields of\nphysics, sketched with only the broadest and crudest of brushes. It\nshould be kept in mind that many investigators in each of these fields\ndo not use, or even accept as reasonable, what is given in the table.\n", "\nWhat seems to be the most common practice today is, during the course\nof an investigation, to fix a list of important, characteristic\nproperties of and phenomena associated with black holes required for\none's purposes in the context of interest, and then to determine which\nof the known definitions imply the members of that list. If no known\ndefinition implies the list, one either attempts to construct a new\ndefinition that does (and is satisfactory in other ways), or else one\nconcludes that there is an internal inconsistency in one's list, which\nmay already be of great interest to learn. Examining the way the idea\nof black holes are used across physics—in astrophysics,\ncosmology, classical general relativity, semi-classical gravity,\nparticle physics, various programs in quantum gravity, fluid\nmechanics, condensed matter, and analogue gravity—yields a list\nof potentially characteristic properties and phenomena some subset of\nwhich may plausibly be required or wanted in a characterization of a\nblack hole in a given investigative context (Curiel 2019): ", "\nThis list is not meant to be exhaustive. There are many other such\nproperties and phenomena that might be needed for a given purpose. It\nis already clear from this partial list, however, that no single\ndefinition can accommodate all of them. It is also clear from\nexamining the literature, moreover, that, even within the same\ncommunities, different workers will choose different subsets of these\nproperties for different purposes in their thinking about black holes.\n", "\nAs in the case of singularities, these alternative definitions of\nblack holes raise philosophical questions about the relations among\nthe different definitions that attempt to capture different aspects\nof, intuitively speaking, the “same kind” of physical\nobject. One can, for instance, view the standard definition of a black\nhole, with its global event horizon, as an extreme idealization of an\nisolated system (one with no neighboring systems at all), and the\ndefinitions based on isolated or trapping horizons as trying to\ncapture a more general, less idealized representation of an isolated\nsystem, one that has neighboring systems at a finite remove, or a\nrepresentation of a system that may be non-trivially interacting with\nother systems. For the looser, less precise definitions used by\nastrophysicists, for example, and some of the gestures at definitions\nproposed in some programs of quantum gravity, however, it is difficult\nto know how even to begin to compare them to the precise global and\nquasi-local ones. It is simply not clear that the same type of\nphysical system is being characterized. ", "\nThis situation provides a fascinating case study, from both a physical\nand a philosophical point of view, for questions about the nature of\nidealization and de-idealization, and the definition of theoretical\nentities more generally. On what grounds, e.g., could one\nascertain the relative merits of each type of definition on its own,\nand each as proposed for a particular sort of investigation, in the\nabsence of empirical data? In what sense do the different definitions\ncharacterize the “same” type of physical system, if they\ndo so at all? Is there a need to settle on a single canonical\ndefinition of a black hole? What would be gained or lost with or\nwithout one? The situation is closely analogous to that of the lack of\na canonical definition of a singularity, except it is even more\nextreme here: the different definitions of singularities used by\ndifferent physicists are (almost always) not actually\ninconsistent with each other. ", "\nFor the remainder of this encyclopedia entry, unless explicitly stated\notherwise, when we speak of a black hole it should be understood that\nwe mean one as determined by the standard definition of a global event\nhorizon, because this is the one most often used in current\nfoundational work. " ], "subsection_title": "3.4. Different Definitions of Black Holes" } ] }, { "main_content": [ "\nWhile spacetime singularities in general are frequently viewed with\nsuspicion, physicists often offer the reassurance that, even if they\nare real, we expect most of them to be hidden away behind the event\nhorizons of black holes. Such singularities therefore could not affect\nus unless we were actually to jump into the black hole. A naked\nsingularity, on the other hand, is one that is not hidden behind an\nevent horizon. Such singularities appear much more threatening because\nthey are uncontained, freely accessible to the rest of spacetime. ", "\nThe heart of the worry is that singular structure seems to signify so\nprofound a breakdown in the fundamental structure of spacetime that it\ncould wreak havoc on any region of the universe that it were visible\nto. Because the structures that break down in singular spacetimes are\nin general required for the formulation of our known physical laws,\nand of initial-value problems for individual physical systems in\nparticular, one such fear is that determinism would collapse entirely\nwherever the singular breakdown were causally visible. In Earman's\n(1995, pp. 65–6) evocative conceit, nothing would seem to stop\nthe singularity from disgorging any manner of unpleasant jetsam, from\nTVs showing Nixon's Checkers Speech to old lost socks, in a way\ncompletely undetermined by the state of spacetime in any region\nwhatsoever. As a result, there could be no reasonable expectation of\ndeterminism, nor even just predictability, for any region in causal\ncontact with what it spews out. ", "\nOne form that such a naked singularity could take is that of a\nwhite hole, which is a time-reversed black hole. Imagine\ntaking a film of a black hole forming from the collapse of a massive\nobject, say, a star, with light, dust, rockets, astronauts and old\nsocks falling into it during its subsequent evolution. Now imagine\nthat film being run backwards. This is the picture of a white hole:\none starts with a naked singularity, out of which might appear people,\nrockets, socks—anything at all—with eventually a star\nbursting forth. Absolutely nothing in the causal past of such a white\nhole would determine what would pop out of it, since, as follows from\nthe No Hair Theorems\n (section 3.2),\n items that fall into a black hole leave no trace on the future\noutside of it. (This description should feel familiar to the canny\nreader: it is the same as the way that increase of entropy in ordinary\nthermodynamics as embodied in the Second Law makes retrodiction\nimpossible; the relationship of black holes to thermodynamics is\ndiscussed in\n section 5.)\n Because the field equations of general relativity do not pick out a\npreferred direction of time, if the formation of a black hole is\nallowed by the laws of spacetime and gravity, then those laws also\npermit white holes. ", "\nRoger Penrose (1969, 1973) famously suggested that although naked\nsingularities are compatible with general relativity, in physically\nrealistic situations they will never form; that is, any process that\nresults in a singularity will safely ensconce that singularity behind\nan event horizon. This conjecture, known as the Cosmic Censorship\nHypothesis, has met with some success and popularity; however, it also\nfaces several difficulties. As in our previous discussions of\nsingularities and black holes, there are questions about how exactly\nto formulate the hypothesis, and, once formulated, about whether or\nnot it holds in general relativity as a whole, or at least in some\nphysically reasonable subset of spacetimes—where, again,\n“physically reasonable” will likely be a vague and\ncontroversial notion. ", "\nPenrose's original formulation relied on black holes: a suitably\ngeneric singularity will always be contained in a black hole (and so\ncausally invisible outside the black hole). As the counter-examples to\nvarious ways of articulating the hypothesis based on this idea have\naccumulated over the years, however, it has gradually been abandoned\n(Geroch and Horowitz 1979; Krolak 1986; Penrose 1998; Joshi et\nal. 2002; Joshi 2003, 2007a; Joshi and Malafarina 2011a, 2011b).\nMore recent approaches either begin with an attempt to provide\nnecessary and sufficient conditions for cosmic censorship itself,\nyielding an indirect characterization of a naked singularity as any\nphenomenon violating those conditions, or else they begin with an\nattempt to provide a characterization of a naked singularity without\nreference to black holes and so conclude with a definite statement of\ncosmic censorship as the absence of such phenomena (Geroch and\nHorowitz 1979). The variety of proposals made using both approaches is\ntoo great to canvass here; the interested reader is referred to\nRingström (2010) for a review of the current state of the art for\nstandard black holes, Nielsen (2012) for cosmic censorship regarding\nHayward's quasi-local black holes\n (section 3.3),\n Ringström (2010) for a review of the bearing of the\ninitial-value problem in general relativity on cosmic censorship, and\nto Earman (1995, ch. 3) and Curiel (1999) for philosophical discussion\nof many of the earlier proposals. Manchak (2011) gives reasons for\nthinking that the question of providing a completely satisfactory\nformulation of the Cosmic Censorship Hypothesis may never be settled,\non the grounds that the idea of what counts as “physically\nreasonable” is not an empirically determinable question. Still,\nthe possibility may remain open that there be several different,\ninequivalent formulations of the Cosmic Censorship Hypothesis, each\nhaving its own advantages and problems, none “canonical”\nin a definitive sense, as may be the case for definitions of\nsingularities and black holes themselves. ", "\nThere is another area of investigation intimately related to issues of\nCosmic Censorship in general, and issues of determinism in general\nrelativity in particular: whether or not spacetime is\n“hole-free”. This has been the subject of recent\nphilosophical work, primarily by Manchak (2009b, 2014a, 2016a). Geroch\n(1977) originally proposed the idea of a generic “hole” in\nspacetime in trying to capture in as general terms as possible the\nidea that spacetime has no obstruction of any kind that would prevent\nit from “evolving as far into the future as it reasonably\ncould”. (Recall the discussion of maximality and extendibility\nin\n section 1.1.)\n Although Geroch's definition had powerful conceptual appeal, in the\nevent it has proven untenable: Krasnikov (2009) showed that, according\nto it, even Minkowski spacetime fails to be hole-free. Manchak (2009b)\nshowed how an emendation of Geroch's definition could fix the problem.\nHe then showed that, under the assumption of global hyperbolicity (a\nstrong condition of causal well-behavedness for a spacetime), one gets\na nice hierarchy of conditions relating to determinism: geodesic\ncompleteness implies effective completeness (Manchak's own condition),\nwhich implies inextendibility, which implies hole-freeness (Manchak\n2014a; see\n section 1.1\n for the definitions of these conditions). In related work, Manchak\n(2014b) showed that, in a sense one can make precise, it should be\neasier to construct a machine that would result in spacetime's having\nsuch a hole than one that would result in time-travel. In short,\ncreating the possibility for indeterminism seems easier in the theory\nthan the possibility for causal paradox! ", "\nManchak (2016a) also recently introduced a new kind of pathology a\nspacetime can have, an “epistemic hole”: roughly speaking,\na spacetime has an epistemic hole if two observers in initially\nidentical epistemic states can evolve in such a way that what one can\nlearn can only ever be, in principle, a proper subset of what the\nother can learn. Manchak shows that, if a spacetime has no epistemic\nholes then (under mild conditions on the niceness of the causal\nstructure) the spacetime has no naked singularities as standardly\nconstrued. The condition differs also in its modal character from\nother such hole-freeness conditions, for it makes significantly weaker\nand more conceptually and technically tractable modal claims. ", "\nIssues of determinism, from an epistemic perspective, are intimately\nbound up with the possibility of reliable prediction. (See the entry\n Causal Determinism.)\n The general issue of predictability itself in general relativity,\neven apart from the specific problems that singular structure may\nraise, is fascinating, philosophically rich, and very much unsettled.\nOne can make a prima facie strong argument, for example, that\nprediction is possible in general relativity only in spacetimes that\npossess singularities (Hogarth 1997; Manchak 2013)! See\nGeroch (1977), Glymour (1977), Malament (1977), and Manchak (2008,\n2013) for discussion of these and many other related issues. ", "\nHere again, as with almost all the issues discussed up to this point\nin this entry regarding singularities and black holes, is an example\nof a sizable subculture in physics working on matters that have no\nclearly or even unambiguously defined physical parameters to inform\nthe investigations and no empirical evidence to guide or even just\nconstrain them, the parameters of the debate imposed by and large by\nthe intuitions of a handful of leading researchers. From sociological,\nphysical, and philosophical vantage points, one may well wonder, then,\nwhy so many physicists continue to work on it, and what sort of\ninvestigation they are engaged in. Perhaps nowhere else in general\nrelativity, or even in physics, can one observe such a delicate\ninterplay of, on the one hand, technical results, definitions and\ncriteria, and, on the other hand, conceptual puzzles and even\nincoherence, largely driven by the inchoate intuitions of physicists.\nNot everyone views the situation with excitement or even equanimity,\nhowever: see Curiel (1999) for a somewhat skeptical discussion of the\nwhole endeavor. " ], "section_title": "4. Naked Singularities, the Cosmic Censorship Hypothesis, and Indeterminism", "subsections": [] }, { "main_content": [ "\nThe challenge of uniting quantum theory and general relativity in a\nsuccessful theory of quantum gravity has arguably been the greatest\nchallenge facing theoretical physics for the past eighty years. One\navenue that has seemed particularly promising is the attempt to apply\nquantum theory to black holes. This is in part because, as purely\ngravitational entities, black holes present an apparently simple but\nphysically important case for the study of the quantization of\ngravity. Further, because the gravitational force grows without bound\nas one nears a standard black-hole singularity, one would expect\nquantum gravitational effects (which should come into play at\nextremely high energies) to manifest themselves in the interior of\nblack holes. ", "\nIn the event, studies of quantum mechanical systems in black hole\nspacetimes have revealed several surprises that threaten to overturn\nthe views of space, time, and matter that general relativity and\nquantum field theory each on their own suggests or relies on. Since\nthe ground-breaking work of Wheeler, Penrose, Bekenstein, Hawking and\nothers in the late 1960s and early 1970s, it has become increasingly\nclear that there are profound connections among general relativity,\nquantum field theory, and thermodynamics. This area of intersection\nhas become one of the most active and fruitful in all of theoretical\nphysics, bringing together workers from a variety of fields such as\ncosmology, general relativity, quantum field theory, particle physics,\nfluid dynamics, condensed matter, and quantum gravity, providing\nbridges that now closely connect disciplines once seen as largely\nindependent. ", "\nIn particular, a remarkable parallel between the laws of black holes\nand the laws of thermodynamics indicates that gravity and\nthermodynamics may be linked in a fundamental (and previously\nunimagined) way. This linkage strongly suggests, among many things,\nthat our fundamental ideas of entropy and the nature of the Second Law\nof thermodynamics must be reconsidered, and that the standard form of\nquantum evolution itself may need to be modified. While these\nsuggestions are speculative, they nevertheless touch on deep issues in\nthe foundations of physics. Indeed, because the central subject matter\nof all these diverse areas of research lies beyond the reach of\ncurrent experimentation and observation, they are all speculative in a\nway unusual even in theoretical physics. In their investigation,\ntherefore, physical questions of a technically sophisticated nature\nare inextricable from subtle philosophical considerations spanning\nontology, epistemology, and methodology, again in a way unusual even\nin theoretical physics. ", "\nBecause this is a particularly long and dense section of the article,\nwe begin with an outline of it.\n Section 5.1\n states the laws of black holes in classical general relativity, and\nexpounds the formal analogy they stand in with the laws of ordinary\nthermodynamics.\n Section 5.2\n briefly describes how taking account of quantum effects in the\nneighborhood of a black hole leads to the prediction of Hawking\nradiation and the subsequent conclusion that the analogy with the laws\nof ordinary thermodynamics is more than just formal, but represents a\ntrue and intimate physical connection.\n Section 5.3\n discusses the puzzles that arise when trying to understand the\nattribution of a physical entropy to a black hole.\n Section 5.4\n consists of several subsections, each examining a different puzzling\naspect of the so-called Generalized Second Law: the hypothesis that\nthe total entropy of the universe, that of ordinary matter plus that\nof black holes, never decreases. We conclude in\n Section 5.5\n with a brief account of attempts to extend the attribution of a\nphysical entropy to gravitational systems more general than just black\nholes. " ], "section_title": "5. Black Holes and Thermodynamics", "subsections": [ { "content": [ "\nSuppose one observes a quiescent black hole at a given moment,\nignoring any possible quantum effects. As discussed above in\n section 3.2,\n there are three physical quantities of dynamical interest the black\nhole possesses that are, more or less, amenable to measurement, and\nthat completely characterize the physical state of the black hole: its\nmass, its angular momentum, and its electric charge. These quantities,\nlike those of systems in classical mechanics, stand in definite\nrelation to each other as the black hole dynamically evolves, which is\nto say, they satisfy a set of equations characterizing their\n behavior.[11]\n ", "\n(A black hole is stationary if, roughly speaking, it does not\nchange over time; more precisely, it is stationary if its event\nhorizon is generated by an asymptotically timelike Killing field.)\n", "\nOn the face of it, the Zeroth, First and Third Laws are\nstraightforward to understand. The Second Law, however, is not so\n“obvious” as it may at first glance appear. It may seem\nthat, because nothing can escape from a black hole once it has\nentered, black holes can only grow larger or, at least, stay the same\nsize if nothing further falls in. This assumes, however, that\nincreased mass always yields increased surface area as opposed to some\nother measure of spatial extent. Surprising as it may sound, it is\nindeed the case that, although nothing that enters a black hole can\nescape, it is still possible to extract energy (i.e., mass)\nfrom a spinning black hole, by means of what is known as the Penrose\nprocess (Penrose and Floyd 1971). It is therefore not obvious that one\ncould not shrink a black hole by extracting enough mass-energy or\nangular momentum from it. It also seems to be at least possible that a\nblack hole could shrink by radiating mass-energy away as gravitational\nradiation, or that the remnant of two colliding black holes could have\na smaller surface area than the sum of the original two. ", "\nIt is most surprising, therefore, to learn that the Second Law is a\ndeep, rigorous theorem that follows only from the fundamental\nmathematics of relativistic spacetimes (Hawking 1971), and does not\ndepend in any essential way on the particulars of relativistic\ndynamics as encapsulated in the Einstein field equation (Curiel\n2017). This is in strict opposition to the Second Law in classical\nthermodynamics, which stands as a more or less phenomenological\nprinciple derived by empirical generalization, perhaps justified in\nsome sense by a “reduction” to statistical mechanics, with\nthe temporal asymmetry of entropy non-decrease argued to hold based on\nthe likelihood of initial states in conjunction with the forms of\ndynamical evolution “physically permissible” for matter\nfields. (See the entry\n Philosophy of Statistical Mechanics.)\n ", "\nFor those who know classical thermodynamics, the formal analogy\nbetween its laws and the laws of black hole as stated should be\nobvious. (For exposition and discussion of the laws of classical\nthermodynamics, see, e.g.: Fermi 1937 for a less technical,\nmore physically intuitive approach; Fowler and Guggenheim 1939 for a\nmore technical and rigorous one; and Uffink 2007 for a more\nhistorically and philosophically oriented one.) One formulation of the\nZeroth Law of thermodynamics states that a body in thermal equilibrium\nhas constant temperature throughout. The First Law is a statement of\nthe conservation of energy. It has as a consequence that any change in\nthe total energy of a body is compensated for and measured by changes\nin its associated physical quantities, such as entropy, temperature,\nangular momentum and electric charge. The Second Law states that\nentropy never decreases. The Third Law, on one formulation, states\nthat it is impossible to reduce the temperature of a system to zero by\nany physical process. Accordingly, if in the laws for black holes one\ntakes ‘stationary’ to stand for ‘thermal\nequilibrium’, ‘surface gravity’ to stand for\n‘temperature’, ‘mass’ to stand for\n‘energy’, and ‘area’ to stand for\n‘entropy’, then the formal analogy is perfect. ", "\nIndeed, relativistically mass just is energy, so at least the\nFirst Law seems already to be more than just formal analogy. Also, the\nfact that the state of a stationary black hole is entirely\ncharacterized by only a few parameters, completely independent of the\nnature and configuration of any micro-structures that may underlie it\n(e.g., those of whatever collapsed to form the thing),\nalready makes it sound more than just a little thermodynamical in\ncharacter. (Recall the discussion of the No Hair Theorems in\n section 3.2\n above.) Still, although the analogy is extremely suggestive in\ntoto, to take it seriously would require one to assign a non-zero\ntemperature to a black hole, which, at the time Bardeen, Carter and\nHawking first formulated and proved the laws in 1973, almost everyone\nagreed was absurd. All hot bodies emit thermal radiation (like the\nheat given off from a stove, or the visible light emitted by a burning\npiece of charcoal); according to general relativity, however, a black\nhole ought to be a perfect sink for energy, mass, and radiation,\ninsofar as it absorbs everything (including light), and emits nothing\n(including light). So it seems the only temperature one might be able\nto assign it would be absolute zero. (See\n section 5.4.2\n below for more detailed arguments to this effect.) ", "\nIn the early 1970s, nonetheless, Bekenstein (1972, 1973, 1974) argued\nthat the Second Law of thermodynamics requires one to assign a finite\nentropy to a black hole. His worry was that one could collapse any\namount of highly entropic matter into a black hole—which, as we\nhave emphasized, is an extremely simple object—leaving no trace\nof the original disorder associated with the high entropy of the\noriginal matter. This seems to violate the Second Law of\nthermodynamics, which asserts that the entropy (disorder) of a closed\nsystem—such as the exterior of an event horizon—can never\ndecrease. Adding mass to a black hole, however, will increase its\nsize, which led Bekenstein to suggest that the area of a black hole is\na measure of its entropy. This conjecture received support in 1971\nwhen Hawking proved that the surface area of a black hole, like the\nentropy of a closed system, can never decrease (Hawking 1971). Still,\nessentially no one took Bekenstein's proposals seriously at first,\nbecause all black holes manifestly have temperature absolute zero, as\nmentioned above, if it is even meaningful to ascribe temperatures to\nthem in the first\n place.[12]\n ", "\nThus it seems that the analogy between black holes and thermodynamical\nobjects, when treated in the purely classical theory of general\nrelativity, is merely a formal one, without real physical\nsignificance. " ], "subsection_title": "5.1. The Classical Laws of Black Holes" }, { "content": [ "\nThe “obvious fact” that the temperature of a black hole\ncan be, at best, only absolute zero was shown to be illusory when\nHawking (1974, 1975) demonstrated that black holes are not completely\nblack after all. His analysis of the behavior of quantum fields in\nblack-hole spacetimes revealed that black holes will emit radiation\nwith a characteristically thermal spectrum: a black hole generates\nheat at a temperature that is inversely proportional to its mass and\ndirectly proportional to its surface gravity. It glows like a lump of\nsmoldering coal even though light should not be able to escape from\nit! The temperature of this Hawking radiation is extremely low for\nstellar- and galactic-scale black holes, but for very, very small\nblack holes the temperatures would be high. (The Hawking temperature\nof the black hole at the center of the Milky Way, Sagittarius\nA*, having a mass of approximately 4 million solar masses,\nis approximately 10-14 Kelvin; for a black hole to be room\ntemperature, it would have to have a mass of about 1018\nkg—about 1000 times the mass of Mt. Everest—and so be\nabout 10-7 m across, the size of a virus.) This means that\na very, very small black hole should rapidly evaporate away, as all of\nits mass-energy is emitted in high-temperature Hawking radiation.\nThus, when quantum effects are taken into account, black holes will\nnot satisfy the Area Theorem, the second of the classical laws of\nblack hole, as their areas shrink while they evaporate. (Hayward\net al. 2009 discuss the status of deriving a\n“local” flux of Hawking radiation for quasi-local black\nholes; Nielsen 2009 discusses this along with the status of attempts\nto prove the laws of black holes for quasi-local black holes.) ", "\nThese results—now referred to collectively as the Hawking\neffect—were taken to establish that the parallel between the\nlaws of black hole and the laws of thermodynamics was not a mere\nformal fluke: it seems they really are getting at the same deep\nphysics. The Hawking effect establishes that the surface gravity of a\nblack hole can, indeed must, be interpreted as a physical temperature.\n(The surface gravity, therefore, is often referred to as the\n‘Hawking temperature’.) Connecting the two sets of laws\nalso requires linking the surface area of a black hole with entropy,\nas Bekenstein had earlier suggested: the entropy of a black hole is\nproportional to the area of its event horizon, which is itself\nproportional to the square of its mass. (The area, therefore, is often\nreferred to as the ‘Bekenstein entropy’.) Furthermore,\nmass in black hole mechanics is mirrored by energy in thermodynamics,\nand we know from relativity theory that mass and energy are identical,\nso the black hole's mass is its thermodynamical energy. The\noverwhelming consensus in the physics community today, therefore, is\nthat black holes truly are thermodynamical objects, and the laws of\nblack hole mechanics just are the laws of ordinary thermodynamics\nextended into a new regime, to cover a new type of physical system.\n", "\nWe will return to discuss Hawking radiation in more detail in\n section 6.1\n below, but for now we note that this all raises deep questions about\ninter-theoretic relations that philosophers have not yet come to grips\nwith: although it seems undeniable, what does it mean to say that a\npurely gravitational system is also “a thermodynamical\n object”?[13]\n How can the concepts and relations of one theory be translated so as\nto be applicable in the context of a radically different one? (See the\nentries\n Scientific Unity\n and\n Intertheory Relations in Physics.)\n ", "\nAlthough it is still orthodoxy today in the physics community that\nthere is no consistent theory of thermodynamics for purely classical\nblack holes (Unruh and Wald 1982; Wald 1999, 2001), i.e.,\nwhen quantum effects are not taken into account, primarily because it\nseems that they must be assigned a temperature of absolute zero, if\nany at all. Curiel (2017a, Other Internet Resources)\n has recently argued that this is not so. He argues, to the contrary,\nthat there is a consistent way of treating purely classical black\nholes as real thermodynamical systems, that they should be assigned a\ntemperature proportional to their surface gravity, and, in fact, that\nnot to do so leads to the same kinds of inconsistencies as occur if\none does not do so for black holes emitting Hawking radiation. ", "\nIn a recent article, Dougherty and Callender (2019) challenge the\northodoxy from the opposite direction. They argue that we should be\nfar more skeptical of the idea that the laws of black holes are more\nthan just formal analogy, and that, indeed, there are strong reasons\nto think that they are not physically the laws of thermodynamics\nextended into a new domain. Their main argument is that the Zeroth Law\nof black holes cannot do the work that the standard formulation of the\nZeroth Law does in classical thermodynamics. In classical\nthermodynamics, the standard formulation of the Zeroth Law is\ntransitivity of equilibrium: two bodies each in equilibrium with a\nthird will be in equilibrium with each other. They point out that this\ntransitivity of equilibrium underlies many of the most important\nconstructions and structures in classical thermodynamics, which mere\nconstancy of temperature (surface gravity) for a single system in\nequilibrium does not suffice for. Curiel (2018), however, recently\nproposed a strengthened version of the Zeroth Law for black holes,\nbased on a characterization of transitivity of equilibrium among them,\nin an attempt to address this challenge. It suffers from several\nproblems, however, most importantly the fact that it relies on a\nnotion of “approximate symmetry” in general relativity\nthat is not well defined. This is an area of active dispute. ", "\nWallace (2018, 2019) provides a more comprehensive exposition and\ndefense of the claim that black holes truly are thermodynamical\nobjects, attacking the problem from several different directions, and\noffers specific rejoinders to several of the other arguments made by\nDougherty and Callender (2019). " ], "subsection_title": "5.2. Black Hole Thermodynamics" }, { "content": [ "\nThe most initially plausible and promising way to explain what the\nentropy of a black hole measures, and why a black hole has such a\nproperty in the first place, is to point to the Hawking radiation it\nemits, and in particular the well defined temperature the radiation\nhas. (For exposition and discussion of the standard relations between\ntemperature and entropy in classical thermodynamics, see,\ne.g.: Fermi 1936 for a less technical, more physically\nintuitive approach; Fowler and Guggenheim 1939 for a more technical\nand rigorous one; and Uffink 2007 for a more historically and\nphilosophically oriented one.) Indeed, it is not uncommon to see such\n“explanations”, not only in popular accounts but even in\nserious research papers. There are, however, many technical and\nconceptual reasons why such an explanation is not viable (Visser\n1998b, 2003), summed up in the slogan that Hawking radiation is a\nstrictly kinematical effect, whereas black hole entropy is a dynamical\nphenomenon. (This fact is discussed in more detail in\n section 8\n below.) What, then, is the origin and nature of the entropy we\nattribute to a black hole? ", "\nIn classical thermodynamics, that a system possesses entropy is often\nattributed to the fact that in practice we are never able to give it a\n“complete” description (Jaynes 1967). When describing a\ncloud of gas, we do not specify values for the position and velocity\nof every molecule in it; we rather describe it using quantities, such\nas pressure and temperature, constructed as statistical measures over\nunderlying, more finely grained quantities, such as the momentum and\nenergy of the individual molecules. On one common construal, then, the\nentropy of the gas measures the incompleteness, as it were, of the\ngross description. (See the entry\n Philosophy of Statistical Mechanics.)\n In the attempt to take seriously the idea that a black hole has a\ntrue physical entropy, it is therefore natural to attempt to construct\nsuch a statistical origin for it. The tools of classical general\nrelativity cannot provide such a construction, for it allows no way to\ndescribe a black hole as a system whose physical attributes arise as\ngross statistical measures over underlying, more finely grained\nquantities. Not even the tools of quantum field theory on curved\nspacetime can provide it, for they still treat the black hole as an\nentity defined entirely in terms of the classical geometry of the\nspacetime (Wald 1994). Any such statistical accounting, therefore,\nmust come from a theory that attributes to the classical geometry\nitself a description based on an underlying, perhaps discrete\ncollection of microstates, themselves describing the fine-grained\ndynamics of “entities”, presumably quantum in nature,\nunderlying the classical spacetime description of the black hole. Note\nthat any program aimed at “counting black-hole\nmicrostates” need not accept a subjectivist interpretation of\nentropy à la Jaynes. In any event, on any view of the\nnature of entropy, there arises a closely related problem,\nviz., to locate “where” black-hole entropy\nresides: inside, on, or outside the event horizon? See Jacobson et\nal. (2005) for a thoughtful dialogue among three eminent\nphysicists with different point of views on the matter. ", "\nExplaining what these microstates are that are counted by the\nBekenstein entropy has been a challenge that has been eagerly pursued\nby quantum gravity researchers. In 1996, superstring theorists were\nable to give an account of how M-theory (an extension of\nsuperstring theory) generates the number of string-states underlying a\ncertain class of classical black holes, and this number matched that\ngiven by the Bekenstein entropy (Strominger and Vafa 1996). At the\nsame time, a counting of black-hole states using loop quantum gravity\nalso recovered the Bekenstein entropy (Rovelli 1996). It is\nphilosophically noteworthy that this is treated as a significant\nsuccess for these programs (i.e., it is presented as a reason\nfor thinking that these programs are on the right track), even though\nno quantum effect in the vicinity of a black hole, much less Hawking\nradiation itself, has ever been experimentally observed. (Sadly, we\nhave no black holes in terrestrial laboratories, and those we do have\ngood reason to think we indirectly observe are too far away for\nanything like these effects to be remotely detectable, given their\nminuscule temperatures.) It is also the case that all known\nderivations held only for a very special class of black holes\n(“extremal” ones), which everyone agrees are unphysical.\nThere are no convincing derivations for more general, physically\nrelevant black holes. ", "\nNonetheless, the derivation of the Bekenstein entropy by the counting\nof “microstates” has become something of a sine qua\nnon for programs of quantum gravity, even if only for the special\ncase of extremal black holes: if one cannot do it from something like\nthe first principles of one's program, no one will take you seriously.\nThis is noteworthy because it poses a prima facie problem for\ntraditional accounts of scientific method, and underscores the\ndifficulties faced by fundamental physics today, that in many\nimportant areas it cannot make contact with empirical data at all. How\ndid a theoretically predicted phenomenon, derived by combining\nseemingly incompatible theories in a novel way so as to extend their\nreach into regimes that we have no way of testing in the foreseeable\nfuture, become the most important touchstone for testing novel ideas\nin theoretical physics? Can it play that role? Philosophers have not\nyet started to grapple seriously with these issues. ", "\nIn a thoughtful survey, Sorkin (2005) concisely and insightfully\ncharacterizes in ten theses what seems to be a popular view on the\nnature of black-hole entropy when studied as an essentially quantum\nphenomenon, which is distilled into the essential parts for our\npurposes as follows. The entropy: ", "\nThese theses concisely capture how radically different black-hole\nentropy is from ordinary thermodynamical entropy. The first, as is\nalready obvious from the Second Law of black hole mechanics,\nunderscores the fact that black-hole entropy is proportional to the\nsurface area of the system, not to the bulk volume as for ordinary\nthermodynamical systems. The second articulates the fact that the\nunderlying entities whose statistics are conjectured to give rise to\nthe entropy are the constituents of perhaps the most fundamental\nstructure in contemporary physics, spacetime itself, not high-level,\nderivative entities such as atoms, which are not fundamental in our\ndeepest theory of matter, quantum field theory. The third emphasizes\nthe fact that, contrary to the way that there is no\n“natural” coarse-graining of underlying micro-degrees of\nfreedom in the statistical mechanics of ordinary matter, there is a\nunique natural one here, intimately related to the fact that the\ngeometry of the event horizon is unique, and the Planck scale provides\na measure of units of area thought by many to be physically privileged\n(albeit in a sense never made entirely clear). The fourth states that\nthe Second Law of black hole thermodynamics, generalized to include\ncontributions from both black holes and ordinary matter (as discussed\nin\n section 5.4\n below), is not a phenomenologically derived empirical generalization,\nas is the Second Law for ordinary matter; rather, it follows directly\nfrom the most fundamental dynamical principle, quantum evolution, in\nconjunction with the basic geometry of spacetimes in general\nrelativity. (This will be discussed further in\n section 6.2\n below.) This is of a piece with the fact that the Second Law for\nblack holes in the classical regime is a theorem of pure differential\ngeometry\n (section 5.1).\n ", "\nIn so far as one takes Bekenstein entropy seriously as a true\nthermodynamical entropy, then, these differences strongly suggest that\nthe extension of entropy to black holes should modify and enrich our\nunderstanding not only of entropy as a physical quantity, but\ntemperature and heat as well, all in ways perhaps similar to what that\nof the extension of those classical quantities to electromagnetic\nfields did at the end of the 19th century (Curiel 2017a, \nOther Internet Resources).\n This raises immediate questions concerning the traditional\nphilosophical problems of inter-theoretic relations among physical\nquantities and physical principles as formulated in different\ntheories, and in particular problems of emergence, reduction, the\nreferential stability of physical concepts, and their possible\nincommensurability across theories. One could not ask for a more novel\ncase study to perhaps enliven these traditional debates. (See the\nentries\n Scientific Unity,\n Scientific Reduction, and\n Intertheory Relations in Physics.)\n ", "\nDougherty and Callender (2019) have challenged orthodoxy here, as\nwell, by arguing that the many ways in which the area of a black hole\ndoes not behave like classical entropy strongly suggests that we\nshould be skeptical of treating it as such. Curiel (2017b, Other\nInternet Resources) attempts to rebut them using exactly the idea that\nany extension of a known physical quantity into a new regime will\ninevitably lead to modifications of the concept itself, and\nemendations in the relations it may enter into with other physical\nquantities. Thus, we should expect that black-hole entropy will not\nbehave like ordinary entropy, and it is exactly those differences that\nmay yield physical and philosophical insight into old puzzles. " ], "subsection_title": "5.3. What Is Black Hole Entropy?" }, { "content": [ "\nIn the context of thermodynamic systems containing black holes, one\ncan easily construct apparent violations of both the ordinary laws of\nthermodynamics and the laws of black holes if one applies these laws\nindependently of each other. So, for example, if a black hole emits\nradiation through the Hawking effect, then it will lose mass—in\napparent violation of the classical Second Law of black hole\nmechanics. Likewise, as Bekenstein argued, we could violate the\nordinary Second Law of thermodynamics simply by dumping matter with\nhigh entropy into a black hole: for then the outside of the black\nhole, a causally isolated system, spontaneously decreases in entropy.\nThe price of dropping matter into the black hole, however, is that its\nevent horizon will increase in size. Likewise, the price of allowing\nthe event horizon to shrink by giving off Hawking radiation is that\nthe entropy of external matter fields will increase. This suggests\nthat we should formulate a combination of the two laws that stipulates\nthat the sum of a black hole's area and the entropy of external\nsystems can never decrease. This is the Generalized Second Law of\nthermodynamics (Bekenstein 1972, 1973, 1974). ", "\nThe Second Law of ordinary thermodynamics has a long, distinguished,\nand contentious history in the Twentieth Century debates about the\nphilosophical foundations of physics, ramifying into virtually every\nimportant topic in the philosophy of physics in particular, and into\nmany important topics in philosophy of science in general, including:\nthe relation between thermodynamics and statistical mechanics; the\nMeasurement Problem of quantum mechanics, and the status and meaning\nof theories of quantum information and computation; the definition of\nvarious arrows of time and the relations among them; the so-called\nPast Hypothesis in cosmology; determinism; causation; prediction\nversus retrodiction; the nature of reasoning based on idealization and\napproximation; emergence and reduction; and problems with theory\nconfirmation. ", "\nThat black holes and other purely gravitational and geometrical\nsystems possess an entropy naturally leads to the idea that the Second\nLaw of thermodynamics ought to be modified in order to accommodate that\nfact. It is an almost completely unexplored issue how this Generalized\nSecond Law itself may require modifications to the traditional\nquestions about the Second Law, and possibly lead to new insights\nabout them. Thus the postulation of the Generalized Second Law and its\nbroad acceptance by the physics community raises many interesting\npuzzles and questions. ", "\nIn the remainder of this section, we will review the issues raised by\nthe Generalized Second Law that bear on those puzzles and questions,\nnamely that: contrary to the case in classical thermodynamics, the\nGeneralized Second Law admits not only of proof, but of many kinds of\nproof\n (Section 5.4.1);\n several different physically plausible mechanisms have been proposed\nthat seem to violate the Generalized Second Law\n (Section 5.4.2)\n under relatively benign conditions; the Generalized Second Law seems\nto allow for the possibility of formulating and proving the existence\nof a universal bound on the amount of entropy any physical system can\nhave, along with a related constellation of ideas known as\n‘holography’\n (Section 5.4.3);\n and, contrary to the Second Law of classical thermodynamics, the\nGeneralized Second Law seems to imply novel and deep propositions of\ninterest in their own right\n (Section 5.4.4).\n The possible connection of the Generalized Second Law to the arrow of\ntime is discussed in\n Section 7\n below. ", "\nThe ordinary Second Law of thermodynamics is, at bottom, an empirical\ngeneralization based on observation of the behavior of ordinary\nmaterial systems, albeit one with confirmation and thus entrenchment\nmore profound than probably any other single principle in all of\nphysics. One of the most remarkable features of the Generalized Second\nLaw, by contrast, is that it seems to admit of proof in ways much more\nmathematically rigorous than does the ordinary Second Law (such as,\ne.g., the proof of Flanagan et al. 2000, in the\ncontext of classical general relativity and theories of matter, and a\nnumber of proofs in different contexts given in and discussed by Wall\n2009). That already raises interesting philosophical questions about\nthe relations between what seems prima facie to be the\n“same” fundamental principle as formulated, evaluated and\ninterpreted in different physical theories. ", "\nAt least as interesting, from both a physical and a philosophical\npoint of view, is the fact that the Generalized Second Law in fact\nadmits a wide variety of different ways of being proven (Wall 2009).\nSome of those ways are more mathematically rigorous than others, some\nmore physically perspicuous and intuitive, some more general, and\nalmost all have their respective validity in different regimes than\nthe others, using different types of physical systems, different\napproximations and idealizations, and different physical and\nmathematical starting points. “Proofs” have been given,\nfor example, in the classical, hydrodynamic, semiclassical, and full\nquantum gravity regimes of black holes. ", "\nAlthough the results of all those proofs are called by the same\nname—the Generalized Second Law—they seem prima\nfacie to be different physical principles, just because of the\nextreme differences in the assumptions and content of their respective\nproofs. Here is just a sample of some of the many questions and issues\none must take a stand on in order to formulate a version of the\nGeneralized Second Law and attempt to prove it. ", "\nThe dizzying variety of proofs on offer, which can be roughly\nclassified by how each answers these (and other related) questions,\nthus prompts the question: what is the relation among all the\ndifferent principles actually derived by each proof? Do they represent\nthe same physical principle as it manifests itself in different\nregimes, and as it is viewed from different perspectives? Again, the\nanswer one gives to this question will depend sensitively on,\ninter alia, one's views on inter-theoretic relations. Indeed,\nbecause different answers to these questions can lead to\n“proofs” that have, respectively, contradictory\nassumptions, one may well worry that the derived principle, if it is\nto be the same in all cases, will turn out to be a tautology! ", "\nEven putting aside the contradictory assumptions used in different\nderivations, one should, in any event, note that one cannot try to\njustify the multifariousness of proofs by using an argument based on\nsomething like consilience, for it will not be consilience in anything\nlike the standard form. (See the entry on\n Scientific Discovery.)\n This is not a case in which the same equations or relations or model,\nor values of quantities, are being derived for a given phenomenon\nbased on studies of different types of interactions among different\ntypes of physical systems, as in the classic case of Perrin's\ncalculation of Avogadro's number. This is rather a case in which\ndifferent physical assumptions are made about the very same class of\nphysical systems and interactions among them, and calculations and\narguments made in very different physical and mathematical frameworks,\nwith no clear relation among them. ", "\nWhen Bekenstein first proposed that a black hole should possess\nentropy, and that it should be proportional to its area, difficulties\nthat appeared insurmountable immediately appeared. In a colloquium\ngiven at Princeton at 1970, Geroch proposed a mechanism that seemed to\nshow that, if one could attribute a temperature to a black hole at\nall, it should be absolute zero; an immediate consequence of the\nworking of the mechanism showed that to do otherwise would seem to\nallow arbitrarily large violations of what was to become known as the\nGeneralized Second\n Law.[14]\n Far away from a black hole, prepare an essentially massless box to be\nfull of energetic radiation with a high entropy; then the mass of the\nradiation will be attracted by the black hole's gravitational force.\nOne can use this weight to drive an engine to produce energy\n(e.g., to produce friction from the raising of a\ncounter-weight) while slowly lowering the box towards the event\nhorizon of the black hole. This process extracts energy, but not\nentropy, from the radiation in the box. One can then arrange for all\nthe mass-energy of the radiation to have been exhausted when the box\nreaches the event horizon. If one then opens the box to let the\nradiation fall into the black hole, the size of the event horizon will\nnot increase (because the mass-energy of the black hole does not\nincrease), but the thermodynamic entropy outside the black hole has\ndecreased. Thus we seem to have violated the Generalized Second Law.\nMany ways to try to defuse the problem have been mooted in the\nliterature, from entropy bounds (discussed below in\n section 5.4.3)\n to the attribution of an effective buoyancy to the object being\nlowered due to its immersion in radiation generated by its\nacceleration (Unruh and Wald 1982), a consequence of the so-called\nUnruh effect (for an account of which, see\n note 16).\n None of them is completely satisfying. ", "\nThe question of whether we should be troubled by this possible\nviolation of the Generalized Second Law touches on several issues in\nthe foundations of physics. The status of the ordinary Second Law is\nitself a thorny philosophical puzzle, quite apart from the issue of\nblack holes. Many physicists and philosophers deny that the ordinary\nSecond Law holds universally, so one might question whether we should\ninsist on its validity in the presence of black holes. On the other\nhand, the Second Law clearly captures some significant\nfeature of our world, and the analogy between black holes and\nthermodynamics seems too rich to be thrown out without a fight.\nIndeed, the Generalized Second Law is the only known physical law that\nunites the fields of general relativity, quantum mechanics, and\nthermodynamics. As such, it seems currently to be the most promising\nwindow we have into the most fundamental structures of the physical\nworld (for discussion of which, see\n section 6.3\n below). ", "\nIn response to the apparent violation of the Generalized Second Law\nconsequent on Geroch's proposed process, Bekenstein postulated a limit\nto how much entropy can be contained in a given region of spacetime in\norder to try to avoid such seeming violations, the limit being given\nby the entropy of a black hole whose horizon would encompass the\nregion. Current physics imposes no such limit, so Bekenstein (1981)\npostulated that the limit would be enforced by the underlying theory\nof quantum gravity that, it is hoped, black hole thermodynamics\nprovides our best current insight into. There is, moreover, a further,\nrelated reason that one might think that black hole thermodynamics\nimplies a fundamental upper bound on the amount of entropy that can be\ncontained in a given spacetime region. Suppose that there were more\nentropy in some region of spacetime than the Bekenstein entropy of a\nblack hole of the same size. Then one could collapse that entropic\nmatter into a black hole, which obviously could not be larger than the\nsize of the original region (or the matter would have already\ncollapsed to form a black hole). But this would violate the\nGeneralized Second Law, for the Bekenstein entropy of the resulting\nblack hole would be less than that of the matter that formed it. Thus\nthe Generalized Second Law itself appears to imply a fundamental limit\non how much entropy a region can contain (Bekenstein 1983; Bousso\n1999a, 2006). If this is right, it seems to be a deep insight into the\nfundamental structure of the world, and in particular it should\nprovide an important clue to the nature of an adequate theory of\nquantum gravity. ", "\nArguments along these lines led ’t Hooft (1993, in\n OIR)\n to postulate the Holographic Principle (though the name is due to\nSusskind 1995). This principle claims that the number of fundamental\ndegrees of freedom in any spherical spatial region is given by the\nBekenstein entropy of a black hole of the same size as that region.\nThe Holographic Principle is notable not only because it postulates a\nwell-defined, finite number of degrees of freedom for any region, but\nalso because this number grows in proportion to the area surrounding\nthe region, not the volume. This flies in the face of the standard\npicture of the dynamics of all other known types of physical systems,\nwhether particles or fields. According to that picture, the entropy is\nmeasured by the number of possible ways something can be, and that\nnumber of ways increases as the volume of any spatial region. To the\ncontrary, if the Holographic Principle is correct then one spatial\ndimension of any physical system can, in a sense, be viewed as\nsuperfluous: the fundamental “physical story” of a spatial\nregion is actually a story that can be told merely about the boundary\nof the region (Luminet 2016). ", "\nStill, there are reasons to be skeptical of the validity of the\nproposed universal entropy bounds, and the corresponding Holographic\nPrinciple. Unruh and Wald (1982), in response to Bekenstein's\npostulated entropy bound, argued convincingly that there is a less\nad hoc way to save the Generalized Second Law, namely by\nexploiting the Unruh effect (for an explanation of which, see\n note 16).[15]\n Flanagan et al. (2000), moreover, have offered strong\narguments that the validity of the Generalized Second Law is\nindependent of Bousso's proposed entropy bound (widely thought to be\nsuperior to Bekenstein's original one), thus removing much of the\nprimary historical and conceptual motivation for the Holographic\nPrinciple. ", "\nAgain, all these questions are of great interest in their own right in\nphysics, but there is strong reason to believe that their analysis may\nshed new light on several ongoing philosophical discussions about the\nnature of spacetime, with which they have obvious direct connections,\nespecially concerning the dimensionality of space and spacetime, and\nthe substantivalism-versus-relationalism debate. The interested reader\nshould see de Haro et al. (2015) for a discussion of the\nrelation of holography to gauge/gravity dualities in general, and a\nreview of the philosophical issues that raises, and Castellani (2016)\nfor philosophical discussion of the ontological issues raised by these\ndualities. ", "\nThe ordinary Second Law has profound philosophical implications. It\nis, however, rarely if ever used to prove other physical principles or\nresults of real depth, all of its important consequences being more or\nless immediate. Once again, the Generalized Second Law stands in\ncontrast to the ordinary Law, for, as has recently been realized, it\ncan be used to prove several physical results of deep interest, over\nand above heuristically motivating the Holographic Principle. ", "\nIn a tour de force of physical argument, Wall (2013a, 2013b)\nshowed that assumption of the Generalized Second Law rules out\ntraversable wormholes, other forms of faster-than-light travel between\ndistant regions, negative masses for physical systems, and closed\ntimelike curves. (See the Encyclopedia entries\n Time Machines\n and\n Time Travel,\n and Visser 1996.) Furthermore, if the Generalized Second Law is to be\nsatisfied, then it is impossible for “baby universes” that\neventually become causally independent of the mother universe to form.\nSuch baby universes and their eventual independence, however,\nconstitute the fundamental mechanism for currently popular\n“multiverse” scenarios in cosmology. ", "\nIn the same work, Wall also shows that the Generalized Second Law has\na striking positive conclusion: a “quantum singularity\ntheorem”, which shows that, even when quantum effects are taken\ninto account, spacetime will still be geodesically incomplete inside\nblack holes and to the past in cosmological models (like the currently\nmost well supported ones, which start with a Big Bang singularity).\nThis flies directly in the face of the pious hopes of most physicists\nthat quantum effects, and in particular the hoped-for theory of\nquantum gravity, will efface singularities from spacetime. (See,\ne.g., Ashtekar and Bojowald 2006, Ashtekar et al.\n2006, and Kiefer 2010 for typical sentiments along these lines, along\nwith typical arguments forwarded to support them, in the context of\ncanonical quantum gravity, and Roiban 2006 and Das 2007 for the same\nin the context of string theory; it is noteworthy that Roiban also\ndiscusses known cases where it appears that string theory does\nnot necessarily efface singularities.) ", "\nAnother striking positive consequence of the Generalized Second Law is\nthat it allows one to derive energy conditions in the context of\ngeneral relativity. An energy condition is, crudely speaking, a\nrelation one demands the properties of matter to satisfy in order to\ntry to capture the idea that “mass-energy should be\npositive”. Energy conditions play a central and fundamental role\nin general relativity, since they are needed as assumptions in\nessentially every deep, major result proven in the last 60 years,\nespecially those pertaining to singularities and black holes (Curiel\n2017). One thing that makes them unusual is the fact that, uniquely\namong the central and fundamental tenets of general relativity, they\nthemselves do not admit of derivation or proof based on other such\nprinciples. At least, no such derivations or proofs were known until\nvery recently, when Wall (2010) argued that the Generalized Second Law\nimplies one. There are several problematic aspects to Wall's argument\n(Curiel 2017), but the mere fact that he was able to produce a\nprima facie decent one at all is remarkable, showing that the\nGeneralized Second Law may be a very deep physical principle indeed.\nOne, however, may contrarily conclude that the argument shows rather\nthat the Generalized Second Law is a contingent matter, depending\nsensitively on the kinds of matter fields that actually exist—if\nmatter fields were such as to violate the energy condition Wall argued\nfor, then his argument would show that the Generalized Second Law is\nnot valid. ", "\nFinally, Bousso et al. (2016) showed that a form of the\nGeneralized Second Law applicable to generalized horizons strongly\nsuggests that causal geodesics in the regime where quantum field\ntheory effects become important will focus and converge on each even\nwhen the standard energy conditions are violated. This is significant\nbecause it is propositions about the focusing properties of geodesics\nthat lie at the heart of all the standard singularity theorems and\nmost other results about horizons of all kinds, and all of the\npropositions that show focusing assume a standard energy condition. If\nthis conjecture is correct, it would provide further strong evidence\nthat quantum effects may not remove singularities from generic\nspacetimes. " ], "subsection_title": "5.4. The Generalized Second Law of Thermodynamics" }, { "content": [ "\nThat black holes, purely gravitational objects, possess a physical\nentropy strongly suggests that the gravitational field itself in\ngeneral may possess entropy, as Penrose (1979) hypothesized. Indeed,\nthere are a number of reasons to suspect that the thermodynamical\ncharacter of gravity should extend to gravitational systems and\nstructures beyond just those provided by black holes. Because\ngravitational “charge” (i.e., mass-energy) comes\nwith only one sign (as opposed, e.g., to electromagnetic\ncharge, which can be of either positive or negative sign), bits of\nmatter tend to accelerate towards each other, other things being\nequal. This already suggests that gravity has a built-in\nthermodynamical character, since it provides an objective, invariant\nmeasure of a direction for time: it is characteristic of future\ntime-flow that bits of matter tend to accelerate towards each other,\nand so become more inhomogeneous in the aggregate. (See\n section 7\n for discussion of the possible relation of gravitational entropy to\nan arrow of time.) ", "\nSince the work of Gibbons and Hawking (1977), Bekenstein (1981),\nSmolin (1984), Bousso (1999a), Jacobson and Parentani (2003), and\nPadmanabhan (2005), among others, it has been known that an entropy\nand a temperature can be attributed to spacetime horizons more general\nthan just the event horizon of a black hole. From another direction,\nthe attractiveness of Penrose's Conformal Curvature Hypothesis\n(Penrose 1979), discussed below in\n section 7,\n along with subsequent work attempting to make the Hypothesis precise,\nall suggest that certain types of cosmological singularities, such as\nthe Big Bang, should themselves be attributed an entropy. This has led\nin recent years to several interesting proposals for a completely\ngeneral measure of gravitational entropy, such as that of Clifton\net al. (2013). Indeed, Anastopoulos and Savvido (2012) have\neven attempted to attribute entropy directly to non-cosmological\nsingularities, those associated with collapse phenomena. Pavón\nand Zimdahl (2012), in a similar spirit, attempt to provide a\nthermodynamical analysis of future cosmological singularities and so\ncharacterize them by their thermodynamical properties. ", "\nThese facts raise several fundamental puzzles about the nature of\nentropy as a physical quantity and the relations among the different\ntheories that involve it. How can such a quantity, which hitherto has\nbeen attributed only to material systems such as fluids and Maxwell\nfields, be attributed to simple regions of spacetime itself? How does\ngeneral gravitational entropy relate to more standard forms of\nentropy, and how may the nature of general gravitational entropy\nitself inform our understanding of the standard forms? Does it shed\nnew light on traditional general philosophical topics of interest,\nsuch as questions about reduction and emergence of thermodynamics to\nand from statistical mechanics? " ], "subsection_title": "5.5. General Gravitational Entropy" } ] }, { "main_content": [ "\nAs discussed already in\n Section 5.2\n and\n Section 5.3,\n it is the addition of quantum field theory to general relativity that\ndefinitively settles the issue of the thermodynamical character of\nblack holes. There are, however, many other fascinating phenomena that\narise when one adds quantum field theory to the mix of black holes and\nsingularities, and general relativity in general, than just that, and\na concomitant broadening and deepening of the philosophical issues and\npuzzles that confront us. ", "\nIn\n Section 6.1,\n we discuss the Hawking effect (the predicted emission by black holes\nof thermal radiation) and its associated problems and puzzles in\ndetail. One puzzle in particular that seems to follow the prediction\nof the Hawking effect has exercised physicists and philosophers the\nmost, the so-called Information Loss Paradox: the evaporation of black\nholes by the emission of Hawking radiation seems to lead in the end to\na violation of one of the most fundamental tenets of quantum\nmechanics. We discuss that in\n Section 6.2.\n We conclude in\n Section 6.3\n with an examination of the claims that black hole thermodynamics\nprovides the best evidence to guide us in the search for a theory of\nquantum gravity. " ], "section_title": "6. Black Holes and Quantum Theory", "subsections": [ { "content": [ "\nIn light of the notorious difficulty of constructing a theory that\nincorporates and marries quantum mechanics and general\nrelativity—a theory of quantum gravity—it may come as a\nsurprise to learn that there is a consistent, rigorous theory of\nquantum fields posed on the background of a classical relativistic\nspacetime. (Wald 1994 is a standard text on the subject; Jacobson\n[2003, in\n OIR]\n gives a less rigorous overview, discussing possible relations to\nproposed theories of quantum gravity; Wald [2006b, in\n OIR]\n gives a synoptic history of the technical aspects of the entire\nsubject, and an exposition of the advances in the field subsequent to\nthe publication of Wald 1994; and Hollands and Wald 2015 provides a\ntechnically sophisticated overview of the most recent results.)\nQuantum field theory on curved spacetime, however, differs from\nstandard quantum field theory (set on the flat Minkowski spacetime of\nspecial relativity) in one profound respect, that difference ramifying\ninto every part of the theory: a generic relativistic spacetime has no\ngroup of symmetries comparable to the Poincaré Group for\nspecial relativity. There is correspondingly no distinguished vacuum\nstate and no natural notion of a particle. This means, for instance,\nthat one cannot employ many familiar and useful techniques from\nstandard quantum field theory, and one must take care in the use of\nmost of the others. ", "\nOne expects that such a framework would find its most natural\napplication in the treatment of problems in which, in some sense or\nother, the curvature of spacetime is well above the Planck length, in\nso far as there are some theoretical grounds for suspecting that in\nthis regime one can safely ignore any quantum properties of the\nspacetime geometry itself. (Hence, the framework is often called\n‘the semi-classical approximation’ or\n‘semi-classical gravity’.) In this vein, its most popular\nand successful applications have been to problems involving particle\ncreation in the early universe and in the vicinity of black holes.\nNow, according to general relativity a black hole ought to be a\nperfect sink for energy, mass and radiation, in so far as it absorbs\neverything (including light), and emits nothing (including light). It\nwas therefore more than shocking when Hawking (1974, 1975) predicted\nthat, when quantum effects are taken into account, a black hole ought\nto behave rather like a perfect black body, in the sense of ordinary\nstatistical thermodynamics: a stationary black hole should emit\nthermal radiation with the Planckian power spectrum characteristic of\na perfect blackbody at a fixed temperature. It glows like a lump of\nsmoldering coal even though light should not be able to escape from\n it![16]\n ", "\nAs with the Generalized Second Law, one of the most fascinating\naspects of Hawking radiation from a foundational point of view is the\nmultiplicity and multifariousness of the derivations known for it.\nThey also differ radically among themselves with regard to the\nmathematical rigor of the framework they adopt and the mathematical\ncharacter of the structures they assume, and almost all are valid in\ndifferent regimes than the others, using different types of physical\nsystems and different approximations and idealizations, basing their\narguments on different physical principles, with varying degrees of\nphysical perspecuity and intuitiveness. In consequence, these\ndifferent derivations seem to suggest different physical\ninterpretations of Hawking radiation itself, both for its origin and\nfor its character (Brout et al. 1995). It is thus not even\nclear, at a foundational level, what the physical content of the\nprediction of Hawking radiation is. Indeed, as in the case of the\nGeneralized Second Law, some of the derivations of Hawking radiation\nmake assumptions that seem to contradict some of the assumptions of\nother derivations—but if A implies B and\nnot-A implies B, then B must be a tautology.\nSince this is an unappealing attitude to take towards Hawking\nradiation, some other way must be found to reconcile the contrary\nderivations. Again, standard consilience cannot be invoked here, for\nthe same reasons as discussed at the end of\n section 5.4.1\n for different proofs of the Generalized Second Law. ", "\nBecause the interpretation of quantum field theory itself, even in the\nflat spacetime of special relativity, is already so contested, fraught\nwith problems, and just poorly understood in general (see the\nEncyclopedia entry\n Quantum Field Theory),\n one may think that there is even less of a chance here to get a grip\non such issues. Contrarily, one may also think that the very fact that\nthe phenomena are so different here than in ordinary quantum field\ntheory may suggest or afford us new avenues of approach to the\ntraditional problems that have so long frustrated us. " ], "subsection_title": "6.1. Hawking Radiation" }, { "content": [ "\nThe existence of Hawking radiation has a remarkable consequence: as\nHawking (1976) pointed out and Unruh (1976) elaborated, the fact that\na black hole radiates implies that it loses mass-energy, and so will\nshrink, in seeming violation of the Area Theorem. (The Area Theorem is\nnot in fact violated; rather, one of its assumptions is,\nviz., that locally energy is always strictly positive.)\nBecause there is no limit to this process except that imposed by the\ntotal initial mass of the black hole itself, eventually the black hole\nwill radiate itself entirely away—it evaporates. This prediction\nclearly bears on the issue of cosmic censorship: if the end-state of\nthe evaporation leaves the previously hidden singularity open for the\nrest of the universe to see, all the potential problems raised in\n section 4\n can arise. ", "\nThere is, however, a seemingly even deeper problem posed by the\npossibility of black-hole evaporation, one that raises doubts about\nthe possibility of describing black holes using any standard\nformulation of quantum theory. According to standard quantum theory,\nthe entropy of a closed system never changes; this is captured\nformally by the nature of the evolution of a quantum system, by the\ntechnical property of unitarity. Unitary evolution guarantees that the\ninitial conditions, together with the Schrödinger equation (the\nequation governing the temporal evolution of quantum systems), will\nfix the future state of the system. Likewise, a reverse application of\nthe Schrödinger equation will take us from the later state back\nto the original initial state. In other words, the states at each time\ncontain enough information to fix the states at all other times, given\nthe unitarity of dynamical evolution for quantum systems. Thus there\nis a sense in which the completeness of the state is\nmaintained by the standard time evolution in quantum theory. (See the\nentry\n Quantum Theory.)\n ", "\nIt is usual to characterize this feature by the claim that quantum\nevolution “preserves information”. If one begins with a\nsystem in a precisely known quantum state, then quantum theory\nguarantees that the details about that system will evolve in such a\nway that one can infer the precise state of the system at some later\ntime, and vice versa. This quantum preservation of details implies\nthat if we burn a chair, for example, it would in principle be\npossible to perform a complete set of measurements on all the outgoing\nradiation, the smoke, and the ashes, and reconstruct exactly what the\nchair looked like. If we were instead to throw the chair into a black\nhole, however, then orthodoxy holds that as a consequence of the No\nHair Theorems (discussed in\n section 3.2\n above) it would be physically impossible for the details about the\nchair ever to escape to the outside universe. This might not be a\nproblem if the black hole continued to exist for all time, since one\ncould then assume the information encoded in the chair still existed\nbehind the event horizon, preserved by the unitary evolution in that\nregion. The existence of Hawking radiation, however, tells us that the\nblack hole is giving off energy, and thus it will shrink down and\npresumably will eventually disappear altogether, along with whatever\nstuff had fallen past the event horizon before that. At that point,\nthe details about the chair will be irrevocably lost; thus such\nevolution cannot be described by the standard laws of quantum theory.\nThis is the Information Loss Paradox of quantum black holes\n(Hawking\n 1976).[17]\n Although the paradox is usually formulated in terms of\n“information”, the issues is often put here as being the\nmaintenance of correlations between different systems, as this is a\nphysically more perspicuous notion that lies at the bottom of the\nparadox, and is much less problematic than the notoriously vexed and\nnebulous concept of “information”. ", "\nThe attitude that individual physicists adopt towards this problem is\nstrongly influenced by their intuitions about which theory, general\nrelativity or quantum theory, will have to be modified to achieve a\nconsistent theory of quantum gravity. Spacetime physicists tend to\nview non-standard quantum evolution as a fairly natural consequence of\nsingular spacetimes: one would not expect all the details of systems\nat earlier times to be available at later times if they were lost in a\nsingularity. Hawking (1976), for example, argued that the paradox\nshows that the full theory of quantum gravity will be a theory that\ndoes not obey the standard dynamical principles of quantum theory, and\nhe began working to develop such a theory very soon after first\npromulgating the paradox. (He has since abandoned this position.)\nUnruh and Wald (2017) develop an extended review and defense of this\nposition. Particle physicists (such as superstring theorists),\nhowever, tend to view black holes as being just another state of a\nquantum field. If two particles were to collide at extremely high\nenergies, they would form a very small black hole. This tiny black\nhole would have a very high Hawking temperature, and thus it would\nvery quickly give off many high-energy particles and disappear.\n(Recall, as discussed in\n section 5.2\n above, that Hawking temperature is inversely proportional to the mass\nof black hole.) Such a process would look very much like a standard\nhigh-energy scattering experiment: two particles collide and their\nmass-energy is then converted into showers of outgoing particles. The\nfact that all known scattering processes obey the standard dynamical\nprinciples of quantum theory, and above all unitarity, then, seems to\ngive us some reason to expect that black hole formation and\nevaporation should also do so. ", "\nThe reactions to the puzzle are legion. (A helpful overview of earlier\nstages of this debate can be found in Belot et al. 1999.) It\nis useful to classify them as belonging to one of six broad groupings:\n", "\nIn particular, today there are four main ways of trying to address the\nproblem that have a fair amount of support in different segments of\nthe physics community: ", "\nWe will briefly sketch each of them, along with their pros and cons.\nChakraborty and Lochan (2017), Bryan and Medved (2017), Marolf (2017),\nand Unruh and Wald (2017) provide recent reviews of the most popular\napproaches, with Marolf's emphasizing possible approaches that save\nunitarity, and Unruh and Wald's emphasizing ones that violate it. (See\nMathur 2009 and Chen et al. 2015 for recent discussions of\napproaches based on remnants, which we will not cover here.) ", "\nThe arguments that we should accept the calculations that predict\nfailure of unitarity at face value are straightforward (Unruh and Wald\n2017). The calculations represent a regime (the semi-classical one) in\nwhich we have good theoretical grounds for trusting our theoretical\nmachinery, and nothing is required that deviates from standard\napplications of quantum field theory and general relativity,\nrespectively. Even though there is failure of unitarity, there is no\nviolation of conservation of probability—all quantum\nprobabilities sum to 1 over the course of the entire\nevolution—and there is no other manifest form of indeterminism\npresent. Nor is there any violation of energy conservation attendant\non the failure of unitarity, as some have alleged must happen. Unitary\nevolution, moreover, is arguably not a fundamental tenet of\nquantum theory: so long as probability is conserved, one can calculate\nwith confidence. Indeed, there are examples of just such non-unitary,\nbut probability-conserving and energy-conserving evolution in standard\napplications of ordinary quantum theory, with no need for anything as\nhigh-falutin' as quantum field theory on curved spacetime and black\nhole thermodynamics (Unruh 2012). ", "\nThe conclusion, however—that what many still take to be one of\nthe most fundamental principles of quantum theory is violated—is\ntoo distasteful for many physicists to swallow, especially those\ntrained in the tradition of particle physics, where unitarity is taken\nto be inviolate. The sanguine acceptance of the loss of unitarity\nseems to come mostly from the trust the physicists in question have in\ngeneral relativity. This raises the question why general relativity\nought to be trusted enough in this regime to conclude that unitarity\nwill fail in any deeper quantum theory, but not trusted enough when it\ncomes to the prediction of singularities\n (section 2.2)—on\n what grounds do they pick and choose when and when not to trust it?\nThis question becomes especially piquant when one considers that loss\nof unitarity is, on its face, an extraordinarily strong constraint to\nplace on any proposed theory of quantum gravity, especially when it\ncomes from a calculation made in the context of a merely effective and\nnot a fundamental theory, and when it is exactly that still unknown\nfundamental theory that is supposed to efface singularities. In any\nevent, Manchak and Weatherall (2018) have recently argued that, even\nif one does accept loss of unitarity—what seems to be a\nstraightforward conclusion of the standard calculations—the\nstate of affairs is still justly called paradoxical. ", "\nThe idea of black-hole complementarity, initiated by Susskind et\nal. (1993), tries to resolve the paradox by pointing out that the\nself-description of the experience of an astronaut falling into a\nblack hole will differ from the description made by an external\nobserver, and then playing the contrary descriptions off each other in\na dialectical fashion. It has been the subject of philosophical\ncontroversy because it includes apparently incompatible claims, and\nthen tries to reconcile them by appeal to a form of so-called quantum\ncomplementarity, or (so charge the critics) simple-minded\nverificationism (Belot et al. 1999). An outside observer will\nnever see the infalling astronaut pass through the event horizon.\nInstead, she will seem to hover just above the horizon for all time\n(as discussed in\n section 3.1\n above). But all the while, the black hole will also be giving off\nheat, shrinking, and getting ever hotter. The black hole\ncomplementarian therefore suggests that an outside observer should\nconclude that the infalling astronaut gets burned up before she\ncrosses the event horizon, with the result that all the details about\nher state will be returned in the outgoing radiation, just as would be\nthe case if she and her belongings were incinerated in a more\nconventional manner; thus the information (and standard quantum\nevolution) is saved. ", "\nThis suggestion, however, flies in the face of the fact that for an\ninfalling observer, nothing out of the ordinary would be experienced\nat the event horizon (as discussed in\n section 3.1\n above). Indeed, in general she could not even know that she was\npassing through an event horizon at all, unless classical general\nrelativity were very wrong in regimes where we expect no quantum\neffects to show themselves. This obviously contradicts the suggestion\nthat she might be burned up as she passes through the horizon. The\nblack hole complementarian tries to resolve this contradiction by\nagreeing that the infalling observer will notice nothing\nremarkable at the horizon, but then suggests that the account of the\ninfalling astronaut should be considered to be complementary to the\naccount of the external observer, rather in the same way that position\nand momentum are complementary descriptions of quantum particles\n(Susskind et al. 1993). The fact that the infalling observer\ncannot communicate to the external world that she survived her passage\nthrough the event horizon is supposed to imply that there is no\ngenuine contradiction here. This solution to the information\nloss paradox has been criticized for making an illegitimate appeal to\nverificationism (Belot et al. 1999). Bokulich (2005), to the\ncontrary, argues that the most fruitful way of viewing black hole\ncomplementarity is as a novel suggestion for how a non-local theory of\nquantum gravity will recover the local behavior of quantum field\ntheory while accommodating the novel physics of black holes. ", "\nAlmheiri et al. (2013) have recently claimed that black hole\ncomplementarity is not viable on different, more physically oriented\ngrounds. They argue that the following three statements, assumed by\nblack-hole complementarity, cannot all be true: (i) Hawking radiation\nis in a pure state; (ii) the information carried by the radiation is\nemitted from the region near the horizon, with low energy effective\nfield theory (i.e., the standard semi-classical\napproximation) valid beyond some microscopic distance from the\nhorizon; and (iii) the infalling observer encounters nothing unusual\nat the horizon. Based on powerful grounds for believing the first two\npropositions, they conclude that the appropriate response to the\nparadox is to posit that there is a “firewall” at the\nevent horizon: the flux of Hawking radiation from the black hole\nbecomes in general so intense that highly accelerated infalling bodies\nare themselves incinerated as soon as they enter the black hole. This\nproposal is too recent for any consensus to have been reached about\nits viability; vigorous debate about it is ongoing. ", "\nPerhaps the physically most conservative—and correlatively the\nphilosophically least thrilling—proposal is to deny the implicit\nassumption that during black-hole evaporation the deviations of\nHawking radiation from exact thermality are negligible. Thus the\nproblem prima facie does not ever arise, because all the\nquantum information does manage to escape in those non-thermal\ncorrelations. This proposal faces the serious challenge of showing\nthat such non-thermal corrections are rich and large enough to carry\naway all possible information encoded in all possible bodies falling\ninto black holes. Hawking et al. (2016) argue, in this vein,\nthat black holes do indeed have hair, violating the No Hair theorems,\nwhich makes possible the maintenance of correlations between early and\nlate time Hawking radiation in such a way as to preserve information.\nDvali (2015) argues that exact thermality of Hawking radiation, in\nconjunction with other well established results about black hole\nthermodynamics and quantum field theory on curved spacetime, imply\nthat the black-hole entropy would be infinite; thus, he concludes,\nthere must be large deviations from thermality. Any such\nargument, note, will have to conclude that the deviations from perfect\nthermality are large—otherwise there would be no hope of\nencoding enough information to record recovery data about every\nphysical system that fell into the black hole before evaporation.\nAgain, the particular arguments in favor of this sort of proposal are\ntoo recent for real consensus one way or another to have been\nachieved. ", "\nThe evaporation of black holes has another startling consequence that\nraises far-reaching philosophical and physical problems for our\ncurrent picture of quantum field theory and particle physics: it\nimplies that baryon and lepton number need not be conserved. Suppose a\nneutron star composed of ∼1057 baryons collapses to\nform a black hole. After evaporation, the resultant baryon number is\nessentially zero, since it is overwhelmingly likely that the black\nhole will radiate particles of baryon number zero. (The radiation is\nnot energetic enough to produce baryons, until, perhaps, the very late\nstages of the evaporation.) This issue seems not to have agitated\nresearchers in either the particle physics or the general relativity\ncommunity so much as the idea of non-standard quantum evolution even\nthough conservation of baryons and leptons are surely principles as\nwell entrenched as that of the unitarity of quantum\n evolution.[18]\n One could perhaps argue that they are even more entrenched, since our\nempirical evidence for the conservation principles is simple and\nimmediate in a way that our evidence for standard evolution is not:\none simply counts particles before and after an observed\ninteraction—interpretational questions arising from the\nMeasurement Problem in quantum theory and a possible\n“collapse” of the wave function do not bear on it. (See\nthe entry\n Quantum Mechanics.)\n ", "\nOkon and Sudarsky (2017) have in fact recently argued that there is an\nintimate connection between the Information Loss Paradox and the\nMeasurement Problem in quantum mechanics. Their arguments raise\nfurther questions about the Information Loss Paradox. Why are\nphysicists so exercised by the possible violation of unitarity\nseemingly entailed by black-hole evaporation, when almost all of those\nself-same physicists do not worry at all about the Measurement Problem\nof quantum mechanics, and the seeming violations of unitarity that\nhappen every time a measurement is performed? One possible explanation\nis perhaps best described as “sociological”: most\ntheoreticians, as the ones involved in this debate, never model\nexperiments, and so do not face the Measurement Problem directly in\ntheir work. Thus it is generally not an issue that is at the forefront\nof their thought. Along the same lines, many theoreticians in this\narea also work in cosmology, in which one considers the “wave\nfunction of the universe”, an object that seems not to admit of\nexternal observers making measurements on it, and so the issue of\ncollapse does not arise in their work. Perhaps a more intriguing\nexplanation, one not discussed by Okon and Sudarsky, is that the\nInformation Loss Paradox provides an explicit physical mechanism for\nviolations of unitarity. It is perhaps easier to dismiss seeming\nviolations of unitarity during measurements as an artifact of our lack\nof understanding of quantum mechanics, not as a reflection of what\nhappens in the world. One cannot dismiss the possible violation of\nunitarity in the Information Loss Paradox with such equanimity: it\nappears to be an integral, explicit part of a model of the behavior of\na physically possible system, with an articulated mechanism for\nbringing it about. ", "\nRecently, Wallace (2020) has introduced philosophers to another\npuzzle, intimately related to information loss in the context of\nblack-hole evaporation. For lack of a better term, and so as to\ndistinguish it from the standard problem, we call this\n‘Page-time paradox’, as it was first formulated by Page\n(1993), and turns on calculation of a distinguished time in the\nevolution of an evaporating black hole, the so-called Page time, that\ntime at which half of the black hole's original entropy has been\nradiated away. Page showed that there is a manifest inconsistency\nbetween a treatment of black hole evaporation that is wholly\nformulated in the terms of statistical mechanics, and the standard\nsemi-classical treatment used in derivations of Hawking radiation.\nWallace argues forcefully that this puzzle is incontrovertibly\nparadoxical, completely divorced from the issue of whether or not\nunitarity fails, and raises deep philosophical problems of its own.\n", "\nIn sum, the debate over the Information Loss Paradox highlights the\nconceptual importance of the relationship between different effective\ntheories. At root, the debate is over where and how our effective\nphysical theories will break down: where can they be trusted, and\nwhere must they be replaced by a more adequate theory? This has\nobvious connections to the issue of how we are to interpret the\nontology of merely effective physical descriptions, and how we are to\nunderstand the problems of emergence and reduction they raise. (See,\ne.g., Williams 2017 for an interesting survey of such issues\nin the context of quantum field theory on flat spacetime.) The\nInformation Loss Paradox ramifies into questions of ontology in other\nways as well. When matter forms a black hole, it is transformed into a\npurely gravitational entity. When a black hole evaporates, spacetime\ncurvature is transformed into ordinary matter. Thus black holes appear\nto be crucial for our understanding of the relationship between matter\nand spacetime, and so provide an important arena for investigating the\nontology of spacetime, of material systems, and of the relations\nbetween them. " ], "subsection_title": "6.2. Information Loss Paradox" }, { "content": [ "\nBlack hole thermodynamics and results concerning quantum fields in the\npresence of strong gravitational fields more generally are without a\ndoubt the most widely accepted, most deeply trusted set of conclusions\nin theoretical physics in which our current best, deepest\ntheories—general relativity and quantum field theory—work\ntogether in seemingly fruitful harmony. Indeed, that black holes\npossess a physical temperature and entropy, and correlatively that\nthere is a hitherto unsuspected and profound connection among gravity,\nquantum field theory and thermodynamics, is now as widely accepted an\nidea in theoretical physics as an idea with no direct empirical\nsubstantiation can be. As such, the study of black hole thermodynamics\nprima facie holds out the most promise for guidance in our\nsearch for a deeper theory of quantum gravity, in which the two would\nbe intimately combined in a unified account of all known physical\nphenomena, from the behavior of quarks at the scale of\n10-17 cm, to the cosmological structure of superclusters of\ngalaxies at the scale of 1032 cm. (See the entry\n Quantum Gravity.)\n What is not widely shared is the vision of the path that this\nguidance purportedly shows us. ", "\nI list only a small sample of the many foundational and philosophical\nissues that arise here. A full discussion is beyond the scope of this\narticle. ", "\nWallace (2019) provides an overview of the relation of black hole\nthermodynamics to a few programs in quantum gravity, especially those\nrelated to string theory and the AdS/CFT correspondence, and\nassociated foundational problems. " ], "subsection_title": "6.3. A Path to Quantum Gravity?" } ] }, { "main_content": [ "\nThe Second Law of thermodynamics has long been connected to the\nseeming asymmetry of the arrow of time, that time seems to flow, so to\nspeak, in only one direction for all systems no matter how different\nin kind they are and no matter how spatiotemporally separated. Indeed,\none of the fundamental problems is that different types of system seem\nprima facie to give rise to independent arrows of time,\ne.g., thermodynamical, electromagnetic, cosmological, and so\non, with no a priori reason why they should all point in the\nsame direction. (See Zeh 2014 for a thorough recent review; see also\nthe Encyclopaedia entry\n Thermodynamic Asymmetry in Time.)\n The Generalized Second Law and the corresponding idea of general\ngravitational entropy\n (section 5.5)\n introduces a new possible arrow of time, the gravitational. ", "\nThere is a peculiar and intimate relation between the Second Law of\nordinary thermodynamics and time. That physical systems always seem to\nchange in such a way that entropy never decreases picks out a\nprivileged direction in time, as it were. At the present moment, there\nare two “directions” in time one may consider: that\npointing to the future, and that to the past. The Second Law says,\nroughly speaking, that order never spontaneously increases toward the\nfuture. Looking back towards the past, however, that is exactly how it\nmay appear to us: if one thinks of the ordinary change of physical\nsystems as running backwards in time, then it will exactly appear as\nthough order is spontaneously increasing. ", "\nThat fact is already on its own remarkable: all other known\nfundamental principles and laws of physics are time-symmetric (putting\naside the minuscule violations of time-reversal symmetry manifested by\nthe weak nuclear force). That means that if a given sequence of\nchanges of a physical system governed by those principles and laws is\nallowed, then the same sequence in reversed order is also allowed as a\nphysical possibility. If a tea cup drops to the floor and smashes into\nlittle bits, then the reverse process is also possible: the smashed\nbits can spontaneously leap up into the air towards each other and\nre-assemble into an undamaged tea cup. If an antenna can absorb a\ngiven type of radio wave, it can also emit that same wave. And so on.\nThat is not what we see in physical systems governed by thermodynamics\nand the Second Law. An ice cube in a glass of warm water spontaneously\nmelts, and the water cools a bit. We never see a cool glass of water\nspontaneously warm while an ice cube forms in the middle of it. This\nis even more mysterious when one considers the fact that we know that\nthe water and ice are, at a deeper level of description, really just a\ncollection of an enormous number of molecules and atoms themselves\nmoving around, bouncing off each other, and connected\ntogether—and, to the best of our knowledge, the principles and\nlaws governing the changes in that collection of molecules\nare time symmetric. Why is it that the laws governing the\nmicro-structure of water and ice are time symmetric, but, when one\nlooks at the water and ice in the aggregate, ignoring the fine details\nof the micro-structure, the governing principle becomes time\nasymmetric? That is one of the deepest and most hotly debated\nquestions in the foundations of physics. ", "\nThis all raises a second question: if entropy tends only to increase,\nand so order in the universe continually degrades, where did all the\norder around us come from in the first place? Life, for instance,\nseems like an extraordinarily highly structured phenomenon. Living\norganisms are much more highly structured than the air and earth and\nwater surrounding us, and certainly more so than the food we consume\nto build and replenish our highly structured bodies. The same holds\ntrue of planets themselves, stars, galaxies, and clusters and\nsuperclusters of galaxies—they all are prima facie much\nmore highly ordered and structured than the homogeneous and highly\nrarefied plenum of interstellar dust surrounding them, and the vast\nreaches of empty space itself. How did such highly structured physical\nsystems evolve in the first place? Are they all not manifestly a\nviolation of the Second Law? (See Schrödinger 1944 for the\nlocus classicus of discussion of these issues.) ", "\nIndeed, the problem for physical systems on the cosmological scale\n(planetary systems and larger) is made even more urgent by what we\nknow about conditions in the very early universe, very soon after the\nBig Bang, that we think obtained at the start of the cosmos. We have\nstrong evidence that the very early universe consisted of a highly\nhomogeneous, extremely hot and condensed gaseous soup of fundamental\nparticles. According to ordinary thermodynamics, however, that is a\nstate of extremely high entropy. That such a physical system evolved\ninto ordered structures such as stars and galaxies—prima\nfacie a state of much lower entropy for the same matter and\nenergy now redistributed—seems on the face of it to be a massive\nviolation of the Second Law. ", "\nOne might with some justice ask: well, so what? Entrenched scientific\ntheories and principles get overthrown all the time. The caloric\ntheory of heat got overthrown by thermodynamics and the theory of\nmolecular kinetics. Classical Newtonian mechanics got overthrown by\nquantum mechanics. Newtonian gravitational theory got overthrown by\ngeneral relativity. Now the evidence from cosmology tells us that the\nSecond Law is just one more in a long line of principles that have not\npassed the test of confrontation with empirical data. That response,\nhowever, does not do justice to the profound faith that physicists\nhave in the Second Law. When Einstein was once asked what he thought\nphysics would look like a century from then, he famously said he\nthought nothing currently believed would still be held as fundamental,\nexcept only the Second Law. Everything else—quantum theory,\ngeneral relativity—could go, but he could not imagine the Second\nLaw being overthrown. Contemporary physicists feel the same\n way.[19]\n They love the Second Law. There must be, they demand, a way to\nreconcile the universality of the Second Law with its seeming\nviolation in the way the universe has evolved on cosmological scales.\n", "\nWhat does all this have to do with black holes? At first glance,\nnothing. On deeper reflection, however, quite a lot. Hawking's Area\nTheorem, that black holes never decrease in size and can only\nincrease, is time asymmetric in the same way as the behavior of\nordinary physical systems governed by the Second Law. This, recall,\nwas the basis for the postulation of the Generalized Second Law, based\non the idea that black holes themselves possess entropy, itself one of\nthe motivating reasons that have led physicists to hypothesize that\nthe gravitational field in general, not just black holes, possess an\nintrinsic entropy\n (section 5.5),\n as Penrose (1979) hypothesized. Indeed Penrose did far more than just\nargue that the gravitational field itself possesses a generalized\nentropy. He also proposed what has come to be known as the Conformal\nCurvature Hypothesis, which states that the gravitational and\ncosmological arrows of time are driven, if not determined, by this\ngeneralized gravitational entropy. ", "\nThe existence of such a general gravitational entropy may provide a\nkey to answering the question about the development of stars,\ngalaxies, and other large-scale structure in the universe, as well as\nthe puzzle about the fact that the very early universe seems prima\nfacie to have been already a state of very high\n entropy.[20]\n Just as the thermodynamical behavior of ordinary matter picks out a\npreferred direction in time, the idea goes, so does the way gravity\ntends to shape the evolution of matter on cosmological scales, and,\nmoreover, it picks out the very same direction in time. If\none could show that the extremely homogeneous conditions of the very\nearly universe was a state of low gravitational entropy, and\nthat the current inhomogeneous clumping of matter into stars,\ngalaxies, etc., is a state of high gravitational entropy, and\nthat the difference in gravitational entropy is enough to\ncounterbalance the decrease in the entropy of ordinary matter as the\nuniverse evolved from homogeneity to clumpiness, then one would have\nsaved the Second Law by replacing it with the Generalized Second Law.\nAnd that is exactly what many physicists today think is the solution\nto our problem: how to reconcile the appearance of an early state of\nthe universe of high entropy with the demanded universal validity of\nthe Second Law. ", "\nAs remarked above, Penrose (1979) started this suite of ideas when he\nproposed the Conformal Curvature Hypothesis: that an entropy should be\nattributed to the gravitational field proportional to some measure of\n“purely gravitational” degrees of freedom, with a low\nentropy attibuted to homogeneous and isotropic gravitational fields.\nSome work in subsequent decades has been done, primarily based on\nGoode and Wainwright (1985) and Newman (1993a, 1993b), to try to\ngeneralize Penrose's proposal and make it rigorous. Almost all this\nwork has focused on the behavior of conformal singularities\n(characterized at the end of\n section 1.3)\n which are, in a natural sense, “early” cosmological\nsingularities, such as the Big Bang, and on the behavior of various\nmeasures of gravitational degrees of freedom moving to the future away\nfrom such singularities. (There has been some work, such as Rudjord\net al. 2008, attempting to link the Conformal Curvature\nHypothesis directly to black-hole entropy.) The idea is that the\ninitial cosmological singularity, in accord with Penrose's Conformal\nCurvature Hypothesis, had extraordinarily low entropy, thus\ncompensating the high entropy of the homogeneous ordinary matter\npresent then, making the early universe a state of low total entropy.\nAs the universe develops over time, and matter clumps into individual\nsystem (stars, galaxies, clusters and super clusters of galaxies,\netc.), the entropy of ordinary matter seems to drop, but,\nagain, that is more than compensated for by the enormous increase in\ngravitational entropy, thus saving the Generalized Second Law. ", "\nThis is all in accord with the so-called Past Hypothesis—the\nneed to postulate that the universe must have started in an extremely\nspecial, low-entropy state—if one admits the existence of\ngeneralized gravitational entropy. It has long been held by many\nphysicists and philosophers that the Past Hypothesis is the only way\nto preserve the validity of the Second Law of thermodynamics over\ncosmological scales (Albert 2000). Many philosophers and physicists\nhave balked at the Past Hypothesis, however, claiming it is\nexplanatorily vacuous or that it itself raises further difficult\nquestions, such as why the universe should have started in such a\n“special and unlikely” state at all. (See Albert 2000,\nEarman 2006, Callender 2010, and Wallace 2010 for discussion of many\nof these issues, from competing perspectives.) Penrose (1979) put\nforward the intriguing possibility that his Conformal Curvature\nHypothesis itself could point to an answer to all these questions: the\nseemingly required “specialness” of the state of the early\nuniverse may have a dynamical explanation in a more fundamental theory\nof quantum gravity. As intriguing as that possibility may be, it by no\nmeans has universal support. Wald (2006a), for example, gives\ncompelling arguments against the possibility that the low entropy of\nthe early state of the universe could have a dynamical origin. " ], "section_title": "7. Cosmology and the Arrow of Time", "subsections": [] }, { "main_content": [ "\nThe Hawking temperature of a macroscopic black hole is unimaginably\nsmall. For the black hole at the center of the Milky Way (Sagittarius\nA*), approximately 4 million solar masses, it is\napproximately 10-14 Kelvin. Even a black hole of one solar\nmass would have a temperature of only about 60 billionths of a Kelvin.\nDirect experimental verification of its existence therefore seems\nbeyond the realm of the imaginable, at least for macroscopic black\nholes. (If nothing else, it would be utterly swamped just by the\nordinary cosmic microwave background radiation, itself approximately\n2.7 Kelvin, a raging inferno in comparison.) ", "\nIn 1981, Unruh pointed out that a direct analogue of Hawking radiation\nshould occur in the most mundane and ordinary of physical systems,\nflowing water (under particular conditions). The physical basis for\nhis idea is almost ridiculously simple: if water is flowing past a\nboundary more rapidly than its speed of sound, than an effective event\nhorizon forms, for any disturbances in the water, which will propagate\nwith the speed of sound, will necessarily be “trapped”\nbehind the boundary. He then argued that the scattering of water\nwavelets at the boundary will occur with a thermalized spectrum, in\nexact accord with Hawking radiation (Unruh 1981, 2008). Since then,\nanalogue models for Hawking radiation in a wide variety of fluid,\nsolid-state, optical and quantum systems have been found. (See\nBarceló et al. 2011, Robertson 2012, Jacobson 2013,\nand Faccio et al. 2013 for recent reviews.) ", "\nThe remarkable fact that is of most interest to us is that, because\nUnruh's arguments relied only on simple physical properties of\nno-escape boundaries and the low-energy behavior of thermalized\nradiation caused by scattering of fields off of such boundaries, Unruh\nconcluded that these so-called “dumb holes” (dumb because\nsilent) could serve as experimentally viable proxies for testing the\nexistence of Hawking radiation for black holes (Leonhardt and Philbin\n2008). In particular, the validity of the analogue models is argued\nfor on the grounds that the essential features of Hawking radiation\nare due solely to a few simple, formal kinematical conditions\nsatisfied by a wide range of kinds of physical systems (Visser 1998a,\n2013; Unruh and Schützhold 2005; Unruh 2014). In particular, the\nmanifestation of radiation-like behavior formally analogous to true\nHawking radiation from a black hole has nothing to do with any\nspecific, dynamical features of general relativity. Therefore, the\nthought goes, to detect the analogue of Hawking radiation in any of\nthese systems provides indirect but strong confirmational support for\nthe existence of actual Hawking radiation. There are, moreover, now\nseveral claims to have experimentally detected analogue Hawking\nradiation: Belgiorno et al. (2010) based on ultrashort laser\npulse filaments, i.e., intense laser pulses in a transparent\nKerr medium (those with a third-order optical nonlinearity);\nWeinfurtner et al. (2011) based on obstructed supersonic\nfluid flow; Steinhauer (2014) based on a “black-hole\nlaser” composed of phonons in an Einstein-Bose condensate; and\nthe list goes on. So, has Hawking radiation been experimentally\nconfirmed, even if only indirectly? ", "\nUntil recently, little philosophical work has been done on these\nanalogue black holes. Dardashti et al. (2017) argue that such\nanalogue models of event horizons and Hawking radiation can provide\npowerful confirmatory support for the existence of Hawking radiation\naround actual black holes. Indeed, they argue that these particular\nkinds of analogue model and the concomitant support they purport to\nprovide are novel, both in the sense of being of a sort not\ninvestigated before in the philosophical literature and in the sense\nof representing an innovation in actual scientific practice. (See the\nEncyclopaedia entry\n Analogy and Analogical Reasoning.)\n They base their claim on the fact that these are not only theoretical\nmodels, but that they can be—and are—implemented as actual\nexperiments, and thus constitute not merely analogical reasoning, but\nexperimentally controlled physical simulation. If one accepts a\ncertain kind of universality argument (Unruh and Schützhold\n2005), they claim, then it is this latter characteristic that lends\nthe analogue models the possibility of strong confirmatory support of\nactual Hawking radiation; and to the contrary, without acceptance of\nthat universality argument—if the models were based merely on\nstandard analogical theoretical reasoning—no confirmatory\nsupport at all would be had. ", "\nGryb et al. (2018) compare the kinds of universality argument\nseemingly needed in this case to the more standard, familiar form of\nsuch arguments made in the context of renormalization group methods.\nThey conclude that all available universality arguments made to\nsupport taking analogue experiments to confirm the existence of\nHawking radiation are wanting in at least one of six categories that\nthey collectively deem necessary for such arguments to work\n(robustness, physical plausibility, degree of universality, empirical\nsupport, and integration of robustness and universality), with failure\nof integration being the most serious problem. ", "\nThere is room, moreover, for yet more skepticism here. The arguments\nare prima facie strong that the analogue of Hawking radiation\nshould manifest in a wide range of systems, as a purely kinematical\neffect following directly from a few simple kinematical principles\nthat all those systems satisfy (Unruh 2014). Nonetheless, true\ngravitational black holes are radically different from all the\nproposed analogue systems, in a variety of extensive and deep ways, as\nis general relativity as a physical theory from all the theories\ngoverning those other types of systems. As the debate and dissension\ndiscussed in\n section 6.1\n illustrates, the fundamental physics of Hawking radiation may not be\nwell enough understood to have confidence that some confounding\nphysical factor cannot be present in purely gravitational systems that\nis not present in any of the analogue systems, a factor that would\nblock production of Hawking radiation by true black holes. In other\nwords, there seems prima facie little reason to have faith\nthat the universality condition holds, except on the basis of purely\ntheoretical arguments pertaining to systems we have no empirical\nexperience of nor access to whatsoever. " ], "section_title": "8. Analogue Black Holes and Hawking Radiation", "subsections": [] } ]

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[ "\nA supertask is a task that consists in infinitely many component\nsteps, but which in some sense is completed in a finite amount of\ntime. Supertasks were studied by the pre-Socratics and continue to be\nobjects of interest to modern philosophers, logicians and physicists.\nThe term “super-task” itself was coined by J.F. Thomson\n(1954).", "\nHere we begin with an overview of the analysis of supertasks and their\nmechanics. We then discuss the possibility of supertasks from the\nperspective of general relativity.\n" ]

[ { "content_title": "1. Mechanical properties", "sub_toc": [ "1.1 Missing final and initial steps: The Zeno walk", "1.2 Missing limits: Thomson’s Lamp", "1.3 Discontinuous quantities: The Littlewood-Ross Paradox", "1.4 Classical mechanical supertasks", "1.5 Quantum mechanical supertasks" ] }, { "content_title": "2. Supertasks in Relativistic Spacetime", "sub_toc": [ "2.1 Time in Relativistic Spacetime", "2.2 Malament-Hogarth Spacetimes ", "2.3 How Reasonable Are Malament-Hogarth Spacetimes? " ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nStrange things can happen when one carries out an infinite task.", "\nFor example, consider a hotel with a countably infinite number of\nrooms. One night when the hotel is completely occupied, a traveler\nshows up and asks for a room. “No problem,” the\nreceptionist replies, “there’s plenty of space!” The first\noccupant then moves to the second room, the second to the third room,\nthe third to the fourth room, and so on all the way up. The result is\na hotel that has gone from being completely occupied to having one\nroom free, and the traveler can stay the night after all. This\nsupertask was described in a 1924 lecture by David Hilbert, as\nreported by Gamow (1947).", "\nOne might take such unusual results as evidence against the\npossibility of supertasks. Alternatively, we might take them to seem\nstrange because our intuitions are based on experience with finite\ntasks, and which break down in the analysis of supertasks. For now,\nlet us simply try to come to grips with some of the unusual mechanical\nproperties that supertasks can have." ], "section_title": "1. Mechanical properties", "subsections": [ { "content": [ "\nSupertasks often lack a final or initial step. A famous example is the\nfirst of\n Zeno’s Paradoxes,\n the Paradox of the Dichotomy. The runner Achilles begins at the\nstarting line of a track and runs ½ of the distance to the\nfinish line. He then runs half of the remaining distance, or ¼\nof the total. He then runs half the remaining distance again, or\n⅛ of the total. And he continues in this way ad infinitum,\ngetting ever-closer to the finish line (Figure 1.1.1). But there is no\nfinal step in this task.", "\nThere is also a “regressive” version of the Dichotomy\nsupertask that has no initial step. Suppose that Achilles does reach\nthe finish line. Then he would have had to travel the last ½ of\nthe track, and before that ¼ of the track, and before that\n⅛ of the track, and so on. In this description of the Achilles\nrace, we imagine winding time backwards and viewing Achilles getting\never-closer to the starting line (Figure 1.1.2). But now there is no\ninitial step in the task.", "\nZeno, at least as portrayed in Aristotle’s Physics, argued\nthat as a consequence, motion does not exist. Since an infinite number\nof steps cannot be completed, Achilles will never reach the finish\nline (or never have started in the regressive version). However,\nmodern mathematics provides ways of explaining how Achilles can\ncomplete this supertask. As Salmon (1998) has pointed out, much of the\nmystery of Zeno’s walk is dissolved given the modern definition of a\nlimit. This provides a precise sense in which the following sum\nconverges:", "\nAlthough it has infinitely many terms, this sum is a geometric series\nthat converges to 1 in the standard topology of the real numbers. A\ndiscussion of the philosophy underpinning this fact can be found in\nSalmon (1998), and the mathematics of convergence in any real analysis\ntextbook that deals with infinite series. From this perspective,\nAchilles actually does complete all of the supertask steps in the\nlimit as the number of steps goes to infinity. One might only doubt\nwhether or not the standard topology of the real numbers provides the\nappropriate notion of convergence in this supertask. A discussion of\nthe subtleties of the choice of topology has been given by Mclaughlin\n(1998).", "\nMax Black (1950) argued that it is nevertheless impossible to complete\nthe Zeno task, since there is no final step in the infinite sequence.\nThe existence of a final step was similarly demanded on a priori terms\nby Gwiazda (2012). But as Thomson (1954) and Earman and Norton (1996)\nhave pointed out, there is a sense in which this objection equivocates\non two different meanings of the word “complete.” On the\none hand “complete” can refer to the execution of a final\naction. This sense of completion does not occur in Zeno’s Dichotomy,\nsince for every step in the task there is another step that happens\nlater. On the other hand, “complete” can refer to carrying\nout every step in the task, which certainly does occur in Zeno’s\nDichotomy. From Black’s argument one can see that the Zeno Dichotomy\ncannot be completed in the first sense. But it can be completed in the\nsecond. The two meanings for the word “complete” happen to\nbe equivalent for finite tasks, where most of our intuitions about\ntasks are developed. But they are not equivalent when it comes to\nsupertasks.", "\nHermann Weyl (1949, §2.7) suggested that if one admits that the\nZeno race is possible, then one should equally admit that it is\npossible for a machine to carry out an infinite number of tasks in\nfinite time. However, one difference between the Zeno run and a\nmachine is that the Zeno run is continuous, while the tasks carried\nout by a machine are typically discrete. This led Grünbaum (1969)\nto consider the “staccato” version of the Zeno run, in\nwhich Achilles pauses for successively shorter times at each\ninterval." ], "subsection_title": "1.1 Missing final and initial steps: The Zeno walk" }, { "content": [ "\nSupertasks are often described by sequences that do not converge. J.\nF. Thomson (1954) introduced one such example now known as Thomson’s\nLamp, which he thought illustrated a sense in which supertasks truly\nare paradoxical.", "\nSuppose we switch off a lamp. After 1 minute we switch it on. After\n½ a minute more we switch it off again, ¼ on, ⅛\noff, and so on. Summing each of these times gives rise to an infinite\ngeometric series that converges to 2 minutes, after which time the\nentire supertask has been completed. But when 2 minutes is up, is the\nlamp on or off?", "\nIt may seem absurd to claim that it is on: for each moment that the\nlamp was turned on, there is a later moment at which it was turned\noff. But it would seem equally absurd to claim that it is off: for\neach moment that the lamp is turned off, there is a later moment that\nit was turned on. This paradox, according to Thomson, suggests that\nthe supertask associated with the lamp is impossible.", "\nTo analyze the paradox, Thomson suggested we represent the\n“on” state of the map with the number 1 and the\n“off” state with 0. The supertask then consists in the\nsequence of states,", "\nThis sequence does not converge to any real number in the standard\nreal topology. However, one might redefine what it means for a\nsequence to converge in response to this. For example, we could define\nconvergence in terms of the arithmetic mean. Given a sequence\n\\(x_n\\), the Cesàro mean is the sequence\n\\(C_1 = x_1\\), \\(C_2 = (x_1 + x_2)/2\\), \\(C_3 = (x_1 + x_2 +\nx_3)/3\\), and so on. These numbers describe the average value\nof the sequence up to a given term. One says that a sequence\n\\(x_n\\) Cesàro converges to a number \\(C\\) if and\nonly if \\(C_n\\) converges (in the ordinary sense) to \\(C\\). It is\nthen well-known that the sequence \\(0, 1, 0, 1, \\ldots\\) Cesàro\nconverges to ½ (see e.g. Bashirov 2014).", "\nThomson pointed out that this argument is not very helpful without an\ninterpretation of what lamp-state is represented by ½. We want\nto know if the lamp is on or off; saying that its end state is\nassociated with a convergent arithmetic mean of ½ does little\nto answer the question. However, this approach to resolving the\nparadox has still been pursued, for example by Pérez\nLaraudogoita, Bridger and Alper (2002) and by Dolev (2007).", "\nAre there other consistent ways to describe the final state of\nThomson’s lamp in spite of the missing limit?", "\nBenacerraf (1962) pointed out a sense in which the answer is yes. The\ndescription of the Thomson lamp only actually specifies what the lamp\nis doing at each finite stage before 2 minutes. It says nothing about\nwhat happens at 2 minutes, especially given the lack of a converging\nlimit. It may still be possible to “complete” the\ndescription of Thomson’s lamp in a way that leads it to be either on\nafter 2 minutes or off after 2 minutes. The price is that the final\nstate will not be reached from the previous states by a convergent\nsequence. But this by itself does not amount to a logical\ninconsistency.", "\nSuch a completion of Thomson’s description was explicitly constructed\nby Earman and Norton (1996) using the following example of a bouncing\nball.", "\nSuppose a metal ball bounces on a conductive plate, bouncing a little\nlower each time until it comes to a rest on the plate. Suppose the\nbounces follow the same geometric pattern as before. Namely, the ball\nis in the air for 1 minute after the first bounce, ½ minute\nafter the second bounce, ¼ minute after the third, ⅛\nminute after the fourth, and so on. Then the entire infinite sequence\nof bounces is a supertask.", "\nNow suppose that the ball completes a circuit when it strikes the\nmetal plate, thereby switching on a lamp. This is a physical system\nthat implements Thomson’s lamp. In particular, the lamp is switched on\nand off infinitely many times over the course of a finite duration of\n2 minutes.", "\nWhat is the state of this lamp after 2 minutes? The ball will have\ncome to rest on the plate, and so the lamp will be on. There is no\nmystery in this description of Thomson’s lamp.", "\nAlternatively, we could arrange the ball so as to break the circuit\nwhen it makes contact with the plate. This gives rise to another\nimplementation of Thomson’s lamp, but one that is off after 2 minutes\nwhen the ball comes to its final resting state.", "\nThese examples show that is possible to fill in the details of\nThomson’s lamp in a way that either renders it definitely on after the\nsupertask, or definitely off. For this reason, Earman and Norton\nconclude with Benacerraf that the Thomson lamp is not a matter of\nparadox but of an incomplete description.", "\nAs with the Zeno Dichotomy, there is a regressive version of the\nThomson lamp supertask. Such a lamp has been studied by Uzquiano\n(2012), although as a set of instructions rather than a set of tasks.\nConsider a lamp that has been switched on at 2 seconds\npast the hour, off at 1 second past, on at ½ a second past, off\nat ¼ a second past, and so on. What is the state\nof the lamp on the hour, just before the supertask has begun? This\nsupertask can be viewed as incomplete in the same way as the original\nThomson lamp. Insofar as the mechanics of bouncing balls and electric\ncircuits described in Earman and Norton’s lamp are time reversal invariant, it follows that the time-reversed system is a possibility as well, which is spontaneously excited to begin bouncing, providing a physical implementation of the regressive Thomson\nlamp. However, whether the reversed Thomson lamp is a physical possibility\ndepends on whether or not the system is time reversible. A difficulty is that its initial state will not determine the subsequent history of an infinity of alternations." ], "subsection_title": "1.2 Missing limits: Thomson’s Lamp" }, { "content": [ "\nSometimes supertasks require a physical quantity to be discontinuous\nin time. One example of this, known as Ross’ paradox, was described by\nJohn Littlewood (1953) as an “infinity paradox” and\nexpanded upon by Sheldon Ross (1988) in his well-known textbook on\nprobability. It goes as follows.", "\nSuppose we have a jar—a very large jar—with the\ncapacity to hold infinitely many balls. We also have a countably\ninfinite pile of balls, numbered 1, 2, 3, 4, …. First we drop balls\n1–10 into the jar, then remove ball 1. (This adds a total of nine\nballs to the jar.) Then we drop balls 11–20 in the jar, and remove\nball 2. (This brings the total up to eighteen.) Suppose that we\ncontinue in this way ad infinitum, and that we do so with\never-increasing speed, so that we will have used up our entire\ninfinite pile of balls in finite time (Figure 1.3.1). How many balls\nwill be in the jar when this supertask is over?", "\nBoth Littlewood (1953) and Ross (1976) responded that the answer is\nzero. Their reasoning went as follows.", "\nBall 1 was removed at the first stage. Ball 2 was removed at the\nsecond stage. Ball n was removed at the nth stage, and so on ad\ninfinitum. Since each ball has a label n, and since each label n was\nremoved at the nth stage of the supertask, there can be only be zero\nballs left in the jar at the end after every stage has been completed.\nOne can even identify the moment at which each of them was\nremoved.", "\nSome may be tempted to object that, on the contrary, the number of\nballs in the jar should be infinite when the supertask is complete.\nAfter the first stage there are 9 balls in the jar. After the second\nstage there are 18. After the third stage there are 27. In the limit\nas the number of stages approaches infinity, the total number of balls\nin the jar diverges to infinity. If the final state of the jar is\ndetermined by what the finite-stage states are converging to, then the\nsupertask should conclude with infinitely many balls in the jar.", "\nIf both of these responses are equally reasonable, then we have a\ncontradiction. There cannot be both zero and infinity balls in a jar.\nIt is in this sense that the Littlewood-Ross example might be a\nparadox.", "\nAllis and Koetsier (1991) argued that only the first response is\njustified because of a reasonable “principle of\ncontinuity”: that the positions of the balls in space are a\ncontinuous function of time. Without such a principle, the positions\nof the balls outside the jar could be allowed to teleport\ndiscontinuously back into the jar as soon as the supertask is\ncomplete. But with such a principle in place, one can conclude that\nthe jar must be empty at the end of the supertask. This principle has\nbeen challenged by Van Bendegum (1994), with a clarifying rejoinder by\nAllis and Koetsier (1996).", "\nEarman and Norton (1996) follow Allis and Koetsier (and Littlewood and\nRoss) in demanding that the worldlines of the balls in the jar be\ncontinuous, but point out that there is a different sense of\ndiscontinuity that develops as a consequence. (A\n‘worldline’ is used here to describe the trajectory of a\nparticle through space and time; it is discussed more below in the\nsection on Time in Relativistic Spacetime.)\nNamely, if one views the number of balls in the jar as approximated by\na function \\(N(t)\\) of time, then this “number\nfunction” is discontinuous in the Littlewood-Ross supertask,\nblowing up to an arbitrarily large value over the course of the\nsupertask before dropping discontinuously to 0 once it is over. In\nthis sense, the Littlewood-Ross paradox presents us with a choice, to\neither,", "\nbut not both. The example thus seems to require a physical quantity to\nbe discontinuous in time: either in the worldlines of the balls, or in\nthe number of balls in the jar.", "\nA variation of the Littlewood-Ross example has been posed as a puzzle\nfor decision theory by Barrett and Arntzenius (1999, 2002). They\npropose a game involving an infinite number of $1 bills, each numbered\nby a serial number 1, 2, 3, …, and in which a person begins with $0.\nThe person must then choose between the following two options.", "\nAt each finite stage of the game it appears to be rational to choose\nOption B. For example, at stage n=1 Option B returns $3, while\nOption A returns $1. At stage n=2 Option B returns $7 while\nOption A returns $1. And so on.", "\nHowever, suppose that one plays this game as a supertask, so that the\nentire infinite number of offers is played in finite time. Then how\nmuch money will the player have? Following exactly the same reasoning\nas in the Littlewood-Ross paradox, we find that the answer is $0. For\neach bill’s serial number, there is a stage at which that bill was\nreturned. So, if we presume the worldlines of the bills must be\ncontinuous, then the infinite game ends with the player winning\nnothing at all. This is a game in which the rational strategy at each\nfinite stage does not provide a winning strategy for the infinite\ngame.", "\nThere are variations on this example that have a more positive yield\nfor the players. For example, Earman and Norton (1996) propose the\nfollowing pyramid marketing scheme. Suppose that an agent sells two\nshares of a business for $1,000 each to a pair of agents. Each agent\nsplits their share in two and sells it for $2,000 to two more agents,\nthus netting $1,000 while four new agents go into debt for $1,000\neach. Each of the four new agents then do the same, and so on ad\ninfinitum. How does this game end?", "\nIf the pool of agents is only finitely large, then the last agents\nwill get saddled with the debt while all the previous agents make a\nprofit. But if the pool is infinitely large, and the pyramid marketing\nscheme becomes a supertask, then all of the agents will have profited\nwhen it is completed. At each stage in which a given agent is in debt,\nthere is a later stage in which the agent sells to shares and makes\n$1,000. This is thus a game that starts with equal total amount of\nprofit and debt, but concludes having converted the debt into pure\nprofit." ], "subsection_title": "1.3 Discontinuous quantities: The Littlewood-Ross Paradox" }, { "content": [ "\nThe discussions of supertasks so far suggest that the possibility of\nsupertasks is not so much a matter of logical possibility as it is\n“physical possibility.” But what does “physical\npossibility” mean? One natural interpretation is that it means,\n“possible according to some laws of physics.” Thus, we can\nmake the question of whether supertasks are possible more precise by\nasking, for example, whether supertasks compatible with the laws of\nclassical particle mechanics.", "\nEarman and Norton’s (1996) bouncing ball provides one indication that\nthe answer is yes. Another particularly simple example was introduced\nby Pérez Laraudogoita (1996, 1998), which goes as follows.", "\nSuppose an infinite lattice of particles of the same mass are arranged\nso that there is a distance of ½ between the first and the\nsecond, a distance of ¼ between the second and the third, a\ndistance of ⅛ between the third and the fourth, and so on. Now\nimagine that a new particle of the same mass collides with the first\nparticle in the lattice, as in Figure 1.4.1. If it is a perfectly\nelastic collision, then the incoming particle will come to rest and\nthe velocity will be transferred to the struck particle. Suppose it\ntakes ½ of a second for the second collision to occur. Then it\nwill take ¼ of a second for the third to occur, ⅛ of a\nsecond for the fourth, and so on. The entire infinite process will\nthus be completed after 1 second.", "\nEarman and Norton (1998) observed several curious facts about this\nsystem. First, unlike Thomson’s lamp, this supertask does not require\nunbounded speeds. The total velocity of the system is never any more\nthan the velocity of the original moving particle. Second, this\nsupertask takes place in a bounded region of space. So, there are no\nboundary conditions “at infinity” that can rule out the\nsupertask. Third, although energy is conserved in each local\ncollision, the global energy of this system is not conserved, since\nafter finite time it becomes a lattice of infinitely many particles\nall at rest. Finally, the supertask depends crucially on there being\nan infinite number of particles, and the width of these particles must\nshrink without bound while keeping the mass fixed. This means the mass\ndensity of the particles must grow without bound. The failure of\nglobal energy conservation and other curious features of this system\nhave been studied by Atkinson (2007, 2008), Atkinson and Johnson\n(2009, 2010) and by Peijnenburg and Atkinson (2008) and Atkinson and\nPeijnenburg (2014).", "\nAnother kind of classical mechanical supertask was described by\nPérez Laraudogoita (1997). Consider again the infinite lattice\nof particles of the same mass, but this time suppose that the first\nparticle is motionless, that the second particle is headed towards the\nfirst with some velocity, and that the velocity of each successive\nparticle doubles (Figure 1.4.2). The first collision sets the first\nparticle in motion. But a later collision then sets it moving faster,\nand a later collision even faster, and so on.", "\nIt is not hard to arrange this situation so that the first collision\nhappens after ½ of a second, the second collision after\n¼ of a second, the third after ⅛ of a second, and so on\n(Pérez Laraudogoita 1997). So again we have a supertask that is\ncompleted after one second.", "\nWhat is the result of this supertask? Their answer is that none of the\nparticles remain in space. They cannot be anywhere in space, since for\neach horizontal position that a given particle can occupy there is a\ntime before 1 second that it is pushed out of that position by a\ncollision. The worldline of any one of the particles from this\nsupertask can be illustrated using Figure 1.4.3. This is what Malament\n(2008, 2009) has referred to as a “space evader”\ntrajectory. The time-reversed “space invader” trajectory\nis one in which the vacuum is spontaneously populated with particles\nafter some fixed time.", "\nEarman and Norton (1998) gave some variations on this supertask,\nincluding one which occurs in a bounded region in space. Unlike the\nexample of Pérez Laraudogoita (1996), this supertask also\nessentially requires particles to be accelerated to arbitrarily high\nspeeds, and in this sense is essentially non-relativistic. See\nPérez Laraudogoita (1999) for a rejoinder.", "\nThis supertask is modeled on an example of Benardete (1964), who\nconsidered a space ship that successively doubles its speed until it\nescapes to spatial infinity. Supertasks of this kind were also studied\nby physicists like Lanford (1975, §4), who identified a system of\nparticles colliding elastically that can undergo an infinite number of\ncollisions in finite time. Mather and McGehee (1975) pointed out a\nsimilar example. Earman (1986) discussed the curious behavior of\nLanford’s example as well, pointing out that such supertasks provide\nexamples of classical indeterminism, but can be eliminated by\nrestricting to finitely many particles or by imposing appropriate\nboundary conditions." ], "subsection_title": "1.4 Classical mechanical supertasks" }, { "content": [ "\nIt is possible to carry some of the above considerations of supertasks\nover from classical to quantum mechanics. The examples of quantum\nmechanical supertasks that have been given so far are somewhat less\nstraightforward than the classical supertasks above. However, they\nalso bear a more interesting possible relationship to physical\nexperiments.", "Example 1: Norton’s Lattice", "\nNorton (1999) investigated whether there exists a direct quantum\nmechanical analogue of the kinds of supertasks discussed above. He\nbegan by considering the classical scenario shown in Figure 1.5.1 of\nan infinite lattice of interacting harmonic oscillators. Assuming the\nsprings all have the same tension and solving the equation of motion\nfor this system, Norton found that it can spontaneously excite,\nproducing an infinite succession of oscillations in the lattice in a\nfinite amount of time.", "\nUsing this example as a model, Norton produced a similar supertask for\na quantum lattice of harmonic oscillators. Begin with an infinite\nlattice of 2-dimensional quantum systems, each with a ground state\n\\(\\ket{\\phi}\\) and an excited state \\(\\ket{\\chi}\\). Consider the\ncollection of vectors,", "\nFor simplicity, we restrict attention to the possible states of the\nsystem that are spanned by this set. We posit a Hamiltonian that has\nthe effect of leaving |0〉 invariant; of creating |1〉 and\ndestroying |2〉; of creating |2〉 and destroying |3〉; and\nso on. Norton then solved the differential form of the\nSchrödinger equation for this interaction and argued that it\nadmits solutions in which all of the nodes in the infinite lattice\nstart in their ground state, but all become spontaneously excited in\nfinite time.", "\nNorton’s quantum supertask requires a non-standard quantum system\nbecause the dynamical evolution he proposes is not unitary, even\nthough it obeys a differential equation in wavefunction space that\ntakes the form of the Schrödinger equation (Norton 1999,\n§5). Nevertheless, Norton’s quantum supertask has fruitfully\nappeared in physical applications, having been found to arise\nnaturally in a framework for perturbative quantum field theory\nproposed by Duncan and Niedermaier (2013, Appendix B).", "Example 2: Hepp Measurement", "\nAlthough quantum systems may sometimes be in a pure superposition of\nmeasurable states, we never observe our measurement devices to be in\nsuch states when they interact with quantum systems. On the contrary, our measurement devices always seem to display definite values. Why? Hepp (1972)\nproposed to explain this by modeling the measurement process using a\nquantum supertask. This example was popularized by Bell (1987,\n§6) and proposed as a solution to the measurement problem by Wan\n(1980) and Bub (1988).", "\nHere is a toy example illustating the idea. Suppose we model an\nidealised measuring device as consisting in an infinite number of\nfermions. We imagine that the fermions do not interact with each\nother, but that a finite number of them will couple to our target\nsystem whenever we make a measurement. Then an observable\ncharacterising the possible outcomes of a given measurement will be a\nproduct corresponding to some finite number n of observables,", "\nRestricting to a finite number of fermions at a time has the effect of\nsplitting the Hilbert space of states into special subspaces called\nsuperselection sectors, which have the property that when \\(\\ket{\\psi}\\)\nand \\(\\ket{\\phi}\\) come from different sectors, any superposition\n\\(a\\ket{\\psi} + b\\ket{\\phi}\\) with \\(|a|^2 + |b|^2 = 1\\) will be a mixed state. It turns out in\nparticular that the space describing the state in which all the\nfermions are \\(z\\)-spin-up is in a different superselection sector than\nthe space in which they are all spin down. Although this may be puzzling\nfor the newcomer, it can be found in any textbook that deals with\nsuperselection. And it allows us to construct an interesting supertask\ndescribing the measurement process. The following simplified version\nof it was given by Bell (1987).", "\nSuppose we wish to measure a single fermion. We model this as a\nwavefunction that zips by the locations of each fermion in our\nmeasurement device, interacting locally with the individual fermions\nin the device as it goes (Figure 1.5.2). The interaction is set up in\nsuch a way that every fermion is passed in finite time, and such that\nafter the process is completed, the measurement device indicates what\nthe original state of the fermion being measured was. In particular,\nsuppose the single fermion begins in a \\(z\\)-spin-up state. Then,\nafter it has zipped by each of the infinite fermions, they will all be\nfound in the \\(z\\)-spin-up state. If the single fermion begins\nin a \\(z\\)-spin-down state, then the infinite collection of\nfermions would all be \\(z\\)-spin-down. What if the single fermion\nwas in a superposition? Then the infinite collection of fermions would\ncontain some mixture of \\(z\\)-spin up and \\(z\\)-spin down\nstates.", "\nHepp found that, because of the superselection structure of this\nsystem, this measurement device admits mixed states that can indicate\nthe original state of the single fermion, even when the latter begins\nin a pure superposition. Suppose we denote the \\(z\\)-spin\nobservable for the nth fermion in the measurement device as, \\(s_n = I\n\\otimes I \\otimes \\cdots (n\\,times) \\cdots \\otimes \\sigma_z \\otimes I\n\\cdots.\\) We now construct a new observable, given by,", "\nThis observable has the property that \\(\\langle \\psi, S\\phi\\rangle =\n1\\) if \\(\\ket{\\psi}\\) and \\(\\ket{\\phi}\\) both lie in the same\nsuperselection sector as the state in which all the fermions in the\nmeasurement device are \\(z\\)-spin-up. It also has the property\nthat \\(\\langle\\psi,S\\phi\\rangle = -1\\) if they lie in the same\nsuperselection sector as the all-down state. But more interestingly,\nsuppose the target fermion that we want to measure is in a pure\nsuperposition of \\(z\\)-spin-up and \\(z\\)-spin-down\nstates. Then, after it zips by all the fermions in the measurement\ndevice, that measurement device will be left in a superposition of the\nform \\(a\\ket{\\uparrow} + b\\ket{\\downarrow}\\), where \\(\\ket{\\uparrow}\\)\nis the state in which all the fermions in the device are spin-up and\n\\(\\ket{\\downarrow}\\) is the state in which they are all spin\ndown. Since \\(\\ket{\\uparrow}\\) and \\(\\ket{\\downarrow}\\) are in\ndifferent superselection sectors, it follows that their superposition\nmust be a mixed state. In other words, this model allows the\nmeasurement device to indicate the pure state of the target fermion,\neven when that state is a pure superposition, without the device\nitself being in a pure superposition.", "\nThe supertask underpinning this model requires an infinite number of\ninteractions. As Hepp and Bell described it, the model was unrealistic\nbecause it required an infinite amount of time. However, a similar\nsystem was shown by Wan (1980) and Bub (1988) to take place in finite\ntime. Their approach appears at first glance to be a promising model\nof measurement. However, Landsman (1991) pointed out that it is\ninadequate on one of two levels: either the dynamics is not\nautomorphic (which is the analogue of unitarity for such systems), or\nthe task is not completed in finite time. Landsman (1995) has argued\nthat neither of these two outcomes is plausible for a realistic local\ndescription of a quantum system.", "Example 3: Continuous Measurement", "\nAnother quantum supertask is found in the so-called Quantum Zeno\nEffect. This literature begins with a question: what would happen if\nwe were to continually monitor a quantum system, like an unstable\natom? The predicted effect is that the system would not change, even\nif it is an unstable atom that would otherwise quickly decay.", "\nMisra and Sudarshan (1977) proposed to make the concept of\n“continual monitoring” precise using a Zeno-like\nsupertask. Imagine that an unstable atom is evolving according to some\nlaw of unitary evolution \\(U_t\\). Suppose we measure whether or\nnot the atom has decayed by following that regressive form of Zeno’s\nDichotomy above. Namely, we measure it at time \\(t\\), but also at time\n\\(t/2\\), and before that at time \\(t/4\\), and at time \\(t/8\\), and so on. Let \\(E\\) be\na projection corresponding to the initial undecayed state of the\nparticle. Finding the atom undecayed at each stage in the supertask\nthen corresponds to the sequence,", "\nMisra and Sudarshan use this sequence as a model for continuous\nmeasurement, by supposing that the sequence above converges to an\noperator \\(T(t)=E\\), and that it does so for all times \\(t\\) greater than or\nequal to zero. The aim is for this to capture the claim that the atom\nis continually monitored beginning at a fixed time \\(t=0\\). They prove\nfrom this assumption that, for most reasonable quantum systems, if the\ninitial state is undecayed in the sense that \\(\\mathrm{Tr}(\\rho E)=1\\), then the\nprobability that the atom will decay in any given time interval \\([0,t]\\)\nis equal to zero. That is, continual monitoring implies that the atom\nwill never decay.", "\nThese ideas have given rise to a large literature of responses. To\ngive a sampling: Ghirardi et al. (1979) and Pati (1996) have objected\nthat this Zeno-like model of a quantum measurement runs afoul of other\nproperties of quantum theory, such as the time-energy uncertainty\nrelations, which they argue should prevent the measurements in the\nsupertask sequence above from being made with arbitrarily high\nfrequency. Bokulich (2003) has responded that, nevertheless, such a\nsupertask can still be carried out when the measurement commutes with\nthe unitary evolution, such as when \\(E\\) is a projection onto an energy\neigenstate." ], "subsection_title": "1.5 Quantum mechanical supertasks" } ] }, { "main_content": [ "\nIn Newtonian physics, time passes at the same rate for all observers.\nIf Alice and Bob are both present at Alice’s 20th and 21st birthday\nparties, both people will experience an elapsed time of one year\nbetween the two events. (This is true no matter what Alice or Bob do\nor where Alice and Bob go in between the two events.) Things aren’t so\nsimple in relativistic physics. Elapsed time between events is\nrelative to the path through spacetime a person takes between them. It\nturns out that this fact opens up the possibility of a new type of\nsupertask. Let’s investigate this possibility in a bit more\ndetail." ], "section_title": "2. Supertasks in Relativistic Spacetime", "subsections": [ { "content": [ "\nA model of general relativity, a spacetime, is a pair \\((M,g)\\).\nIt represents a possible universe compatible with the theory. Here, \\(M\\)\nis a manifold of events. It gives the shape of the universe. (Lots of\ntwo-dimensional manifolds are familiar to us: the plane, the sphere,\nthe torus, etc.) Each point on \\(M\\) represents a localized event in space\nand time. A supernova explosion (properly idealized) is an event. A\nfirst kiss (properly idealized) is also an event. So is the moon\nlanding. But July 20, 1969 is not an event. And the moon is not an\nevent. ", "\nManifolds are great for representing events. But the metric \\(g\\) dictates\nhow these events are related. Is it possible for a person to travel\nfrom this event to that one? If so, how much elapsed time does a\nperson record between them? The metric \\(g\\) tells us. At each event, \\(g\\)\nassigns a double cone structure. The cone structures can change from\nevent to event; we only require that they do so smoothly. Usually, one\nworks with models of general relativity in which one can label the two\nlobes of each double cone as “past” and\n“future” in a way which involves no discontinuities. We\nwill do so in what follows. (See figure 2.1.1.) ", "\nIntuitively, the double cone structure at an event demarcates the\nspeed of light. Trajectories through spacetime which thread the inside\nof the future lobes of these “light cones” are possible\nroutes in which travel stays below the speed of light. Such a\ntrajectory is a worldline and, in principle, can be traversed\nby a person. Now, some events cannot be connected by a worldline. But\nif two events can be connected by a worldline, there is an\ninfinite number of worldlines which connect them. ", "\nEach worldline has a “length” as measured by the metric \\(g\\);\nthis length is the elapsed time along the worldline. Take two events\non a manifold \\(M\\) which can be connected by a worldline. The elapsed\ntime between the events might be large along one worldline and small\nalong another. Intuitively, if a worldline is such that it stays close\nto the boundaries of the cone structures (i.e. if the trajectory stays\n“close to the speed of light”), then the elapsed time is\nrelatively small. (See Figure 2.1.2.) In fact, it turns out that if\ntwo events can be connected by a worldline, then for any number \\(t>0\\),\nthere is a worldline connecting the events with an elapsed time less\nthan \\(t\\)! " ], "subsection_title": "2.1 Time in Relativistic Spacetime" }, { "content": [ "\nThe fact that, in relativistic physics, elapsed time is relative to\nworldlines suggests a new type of bifurcated supertask. The idea is\nsimple. (A version of the following idea is given in Pitowsky 1990.)\nTwo people, Alice and Bob, meet at an event \\(p\\) (the start of the\nsupertask). Alice then follows a worldline with a finite elapsed time\nwhich ends at a given event \\(q\\) (the end of the supertask). On the other\nhand, Bob goes another way; he follows a worldline with an infinite\nelapsed time. Bob can use this infinite elapsed time to carry out a\ncomputation which need not halt after finitely many steps. Bob might\ncheck all possible counterexamples to Goldbach’s conjecture, for\nexample. (Goldbach’s conjecture is the statement that every even\ninteger n which is greater than 2 can be expressed as the sum\nof two primes. It is presently unknown whether the conjecture is\ntrue. One could settle it by sequentially checking to see if each\ninstantiated statement is true\nfor \\(n=4\\), \\(n=6\\), \\(n=8\\), \\(n=10\\), and so on.) If\nthe computation halts, then Bob sends a signal to Alice at \\(q\\) saying as\nmuch. If the computation fails to halt, no such signal is sent. The\nupshot is that Alice, after a finite amount of elapsed time, knows the\nresult of the potentially infinite computation at \\(q\\). ", "\nLet’s work a bit more to make the idea precise. We say that a \nhalf-curve is a worldline which starts at some event and is\nextended as far as possible in the future direction. Next, the \nobservational past of an event q, OP(q), is\nthe collection of all events x such that there a is a worldline\nwhich starts at x and ends at q. Intuitively, a (slower\nthan light) signal may be sent from an event x to an\nevent q if and only if x is in the\nset OP(q). (See figure 2.2.1.) ", "\nWe are now ready to define the class of models of general relativity\nwhich allow for the type of bifurcated supertask mentioned above\n(Hogarth 1992, 1994).", "\nDefinition. A spacetime \\((M,g)\\) is Malament-Hogarth if there is\nan event \\(q\\) in \\(M\\) and a half-curve \\(\\gamma\\) in \\(M\\) with infinite elapsed\ntime such that \\(\\gamma\\) is contained in \\(OP(q)\\).\n", "\nOne can see how the definition corresponds to the story above. Bob\ntravels along the half-curve \\(\\gamma\\) and records an infinite elapsed\ntime. Moreover, at any event on Bob’s worldline, Bob can send a signal\nto the event \\(q\\) where Alice finds the result of the computation; this\nfollows from the fact that \\(\\gamma\\) is contained in \\(OP(q)\\). Note that\nAlice’s worldline and the starting point \\(p\\) mentioned in the story did\nnot make it to the definition; they simply weren’t needed. The half\ncurve \\(\\gamma\\) must start at some event – this event is our starting\npoint \\(p\\). Since \\(p\\) is in \\(OP(q)\\), there is a worldline from \\(p\\) to \\(q\\). Take\nthis to be Alice’s worldline. One can show that this worldline must\nhave a finite elapsed time.", "\nIs there a spacetime which satisfies the definition? Yes. Let \\(M\\) be the\ntwo-dimensional plane in standard \\(t,x\\) coordinates. Let the metric \\(g\\)\nbe such that the light cones are oriented in the \\(t\\) direction and open\nup as the absolute value of \\(x\\) approaches infinity. The resulting\nspacetime (Anti-de Sitter spacetime) is Malament-Hogarth (see Figure\n2.2.2). " ], "subsection_title": "2.2 Malament-Hogarth Spacetimes " } ] } ]

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[ "\nSpinoza’s epistemology and philosophy of mind are governed by\nsome rather unintuitive commitments: first, a commitment to universal\nintelligibility, often described as Spinoza’s version of what,\nwith Leibniz, came to be known as the Principle of Sufficient Reason\n(PSR); second, a commitment to the explanatory closure of the mental\nand the physical; third, a commitment to the explanatory and\nontological priority of an infinite thinker over any finite mind. The\nentry discusses these commitments before diving into the details of\nSpinoza’s theories of cognition and mindedness. (In line with\nSpinoza’s own practice, what follows treats\n“conceive”, “understand”, “think”,\n“explain”, and “cognize” as roughly\ninterchangeable [cf. Wilson 1999: ch.10; Della Rocca 1996].)" ]

[ { "content_title": "1. Guiding commitments", "sub_toc": [ "1.1 Universal intelligibility", "1.2 Attribute barrier", "1.3 The priority of an infinite thinker", "1.4 Philosophy as a way of life" ] }, { "content_title": "2. Philosophy of mind", "sub_toc": [ "2.1 Minds", "2.2 Human minds", "2.3 Consciousness and ideas of ideas", "2.4 Willing or affirming" ] }, { "content_title": "3. Epistemology", "sub_toc": [ "3.1 Truth and adequacy", "3.2 Knowledge (cognitio)" ] }, { "content_title": "4. Eternity of the mind", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Spinoza’s Works", "Secondary Literature" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Guiding commitments", "subsections": [ { "content": [ "\nOne of Spinoza’s most fundamental epistemological and\nmethodological commitments is a commitment to universal\nintelligibility. In his most influential treatise, the\nEthics, Spinoza expresses this commitment in two ways: first,\nas the axiom that there is nothing that cannot be\n“conceived”, either “through itself” or\nthrough “another thing” (Ethics [=\nE] 1ax2); second, as the claim that there is a\n“reason or [i.e.] cause” for the “existence\nor nonexistence” of every thing (E1p11atld1).", "\nThese formulations immediately raise several questions. What does it\nmean for something to be conceived “through itself”, i.e.,\nin some sense be self-explanatory? Does the equivalence of\ncauses and reasons suggested by E1p11altd1 mean that only appeals to\ncauses can furnish reasons? Indeed, what counts as a\n“reason” (cf. Lin 2018)? It’s often assumed that in\nSpinoza’s view to give a “reason” for something\nrequires engaging in the sort of apriori deductions that fill large\nswathes of the Ethics. The opening definition of the\ntreatise, according to which something is a “cause of\nitself” if its existence is implied by its essence (E1def1),\nsuggests that at least some of the relevant “reasons” will\nindeed be accessible apriori. But could sense experience also furnish\nus with reasons? Is seeing my dog play with a stick enough of a\n“reason” to “conceive” of her as existing, or\nmust I deduce her necessary existence from the infinitely long series\nof prior causes (E1p28), a task Spinoza admits is impossible for\nfinite minds like ours (Treatise on the Emendation of the\nIntellect [= TIE] §100)?", "\nControversially but influentially, Michael Della Rocca 2008 has argued\nthat Spinoza’s philosophy as a whole can be derived from his\ncommitment to intelligibility. (For criticisms see e.g. Laerke 2011,\nNewlands 2018, Renz 2018.)" ], "subsection_title": "1.1 Universal intelligibility" }, { "content": [ "\nA second guiding but unintuitive commitment of Spinoza’s\nepistemology has come to be known as the “attribute\nbarrier”. A Spinozistic “attribute” is a descendant\nof the Cartesian “principal attribute” (AT 8a.25):\nroughly, it is the most basic qualitative kind under which something\ncan fall. For example, to say that something is a mental thing or a\nphysical thing – or, in Spinoza’s and Descartes’s\nterminology, “thinking” or “extended” –\nis to understand it in terms of its particular\n“attribute”.", "\nMost commentators take Spinoza to uphold a total explanatory\nclosure of mental and physical realms: pace Descartes, no\nphysical thing can enter into conceptual or explanatory relations with\nanything mental, and vice versa. For example, regardless of how we\nmight experience things, no physical occurrence, such as shaking a\nfist at someone, can be made intelligible by appealing to anything\nmental, like a menacing intention. Analogously, no bodily injury can\nmake intelligible the feeling of pain.", "\nThis prohibition on any “explanatory flow” (Bennett 1984)\nbetween mental and physical realms is the core meaning of\nSpinoza’s attribute barrier doctrine. Given Spinoza’s\ncommitment to universal intelligibility (see 1.1), derivatively, the\nimpossibility of conceptual relations between minds and bodies implies\nthe impossibility of causal relations between them (E3p2s).\nFor if something is in principle unintelligible (as any purported\ncausal relation between minds and bodies would be), it is also\nmetaphysically impossible. This prohibition on causal interactions\nbetween mental and physical things is the key secondary meaning of the\nbarrier doctrine.", "\nGiven that ordinarily we do appeal to intentions in\nexplaining our physical actions and to bodily states in explaining\nsensations, what would lead Spinoza to such a prima facie implausible\ndoctrine? The reason ultimately has to do with how Spinoza understands\nthe nature of the most fundamental entity in his metaphysics,\n“substance”. Building on philosophical tradition that goes\nback to Aristotle, Spinoza associates being a “substance”\nwith existential and explanatory self-sufficiency or independence\n(E1def3). Each essential quality or “attribute” of\nsubstance also must, Spinoza believes, manifest this independence\nproper to substance: “Each attribute of a substance must be\nconceived through itself” (E1p10). As a result, we cannot look\nfor an explanation of the fact that substance thinks, or of how it\nthinks, anywhere else but in substance’s thinking nature (for\nexample, we cannot appeal to the fact that it is also a material\nthing, i.e., a substance with the attribute of\n“extension”). In this sense substance as thinking is\n“conceived through itself”. The same reasoning will be\ntrue of any other substantial attribute.", "\nThis gives us the basic application of the barrier doctrine: the fact\nthat God is a physical thing cannot explain God’s nature as a\nthinking thing; nor is explanation possible in the other direction.\nBut the barrier doctrine also extends to creaturely\nintentions, sensations, and movements. Ontologically, all the things\nfamiliar to us from ordinary experience – animals, plants,\ninanimate objects – are for Spinoza merely modifications or\n“modes” of the single substance, “ways\n[modis]” that God is, just as (to borrow examples from\nLin 2018) a wrinkle in a rug is one way a rug can be, and a fist one\nway a hand can be. Spinoza explicitly applies the barrier doctrine\nalso to modes, stating that no modification of the thinking substance\ncan require for its explanation the concept extension, and no\nmodification of the extended substance can require for its explanation\nthe concept thought:", "\neach attribute is conceived through itself without any other (by\n1p10). So the modes of each attribute involve the concept of their own\nattribute, but not of another one. (E2p6d)\n", "\n(On attributes, see e.g. Gueroult 1958, Deleuze 1968, Shein 2009, Lin\n2019.)" ], "subsection_title": "1.2 Attribute barrier" }, { "content": [ "\nAs we just saw, Spinoza derives his prohibition of mental explanations\nof physical actions from what he takes to be true of the relation\nbetween the mental and the physical in the case of God. This\nis an instance of a more general methodological and epistemological\nprinciple Spinoza holds dear, that of the explanatory\npriority of claims about substance (God) to claims about modes\n(creatures) (E1p1, E1p15). To return to our toy analogy, we can only\nunderstand what it is to be a wrinkle in a rug if we first understand\nwhat it is to be a rug. For Spinoza, philosophizing in proper order\nalways requires us to start with God (E2p10s).", "\nGiven this explanatory priority of substance, to understand what it\nmeans to think or to have a mind we also cannot\nsimply extrapolate from our own case (for example, from\nintrospection, or from observing the behavior of fellow humans).\nRather, to understand thought and mindedness we first have to\nunderstand the nature of divine thought, i.e., what it means\nto be an “infinite” – unlimited and self-sufficient\n– thinker. This is the fundamental case of thinking for\nSpinoza.", "\nWhat does this infinite thought amount to? In one sense, it is simply\nan endorsement of the traditional doctrine of divine omniscience. In\nSpinoza’s framework, this doctrine becomes the claim that, as a\nthinking thing (i.e., a substance with the attribute of thought) God\nnecessarily produces an “infinite idea”, that is,\nan infinite modification of God’s nature as a thinking thing\n(E2p1, E2p3, E2p7c). This infinite idea is a complete and veridical\nrepresentation of everything that is, every bit of reality (E2p32).\n(Spinoza also calls this infinite mode an “infinite\nintellect” [E2p11c], seemingly without distinguishing the two\nterms.)", "\nIt’s worth keeping in mind that Spinoza is making here two\ndistinct claims: to say that God is a substance with the attribute of\nthought (that is, a thing whose essential nature it is to think) is\nontologically and explanatorily prior to the claim that this\nthinking substance also produces an actual representation or\nidea of everything (which is a claim about the existence of a certain\nkind of infinite mode). So although Spinoza faithfully\nfollows tradition in endorsing the claims that God thinks and is\nomniscient, he also ends up with a quite nontraditional result: the\ndivine “infinite intellect” is not part of, or identical\nwith, divine nature or essence. In terms of its\nontological status, the divine intellect is on par with finite minds\ninsofar as these too are merely modes.", "\nThe belief that the metaphysically basic instance of thinking is the\nthinking done by an infallible and omniscient thinker goes some way\ntoward explaining why Spinoza seems unconcerned about the threat of\nskepticism, so salient for Descartes (see also 3.1). For Spinoza\nthought in its fundamental instance is necessarily true; it\n“agrees” (E1ax6) with how things really are. So\nglobal skepticism is simply a metaphysical impossibility; all\nthat remains of the skeptical threat is to be on guard against local\ninstances of confusion and error that become possible in the\nderivative case of finite thought. Moreover, all such confusion and\nerror need some further cause beyond the intrinsic nature of thought.\n(Indeed, one might worry that Spinoza lets the pendulum swing too far\nin the opposite direction: global skepticism might no longer be\npossible, but it might now be hard to see how error could be\npossible, if, in Spinoza’s substance-monistic framework, all\nideas are ultimately God’s own [see 3.2.2].)", "\n(On Spinoza’s understanding of thinking, see e.g. Melamed 2013,\nNewlands 2018, Renz 2018; on his two proofs that God thinks, e.g.\nDella Rocca 1996, Gueroult 1974; on skepticism, e.g. Carriero 2020,\nPerler 2018, Primus 2017.)" ], "subsection_title": "1.3 The priority of an infinite thinker" }, { "content": [ "\nLast but not least, we should not forget that Spinoza’s magnum\nopus carries the title Ethics. For him knowledge is not\nmerely a theoretical achievement, as if we were solving\nconceptual puzzles for their own sake. For Spinoza, what is at stake\nin understanding anything, including thinking and knowledge, is a\nwhole slew of practical goods: freedom, virtue, blessedness.\nOf the infinity of knowable things, Spinoza writes, he wants to write\nonly about “those that can lead us, by the hand, as it were, to\nthe knowledge of the human Mind and its highest blessedness”\n(E2pref)." ], "subsection_title": "1.4 Philosophy as a way of life" } ] }, { "main_content": [], "section_title": "2. Philosophy of mind", "subsections": [ { "content": [ "\nOne reason why Spinoza might not care about distinguishing between\ncalling something God’s “idea” and calling it\nGod’s “intellect” (see 1.3) is that, like Hume, he\nappears to endorse what we today would call the “bundle\ntheory” of mind. On this theory, there is nothing more to\n“minds” and “intellects” than collections of\nideas of various complexity. (For example, the “idea that\nconstitutes the formal being of the human mind is…composed of a\ngreat many ideas” [E2p15].) In particular, minds do not contain\nany specialized “faculties”, such as will or intellect\n(E2p48). If notions of such faculties are to have any validity at all,\nthey must be understood as mere abstractions from particular\nideas and particular volitions (E2p48s; G/II/130).", "\nFor Spinoza, what individuates one bundle of ideas from\nanother seem to be their intentional objects, i.e., what they represent\n(E2p13s; see 2.1.3–4). For example, the aforementioned highly\ncomposite idea that is the “human mind” has a certain\n“actually existing body” as its essential object (see\n2.2).", "\n(On Spinoza’s bundle view of the mind, see e.g. Della Rocca\n1996; Hübner 2019; Renz 2018. On abstraction, see 3.2.4; on the\nrelation between ideas and affirmations, see 2.4; on the human mind\nspecifically see 2.2.)", "\nSpinoza’s ground-floor commitment to substance monism (i.e., to\nthe metaphysical possibility of only one “substance”, or\nexistentially and explanatorily independent thing) leaves him with the\nproblem of how to understand the ontological status of finite\nthought. If only one substance exists, what are we to make of human\nminds? These cannot be thinking substances as they are, say,\nfor Descartes or Leibniz. Short of condemning all finite thinking as\nillusory, Spinoza seems to have only one option left: to identify\ncertain instances of God’s own thoughts with finite\nthinking. And this is exactly what Spinoza does: he proposes that we\nregard all finite ideas, and all the finite “minds” these\nideas compose (see 2.1.1), as “parts” of the divine\n“infinite intellect”:", "\nthe human mind is a part [pars] of the infinite intellect of\nGod. Therefore, when we say that the human mind perceives this or\nthat, we are saying nothing but that God, not insofar as he is\ninfinite, but insofar as he is explained through the nature of the\nhuman mind, or insofar as he constitutes the essence of the human\nmind, has this or that idea. (E2p11c)\n", "\nFinite minds are thus for Spinoza both modes of a thinking\nsubstance and parts of an infinite\nmode that is God’s own “intellect”.", "\nThe claim that finite minds are parts of the divine intellect may\nanswer the question of the ontological status of finite thought, but\nit creates another puzzle: in what sense can a non-extended mind or\nintellect be a “part”, or have “parts”,\nmoreover parts that are themselves “minds”?", "\nAs we just saw, Spinoza accommodates human minds within his\nsubstance-monistic framework by carving up God’s “infinite\nintellect” into “parts”. But he isn’t\nconcerned solely with making room in his metaphysics for\nhuman minds:", "\nthe things we have shown so far are completely general and do not\npertain more to man than to other individuals, all of which, though in\ndifferent degrees, are nevertheless animate [animata]. For of\neach thing there is necessarily an idea in God, of which God is the\ncause in the same way as he is of the [human mind] (E2p13s)\n", "\nThis is Spinoza’s thesis of panpsychism, or universal mindedness\n(more precisely, universal at least for all “individuals”\nor composite entities [E2def; G/II/100]). Panpsychism follows because\nall it takes for there to be a finite “mind” in\nSpinoza’s view is that there be some “part” of the\nomniscient divine intellect – some component idea of it –\nthat represents some discernible bit of being. So not only is there\nnothing more to minds than ideas (2.1.1), there is nothing more to\ncreaturely minds than God’s ideas.", "\nSpinoza’s panpsychism may certainly seem more morally\nappealing than the vivisection-friendly Cartesian view that animals\nare just more complex versions of tables and clocks. Yet one may also\nwonder whether an account that can explain how human\nmindedness is possible only by instituting a general principle –\nnamely, the divisibility of an omniscient infinite intellect into\ncomponent ideas – that ushers in also plant and mineral minds\nhas diluted the meaning of “mind” beyond recognition or\nusefulness. Can an account that sees mindedness everywhere explain\nphenomena that, to all appearances, are particular to human\nrationality and self-consciousness? And is Spinoza not guilty here\nsimply of a profound confusion of categories: how can my\nmind just be God’s idea of something? Margaret\nWilson expressed the classic version of these worries, pessimistically\njudging against Spinoza (1999: ch.9).", "\n(On Spinozistic minds, see e.g. Alanen 2011, Koistinen 2018, Lin 2017,\nNewlands 2012; on mind-relativity of representing, see e.g. Matheron\n1969, Donagan 1988, Della Rocca 1996; on individuation of subjects,\nRenz 2018.)" ], "subsection_title": "2.1 Minds" }, { "content": [ "\nAny plausible panpsychism will have to say something about how human\nminds differ from all other minds that populate reality. Spinoza\naccounts for the distinctiveness of the human mind in two ways. First,\nas already noted, he underscores its complexity as a mental\noperation or act of thinking. Using the Scholastic term “formal\nbeing” to pick out this aspect of thinking, he writes,\n“the idea that constitutes the formal being of the human mind\nis…composed of a great many ideas” (E2p15). Second,\nSpinoza proposes that human minds are also distinct by virtue of what\nthey essentially represent: the essential intentional object\nof the human mind is an actually existing body:", "\n\n\nThe object of the idea constituting the human mind is the body,\nor a certain mode of Extension which actually exists, and\nnothing else (E2p13)\n\n\nthe essence of the mind consists in this…that it affirms the\nactual existence of its body (E3GenDefAff [G/II/204]; cf. E2p11,\nE2p17s [G/II/105/32])\n", "\nIn other words, a certain (itself complex) “part” of the\ndivine infinite intellect will count as a “human mind” iff\nit essentially represents a certain physical existent. It is in this\nintentional or representationalrelation (and not for example, per\nimpossibile, in some causal relation [see 1.2]) that the\nmind-body “union” consists in Spinoza’s view:\n“We have shown that the Mind is united to the Body from the fact\nthat the Body is the object of the Mind” (E2p21d) (cf. Renz\n2018).", "\nA few clarifications are in order. First, on hearing of\nSpinoza’s view we might be inclined to protest that human minds\nrepresent all sorts of things other than our own bodies:\nideas, abstractions, other bodies, etc. (Wilson 1999: ch. 9). But, to\nbe clear, Spinoza isn’t proposing here, rather\nimplausibly, that we represent nothing but our own bodies.\nHis claim is rather about what constitutes the essential\nintentional object of the human mind: other ideas composing my mind\nmay come and go, but to remain the same mind across time, and distinct\nfrom other equally complex bundles of ideas, my mind must continue to\nrepresent a particular physical entity. Moreover, Spinoza holds that\nwe are able to represent all the other things we represent only\nbecause we first conceive of our own body (for details, see 3.2 and\n4).", "\nSecond, that my mind has some actually existing body for its essential\nintentional object also doesn’t mean that I know this\nbody adequately. Far from it: “we have only completely\nconfused cognition of our body” (E2p13s; cf. E2p27). There are\nseveral reasons Spinoza is led to this pessimistic verdict. For one,\nas we saw, the human mind is essentially an idea of some existing body\nand of “nothing else” (E2p13). In particular, the human is\nnot essentially an idea of the many causes\nresponsible for that body’s composition and continued\nfunctioning. But, on Spinoza’s conception of knowledge,\nunderstanding these causes would be necessary for a complete knowledge\nof that body (E1ax4; cf. Donagan 1988: 129).", "\nHere is another reason why the idea that makes our minds our minds is\n“completely confused”. According to Spinoza, the only way\nI can cognize my own body as a particular thing existing in time (as\nopposed to knowing its atemporal “essence”, or knowing the\ngeneral properties of all bodies) is through its modes or\n“affections” – that is, through the changes or\ndeterminations that this body undergoes, mostly under the influence of\nexternal causes (E2p19). “We feel that a certain body is\naffected in many ways” (E2ax4): we stub our toes, hear a voice,\nare warmed by the sun, etc. But what we grasp in such experiences is,\naccording to Spinoza, only a “confused” amalgam\nof the nature of our own body and the nature of the external\ncauses affecting it (for details, see 3.2.2). But, however confused,\nmy first-personal “feeling” of what happens to my body\nsuffices for distinguishing my “mind” from my ideas of\nother bodies: I don’t “feel” in the same way what\nhappens to my sister’s equally complex body (her mind\ndoes), even if I can observe it (and even imitate it empathetically;\nsee E3p27).", "\n(See 4 for continuation of this account; on sense experience and\nerror, see 3.1.2, 3.2.3.)", "\nRecognition that the idea of the body that essentially constitutes a\nhuman mind is “completely confused” (E2p13s) goes some way\ntoward defusing Spinoza’s otherwise baffling assertion that we\n“perceive” “[w]hatever happens\nin” that body (E2p12, emphasis added). Prima facie this\nproposition ascribes, implausibly, a godlike omniscience to human\nminds. But experience clearly tells against such a proposal: we\ncertainly aren’t aware of all of the affections of our\nbodies (i.e., of all that “happens in” them), down to the\ncellular (and even quantum) level of each organ. It’s much more\nplausible to take Spinoza’s claim to be that we have such\nperceptions, but their utter confusedness or lack of clarity and\ndistinctness makes them indiscernible to us.", "\nThe initial implausible appearance of E2p12 dissolves even further\nonce we make note of Spinoza’s functional understanding\nof bodies: not everything that we might ordinarily consider a\n“part” of a body falls under this concept for Spinoza (cf.\nDonagan 1988:123):", "\nparts composing the human Body pertain to the essence of the Body\nitself only insofar as they communicate their motions to one another\nin a certain fixed manner…and not insofar as they can be\nconsidered as Individuals, without relation to the human Body.\n(E2p24d)\n", "\nAccordingly, Spinoza will have a suitably narrower understanding of\nthe scope of “whatever happens in” the parts of our own\nbodies: we will “perceive” only those affections of the\npancreas, say (to use Della Rocca’s example [2018]), that bear\non the whole body’s ability to function as an integrated\norganism (cf. Garrett 2018: ch.14).", "\nEven if we manage to make sense of the apparent ascription of\nomniscience to human minds, at least two other problems for\nSpinoza’s account of the mind-body relation remain.", "\nFirst, although tying the individuation of certain “parts”\nof the infinite intellect to certain bits of reality that these parts\nessentially represent may well solve the problem of individuating\nfinite minds in a substance-monistic framework (see 2.1.2), it also\nseems to generate a new problem. This is that to explain the nature of\nthe human mind we must now appeal to the existence of\nbodies:", "\nto determine what is the difference between the human Mind and the\nothers, and how it surpasses them, it is necessary for us, as we have\nsaid, to know the nature of its object, i.e., of the human body\n(E2p13s)\n", "\nThe problem is that, as we know (1.2), Spinoza prohibits\ncross-attribute explanations: no physical thing can explain anything\nmental, and vice versa. Yet Spinoza’s own account of the\nessential constitution of human minds seems not just to allow\nfor such cross-attribute explanations, but to require\nthem.", "\nHere is another interpretative problem that seems to plague\nSpinoza’s account of the human mind. How should we understand\nthe relation between 1) the intentional or representational relation\nthat human minds essentially bear to bodies, and 2) Spinoza’s\nclaim that minds and bodies are “one and the same thing”\n(E2p7s)? The doctrine of mind-body identity seems to follow directly\nfor Spinoza from substance’s identity under different\nattributes: since thinking substance and extended substance are in\nfact just a single substance considered or described in two different\nways, so also all of substance’s modifications will be\nsubject to that same sort of multiplicity of descriptions.\nAccordingly, the human mind and the human body are numerically\n“one and the same thing” (namely, a certain finite mode)\nbut this mode can be veridically described as a mind or as a\nbody. But when we pair this doctrine of mind-body identity with the\nthesis of an essential representational relation between the mind and\nthe body, we are faced with the question, Why should a mind represent\nwhat it is numerically identical with, or be identical with what it\nrepresents? How do we make this twofold nature of the mind-body\nrelation intelligible?", "\n(On mind-body identity, see e.g. Delahunty 1985; Della Rocca 1996;\nJarrett 1991; C. Marshall 2009; on its relation to mind-body\nintentionality, Garrett 2018: ch.15; Hübner forthcoming; for\nsolutions to the barrier violation, e.g. Della Rocca 1996, Hübner\nforthcoming, 2019.)" ], "subsection_title": "2.2 Human minds" }, { "content": [ "\nGiven the importance of the concept of consciousness to contemporary\nphilosophy of mind, it is perhaps unsurprising that Spinoza’s\nreaders have tried to extract a full-blown theory of consciousness\nalso from the rare appearances of terms such as conscius and\nconscientia in his writings. Such efforts are also\nunsurprising given Spinoza’s historical placement between\nDescartes (often taken to define thought in terms of consciousness)\nand Leibniz (who distinguishes thinking as a perfectly general\nproperty from consciousness as a property of higher minds alone) (cf.\nLeBuffe 2010). Interpreters return again and again to certain\nquestions: did Spinoza even have a theory of consciousness in\na recognizable sense? If he did, was it an internally consistent and\nadequately defended theory? Was it meant to distinguish conscious and\nunconscious ideas (and so also conscious and unconscious minds [see\n2.1.1])? Did Spinoza posit universal (but perhaps scalar or graded)\nconsciousness, just as he posited universal (but scalar or graded)\nmindedness (see 2.1.3)?", "\nThe existing array of interpretations ranges widely, from\nCurley’s 1969 conclusion that for Spinoza\n“consciousness” picks out higher order ideas\n(that is, ideas of ideas); through proposals that the term is intended\nto track the complexity (Nadler 2008) or the power\n(D. Garrett 2018: ch.14, E. Marshall 2013) of ideas; to the claim that\nSpinoza uses conscius and conscientia in several\ndifferent senses (LeBuffe 2010b).", "\nThe ideas-of-ideas reading of consciousness gets going because of\npassages like E4p8d, where Spinoza characterizes\n“cognition” of good and evil as\n“consciousness” of certain emotions (given that\nSpinozistic emotions or “affects” are already themselves\nconstituted in part by “ideas” [E3def3]) and E3p9s, where\nSpinoza characterizes “desire” as “appetite together\nwith consciousness of appetite” (given that\n“appetite” is already “related to the mind”\n[E3p9s]). In both cases the implication seems to be that consciousness\nis or involves higher order ideas.", "\nOf course, this interpretation of consciousness is of no use to\nsomeone looking to Spinoza for a theory of selective\nconsciousness, on which consciousness distinguishes some mental states\nfrom others. This is because in Spinoza’s framework there is no\nidea of which there is no higher order idea. This follows, first, from\ndivine omniscience (an all-knowing God has ideas of all things,\nincluding all ideas) and, second, from Spinoza’s understanding\nof ideas of ideas as ways of regarding the\nfirst-order ideas, not numerically distinct from them. More precisely,\nfor Spinoza, an idea of idea A is just A considered only as an\nact of thinking (leaving aside its representational content)\n– or, to use his Scholastic terminology, it is the original idea\nconsidered in its “formal reality” alone: it is “the\nform of the idea…considered as a mode of thinking without\nrelation to the object” (E2p21s).", "\nInterpretations on which consciousness is a scalar property tracking\ncomplexity or power fare much better in accounting for texts in which\nSpinoza depicts consciousness as a matter of selective causal and\ncognitive achievement, as in the following:", "\nHe who, like an infant or child, has a body capable of very few things\nand very heavily dependent on external causes, has a mind which\nconsidered solely in itself is conscious of almost nothing of itself,\nor of God, or of things. On the other hand, he who has a body capable\nof a great many things, has a mind which considered only in itself is\nvery much conscious of itself, and of God, and of things (E5p39s)\n", "\n(On consciousness see also Miller 2007.)" ], "subsection_title": "2.3 Consciousness and ideas of ideas" }, { "content": [ "\nSpinoza’s account of willing is developed in opposition to\nDescartes’s account, on several fronts. First, and perhaps most\nfamously, Spinoza denies that human beings have a free\n(undetermined) will (E1app; G/II/78). The freedom that Descartes finds\nundeniable in introspection is for Spinoza only a manifestation of the\ndepths of our ignorance about how we actually have been determined to\nact. Second, Descartes had proposed that we distinguish intellect as a\nfaculty for forming representations, from will as a faculty for\njudging the truth value of these representations. Spinoza rejects both\nthe idea that there are any faculties over and above\nparticular ideas and volitions (cf. 2.1.1), and the separation of the\nrepresentational and volitional elements. Instead he proposes that we\nsee the volitional element as intrinsic to representation,\nsuch that we “affirm insofar as [we] perceiv[e]” (E2p49s\n[III.B(ii)]; G/II/134). In consequence Spinozistic ideas are\nbelief-like: they “affirm” – posit the\nexistence of – the things they represent. On this picture, in\nthinking of my dog, for example, I thereby affirm her existence.", "\nOne obvious objection a Cartesian might make to this account is that\nit seems incapable of explaining the familiar experience of merely\nentertaining (imagining, hypothesizing, exploring, etc.) some idea\nwithout committing ourselves to its truth or falsity. As Spinoza puts\nthe objection in the mouth of an imaginary opponent,", "\nsomeone who feigns a winged horse does not on that account grant that\nthere is a winged horse, i.e., he is not on that account\ndeceived…Therefore, experience seems to teach…that the\nwill, or faculty of assenting, is free, and different from the faculty\nof understanding. (E2p49s [III.A.(ii)])\n", "\nTo fend off this objection Spinoza must find a way of explaining the\npossibility of representing something (such as a winged horse) without\ncommitting to its existence, while drawing solely on the resources of\nparticular, intrinsically affirmative ideas. His proposal focuses on\ncountervailing ideas: ideas that affirm or posit something\nthat negates or “excludes [tollere]” the\nexistence of an object represented by other ideas. For example, a\nchild “imagining a winged horse, and not perceiving anything\nelse…that excludes the existence of the horse….will\nnecessarily regard the horse as present” (E2p49s [III.B.(ii)];\nG/II/134). But, with some schooling, the child’s original idea\nof a winged horse can be offset by another idea (say, by the rational\nrepresentation of equine bones as, in general, too heavy to be lifted\nby feathers). Spinoza’s proposal explains not only how the\nordinary experience of mere entertainment of ideas is possible, but,\nmore significantly, it arguably offers a genealogy of\nnegation as a basic mental operation derived from affirmation\n(cf. Donagan 1988:46).", "\nThe obvious question Spinoza’s account raises is why, in such\ncases of mental conflict, in which certain ideas “exclude”\none another, should one of these ideas prevail? As Diane Steinberg\nnotes, Spinoza cannot have in mind purely logical\ninconsistency or contradiction between ideas, since this doesn’t\nyet give us a reason to nonarbitrarily prefer one idea over another\n(2003). The psychology of “exclusion” must involve not\nmerely such logical incompatibility of contents, but something that\nwould asymmetrically tip the scales in favor of one idea. Commentators\nhave proposed that greater causal power as the best candidate\nfor this role: the winning idea is the idea with more power to\ncontinue existing and to produce further ideas (in short, greater\npower to “strive” [E3p7]), or greater power to determine\nthe mind’s activity or causal power as a whole (e.g. Della Rocca\n2003; J. Steinberg 2018b).", "\n(On affirmation, will and excluding ideas see also 3.2.2. On\n“fictions”, see e.g. D. Garrett 2018: ch. 5, J. Steinberg\n2018b; on striving, see e.g. Carriero 2011, Kisner 2011, LeBuffe 2010,\nViljanen 2011, Youpa 2020 and entry on\n Spinoza’s psychological theory.)" ], "subsection_title": "2.4 Willing or affirming" } ] }, { "main_content": [], "section_title": "3. Epistemology", "subsections": [ { "content": [ "\nSpinoza is often taken to endorse the correspondence theory of truth,\nthat is, roughly, the view that truth consists in some sort of\nconformity of thought to reality. Spinoza himself puts the point in\nterms of “agreement”: “A true idea must agree with\n[convenire] its object” (E1ax6).", "\nHowever, this relational property of “agreement” is not\nthe only way Spinoza characterizes truth. True Spinozistic ideas also\nhave an intrinsic and, arguably, introspectable (cf. Garrett\n2018: ch.5) property which distinguishes them as true without\nrequiring us to look beyond the ideas themselves. An\n“adequate” idea is one with this intrinsic property:", "\nBy adequate idea I understand an idea which, insofar as it is\nconsidered in itself, without relation to an object, has all the\nproperties, or intrinsic denominations of a true idea. Exp.:\nsay intrinsic to exclude what is extrinsic, viz. the agreement of the\nidea with its object. (E2def4)\n", "\nConsequently, truth can be “its own standard”, such that\n“he who has a true idea at the same time knows that he has a\ntrue idea, and cannot doubt the truth of the thing” (E2p43, cf.\nTIE §36).", "\nThe view is surely puzzling: How is it that just by considering an\nidea on its own, we can be certain that it in fact conforms to what it\nrepresents? What might these intrinsic signs of truth be?", "\nOne plausible answer is that Spinoza has in mind here something like\nclarity and distinctness (cf. e.g. E2p38c), and so is in broad\nagreement with Descartes’s “rule” that true ideas\ncan appear to us as clear and distinct. Don Garrett has suggested\nthat, in addition to clarity and distinctness, we should understand\nadequacy as the “logical consistency of the represented\nobject” (2018: ch.6). On this reading, true ideas are\nself-evidently true insofar as we can clearly and distinctly perceive\nthe logical consistency of what they represent. This proposal has the\nvirtue of tying together Spinoza’s two characterizations of\ntruth – the extrinsic and the intrinsic one – into one\nneat package: given Spinoza’s commitment to necessitarianism\n(E1p33, E1p35), any logically consistent idea will represent not just\na possible object but a necessary and actual one; hence we can know\nfrom the logical consistency of an idea alone that it in fact\ncorresponds to its object.", "\nThe above definition of adequate idea in terms of a true idea’s\nintrinsic or nonrelational properties is, however, not the only way\nSpinoza characterizes mental “adequacy”. He also gives\nwhat we could call a mind-relative account of adequacy. It is\nmade possible by his belief that finite minds are “parts”\nof the omniscient “infinite intellect” (see 2.1.2). As he\nexplains, “there are no inadequate or confused ideas except\ninsofar as they are related to the singular mind of someone”\n(E2p36d):", "\nwhen we say that God has this or that idea, not only insofar as he\nconstitutes the nature of the human Mind, but insofar as he also has\nthe idea of another thing together with the human Mind, then we say\nthat the human Mind perceives the thing only partially, or\ninadequately (E2p11c)\n", "\nIn other words, if ideas constituting a given finite mind suffice for\nrepresenting x in the same way that a perfect\nintellect would represent x, the mind in question represents\nx “adequately”. Eugene Marshall has usefully\nexpressed this point in terms of part-whole “containment”:\nideas are adequate iff they are entirely a part of, i.e., contained in,\nthe relevant finite mind (2013:26).", "\nHere is an example of how this might work. Consider once again\nSpinoza’s claim that the idea of the body that essentially\nconstitutes a human mind is “completely confused” (see\n2.2.1). We can put this point in terms of inadequacy: a human\nmind knows its body as a particular in duration only by perceiving how\nit is “affected” or changed. This idea of the body is\n“inadequate” in Spinoza’s technical sense because\nGod’s conception of that body includes many components that are\nnot also part of the human mind’s conception of it: God\nconceives of all the many bodies that go into composing, preserving,\nand “regenerating” the affected human body, as well as of\nall the affecting external bodies, and of the infinite series of\ncauses on which these bodies in turn depend (E2p19d).", "\nConfronted with Spinoza’s account of mental adequacy, we might\nwonder how his two characterizations of this concept are supposed to\nhang together: why should an idea entirely contained in a mind also\nhave certain intrinsic markings of truth, such as clarity and\ndistinctness? One way to reconcile these two claims is to infer that\nfor Spinoza only ideas whose “premises”, so to speak, are\nwholly contained in a given mind can also appear as manifestly or\nself-evidently true. (One might also wonder if finite minds like ours\ncan ever manage to think anything truly “adequately”, if\nthis requires that all of the “premises” of a\ngiven idea be contained in our minds [cf. Della Rocca 1996]. We come\nback to this question in 3.2.1.)", "\nFinally, some commentators have concluded, further, that an\n“adequate” idea must be contained in a mind insofar as it\nmust also have been “adequately caused” – i.e.,\nself-sufficiently or autonomously caused – by the mind in\nquestion, and as such counts as a true “action” of that\nmind, in Spinoza’s technical sense of these terms\n(E3def1–2). If that’s right, then adequate ideas must all\nbe innate (LeBuffe 2010, E. Marshall 2013, J. Steinberg\n2018a: ch.8). For having a cause external to the mind – for\nexample, arising from experience – would be incompatible by\ndefinition with having been “adequately caused”. On such\nreadings, what we might experience as an acquisition of an\nadequate idea (say, in a philosophy class) is in fact only a matter of\nbecoming more conscious of it (J. Steinberg 2018a: ch.8; see\n2.3).", "\n(See also Kisner 2011.)" ], "subsection_title": "3.1 Truth and adequacy" }, { "content": [ "\nThe common English translation of Spinoza’s cognitio as\n“knowledge” does not do justice to his understanding of the term,\nwhich includes not just true and adequate ideas, but also inadequate\nand false ones.", "\nPerhaps the most important epistemological principle standardly\nascribed to Spinoza is that to conceive of or cognize x, one\nmust conceive of or cognize its causes. The text cited most\nfrequently in support of this causal interpretation of Spinozistic\ncognition is E1ax4: “Cognition of an effect depends on, and\ninvolves, cognition of its cause” (transl. altered). The\ninterpretation finds further support in what has come to be known as\nSpinoza’s “parallelism doctrine”, the proposition\nstating that “The order and connection of ideas is the same as\nthe order and connection of things” (E2p7). Spinoza’s\nappeal to E1ax4 in the demonstration of this proposition makes clear\nthat the “order and connection of things” he has in mind\nin E2p7 is a causal order and connection (cf.\nE2p9d). The idea that at least for the omniscient\n“infinite intellect” the connections between ideas\nperfectly mirror the causal connections between things in nature\nfurther supports the thought that for Spinoza cognizing something\nrequires tracking its causes.", "\nDespite the fact that commentators often appeal to E1ax4, the meaning\nof this important axiom is far from clear. There are two main\ninterpretive problems (leaving aside the question of what sorts of\ncauses, out of the rich panoply envisioned by the Aristotelians,\nSpinoza might allow in his metaphysics). The first problem concerns\nthe kind of cognition at stake in E1ax4. Some readers (e.g.\nBennett 1984; Gueroult 1969) have proposed that the axiom governs\nadequate cognition alone. So understood, the axiom expresses\na version of the traditional view that truly “scientific”\nknowledge requires a knowledge of causes – the knowledge\nwhy something happened, not merely that it happened.\nBut, as Margaret Wilson points out (1999: ch.10), this restricted\nreading of the scope of the axiom can’t be correct, since in\nSpinoza’s view even inadequate ideas formed in sense\nexperience “involve” their causes. (For example, the\ninadequate knowledge I have of any bodily change\n“involves” the inadequate knowledge of its external cause\n[E2ax1’, E2p25, E2p28].)", "\nA second interpretive problem concerns the meaning of the two terms\n– “dependence” and “involvement” –\nused by Spinoza to characterize the relation between causes and\ncognitions in E1ax4. “Involvement” is most often glossed\nas “implication”. But Wilson has argued that in key\npassages (e.g. E2p45) involvere stands more specifically for\nthe relation of implication between an attribute concept\n(e.g. extension, thought) and cognition of a mode (1999:\nch.10). On this reading of “involvement”, Spinoza’s\nclaim in E1ax4 that cognition of effects “involves” a\ncognition of causes amounts to the relatively intuitive claim that\nconceiving of extension or thought is necessary for conceiving of any\nparticular mind or body. So understood, the axiom doesn’t direct\nus to discover the causes of things so that we may have truly\nscientific knowledge of them, but instead merely describes what is\nentailed by even the most minimal and inadequate conception of\nanything whatsoever.", "\nIn addition to E1ax4 and E2p7, the claim that for Spinoza all\ncognition is cognition of causes also fits with his definition of\n“adequate cause” as one “whose effect can be clearly\nand distinctly perceived through it” (E3def1), which suggests\nthat causes are at least sufficient for adequately conceiving\nof a thing. Likewise, in E1p11altd1, Spinoza appears to\nidentify the “causes” of a thing’s\nexistence or nonexistence with “reasons [ratio]”\nfor that existence or nonexistence by means of the conjunction\nsive.", "\nNonetheless, the claim that for Spinoza to conceive of x, one\nmust conceive of its causes, faces at least two problems.\nFirst, it’s not clear how to reconcile this position with\nSpinoza’s account of the human mind. As we saw (2.2), cognition\nof the essence of human minds requires reference to actually existing\nbodies; yet, given Spinoza’s commitment to the attribute barrier\n(1.2), bodies cannot stand in a causal relation to anything mental. So\neither Spinoza’s account of the human mind is invalid by his own\nlights or (more likely) Spinoza allows for cognitions that do\nnot depend on a thing’s causes. Second, since each\nfinite thing depends on an “infinite” series of prior\nfinite causes (E1p28), if cognition of a thing (or at least\nadequate cognition of it) requires a grasp of all\nits causes, this would put an implausible, “stratospherically\nhigh” (Bennett 1984) requirement on cognition. Indeed it would\nput such cognition outside the reach of minds like ours, since, as\nSpinoza admits, we simply cannot know the entire infinite series of\nfinite things responsible for any given state of affairs in nature\n(TIE §100). Here Wilson’s insight about how Spinoza uses\n“involvement” is helpful: we can have adequate\ncausal cognition of particular things, as long as we look to God (the\nfirst and universal cause of all things) and not to the infinite\nseries of prior finite things as the relevant cause, and as\nlong as we attempt to explain the essence of the particular,\nnot its durational states. Spinoza’s doctrine of “common\nnotions” (see 3.2.3) guarantees that we have adequate ideas of\nGod under the attributes of extension and thought. And to know God as\nthe cause of the essence of a particular thing is just to have what\nSpinoza calls “intuitive cognition” (see 3.2.5.)", "\n(On causal cognition, see e.g. Koistinen 1996, Morrison 2013, 2015; on\nreconciling it with mind-body account, Della Rocca 1996, Hübner\n2020; on possibility of adequate cognition, e.g. Marshall 2013.)", "\nSpinoza divides cognition into three kinds: imagination;\nreason [ratio]; and intuition [scientia intuitiva].\nThis section focuses on the first of these.", "\nFirst, a terminological warning: what Spinoza calls\n“imagination” shouldn’t be confused with what\nwe are likely to mean by that term today. By\nimaginatio Spinoza understands sense experience (including\ncognition from signs and testimony) and derivative mental processes\n(including memory and the sort of manipulation of mental imagery we\nindeed might call “imagination”). Spinozistic\nimaginatio is distinct in virtue of both its content and its\ncauses. First, it is cognition of external bodies as\npresent; secondly, it is cognition acquired through ideas of\naffections, i.e., changes, of our own body, caused by\nother bodies:", "\naffections of the human body whose ideas present external bodies as\npresent to us, we shall call images of things, even if they do not\nreproduce the [NS: external] figures of things. And when the mind\nregards bodies in this way, we shall say that it imagines (E2p17s;\nG/II/106)\n", "\n(NB: “image” is another potential terminological trap for\ntoday’s readers: it’s Spinoza’s label for something\nphysical, a modification of the body. In contrast,\n“imagination” names something mental: the act or operation\nof representing, or forming ideas of, these physical\n“images”.)", "\nOne of the most important claims Spinoza makes about imaginative\ncognition is that it comprises “all those ideas which are\ninadequate and confused and so…is the only cause of\nfalsity” (E2p41d). That is, only ideas derived from sense\nexperience alone can give rise to false beliefs. The list of\nobjects of which, Spinoza thinks, we have only such inadequate and\nconfused cognition is staggering: it includes our own bodies; external\nbodies; the affections, parts, and durations of both; finally, even\nour minds (E2p19–31) (cf. 2.2.1). As Spinoza concludes\npessimistically, “all the notions by which ordinary people are\naccustomed to explain nature are only modes of imagining, and do not\nindicate the nature of anything” (E1app; G/II/83).", "\nWhat sort of “confusion” does Spinoza have in mind in\nE2p41d? Recall that imaginative cognition consists in ideas of\naffections of, or changes in, our own bodies that also\npresent us, indirectly, with the external causes of\nthese changes. (As Spinoza puts it, all our ideas of our own,\nexternally-caused bodily affections “involve” the nature\nof the external cause [E2p16].) So the “confusion”\ninherent to imaginative cognition seems to do, first, with the fact\nthat imaginative ideas have a content that is an amalgam of\ntwo distinct things: the current condition of some part of my body\nand the properties of the external cause (E2p16, E2p25; cf.\nDella Rocca 1996). For example, when I’m warmed by the sun, the\nnature of that bodily change depends on the nature of the sun\ntogether with the nature and current state of my own body. My\nperception of the bodily affection – of the increased warmth\n– tells me something about my own body and\nsomething about the sun; I have some insight into the\nrelative properties of both things. But it doesn’t tell\nme about the intrinsic or fundamental nature either of my own body or\nthe sun. It also doesn’t allow me to clearly separate out the\nrelative contributions of the external cause and of my own body.\n(Indeed, Spinoza goes so far as to propose that that such ideas\n“indicate the condition of our own body more\nthan the nature of the external bodies” [E2p16c2;\nemphasis added].)", "\nWhat about Spinoza’s characterization of imaginative ideas as\n“inadequate” (E2p41d)? Recall that “adequate”\nideas are manifestly true ideas fully explained by the\nmind they help constitute (3.1). So, first, a lack of\nadequacy is a lack of an intrinsic marker of truth, and hence of\ncertainty that we are dealing with true ideas. Hence when\ndealing with imaginative ideas we’re not yet able to\n“distinguish” with certainty “between the true and\nthe false” (E2p402). Of course, we may stumble on the right\nresult (as when we correctly apply a memorized mathematical rule\naccepted on authority [cf. E2p40s2]). But we cannot yet be sure that\nour ideas manage to “agree” with, or correspond to,\nreality.", "\nSecond, as inadequate, imaginative ideas won’t fully\nexplain what they purport to be about. Arguably, the mind thinking\nthem won’t possess all of the “premises” that\nnecessarily conclude in the idea in question. Instead, that idea will\nhave been produced by, and so will “involve”, the natures\nof the external causes that brought about the relevant affection of\nthe body. Instead of being orderly connected to all their premises in\nthe mind (according to what Spinoza calls the “order of the\nintellect”), imaginative ideas will be connected to one another\naccording to the “common order of Nature” (E2p29s), that\nis in a way that reflects the order of our happenstance encounters\nwith other bodies, and the idiosyncratic psychological associations\nsuch encounters generate:", "\nFor example, a soldier, having seen traces of a horse in the sand,\nwill immediately pass from the thought of a horse to the thought of a\nhorseman, and from that to the thought of war, etc. But a Farmer will\npass from the thought of a horse to the thought of a plow, and then to\nthat of a field, etc. And so each one, according as he has been\naccustomed to join and connect the images of things in this or that\nway, will pass from one thought to another. (E2p18s)\n", "\nIt is fairly easy to see how ideas whose premises are only partially\ngrasped, and which are haphazardly connected together, could become a\n“cause of falsity” – that is, could easily generate\nerroneous inferences and associations, as long as we have not yet\ngrasped ideas that would be needed to offset or “exclude”\n(see 2.4) such erroneous inferences and associations:", "\nthe mind does not err from the fact that it imagines, but only insofar\nas it is considered to lack an idea which excludes the existence of\nthose things which it imagines to be present to it (E2p17s)\n", "\nTo take an example important for the history of philosophy, our belief\nin free will, on Spinoza’s analysis, is precisely a false belief\nthat follows from sense experience not offset by countervailing ideas:\nit arises because “we are conscious of [our] actions and\nignorant of [their] causes” (E2p35s). Any perception of my own\naction will be “inadequate” (i.e., merely partial or\n“mutilated” by comparison to God’s infallible idea\nof that same action) if the ideas of all the necessitating causes of\nthat action are not also part of my mind. Such a\n“mutilated” and “inadequate” idea of my own\naction can generate a false belief in free will as long as I lack\npotentially offsetting ideas – say, of the general\nnecessity of all actions in nature (e.g. E1p33), together with an\nunderstanding of myself as subject to the very same laws as\nany other natural thing (E3pref; G/II/138).", "\nThis picture of falsehood as the result of the confusion and\nmutilation of ideas generated by sense experience, combined with the\nabsence of countervailing ideas, is behind Spinoza’s claim that\n“falsity” is “nothing positive”, only a\nrelative “privation of knowledge” (E2p35) about the matter\nat hand. (Falsity so understood must also be distinguished from an\n“absolute” “ignorance” of something\n[E2p35d].)", "\nThe lack of ideas that could exclude or offset false conclusions\ncarries another epistemic danger, and contributes to the loss of our\n“power” to think in yet another way: any ideas we have\nfailed to exclude lie in the mind ready to be combined with any\nadequate ideas we’ve managed to secure, thereby\nundermining the epistemic good that the latter bring with them. For\nexample, if we have not yet excluded the ideas of divine\ngoodness or divine purposiveness from our\nminds (see E1app), we can easily “join” such inadequate\nideas to the concept God.", "\nSpinoza contrasts confused and falsehood-inviting imagination with\n“intellect”, which he subdivides further into\n“reason” and “intuition”. Given\nSpinoza’s bundle-theoretic approach to minds (2.1.1), talk of\n“intellect” is not intended to conjure up here some sort\nof mental “faculty” over and above particular ideas.\n“Intellect” is instead Spinoza’s name for a certain\ntype of cognition, namely cognition that is “necessarily\ntrue” (E2p41). That is, intellectual ideas necessarily\n“agree” with, or correspond to, represented objects\n(E1ax6; see 3.1). This “agreement” with how things really\nare in the world allows intellectual ideas to both be “the same\nin all men” (E2p18s), and to reflect the actual causal order of\nthings in nature. Hence Spinoza can also describe intellect as\ncognition of things “through their first causes” (E2p18s,\ncf. E2p7), that is, ultimately through the all-necessitating divine\nessence that determines the causal order of things (E1p15, E1p16).\nIntellectual ideas are also “adequate” (E2p41d), that is,\nmanifestly true and fully explained by the mind they help constitute\n(3.1). Because intellectual ideas of truth and falsity in particular\nare manifestly true, intellectual cognition enables us to\n“distinguish the true from the false” with certainty\n(E2p42).", "\nSo how do we get our hands on this cornucopia of epistemic goods?\nSpinoza warns that “ideas which are clear and distinct in\nus” (i.e., “adequate”, or manifestly true, ideas)\n“cannot follow from mutilated and confused ideas”\n(E5p28d; emphasis added). This would seem to preclude any\npossibility of progressing from imagination to intellect. Fortunately\nSpinoza leaves an escape hatch in the form of “common\nnotions”, which he calls, appropriately, the\n“foundations” of reason, i.e., of the first of two kinds of\nintellectual cognition (E2p40s1). We may not be able to generate clear\nand distinct ideas from confused ideas, but not all is yet\nlost, because according to Spinoza even brute sense experience\nfurnishes us with some necessarily true and adequate ideas\n(or, on innatist readings [see 3.1], triggers or activates such\nideas).", "\nMore precisely, in Spinoza’s view, in every encounter with\nanother thing, not matter how confused my ideas of both my own body\nand the external body (3.2.2), I also form necessarily\nadequate ideas of any properties that are both 1)\n“common” to the interacting bodies and 2) “equally\nin the part and in the whole” (E2p38). That is, I form\nnecessarily adequate ideas of any properties wholly and without\ndistinction present in each particular thing. For example, the\nproperty of being extended is one such property: extension is\nextension is extension, whether it belongs to me or to a mosquito\nbiting me; I am neither more nor less of a physical thing than a\nmosquito is. Likewise, every body possesses the property of having a\ncapacity for “motion and rest” (“all bodies\nagree…in that they can move now more slowly, now more quickly,\nand that now they move, now they are at rest” [E2Ld]). For\nSpinoza, all such properties that are both universally instantiated\n(“common” to all things) and non scalar (“equally in\nthe part and in the whole”) are necessarily grasped correctly by\nany mind. And all ideas of such properties – all\n“common notions” – are necessarily adequate.", "\nWhat is Spinoza’s argument for this rather implausible claim,\nthat we simply cannot get certain properties (such as extension,\nthought, motion and rest) wrong? As we have seen, a lot\nhinges on this doctrine: nothing less than the very possibility of\nintellectual emendation, of transcending the confusion and inadequacy\nof mere imagination. The answer has to do with how Spinoza thinks\nabout what is responsible for the absence of adequacy. As we\nsaw above (3.2.2), in his view, any ideas of external bodies that I\nform through mere sense experience will in fact be ideas of how those\nbodies affect me. (For example, my empirical idea of the sun\nin fact only represents one way the sun can affect my body in its\ncurrent state.) But common properties like extension are\n“equally in the part and in the whole”: wholly and without\ndistinction in each thing. So for the adequacy of my idea of the sun\nas extended it does not matter if I’m representing\nextension as it is in the sun, or as it is in my body, or as it is in\nthe “confused” amalgam of the two. Extension is extension\nis extension. Because common notions are insulated against error in\nthis way, and because no idea inferable from an adequate idea can\nitself be inadequate (E2p40), these notions can indeed form a\n“foundation” of reasoning, and so be our entry point into\nthe realm of the intellect.", "\nWhat is sometimes overlooked in discussions of common notions is that\nSpinoza allows for two kinds of common notions: what we could\ncall 1) universal common notions, notions of truly\nuniversally instantiated non-scalar properties, such as extension; and\n2) relative common notions, ideas of properties “common\nto, and peculiar to [proprium], the human body and certain\nexternal bodies by which the human Body is usually affected\n[affici solet], and is equally in the part and in the whole\nof each of them” (E2p39). It’s not obvious what to make of\nthis characterization of the second type of common notion. What counts\nas being “peculiar” to what “usually” affects\nus? For example, are the general ideas Spinoza relies on in his\naccount of the human mind and human emotions (“affects”)\ncommon notions in this more circumscribed sense? We could pose the\nsame question of universal common notions: what should we\ninclude in that list, beyond the fairly uncontroversial examples of\nextension, thought, motion-and-rest?", "\nOne interesting upshot of Spinoza allowing for this second, relative\ntype of common notion is that our ability to transcend mere sense\nexperience into the realm of reason is not simply a function of the\ninvariable ontological make-up of the world, of there being only so\nmany truly universal on/off properties. We can also do\nsomething to increase the number of common notions that it is possible\nfor beings like us to have given our “usual” environments.\nThe more we can make it the case that we have something in common with\nthings around us – and in part this means, the more diverse\nwe ourselves are (cf. Sharp 2011: 98–9) – the\nbroader the epistemic “foundation” on which we can rely in\nreasoning.", "\nFinally, once again, the fact that no common notion on its\nown can be a cause of falsity doesn’t mean that we cannot\nput common notions, of either kind, to bad use: we can still\n“join” adequate ideas to ideas of more dubious value,\nproducing more complex inadequate representations (cf.\n3.2.2). Hence even if we necessarily adequately conceive of God as\na thinking thing, we still are in danger of joining this adequate\nidea to that of a benign or vengeful ruler as the referent of the name\nGod.", "\n(On reason, see e.g. Kisner 2011; LeBuffe 2017, Malinowski-Charles\n2010; on common notions, Donagan 1988; Primus 2017.)", "\nSpinoza’s doctrine of common notions is inseparable from a\nlarger interpretative puzzle. This puzzle concerns Spinoza’s\nstance on the validity of general concepts more broadly\n– in particular, of concepts of kinds, such as horse,\nanimal, or being.", "\nCertain things are fairly clear. For example, it’s clear that in\nhis ontology, Spinoza is committed to the existence of particulars\nalone (that is, roughly, things that cannot exist in many places at\nthe same time). It is also clear that, in his view, conceptual\ngenerality – and in particular the operation of\nabstracting from particulars – are rife with the\npossibility of error. (For example, we can be led to overlook\ndifferences among particulars [TIE §76], or mistake the products\nof our own abstraction for “real beings”, when in fact the\nresulting ideas present only mind-dependent “beings of\nreason” [Metaphysical Thoughts [= CM]\n1.1; TIE §93]). Finally, it’s also clear that for Spinoza\nideas of universals and abstractions often have lower\nepistemic value than ideas of particulars (e.g. TIE §93).", "\nThese considerations have led some readers to take Spinoza to reject\nall general and abstract ideas as inadequate (e.g. Curley\n1973; Savan 1958). Such readings have trouble explaining\nSpinoza’s own reliance on words that seem to refer to general\nconcepts (such as mode, idea, body, etc.). In particular,\nmany of Spinoza’s moral and socio-political doctrines –\nand so the whole enterprise of the Ethics (see 1.4) –\nseem to hinge on the validity of the general idea of “human\nnature”. Spinoza seems to believe that human beings share an\nessential nature, even if they realize it to different degrees, and\nhence also a common good. Here is a representative passage:", "\nthe greatest good of those who seek virtue is to know God,\ni.e.…a good that is common to all men, and can be possessed\nequally by all men insofar as they are of the same nature (E4p36d; cf.\nE4p35, E4AppIX)\n", "\nOne interpretative option here is to conclude that for Spinoza general\nand abstract ideas such as “human nature” have only some\npragmatic value (cf. Carriero 2005). Spinoza clearly\nrecognizes usefulness as an epistemic good (for example, he describes\nAristotelian ideas of genera and species as handy mnemonic devices\n[CM1.1]). On such a reading, it might not be strictly speaking true\nthat there is a common human nature, instantiated by each particular\nhuman being; nonetheless, for ethical or political ends it might be\nuseful to invoke such an idea. But even this reading will have trouble\nexplaining how Spinoza can nonetheless insist that the “true\nknowledge we have of good and evil” – again, hardly a\nminor issue for an Ethics – is “abstract,\nor universal” (E4p62s; G/II/257).", "\nIt helps to be precise about the nature of Spinoza’s\ncriticisms of general and abstract ideas: falling short of an\nepistemic ideal is not the same as utter inadequacy. Likewise,\nmind-dependence is not the same as illusion or error. (Neither Leibniz\nnor Kant, for example, would want to say that the idea or form of\nspace is an error or an illusion.) Finally, Spinoza’s most\nextensive criticism of general ideas, in E2p40s2, is not a criticism\nof general ideas simpliciter, but only of most general ideas\nderived from sense experience (cf. Bennett 1984). In Spinoza’s\nview, as finite and embodied beings whose minds are essentially ideas\nof what happens to our bodies (2.2.1), we can’t avoid\nthinking in general terms. When our bodies interact with other bodies\n– when we smell roses, or stub our toes – these encounters\nleave impressions (“images”) on our bodies; the finitude\nof our bodies allows them to retain only a limited number of\ndistinct “images” since over time they get\noverlaid and confused. The ideas we form by thinking the resulting\ncomposite “images”, and then predicate of indefinitely\nmany other entities – ideas such as horse,\nanimal, or being – represent distinctly only\nwhat the bodies we happen to come across have in common insofar as\nthey can affect a human body. General ideas formed in this way are\njust as “confused”, inadequate and idiosyncratic, as any\nother imaginative idea (see 3.2.2). So, contrary to what the\nAristotelians held, sense experience doesn’t suffice\nfor true ideas of the essences of things. (Rather it gives rise to\nunending philosophical controversies, as each one of us fashions\ngeneral types according to what we have experienced.)", "\nMoreover, we also can’t forget that, as we know from our\ndiscussion of common notions (3.2.3), Spinoza doesn’t think that\nall general ideas grounded in sense experience alone result\nin confused representations. Indeed, beyond this foundational\nsphere of common notions, Spinoza seems to think of\n“reason” on the whole as a necessarily adequate\nway of forming general ideas:", "\nit is clear that we perceive many things and form universal\nnotions: I. from singular things which have been\nrepresented to us through the senses… II. from\nsigns… These two ways of regarding things I shall henceforth\ncall knowledge of the first kind, opinion or imagination. III.\nFinally, from the fact that we have common notions and adequate\nideas of the properties of things…This I shall call reason\nand the second kind of knowledge (E2p40s2; emphases added)\n", "\nIn other words, for Spinoza both (confused and inadequate) imagination\nand (necessarily adequate) reason are ways of forming general ideas;\nwhat distinguishes reason and imagination is in part the epistemic\nvalue of their respective “universal notions”. The general\nideas that belong to imagination are, as we have seen, confused and\ninadequate and can lead us into error (3.2.2). The general ideas that\nbelong to reason – in particular, common notions and their\nderivatives – are, like all ideas of reason, necessarily\nadequate (3.2.3). The question that remains is whether Spinoza\nrecognizes any other rational and general “adequate ideas of\nproperties” beyond those implied by common notions.", "\n(See also e.g. Newlands 2015, Hübner 2016.)", "\nSpinoza characterizes scientia intuitiva as the kind of\ncognition that “proceeds from an adequate idea of the formal\nessence of certain attributes of God to the adequate knowledge of the\n[NS: formal] essence of things” (E2p40s2). Given Spinoza’s\nclaim that only infinite things can follow from infinite things\n(E1p21–23), it seems that the “formal essences” of\nparticular things that intuition infers from the essences of divine\nattributes must themselves be infinite (D. Garrett 2018:ch.7).", "\nAs noted above (3.2.3), Spinoza classifies intuition, alongside\nreason, as intellectual rather than imaginative cognition. As such,\nintuition is “necessarily true” (E2p41); allows us to\n“distinguish the true from the false” (E2p42); is\n“the same in all men” (E2p18s); and is cognition of things\n“through their first causes” (E2p18s). Yet intuition also\nclearly exceeds reason as an epistemic achievement in\nSpinoza’s eyes: it is intuition and not reason that he describes\nas “the greatest virtue of the mind” (E5p25) and the\n“greatest human perfection” (E5p27d), capable of affecting\nthe mind with a unique degree of force (E5p36s). Intuition is also the\nonly cognition on which Spinoza bestows the traditional honorific of\n“scientia” (D. Garrett 2018:ch.7).", "\nWhat is responsible for this singular place of intuition? Commentators\nare divided. Some (e.g. Soyarslan 2016) propose that it allows us to\nknow truths that reason doesn’t. Others (e.g. Nadler 2003) think\nintuition is superior to reason as an epistemic method alone.\nThis latter interpretation is a natural way to understand\nSpinoza’s own mathematical illustration of the ways all\nkinds of cognition, from imagination to intuition, can achieve the\nsame correct result (E2p40s2). Likewise, as many of Spinoza’s\npredecessors have also held, intuition is an immediate\nknowledge, an insight “in one glance” (E2p40s2) into\nessences. The principal superiority of intuition seems to stem from\nthe fact that it is in the business of cognizing essences\ndirectly, without the mediation of ideas of mere properties\nof things, whether “common” properties or other\n“adequate ideas of properties”, which form, as we have\nseen, the foundations of reason (3.2.3).", "\n(See also e.g. Carriero 2020, Primus 2017, Wilson 1999: ch.11.)" ], "subsection_title": "3.2 Knowledge (cognitio)" } ] }, { "main_content": [ "\nSpinoza’s doctrine of the eternity of the mind, one of last\nsubjects of the Ethics, has occasioned some of the most\nimpatient and uncharitable comments on the part of his readers (most\nfamously perhaps, Bennett 1984 describes it as “rubbish”\nleading others to write rubbish). The cause for this impatience is\nSpinoza’s declaration that in Part 5 he will discuss “the\nmind’s duration without relation to the body” (E5p20s), a\ndeclaration some see as a blatant violation of his commitment to\nmind-body identity in Part 2 (E2p7s). But of course an identity of one\nthing with another doesn’t rule out the possibility of\ndiscussing one but not the other, a procedure in which\nSpinoza engages again and again (for example, in introducing the\npossibility of ideas of ideas [see 2.3]). Spinoza is moreover quite\nexplicit that there is no eternity of human minds without a\ncorresponding eternity of bodies, and, far from contradicting any\ncommitments about mind-body relations made in Part 2, the doctrine of\nthe eternity of the mind in Part 5 arguably brings to light the full\nmeaning of those earlier commitments.", "\nTo recall (2.2.1), in Part 2 Spinoza proposes that the “first\nthing” that constitutes this “actual being” of a\nhuman mind is an idea of an “actually exist[ing]” body\n(E2p11–13). Only in Part 5 does Spinoza clarify that\n“actual” being or existence can be understood in two ways:\nfirst, in the temporal or durational sense key to the claims made in\nPart 2, and second, in an atemporal or purely ontological sense of\nsimply having being or reality at all (as opposed to, for example,\nbeing merely possible):", "\nWe conceive things as actual in two ways: either insofar as we\nconceive them to exist in relation to a certain time and place, or\ninsofar as we conceive them to be contained in God and to follow from\nthe necessity of the divine nature. But the things we conceive in this\nsecond way as true, or real, we conceive under a species of\neternity (E5p29s)\n", "\nGiven these two senses of “actuality”, Spinoza’s\noriginal claim in Part 2 that the “actual being” of the\nhuman mind is an idea of an “actually exist[ing]” body can\nalso be understood in two ways. First, it can be understood as a claim\nabout what it takes for a human mind to begin existing in\ntime, as we have done in 2.2.1: any human mind starts to\nactually exist in a durational sense when the nexus of bodily causes\nin nature generates a new body, which then begins to be variously\naffected or changed by external causes. The infinite intellect, in its\nindefatigable omniscience, begins to represent these affections or\nchanges. The relevant “part” of God’s omniscient\nidea (see 2.1.2) is a new, temporally existing human mind. More\nplainly put, a human “infant” is born, with “a body\ncapable of very few things, and…a mind…conscious of\nalmost nothing” (E5p39s).", "\nThis is the first, more intuitive sense in which human minds can be\nsaid to “actually exist”, the sense in which your mind\nexists now when processing these words. But however much we may be\nattached to our temporal selves and all that they feel, for Spinoza\nthere is another sense of “actual existence”. In that\nsecond sense, a human mind is still essentially an “actually\nexisting” idea of a certain “actually existing” bit\nof extension. But the relevant bit of extension is not the living\nhuman body, but its eternal essence – a certain\neternally possible way that divine extension can modify itself to take\non a certain ratio of motion and rest (cf. E2def[8]; G/II/100), i.e., a\ncertain determinate functional pattern of physical activity. In its\nomniscience, the divine substance eternally understands itself as\nbeing capable of being modified in such more determinate ways –\nthat is, of manifesting its own physical being as this or that snail\nor sunflower or human infant. Ideas of these eternal bodily\nessences are eternal “parts” of substance’s\ninfinite intellect (E2p8). That is, for each bodily essence there is a\ndivine idea that “expresses the essence of the body under a\nspecies of eternity” (E5p23s), as an eternal part of the\ninfinite intellect.", "\nThe eternal idea of a bodily essence is not only a part of God’s\nintellect (as all ideas are), it is also an eternal “part”\nof the relevant human mind, a “part” that\n“remains” (E5p23) even after the body’s demise, when\nthere are no more ideas of bodily affections to be “felt”.\nThis then is all there is also to human immortality, in\nSpinoza’s view: the eternal existence of the essences of our\nbodies, and of ideas of those bodies. As Nadler emphasizes (2002), we\nare far here from any traditional doctrine of personal immortality:\nnothing that does not belong to us essentially, and nothing that\ndepends on sense experience, such as memories, persists beyond\ndeath.", "\nSpinoza attaches an epistemic challenge to this ontological\npicture. He writes that we always “understand” and\n“feel” “that we are eternal” (E5p23s):\npresumably this means that we have some joyful, i.e., empowering\n(E3p11d), intellectual grasp of our own eternity (even if we often\njoin these adequate ideas with inadequate ones [see 3.2.2], such as\nreward or punishment). But he also suggests, prima\nfacie puzzlingly, that we can increase the degree of our own\neternity: “the more the mind understands things by the second\nand third kind of cognition, the greater the part [maxima\npars] of it that remains” after the destruction of the body\n(E5p38d). This suggestion might seem puzzling if we assume that the\n“eternal part” of my mind is just the eternal\nidea of the eternal essence of my own body. For then there\nseems to be nothing that would be subject to improvement or\nenlargement: my eternal essence just is my eternal essence.", "\nBut arguably this is not how Spinoza understands the eternal part of\nthe mind. The idea of the eternal essence of the body is just the\n“first thing [primum]” (cf. E2p11) that grounds\nmy mind’s eternal existence: it is the foundation of\neternal ideas of other things, just as the durational idea of this\nbody as changing is the foundation of imaginative ideas of other\nthings. “[T]he Mind is eternal, insofar as it conceives things\nunder a species of eternity” (E5p31s). Since for Spinoza any\nhuman mind is essentially an idea of a certain “actually\nexisting” body, cognition of that body is the foundation of\nall cognition whatsoever. This is true whether we are talking\nabout imaginative cognition of the external bodies we bump up against\nin duration; or about intellectual cognition of eternally existing\nessences: “Whatever the mind understands under a species of\neternity, it understands…from the fact that it conceives the\nbody’s essence under a species of eternity” (E5p29). In\nshort, for Spinoza all cognition of eternal truths rests on a\ncognition of our own body as an eternal essence. We can thus\nunderstand the idea of enlarging or maximizing the eternal\n“part” of our minds in terms of the number of eternal\ntruths, intuitive and rational, that we can acquire in the course of\nour existence – or, as on innatist readings (see 3.1), the\nnumber of eternal truths that we can make into powerful\n“parts” of our minds.", "\n(On consciousness, see 2.3; on imaginative cognition of the body see\n2.2 and 3.2.2. On eternity of the mind, see also e.g. Garrett 2018:\nch.9. On Spinoza’s debt to medieval Jewish views about\nmind’s eternity, see e.g. Klein 2014, Nadler 2002, Ravven and\nGoodman 2002.)" ], "section_title": "4. Eternity of the mind", "subsections": [] } ]

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[ "\nSpinoza's thought stands at an uneasy and volatile period in the\ndevelopment of physical theory. His physical science is largely\nCartesian, both in content and rationalistic method. It is harshly\ndismissive of the “occult qualities, intentional species,\nsubstantial forms, and a thousand other trifles” (letter 60, to\nBoxel) of pre-revolutionary scholastic natural philosophy. It is\nlikewise antagonistic to the new Baconian experimentalism, holding\nthat empirical findings can at best present examples of what reason\nitself demonstrates. Spinoza neither perceives the\nparticular difficulties for Cartesian physical theory that lead\nLeibniz to revive both finalism and substantial forms, nor foresees\nthe Newtonian theory of universal gravitation whose mathematical and\nempirical superiority to the Cartesian vortex theory lead to its\nuniversal acceptance, despite its own revival of occult powers in the\nform of forces operating at a distance.", "\nYet Spinoza is no orthodox Cartesian. He recognizes a variety of\nshortcomings in Descartes' physical views and moreover rejects much of\nthe metaphysical foundation upon which these views rest. In light of\nthese disagreements, Spinoza holds that bodies are not substances, but\nrather modifications of a single substance, and he develops a\ndistinctive and novel view of their individuation. He must also find\nan alternative basis for the basic principles that underlie and\nexplain the motion and interaction of bodies. The resulting physical\nview arguably contains anticipations of the fundamental character of\nmodern physics, and certainly anticipates modern theory of homeostatic\nsystems. Yet in spite of its express mechanistic and deterministic\ncharacter, Spinoza's physical theory appears to exploit an irreducible\nelement of finalism, and to accord an important explanatory role to\nindividual bodily essences.", "\nThis article first briefly discusses and places in context the textual\nsources most relevant to a consideration of Spinoza's physics. It then\npresent in brief summary those of Spinoza's philosophical views that\nbear most directly on his physical theory. Having identified the\ncentral issues for physical theory that emerge, it then clarifies\nthose issues by examining the sources in more detail. Finally, it\nsituates Spinoza's views vis-à-vis contemporary\nexperimental and mathematical science.", "\nNote on citation form. Citations to Spinoza's\nEthics give the part in roman capitals, then the proposition,\ndefinition, or axiom number, (e.g., p13, or d5)), and then specify\nwhether the cited material is in a scholium (s), corollary (c), or\nlemma (l). Citations to other works are given in the same style,\nexcept that they are prefaced by the abbreviated title of the work, in\nitalics (e.g., “PCP ” for Principles\nof Cartesian Philosophy)." ]

[ { "content_title": "1. Sources and context", "sub_toc": [] }, { "content_title": "2. Overview of the ", "sub_toc": [] }, { "content_title": "3. Physical cartesianism and the consequences of metaphysical divergence", "sub_toc": [ "3.1 Areas of agreement and divergence", "3.2 The principle of least modal mutation", "3.3 The principle of inertia and striving", "3.4 Striving and teleology" ] }, { "content_title": "4. Bodies as modes of substance and as individuals.", "sub_toc": [] }, { "content_title": "5. Individuation of bodies and the variety in matter", "sub_toc": [ "5.1 The Physical Interlude", "5.2 Interpreting “motion and rest”", "5.3 Individuation by essence" ] }, { "content_title": "6. Spinoza and the experimental and mathematical sciences", "sub_toc": [ "6.1 Observation", "6.2 Experimentation", "6.3 Mathematical science" ] }, { "content_title": "7. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Primary Sources", "Secondary Sources" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nWhile the other two great rationalists, Descartes and Leibniz, were\nphysical theorists and mathematicians of the first rank, who made\nsubstantial contributions to the development of physical science, the\nsame cannot be said of Spinoza. Nor was Spinoza a systematic\nexperimentalist. Indeed, his contributions to the historical\ndevelopment of physical theory are minimal. This is not because the\nphysical theory he presented was rejected or overlooked, but rather\nbecause Spinoza simply never presented a physical theory as such. Most\nof his writing concerning physical theory is instead in the service of\nother ends: exegetical, as an expositor of Descartes' philosophy;\nmetaphysical, in elaborating, for example, the relationships between\nGod or Nature as the single substance and the finite things he treats\nas “modes” thereof; or psychological, in explaining the\ndistinctive characteristics and possible blessedness of the human mind\nas the idea of an especially complex individual body.", "\nThe main sources of evidence for Spinoza's thought concerning physical\nnature are his Principles of Cartesian Philosophy, the first\nhalf of his magnum opus the Ethics, and a number of important\nletters from his correspondence. The PCP contains by far the\nmost focused and detailed of Spinoza's writing on physics proper, but\nis officially billed as an exposition of Descartes. The first half of\nthe Ethics presents a physical theory only insofar as Spinoza\nfinds this necessary to serve his goals in that work to explicate the\nnature of God and the natures and origins of the human mind and its\naffects. Discussion of the physical in the correspondence, though\noften illuminating, is typically directed at providing either\nclarification or defense of his views in response to queries and\nobjections, or at discussing contemporary views and developments in\nexperimental and theoretical science in order to show that they are\neither mistaken or consistent with his own views." ], "section_title": "1. Sources and context", "subsections": [] }, { "main_content": [ "\nThe philosophical view that emerges from the Ethics, in so\nfar as it bears on physical theory, can be outlined as follows. God or\nNature is the unique substance (Ip14), existing essentially (Ip7),\ninfinite in power (Ip8), and characterized by infinite attributes,\neach constituting its essence (Id4). Finite things are but\nmodifications of that substance, and not themselves independent beings\n(Ip14); bodies in particular are modes of substance conceived under\nthe attribute Extension. God or Nature, as the ultimate cause of all\nthings, is also the cause of all the particular modifications of\nextended nature (Ip18). However, substance's power is not expressed\nthrough the operations of will and intellect; the one substance does\nnot act by conceiving a design in the intellect and bringing it to\nexistence through the will (Ip23cl, Appendix, I). Hence Nature is not\na teleological system, natural phenomena do not have purposes, and all\ncausation between modes is efficient, none final. Since things are\nconceived through their causes, and modes are conceived always through\nthe attribute to which they belong, there can be no trans-attribute\ncausation. Bodies and their modifications cannot cause ideas, and\nideas cannot cause modifications of bodies (IIp6). All modes are\nconceived through the substance in which they inhere; in this sense\nGod or nature is an indwelling cause of all things (Ip18). But the\nparticular modifications of Extension are causally necessitated\nentirely by the determining operation of prior modes of the same\nattribute, themselves so determined, ad infinitum (Ip28). The\nphysical domain is thus completely closed causally, impervious to\ninfluence from modes of other attributes and to intervention of divine\nwill, and fully deterministic (Ip29).", "\nThought is another attribute through which substance is conceived\n(IIp1). Since substance is unique, and the attributes simply various\nessences under which it is conceived, the series of finite modal\ncauses in each attribute must operate strictly in parallel with one\nanother (IIp7). For every modification of Thought there is a\nmodification of Extension it mirrors, and vice versa; and the causal\norder of the one is perfectly matched with that of the other. The\nmind, a finite mode of Thought, is, under this parallelism, simply the\nidea of the body to which it corresponds under the parallelism\n(IIp13). The economy of ideas is precisely as closed, necessitated and\ndeterministic as that of bodies.", "\nBodies are individuated one from the other, not by reason of\nsubstance, but rather by reason of motion and rest (IIp13sl1),\nindividual identity through time and change being a matter of the\ndynamic maintenance of a distinctive ratio of motion and rest of a\nbody's parts (IIp13s Def.). The human body is simply a particularly\ncomplex individual body, capable of maintaining its distinctive\nstructure through a wide variety of externally imposed modifications,\nand capable of forming corporeal images of those bodies that affect\nit. An affect that increases the body's ability to maintain its\ndistinctive ratio is paralleled in the mind by a modification that\nincreases that mind's power of thought, and the passage from lesser to\ngreater power is joy (IIIp11s, Affect Def. II). Modifications that\ndecrease the power of a body to maintain its individual ratio are\nparalleled by modifications decreasing the mind's power of thought,\nand such passages are sadness (IIIp11s, Affect Def. III). Further,\nindividuals, both minds and bodies, strive to persevere in their\nexistence as far as they can; that is to say, they strive to increase\nthe power by which they maintain their distinctive natures (IIIp6).\nBodies, then, have essences, which are powers of striving (IIIp7). The\ncausal interactions in which a body participates that are attributable\nto the action of that body increase its power of perseverance; it is\nin contrast passive with respect to those that diminish its power.\nEvidently, for Spinoza, strict necessitarian determinism is consistent\nwith a genuine distinction between action and passion, between doing\nand suffering an act.", "\nSeveral fundamental and distinctive issues of interpretation\npertaining to the physical arise from this picture. How are bodies to\nbe conceived, if not as independent substances? How are motion and\nrest to be conceived so as to make sense of the claim that bodies are\nindividuated by them? How are the principles of inertia and the\ncollision laws that follow from it to be accounted for, given that\nthey cannot be grounded in God's immutable will? What is the nature of\nthe individual striving of bodies, and how can it be reconciled with\nSpinoza's deterministic dynamics of Extension? These issues cannot be\naddressed independently of one another. The present discussion will\napproach them as they emerge from Spinoza's engagement with Cartesian\nphysics, beginning with the PCP‘s exposition of\nDescartes’ views." ], "section_title": "2. Overview of the Ethics as it bears on physical theory", "subsections": [] }, { "main_content": [], "section_title": "3. Physical cartesianism and the consequences of metaphysical divergence", "subsections": [ { "content": [ "\nSpinoza agrees with the Cartesian conception of body as res\nextensa (Latin, extended thing), i.e., things necessarily and\nexhaustively conceived through\n extension.[1]\n He was, like Descartes, a plenist, rejecting the intelligibility of a\nvacuum. Furthermore, we know from Spinoza's correspondence that he\naccepted nearly all of Descartes' kinematic views, that is, the laws\nhe articulated describing the course of physical phenomena.\nHe likewise agrees with Descartes that physical nature should not be\nconceived as a teleological system, and that appeals to final causes\nshould be banished from physical theory.", "\nYet Spinoza had substantial disagreements with Descartes over a wide\nrange of metaphysical issues that bear on physical theory. Most\nobviously, he rejected Descartes' dualism of extended and mental\nsubstances in favor of substance monism, and correspondingly rejected\nCartesian mind-body interactionism. Some of these metaphysical\ndisagreements penetrate right to the grounds of the physical views the\ntwo thinkers share, revealing much of their agreement to be quite\nsuperficial. Consider, for example, their shared rejection of appeals\nto final causes in physics. Descartes held that final causal or\nteleological thinking is useless in physics, not because physical\nnature is not in fact teleological, but because our finite\nunderstanding cannot hope to understand the divine will, hence cannot\ngrasp the purposes with which physical nature is imbued. For Spinoza,\nin contrast, the problem is not epistemological but metaphysical. The\ndivine cause of the world has no will, and does not create things with\na plan in mind (1p32c, p33d, s2); hence nature is simply not a\nteleological system at all.", "\nSpinoza's agreement with the Cartesian laws of nature and collision\nprovides a telling set of further examples. Spinoza explicated and\nelaborated on these at length and in detail in the PCP.\nInterpreting this work as an expression of Spinoza's own thinking is a\ndelicate matter, since its explicit aim is to present and explicate\nDescartes' views, not Spinoza's own. Despite this, the PCP\nprovides a number of indications of where Spinoza diverges from\nDescartes on the metaphysical foundations of physics. In particular,\nthe demonstrations Spinoza offers of most of the basic principles of\nCartesian physics are often significantly different from or\nsupplementary to Descartes' own, and seem to presage important\nelements of Spinoza's mature thought as expressed in the\nEthics.", "\nOne such supplement involves Spinoza's attempt to extend the range of\napplication of Descartes' collision rules. Descartes' collision rules\nare limited in scope to the special case of bodies moving along a\nsingle line. In a scholium following a corollary Spinoza adds to\nDescartes' third rule, Spinoza explains that the vexed Cartesian term\n“determinatio” (determination) signifies not just\nthe direction of a motion, but also a force of motion along that\ndirection (PCP IIp27s). He then attempts to demonstrate how\nthe Cartesian collision laws can be extended to oblique collisions, by\nshowing how this force can be resolved into components by the rule of\nparallelograms. Spinoza's confused attempt fails, but this failure is\nnot of much interest on its own. Given that the oblique case is surely\nmore ordinary than the collinear case, and given that generality of\napplication is something one would surely want in collision laws, what\nis interesting is why Descartes did not himself attempt to provide\nrules of more general coverage, and why Spinoza felt that he had to do\nso.", "\nA plausible answer lies in a difference in their views as to the\ndegree and way in which physical nature forms a closed system.\nDescartes held that quantity of motion, conceived as the product of\nspeed and bulk, is conserved in all physical\n interactions.[2]\n This view allowed him to hold that mental substances can interact\nwith bodies and influence their motions, so long as they influence\nonly their direction. But given such influence, there can be no fully\ngeneral physical laws covering collisions. The precise state of a\nphysical system for Descartes cannot be determined by its prior state\nplus the laws of\n nature.[3]\n In this sense Descartes was not a physical determinist. Given that\nthe possible intrusion of extra-physical influence precludes fully\ngeneral collision laws, Descartes might not have thought it worthwhile\nto puzzle too much over the formulation of laws concerning non-linear\nmotion, thinking it sufficient to illustrate the application of the\nprinciples governing interaction only in the simplest cases.", "\nSpinoza emphatically rejected Cartesian interactionism. For him,\nextended nature is an entirely closed system. All the determinations\nof body, including not just quantity of motion but also direction, are\nwholly accounted for by the causal determination of other bodies,\ncombined with the nature of the body in question. Spinoza makes this\nquite clear in Ip28:", "\nEvery singular thing, or any thing which is finite and has a\ndeterminate existence, can neither exist nor be determined to produce\nan effect unless it is determined to exist and produce an effect by\nanother cause, which is also finite and has a determinate existence\n… and so on, to infinity.\n", "\nSince modes of distinct attributes cannot cause or explain one\nanother, and since God is the cause of modes only insofar as he is\nconsidered to be affected by another thing under the attribute of\nwhich they are modes (IIp6, IIp9), it follows that every determination\nof an extended thing results from the exclusive determining operations\nof other extended things. In this light, Spinoza should have felt more\nacutely than Descartes the need for a set of collision laws of fully\ngeneral application.", "\nUnbeknownst to him this need could only be met effectively by the\nrejection of Descartes' conservation law. Spinoza nowhere calls this\nlaw explicitly into question, and his acceptance of Descartes'\ncollision laws strongly suggests that he did in fact accept it. But he\ncannot have accepted the metaphysical grounds Descartes offers for it.\nFor Descartes, substances are dependent for their existence at every\nmoment upon God's concurrent creative activity, and since God's will\nis constant, he always recreates the whole of the extended world with\nexactly the same quantity of motion as he put there in the beginning.\nEach and every one of Descartes' laws of motion is for him\nmetaphysically grounded in the immutability of the divine will. But\nSpinoza's God has no will, and the world is not a product of creation,\nin the sense in which creation follows from a decision to act in\naccord with a conception formed in the understanding. Spinoza's own\ncommitment to rationalism nonetheless demands that there be some\nreason for the conservation of motion." ], "subsection_title": "3.1 Areas of agreement and divergence" }, { "content": [ "\nThis divergence over the possible metaphysical grounds for natural\nlaws and collision rules is important for understanding what is\nfundamentally at stake in another of Spinoza's supplements to what\nDescartes had himself offered in his Principles of\nPhilosophy. In a letter to Clerselier, Descartes makes clear that\nof all of his rules of collision “depend on only a\nsingle principle, which is that when two bodies collide, and have in\nthem incompatible modes, there must undoubtedly occur some mutation of\nthese modes to make them compatible, but this mutation is always the\nleast possible” (Descartes 1964–74: V, 185, emphasis\nadded). Following Gabbey (1996), call this the “Principle of\nLeast Modal Mutation” (PLMM). Despite is importance, Descartes\nneither mentions the PLMM is his Principles, nor offers a\njustification for it in the letter to Clerselier or elsewhere.", "\nIn the PCP, Spinoza includes the principle Descartes left\nout, and offers the demonstration Descartes never attempted.\nPCP IIp23 states: “When the modes of a body are forced\nto undergo variation, that variation will always be the least that can\nbe.” The demonstration consists of a concise and exclusive\nappeal to PCP IIp14, Spinoza's rendering of Descartes' law of\ninertia, according to which “Each single thing, insofar as it is\nsimple and undivided and is considered only in itself, always\nperseveres in the same state, as far as it can”. But just as\nDescartes never explains why the PLMM is true, Spinoza never explains\nwhy the principle of inertia supports the PLMM. Moreover, as\nformulated in PCP IIp14, it seems prima facie\ninadequate to do so. PCP IIp14 speaks of what happens to a\nbody only as it is considered in itself, simple and\nundivided, whereas PCP IIp23 speaks of bodies undergoing\nvariation imposed by other bodies, and is not limited to simple and\nundivided bodies. And even supposing PCP IIp14 relevant to\nwhat goes on with bodies when considered as affected by other bodies,\nit does not give any obvious guidance as to what then occurs. It seems\non the face of it quite possible that the least total modal variation\ncommanded by PCP IIp23 might involve a greater variation on\nthe part of each of the colliding bodies than would be consistent with\neither body in question persevering in its state as far as it can on\nits own. We are of course told they always remain in the same state\n“as far as they can.” But for this qualification to be of\nany relevance, it will obviously have to mean “as far as they\ncan, in the face of the influence of external bodies”; but until\nwe know the content of the collision laws, we are not entitled to say\nhow the influence of external bodies affects a body's inertial\ntendency. Yet it is just this content we need PCP IIp23 to\nderive.", "\nHow, then, might inertia be understood so that it supports the PLMM?\nIn good rationalist fashion, we should expect to come to a sound\nunderstanding of the principle of inertia by attending to the grounds\nfrom which it follows. But just as in the case of the Cartesian\nconservation law, Spinoza cannot himself have accepted the Cartesian\nstrategy of grounding inertia in the immutability of God's will.\nSpinoza offers his own principle of inertia in the so-called\n“physical interlude” of the Ethics, at IIp13 L3C:\n“a body in motion moves until it is determined by another body\nto rest; and a body at rest also remains at rest until it is\ndetermined to motion by another”. Rather than appealing to\ndivine will, Spinoza's demonstration of this principle seems to\nproceed from causal rationalism alone.", "\nWhen I suppose, for example that a body A is at rest and I give no\nconsideration to other moving bodies, I can assert nothing about body\nA but that it is at rest. Now if it should thereafter happen that body\nA is in motion, this surely could not have resulted from the fact that\nit was at rest; for from that fact nothing else could have followed\nthan that body A should be at rest.\n", "\nSince nothing in the conception of a thing as moving or at rest,\nwithout regard to other things, could explain a change in its motion\nor rest, something outside that conception is required to do so. This\ndemonstration cites no previous propositions or axioms of the\nEthics; indeed Spinoza claims his principle of inertia is\n“self-evident”.", "\nBut it would be unsatisfying to take inertia as primitive—to say\nthat bodies in fact do tend to persist in their states, though there\nis no reason to be discerned in their nature why they do so. To say\nthis would be to take it that Spinoza accepted the Cartesian principle\nas Descartes understood it, while rejecting the grounds Descartes\noffered for it, and without providing any substitute for it. This is\ndissonant indeed with the general tenor of Spinoza's\n rationalism.[4]\n Moreover, on this view, Spinoza would have taken the trouble to make\nexplicit the PLMM Descartes' rules require, only to justify it by a\ndirect and unelaborated appeal to a groundless principle of inertia,\nwhich seems, on Descartes' understanding of it, quite inadequate to do\nthe job. Yet Spinoza evidently did think that the PLMM followed from\nthe principle of inertia. This suggests that he had a different\nconception than did Descartes of both the nature and ground of that\nprinciple." ], "subsection_title": "3.2 The principle of least modal mutation" }, { "content": [ "\nAn intriguing shift in the language Spinoza uses in the PCP\nto articulate the Cartesian laws of motion is suggestive of how\nSpinozistic and Cartesian inertia may differ. In PCP IIp16,\nSpinoza states “every body which moves in a circle, as for\nexample, a stone in a sling, is continuously determined to go on\nmoving along a tangent.” The immediately succeeding proposition,\nPCP IIp17, states, “Every body that moves in a circle\nstrives to move away from the center of the circle that it\ndescribes” (emphasis added). Spinoza has substituted\n“strives” for “is continuously determined to\ndo”, the Latin “conari” for the\n“tendere” of PCP IIp16, which is what\nDescartes had used in expressing his own version of the law of\ncentrifugal motion. This substitution arguably involves a shift in\ndynamical implication. Conari usually has the sense of the\nEnglish “exertion”, “effort”\n“undertaking”, or “impulse”; reading\nconari in accord with this usual sense, PCP IIp17\nnot only describes what a body moving circularly will do when it is\nnot compelled by an external cause, but attributes that action to the\neffort or impulse of the moving body. PCP IIp17's invocation\nof conari, if we read it in this active sense, signals an\nongoing effort, a continuous directedness, in this case, at\nhomeostasis.", "\nOne must be quite circumspect in drawing inferences from this\nterminological shift on Spinoza's part. For one thing, the word for\nwhich conari is substituted, tendere, can have\nsimilar connotations itself, carrying the sense of a try or an\nattempt. For another, “conari” is, as Curley\npoints out (Spinoza 1985, p. 280 n. 43), a perfectly good Cartesian\nword, and in Descartes' usage, it is quite clear that\n“conari” is not intended to imply anything really\nactive on the part of the “striving” body. In\nPrinciples 3.56, Descartes tells us that the striving\n(conari) after some motion of inanimate things “merely\nmeans that they are positioned and pushed into motion in such a way\nthat they will in fact travel in that direction, unless they are\nprevented by some other cause”. Spinoza faithfully reiterates\nthis passive sense of “striving” on Descartes' behalf in\nPCP IIId3. On the other hand, “conari”\nis also cognate with a perfectly good Spinozistic word,\n“conatus”, which is his term in the\nEthics for an individual's inherent power of striving to\npersevere in its being (IIp6). Spinoza identifies this power as the\nessence of the individual (IIIp7), and further identifies its increase\nwith the individual's increased power of action, as opposed to\npassion, that is, with an increase in power of self-determination as\nopposed to external determination (IIIp11). This suggests that\n“conari”, as Spinoza intends it, involves\nsomething more than the mere passive tendency the term signifies for\nDescartes. Recalling once again that the inertial tendency of bodies\ndescribed in PCP IIp14 cannot, for Spinoza, be accounted for\nby appeal, in the manner of Descartes, to divine will, the\nsubstitution of “conari” for\n“tendere” in PCP IIp17 may signal the\nfact that Spinoza is all along thinking of inertia as resulting from\nan active principle in bodies as such.", "\nIf Spinoza's principle of inertia is to provide a ground for\nPCP IIp17 taken as involving “conari” in\nan active sense, then it must be taken to amount to the claim not just\nthat bodies will not in fact change their state unless externally\ndetermined to do so, but also that even while external causes are\nacting on a body (e.g., the sling holding the stone in circular\nmotion), the body's own impulse is at work actively endeavoring to\ndetermine it to move as it would in the absence of that external\ncause. And reading Spinozistic inertia this way, imputing to the body\na continuous effort to move so as to maintain the state it\nwould be in absent external determination, also suits it to ground the\nPLMM. Given the symmetry of interaction, each of the bodies to an\ninteraction, being externally determined to change by the other, will\nstrive to resist change as far as it is able. Plausibly, then, the\ntotal change of state resulting from the resolution of the opposition\nof the interacting bodies will be the least total possible. This\nsuggests, at least tentatively, that even in the PCP, Spinoza\nis at work attempting to shore up worries in the foundations of\nCartesian physics that stem from the unduly passive Cartesian\nconstrual of the equation of body with extension." ], "subsection_title": "3.3 The principle of inertia and striving" }, { "content": [ "\nQuite apart from the question whether Spinoza intended to impose this\nmore active reading of inertial dynamics on Cartesian philosophy,\neither deliberately or unawares, he clearly made the striving conatus\nof individual modes an important centerpiece of the mature philosophy\nhe presented in the Ethics. IIIp6, which articulates the\nconatus doctrine according to which “each thing, as far as it\ncan by its own power, strives to persevere in its own being”,\nhas been the subject of a great amount of interpretive puzzlement in\nthe literature. A main focus of this puzzlement is the extent to which\nIIIp6 represents a teleological element in Spinoza's natural\nphilosophy. It is certainly central to Spinoza's subsequent treatment\nof human psychology, according to which we strive to obtain those\nthings that increase our power and to avoid those that diminish it.\nSpinoza takes his conatus principle to license inferences from\nsentences of the form “x would increase\nA‘s power” to sentences of the form\n“A does x so far as A is able”;\nthis is genuine explanatory teleology, treating a state to be\nachieved—the increase of power—as an end towards which a\nthing's activity is directed, and thus as an explanatory ground for\nbehaviors.", "\nOne ground for reading teleology out of the conatus principle and for\nregarding both teleology and that principle as fundamentally\nirrelevant to Spinoza's physical theory is that the latter's first\nexplicit appearance in part III of the Ethics comes long\nafter Spinoza presents his accounts of extended nature and the basic\nmechanics of modes thereof, indeed in a way that makes it very hard to\nsee how any teleology could be involved at all. Ip28 denies that any\nsingular thing can be determined to exist or to produce an effect\nunless it has been so determined by a prior finite cause, ad\ninfinitum. The use made of Ip28 in IIp9 suggests that Spinoza intends\nIp28 to articulate not just a necessary condition on modal existence\nand determination, but the exclusive means by which finite modes are\nbrought to existence and determined to have any particular effects.\nThis seems to allow no room for action of bodies in their own right,\nno residual space for any contribution to the motions of bodies of the\nactive striving of the moving bodies themselves. Moreover, Spinoza\nexpressly denies that nature is a teleological system, and claims that\nfinal causal/teleological explanations “turns nature completely\nupside down. For what is really a cause it considers as an effect, and\nconversely, what is an effect it considers as a cause”\n(Appendix, I).", "\nIn this light, the problem from the standpoint of the metaphysics of\nExtension — the basis of physical theory—is to explain why\nthe specific configuration of a given existing mode makes any\ncontribution at all to the determinations that result from the\noperation of external modal causes. It would be rash to read Ip28 in\nsuch a way that the causal powers of a body owe everything to the\ncontributions of extrinsic causes, and nothing to the intrinsic nature\nof the body itself. Spinoza says in IIp13s A1 that “all modes by\nwhich a body is affected by another body follow both from the nature\nof the body affected and at the same time the nature of the affecting\nbody, so that … different bodies may be moved differently by\none and the same body.” (This is a key point in Spinoza's\naccount of corporeal imagination, mental representation and the first\nkind of knowledge, offered at IIp17–41.) So the nature of an\naffected body makes a difference to the way it is affected\nextrinsically. This is not surprising. But then what explains why a\nbody's nature makes a contribution to the way extrinsic influences\ndetermine it? As we saw in the previous sections, some answer to this\nquestion is required to make sense of the PLMM, and hence of all of\nthe collision laws. The notion, shared by the teleological reading of\nconatus and the active reading of Spinozistic inertia, that it is in\nthe nature of bodies actively to strive of their own power, would seem\nto help. But is it Spinozistic? At a minimum, any articulation of this\nnotion must be free from illicit teleology. Carriero (2017)\nsuggests a non-teleological reading of the conatus doctrine that seems\nsuitable. On his view, conatus should be understood as an\nexpression of the idea that it is constitutive of their finite\nindividuality that individuals maximize their being. \n“Dynamic constructions do tend to maximize their being. But\nthis is not because their reality is their end or good; it is an\nartifact of their stability as real individuals in the plenum”\n(152). But what accounts for this stability? We require a\nmore probing examination into Spinoza's conception of the nature of\nindividual bodies." ], "subsection_title": "3.4 Striving and teleology" } ] }, { "main_content": [ "\nAs noted above, Spinoza accepts the basic Cartesian view that physical\nthings are res extensa—extended things. However,\nwhereas Descartes held that distinct bodies are distinct extended\nsubstances, Spinoza famously holds that there is but one\nsubstance—God or nature—and that distinct bodies are\nmerely modes of this one substance, considered as extended. Spinoza's\nsubstance monism is in part motivated by inadequacies in the Cartesian\nview. Descartes officially defines substance in terms of independence:\na substance is that whose existence depends upon no other thing. But\nonly God satisfies this definition, all other beings depending on God\nfor their existence. So Descartes also allows for finite\nsubstances—minds and bodies—that are dependent only upon\nGod. But it is only in an equivocal sense that both God and created,\nfinite bodies and minds are substances. Spinoza will have none of\nthis. For him, independence is the sine qua non of substance,\nand nothing that is not its own cause — nothing whose existence\nis not of its essence—is independent. Hence nothing finite and\ncreated is substantial. Further, since everything is either in itself\nor in another (Ia1), finite things like bodies are in substance, that\nis, they are in some way features of the one substance.", "\nThis denial of substantiality to bodies gives rise to an important\ninterpretive issue. The traditional concept of a substance has at\nleast two important strands. One is the idea we have already seen, of\nsubstance as independent. Spinoza clearly means his\n‘demotion’ of bodies to modal status to be a denial that\nthey are substances in this sense. But another is the idea of a\nsubstance as an ultimate subject of predication, that is, as something\nof which properties or relations may be predicated, but which is\nitself never predicated of anything else. Does Spinoza mean to deny to\nbodies and other finite things this status as an ultimate subject as\nwell? That is, is talk of bodies fundamentally to be construed for\nSpinoza as predicative or adjectival on substance? Or do bodies,\nthough they are not substances, nonetheless lie on the subject side of\nthe subject/predicate divide, themselves bearers of properties, but\nnot strictly properties of anything else? This matter is of the utmost\nimportance for the understanding of Spinoza's physical theory, since\ndeciding that Spinoza held bodies to be in fact ways substance is and\nadjectival on it, in accord with the former interpretation, requires\nthat bodies as ordinarily conceived must be thought of as arising from\nand reducible to some more fundamental qualitative variation in\nspatiotemporal regions of extension. This has the consequence, to some\ncommentators salutary, of rendering Spinoza physical theory strongly\nprescient of contemporary physical views, in which ultimately physical\nnature is conceived as a field of gradient forces, bodies being not\nultimate, but rather the consequences of particular local\nconcentrations of certain classes of those forces, yielding certain\ncharacteristic effects in interactions, which effects we take as\nmarking the presence of bodies.", "\nIn favor of the adjectival reading (promoted by Bennett 1984) is\nSpinoza's use of the term “modus”, or “mode”,\nin connection with bodies; this term regularly signifies a way\nsomething is, or a feature it has, functioning to group what are\nclearly predicates of things, and in Cartesian usage it means both\nthis and a dependent being. Against the adjectival reading, and in\nfavor of the view (promoted by Curley 1988) that Spinozistic bodies\nand minds are ultimate subjects of predication, is Spinoza's\npersistent references to bodies as individuals and as \n things.[5]\n\nThe\nadjectival view of bodies, unlike the subjectival, must therefore face\nthe difficult general question how individuals or things can be\npredicated of other individuals or things. However, the question of\nhow bodies are individuated—the principles according to which\nthey are distinguished from one another and maintain identity through\ntime and change—presents especially interesting and thorny\ndifficulties for both the adjectival and subjectival views of\nbodies." ], "section_title": "4. Bodies as modes of substance and as individuals.", "subsections": [] }, { "main_content": [ "\nWhile Descartes does claim (at least most of the time) that individual\nbodies are distinct substances, he does not invoke this claim in his\nofficial account of the individuation of bodies. The account he does\noffer is highly problematic. Descartes holds “all the variety in\nmatter, and all the diversity of its forms, depends on motion”\n(Principles 2.23). Thus the distinction between bodies is\nconstituted of distinctions in the motions of regions of extension. On\nthe other hand, Descartes defines motion “in the strict sense of\nthe term”, as the relative change of position of a body relative\nto those bodies with which it is immediate contact\n(Principles 2.25). The circularity here is obvious, and\ncrippling. Diversity and variety of bodies depends on motion, but\nmotion depends upon a prior distinction between bodies.", "\nThat Spinoza was aware of the problem Descartes' views had accounting\nfor variety in extension is clear: in the late and much discussed\nletter 83 to Tschirnhaus, Spinoza writes,", "\nWith regard to your question as to whether the variety of things can\nbe demonstrated a priori solely from the conception of Extension, I\nbelieve I have already shown sufficiently clearly that this is\nimpossible, and that therefore Descartes is wrong in defining matter\nthrough extension; it must be explicated through an attribute that\nexpresses eternal and infinite essence.\n", "\nSpinoza goes on to express the hope that he may live long enough to\ndiscuss these matter more clearly, since “there has been no\nopportunity … to arrange these matters in proper order.”\nHe died before the opportunity arose." ], "section_title": "5. Individuation of bodies and the variety in matter", "subsections": [ { "content": [ "\nBut perhaps he did present all the elements of these matters, though\nin improper, hence inadequate, order. The obvious place to look for\nsuch a presentation is in the so-called “Physical\nInterlude” (hereinafter PI) following IIp13s, in which Spinoza\ngives his most extended and detailed discussion of his own views about\nthe nature of bodies and their principles of distinction and\nindividuation. But the PI seems to offer little\n help.[6]\n First, at least at the time of letter 83, Spinoza thought that what\nwas needed to help explain variety in matter was an appeal to an\nattribute that expresses infinite and eternal essence. Yet the text of\nthe PI makes no appeal to the infinitude, eternality or expressive\nnature of extension or any other attribute. More importantly, at least\non the face of it, the account of the individuation of bodies\npresented in the PI moves in much the same futile circle as that\noffered by Descartes. That motion serves to individuate bodies is\nquite explicit in PIDL1: “Bodies are distinguished from one\nanother by reason of motion and rest, speed and slowness.” PID5\ngoes on to define “body, or Individual”, in terms of\nmotion, and in a way that presupposes a plurality of bodies:", "\nWhen a number of bodies, whether of the same or of different size, are\nso constrained by other bodies that they lie upon one another, or, if\nthey so move, whether with the same degree or different degrees of\nspeed, that they communicate their motions to each other in a certain\nfixed manner, we shall say that those bodies are united with one\nanother and that they all together compose one body or Individual,\nwhich is distinguished from the others by this union of bodies.\n", "\nSince “body or individual” is here defined in terms of the\nrelations among a plurality of bodies, PID5, to the extent it is meant\nto cover all bodies, is at best an inductive step of an inductive\ndefinition of body. The obvious candidates for the base case are what\nSpinoza calls “the simplest bodies”, but the description\nand differentiation of these is likewise in terms of their motion and\nrest. Indeed, they “are distinguished from one another\nonly by motion and rest” (PIL7s, italics\nadded).[7]\nSpinoza, then, appears to\naccord with Descartes in taking bodies to be distinguished by their\nrespective motion and rest. But motion and rest seem in the first\ninstance to be determinations of bodies. So the motion of\nbodies seems to presuppose a prior ground of their individuation.", "\nCommentators have tried various strategies for finessing the apparent\ncircularity in the PI's account of the diversity in matter. Klever\n(1988) urges that the key to understanding Spinoza's concept of matter\nis to see that physical nature is not to be conceived as an infinite\nextended expanse that somehow is put into motion, but as,\nfundamentally, matter-in-motion (“moles in\nmotu”). According to Klever, “movement and rest in\nextension are examples of immediate production by God, whereas the\nface of the universe with its infinite variations is an example of the\nmediate effects, which are a product of movement in its turn.”\nOn this interpretation, Spinoza, rather than seeing motion as a\nreceived quality of matter, conceives “matter as consequence of\nmotion” (Klever 1988, p. 171). This reading arguably answers\nSpinoza's call to explain the variety in matter through an attribute\nthat expresses eternal and infinite essence. If God creates extended\nmatter, and then, in a separate act, sets it in motion, the attribute\nof Extension would not suffice as an eternal expression of infinite\nessence, since it requires God's additional action in its expression\nof power." ], "subsection_title": "5.1 The Physical Interlude" }, { "content": [ "\nBut if this is right, then “motion and rest” of the\nphysical interlude cannot simply be the ordinary motion and rest of\nbodies. What then are they? Klever waxes vague and anachronistic here,\nstraightaway seeking to validate his claim rhetorically by citing it\nas precedent of the view of contemporary physics: “in this\nreversal [Spinoza] anticipates modern physics by which mass is\nconsidered as product of energy” (ibid). (Hampshire (1987)\ncontains similar remarks).", "\nJonathan Bennett's influential reading agrees that Spinoza's physical\ntheory anticipates contemporary views. He also agrees that when\nSpinoza talks about “motion and\n rest”[8]\n he is not invoking these terms in their ordinary senses. But rather\nthan simply identifying motion and rest with energy or any other trope\nof contemporary physical theory, Bennett holds that the terms function\nas mere placeholders for some basic physical quality, unknown to\nSpinoza, but required to make sense of the appearance of\nbodies—ostensible things or subjects of predication\n— in the context of a metaphysics that holds that bodies, as\nmodes rather than substances, are not things or subjects at all, but\nrather ways that the one substance is. According to Bennett, Spinoza's\nExtension is, at the fundamental metaphysical level, a four\ndimensional field whose regions differ in the distribution and degree\nof this basic quality. Bodies are appearances, at one or more levels\nremoved from this base, of the continuous path in this field\nconstituted by relatively consistent local patterns of distribution of\nthis quality. The ordinary “motion” of an ordinary\n“body” is to be understood on the analogy with the way a\nthaw traverses a terrain. When the snow line recedes, there is no\nthing that changes its place; rather, there is a change in which\nregions of the landscape have the quality of being snow-covered, and\nthat change describes a continuous path.", "\nOne might object to that this analogy is not clearly persuasive.\nShifts of temperature lead to a thaw only because\nbodies—ice crystals and aggregates thereof—melt as\ntemperature rises, and their boundaries recede along the backdrop of a\nvery bodily landscape. Indeed, to thaw is just to pass from a solid to\na liquid state, and solidity is a benchmark of the bodily. If we\nexcise these bodily aspects of the analogy, it is unclear how much of\nits explanatory force remains. But then it is unclear just how well\nqualitative variations of fields can explain the appearance of bodies.\nPerhaps if we knew more about this quality, the sense in which such\ncontinuous paths of patterns of it could appear as or constitute\nbodies would be clearer. Garrett (1994) adopts Bennett's field\nmetaphysic, and attempts to fill in the explanatory gap by providing\ndefinite senses to the PI's uses of the terms “motion” and\n“rest”. Relying on Spinoza's remark, following\nPCP IIp22, that “by force of moving bodies, we\nunderstand a quantity of motion …. In bodies at rest, we\nunderstand by force of resisting a quantity of rest”, Garrett\nclaims that by “motion” and “rest” in the PI,\nSpinoza means a quantity of force that moves a thing and a quantity of\nforce resisting such imposed movement, respectively. Furthermore,\nthese quantities can be ascribed, he says, to the regions of extension\nthemselves, rather than to bodies, thus overcoming the circularity\nproblem we found in Descartes. But it is unclear that Spinoza's text\ncan support this interpretation. PCP IIp22 speaks of the\nforce or motion “in” a body. Spinoza elaborates: “By\nforce in moving bodies, we understand a quantity of motion, which must\nbe greater, in bodies of equal size, as the speed of motion\nis greater … . But in bodies at rest we understand by\nforce of resisting a quantity of rest” (emphasis added). In each\nmention, the force or resistance is attributed to a body. This\nstrongly suggests that quantity of motion and rest, as force and\nresistance, are features of\n bodies.[9]\n Moreover, even supposing that it makes interpretive sense to ascribe\nforce and resistance directly to regions, what is being attributed to\nthese regions seems to be a power to move bodies or to slow\nbodies down. Rather than showing how bodies could just be, or\narise from, fields of such forces, the forces themselves seem to be\ncharacterized in ways that presuppose body; the circularity, then,\nremains.", "\nIndividual bodies have an inherent stability, or robustness. They\nresist destructive incursion or change in their distinctive mode of\nendurance; they tend to persist in their configuration and motion in\nthe face of opposition to this persistence. Spinoza certainly accepts\nthis, as PID and IIIp6 show. If bodies either are, or are appearances\nof, persistent patterns of qualitative variation of extended regions,\nthen it seems necessary, though hardly sufficient, that something\nabout such patterns would have to account for this stability. But what\nmight do so? In effect, this is to ask what would account for the fact\nthat distributions of “motion” and “rest”,\nconceived of as predicates of extended regions, do not vary randomly\nthrough time. One suggestion is that nothing accounts for this\nstability at all, and that the duration of a body is nothing more than\nthe time through which a given complex ratio of motion and rest\nhappens, de facto, to characterize regions of extension whose sum over\ntime describes what can be construed as a continuous path. There is\nnothing to prevent such spatiotemporally continuous patterns from\noccurring. But there is nothing in being a time slice of such a\npattern that explains why the same pattern should also characterize\nany other spatiotemporal region continuous with it. There may, indeed\nmust, be kinematic 'laws' describing how such patterns vary (the scare\nquotes cause the counterfactual supporting status of such 'laws' would\nbe secured only by Spinoza's necessitarianism), but nothing about any\ngiven time slice of such patterns accounts for the fact that they are\nsubject to just those descriptive 'laws'. Individual time-slices of\nsuch patterns would be wholly passive with respect to the persistence\nand trajectory of the pattern as a whole.", "\nA significant problem with this\n line[10]\n is that Spinoza uses manifestly active language to describe the\ndoings of individuals. For example, IIId3 defines “affect”\nas “affections of the body by which the body's power of\nacting is increased or diminished, aided or restrained, and at\nthe same time the idea of these affections” (emphasis added).\nAnd in IIIp6, on which the entire psychological theory of the second\nhalf of the Ethics depends, Spinoza claims that individual\nthings strive to persevere in their being; his subsequent\nuses of the IIIp6 seem clearly to suggest that Spinoza intends this\nstriving to be understood as an a active principle rather than a mere\ntendency. On the conception of individuals as ratios of motion and\nrest that simply happen to endure, none of this would make\nany sense at all.", "\nViljanen, who also adopts Bennett's field metaphysic, with its\nimplicit denial that Spinozistic “motion and rest” is to\nbe granted an ordinary signification, attempts to accommodate this\nconception of bodies as active and potent by reading the spatial field\nas a field of power, and bodies as constituted by differences in the\nintensity or strength of this power (Valjanen 2007, p. 402), and\napparent motion as the redistribution in that field of various\npatterns of intensification of that power (ibid., p. 403). He\nfurther interprets the “simplest bodies” of the PI —\nthe basic constituents of all complex individuals — to be\ndistinguished as “rudimentary intensifications of spatial power,\nor extended power quanta, that invariably change place” (Ibid.,\np. 408). But the question arises once again what the powers of which\nthese quanta are “intensifications” are powers to\ndo. They cannot, for reasons already mentioned, be powers to move\nor to resist bodies. The most obvious answer, in the Spinozistic\ncontext, would be “powers to persevere in its own being”.\nBut to let the matter stand there would be simply to name the problem\nrather than to explain it. To the questions “why does this\ndegree of spatial power persevere and endure in the (continuous) place\nand time to the extent that it does?”, the answer would seem to\nbe “because of the degree of power to persevere that constitutes\nit”. But that is just to say that it manifests the powers it\ndoes because of the powers it has to do so — not very\nilluminating. “Motion and rest” as power appears to\nprovide either an incomplete or vacuous theory of indivuation.", "\nMoreover, if a body's motion in a spatial field, including that of the\nsimplest bodies, is just a change of location at which a given degree\nof power is instantiated, then there seems to be no means of\nexplaining why a particular degree of power would necessarily change\nlocations — move — continuously, as opposed to\ndiscontinuously. But surely it is in the nature of bodies as\nexplananda here that they are spatiotemporally continuous.\nFurthermore, if what individuates “quanta of power” are\njust their degrees of intensity — their degrees of power to\npersevere — then anywhere that degree is instantiated, that very\nsame body should be. But this would be consistent with the unlikely\nidea of discrete, discontinuous motion of a body, and indeed with the\nbi-location of bodies, that is, with the idea that a single body might\nbe wholly present in each of multiple regions. Assuming that Spinoza\nwould not accept these possibilities, the theory of “motion and\nrest” as signifying spatial regions of power distinguished by\ndegrees of power fails to account for signal characteristics of body.\nIt is thus doubtful that the inadequacy of Descartes' identification\nof body with extension can be overcome simply by predicating regions\nof extension with different degrees of “power”.", "\nThere are, then, reasons to doubt that granting Spinoza's “rest\nand motion” a non-ordinary signification—energy, an\nunspecified basic quality, force of motion and resistance,\nintensifications of power — can in fact give us insight into the\nconstitution or appearance of persisting, resistant, active bodies.\nBut it is worth asking whether these doubts in fact rest on an\ninappropriate imaginative basis. It seems difficult imaginatively to\nrepresent variegated fields of energy, force, or any other quality in\nsuch a way as to make clear how bodies, with the persistent resistance\nand capacities for interaction we ordinarily represent them to have,\ncould possible appear from or be constituted by them. But this sort of\nfailure of imaginative thinking cannot count against the acceptability\nof a theory from a proper Spinozistic perspective. On his view, our\nknowledge of body as an object of imagination is inherently\ninadequate. Our imaginative ideas of bodies in their corporeality are\nlimited to the ideas of modifications of our own bodies. These in turn\nreflect only in a confused and partial way the natures of both the\nbodies with which we are affected and our own. At no time is the full\nnature of any body reflected in any of the ideas we have through these\naffections, hence through anything we can imagine. Hence our\nimaginations cannot grasp the nature of body, and failure of the\nfaculty of imagination to provide insight into the link between the\nfundamental basis for variety in matter and that variety itself is to\nbe expected. All of this is clear from IIp16–31. Any appearance\nof insight into the nature of body gleaned from the imagination is as\nlikely to be illusion as illumination. And, as Schliesser (2017)\nremarks in emphasizing Spinoza's skepticism about knowledge of the\nnatural world, for Spinoza, “when we locate things at a time and\nplace, we are always in the realm of the imagination”\n(p. 175).", "\nBut if we cannot come to an imaginative grasp of how bodies or their\nappearances might be constituted out of fields, then through what sort\nof intellectual act might we do so? In the context of early modern\nphilosophy of physical nature, and in particular the Cartesian\nphilosophy in which Spinoza is steeped, the clarity and distinctness\nof mathematical ideas provides the contrast to the incompleteness and\nconfusion of ideas of the imagination and sensation. And certainly the\nquantifiability of properly physical qualities, and consequently their\ncomprehensibility within a closed system of mathematical laws, is of\nthe utmost importance to the credentials of the fundamental notions of\nthe contemporary physical theory Spinoza is alleged to have\nanticipated. The scientific success of classical mechanics, relativity\ntheory, and, especially, quantum mechanics owes much more to the\npredictive and formal success of these theories than it does to our\nabilities to represent phenomena in the imagination that answer to the\nbasic physical elements they countenance. Point masses, gravitational\nforces operating at a distance, curvatures of space time, finite but\nunsurpassable velocities, and wave-packets all seem to surpass our\npowers of imaginative representation. We have no real capacity to\nimagine how the solid table on which my computer rests can be\nidentical to both a swirling cloud of particles and a warp in the very\nfabric of space. On the other hand, these fundamental scientific\nnotions can be rendered mathematically, placed within a system of\nlaws, and employed to great effect in predicting and manipulating,\nhence effectively representing, the same nature we represent\nimaginatively.", "\nThus perhaps the proper criterion, or at any event a proper\ncriterion, for the success of an Spinozistic account of variety in\nmatter and its individuation into bodies is the quantifiability of the\nbasic properties in which it proceeds. Gabbey stresses this line with\nadmirable clarity.", "\nTo talk of bodies maintaining among themselves “the same\nproportion of motion and rest,” or communicating motion to each\nother “in a certain fixed proportion” is to say nothing\neffective, unless a mathematical account is provided of those\nproportions and of the measures of motion and rest from which they are\nformed, and unless there is some account of the laws that ensure the\nclaimed invariance in proportionalities. Spinoza provides no such\nlaws, nor does he say how the proportions are to be mathematically\nexpressed (Gabbey 1996, p. 168).\n", "\nGabbey concludes that the theory of bodily individuation by ratio of\nmotion and rest “lacks quantitative anchoring”, and is\nthus “too vague to allow a assessment of what is being\nclaimed” (Gabbey 1996, p. 169).", "\nThat Spinoza did not himself provide the mathematicization of his\nnotion of motion-and-rest that would render his theory of body\nnon-circular and sufficiently clear to be understood (or imagined)\ndoes not entail that this cannot be done. A number of commentators\nhave attempted to show that Spinoza's account of variety in matter by\nappeal to “motion and rest” can be so rendered. Garrett,\nwhose account we have already examined, nods his head in this\ndirection. Recall that PId5 defines an individual as being composed of\nbodies that “communicate their motions to one another in a\ncertain fixed manner”. Later lemmas characterize this fixed\nmanner as a “ratio” of motion and rest. Notwithstanding\nhis realization that, for a number of reasons, such a ratio must be\nunderstood as a pattern rather than a numerical proportion, Garrett's\nexpresses sanguine confidence that “any such pattern could be\nexpressed by a mathematical formula” (1994, p. 86). Matson\n(1990) also places weight on the possible quantifiability of motion\nand rest as a means of in rendering it a clear and distinct,\nnon-imaginary basis for our understanding of the individuation of\nbodies, taking the idea of an atomic number as his model:", "\nBeing element No. 16 “pertains to the essence” of sulfur,\nas being yellow and smelly do not. One can in a sense\n“imagine” sulfur by its color and odor; but only by\narticulating it into the attribute, as the atomic number does, can one\nunderstand it…. ‘Element No. 16’, together with the\ncomprehensive theory in which this conception is embedded, is a\nspecification of ‘motion and rest’, indicating, in fact,\nthat particular unique ‘proportion of motion and rest’\nthat is the necessary and sufficient condition for being sulfur.\n(Matson 1990, pp. 88–89).\n", "\nMatson piggybacks on to this analogy the formula for the identity of\nany living thing supposedly found in its genetic code.", "\nIf it is right to think of atomic numbers as the specifications of\nmotion and rest for certain stuffs, in the case of the human being (or\nany living creature) the obvious analogue is the genetic code, the\nformula for the structure of the individual's (quasi-unique) DNA\nmolecule (Matson 1990, p. 89).\n", "\nTreating such structures as representable by formulae enhances the\nimpression that they are expressible in numerically quantifiable\nterms.", "\nSuch attempts to interpret motion and rest as numerically expressible\nquantities constitute efforts to make Spinoza's physical theory\nrelevant to contemporary science, by displaying how it can conform to,\nand even constitute a blueprint for, its mathematical structure. They\nstand, then, as responses both to Gabbey's implication that because\nSpinoza does not say how his notion of motion and rest can be\nexpressed mathematically, his views are too vague and sterile to be of\nsuch contemporary relevance, and to the difficulties we have seen, in\nconceiving how motion and rest, as we conceive them imaginatively,\ncould possibly serve to individuate bodies. But at the end of the\nfinal section of this article, we will see that, quite apart from the\nvagueness, anachronism (Spinoza anticipating not just Mendeleyev, but\nalso Watson and Crick?) and other interpretative difficulties faced by\nsuch attempts, there are reasons to suppose that any effort to render\nbasic principles of physical theory through numerical quantification\nmay run deeply counter to Spinoza's own attitude." ], "subsection_title": "5.2 Interpreting “motion and rest”" }, { "content": [ "\nIn the previous sub-section, we saw reasons for doubting the adequacy\nof readings that treat the PI's talk of motion and rest as\nconstituting his entire account of \n individuation.[11]\nThis section considers an\nalternative interpretation of Spinoza's approach to individuation.\nThis account appeals to the notion of individuating essences.", "\nIn IId2 Spinoza says:", "\nto the essence of a thing belongs that which, being given, the thing\nis necessarily posited and which, being taken away, the thing is\nnecessarily taken away; or that without which the thing can neither be\nnor be conceived, and which can neither be nor be conceived without\nthe thing.\n", "\nThis does not quite offer a definition of “essence”, but\nrather defines what belongs to it. IId2 speaks of the essences of\n“things.” Individuals, or singular things, are surely\nthings. If what belongs to the essence of an individual is given (by\n“given” Spinoza means “posited as existing”),\nthen so too is the individual. This suggests that the essence of an\nindividual is particular to that individual, since otherwise, what\nbelongs to it could be given without that individual being posited, so\nlong as some other individual with that essence were\n posited.[12]", "\nBut how are we to conceive essences, and how can they help solve the\nproblems we have encountered with claiming the PI, with its talk of\nmotion and rest, provides Spinoza's full account of individuation? In\nthe Preface to Ethics Part IV, Spinoza writes:", "\nWhen I say that someone passes from a lesser to a greater perfection,\nand the opposite, I do not understand that he is changed from one\nessence, or form, to another… . Rather, we conceive that his\npower of acting, insofar as it is understood through his nature, is\nincreased or diminished.\n", "\nHere Spinoza writes as if a body's essence and its form are one and\nthe same. In each of PIl4, 5 and 6, Spinoza speaks of bodily\npersistence in terms of its parts keeping the same ratio of motion and\nrest. If the parts do so, the body, says Spinoza “will retain\nits nature, as before, with no change of form”\n(emphasis added). PIl7 also speaks of a body's retaining its\n“nature”, despite change. These are plainly meant to state\nconditions on individual persistence. These lemmas seem to equate\nnature and form. So by transitivity of identity, form=nature=essence.\nMoreover, Spinoza implies that so long as this form or essence is\nretained, a thing is not destroyed. “Form”,\n“nature” and “essence” than, refer to\nsomething in virtue of the persistence of which an individual retains\nits identity.", "\nIn a series of propositions leading up to and supporting IIIp6's\narticulation of the conatus doctrine, Spinoza also treats\n“essence” and “nature” as synonyms, and\nassigns them to things independently of the attribute under which they\nare considered. IIIp4 is worthy of particular attention here. It\nstates: “No thing can be destroyed except through an external\ncause”. Garrett (2002) persuasively argues that\n“external” here contrasts, not with “on the\ninside”, but with “inherent”, where inherence is a\ntechnical notion referring to what belongs to a thing in virtue of its\nessence. This includes both the thing's essence and those properties\nfollowing from it. These are all “in” the thing. However,\na thing may also have accidental properties, which are\n“in” it in the general sense in which that which is\npredicated of a thing is in it, and may also be “in” it in\nthe sense in which one region surrounded by another is in it, but\nwhich do not inhere in it. Such properties, in the thing in one sense\nbut external to it in another, may be destructive of the thing. In\nIIIp4d, Spinoza writes “while we attend only to a thing\nitself, and not to the external causes, we shall not be able to\nfind anything in it which can destroy it” (emphasis\nadded). Reading “in” here in the sense of\n“inherent”, and “external” in the sense of\n“not inherent”, this passage suggests that to attend to a\nthing itself is just to attend to its essence—what is affirmed\nin its definition—and what follows from it. To attend to what is\nnot inherent in it is to attend to what is external to it, to\nsomething else. An actually existing thing, then, such as an existing\nbody, is its essence brought to existence. So long as a thing retains\nits essence=nature=form, it retains whatever inheres in it, and\nendures as the same individual.", "\nThe appeal to individuating essences accounts for the robust\npersistence of bodies. In IIIp6 Spinoza says that “Each thing,\nas far as it can by its own power, strives to persevere in is own\nbeing”. In arguing for this conatus doctrine, Spinoza states\nthat “singular things” are that “by which God's\nattributes are expressed in a certain and determinate way, i.e.,\nthings that express, in a certain and determinate way, God's power, by\nwhich God is and acts”. “Things” here takes the\nactive position. Things express power; they do the\nexpressing. They are not mere expressions of it. Power is\nexpressed by things, rather than merely through them. Because\nthis is an active expression of power, the thing not only persists\nthrough externally caused changes, but opposes those changes which\nwould tend to destroy it, i.e., to keep it from expressing God's power\nin the way which constitutes its essence. Finally, in IIIp7, Spinoza\nexpressly identifies this striving with the thing's essence;\n“the striving by which each thing strives to persevere in its\nbeing is nothing but the actual essence of the thing.”", "\nThus the form or essence of a thing, which individuates it, and whose\nretention through change constitutes the persistence of an individual,\njust is its inherent and individual power of striving to retain just\nform, hence to resist those extrinsic determinants that would diminish\nits power and destroy it. In the case of body, striving is expressed\nby the active tendency of a pattern of relative motion and rest, in\ntheir ordinary sense, of its parts to persist. The active tendency of\nthat pattern to persist is the essence of the individual body. That\npattern is determined in its existence transiently and externally; now\nthis way, and now that, now larger, now smaller, now swifter, now\nslower, now with these parts, now those. Such transient, external\ndetermination may give it accidental properties that oppose and hinder\nthe power of action it has in virtue of what inheres in it, and hence\nlimit its power of action. Another virtue of the idea that essence as\nactive striving is what individuates bodies is that it would provide a\nbasis in the nature of body for the principle of inertia, in such a\nway that inertia could be taken as a ground for the PLMM we earlier\nsaw was needed to underwrite the collision laws.", "\nHowever, this view is certainly not without its \nproblems.[13]\nIndeed, one of its strengths—helping to ground inertia in the\npersistent activity of bodies — is a weakness. We saw earlier\nthat it is not easy to square this active reading of inertia, grounded\nas it is in the idea of motion pertaining to the action proper to a\nbody, with a good deal of what Spinoza says in the first and second\nparts of the\nEthics about how no body can be determined to produce an\neffect unless is it so determined externally. Another, related problem\nfor this interpretation is that it represents Spinoza as, not an\navant-garde thinker anticipating modern physics, but as a rear guard\ndefender, despite his official anti-scholastic stance, of the\ntraditional neo-Aristotelian doctrines of essence and substantial\nform, open to the same charges of ad hoc theorizing and of\nappeal to occult powers that Modernity and the Scientific Revolution\nlevelled against that tradition in their rise to intellectual\ndominance. Indeed, the notion of the individual essence of a body\nconceived as a power to maintain itself is of dubious intelligibility.\nSpinoza clearly believes that an individual's power to persevere can\nincrease or diminish. But if this power is to constitute the thing's\nessence and identity, such changes in degree cannot alter the identity\nof the power. But what then constitutes the individuality and identity\nof a power? In this light, the account of individuation by essence\nseems unexplanatory: either it amounts to an elaborate name for the\nproblem of the individuation of bodies it is supposed to solve, or it\nsimply displaces the same sort of problem from bodies to powers.", "\nThe problem we have been addressing is to find in Spinoza a\nsatisfactory ground for the idea that modes of extension consititute\nbodies to which dynamical laws like the laws of collision should\napply. We have characterized that problem in terms of the\n“robust persistence” of bodies – their resistance to\nchange. Barry (2021) presents a detailed and complex treatment of\npossible ways Spinoza might be thought to account for the resistence\nto change bodies manifest in the dynamics of collision. He argues\nthat neither Spinoza's account of inertia nor the conatus doctrine can\nsupport resistance, and that a more direct appeal to modes as\nexpressions of God's power or activity cannot do so either. He\nsuggests tentatively that, via Spinoza's parallelism (EP27), the\nresistance characteristic of bodies might instead be read off of the\nresistance relatively adequate ideas have to alteration in the face of\nrelatively less adequate ideas. This reverses the more usual\ndirection of reading off features of ideas from those of their modal\ncounterparts in extension; but, despite Spinoza's remark in letter 27\n(to de Vries) that ethics is to be founded on metaphysics and physics,\nturnabout here should be fair play. As Barry recognizes, however,\nsince not all features of modes of one attribute can be applied to the\ncounterparts under the other attributes, there must be something\nidentifiable in bodies that corresponds to the adequacy of ideas in\nvirtue of which they resist other ideas if the strategy is to work.\nThe extended counterpart of adequacy Barry fixes on is the degree to\nwhich the collection of component bodies whose relation consitutues a\ncomposite individual body communicate their rest and motion to one\nanother in a fixed manner, as discussed in the PI. One might argue\nthat, had Barry taked that idea seriously enough in his discussion of\ninertia and the PI, the detour through Thought via the parallelism\nwould have been unnecessary. In any event, Barry worries here that\nappreal to adequacy explains at best resistance to change i.e., the\nability of a body to retain the same ratio of motion and rest in a\ncollision, but not the ability to produce a change; i.e., the power of\na body to move or alter another, both of which powers Spinoza clearly\nattributes to bodies.", "\nWhether there is a sufficient Spinozistic ground for for a unified\nconception of the power of modes both to resist and to bring about\nchanges in other modes of the the attribute under which they are\nconsidered remains an open question. It seems likely, however,\nthat reading the PI, the conatus doctrine, and Spinoza's accounts and\njustifications of inertia and the dynamical laws in the light of\nthe fact that modes each express in their own way the\ninfinite actvity and power of the one substance provides the\nbest hope for illuminating such ground. " ], "subsection_title": "5.3 Individuation by essence" } ] }, { "main_content": [ "\nAttempts to find anticipations of contemporary scientific physics in\nSpinoza's thinking about the physical face a number of challenges\nbeyond simple anachronism. Contemporary physics is both resolutely\nexperimental and resolutely mathematical. However, there is reason to\nsuppose that Spinoza had dim views of both experimental method in\n science[14]\n and the prospects for an insightful mathematical description of\nnature." ], "section_title": "6. Spinoza and the experimental and mathematical sciences", "subsections": [ { "content": [ "\nIt is by now widely accepted that observation is “theory\nladen”, and that therefore the idea that scientific theory\nproceeds through the neutral collection of data is bogus. Studies in\nthe logic of confirmation have likewise put an end to the\nsimple-minded idea that experimental method involves devising crucial\nexperiments whose results can, as a matter of logic, falsify a theory,\nor force a choice among competing theories. Nonetheless, modern\nscience is still thoroughly empirical, relying heavily and essentially\non observation and experimentation in the generation, development, and\ntesting of theories. The truism that one can always save a theory by\nrejecting auxiliary assumptions or discrediting data—reports of\nobservation—does not change the facts that, in practice,\nobservational results are taken to refute theories, and the ability to\npredict and explain a wide range of observable phenomena better than\nrivals remains the gold standard in scientific method.", "\nSpinoza, however, discounted the relevance of observational data to\nthe discovery of truths of nature. His conception of sense experience\nseems, in fact, to disqualify it from being a reliable source of\ninformation about the world altogether. He held that sense experience,\nin which the human body is affected by external bodies, can never\nprovide us with adequate ideas of either external bodies or our own.\nHe seems moreover to have denied that the method by which we discover\nnew truths involves either the collection of new sensory evidence or\nthe construction of crucial experiments. Indeed, much of the early\nTreatise on the Emendation of the Intellect is devoted to\nestablishing that “the fictitious, the false, and the other\n[ideas falling short of truth] have their origin in the imagination,\ni.e., in certain sensations that are fortuitous, and as it were\ndisconnected, since they do not arise from the very power of the mind,\nbut from external causes, as the body (whether awake or dreaming)\nreceives various motions” (EMI, ¶84). The intellect unaided\nby imagination, however construed, is the sole source of knowledge.\nObservation, which involves sensory ideas derived from external\ncauses, has no role in the true method for acquiring adequate\nknowledge.", "\nIn IIp25 Spinoza states “The idea of any affection of the human\nbody does not involve adequate knowledge of an external body”.\nSense perception—the basis of experimental observation—is\na matter of the body's being affected by external bodies. So it would\nseem that, prima facie, Spinoza cannot have held that\nobservation can be a means to an adequate knowledge of things.\nScientific knowledge—scientia—would, for Spinoza,\nhave to be adequate. Hence it seems that experimental observation\nought to be, for Spinoza, irrelevant to science. There is strong\nconfirmation to be found for this conclusion in Spinoza's accounts of\nthe kinds of knowledge.", "\nIn IIp40s2, Spinoza discusses four kinds of knowledge or modes of\ncognition. These are I) knowledge from singular things; II) knowledge\nfrom signs; III) knowledge from common notions; and IV) intuitive\nknowledge. The first two are prone to falsity, as they generate\ninadequate ideas. Cognition of kind (I) arises from objects\nrepresented “through the senses in a way that is mutilated,\nconfused, and without order for the intellect”. This is\nperception from “experientia vaga”, vague or\nrandom experience. Knowledge of kind (II) arises from hearsay, arising\n“from the fact that having heard or read certain words, we\nrecollect things, and form certain ideas of them … through\nwhich we imagine them.” Spinoza groups (I) and (II) together as\nknowledge of the first kind: opinion or imagination. Inadequate and\nconfused ideas pertain to knowledge of the first kind, and so it is\nthe sole cause of falsity. Both of the sorts of knowledge of the first\nkind depend upon what we would ordinarily call sense experience.\nSpinoza does not go so far as to assert explicitly that no true\nknowledge can ever arise from sense experience. It is only when the\nsenses present us with representations in a way that is\n“mutilated, confused and without order for the intellect”\n(IIp40s2), i.e., random, that our resulting conceptions are\ninadequate. But the question is whether there is any other way, on\nSpinoza's views about sense perception, that the senses can represent\nobjects to us. Knowledge of the third kind, intuitive knowledge, does\nnot appear to involve the senses at all. It is knowledge proceeding\n“from an adequate idea of the formal essence of certain\nattributes of God to the adequate knowledge of the essence of\nthings” (IIp40s2). This knowledge, then, arises from the\nintellectual consideration of the essence of an attribute itself,\nrather than from sensuous commerce with modes of that attribute.\nKnowledge of the second kind, reason, seems a more plausible candidate\nfor arising from experience. This is based on the so-called\n“common notions”. Common notions are conceptions of things\n“which are common to all, and which are equally in the part as\nin the whole” IIp38. Such conceptions can only be adequate, and\nthis would guarantee that the knowledge arising from such conceptions\nis true. Spinoza also allows that if there were something common and\npeculiar to the human body and external bodies by which it is\naffected, and equally in the part as in the whole of each, then the\nhuman mind will conceive that thing adequately. The problem, however,\nis that given Spinoza's views about sensation is it hard to see how\nsuch common notions could arise from sensation, and to the extent we\ncan make sense of this, the common notions seem limited to ideas of\nextremely general features of physical objects, far too general to be\na source of any of the kinds of particular observational knowledge\nrequired for experimental practice. The inadequacy of a conception of\na thing results from its not reflecting the entire nature of a thing's\ncauses. Knowledge of effects is by knowledge of causes, and while\nthings can interact causally only insofar as they share something in\ncommon, there can be aspects of the causes of things not reflected in\ntheir effects. However, if a conception is of something common to an\nobject and all other things, then there can be nothing in any of its\ncauses not reflected in the conception of it itself; whatever is\npresent in the cause will be present in it as well, hence reflected in\nthe idea of it. But what, we may ask, is even possibly shared by each\nthing and equally in the part of each as in the whole? The only\nobvious candidates are properties that, as Schliesser (2017, p. 15)\nputs it, “reflect the peculiar modal qualities of … a\nmode”: in the case of extended modes, those sorts of properties\nthat follow from the nature of extension: e.g., motion and rest,\ntaking up space, being subject to motion and to the laws of geometry,\netc.. But the sorts of observational knowledge that are crucial to\nexperimental method in science are hardly exhausted by the knowledge\nthat pertains to bodies as such. Indeed, experimental observation\ndepends precisely on the observational knowledge of differences,\nrather than similarities.", "\nSpinoza characterizes experiential vaga as experience that is\n“without order for the intellect” and as “experience\nthat is not determined by the intellect” (Treatise on the\nEmendation of the Intellect, ¶19). This experience is called\n“random” because “it comes to us by chance, and\nsince ”we have no other experiment to oppose it“;\nperception attained in this mode it ”remains with us\nunshaken“. Perception from random experience can, then, be\nshaken by opposing experiment, but there is nothing here that suggests\nthis is a matter of less random experience overruling more, rather\nthan multiple random experiences conflicting with one another.\nMoreover, Spinoza really never tells us what it would be for\nexperience to be ”ordered for“ or ”determined\nby“ the intellect. It is tempting to suppose that he meant,\nfollowing Bacon, from whom the term ”experientia\nvaga“ is borrowed, that experience is not vague insofar as\nit ”proceeds by fixed law, without interruption and in regular\norder“. (Bacon, Novum Organon, Book I, Aphorism 100).\nBut it is unclear, given Spinoza's general denigration of sense\nexperience as generating only inadequate ideas of things, how the\nintellect could order the collection of sense experience by law, and\nit is equally unclear how the result of doing so would shore up the\ninadequacy of the resulting\n observations.[15]\n Bennett, who resists the standard view that Spinoza thought\nexperience irrelevant to knowledge, and cites the possibility of\nexperientia non-vaga, i.e., experience as directed\nby the intellect, as evidence for this, concedes that Spinoza is\nentirely silent about experientia non-vaga, offering\nno account of what it might be, other than ”the experience of\nsomeone who puts to nature questions dictated to him by Spinoza's\nphilosophy“ (Bennett 1984, p. 24). Bennett's suggestion that a\ncharacterization of this might have to wait until we learn more about\nhow the senses function seems a non-starter, though. For if we\nconceive the senses as objects of empirical, experimental study, then\nwe cannot learn about them until we know how to order our experience,\nso the question is begged; and if we conceive of them as objects for\nnon-experiential, non-experimental philosophical reflection, then what\nmore by way of the Spinozistic carrying out of this sort of work is\nthere to be done than Spinoza does in the\n Ethics?[16]" ], "subsection_title": "6.1 Observation" }, { "content": [ "\nSpinoza engaged in very little experimentation of his own, but he did\nshow some interest in the experimental results of others. His letters\ncontain several discussions of experimental and theoretical dioptrics,\nto be expected from a lens grinder and man of letters, as well as\ndiscussions of recent observations of comets and whether they can be\nexplained on Cartesian principles, of the new microscope, and of\nmedical and alchemical experiments. Far and away the most famous and\nsignificant discussion of experimentation are found in his exchanges\nwith Henry Oldenburg, the first Secretary of the Royal Society, who\noperated largely as the mouthpiece of Robert Boyle, and in particular\nthose concerning Boyle's experiments on solidity, fluidity, and on\nnitre. The latter of these is the most telling of Spinoza's attitude\ntowards the relevance of experiment to theorizing about nature. Boyle\nhad claimed to show that nitre (potassium nitrate) is a chemical\ncompound rather than a mixture, by having decomposed it into fixed and\nvolatile parts (potash and spirit of nitre), and then recombining them\ninto nitre with little or no loss of quantity. The disparate\nproperties of the components, he argued, showed that the nitre itself\nwas a compound, in which the components were altered and transformed,\nrather than a mere mixture. This, in turn, suggested that the basic\nconstituents of the components were preserved through the interaction,\nconfirming the corpuscular chemical theory over the scholastic view\nthat chemical transformation involves the substantial form of given\nmatter being destroyed and replaced by some other substantial\nform.", "\nSpinoza in fact agrees with Boyle that the scholastic view is\nbankrupt, but he rejects Boyle's claim that the separation of the\nnitre into two parts is actually a decomposition of a distinctive\nsubstance into two others; rather, he claims that the experiment is\nconsistent with the Cartesian view, itself based on reason, that\ndifferentiations among extended substance are always owing to\ndifferent quantities of motion and rest. He claimed that the\n”fixed nitre“ (potash) was actually an impurity mixed into\nthe original sample, and that the spirit of nitre was simply the\nvolatile state of the pure, crystallized nitre portion of the original\nmix. Thus the different chemical properties of spirit of nitre and the\noriginal sample owe not to a difference of substantial\nstructure—the basic shape of the particles of each is the\nsame—but to a difference in their motion. In support of this\nreading and against Boyle's interpretation, Spinoza claimed that, if\nBoyle were actually to show what he claimed, ”further experiment\nseems to be required to show that Spirit of Nitre is not really Nitre,\nand cannot be reduced to solid state or crystallized without the help\nof salt of lye“ (Letters, p. 71). Spinoza then went on at some\nlength to show how, in the absence of such a demonstration, it is easy\nenough to explain the results of Boyle's experiments along Cartesian\nlines. He further explains several experiments he himself performed\nwhich he takes to support the Cartesian interpretation, claiming that\nhe ”might have added further experiments which would perhaps\nmake the matter quite clear“ (Letters, p. 76).", "\nWhat matters here is not who is right in this dispute, nor whether\nSpinoza's Cartesian view is in fact coherent, but Spinoza's strategy.\nFor it is hardly an evenhanded assessment of the experimental results.\nSpinoza shows considerable ingenuity in interpreting the results of\nBoyle's own experiments to be consistent with the Cartesian view, and\nhis own as (nearly, anyway) proof positive of it. But he shows no\ninclination to pursue the question whether his own experimental\nresults can be interpreted along the lines of Boyle's hypothesis,\nwhich they can be, easily enough, as Boyle's response (letter 11)\nshows. Indeed, Boyle complains overall that Spinoza's interpretations\nof the experimental results are wholly driven by Cartesian theory,\nrather than a fair attempt to adjudicate between the two alternatives.\nFor example, far from proving the need for the ”very fine\nmatter“ of Cartesian physics, this conclusion has been\n”assumed“, by Spinoza, ”simply from the hypothesis\nof the impossibility of a vacuum“. In other aspects of his\ninterpretation, claims Boyle, Spinoza ‘presupposes Descartes'\ntheory of fire”. Now Boyle's readings of the experimental data\nare hardly less theory driven than are Spinoza's. But where they\ndiffer strategically is in the fact that since the Cartesian theory\nthat drives Spinoza's interpretations is derived by the method of pure\nrational reflection on perceptions that are a priori clear\nand distinct, Spinoza clearly grants it a privileged standing in the\ncourt of experimentation. On his view, to prove a conclusion that is\nat odds with one dictated by reason itself, like Descartes', one has\nto establish impossibility experimentally—which cannot,\nof course, be done. So long as it is possible to interpret results as\nconsistent with a theory determined by rational reflection alone,\nthose results cannot weigh at all against the theory. Yet experimental\nresults that conform to rationally determined theory confirm it.", "\nIndeed, where there are properly philosophical arguments to be had for\na thesis, experimentation is superfluous. In assessing Boyle's\nexperiments designed to prove that all tangible properties depend on\nthe mechanical features of objects, Spinoza wonders why Boyle\nbothered, since this conclusion “has already been abundantly\nproved by Verulam, and later Descartes”. (Letter 6). Descartes\nhad proved this a priori from the fact that the sole nature\nof body is extension, whose sole attributes are size, shape and\nmotion. Moreover, ordinary, mundane observations offer as good proof\nas any that might be afforded by controlled observation. Boyle's\ncareful experiments could not add any weight to the evidence already\navailable from such ordinary phenomena as the facts that even cold\nsticks will spark a fire when rubbed together, that water makes sound\nwhen it comes to a moving boil, and that stirring and warming foul\nsmelling bodies make them smell yet worse. Spinoza's attitude towards\nexperimental observation seems to be, then, that it can have no weight\nagainst a theory based in sound a priori philosophical intuition and\ngeometrical demonstration, and is easy available, though not\nnecessary, to confirm the results of such pure theorizing.\nExperimentation can help us discover new phenomena, but it cannot help\nus to prove any scientific propositions we do not already know to be\ntrue. As Gabbey (1996) puts it, experimentation “cannot uncover\nthe nature of things; sensory knowledge belongs to the imagination,\nthe knowledge of essences and causes to the intellect alone”\n(Gabbey 1996, p. 171)." ], "subsection_title": "6.2 Experimentation" }, { "content": [ "\nObservation and experimentation are no more central to contemporary\nscientific practice than is quantification. Contemporary physical\ntheory, which Spinoza is said to have anticipated, is thoroughly\nquantitative in character. Theories are expressed in quantitative\nterms; giving an explanation of a phenomenon is typically a matter of\ngenerating a mathematically formulated law that covers it. Unifying\ntheories is a matter of showing how the mathematical formulae that\ncomprise them can be derived from one another, how the phenomena they\nconcern can be commensurated. Indeed, observation itself is irrelevant\nto modern physical theory unless it is expressed in quantitative\nterms, since the prediction yielded by physical theories are\npredictions of what the observed measures of things will be. This, in\nturn, requires that the phenomena observed must be measurable.", "\nSpinoza is, in a fairly obvious way, a champion of a mathematical\napproach to understanding the physical world. But Spinoza's\nmathematical model is Euclidean geometry, and this is not a domain of\nmathematics that deals with quantities as measurable. And indeed,\nthere is strong evidence that Spinoza thought that a proper\nunderstanding of physical nature can never be expressed in terms of\nmeasurable quantities. For measure, both of spatial extent and\ntemporal duration, is a mere aid to the imagination, and not a means\nof intellectually understanding. In Letter 12 to Meyer, Spinoza\ndistinguishes two ways of conceiving quantity. One is abstract and\nsuperficial, as we have it is sensation and imagination; on this\nconception quantities can be finite, divisible, and composed of parts.\nThe other is through the intellect's grasp of substance in which\n“we apprehend the thing as it is in itself”; on this\nconception, quantity is infinite, indivisible, and a unity. Spinoza\ngoes on to elaborate how measure of spatial and temporal quantity\nderives from the abstract, superficial conception of quantity, and\nleads to nothing but confusion in the attempt to understand physical\nnature. His discussion is worth quoting at length.", "\nFrom the fact that we are able to delimit Duration and Quantity as we\nplease, conceiving quantity in abstraction from Substance and\nseparating the efflux of duration from things eternal, there arise\nTime and Measure: Time to delimit Duration and Measure to delimit\nQuantity in such wise as enables us to imagine them easily, as far as\npossible. Again, from the fact we separate the affections of substance\nfrom substance itself, and arrange them in classes so that can easily\nimagine them as far as possible, there arises Number, whereby we\ndelimit them. Hence it can be seen clearly that measure, Time and\nNumber are nothing other than modes of thinking, or rather, modes of\nimagining. It is therefore not surprising that all who have attempted\nto understand the workings of nature by such concepts, and furthermore\nwithout really understanding these concepts, have tied themselves into\nsuch extraordinary knots that in the end they have been unable to\nextricate themselves except by breaking through everything and\nperpetrating the grossest absurdities. (Letter 12).\n", "\nAs if to emphasize that he is speaking not just of the understanding\nof nature as substance (natura naturans), but also of the\npassive nature of the existing finite modes (natura\nnaturata), Spinoza cites the troubles one gets into as soon as\none attempts to conceive duration through the abstraction of time. The\neternity of the attributes and active nature is to be contrasted with\nthe duration of existing modes. Yet to attempt to understand the\nduration of modes through the abstraction Time, and by implication, to\ntry to understand the spatial extension of modes through Measure and\nNumber, is to employ aids to the imagination only, and inevitably\nleads not to understanding, but to\n absurdities.[17]\n We must conclude that Spinoza's views of Measure, Time and Number\nconfound the easy impression that he thought that the variety in\nmatter could be accounted for by motion and rest considered as\nnumerical quantities. Even if we could satisfy Gabbey's demand for a\n“mathematical account of … proportions of motion and rest\nand of the measures of motion and rest from which they are\nformed”, that would not meet Spinoza's own demands for the\nintellectual understanding of the nature and existence of bodies.", "\nRelying largely on Spinoza's denial of the divisibility or\nmeasurability of extension as it is properly conceived (as opposed to\nimagined), Alison Peterman (Peterman 2012, 2015) has advanced the bold\nthesis that Spinoza's extension is not spatial or dimensional at all,\nand that, accordingly, Spinoza's bodies do not occupy space. On this\nview, Spinoza means something quite different by\n“extension” than Descartes or anyone else has meant. For\nPeterman, it is not just the apparent divisibility and measurability\nof extension that is an illusion of the imagination, but its very\nspatiality. Peterman argues that spatial extent would necessarily be,\nat least potentially, divisible, and that since Spinoza denies that\nextension is even potentially divisible, he must not understand\nextension as spatial (Peterman 2012, \np. 50).[18]\nShe further supports this\nview by noting that, while Spinoza explicitly characterizes extension\nin spatial terms in his exposition of Descartes' view in the\nPCP, he does not so define extension in expounding his own\nviews in the Ethics, but rather says that extension is\n“conceived through itself” .", "\nPeterman's view has the benefit of helping Spinoza avoid the\ndifficulties of making clear how something genuinely spatial cannot be\ndivided or measured. But this benefit comes at substantial costs. For\none thing, Spinoza is hardly shy in the Ethics about making\nhis heterodox views explicit. If he thought that the wildly heterodox\nclaims that extension is not dimensional and that bodies do not occupy\nspace followed from the indivisibility of extension, and endorsed\nthose claims, one would expect him to have made the inference\nexplicit, rather than leaving it for the reader to draw. Second, the\nview renders Spinoza's philosophy oddly irrelevant to the physical,\nwhich certainly concerns nature as a spatiotemporal domain, and which\nis a preoccupation of everyone with whom Spinoza is in intellectual\ncommerce. Third, and relatedly, even conceding, as one must, that no\nimaginative grasp of extension or bodies can constitute an adequate\nconception of them, if extension is not dimensional and bodies do not\noccupy space, the question arises why we so much as imagine them that\nway, that is, why the ideas of the affections of our bodies are\nimages at all. Leibniz, in the more idealistic phases in\nwhich he denies the ultimate reality of space and time, feels acutely\nthe obligation to explain why spatiotemporal phenomena are\nwell-grounded in what is ultimately real. And Kant, who denies the\nspatiotemporality of things in themselves, goes to great lengths to\nexplain why the phenomenal appearances of these things must be in\nspace and time, and conform to the categories as well. Even if Kant's\nclaim that space and time are the forms of intuition looks like a\nlabel for the problem rather than a genuine explanation, it least it\nis a recognition of the problem. But Spinoza, on Peterman's view,\nequally rejects the reality of space and its apparent occupants, but\nseems to have nothing at all to say about why the appearances are as\nthey are, i.e., imagined. Finally, it is obvious that, on Peterman's\nview, “motion and rest”, which Spinoza invokes as an\ninfinite mode of extension and in the individuation of bodies, cannot\nhave their ordinary signification of local motion and rest. So she,\nlike others who deny that “motion and rest” have their\nordinary sense for Spinoza (see section 5.2 above) owes an account of\nwhat they are. But the burden seems even greater for her view, since\nit is quite unclear just what extension might properly be conceived to\nbe, if not dimensional. The only characterizations available seem\npurely negative: not finite, not measurably, not spatial. But what,\nthen? Peterman argues that it is not surprising that the attribute of\nextension should be undefined, since it is “conceived through\nitself”. But to say that something is conceived through itself\nis surely not to say that it is conceived only negatively or in no way\nat all.", "\nFor these reasons, it seems preferable to take the interpretive path\nPeterman considers and rejects, of holding that Spinoza's extension is\nindeed dimensional and his bodies occupants of space, but that\nextension is not really, but only imaginatively, divisible and\nmeasurable. To reconcile the indivisibility of extension and the\nimmeasurability of bodies with the extension's spatiality, we can\nsimply say that one way of conceiving substance is as spatially\nexpended, but that so conceived, it is not divisible, in the sense\nthat it cannot be divided into multiple substances; and we can say\nthat bodies take up space, but cannot be measured, because there is no\nsense to be made of the idea that there is some definite portion of\nthe infinite extension any part thereof occupies, as there would be if\nextension were finite. To conceive extension through itself\nwould just be to conceive spatiality; this secures the relevance of\nSpinoza's extension to the physical, and likewise provides a ground\nfor the spatiality of appearances in imagination. This preferable\npath, however, takes us no closer to a reconciliation of Spinoza's\nthinking about the physical with the observational, experimental, and\nmathematical character of modern and contemporary physical science.\nIndeed, it seems that, as Schiesser (2017, p. 186) remarks, “it\nis … a mistake to understand Spinoza as a fellow traveler of\nthe scientific revolution.”", "\nWe saw earlier that there are grounds, though hardly conclusive, for\nsupposing that Spinoza held a fundamental metaphysical view of\nphysical nature that is akin to the contemporary view of the physical\nworld as composed of fields of force, with bodies in some sense being\nconstituted by relatively stable patterns, relative to our own, of\nforce. However, Spinoza's hostility to observation as a source of\nknowledge, his view that experimentation can at best provide examples\nof what we know through reason, and his rejection of the idea that\nphysical nature is to be known through number and measurable\nquantities, suggest that his convergence with contemporary physical\nscience goes no farther than this possible anticipation of the theory\nof fields as fundamental." ], "subsection_title": "6.3 Mathematical science" } ] }, { "main_content": [ "\nIt is far from clear that any thorough and consistent account of\nSpinoza's physical theory can be found. He says too little that is\nfocused and direct, and the various partial and indirect discussions\nof such fundamental topics as inertia and the individuation of bodies\nare individually underdeveloped and problematic, as well as in\nprima facie tension with one another. A few general\ninterpretive strategies present themselves. We might take both his\nclaim that all determinations of extended modes of substance are\nextrinsically caused by other finite modes and his talk of essence and\nconatus seriously. On such a reading, Spinoza tried to develop an\necumenical account of bodies that both conformed to the mechanical\nprinciples of the Cartesian view and preserved the sense that bodies\nare centers of real activity; but his entitlement to that sense is\nhard to square with mechanism and only dubiously earned through the\nappeal to essences. We might, on the other hand, focus on either of\nthe two aspects of Spinoza's thinking about the physical, downplaying\nthe other. Focusing on conatus and essence might enable us to take the\nlatter, properly ethical and psychological half of the Ethics\nat face value, but only at the cost of being debarred from seeing how\nit fits with the mechanical view of the physical world, and those\nfield metaphysical refinements of it that form the basis of modern\nphysics. Focusing on the idea of wholly extrinsic modal determinism,\nwe will see Spinoza as a visionary thinker whose physical theory both\nanticipates and provides a metaphysical basis for contemporary\nphysical views, albeit without their central experimental and perhaps\nquantitative dimensions; but then the ethical and psychological half\nof Spinoza's thought, depending as it does on the idea that\nindividuals, including bodies, are centers of active striving, proper\nto themselves, is cut adrift. Or we might take each aspect seriously\nfor what they are worth in their own domains, seeing Spinoza as both a\nvisionary thinker about the physical and a subtle and original\ntheorist of the psychological, but one whose doctrines cannot be\nsquared with each other, or with the sort of naturalism that sees the\nacting subject as fitting seamlessly into physical nature. But in any\nof these cases, we lose the unity of Spinoza's thought, which was\nclearly of vital importance to him.", "\nIn retrospect, Spinoza's view of physical nature appears as an\nunstable hybrid, perhaps even incoherent. But it of great interest as\na testimony to the striking originality of its author and to the\nunsettled state of play in the open field that was mid-17th\ncentury natural philosophy." ], "section_title": "7. Conclusion", "subsections": [] } ]

[ "Spinoza, B. d. and E. M. Curley, 1985. The collected works of\nSpinoza, Princeton, N.J.: Princeton University Press.", "Spinoza, B. d., S. Shirley, et al., 1995. The letters,\nIndianapolis, Ind.: Hackett Pub. Co.", "Spinoza, B. d. and E. M. Curley, 1994. A Spinoza reader: the\nEthics and other works, Princeton, N.J.: Princeton University\nPress.", "Descartes, R., The Philosophical Writings of Descartes,\nCambridge, New York: Cambridge University Press, 1984.", "Descartes, R., Œuvres de Descartes, C. Adam, et al.\n(eds.), Paris: J. Vrin, 1964.", "Allison, H., 1987. Benedict de Spinoza: An Introduction,\nNew Haven: Yale University Press.", "Ariew, R., 1990. “The Infinite in Spinoza's\nPhilosophy”, Spinoza. Issues and Directions. The Proceedings\nof the Chicago Spinoza Conference, E. C. a. P.-F. Moreau, New\nYork/København/Köln: E. J. Brill, 16–31.", "Barber, K. F. and J. J. E. Gracia, 1994. Individuation and\nidentity in early modern philosophy: Descartes to Kant, Albany:\nState University of New York Press.", "Barry, G., 2021. “Spinoza on the Resistance of Bodies”,\nStudies in History and Philosophy of Science (Part A),\n86: 56–67.", "Bennett, J., 1984. A Study of Spinoza's Ethics,\nIndianapolis: Hackett Publishing.", "Bennett, J. F., 2001. Learning from six philosophers:\nDescartes, Spinoza, Leibniz, Locke, Berkeley, Hume, Oxford, New\nYork: Clarendon Press, Oxford University Press.", "Carriero, J., 2017. “Conatus”, in Cambridge\nCritical Guide to Spinoza's ‘Ethics’, Y. Melamed\n(ed.), Cambridge: Cambridge University Press, 142–168.", "Curley, E. M., 1969. Spinoza's metaphysics: an essay in\ninterpretation, Cambridge, MA: Harvard University Press.", "Curley, E. M., 1988. Behind the geometrical method: a reading\nof Spinoza's Ethics, Princeton: Princeton University Press.", "Curley, E. M., P.-F. Moreau, et al., 1990. Spinoza. Issues and\nDirections. The proceedings of the Chicago Spinoza Conference,\nLeiden, New York: E.J. Brill.", "Deleuze, G., 1990. Expressionism in philosophy: Spinoza,\nNew York, Cambridge, MA: Zone Books.", "Della Rocca, M., 1996. Representation and the Mind-Body\nProblem in Spinoza, Oxford: Oxford University Press.", "Gabbey, A., 1996. “Spinoza's Natural Science and\nMethodology”, in The Cambridge Companion to Spinoza, D.\nGarrett (ed.), Cambridge, New York: Cambridge University Press.", "Garrett, D., 1994. “Spinoza's Theory of Metaphysical\nIndividuation”, in Individuation in Early Modern Philosophy:\nDescartes to Kant, Jorge K. a. G. Barber, Albany: State\nUniversity of New York.", "––– (ed.), 1996. The Cambridge Companion to\nSpinoza, Cambridge, New York: Cambridge University Press.", "–––, 2002. “Spinoza's Conatus\nArgument”, in Spinoza: Metaphysical Themes, J. Biro and\nO. Koistinen (eds.), Oxford, New York: Oxford University Press.", "Hampshire, S., 1987. Spinoza, Harmondsworth, Middlesex,\nEngland ; New York: Penguin.", "Klein, J., 2005. “Aristotle and Descartes in Spinoza's\nApproach to Matter and Body”, Graduate Faculty Philosophy\nJournal, 26 (2): 157–176.", "Klever, W., 1988. “Moles in Motu”, Studia\nSpinozana, 4: 165–193.", "–––, 1990. “Anti-falsificationism:\nSpinoza's Theory of Experience and Experiments”, in Spinoza.\nIssues and Directions. The Proceedings of the Chicago Spinoza\nConference, E. Curley and P.-F. Moreau (eds.), Leiden/New\nYork/København/Köln: E. J. Brill, 124–135.", "Koistinen, O. and Biro, J., 2002. Spinoza: metaphysical\nthemes, Oxford, New York: Oxford University Press.", "Lachterman, D., 1977. “The Physics of Spinoza's\nEthics”, Southwest Journal of Philosophy, 8 (3):\n71–111.", "Mason, R., 1986. “Spinoza on the Causality of\nIndividuals”, Journal of the History of Philosophy, 24:\n197–210.", "Matson, W., 1990. “Body Essence and Mind Eternity in\nSpinoza”, in Spinoza. Issues and Directions. The Proceedings\nof the Chicago Spinoza Conference, E. Curley and P.-F. Moreau\n(eds.), Leiden/New York/København/Köln: E. J. Brill,\n82–95.", "McKeon, R. P., 1987. The philosophy of Spinoza: the unity of\nhis thought, Woodbridge, CN: Ox Bow Press.", "Melamed, Y., 2013. Spinoza's Metaphysics: Substance and\nThought, Oxford: Oxford University Press.", "Newlands, S., 2018. Reconceiving Spinoza, Oxford, Oxford\nUniversity Press.", "Miller, J., 2003. “Spinoza and the Concept of a Law of\nNature”, History of Philosophy Quarterly, 20:\n257–276.", "Peterman, A., 2012. “Spinoza on the ‘Principles of\nNaturalThings’”, The Leibniz Review, 22:\n37–65.", "–––, 2014. “Spinoza on Physical\nScience”, Philosophy Compass, 9: 214–223.", "–––, 2015. “Spinoza on Extension”,\nPhilosopher's Imprint, 15: 14.", "–––, 2017a. “Newton and Spinoza”, in\nOxford Handbook of Newton, Schliesser and Smeenk (eds.),\nOxford: Oxford University Press.", "–––, 2017b. “The ‘physical’\ninterlude”, in Cambridge Critical Guide to Spinoza's\nEthics, Y. Melamed (ed.), Cambridge: Cambridge University\nPress: 102–120.", "Rice, L. C., 1996. “Spinoza's Infinite Extension”,\nHistory of European Ideas, 22 (1): 33–43.", "Robinson, T., 2009. “Spinoza on the Vacuum and the\nSimplicity of Corporeal Substance”, History of Philosophy\nQuarterly, 26 (1): 63–81.", "Schliesser, E., 2012a. “Newtonian Emanation, Spinozism,\nMeasurement, and the Baconian Origins of the Laws of Nature”,\nFoundations of Science, 18: 449–466.", "–––, 2012b. “Newton and Spinoza: On Motion\nand Matter (and God, Of Course”, The Southern Journal of\nPhilosophy, 50: 438–458.", "–––, 2012c. “On Reading Newton as an\nEpicurean: Kant, Spinozism and the Changes to the\nPrincipia”, Studies in History and Philosophy of\nScience, 44: 416–428.", "–––, 2017. “Spinoza and the Philosophy of\nScience: Mathematics, Motion, and Being”, The Oxford\nHandbook of Spinoza, M. Della Rocca (ed.), Oxford: Oxford\nUniversity Press: 155–189.", "Schmaltz, T., 2020. The Metaphysics of the Material World:\nSuarez, Descartes, Spinoza, Oxford: Oxford University Press.", "Viljanen, V., 2007. “Field Metaphysic, Power, and\nIndividuation in Spinoza”, Canadian Journal of\nPhilosophy, 37 (3): 393–418.", "Winkler, S., 2016. “The Conatus of the Body in Spinoza's Physics”,\nSociety and Politics, 10 (2): 95–114.", "Wolfson, H., 1934. The Philosophy of Spinoza, Cambridge,\nMA: Harvard University Press." ]

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[ "\n\nAt least in anglophone countries, Spinoza’s reputation as a\npolitical thinker is eclipsed by his reputation as a rationalist\nmetaphysician. Nevertheless, Spinoza was a penetrating political\ntheorist whose writings have enduring significance. In his two\npolitical treatises, Spinoza advances a number of forceful and original\narguments in defense of democratic governance, freedom of thought and\nexpression, and the subordination of religion to the state. On the\nbasis of his naturalistic metaphysics, Spinoza also offers trenchant\ncriticisms of ordinary conceptions of right and duty. And his account\nof civil organization stands as an important contribution to the development of constitutionalism and the rule of law." ]

[ { "content_title": "1. Historical Background", "sub_toc": [ "1.1 Theological and Political Background", "1.2 Intellectual Background" ] }, { "content_title": "2. Basic Features of Spinoza’s Political Philosophy", "sub_toc": [ "2.1 Hobbes and Spinoza on the Right of Nature", "2.2 Hobbes and Spinoza on Obligation", "2.3 Spinoza and Normativity" ] }, { "content_title": "3. The ", "sub_toc": [ "3.1 Countering Superstition", "3.2 Separation Thesis", "3.3 Single Authority Thesis", "3.4 Positive Function of Religion", "3.5 Spinoza’s Argument for Toleration", "3.6 Social Contract in the TTP" ] }, { "content_title": "4. The ", "sub_toc": [ "4.1 Metaphysical Background", "4.2 General Aim of the State", "4.3 Constitutionalism and Model Regimes" ] }, { "content_title": "5. The Place of the State in Spinoza’s Ontology", "sub_toc": [] }, { "content_title": "6. The Reception and Influence of Spinoza’s Political Philosophy", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Primary Sources", "Secondary Sources" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nIn order to situate Spinoza’s political writings, I will\nprovide a brief overview of the theologico-political context of the\nUnited Provinces, followed by a sketch of intellectual background to\nthese works." ], "section_title": "1. Historical Background", "subsections": [ { "content": [ "\n\nDespite being perhaps the most tolerant country in early-modern\nEurope—a sanctuary for free thinkers and members of religious\nminorities—the United Provinces were riven by religious conflict,\nas the Dutch sought to establish their identity after gaining\nindependence from Spain. The confessional rifts of the seventeenth\ncentury were certainly an important part of context in which Spinoza\ncomposed his Tractatus Theologico-Politicus [hereafter:\nTTP].", "\n\nThe early part of the seventeenth century was marked by a religious\nschism that rapidly took on political significance. In 1610,\nforty-four followers of liberal theologian Jacobus\nArminius—referred to as Arminians—wrote a formal\n“Remonstrance,” which articulated the ways in which they\ndeviated from orthodox Calvinism, particularly with respect to\nthe issues of self-determination and grace. The Arminians, or\nRemonstrants, defended religious toleration on the grounds that faith\nis expressed in the conscience of the individual, and so is not subject to the\ncoercive power of the state. The doctrinal and political views of the\nRemonstrants were opposed by the conservative Gomarists (followers of\nFranciscus Gomarus), or Counter-Remonstrants. For a little over a\ndecade (roughly 1607–1618), the dispute raged on, expanding outward\nfrom Holland and Utrecht. Finally, in 1618, a national synod convened\n(the Synod of Dort) to define the public faith more clearly. The\nfallout from the Synod of Dort was disastrous for the tolerant\nArminians. The Advocate of the States of Holland, Johan\nOldenbarnevelt, who staunchly defended the Remonstrants, was put to\ndeath. And Arminians throughout the country were purged from town\ncouncils and universities (Israel 1995, 452ff).", "\n\nThe second half of the century witnessed its own major\ntheologico-political dispute in the United Provinces. At the center,\nonce again, were two theologians: Johannes Cocceius, a liberal theology\nprofessor at Leiden, and Gisbertus Voetius, Dean of the University of\nUtrecht. Disputes between Cocceian and Voetians began over abstruse\ntheological matters, but developed into a larger political and cultural\naffair. The Voetians led the assault on the Cartesian philosophy being\ntaught in the universities. They thought that the new science advocated\nby Descartes, with its mechanistic view of the material world, posed a\nthreat to Christianity in a variety of ways (Nadler 1999, 151–2 and\n308–310). Spinoza’s philosophy was reviled not only by the\nVoetians, but also by moderate Cocceian-Cartesians, who sought to\ndistance themselves from radicals.", "\n\nSpinoza was no stranger to religious persecution. As is well known,\nhe was himself excommunicated from the Jewish community in Amsterdam in\n1656. While Spinoza apparently endured the excommunication with\ncharacteristic equanimity, fellow Dutch apostate Jew, Uriel da Costa,\nwas unable to bear the indignity of excommunication from the Amsterdam\nJewish community. In 1640—when Spinoza was only eight years\nold—da Costa, who had denied the immortality of the soul and\nchallenged the status of the Torah as divine revelation, took his own\nlife.", "\n\nDa Costa’s suicide surely made a lasting impression on\nSpinoza, but it did not affect him as personally as did the treatment\nof his friend Adriaan Koerbagh at the hands of Dutch authorities in the\nyears leading up to the publication of the TTP. In 1668 Koerbagh\npublished two treatises that provoked the wrath of the Calvinist\nclergy. In the more scandalous of the two—Een Bloemhof van\nallerley lieflijkheyd (A Flower Garden of all Kinds of\nLoveliness)—Koerbagh ridiculed a number of traditional religious\ndoctrines and practices, and, in the process, articulated his own\nreligious and metaphysical views. Among the shocking views that he\nadvanced were that Jesus is not divine, that God is identical with\nnature, that everything is necessitated by the laws of nature (the laws\nof God), and that miracles are impossible. These are all positions that\nSpinoza consistently endorsed. However, while Spinoza was famously\ncautious, Koerbagh was not, publishing the works in Dutch (thereby\nmaking them accessible to the general literate public) under his own\nname. Consequently, Koerbagh was tried and sentenced on charges of\nblasphemy. During his subsequent imprisonment under squalid conditions\nKoerbagh became ill. He died soon thereafter (in 1669). It is\ngenerally supposed that it was Koerbagh’s imprisonment and death\nabove all else that precipitated the publication of the TTP (Nadler\n1999, 170).", "\n\nLiberal republicans were dealt a major blow in\n1672. In this so-called disaster year (rampjaar), French\ntroops, under the command of Louis XIV, invaded the United Provinces,\ncapturing a number of Dutch cities (Nadler 1999, 305). Grand\nPensionary (chief statesman and legal advisor) Johan de Witt\nshouldered much of the blame for this military embarrassment. De Witt\nwas the leader of the States of Holland for much of the republican\nperiod that followed the death of Stadholder (a quasi-monarchical\nposition held by the House of Orange) William II in 1650. After the\nFrench invasion, the stadholdership was reinstituted in the person of\nWilliam III, and De Witt was forced to resign. Shortly afterward he\nand his brother, Cornelis, were brutally killed by a zealous mob. This incident\nevoked uncommon anger in Spinoza, who was an admirer of de Witt and\nthe republican ideals for which he stood. According to one famous\naccount, Spinoza had to be restrained by his landlord from taking a\nsign reading ultimi barbarorum [“ultimate of\nbarbarians”] to the site of the massacre (Freudenthal 1899,\n201). Spinoza’s Tractatus Politicus was composed in the\naftermath of, and perhaps prompted by, the events of 1672." ], "subsection_title": "1.1 Theological and Political Background" }, { "content": [ "\n\nSpinoza’s political thought draws from a number of sources,\nboth classical and modern. As one commentator puts it, “Spinoza\nformed new conclusions from facts and concepts borrowed from\nothers” (Haitsma Mulier 1980, 170). It is worth briefly\nconsidering some of the sources of the “facts and concepts”\nthat he inherits.", "\n\nAt some point in the mid-1650’s (around the time of his\ncherem, or excommunication) Spinoza began studying Latin with\nFranciscus Van den Enden. Van den Enden was an ex-Jesuit and radical\negalitarian with revolutionary tendencies. He was put to death in 1674\nafter having been found guilty of conspiring to depose Louis XIV in\norder to establish a free republic in Normandy. Van dan Enden was an\nanti-clerical democrat who appears to have profoundly influenced\nSpinoza. One commentator has gone so far as to call Van den Enden\n“the genius behind Spinoza,” claiming that Van den\nEnden’s writings “contain a political theory which is in\nfact the same as the one worked out by Spinoza” (Klever 1996,\n26). Whether or not this assessment is fair, it is clear that\nSpinoza’s thinking was nourished through his association with Van\nden Enden and the larger radical Cartesian circle in Amsterdam (Nyden-Bullock 2007).", "\n\nHobbes’ influence on Spinoza is unmistakable. We know that\nSpinoza read De Cive carefully and that it was among his\npossessions when he died in 1677. He might also have read\nLeviathan, which appeared in Latin in 1668, as Spinoza was\ncompleting the TTP (Sacksteder\n1980). I will discuss Spinoza’s work in relationship to\nHobbes’ in some detail below (sections 2.1 and 2.2, below). Here\nI want to mention the impact of Dutch Hobbesians on Spinoza. Hobbesian\nthought was introduced into Dutch political discourse by Lambert van\nVelthuysen, an anti-clerical, liberal physician (Tuck 1979; Blom 1995).\nVelthuysen’s Dissertatio is an unabashed defense of\nHobbes’ thought, in which the duty to preserve oneself is given\npride of place (esp. Sect. XIII). Spinoza read and admired Velthuysen\nas a “man of exceptional sincerity of mind,” and was thus\ndisconcerted when Velthuysen denounced the TTP as the work of\na dangerous atheist (Epistles 42 and 43).", "\n\nAside from Velthuysen, the other primary Dutch conduits for\nHobbesian thought prior to Spinoza were the De la Court brothers (Petry\n1984; Kossmann 2000). Most of the De la Courts’ writings were\npublished by Pieter De la Court after the death of his brother Johan in\n1660. However, because it remains unclear how much Pieter added and how\nmuch he took credit for the work his studious younger brother, I will refer to\nthese authors of these writings simply as the De la Courts, so as to\navoid attribution problems. The De la Courts were ardent republicans\nwho maintained good relations with Johan De Witt. Indeed, De Witt is\nthought to have written two chapters in the second edition of their\nbook Interest van Holland (see Petry 1984, 152). The De la\nCourts adopted the basic features of Hobbesian anthropology, but\neschewed juridical concepts like “right” and\n“contract” (see Malcolm 1991, 548), opting to analyze the\ncivil condition in terms of the competing interests of participants.\nAccording to them, the aim of the state is to ensure that the interests\nof rulers are tied to the interests of the ruled, which is possible\nonly if one adopts a series of institutional measures, such as the use\nof blind balloting, the removal of hereditary posts, and the rotation\nof offices. Republics, they argued, will be marked by greater checks\nagainst self-interested legislation than monarchies (see Blom 1993).\nSpinoza evidently studied these works carefully; his institutional\nrecommendations in the Tractatus Politicus [hereafter: TP]\nreflect his debt to the De la Courts (Petry 1984; Haitsma Mulier\n1980).", "\n\nIt was likely the writings of the De la Courts that impressed upon\nSpinoza the perspicacity of Niccolo Machiavelli. The notion of\nbalancing the interests of competing parties was ultimately derived\nfrom Machiavelli (see Haitsma Mulier 1993, 254–255). Spinoza’s\nPolitical Treatise is shot through with Machiavellian insights\nand recommendations. Right at the outset of the work, Spinoza parrots\nMachiavelli’s critique of utopian theorizing, elevating statesmen\nover philosophers, since only the latter begin with a realistic\nconception of human psychology (TP 1/1; cf. Machiavelli,\nThe Prince I.15). Machiavellian realism pervades Spinoza’s\npolitical writings, playing a particularly significant role in the\nconstitutional theorizing of the TP. Spinoza, like Machiavelli,\nunderstood that prescriptions for improving the governance of a state\ncan be offered only after one has a proper diagnosis of the problems\nand a proper grasp of human nature (see Steinberg 2018a)." ], "subsection_title": "1.2 Intellectual Background" } ] }, { "main_content": [ "\n\nThree of the most striking and important claims of Spinoza’s\nEthics are that (1) all things come to exist and act\nnecessarily from the laws of God’s nature (e.g., EIP29\nand EIP33), (2) nature does not act on account of some end or\npurpose (EI Appendix), and (3) nature is everywhere and always\nthe same (EIII Preface). Collectively, these three claims\nentail that human behavior, like the behavior of everything else, is\nfully necessitated by, and explicable through, the immutable—and\nnon-providential—laws of God or Nature. This forms a significant\npart of the metaphysical backdrop against which Spinoza develops his\npolitical theory. For the sake of simplicity, I will call the view that\nis constituted by these three theses Spinoza’s naturalism. This\nnaturalism led him to adopt bold views about the source and\nstatus of rights, obligations, and laws that distinguished his work from that of\nother seventeenth-century political theorists.", "\n\nSpinoza’s naturalism excludes the possibility of a transcendent God. Those\nwho believe in a transcendent God “imagine that there are two\npowers, distinct from each other, the power of God and the power of\nnatural things…. they imagine the power of God to be like the\nauthority of royal majesty, and the power of nature to be like a force\nand impetus” (TTP 6/81). Of course, on Spinoza’s account, God is\nnot a transcendent legislator, God is nature itself. Consequently, all accounts of right that are rooted in God’s legislating will are specious. This is a direct rebuke not only of defenders of\nthe divine right of kings, but also of most accounts of natural rights\nas entitlements that were embraced by many seventeenth-century\ntheorists.", "\n\nMoreover, this naturalism also rules out the possibility of a normative order of things, or a way that\nthings should be, distinct from the actual order of\nthings. This undermines the teleological assumptions that form the\nbasis of natural law theory, whether Thomistic or Protestant. Even\nthose who wished to separate natural law from theology (e.g.,\nPufendorf), and those who de-emphasized the role of God’s\nwill—as Grotius does in his famous etiam si daremus\npassage—still supposed that there is a way that things ought to\nbe, a normative natural order that can be decoupled from the actual\norder of things. According to this view, humans act contrary to nature\nwhen they act contrary to the prescriptions of right reason. Spinoza\nattacks this view, according to which “the ignorant violate the\norder of nature rather than conform to it; they think of men in nature\nas a state within a state [imperium in imperio]” (TP\n2/6). The phrase “imperium in imperio” famously\nappears also in the preface to Ethics III, where Spinoza is\ncharacterizing the non-naturalist view that he opposes. In both of\nthese passages, Spinoza criticizes the assumption that man is governed\nby his own set of rational, normative laws, rather than the laws that\ngovern the rest of nature. It is precisely this position that Spinoza\nundercuts when he writes in the Ethics that “the laws\nand rules of Nature…are always and everywhere the same”\n(EIII preface) and in the TP that “whether man\nis led by reason or solely by desire, he does nothing that is not in\naccordance with the laws and rules of nature” (TP 2/5).", "\n\nIn short, by adopting the view that nature is univocal and that man is\ngoverned by the same laws as everything else in nature, Spinoza\nrejects the natural law tradition (Curley 1991; A. Garrett 2003; for\ncontrasting views, see Kisner 2010 and Miller 2012). And even if\nSpinoza’s naturalism is viewed as part of a larger naturalistic trend\nin Dutch political thought (Blom 1995), his disavowal of normative\nconceptions of nature and rejection of teleology indicates a clear\nbreak with tradition. To appreciate the depth and significance of\nSpinoza’s naturalism, it will be helpful to compare his views on\nnatural right and obligation to Hobbes’." ], "section_title": "2. Basic Features of Spinoza’s Political Philosophy", "subsections": [ { "content": [ "\n\nOne of the most notorious features of Spinoza’s political\nthought is his account of natural right. He introduces this concept in\nTTP 16, where he boldly writes:", "\n\nBy the right and order of nature I merely mean the rules determining\nthe nature of each individual thing by which we conceive it is\ndetermined naturally to exist and to behave in a certain way. For\nexample fish are determined by nature to swim and big fish to eat\nlittle ones, and therefore it is by sovereign natural right that fish\nhave possession of the water and that big fish eat small fish. For it\nis certain that nature, considered wholly in itself, has a sovereign\nright to do everything that it can do, i.e., the right of nature\nextends as far as its power extends…since the universal power\nof the whole of nature is nothing but the power of all individual\nthings together, it follows that each individual thing has the\nsovereign right to do everything that it can do, or the right of each\nthing extends so far as its determined power extends. (TTP 16, 195;\ncf. TP 2/4). ", "\n\nIn claiming that the right of nature is coextensive with the power\nof nature and that this applies\nmutatis mutandis to the individuals in nature, Spinoza is\nsimply rejecting non-naturalism, rather than making a positive\nnormative claim. So although Spinoza is often seen as subscribing to\nthe view that “might makes right” (see Barbone and Rice\n2000, 19; McShea 1968, 139), this is misleading if it is\ntaken as a normative claim. In fact, I take it that the coextensivity thesis is not to be\nunderstood as offering a new normative standard; rather, it is\nintended as a denial of any transcendental standard of justice (see\nCurley 1996, 322; Balibar 1998, 59). To say that something is done by\nright in Spinoza’s sense is just to say that there is nothing in\nvirtue of which that action can be judged impermissible. So, even if\nSpinoza’s account implies that Cortés conquered the Aztecs by\nright, it does not follow that it was necessarily the right, or\nproper, thing to do (see TP 5/1; see section 2.3).\n", "\n\nSpinoza’s brazen denial of natural proscriptions on what one\ncan do roused the ire of early readers (e.g., Pufendorf 1934, 159). Of\ncourse, Thomas Hobbes, Spinoza’s great predecessor, had made a\nsimilar claim. Indeed, Spinoza’s account of natural right is\noften taken as evidence that he is a Hobbesian. Hobbes’ account\nof natural right has been the subject of much interpretative dispute,\nin part because it seems to undergo a shift between his early political\nwritings and Leviathan. In De Cive Hobbes defines\nright as “the liberty each man has of using his natural faculties\nin accordance with right reason” (1.7). In other words, natural\nright is the liberty to do anything consistent with the natural law\n(ibid. 2.1). This includes the right to do anything that one judges to\nbe necessary for one’s preservation (1.8–1.9). Hobbes adds one\nproviso here, which might be called the “sincerity clause,”\nnamely that one violates the law of nature, or acts without right, when\none acts in a way that one does not sincerely believe contributes to\none’s preservation (1.10n). And later Hobbes suggests that\nbecause “drunkenness and cruelty” cannot sincerely be\nthought to contribute to self-preservation, drunken and cruel actions\nare not performed by right, even in the state of nature (ibid., 3.27).\nIn short, as A. G. Wernham puts it, on Hobbes’ view, man’s\nnatural right “covers only some of his actions” (Wernham\n1958, 14). Specifically, it covers those actions that are not contrary\nto the law of nature.", "\n\nIn Leviathan, however, Hobbes seems to advance an account\nof natural right that is apparently not bound by such normative\nconstraints (Ch. 14). But while it may seem that in the later work\nHobbes strips the concept of natural right of all normative content,\neven the view expressed in Leviathan may be seen to be at odds\nwith a thoroughgoing naturalism. To see this, consider Spinoza’s\nreply to his friend to Jarig Jelles, when asked what sets his views\napart from Hobbes’:", "\n\nWith regard to political theory, the difference between Hobbes and\nmyself, which is the subject of your inquiry, consists in this, that I\nalways preserve the natural right in its entirety [ego naturale jus\nsemper sartum tectum conservo], and I hold that the sovereign\npower in a State has right over a subject only in proportion to the\nexcess of its power over that of a subject (Epistle 50).", "\n\nWhat Spinoza is criticizing here is the Hobbesian view of contracts\n(covenants) or the transference of one’s natural right. The\ntransferability or alienability of one’s natural right to judge\nhow to defend oneself serves as the foundation of Hobbes’\npolitical theory; it allows him to explain the formation of the\ncommonwealth and the legitimacy of the sovereign. In Spinoza’s\nview, however, Hobbes violates naturalism here. By conceiving of\none’s natural right as something like an entitlement that can be\ntransferred, which in turn leads him to drive a wedge between right and\npower in the commonwealth, Hobbes never fully rids his account of the\nvestiges of the juridical tradition that Spinoza sought to\noverturn." ], "subsection_title": "2.1 Hobbes and Spinoza on the Right of Nature" }, { "content": [ "\n\nThe difference between Hobbes and Spinoza on right bears directly on\ntheir distinct accounts of obligation. Hobbes thinks that we incur\nbinding obligations when we make pledges under the appropriate\nconditions. By contrast, Spinoza maintains that “the validity of\nan agreement rests on its utility, without which the agreement\nautomatically becomes null and void” (TTP 16/182; cf. TP\n2/12). To demand otherwise would be absurd, since men are bound by\nnature to choose what appears to be the greater good or lesser\nevil. We are bound by nature to act on our strongest interest and\ncannot be obligated by previous agreements to break this inviolable\npsychological law of nature.", "\n\nBy adhering to a strict naturalism about right and obligation and\nmaintaining that “the sovereign power in a State has right over a\nsubject only in proportion to the excess of its power over that of a\nsubject” (Epistle 50), Spinoza, unlike Hobbes, places the burden\nof political stability on the sovereign rather than the subject (see\nWernham 1958, 27). The commonwealth must be structured so as to promote\ncompliance; when there is excessive vice or non-compliance, the blame\nmust be “laid at the door of the commonwealth” (TP 5/3).\nSo, whereas Hobbes argues that the sovereign is always vested with\nnearly absolute legislative authority, Spinoza claims that “since\nthe right of a commonwealth is determined by the collective power of a\npeople, the greater the number of subjects who are given cause by a\ncommonwealth to join in conspiracy against it, the more must its power\nand right be diminished” (TP 3/9). If a sovereign is to maintain\nits right, it must legislate wisely, so as not to incite insurrection.\nSo while Spinoza does not accord to the people a proper right of\nrevolution, he proposes a naturalistic equivalent, since the right of\nthe state is essentially constituted, and limited, by the power of the\npeople (TP 2/17) (see Sharp 2013).", "\n\nThus, when Spinoza points to the differences between his view of\nnatural right and Hobbes’ in his letter to Jelles, differences\nthat might appear negligible to the casual reader, he is identifying a\nsignificant distinction (see Wernham 1958, 35). Spinoza’s\nthoroughgoing naturalism leads him to reject the sharp distinction that\nHobbes draws between civil state—the product of\nartifice—and the state of nature, along with the concomitant\nconception of obligation that arises with the inception of the\ncommonwealth. But given his naturalism and repudiation of rights and\nobligations as traditionally understood, one might be left wondering\nhow or whether Spinoza could offer a normative political theory at\nall." ], "subsection_title": "2.2 Hobbes and Spinoza on Obligation" }, { "content": [ "\n\nAs Edwin Curley rightly points out, to deny that there is a transcendental\nstandard of justice is not to deny that there is any normative standard\nby which we can evaluate action (Curley 1996). Even if one can act\nirrationally without violating nature that does not mean that all of\none’s actions have the same normative status. As Spinoza puts it,\n“it is one thing, I say, to defend oneself, to preserve oneself,\nto give judgment, etc., by right, another thing to defend and preserve\noneself in the best way and to give the best judgment” (TP 5/1).\nThe goodness of an action is to be judged in relation to whether the\naction aids one’s striving to preserve and augment one’s power (see\nEIVP18S; TP 2/8; TTP 16/181). The striving to preserve and\naugment one’s power, which constitutes one’s actual essence\n(EIIIP7), provides a standard for moral judgments: things are\ngood or bad to the extent that they aid or diminish one’s power of\nacting (Curley 1973). And just as the individual ought to do those\nthings that maximize his or her own power or welfare, Spinoza takes it\nas axiomatic that the state ought to do those things that maximize the\npower of the people as a whole (e.g., TTP 16/184)." ], "subsection_title": "2.3 Spinoza and Normativity" } ] }, { "main_content": [ "\n\nAs indicated above, throughout the seventeenth century the United\nProvinces were torn apart by disputes concerning, among other things, the\npolitical authority of the church. Spinoza’s Tractatus\nTheologico-Politicus can be seen as an intervention in this broad\ndispute. The stated goals of this work were to parry charges of atheism\n(Spinoza was hilariously unsuccessful in this respect), to oppose the\nprejudices of the theologians, and to defend the freedom to\nphilosophize (Epistle 30). My exposition of the political claims of the\nTTP will focus on the last two goals. Specifically, I will look at the\npolitical significance of Spinoza’s critique of superstition and\nconsider his arguments for the freedom of philosophizing. This will be\nfollowed by an analysis of the role of the social contract in the\nTTP." ], "section_title": "3. The Tractatus Theologico-Politicus", "subsections": [ { "content": [ "\n\nThe TTP contains a good deal of what has come to be known as biblical\ncriticism. Through careful linguistic and historical exegesis Spinoza\nidentifies numerous textual inconsistencies, which, with some\nphilosophical buttressing, lead Spinoza to deny the exalted status of\nprophets, the objective reality of miracles, and ultimately the divine origin of\nthe Pentateuch. The broad features of his critique are vital to our\nunderstanding of Spinoza’s response to the “theologico-political\nproblem” (Smith 1997) that plagued the Dutch Republic. (For two\nrecent first-rate monographs on the TTP that situate Spinoza’s\ncritique of Scripture in historical context, see Nadler 2011 and James\n2012)", "\n\nAmong the politically relevant claims that Spinoza makes in the\nfirst fifteen chapters of the work is that Scripture does not compete\nwith philosophy as a source of knowledge; nor do the injunctions of\nScripture compete with the commands of civil authorities. By separating\nfaith from reason and making religion’s role in the public realm\nsubordinate to that of the state, Spinoza tries to sanitize religion of\nits pernicious superstitious aspects. We may call the claim that faith is distinct\nfrom reason the separation thesis and the claim that religious\nlaw is dependent on and determined by civil law the single\nauthority thesis." ], "subsection_title": "3.1 Countering Superstition" }, { "content": [ "\n\nAt one point Spinoza calls the task of establishing the separation\nof faith from philosophy “the principal purpose of the whole\nwork” (TTP 14/179). And a good deal of the biblical criticism in the\nTTP can be understood as paving the way for the separation thesis,\nsince in the earlier chapters much of what Spinoza is doing is\nundermining the claim of Scripture as a source of genuine knowledge.\nThe value of Scripture does not lie in its mysteries or its abstruse\nmetaphysical content, since to the extent that it is concerned with\nthese matters it is—by Spinoza’s lights—utterly\nconfused. Rather, it lies in the simple moral truths that Scripture\ncontains, which encourage obedience to the state (Ch. 13). The books of\nScripture are written for an unsophisticated, uneducated audience and\nconvey information in a way that is suited to such an audience, in the\nform of fantastical accounts and parables that appeal to the\nimagination rather than the intellect. And so, Spinoza argues, although\nScripture may appear to reveal profound truths about God’s nature\nand his participation in our world, its salient message is not\nmetaphysical, but moral: “Scripture requires nothing of men other than\nobedience, and condemns not ignorance, but disobedience”\n(TTP 13/173). The ethical message of loving God and loving one’s\nneighbor is the backbone of all religion (Ch. 12), the whole of divine\nlaw (TTP 14/178).", "\n\nThis ethical understanding of religion is reflected in the way that\nSpinoza re-conceives of several crucial religious concepts. For\ninstance, he claims that a text is sacred to the extent that it fosters\ndevotion to God and charity to others (e.g., TTP 12/151) and that a\nperson’s piety is measured in terms of her or his commitment to\njustice, charity, and obedience. Since the aim of religion is obedience\nand good works, and the aim of philosophy is truth, religion and\nphilosophy ought not to be seen as rivals. By separating religion and\nphilosophy, faith and reason, Spinoza distances himself both from those\nwho—like Maimonides and Spinoza’s friend Ludwig\nMeyer—contort Scripture to make it conform to reason and those\nwho claim that where Scripture\nconflicts with reason it is reason that we must renounce (TTP, Ch. 15). According to\nSpinoza, because reason and faith have separate domains, neither is\nsubservient to the other. The separation thesis has profound political\nimport, since by claiming that religion is not, like philosophy, a\nsource of knowledge, Spinoza undercuts the grounds for the theological\ndisputes that were the source of considerable unrest in the Dutch\nRepublic. The dominant message of the separation thesis is that\nScripture is not the source of metaphysical knowledge and so we ought\nnot to treat it as authoritative in these matters." ], "subsection_title": "3.2 Separation Thesis" }, { "content": [ "\n\nHowever, since Scripture does have a positive socio-political function in promoting justice and charity, one might wonder\nhow much authority the clergy has in public matters. Spinoza’s\nresponse is that “authority in sacred matters belongs wholly to\nthe sovereign powers ” (Ch. 19, title). Like Hobbes, he\nembraces the Erastian position that religious law is realized through\nthe will of the civil authority (TTP, Ch. 19). The crux of the single\nauthority thesis is this: the sovereign is the sole civil and\nreligious authority. Indeed, because piety consists in practicing\njustice and obedience, and because there is no standard of justice\nother than the will of the sovereign (TTP 19, 239ff; EIVP37S2),\n“it is also the duty of the sovereign authority alone to lay\ndown how a person should behave with piety towards their neighbor,\nthat is, to determine how one is obliged to obey God” (TTP 19,\n242–3). The obvious, yet important, implication of the single\nauthority thesis is that clerics are at best spiritual advisors with\nno real claim to political power. The problem of dual allegiances\n(divine and civil) is overcome, since the two authorities converge in\nthe form of the sovereign.", "\n\nThe argument against ecclesiastical power here depends upon the\nsupposition that there is no transcendental standard of piety. Of\ncourse, a sovereign could delegate authority to religious\nfunctionaries, but Spinoza cautions against this, using the case of\nthe Hebrews to illustrate the dangers of priestly authority. The\ndecisive turn that precipitated the decline of the first Hebrew state\ncame with the ascendance of a priestly order. On Spinoza’s account,\nunder Moses, civil law and religion “were one and the same\nthing” (TTP 17, 213) and the Jews lived peaceably. However, when\nthe priests—chiefly the Levites—were given the right to\ninterpret divine law, “each of them began seeking glory for his\nown name in religion and everything else...As a result religion\ndegenerated into fatal superstition” (TTP 18, 231). The message here\nhad clear application in the Dutch context, where, as we’ve noted,\nCalvinist theocrats—who formed a menacing alliance with the\nhouse of Orange—were increasingly wielding power to the\ndetriment of peace and stability (see Nadler 1999, 283–4).", "\n\nSpinoza punctuates his historical analysis of the Hebrew state by\ndrawing four lessons about the theologico-political problem, three of\nwhich are relevant here: (1) civil stability requires the limitation of\necclesiastical power; (2) it is disastrous for religious\nleaders to govern speculative matters; and (3) the sovereign\nmust remain the sole legislator. These historical observations support Spinoza’s principle of toleration, which I discuss\nbelow." ], "subsection_title": "3.3 Single Authority Thesis" }, { "content": [ "\n\nDespite its potential for harm, Spinoza thinks that religion can\nperform a positive social function. It can help to breed an obedient\nspirit, making people pliable to civil law—in this way religion\nplays a role in bolstering the state (e.g., TTP 14/168; cf. Moses’ use of\na state religion, TTP 5/66). For instance, the ceremonial laws and\npractices of the Jews helped to foster and preserve cohesion among an\nignorant, nomadic populace (TTP Ch. 3 and Ch. 5). The central moral\nmessage of religion—namely, to love one’s neighbor (e.g., TTP 14,\n179)—may be understood through reason; but Scripture presents\nthis message in a manner that is suited to the understanding of the\nmasses (TTP 14, 184; see Strauss 1965, Ch. 9 and Smith 1997,\nCh. 2). Religion also seems to play a crucial role in promoting\ncompliance with the law. Michael Rosenthal has suggested that in\nSpinoza’s scheme “transcendental beliefs” assist in overcoming free rider problems; defections from agreements and\nnon-compliance with the law would likely be widespread among human\nbeings were it not for religion (Rosenthal 1998).", "\n\nThe salutary function of religion is undermined when sectarianism\nemerges. When groups like the Pharisees begin to regard themselves as\nspecial, disparaging and persecuting other groups, civil order is\ndisrupted. In order to prevent such fissures, Spinoza puts forth a\nuniversal or civil religion that captures the moral core of a plurality\nof faiths, to which all citizens can subscribe, irrespective of what\nother private beliefs they hold (TTP 14, 182–3). Like Rousseau after him,\nSpinoza thought that a universal public religion could bolster civic\nsolidarity, channeling religious passions into social benefits." ], "subsection_title": "3.4 Positive Function of Religion" }, { "content": [ "\n\nSpinoza is often remembered for his contribution to the liberal\ntradition, due, in large part, to his defense of the freedoms of\nthought and speech in TTP 20. However, the tolerationism expressed in\nTTP 20 appears to stand in tension with the Erastian claim of TTP 19.\nHow can Spinoza be a liberal about religious practice while also\ndefending the view that the state maintains full right over matters of\nreligion (TTP, Ch. 19)? There are three things worth noting here. First, unlike Locke’s tolerationism, Spinoza’s defense of\ncivil liberties in TTP 20 is not fundamentally a defense freedom of\nworship (Israel 2001, 265–266). Rather, it is essentially a defense of\nthe freedom to philosophize; freedom of worship is at best an\nincidental byproduct of this primary aim. Second, Spinoza\ndistinguishes between outward expressions of faith and one’s\ninward worship of God. Sovereign authority over religious expression\nconcerns only the former, leaving the latter the domain of the\nindividual, for reasons that we will examine in a moment. Both of\nthese positions can be understood as lending support to the Arminian\ncause against Calvinist Theocrats (Nadler 1999, 12). Finally, it\nshould be mentioned that Spinoza’s denial that freedoms concerning\noutward religious expression must be protected points to the limited\nnature of his brand of toleration. The sovereign retains full\ndiscretion to determine which actions are acceptable and what forms of\nspeech are seditious. As Lewis Feuer ruefully notes, Spinoza does not\noffer anything resembling Oliver Wendell Holmes’s standard of\n“clear and present danger” to constrain sovereign\nintervention (1987, 114).", "\n\nWhat are Spinoza’s arguments for his, albeit limited, defense\nfreedoms of thought and speech? The first argument is that it is\nstrictly impossible to control another’s beliefs completely\n(20, 250–51). Since right is coextensive with power,\nlacking the power to control beliefs entails lacking the right to do\nso. However, since Spinoza admits that beliefs can be influenced in\nmyriad ways, even if not fully controlled, this argument amounts to a\nrather restricted defense of freedom of conscience.", "\n\nNext, the argument shifts from considering what the sovereign\ncan do to what it would be practical or\nprudent for a sovereign to do. Spinoza offers a battery of\npragmatic reasons in defense of non-interference. For instance, he\nargues that “a state can never succeed very far in attempting to\nforce people to speak as the sovereign power commands” (TTP 20,\n251). Men are naturally inclined to express what they believe (ibid.),\nand so just as attempts to regulate beliefs fail, so do attempts to\nregulate the expressions of these beliefs. Moreover, even if a state\nwere to regulate speech, this would only result in the erosion of good\nfaith [fides] on which civil associations depend, since men\nwould be “thinking one thing and saying something else”\n(TTP 20, 255). It is thus foolish to seek to regulate all speech, even if\nit is also “very dangerous” to grant unlimited freedom of\nspeech (TTP 20, 252).", "\n\nSpinoza also argues that in general the more oppressively a sovereign\ngoverns, the more rebellious the citizens will be, since most people\nare “so constituted that there is nothing they would more\nreluctantly put up with than that the opinions they belief to be true\nshould be outlawed” (TTP 20, 255). The source of oppression and the\nresistance to it have a common root on Spinoza’s account, namely,\nambition, or the desire for others to approve of the same things that\nwe do (see\nEIIIP29; cf. Rosenthal 2001 and 2003). Men being constituted\nas they are, when differences of opinion arise—as they inevitably\ndo—they are inclined to foist their standard on others and to\nresist others’ attempts to do the same. So, however common\nattempts to regulate the beliefs, speech, and behavior of others may\nbe, it is politically unstable to do so. Moreover, Spinoza argues that\nit is often the least wise and the most obnoxious who initiate moral\ncrusades, and just as it is often the wisest and most peace-loving who\nare the targets of such campaigns (TTP 20, 256–58).", "\n\nIt is worth noting that these arguments in defense of civil liberties\nare thoroughly pragmatic; they rely on psychological principles and\nempirical observations to illustrate the instability and imprudence of\noppressive governance (see Steinberg 2010b). They are not principled\narguments that depend on rights or the intrinsic value of liberty,\nmuch to the frustration of some commentators (Feuer 1987; Curley\n1996)." ], "subsection_title": "3.5 Spinoza’s Argument for Toleration" }, { "content": [ "\n\nA good deal of scholarly attention has been placed on Spinoza’s\naccount of the social contract in the TTP. Spinoza introduces the\ncontract in Chapter 16, when considering how people escape the\npre-civil condition. Here he claims that “[men] had to make a\nfirm decision, and reach agreement, to decide everything by the sole\ndictate of reason” (TTP 16, 198), which requires, as he later makes\nclear, that each transfers one’s right to determine how to live and\ndefend himself to the sovereign (TTP 16, 199–200);\ncf. EIVP37S2). He also cites the establishment of the Hebrew\nstate, with Moses as the absolute sovereign, as an historical example\nof a social contract (TTP 19, 240). The social contract seems to confer\nnearly boundless authority on the sovereign. So long as we are\nrational, “we are obliged to carry out absolutely all commands\nof the sovereign power, however absurd they may be” (TTP 16,\n200).", "\n\nHowever, if Spinoza really relies upon the social contract as a\nsource of legitimacy, several problems arise. First of all, it seems\nunlikely that such a contract could ever have been formed, since the\nlegitimating strength of a social contract depends on farsighted\nrationality that Spinoza clearly thinks most people lack (see Den Uyl\n1983).", "\n\nBut even if such a contract were possible, a much greater problem\nremains for Spinoza. How can we take seriously a legitimacy-conferring\ncontract without violating the naturalism that is at the core of\nSpinoza’s metaphysics? What is this right that is surrendered or\ntransferred? And how can one really transfer one’s right, given\nthe coextensivity of right and power? Spinoza’s\nnaturalistic, utility-based account of obligation (see 2.2, above) also seems to preclude the possibility of a binding social contract.", "\n\nSome commentators take these problems with Spinoza’s social\ncontract to be insurmountable, and for this reason they regard him as\ncoming to his senses when he abandons the contract in the TP (Wernham\n1958, 25–27). Others have tried to reinterpret the contract in a way\nthat is makes it consistent with his naturalism. For instance, Barbone\nand Rice distinguish between two concepts that have been rendered in\nEnglish as “power.” On the one hand there is\npotentia, which is the power that is essential to the\nindividual (Barbone and Rice 2000, 17). This power in inalienable. What\nis transferable is one’s potestas, i.e. one’s\nauthority (Barbone and Rice 2000, 17) or coercive power (Blom 1995,\n211).", "\n\nWhile this interpretation has the virtue of cohering with\nSpinoza’s claim that he “always preserve[s] the natural\nright in its entirety” (Epistle 50), since one’s right, or\npotentia, always remains intact, it leaves unexplained how\npotestas, which Barbone and Rice describe as a\n“super-added” capacity, fits into the natural order. What\ncan it mean to possess, transfer, or renounce one’s\npotestas? And how can transferring or revoking it result in an\nobligation, given Spinoza’s utility-based account of\nobligation?", "\n\nPerhaps the best way to understand what it means to possess or give up one\npotestas is in psychological terms. Curley suggests this when\nhe looks to Hobbes’ claim in Behemoth that the\n“the power of the mighty hath no foundation but in the opinion\nand belief of the people” (EW VI, 184, 237—cited in Curley\n1996, 326) as a way of understanding Spinoza’s conception of\nsovereign formation. One could also cite Hobbes’ famous claim in\nLeviathan that “reputation of power is power” (Ch.\n10) as an expression of the same point. These passages can be\nunderstood as supporting the view that power is not transferred by way\nof a speech act, but rather by standing in the psychological thrall of\nthe sovereign. Sovereignty is the product of psychological deference\nrather than the formal transference of rights or titles. ", "\n\nSome evidence in support of this psychological interpretation comes in\nTTP 17, where Spinoza claims that sovereign power or authority derives\nfrom the will of its subjects to obey (TTP 17, 209–10; cf. TP\n2/9–10). There are places in the text, however, when Spinoza\nseems to imply that we have obligations to the sovereign irrespective\nof our psychological or motivational state. In some of these\ninstances, a careful reading reveals that nothing of the sort is\nimplied. For instance, his claim that “we are obliged to carry\nabsolutely all the commands of the sovereign power, however absurd\nthey may be” (TTP 16, 200) is contingent on our behaving rationally\nand wanting to avoid being regarded as enemies of the state. Still,\nthere are other places when he does imply that de facto\nobedience is neither necessary nor sufficient for establishing the\nlegitimacy of a civil body. For instance, he claims that the sovereign\nalone has right over religious matters such as interpreting Scripture,\nexcommunicating heretics, and making provisions for the poor (TTP 19, 239\n- 40), despite the fact that the church had, in fact, been exercising\npower in these matters. But this too can be reconciled with Spinoza’s\nnaturalism, provided that we understand that the power or authority of\nclerics devolves upon them from the power or authority of the\nsovereign." ], "subsection_title": "3.6 Social Contract in the TTP" } ] }, { "main_content": [ "\n\nOne might wonder why Spinoza, having published the TTP in 1670, spent\nthe last years of his life (until his death in 1677) working on a\nsecond political treatise that covers some of the same ground as the\nfirst. It is tempting to suppose that he must have come to reject many\nof his earlier views. However, with the possible exception of his view\nof the social contract (see 4.1), there is little evidence that\nSpinoza came to reject any of the central claims of his earlier\ntreatise. Rather, the TP is distinguished from the earlier treatise\nchiefly by its aims and rhetorical style. Whereas the TTP was an\noccasional piece, written for an audience of liberal Christian\ntheologians to address the problems posed by officious Calvinist\ntheocrats, the TP is concerned with the general organization of the\nstate and was written for philosophers. In the later treatise, Spinoza\nabandons what has been described as the “theological idiom of\npopular persuasion” in favor of the dispassionate style of a\npolitical scientist (Feuer 1987, 151; cf. Balibar 1998, 50).", "\n\nThe TP is a fitting sequel to the Ethics (Matheron 1969).\nWhereas the Ethics reveals the path to individual freedom, the\nTP reveals the extent to which individual freedom depends on\ncivil institutions (Steinberg 2018a). We should not be surprised to find Spinoza’s philosophy taking a civic turn near the end of his life. From his earliest writings, he claims that he is\nconcerned not just to perfect his own nature but also “to form a\nsociety of the kind that is desirable, so that as many as possible may\nattain [a flourishing life] as easily and surely as possible”\n(TdIE, §14). The TP may be seen as Spinoza’s\nattempt to articulate some of the conditions for the possibility of such a\nsociety.", "\n\nThe work can be divided into three sections. In the first section\n(roughly through Chapter 4), Spinoza discusses the metaphysical basis\nof the state and the natural limits of state power. In the second\nsection (Chapter 5), Spinoza lays out the general aims of the state.\nAnd in the third section (Chapter 6 to the end), Spinoza gives specific\nrecommendations for how various regime forms—monarchy,\naristocracy, and democracy—are to be constituted so as to satisfy\nthe aims of the state as set out in section two." ], "section_title": "4. The Tractatus Politicus", "subsections": [ { "content": [ "\n\nIn the early chapters of the TP, Spinoza puts forth his naturalistic\nprogram, beginning with the premise that the state, like everything\nelse, is a natural thing (res naturalis), governed by the\nlaws of nature (see Bartuschat 1984, 30). It is in this light that we\ncan appreciate Spinoza’s claim that “one should not look for the\ncauses and natural foundations of the state in the teachings of\nreason” (1/7). It has seemed to some (e.g., Wernham 1958, 265n)\nthat this statement indicates a sharp break with the contractarian\nconception of the state formation advanced in the TTP. This view is\nsupported by the fact that virtually no mention of a social contract\nis made in the later treatise (Wernham 1958, 25; Matheron 1990). This\nwould also fit with Lewis Feuer’s suggestion that the later treatise\nbetrays a dimmer view of the masses, perhaps brought on by the events\nof 1672 (1987, ch. 5). At the very least, this passage illustrates a\nbreak with the ultra-rational conception of the social contract that\nappears to lie behind some of the claims of the TTP.", "\n\nHowever, Spinoza’s account of the state as the spontaneous product of\nnatural passions is perfectly consistent with the psychological\ninterpretation of the contract (§3.6, above). Indeed, he seems to\nsupport such a view in his work when he claims that individuals are\nunder the right [sub potestate] of the commonwealth (3/5), regardless of whether they\nobey its laws from fear or love of civic order (2/10; 3/8). They stand\nunder the right or power of the sovereign, because they are held (psychologically) in its sway.", "\n\nBut what exactly does it mean to deduce the foundations of the state\nfrom the nature of men? In the TP Spinoza tells us that men, who are\nindividually weak and effectively powerless compared to the aggregated\npowers of others (2/15; Cf. EIVP5dem.), come together as a\nresult of “some common emotion...a common hope, or common fear,\nor desire to avenge some common injury” (6/1; see Matheron 1969\nand 1990). The state is thus an unintended, but salutary, outcome of\nthe natural interplay of human passions. In this sense, the civil\ncondition is a natural condition. Because, on this view, stable\npatterns of behavior emerge from blind interplay of the passions,\nthereby overcoming coordination problems, some have regarded Spinoza’s\naccount as “evolutionary,” anticipating the theory of\nunintended consequences found in Mandeville, Smith, and Hayek (Den Uyl\n1985 and 1983). However, Spinoza says precious little about the\nprocess of civil formation itself in the TP, making such an\ninterpretation deeply underdetermined, at best. While one can, like\nDen Uyl (ibid.) or Matheron (1969, 1990), construct a genetic story on\nthe basis of Spinozistic psychology, the account that Spinoza himself\noffers is quite thin." ], "subsection_title": "4.1 Metaphysical Background" }, { "content": [ "\n\nHaving established in the preceding chapters that anything that can\nbe done is done by right, Spinoza turns directly the question of how\nthe sovereign should exercise its power in Chapter Five,\nnoting that there is an important distinction between doing something\nby right and doing it in the best way (5/1). Here his concern is just\nto delineate the general aim of the state on the basis of which he can\ngive more fine-grained recommendations relative to regime forms (see\n4.3). The fundamental aim of the state, according to Spinoza, is\n“peace and security of life” [pax vitaeque\nsecuritas] (5/2). To grasp what Spinoza means here we must try to\nunderstand what he means by peace. Spinoza rejects Hobbes’\ndefinition of peace as the “absence of war” (De\nCive 1, 12), calling it instead “a virtue which comes from strength\nof mind” (5/4), or a “union or harmony of minds”\n(6/4). It is one thing for a state to persist or to avoid the ravages\nof war, it is quite another for the state to flourish. Spinoza makes\nthis point by way of an organic metaphor:", "\n\nSo when we say that the best state is one where men pass their lives\nin harmony, I am speaking of human life, which is characterized not\njust by the circulation of the blood and other features common to\nanimals, but especially by reason, the true virtue and life of the\nmind. (5/5)", "\n\nBut if the aim of the state is peace, and peace consists in the\n“harmony of minds” or the rational activity, one might\nwonder how it is that the state could hope to achieve its end in light\nof Spinoza’s skepticism concerning human rationality (1/5; 2/5;\n6/1). How is it that the state can promote the civic virtue or\n“strength of mind” [fortitudo] on which peace\ndepends (5/2, 5/3)? This is perhaps the central normative question of\nthe TP (see Steinberg 2009; Steinberg 2018a). Spinoza addresses this\nquestion by way of offering institutional recommendations for each\nregime type." ], "subsection_title": "4.2 General Aim of the State" }, { "content": [ "\n\nTo see how Spinoza provides a general response to the question of how\npeace or civic agreement is promoted, we must bear in mind that the\nrelation of agreement comes in degrees (see Blom 1993; Steinberg\n2009). Total agreement, what Blom calls “maximal\nagreement,” is possible only to the extent that men are fully\nrational (EIVP31–EIVP35). A society of free men would be a perfect\nunion (EIVP67–73). However, the free man exists only as an ideal; all\nactual men are imperfectly rational. The concern of the state is to\nbring it about that the actual relationships between people most\nclosely approximate the ideal society of free men. That is, the aim of\nthe state is to make irrational, selfish men as rational and virtuous\nas possible. (For tension between idealist and realist features of\nSpinoza’s political thought, see Armstrong 2009).", "\n\nSpinoza’s solution, in broad form, is to adopt constitutional measures\nand institutional procedures that channel the natural passions of men\ntowards the common good. The vision here is one of mechanizing reason\nin much the same way the Venetian Republic is said to have\nmechanized virtù (Pocock 1975, 284), a vision much\nindebted to the works of the De la Courts. Civil rationality is the\nproduct of a republican set of institutions that encourage broad\nparticipation, public deliberation, and the adoption of a variety of\naccountability-promoting mechanisms. A rationally organized state will\nnot only promote the common good, in so doing it will also strengthen\nthe civic commitment of its citizens; this is one key way in which the\nstate contributes to the reorientation of the affects of its citizens\nand increases the level of agreement between citizens, the product of\nwhich is harmony or peace (Steinberg 2009; Steinberg 2018a)", "\n\nGiven that the fundamental aim of the state is peace, the question\nthat Spinoza seeks to address in chapters 6 and 7 of the\nPolitical Treatise is how a monarchy is to be\norganized so as to be maximally peaceful. He begins by repeating the\nclaim that men are largely irrational and selfish. And since the\npassions of common men must be regulated, it is tempting to suppose, as\nHobbes does, that heavy-handed governance is required. But Spinoza\nclaims that even if a despot is able to minimize violence and dissent,\nas the Turkish Sultans were (6/4), this produces only “slavery,\nbarbarism, and desolation,” not the sort of peace or agreement\namong men that is the true end of the state. Indeed, Spinoza claims\nthat the more completely authority is vested in one man the worse off\neveryone is, including the despot himself (6/8). This is because the\nKing is likely to look after his advantage alone, neglecting the\ngeneral welfare, which will ultimately result in the weakening of the\ncivitas. In order to overcome this condition, it is essential\nfor there to be constitutional checks on the behavior of the monarch.\nThese foundational laws are to be understood as the king’s\n“permanent decrees” [aeterna decreta], expressing\nhis real interests, which are not to be contravened. Spinoza likens\nthese “decrees” to Ulysses’ order that his oarsmen\nkeep him bound to the mast of his ship even when he is beckoned by the\nSirens’ song (7/1). One of the central constitutional checks is\nthat the King deliberate with, and in some sense answer to, a large\ncouncil composed of citizens (6/15–30). Moreover, since the council\nmembers too are likely to be selfish and venal, it is important that\ntheir private interests are bound up with the common good (7/4; cf. 7/27–29). As\nMcShea puts it, a properly constituted state will be like a\n“homeostatic mechanism” (1968, 109), correcting divisive or\ndestructive tendencies by ensuring that an individual’s interests\nis always tied to the interests of others. For instance, Spinoza writes\nthat in a properly constituted state:", "\n\nThe king…whether motivated by fear of the people or by his\ndesire to win over the greater part of an armed populace, or whether\nhe is led by nobility of spirit to have regard to the public interest,\nwill always ratify the opinion that is supported by most votes-i.e.,\n(by Section 5 of this Chapter), that is of the greater advantage to\nthe greater part of the state; or else he will try, if possible, to\nreconcile the differing opinions submitted to him so as to gain\npopularity with all (7/11).", "\n\nUltimately, a model monarchy will be a constitutional monarchy that will strongly resemble a democracy. This fits with\nMatheron’s suggestion that, because state power is fundamentally\nbased in the power of the people, those states that deviate least from\na democracy will be most powerful (Matheron 1997). Nevertheless, the\nfact that Spinoza countenanced the possibility that “a people can\npreserve a considerable degree of freedom under a king” (7/31), can be\nseen as a resignation to the reality of Orangism after the events of\n1672 (Blom 2007; Steinberg 2008).", "\n\nSpinoza discusses two types of aristocracy and the best forms of\neach. The first is a centralized aristocracy that appears to have been\nmodeled on the Venetian Republic (McShea 1968, 117; Haitsma Mulier\n1980). The second is a decentralized aristocracy, in which sovereignty\nis held by several cities. This type of aristocracy, which Spinoza\ntakes to be superior (9/15), is evidently modeled on the\nUnited Provinces. While Spinoza’s recommendations vary between these\ntwo types of aristocracy, many of the general features remain the\nsame. Spinoza argues, in proto-Madisonian fashion, that the council of\npatricians must be sizable so as to reduce the potential for\nfactionalism (e.g., 8/1; 8/38). He also claims that a large council\nwill protect against selfish or irrational governance (8/6; 9/14). As\nis the case in Spinoza’s discussion of monarchy, the emphasis here is\non finding mechanisms that balance the interests of participants and\nencourage cohesion (e.g., 8/19–8/24). One important way in which\ncohesion is encouraged is through the promulgation of the\n“universal faith” or civil religion set out in TTP 16\n(8/46).", "\n\nGiven that there will generally be more checks on authority and a\ngreater diffusion of political power in aristocracies than in\nmonarchies, we should not find it surprising that Spinoza claims that\naristocracies are likely to be more absolute than monarchies (8/7),\nsince a state is “absolute” to the extent that it\nincorporates the rights of all its members and minimizes the basis for\ndissent (8/3, 8/4, 8/7; Steinberg 2018b). Absoluteness thus indicates a norm very much\nlike peace, the cardinal civil norm; so to say that one regime form is\nmore absolute than another amounts to declaring its superiority.", "\n\nWhile Spinoza clearly indicates that aristocracies are, on the whole\nand in most cases, superior to monarchies, a more interesting and\nsomewhat more vexed question is how aristocracies compare with\ndemocracies. Raia Prokhovnik, for example, has claimed that\naristocracy is “the form of government [Spinoza] on mature\nreflection prefers” (2004, 210; cf. Feuer 1987 and Melamed 2013). I believe that\nthere are strong reasons for denying that aristocracy displaces\ndemocracy in the TP as Spinoza’s preferred regime. Spinoza does note\nthat the election of patricians as opposed to the birthright\nprivileges of participants in a democracy gives aristocracies an\nadvantage in theory (11/2). However, this advantage is offset by the\nbiased, self-serving practices of most patricians (ibid.). And since\nSpinoza claims that democracy is the most absolute form of regime\n(e.g., 11/1), it would seem that—again, on the whole and in most\ncases—Spinoza favors democracy. Ultimately, though, Spinoza is\nless interested in rank-ordering regimes than he is in determining how\neach regime-type must be organized in order to maximize freedom and\nthe common good.", "\n\nSpinoza had barely begun writing the first of what would likely have\nbeen two chapters on democracy when he died on February 21, 1677. His\nconception of democracy includes any system of popular governance in\nwhich the governing members acquire the right to participate by virtue\nof their civil status rather than by election. This conception of\ndemocracy is broad enough to include even variants of timocracy.\nSpinoza’s own model democracy excludes all those who are not\nsui iuris—e.g., women, servants (servos), and\nforeigners—as well those who do not lead “respectable lives”\n(honesteque vivunt) (11/3). These elitist and exclusionary\naspects of Spinoza’s democracy taint what would otherwise appear to be\na rather progressive form of democracy, from as much as we can glean\nfrom remarks scattered throughout the text.", "\n\nThe general tenor of Spinoza’s democracy is easy to infer from his\ndiscussions of monarchy and aristocracy, both of which include strong\ndemocratic elements. What is particularly interesting is how Spinoza\ndefends these democratic features, since this gives us insight into\nhow democracies are to be defended in general. In the TTP Spinoza seems to\nprovides both principled and instrumental arguments in favor of\ndemocracy. The principled reason is that democracies preserve men’s\nnatural equality (TTP 16, 202) and natural freedom (TTP 5/65). The major\ninstrumental defense of democracy is that “there is less reason\nin a democratic state to fear absurd proceedings” (16/184). In\nthe TP, Spinoza focuses exclusively on the instrumental defense,\nhighlighting what has recently been called the epistemic advantage of\ndemocracy, i.e., the tendency of popular assemblies to legislate more\nwisely than other legislative bodies (e.g., Cohen, 1986; Estlund 1997;\nSteinberg 2010a; cf. entry on\n democracy. \nFor instance, he repeats his claim that larger councils are more\nlikely to be rational because collective decisions force members to\n“have as their objective what is honourable, or at least appears\nso” (8/6). He claims that the deliberative features of\nlarge governing bodies improve competency, since “men’s wits are\ntoo obtuse to get straight to the heart of every question, but by\ndiscussing, listening to others, and debating, their wits are\nsharpened” (9/14). Spinoza also rebuffs those who claim that\nthere is “no truth or judgment in the common people”\n(7/27), claiming that “all men share in one and the same\nnature” and that differences in competency stem primarily from\nthe fact that the masses are kept ignorant of the most important\naffairs of the state (ibid.; cf. 7/4). Contrary to Feuer’s suggestion\nthat events such as the murders of the de Witts led to an\nanti-democratic turn in Spinoza’s thought, these passages reveal the\ndepth of Spinoza’s commitment to democracy and his refusal to endorse\nthe thesis that some men are innately more fit to govern than\nothers. So despite the fact that the explicit discussion of democracy\nin the TP was largely preempted by the author’s death, this work\nremains a significant contribution to democratic theory." ], "subsection_title": "4.3 Constitutionalism and Model Regimes" } ] }, { "main_content": [ "\n\nIn recent years a lively discussion has emerged in the scholarly\nliterature concerning whether or not Spinoza’s state is an individual\nwith its own conatus. At issue in this debate is whether Spinoza was\nmore of a collectivist or an individualist. The answer to this\nquestion is thought to carry implications for how we conceive of\nSpinoza’s relationship to the liberal tradition. Some of the strongest\nevidence in support of the conception of the state as an individual\ncomes from the so-called physical digression between IIP13 and IIP14,\nwhere Spinoza directly discusses individuality. In this section,\nSpinoza tells us that an individual is a composite body whose parts\n“communicate their motion to each other in a certain fixed\nmanner” (II/100, A2, def, A3). The parts of an individual may be\nreplaced, but the individual will persist, provided that the\n“same ratio of motion and rest” is retained (ibid., L5,\nL4). Moreover, individuals who come together to act in a fixed way\nform larger individuals, terminating ultimately in the\nsupreme-individual: the whole of nature (II/101-102, L7). Elsewhere in\nthe Ethics, when remarking on the benefits of human\nassociations, Spinoza claims that “if…two individuals of\nentirely the same nature are joined to one another, they compose an\nindividual twice as powerful as each one” (IVP18S). Here, once\nagain, Spinoza delineates a picture of composite, higher-order\nindividuals, opening up the possibility of viewing the state itself as\nan individual.", "\n\nAlexandre Matheron’s Individu et Communauté chez\nSpinoza contains perhaps the most influential interpretation of\nSpinoza’s account of individuality (1969, esp. Ch. 3). Matheron\nidentifies political societies as individuals, characterized by their\nown “formal element,” i.e., their own unique ratio of\nmotion and rest (see e.g., p. 42, 58). Following Matheron, Etienne\nBalibar views the state as a highly composite individual, as an\n“individual of individuals, having a ‘body’\nand a ‘soul’ or mind” (1998, 64), a status that he\ncalls elsewhere “transindividuality” (1997). Others who\nhave espoused this view include Meinecke (1965) and Blom (2007).", "\n\nThis interpretation has been challenged in a number of ways. One\nargument against the view is that in the opening passages of TTP 17\nSpinoza, in contrast to Hobbes, claims that individuals always retain a\n“considerable part” of their own natural right; in other\nwords, human beings are never fully integrated into the\nsuper-individual, or state (Den Uyl 1983, 70). The problem with this\nobjection is that there is no reason to suppose that all individuals\nare characterized by complete integration of parts. Matheron, for\ninstance, describes the state as complex individual whose parts are\nonly integrated to a limited degree (1969, 58). Balibar, too, claims\nthat the “autonomy” of individuals is maintained even when\none is a part of a larger collective whole (1997, 21). It is perfectly\nconsistent to recognize the discrete individuality of humans while\nallowing that, under certain conditions of association, individuals can\nsimultaneously be members of larger units. One can be both\na collectivist and an individualist. The real\nanti-individualists are the idealists, who read Spinoza as maintaining\nthat “human individuality is illusory and untrue” (Joachim\n1901, 130).", "\n\nA second objection to the view that the state is an individual is\nthat, whereas singular things can only be destroyed by external causes\n(IIIP4), “a commonwealth is always in greater danger from its\ncitizens than from its enemies” (e.g., TP 6/6). If we assume\nthat all individuals are singular things (for a helpful discussion of\nthe relationship between these concepts, see D. Garrett 1994), then\nthe fact that states can ostensibly be destroyed by their parts (i.e.,\ncitizens) would be a sufficient basis for denying that they are\nindividuals (Barbone and Rice 2000, 26–7). This is a forceful\nobjection. However, it seems that an analysis of the apparent\nself-destruction of the commonwealth could be provided that parallels\nSpinoza’s attempt to explain how suicide is possible in light of the\nconatus doctrine (EIVP20S). An apparently self-destructive state could\nbe regarded as one that is so affected by “hidden external\ncauses,” so overwhelmed by destructive passions, that it takes\non a new nature that is contrary to its original nature (ibid.).\nSpecifically, Spinoza could explain cases of apparent civil\nself-destruction by maintaining that they occur only at the hands of\npoorly-integrated individuals who stand, at least to some degree,\noutside of the body politic. While this form of explanation is not\nwithout problems (see Bennett 1984, §56), it is not obvious that\nthese problems are peculiar to collectivist interpretations of the\nstate.", "\n\nA third challenge to the collectivist interpretation is that if the\nstate is an individual, it should have a mind of its own. But Steven\nBarbone points out that references to the mind of the state are\ntypically preceded by qualifying phrases like veluti\n(“as it were”) and\nquasi (“as if”), indicating that the state has a\nmind only in a metaphorical sort of way (Barbone 2001, pp. 104–105).\nThis objection might be mitigated by arguing that individuality is\nitself a matter of degree and that states are at best\n“loose” individuals (Della Rocca 1996, Ch. 2), with limited\ncohesion or regularity of action. This is consistent with the claim,\nnoted above, that integration into a larger union is itself a matter of\ndegree.", "\n\nUltimately, it seems to me that far less hinges on the success or\nfailure of the collectivist interpretation than has been assumed by\nits opponents. The primary concern expressed by critics like Den Uyl\nand Barbone seems to be that Spinoza not be understood as treating the\nstate as an individual with its own interests that might trump the\ninterests of its constituents. Isaiah Berlin condemned Spinoza along\nwith other positive liberty theorists precisely because he took\nSpinoza to be reifying the state and putting state interests above\nindividual interests (1969). But even if the state is an individual,\nit does not follow that its interests would supersede the interests of\nits citizens. Certainly from the perspective of a citizen, there is no\nreason why one would have to put the interests of the state above\none’s own interests if these two were genuinely to come into to\nconflict. In short, the collectivist can embrace the normative primacy\nof the individual human being. If this is allowed, the matter of\nwhether the state is a literal or merely metaphorical individual seems\nto matter far less than many scholars have supposed." ], "section_title": "5. The Place of the State in Spinoza’s Ontology", "subsections": [] }, { "main_content": [ "\n\nIn is difficult to assess adequately the scope of influence of\nSpinoza’s political thought. Even where Spinoza’s influence\non subsequent political thinkers is direct and indisputable, it is not\nalways easy to tease out the extent to this influence is due to his own\npolitical philosophy, as opposed to his metaphysics. Further\ncomplicating the assessment is the fact that Spinoza and Spinozism\nremained a bugbear throughout Europe for much of the late\n17th and 18th centuries, during which time\nSpinozism was widely associated with atheism. For this reason, even\nsympathetic philosophers often sought to distance their views\nfrom Spinoza’s, positioning themselves as critics or downplaying\nfamiliarity with his texts. Nevertheless, we find traces of the\ninfluence of Spinoza’s political writings throughout the\nEnlightenment, along with an array of hostile responses.", "\n\nThe publication of the unfinished TP in Spinoza’s posthumous\nOpera was met with relative indifference, upstaged as it was\nby the simultaneous appearance of Ethics (Laerke 2010, 122).\nHowever, the TTP was read, discussed, and condemned in the decades\nfollowing its publication. The critical reception tended to focus on\nthe perceived anti-religious features of the work—for instance,\nthe refutation of miracles and the denial of the divine origin of the\nPentateuch—but the naturalistic account of right and law and the\narguments for the freedom to philosophize also provoked debate.", "\n\nJakob Thomasius, Leibniz’s teacher in Leipzig, composed a\nwork, Adversus Anonymum, de Libertate Philosophandi,\ndevoted entirely to the refutation of the TTP and its underlying\nnaturalism. Leibniz too seems to have regarded Spinoza’s views on\nright and law as more dangerous even than Hobbes’, for while Hobbes at\nleast allowed conceptual space for a divine legislator, Spinoza did\nnot (Laerke 2010, 125). Even relatively liberal natural lawyers like Lambert van Velthuysen\n(1622–1685) and Samuel Pufendorf (1632–1694), regarded\nSpinoza’s treatment of right and obligation as fundamentally\ndestructive. Velthuysen objects that, without a divine legislator,\nthere is “no room left for precepts and commandments” (Ep.\n42) in Spinoza’s philosophy. And Pufendorf maintains that Spinoza’s\nconception of right is defective in that it fails to produce a\n“moral effect” or to put others under obligations\n(Pufendorf 1934, 391; see Curley 1995).", "\n\nWhile Spinoza’s views on right and law were generally met with\ncontempt, his views on the freedom to philosophize [libertas\nphilosophandi] provoked a more balanced reaction. The doctrine\nhad its critics (see e.g., Israel 2010, 81–2), but it also had\nits admirers, perhaps including some of the most prominent early-modern\ntolerationists. Bayle, Locke, and Toland, for instance, were familiar\nwith Spinoza’s defense and likely found some inspiration in it,\neven while they denied deep acquaintance (Locke) or situated themselves\nas critics (Bayle and Toland). Toland’s use in\nPantheisticon of the same epigram from the opening of\nTacitus’ Histories—“rare are the happy times\nwhen we may think what we wish and say what we think [rara\ntemporum felicitas ubi sentire quae velis et quae sentias dicere\nlicet]”– that Spinoza draws from in the title of TTP,\nCh. 20 indicates an affinity between the two thinkers on matters of\nfreedom of speech and thought (for more on the use of this epigram in\nthe 17th and 18th centuries, see Paul Russell\n2010, Ch. 7),", "\n\nLater enlightenment thinkers reprise Spinoza’s claim that\nwhereas the freedoms of thought and expression should be protected, one\nought to obey the sovereign’s decisions on matters of action (TTP\n20, 251–2). Echoes of this view may be found in Moses\nMendelssohn’s separation of action and conviction in\nJerusalem (Mendelssohn 1983, 40; Gottlieb 2011, 50), a work\nfor which one scholar maintains that the TTP “serves, if not as\nmodel, at least as decisive subtext” (Goetschel 2004, 168). This\ndivision was even adopted by Frederick the Great, whose policy that men\nmay argue about whatever they wish, provided that they obey is famously\ncelebrated in Kant’s essay “What is Enlightenment?”\n[Was ist Aufklärung?].", "\n\nFinally, it is worth mentioning Spinoza’s influence on the\ndemocratic thought of the French Enlightenment. Jonathan Israel has\nexamined the myriad ways in which Spinoza’s philosophy shaped\negalitarian political thought, including, perhaps most significantly,\nthe political thought of the encyclopédistes (Israel 2011).\nSpinoza’s influence here is primarily due to his naturalism,\nwhich inspired the materialist metaphysics that underpinned French\ndemocratic thought, rather than to his political arguments. And\nSpinoza’s realist and arguably anti-revolutionary political\nmethod suggests that even if Spinoza’s philosophy influenced\nrevolutionary democratic thought, it may have had little to do with his\nactual political philosophy. (For divergent assessments of\nSpinoza’s attitude towards revolution, see Rosenthal 2013 and\nSharp 2013). Nevertheless, one finds more than a whiff of\nSpinoza’s absolutist conception of democracy in the accounts of the general will\n[volonté générale] found in\nRousseau (see Ekstein 1944; Williams 2010) and Diderot (Israel\n2011).", "\n\nMore recently, Spinoza’s political philosophy has figured\nprominently in post-1968 leftist French political thought (for a\nsurvey, see van Bunge 2012). However, in the United States, few\npolitical philosophers have seriously engaged Spinoza’s work,\neven while scholarly interest has grown. There is reason to hope,\nhowever, that as Spinoza continues to emerge from Hobbes’ shadow,\npolitical philosophers here may begin to appreciate the rich,\nconsistent, and resourceful arguments contained in his political\nwritings." ], "section_title": "6. The Reception and Influence of Spinoza’s Political Philosophy", "subsections": [] } ]

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[ "\n\nIn Part III of his Ethics, “On the Origin and Nature of\nthe Affects,” which is the subject of this article, Spinoza\naddresses two of the most serious challenges facing his thoroughgoing\nnaturalism. First, he attempts to show that human beings follow the\norder of nature. Human beings, on Spinoza’s view, have causal natures\nsimilar in kind to other ordinary objects, other “finite\nmodes” in the technical language of the Ethics, so they\nought to be analyzed and understood in the same way as the rest of\nnature. Second, Spinoza attempts to show that moral concepts, such as\nthe concepts of good and evil, virtue, and perfection, have a basis in\nhuman psychology. Just as human beings are no different from the rest\nof nature, so moral concepts are no different from other\nconcepts. Spinoza’s detailed account of the human affects—the\nactions and passions of the human mind—is crucial to both\ntasks. For his argument to succeed, the theory of the affects must be\nboth a plausible account of human psychology and also a plausible\nbasis for ethics.\n" ]

[ { "content_title": "1. The Human Being as Part of Nature", "sub_toc": [ "1.1 The Argument to the Striving Doctrine", "1.2 The Striving Doctrine as an Account of the Natures of Particular Objects", "1.3 The Striving Doctrine as an Account of Human Nature" ] }, { "content_title": "2. The Affects", "sub_toc": [ "2.1 The Affects and Striving", "2.2 The Variety of Affects" ] }, { "content_title": "3. The Psychological Basis for a Theory of Value", "sub_toc": [ "3.1 Good and Evil as Modes of Thinking", "3.2 The Psychological Basis for Perfectionism" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nIn the Preface to Part III, Spinoza states his view that all things\nalike must be understood to follow from the laws of nature: ", "The laws and rules of nature, according to which all things\nhappen, and change from one form to another, are always and everywhere\nthe same. So the way of understanding the nature of anything, of\nwhatever kind, must also be the same, viz. through the universal laws\nof nature.", "\n Many philosophers have treated the human mind as an exception to\notherwise universal natural laws, as a thing that is conscious, that\nis capable of good and evil, or that can be an uncaused cause of\naction, for example. Spinoza though insists that human beings are not\n“outside nature.” Any features or deeds of human beings that seem\nexceptional, then, must have for Spinoza some explanation in terms of\nuniversal, natural laws. That is, if there is any sense at all in\nsaying that a human being is aware, does good, and is free, then\nthere must be universal, natural laws that justify and explain these\ndesignations.", "\n\nSpinoza’s thesis (IIIp7) that the essence of any finite mode,\nincluding any human mind (IIIp9), is a striving (conatus) to\npersevere in being is an attempt to give an account of nature under\nwhich human beings with their apparent peculiarities are natural.\nSpinoza argues that all finite modes strive to persevere in being\n(IIIp6), and he uses an analysis of human striving to explain the\nconscious experience of desire, human freedom, and good and evil in\nterms that might apply to any finite modes. Desire, as Spinoza\nunderstands it, just is striving together with consciousness of\nstriving (IIIp9s; the human experience of desire is discussed in more\ndetail in Section 2.1). An action of a human mind cannot be free, for\nSpinoza, in the sense of being determined by a faculty of will that is\nitself undetermined (IIp48; see also letter 58, to Schuller). There is human freedom for Spinoza,\nhowever, in the sense of freedom from external interference: I am free\nin producing some effect (that is, in doing something) to the extent that the effect\nfollows from my essence, or, in other words, to the extent that it is the effect\nof my striving. (For discussions of action and human freedom,\nsee IIId2 and V Preface.) ‘Good’ and ‘evil’\nare labels that describe natural properties in the sense that they\ndescribe changes that might occur in any particular things at all\n(although we reserve the labels for these changes when they occur in\nhuman beings). Although scholars debate the precise meaning of these\nidentifications, an increase in the power with which a mind strives is\ngood, for Spinoza, and a decrease evil (see IIIp11s, IIIp39s and IV\nPreface). Because the striving thesis thus makes central\ncontributions to Spinoza’s accounts of consciousness, of human freedom\nand of good and evil, it is of great importance to Spinoza’s\npsychology and ethics. One might raise questions about the validity of\nSpinoza’s argument to the doctrine, about its plausibility as an\naccount of the nature of particular objects, or about its plausibility\nas an account of human nature. The subsections which follow address\nthese issues in turn." ], "section_title": "1. The Human Being as Part of Nature", "subsections": [ { "content": [ "\n\nSpinoza’s argument to IIIp6 is uncharacteristically insulated from the\nrest of the Ethics. As Spinoza presents the argument at\nIIIp6d, it depends principally upon IIIp4, a proposition which Spinoza\ntakes to be self-evident, and IIIp5 which derives from IIIp4 alone. The\nargument also involves, less directly, IP25C and its gloss at IP34. ", "I Proposition 25 Corollary: Particular things are nothing\nbut affections of God’s attributes, or modes by which God’s attributes are expressed in a certain and determinate way. \n\n\n\nI Proposition 34: God’s power is his essence itself.\n\n\n\nIII Proposition 4: No thing can be destroyed except through an\nexternal cause.\n\n\n\nIII Proposition 5: Things are of a contrary nature, i.e., cannot be\nin the same subject, insofar as one can destroy the other.\n\n\n\nTherefore, III Proposition 6: Each thing, as far as it can by its own\npower, strives to persevere in its being.\n", "\n\nA thing’s essence may not be absolutely equivalent to its nature for\nSpinoza, since a thing such as a square circle has a nature but cannot\nexist (Ip11) and one might interpret Spinoza as holding that anything\nwhich has an essence might exist (IId2). Still, the two terms might be\ntaken interchangeably here because Spinoza is only describing\nexistents. If this assumption is correct, then perhaps Spinoza’s\nreasoning runs like this:", "Particular things are expressions of power,\nsince they are modes of God’s attributes (Ip25) and God’s attributes\nconstitute God’s essence (ID4) and God’s essence is his power (Ip34).\nIt is self-evident that nothing can be destroyed except through an\nexternal cause (IIIp4), so an apparent particular thing which is\nself-destructive is in fact at least two (IIIp5). The power a genuine\nparticular thing expresses, then, must therefore be directed toward its\nown perseverance in being (IIIp6).", "\n\nPace Spinoza, the claim at IIIp4 that no thing can be\ndestroyed except through an external cause is not clearly self-evident.\nEven assuming IIIp4 to be true, however, one might raise questions\nabout Spinoza’s argument. Why is it that, just because a thing does not\nstrive to destroy itself, that thing must therefore strive to persevere\nin being? A thing might, it seems, not strive for anything, or perhaps it\nmight strive to do something which is neither perseverance nor\nself-destruction. Spinoza’s use of IP34 and Ip25c seems intended to\nrule out the first of these possibilities. Although Spinoza’s term\n‘express’ (exprimere) is notoriously unclear, it\nmay mean something like “is a particular form of.” In that case,\nbecause particular things are expressions of God’s essence, his power,\nthey must be particular forms of power. So there cannot be a thing\nwhich does not strive at all or, in other words, there cannot be a\nthing which is not any expression of power at all.", "\n\nThe second version of the objection, the version which notes the\npossibility that a particular thing as described in IIIp4 might strive\nfor something other than either self-destruction or perseverance,\nremains a challenge to sympathetic readers of the Ethics\nhowever. The rejection of IIIp6 and an insistence that at least some\nthing does not strive to persevere in its being, where perseverance in\nbeing is understood as a particular end among many possible options,\nis perfectly consistent with the truth of IIIp4. After all, not\nstriving to persevere in being, which IIIp6 rules out, is not the same\nthing as striving not to persevere in being, which IIIp4 rules out. A\nsympathetic reader of Spinoza might try to resolve the difficulty\nthrough an understanding of what it means to strive to persevere in\nbeing, under which striving to persevere in being comes to mean just\nthe same thing as striving to do something other than destroy oneself,\nin particular, striving to maintain a present state. (See Curley 1,\n109, for an interpretation similar to this one.) This reading comes\ncloser to making the argument from IIIp4 to IIIp6 seem valid, but it\nraises a new problem: that of reconciling this interpretation of\nstriving with Spinoza’s accounts of human motivation which follow from\nIIIp6. For Spinoza consistently regards sane human beings as finite\nmodes who, beyond merely not trying to kill themselves, actively try\nto preserve themselves. People do not merely resist changes to\nwhatever state they are in; they strive to change their states in\norder to know more and in order to live with a greater force. One of\nthe main problems Spinoza faces, then, is reconciling the most\nplausible version of IIIp6 as an account of the natures of ordinary\nobjects (under which IIIp6 is a principle of inertia) with the most\nplausible version of IIIp6 as an account of human nature (under which\nIIIp6 is a version of psychological egoism)." ], "subsection_title": "1.1 The Argument to the Striving Doctrine" }, { "content": [ "\n\nDespite worries that one might have about the validity of Spinoza’s\nargument, the doctrine has at least some claim to plausibility as an\naccount of the nature of particular things. The Ethics stands\nbadly in need of some account of what finite modes are, after all, and\nIIIp4 provides at least one interesting way of distinguishing genuine\nobjects from mere constructs: if the thing in question destroys itself\nit is not a genuine object. Thus, by IIIp4, a thing that destroys\nitself—one might think a lit candle or a time bomb such a\nthing—is not a genuine object but a thing which does not destroy\nitself is. To the extent that IIIp4 makes most of the things we\nintuitively consider genuine objects genuine objects, it captures\nordinary views. To the extent that it rules out some clear class of\nthings that we intuitively consider genuine objects (lit candles and\ntime bombs), it represents a controversial philosophical thesis. The\nplausibility of the doctrine depends on whether we find that there\nreally is reason to find basic metaphysical differences in kind\nbetween “things” which tend to destroy themselves and things which do\nnot. One strategy for defending the plausibility of IIIp4 may be to\ninvestigate what Spinoza means there by an “external cause.”\nSpinoza’s various claims about essences, properties, and accidents\nsuggest that at least some of the cases of destruction that we might\nconsider self-destruction are, for Spinoza, destruction by external\ncauses (Garrett, 2002, pursues this strategy), a suggestion that is supported by Spinoza’s account of suicide later in the Ethics at IVp20s. The class of things which tend to destroy themselves may be different from, and narrower\nthan, one might think it is on a first reading of IIIp4.", "\n\nIIIp6 introduces, perhaps, a slightly different thesis about what it\nmeans to be a particular thing: a particular thing is one which\nstrives to persevere in being. IIIp6’s dependence upon IIIp4 suggests\nthat this thesis means that any object will remain in the same state\nunless external causes affect it. Such a thesis appears to be a\nprinciple of inertia, and, indeed, Spinoza seems to invoke a principle\nof inertia in the terms he uses at IIIp6.\n‘Conatus’ is a technical term of Cartesian\nphysics, referring to an object’s motion. Spinoza himself uses the\nterm in this way in his exposition of Descartes’s Principles of\nPhilosophy. (Compare, for example, Descartes’s\nPrinciples II, art. 37, III, art. 56 and III, art. 58 to\nSpinoza’s exposition IIp14c, IIID3 and IIp17,\nrespectively). Moreover, at IIIp6, in addition to using the term\n‘conatus’ again, Spinoza also uses the same\nphrase that he uses in framing a different principle of inertia at\nIIp14 of his exposition of Descartes’s physics: “as far as\nit can by its own power” quantum in se est. This phrase\nis also one that Descartes himself uses at Principles II,\nart. 37. (Note however that there is some controversy over how this\nphrase is to be understood: see Curley’s footnote to IIIp6 in\nhis translation and Garrett, 1999, note 2.) So there is a good textual\nbasis for the conclusion that IIIp6 indeed has this meaning.", "\n\nApart from the question of how a principle of inertia can give us an\nunderstanding of human nature, this interpretation of IIIp6 raises a\ndifficult question about Spinoza’s use of the striving doctrine. One\nmight object that IIIp6, understood as a restatement of a principle\nof inertia, extends a physical principle to mind without sufficient\nclarity. In stating their versions of a principle of inertia in physics, both Descartes and Spinoza are careful to limit the claim to a claim about bodies.\nSpinoza, for example, in his definition of conatus ad motum,\nIIId3 of his exposition of Descartes, writes:", "By striving for motion we do not understand any thought,\nbut only that a part of matter is so placed and stirred to motion, that\nit really would go somewhere if it were not prevented by any\ncause.", "\n\nIn addition to characterizing matter, however, IIIp6 is a foundational\nclaim about the nature of mind and, in particular, about human\npsychology. There is a basis, in Spinoza’s metaphysics, for thinking\nthat whatever is true about bodies is true about minds also in some\nsense (and see IIIp10 and IIIp11 for Spinoza’s account of striving and\nthe mind/body relation). Striving in physics, however, is understood\nas a tendency to a certain kind of motion, and motion seems, if\nanything does, to belong to bodies alone. So Spinoza needs to supply\nan account of the mental correlate to the physical “striving for\nmotion.” But IIIp6 leaves open the question of what it means for\na mind to strive. On this objection, the striving doctrine uses a kind\nof metaphorical language, the term ‘striving’, where a\nprecise and literal account of what it is that is characteristic of\nmind is required." ], "subsection_title": "1.2 The Striving Doctrine as an Account of the Natures of Particular Objects" }, { "content": [ "\n\nSpinoza’s naturalism benefits rhetorically from his use of the term\n‘conatus’ to describe the essences of human\nbeings and other finite modes alike. For the term is not only a\ntechnical term of Cartesian physics. Cicero uses the term in De\nNatura Deorum (and other Roman and Greek Stoics use close\ncognates) in a psychological sense, referring to human desire, and\nHobbes in his physiology uses the term to refer to the physical causes\nof human desire (Leviathan VI). So\n‘conatus’ has both broad, physical and\nspecifically human, psychological connotations which help to make the\ngap between nature and the human mind appear narrow.", "\n\nWhether Spinoza successfully capitalizes on his rhetorical skill,\nhowever, and draws a plausible account of the nature of the human mind\nout of his general account of the essences of finite modes depends upon\nIIIp9:", "III Proposition 9: Both insofar as the mind has clear and\ndistinct ideas, and insofar as it has confused ideas, it strives, for\nan indefinite duration, to persevere in its being and it is conscious\nof this striving it has.", "\n\nIIIp9 suggests that Spinoza is a psychological egoist of some sort.\nThat is, it suggests that he believes that what human beings desire to\ndo is to secure their own interests (construed here as perseverance in\nbeing). Indeed Spinoza goes on to define desire at IIIp9 as human\nstriving (or appetite) together with the consciousness of striving. So\nclearly human desire for Spinoza is part of the striving for\nperseverance in being and thus shares its character.", "\n\nThere is some question, however, about what variety of psychological\negoism Spinoza holds. Desire might be part of a striving for\nperseverance, after all, without all desires being desires for\nperseverance. One might have a strong instinctual desire for things\nwhich are instrumental to perseverance in being without desiring\nperseverance itself, for example. Or one might desire perseverance in\nbeing but also desire other kinds of things.", "\n\nIIIp9 might be supposed to support a very strong version of\npsychological egoism, orthodox egoism (perhaps Delahunty, 221, holds\nthis view). Orthodox egoism, is the view that human beings are always\nconsciously selfish. Under this view, A consciously desires only those\nobjects which benefit A, B desires only those objects which benefit B,\nand so on for all human beings. At IIIp9, Spinoza writes that the\nhuman mind seeks to persevere in being both insofar as it has clear\nand distinct ideas and insofar as it has confused ideas. It is natural\nto understand this claim to mean something like the following:", "Sometimes people do things which conduce to their\nperseverance and other times people do things which fail to so\nconduce. In both types of case, though, people desire to\npersevere. When I do something that fails to help me to persevere,\nit’s because the ideas on which I based my action were confused; that\nis, I thought I knew what would help me to persevere, but I was\nwrong. When I do something that does help me to persevere, though\n(unless I have simply been lucky in acting from an inadequate idea),\nit is because I acted on clear and distinct ideas or, in other words,\ngenuine knowledge about what would help me to persevere.", "\n\nThe categorical language Spinoza uses in the Appendix to Part I\nprovides explicit support for this interpretation of IIIp9: “men act\nalways on account of an end, viz. on account of their advantage, which\nthey want.” Moreover there are other important passages in Spinoza’s\nworks which are strongly compatible with the interpretation of Spinoza\nas an orthodox egoist. These include Ethics IVp8d, and his\npolitical writings, especially Ethics IVp36s2, and his\nPolitical Treatise, chapter 2)", "\n\nOther evidence suggests that Spinoza is not an orthodox egoist,\nhowever. In particular, there is reason to question whether the\nargument of the Ethics commits Spinoza to the account of\nactions following from confused ideas that the interpretation of IIIp9\nabove attributes to him. Part of IVp44s concerns those agents who are\nthe most confused. That passage is useful because it describes\nexplicitly the conscious thought-processes that precede action:", "Though men are liable to a great many affects, so that one\nrarely finds them to be always agitated by one and the same affect,\nstill there are those in whom one affect is stubbornly fixed. For we\nsometimes see that men are so affected by one object that, although it\nis not present, they still believe they have it with them. When this\nhappens to a man who is not asleep, we say that he is mad or insane.\nNor are they thought to be less mad who burn with Love, and dream, both\nnight and day, only of a lover or a courtesan. For they usually\nprovoke laughter. But when a greedy man thinks of nothing else but\nprofit, or money, and an ambitious man of esteem, they are not thought\nto be mad, because they are usually troublesome and are considered\nworthy of Hate. But Greed, Ambition, and Lust really are species of\nmadness, even though they are not numbered among the\ndiseases.", "\n\nIn this scholium (and in several other notable passages, including III\nDefinition of the Affects XLVIII and IVp20s) Spinoza describes a\nvariety of possible ends of human action, none of which is\nperseverance in being. Moreover, lest one think that the greedy man\nseeks profit because he mistakenly believes that it leads to\nperseverance, Spinoza emphasizes the point here that it is always one and\nthe same object that obsesses these men. A man seeking profit because\nhe believes that it leads to perseverance may be obsessed with two\nobjects, profit and perseverance, not one.", "\n\nIVp44s suggests that Spinoza holds a different kind of view,\npredominant egoism, the view that most people, most of the time\nconsciously desire perseverance in their own being. The particular\ntype of predominant egoism that IVp44s suggests introduces important\naspects of Spinoza’s ethical theory: if the most confused\npeople, people addled by greed or lust or ambition, are those who\nalways seek something other than perseverance in being, then perhaps\nSpinoza’s view is that, for any of us who act on some similar\nsentiments occasionally, we do so just to the extent that we also have\nconfused ideas. Thus human beings are predominantly egoistic because,\nby and large, we act rationally. It is rational to seek to persevere\nin being (see also what “reason demands” at IVP18S). So if\nwe were always rational, we would always pursue our own preservation,\nand orthodox egoism would be true, for Spinoza. But we are not\northodox egoists, on this interpretation of Spinoza as a predominant\negoist, just because we are not fully rational. To the extent that we\nhave confused ideas, we may indeed consciously pursue ends other than\nperseverance in being. On this interpretation of Spinoza, there is a\nright (or at least a rational) end to pursue—perseverance in\nbeing—and other ends are wrong (or at least irrational).", "\n\nIVp20 provides support for this interpretation of Spinoza’s\npredominant egoism:", "IV Proposition 20: The more each one strives, and is able,\nto seek his own advantage, i.e., to preserve his being, the more he is\nendowed with virtue; conversely, insofar as each one neglects his own\nadvantage, i.e., neglects to preserve his own being, he lacks\npower.", "\n\nHere Spinoza explicitly admits that a person may “neglect his own\nadvantage.” So IVp20 apparently contradicts the orthodox egoism of I\nAppendix. Moreover, IVp20 states that, to the extent that a person\ndoes seek perseverance in being, that person is virtuous. Virtue has a\nmetaphysical connotation in the Ethics. A thing’s virtue is\njust the same as its power (IVd8). But the term undeniably has moral\nconnotations as well. So IVp20 suggests, as IVp44s does, that\nconsciously trying to preserve oneself is right and neglecting to\npreserve oneself is wrong.", "\n\nIIIp9 admits of various interpretations. However, the weight of the\ntextual evidence supports the view that he is a predominant, not an\northodox, egoist. Any particular human desire, even a desire\nthat is not a desire for perseverance in being or its means, must on\nSpinoza’s view be related to perseverance in being in some way (by\nIIIp6 and IIIp9s). Spinoza’s discussion of desires for things other\nthan perseverance in being in passages such as IVp44s and IVp20\nsuggests moreover that such desires are part or product of confusion.\nSo passionate desires, for Spinoza, are often desires for things other\nthan perseverance in being, although they may be confused desires for\nperseverance as well (see IVp63s2 and other discussions of\nfear). Recent debates about whether the ends of human desire are\nreally important to his psychological theory and about how Spinoza\nunderstands human consciousness are likely to lend further support to\nthis view by showing how these passages and others like them may be\nreconciled with Spinoza’s more basic commitments in metaphysics and\nmind.", "\n\nFurther reading: For discussion of IIIp4,\nsee Matson 1977 and Garrett 2002. For interpretations of Spinoza’s\nargument from IIIp4–IIIp6, see Curley 1988; Della Rocca 1996;\nGarrett 2002 and Lin 2004. For discussions of historical sources of\nthe striving doctrine, see James 1993, Wolfson 1934, and LeBuffe\n2010a, pp.101–102. Youpa 2003 offers an account of self-preservation\nin Spinoza. For Spinoza’s physics and his use of\nDescartes, see Lachterman 1978, Peterman 2015 and 2017, and Schliesser 2017. Most book-length interpretations of the\nEthics include detailed accounts of Spinoza’s view of human\nnature. For discussion of IIIp9, see LeBuffe 2004 and 2010a, Chapters\n5–7. Some of the best general discussions of psychological\negoism come in the context of the interpretation of Hobbes, to whom\nSpinoza is sometimes compared. For these, see Kavka 1986 and Hampton\n1986." ], "subsection_title": "1.3 The Striving Doctrine as an Account of Human Nature" } ] }, { "main_content": [ "\n\nSpinoza’s account of the affects (affectus) of the human mind\nis a response to one of the central problems for his naturalism. It is\nan attempt to show how the wide range of desires and emotions of the\nhuman mind can be produced by something which follows the order of\nnature. At the start of Part III (see also Chapter 2 of his\nPolitical Treatise), Spinoza notes that traditional accounts\nof the passions, with the exception of Descartes’s, have rested on the\nassumption—one wholly baseless in Spinoza’s view—that\nhuman beings are a separate “dominion” within the dominion of nature,\nwith different kinds of constituents and governed by different sorts\nof laws. Spinoza’s project continues what he finds to be Descartes’s\nimportant innovation: seeking “to explain human affects through their\nfirst causes.” So his account of the affects may be most profitably\ncompared to Descartes’s in his Passions of the Soul. It may\nalso be usefully compared to accounts in the writings of Hobbes\n(especially Leviathan VI), a contemporary who shared many of\nSpinoza’s philosophical commitments, or to some of the “traditional\naccounts” which Spinoza faults, such as Aquinas’s Summa\nTheologiae. (Aquinas’s treatments of the passions appear mainly\nbetween Ia75 and 2a2ae189.)", "\n\nSpinoza, though, because he denies freedom of the will, is more\nthorough than Descartes in his commitment to naturalism. This\ncommitment makes the task Spinoza undertakes in the Ethics an\neven more dramatic revision of traditional understandings of the\npassions than that which Descartes produced. So Spinoza, even more\nthan Descartes, is open to the sort of objection which traditional\nauthors, those to whom it seems beyond question that human beings are\noutside nature, might raise: how can the full range of human\npsychological phenomena be produced by natural causes? For the\nargument of the Ethics to succeed, Spinoza must produce,\nfirst, an account of how human desires and emotions might be a part of\nnature as he has presented it in the Ethics and, second, a\ndescription of those human desires and emotions which is plausibly\ncomplex, that is, plausibly consistent with our experience of\nourselves. The subsections which follow address these issues in turn.\n" ], "section_title": "2. The Affects", "subsections": [ { "content": [ "\n\nThe human affects, for Spinoza, are a part of nature insofar as each\ncan be redescribed in terms of striving, a property which all\nparticular things in nature share. Desire and its varieties are\nstriving itself, under a certain description. Human passions are for\nSpinoza changes, that is, increases or decreases, in the power with\nwhich we, or parts of us, strive. Active affects are all increases in\nthe power with which we strive.", "\n\nSpinoza introduces the first of his primary affects, desire, at\nIIIp9s, directly after introducing the doctrine of human striving,\nwhich, in its most general form, he calls appetite.", "III Proposition 9, Scholium: …Between appetite and\ndesire there is no difference, except that desire is generally related\nto men insofar as they are conscious of the appetite. So desire can be\ndefined as appetite together with consciousness of the\nappetite.", "\n\nThus Spinoza identifies human desire with human essence and especially\nwith consciousness of one’s essence, the striving for perseverance in\nbeing. Spinoza’s theory of consciousness is notoriously difficult, and\nit is not clear which ideas in a human mind are conscious or the\nextent to which things other than human beings have consciousness. For\nhuman beings, at least, however, what seems to us to cause us to act,\nour desire, does, on Spinoza’s view, do just that. If I am asked for\nthe proximate cause of my action in picking up my coffee cup, for\nexample, I will respond that it was my desire for the coffee. In\nidentifying the cause of human action, striving, with conscious\ndesire, then, IIIp9s vindicates common sense to a degree. Had Spinoza\nidentified desire with something other than striving, then he would\nhave committed himself to the view that my desire does not in fact\ncause me to pick up the cup. (Desire for Spinoza, in its narrow\ndefinition at IIIp9s, is both psychological and physical, and in its\nbroader definition at III, Definitions of the Affects I, it may be\neither. This example therefore, perhaps despite appearances, need not run\nafoul of Spinoza’s denial of mind-body interaction.)", "\n\nIIIp9s, then, goes a long way toward showing how the universal\nstriving doctrine can be the basis for an account of human desire. A\nserious problem remains, however. Although we tend to see desire as\nthe proximate cause of action, we tend also to conceive of desire as\ninvolving teleology or final causes. If desire causes me to pick up\nthe cup, how does it do so? The common-sense answer is\nteleological: I have, as an end, coffee, and I am, in a sense, drawn\ntoward it. Spinoza is well-aware of the fact that we commonly\nsuppose that there are teleological causes of our actions, and some accounts of appetite in the Ethics, notably IVd7, seem to incorporate teleological notions. However, Spinoza also explicitly denies that appetite is anything other than an efficient cause. This passage is from Part IV’s Preface:", "What is called a final cause is nothing but a human\nappetite insofar as it is considered as a principle, or primary cause,\nof some thing. For example, when we say that habitation was the final\ncause of this or that house, surely we understand nothing but that a\nman, because he imagined the conveniences of domestic life, had an\nappetite to build a house. So habitation, insofar as it is considered\nas a final cause, is nothing more than this singular appetite. It is\nreally an efficient cause, which is considered as a first cause,\nbecause men are commonly ignorant of the causes of their\nappetites.", "\n\nSpinoza does not clearly deny, here, that there are teleological causes of\naction. (For arguments against the view that Spinoza denies all\nteleology, see Garrett 1999 and Lin 2006. Carriero 2005 is an influential argument that Spinoza does deny all teleology.) He does, however, identify such causes\nwith efficient causes. He needs to show, then, how the ends of human\naction relate to the processes of efficient causation. ", "\n\nFor this task, Spinoza introduces the other primary affects and a\nnumber of psychological laws associated with them. He introduces the\nprimary passions at IIIp11s.", "III Proposition 11, Scholium: We see, then, that the mind\ncan undergo great changes, and pass now to a greater, now to a lesser\nperfection. These passions, indeed, explain to us the affects of Joy\n[laetitia] and Sadness [tristitia]. By Joy,\ntherefore, I shall understand in what follows that passion by which the\nmind passes to a greater perfection. And by Sadness, that passion by\nwhich it passes to a lesser perfection.", "\n\nThe perfectionist language Spinoza uses is important for an\nunderstanding of the basis for ethics that he finds in psychology.\nHere, however, it may be understood in terms of striving. An increased\npower to persevere in being is for Spinoza a transition to greater\nperfection and a decreased power is a transition to lesser perfection\n(see IIIp11, the end of IV Preface, and especially III, Definitions of\nthe Affects, III, Exp.). So, although this generalization is\ncomplicated by Spinoza’s definitions that refer passions either to\nparts of the body or to the body as whole, joy is the passion one\nexperiences in the transition to an increased power to strive, and\nsadness is the passion one experiences in the opposite\ntransition. Spinoza thus provides, in his account of the affects, the\nbasis for an explanation of how it is that introspection into our\nconscious experience of desire might fail to bring us accurate\nknowledge of our own psychological processes. Our conscious\nexperience in forming our desires, has an emotional component: we experience\njoy and sadness and varieties of these. But we may be unaware of why\nwe feel joy or sadness or why, really, we desire what we desire. So\nSpinoza writes repeatedly, in the context of his criticisms of\nteleological reasoning and the introspective experiences of free will\nor mind/body causation (e.g., at IIIp2s): “men are conscious of their\nactions and ignorant of the causes by which they are determined.”", "\n\nSpinoza characterizes the apparent teleology in desire at IIIp28:", "We strive to promote the occurrence of whatever we imagine\nwill lead to joy, and to avert or destroy what we imagine is contrary\nto it, or will lead to sadness.", "\n\nSpinoza reserves the term ‘imagine’ [imaginor]\nfor the description of conscious states, so IIIp28 describes, at least\nin part, the objects of desire. If I imagine that coffee will lead to\njoy, then I will desire that joy and so that coffee. IIIp28, strictly\nspeaking, is not an exhaustive characterization of objects of desire.\nIt implies only that we desire anything which we imagine will lead to\njoy and are averse to whatever we imagine will lead to sadness and not\nthat we might not have other kinds of desires also, desires unrelated\nto either joy or sadness. A review of the particular forms of desire\nSpinoza catalogues in Part III (see, notably, IIIp27c3s, IIIp29s,\nIIIp40c2s,IIIp41, and IIIp56s) suggests, however, that the view is\nstill stronger than the limited claim of IIIp28: it seems that Spinoza\ndoes hold that anything I desire will be a thing which I imagine will\nlead to joy and that anything I am averse to will be something which I\nimagine will lead to sadness.", "\n\nWhat may seem on introspection, then, to be a wholly teleological\ncause of action, the end represented by an object of desire, is for\nSpinoza a peculiar manifestation in consciousness of striving, which\nin turn is an efficient cause of action. I reach for the cup of\ncoffee, I may think, just because the joy that I anticipate in the\ncoffee “pulls” me to it; in fact, however, I reach for the coffee\nbecause my characteristic striving (perhaps as a partial cause in\ncombination with other partial causes such as the memory of past\ncups—IIIp36) has that effect. It “pushes” me toward the cup." ], "subsection_title": "2.1 The Affects and Striving" }, { "content": [ "\n\nPerhaps the psychological view that Spinoza introduces at IIIp28 is\nsusceptible to the sort of objection which one might raise against\npsychological hedonism, the view that human beings only desire\npleasure, the avoidance of pain, and what is instrumental to these\nthings. It may seem to some people that IIIp28 is not consistent with\ntheir own experience of their motives in acting. So, someone with a\nstrong sense of justice might say: ", "It’s not that I like Jones or would get any joy from having\nhim walk. I think the guy’s a jerk, and I hate to think of him out on\nthe street. But I want him to be released from prison. He simply did\nnot do what he’s been convicted of, so he should be set\nfree.", "\n\nOn the basis of introspective observations like this one, one might\ncomplain that, even if Spinoza’s account of the affects can be shown\nto be consistent with the general theory of striving as it is\npresented at IIIp6, still the theory of affects is not itself a\nrealistically complex account of human desire, since it cannot account\nfor desires like this one in which, on the face of it, one anticipates\nsadness in the desired end. The plausibility of Spinoza’s view depends\nupon the extent to which it can reasonably redescribe this desire, and\nother similarly troubling desires, in ways which are consistent with\nIIIp28.", "\n\nSpinoza attempts to show that there are many varieties of joy, sadness,\nand desire. Thus he might attempt to address the complaint by showing\nthat its author offers a slightly inaccurate description of the\nsituation:", "The author denies liking Jones. Let us suppose even that\nhe hates Jones. Even so, that does not mean that the author\nanticipates no joy at all in Jones’s release. Knowing that his\nsociety is just in at least this one case may reassure the author\ninasmuch as it gives him reason to think that he might be fairly\ntreated himself. That is, it might be a kind of hope (IIIp18s2) which\nmotivates the desire. Or perhaps there are people the author likes,\nhis fellow citizens generally perhaps, to whom he wishes a similar\npeace of mind. The author may want the release in order to find a kind\nof joy, whether it be out of his ambition to please them or simply out\nof his human kindness (IIIp29s) or nobility (IIIp59s), in the\nwell-being of these other people.", "\n\nFar from insisting that there is one particular kind of emotion that\nmoves people, Spinoza writes that there is an innumerable variety of\naffects:", "III Proposition 56: There are as many species of Joy,\nSadness and Desire, and consequently of each affect composed of these\n(like vacillation of mind) or derived from them (like love, hate, hope,\nfear, etc.), as there are objects by which we are\naffected.", "\n\nIIIp51 assures us, moreover, that the same object might affect\ndifferent people, or even the same person at different times, in\ndifferent ways. So Spinoza protects himself from the charge that IIIp28\nis obviously false (albeit at the risk of forwarding an unfalsifiable\npsychological claim) by arguing that, despite the seeming simplicity of\nthat proposition, it cannot be falsified by the great variety of\nconscious human motives.", "\n\nAlthough Spinoza repeatedly insists that the variety of affects is\ninnumerable, he nevertheless does characterize, in his own terms, many\nof the traditional passions, each of which is a kind of joy,\nsadness, or desire. A few of Spinoza’s\nparticular accounts are notable.", "\n\nPity (commiseratio) is for Spinoza a species\nof sadness, sadness that arises from injury to another (IIIp22s), and\nso to feel pity, on Spinoza’s view is to experience a decrease in\none’s own power to persevere in being. If continued perseverance in\nbeing is what virtuous agents seek, then, Spinoza will be committed to\nthe view that pity is not a virtue. Indeed, Spinoza writes at IVp50c,\n“A man who lives according to the dictates of reason, strives, as far\nas he can, not to be touched by pity.” So Spinoza stands apart from\ntraditional Christian views on this subject (and also on the subjects\nof humility and repentance), and with Hobbes who conceives of pity in\nLeviathan VI as a kind of grief and so a decreasing of human\nperfection. This revisionary tendency in his thought is tempered,\nhowever, by IIIp54, where he presents pity, and also the other\ntraditional Christian virtues of humility and repentance, as, if not\ngenuine virtues themselves, at least means to virtue, by which people\nare made more able to come to learn to follow the dictates of\nreason.", "\n\nSelf-esteem (acquiescentia in se ipso) which\nSpinoza introduces at IIIp30 as Joy accompanied by the idea of oneself\nas an internal cause becomes an important part of Spinoza’s ethical\ntheory, a species of which is even blessedness (beatitudo,\nsee IV, App. 4), the highest form of human happiness. Human beings, as\nfinite modes, cannot on Spinoza’s view avoid affecting and being\naffected by external objects. Nevertheless, Spinoza’s emphasis on\nself-esteem and, in his ethical theory, on self-knowledge suggests\nthat to the extent that we are able to bring about effects, including our\nown emotions, as whole or adequate causes of those effects we are more free and\nbetter off. His remarks concerning the impossibility of controlling\nthe passions and the desirability of controlling them nevertheless to\nthe extent that we can (V Preface) similarly emphasize the ethical\nimportance of self-knowledge and freedom from external influences.", "\n\nFear (metus) and wonder (admiratio), together with the theory of the imitation of affects, are notions that are fundamental to Spinoza’s accounts of human society. Reasonable citizens (or all citizens insofar as they are reasonable) will willingly obey the rules of the state (IVp37s2, IVp73). Fear, in the Ethics, seems to be government’s most valuable means of bringing passionate citizens to cooperate and obey: at IVp37s2, Spinoza suggests that states should rely on threats. In the Theological Political Treatise, however, Spinoza’s accounts of religion, and particularly of miracles and scripture, suggest that devotion devotio, a passion associated with wonder at Ethics IIIp52s, is a better political motive than fear. In Chapter 5, for example, Spinoza writes of Moses’s introduction of religion into the Hebrew state:", "Two things in particular forced this on him: the stubborn mentality of the people (because it would not allow itself to be compelled solely by force) and the threat of war. For if war is to go well, it is better to encourage the soldiers than to frighten them with penalties and threats. In this way they will be eager to distinguish themselves for excellence and nobility of spirit rather than merely to avoid punishment.", "\n\nThe theory of the imitation of affects informs these and other accounts of social dynamics in Spinoza. Human beings tend, he argues, to imitate the affects of those that we take to be similar to ourselves (IIIp27), and we tend, when we feel a given affect toward a person whom we take to differ from us, to feel that same affect toward that person’s whole class or nation (IIIp46). Spinoza grounds these doctrines on a series of claims about our associative tendencies at Ethics IIIpp14–24. ", "\n\nFinally, active joy and active desire\nwhich Spinoza introduces at IIIp58 represent a separate class of\naffects notable both for their novelty against the background of\ntraditional accounts of the passions and also for their importance to\nSpinoza’s ethical arguments of Parts IV and V. On traditional accounts\nof the passions, even Descartes’s (The Passions of the Soul,\nI.1), actions and passions are the same thing, regarded from different\nperspectives: when A does X to B, X is an action for A but a passion\nfor B. For Spinoza, however, anything which follows in a person where\nthat person is an “inadequate” or partial cause of the thing, is a\npassion, and anything that follows where a person is an “adequate” or\ntotal cause of the thing is an action. Thus Spinoza’s class of active\naffects places a strong emphasis on people’s roles as total causes of\nwhat they do; because it becomes for Spinoza ethically important that a\nperson be active rather than passive, that emphasis raises a host of\nquestions about the extent to which a person, a particular thing\ninteracting constantly with other things and indeed requiring some of\nthem for sustenance, can come to resist passion and guide himself by\nmeans of joy and the active desires. ", "\n\nBecause joy and sadness as introduced at IIIp11s are passions, all\nof the desires arising from them or species of them are passive as\nwell, that is, they are not desires which arise from a person’s\nstriving alone but only as a partial cause in combination with other,\nultimately external causes. Active joy, which must include at least\nsome types of warranted self-esteem, and active desires, among which\nSpinoza lists at IIIp59s tenacity (animositas) and nobility\n(generositas), are wholly active however; that is, they are\nemotions and desires that people have only insofar as they are adequate\ncauses, or genuine actors. (Notice that sadness cannot ever be an\nactive emotion. People cannot, insofar as they are active bring it\nabout that their power of acting is decreased, so passive sadness,\nunlike passive joy and desire, has no active counterpart.)", "\n\nOf these active affects, the most important for an interpretation of\nSpinoza’s ethics and political philosophy is likely\nnobility. Spinoza’s predominant egoism, together with some of his\nstill stronger statements of psychological egoism such as that at I\nAppendix, suggest that individuals are not, or are not often,\naltruistic. Moreover, his ethics, with its emphasis on self-esteem and\nself-knowledge appears in ways to be an individualistic one: the good,\nwhen I attain it, is a perfection of myself, not of society or the\nworld. However, Spinoza does offer an argument (IVp37) for the view\nthat any good that I want for myself I will have reason to want for\nothers as well, and, in the Ethics, this argument forms the\nbasis of morality and the state (IVp37s1 and s2, respectively). This\nis also a theme of the opening sections of the Treatise on the\nEmendation of the Intellect (see, especially, Spinoza (1), II/8\n23-II/9 3). Nobility is the active affect most closely related to\nSpinoza’s views about morality and the state. As Spinoza defines it,\nit is a wholly active desire to join others in friendship and to aid\nthem. It helps to supply, in Spinoza theory of the affects, a basis\nfor the view that aiding others is virtuous and rational.", "\n\nFurther reading: Recent interpretations of\nSpinoza’s theory of consciousness include Miller 2007, Garrett 2008,\nNadler 2008, LeBuffe 2010c, and Marshall 2014. For a discussion of\nSpinoza’s rejection of Cartesianism and of the theory of action that\nfollows from his theory of ideas, see Della Rocca 2003. For\ndiscussions of Spinoza’s theory of affects in a comparative framework,\nsee Voss 1981 and 1993, Hoffman 1991, and James 1997. For discussions\nof the relationship between striving and the affects, see these works\nand also Della Rocca 2008a, which is critical of Spinoza’s view,\nLeBuffe 2009, Davidson 1999, and Schrijvers 1999. Bennett 1990, Curley\n1990, Della Rocca 1996, Garrett 1999, and Lin 2006 discuss Spinoza’s\nviews on teleology. For a discussion of the connection between the\naffects and desire in 3p28, see LeBuffe 2010a, Chapters 5–7 and\nDella Rocca 2008b pp. 156–172. Voss 1981 and 1993 offers an\ninterpretation and a history of Spinoza’s accounts of particular\naffects. Lloyd 1994 offers accounts of various particular\naffects. For discussions of self-esteem, see Rutherford\n1999 and Carlisle 2017. For discussion of fear and wonder, see LeBuffe 2015 and 2018, Chapter Four. For accounts of imitation of affects, see Della Rocca 2008b, Chapter 4 and Shapiro 2017. For discussion of nobility, see Youpa 2020, Chapter 10. " ], "subsection_title": "2.2 The Variety of Affects" } ] }, { "main_content": [ "\n\nSpinoza’s insistence that human beings not be treated as a dominion\nwithin a dominion includes a commitment to ethical naturalism also.\nJust as he insists that the human mind must be explicable in terms of\nthe laws which govern nature, so he insists that ethical properties,\nwhich he sometimes characterizes as human “modes of thinking,” be\nexplicable in terms of natural ones. The theory of the affects serves\nSpinoza’s ethical naturalism by introducing explanations of ethical\nconcepts, most importantly the concepts of good, evil, and perfection,\nin psychological terms. In his ethics, Spinoza in some way “retains\nthese words,” although he may be understood to do so under some formal\nrefinement or revision of them (See IV Preface). So his discussions of\ngood and evil and of human perfection in Part III provide the basis for\nthe formal ethical argument which follows in Parts IV and V. " ], "section_title": "3. The Psychological Basis for a Theory of Value", "subsections": [ { "content": [ "\n\nBefore defining ‘good’ and ‘evil’ formally,\nSpinoza at IV Preface regards good and evil as labels, “modes of\nthinking,” that human beings apply to things but which really reveal\nlittle about the things to which they are applied: ", "As far as good and evil are concerned, they also indicate\nnothing positive in things, considered in themselves, nor are they\nanything other than modes of thinking, or notions we form because we\ncompare things to one another. For one and the same thing can be good,\nand [evil], and also indifferent. For example, Music is good for one\nwho is melancholy, [evil to] one who is mourning, and neither good nor\n[evil] to one who is deaf.", "\n\nThe phrase “nothing positive in things” means perhaps that an\nobserver of people would find that ‘good’ and\n‘evil’, as people use them are two place predicates rather\nthan one place predicates. If Martha calls music evil, then, what that\nindicates to one who knows about the human use of these terms is that\nthe music is evil to Martha. Moreover, since the same music can be good\nor evil for different people, or for people in different states, the\ntwo-place predication reveals more about Martha than about the music.\nIt must be some fact about the person, rather than some fact about the\nthing called good or evil, that is of central importance to the\nunderstanding of the label.", "\n\nIIIp9s suggests that the fact about the person which the label\nreveals is her conative state:", "It is clear that we neither strive for, nor will, neither\nwant, nor desire anything because we judge it to be good; on the\ncontrary, we judge something to be good because we strive for it, will\nit, want it, and desire it.", "\n\nSpinoza finds that the designation of a thing as good follows from a\nperson’s conative state: Martha is averse to music and therefore she\ncalls it evil. Should the music become good to another person, or\nperhaps Martha herself in different circumstances, it would not be\nbecause the music has changed, but because the person’s conative state\nis different: she desires the music. (This analysis of the good is\nsimilar to Hobbes’s at Leviathan VI. Maimonides, another of\nSpinoza’s influences, also has a similar analysis:\nGuide of the Perplexed, III, 13.)", "\nIIIp39s builds upon IIIp9s. There Spinoza writes that, “each\none, from his own affect, judges, or evaluates, what is good and what\nis [evil]…So the greedy man judges an abundance of money best,\nand poverty worst. The ambitious man desires nothing so much as esteem\nand dreads nothing so much as shame.” However, IIIp39s also uses\nSpinoza’s theory of the affects to introduce new definitions of\ngood and evil:", "By good here I understand every kind of joy, and whatever\nleads to it, and especially whatever satisfies any kind of longing,\nwhatever that may be. And by evil, every kind of sadness and especially\nwhat frustrates longing.", "\n\nIIIp28, the proposition establishing Spinoza’s doctrine that human\nbeings desire whatever will bring joy and are averse to whatever will\nlead to sadness, allows Spinoza to connect the objects of any human\ndesire with joy or the avoidance of sadness. So, if it is true that we\ncall a thing good only if we desire it, then it will also be true that\nanything we call good will be joy or what leads to it. Understood in\nthis way, IIIp39s simply restates the doctrine of IIIp9s in light of\nIIIp28.", "\n\nHowever, Spinoza might be extending rather than merely restating his\nposition at IIIp39s. Every kind of joy we experience is not presumably\na result of conscious desire, and Spinoza allows at IIIP39s that these\ninstances of joy (i.e., those which do not satisfy any kind of\nlonging) are also good. On this view, not only is whatever Martha desires good\nfor her, but, in addition, anything which she does not desire but\nwhich nonetheless might bring her joy will also be good. Perhaps, for example, Martha will take delight in a view that she never anticipated, a serendipitous good. IIIp39s, so understood, identifies the good and evil for a person with broader\nclasses of things, and makes possible an analysis of good and evil in\nterms of something other than an individual person’s current\ndesires. Because, in giving an account of the right way of living in\nParts IV and V, Spinoza presumably urges people to desire and do\nthings in a way different from what they desire and do already, this\nbroadening of the application of the terms ‘good’ and\n‘evil’ (to apply to things other than what people\npresently desire or are averse to) contributes to the plausibility of\nhis ethical naturalism." ], "subsection_title": "3.1 Good and Evil as Modes of Thinking" } ] } ]

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[ { "href": "../descartes/", "text": "Descartes, René" }, { "href": "../emotions-17th18th/", "text": "emotion: 17th and 18th century theories of" }, { "href": "../hobbes/", "text": "Hobbes, Thomas" }, { "href": "../spinoza/", "text": "Spinoza, Baruch" } ]

[ "\n\nAttributes sit at the very heart of Spinoza’s metaphysics.\nThey enable us to understand and talk about an extended world and a\nthinking world in terms of which we understand such things as bodies and minds.\nFurthermore, it is due to the relation of attributes to one another and\nto the infinite substance that an elegant resolution to the Cartesian\nmind–body problem is possible. Attributes furnish Spinoza’s\nsubstance with variety while preventing it from being an ephemeral,\nhomogenous totality—an eleatic “one” of which nothing\ncan be said or known. They constitute variety without dissolving the\ninfinite substance into multiple substances.", "\n\nSpinoza defines the term “attribute” in Definition 4 of\nPart One of the Ethics thus: “Per attributum\nintelligo id, quod intellectus de substantia percipit, tanquam ejusdem\nessentiam constituens.” That is, “By attribute I\nunderstand what the intellect perceives of substance as constituting\nits essence.”[1]\n Nonetheless, it is astonishing how little agreement there is among\nscholars as to some of the most basic features of Spinoza’s\ntheory of attributes. For this reason, this article first considers the important\nplaces where Spinoza establishes fundamental characteristics of\nattributes: such as their definition, their real distinction, and their\nidentification with the substance. It then explains the main\nissue on which interpretations diverge and signals in broad terms which\ninterpretative avenues have been taken or are conceptually open\n(without delving too deeply into any one of them). In light of these\nvery different interpretative avenues the article revisits some of the\ncharacteristics explained in the first part and considers how they are\naffected by the different kinds of interpretations. Finally, and\nperhaps most importantly, given the holistic and systematic nature of\nSpinoza’s metaphysics and the central role attributes play in it,\nthe article points out how the different interpretative options on one\nissue bear on others (e.g. the number of attributes and the\nunderstanding of 2P7 and its scholium). The different ways of\nunderstanding Spinoza’s theory of attributes inevitably give rise\nto very different conceptions of Spinoza’s metaphysics as a\nwhole." ]

[ { "content_title": "1. Attributes in the ", "sub_toc": [ "1.1 What are Attributes?", "1.2 Definition of Attribute", "1.3 Real Distinction", "1.4 The Identification of Attributes with Substance", "1.5 Extension as a Divine Attribute", "1.6 The 2P7 Doctrine", "1.7 The Two Known Attributes", "1.8 Ambiguities and Interpretative Directions", "1.9 Implications of the Various Readings on Other Spinozistic Doctrines" ] }, { "content_title": "2. Attributes in the ", "sub_toc": [] }, { "content_title": "3. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nBefore discussing the theory of attributes in the Ethics,\nit will be helpful to keep in mind a rudimentary sketch of the general\nstructure of Spinoza’s\nontology:[2]\n", "\n\nThere is only an infinite substance (1P14), that is, there are no\ncreated substances. The infinite substance consists of infinite\nattributes (1D6). Every mode, be it finite or infinite, must be\nconceived through an attribute (1D5, 1P10Schol, 2P6 and 2P6Dem).\nFinally, what other philosophers consider to be “created\nsubstances,” such as my mind (as well as my body), are finite\nmodes for Spinoza\n(1P11).[3]\n" ], "section_title": "1. Attributes in the Ethics", "subsections": [ { "content": [ "\n\nSpinoza is not the first to furnish his metaphysics with attributes\nand in that he is following a very long tradition. He is, though,\nmostly influenced by Descartes, and in some ways is trying to keep with\nDescartes’ notion of “attribute.” It therefore will\nbe useful to look back and get a sense of what Descartes had in mind\nand thus get a preliminary grasp (which will be revised) of what\nSpinoza means by “attribute.” Descartes states in the\nPrinciples of Philosophy that attributes are the essence of a\nthing, so the essence of mind is thought or thinking, and the\nessence of body is to be extended (Principles, I, §53,\nCSM, I, p. 210, AT 25). To see why this is so, it is worth revisiting\nthe first and second Meditations, even if very briefly. Let us\nbegin with body and Extension. To understand the essence of body, we\ncan look to the famous wax example in Meditation Two\n(CSM, II, p. 20–21, AT 30–32). While sitting by the\nfireplace, Descartes inspects a piece of wax and asks himself what he\nknows of the wax. He begins by listing all the sensory properties of\nthe wax: it is white, has a certain smell, makes a certain sound when\none raps it with one’s finger, is hard, and has a certain taste.\nAfter listing all its sensory properties, he then places the piece of\nwax by the fire and sees how it loses all those properties: it\nchanges color, smell, texture, taste, etc. Descartes concludes, among\nother things, that the essence of the wax, insofar as it is a body, is\nthat it is extended in length, breadth, and depth since that\nis the only thing that remains constant about the wax. In this respect,\nthe piece of wax is no different from any other body—that is, its\nessence is to be extended. Extension, then, according to Descartes, is\nthe essence of body. In the Meditations we also, famously,\ncome to recognize our own essence as thinking things. We realize this\nby recognizing that we cannot doubt that we are doubting while\ndoubting. Furthermore, we realize that doubting in this sense is no\ndifferent from understanding, affirming, denying, willing, unwilling,\nimagining, and having sense perceptions (seeming to see, etc.) (CSM,\nII, p. 19, AT 28). Descartes then reaches the conclusion that the\nessence of the mind is Thought. For these reasons, Descartes claims\nthat Thought and Extension are the principal attributes of mind and\nbody and that they are “really distinct”, that is, they\nexist independently one from the\nother.[4]\n It is important to note\nthat for Descartes, any created substance has only one\nprincipal attribute, as opposed to God who has infinite attributes.", "\n\nSpinoza adopts some aspects of the Cartesian set up while rejecting\nothers. He agrees that Thought and Extension are attributes (2P1, 2P2)\nand are related to essences (1D4). He agrees they are “really\ndistinct” from each other\n(1P10Schol).[5]\n Furthermore, he agrees\nthat “mind” has to be conceived through Thought, and\n“body” through Extension. (2P5 and its demonstration make\nthe case with regard to ideas and Thought; 2D1 establishes it for\nbodies and Extension. This is also made very clear in 3P2 and its\ndemonstration.) However, he does not agree that they are attributes of\ncreated substances, since he rejects the possibility of\ncreated substances altogether (1P6Cor., 1P8Schol1, 1P14). One way to\nunderstand Spinoza is to see how he can hold both Thought and Extension\n(and other attributes, if there are others) to be divine attributes or\nattributes of one and the same (infinite)\nsubstance.[6]\n" ], "subsection_title": "1.1 What are Attributes?" }, { "content": [ "\n\nSpinoza defines the term “attribute” thus:\n“By attribute I understand what the intellect perceives\nof substance as constituting its essence” (1D4). This definition\nis reminiscent of Descartes’ notion of attributes as it appears\nin the Principle of Philosophy insofar as attributes are\nrelated to the essence (or essences) of substance. However, as many\nhave noticed, it is not clear from the definition alone what exactly\nSpinoza means. There are several, by now famous, ambiguities in\nthe\n definition.[7]\n These, together with the different\ninterpretative options, are discussed in\n Section 1.8." ], "subsection_title": "1.2 Definition of Attribute" }, { "content": [ "\n\nSpinoza makes a very important claim about attributes in the\nScholium to Proposition 10 of Part One: “…although two\nattributes may be conceived to be really distinct (i.e., one may be\nconceived without the aid of the other), we still cannot infer from\nthat that they constitute two beings, or two different\nsubstances.” Spinoza here is explaining something about the\nrelationship among attributes—one may be conceived without the\naid of the other—and about the relation of the attributes to the\nsubstance, namely, that conceiving attributes independently is not\nevidence of the existence of independent substances.", "\n\nTo understand why this scholium is so important, it is helpful to\nrecall Descartes’ definition of a “real distinction.”\nIn the Principles of Philosophy, Descartes says:\n“Strictly speaking, a real distinction exists only\nbetween two or more substances; and we can perceive that two substances\nare really distinct simply from the fact that we can clearly and\ndistinctly understand one apart from the other”\n(Principles, I, §60, CSM, I, p. 213, AT 28). For\nDescartes, this anchors the strict epistemological and ontological separation between mind and\nbody. One of the things we learn from going through the\nMeditations is that we are capable of clearly and distinctly\nperceiving ourselves without a body—the cogito in the\nSecond Meditation, and we clearly and distinctly perceive body\nwithout thinking in the Fifth Meditation. (Of course, in\nretrospect, we realize that we already did this in a sense with the wax as\nwell). Descartes thus concludes that mind and body are really distinct,\nthat is, one can exist without the other.", "\n\nOne important implication of this distinction is that it allows for\na fully mechanistic explanation of the physical world. To explain the\ninteraction between two bodies requires alluding only to their physical\nproperties (size, shape and motion) without the need to take recourse\nto any Aristotelian explanation involving\n final causes.\nMaking room for mechanistic explanations, that is, for the\nNew Science, was one of Descartes’ chief motivations for writing\nthe Meditations. Spinoza preserves this aspect of\nCartesian doctrine (cf. appendix to Part One of the Ethics and\ndiscussion in\n Section 1.3.1).", "\n\nHaving separated the mind so sharply from the body, Descartes is\nleft with having to explain their evident unity. More specifically, he\nis burdened with trying to explain how two really distinct substances\nseem to interact causally. Their causal interaction seems\nproblematic because, according to Descartes, each substance is\nindependent; the infinite substance depends on nothing but itself\n(Principles, I, §51, CSM, I, p. 210, AT 24), while\ncreated substances depend on nothing but God for their\nexistence (Principles, I, §52, CSM I, p. 210, AT 25). If\ndistinct substances interact causally then they seem to depend on one\nanother, and this would go against their nature qua\nsubstances. This is why the union of the mind and body is a\nthorny issue for Descartes, and was and continues to be a source of\nmuch debate (Cf. for example, Hoffman, 1986). For some, a version of\nthis problem translates into Spinoza’s metaphysics (cf.\nSection\n 1.9.4).\nThe issue of the nature of the\n“real distinction” for Spinoza is discussed in the\nsubsequent section.", "\n\nFor Descartes, then, there is the epistemological claim that\nperceiving Thought does not involve perceiving Extension and vice\nversa. Each is explanatorily independent from the other, (although not\nfrom God). Spinoza adopts this aspect of Cartesian philosophy and\nholds, as well, that there is what Della Rocca calls, “a\nconceptual barrier” between Thought and Extension as Spinoza\nstates in the scholium “i.e., one may be conceived without the\naid of the other” (Della Rocca, 1996, 9–17). Spinoza holds\nThought and Extension to be explanatorily self-contained. Physical\nchanges are to be understood in terms of other physical items, and\nideas are to be understood in terms of other ideas. What is ruled out\nis what can be called “cross attribute explanations.” For\nexample, explaining the movement of my hand by my desire to move my\nhand. According to Spinoza, the movement of my hand is to be explained\npurely physically by alluding to other bodies and their motions, while\nmy desire is to be explained by other desires and ideas. Spinoza makes\nthis very clear in 3P2, its demonstration and scholium:", "\n\n\n\n3P2: The body cannot determine the mind to thinking, and the mind\ncannot determine the body to motion, to rest, or to anything else (if\nthere is anything else).\n\n\n\nDem.: All modes of thinking have God for a cause, insofar as he is a\nthinking thing, and not insofar as he is explained by another attribute\n(by 2P6). So what determines the mind to thinking is a mode of thinking\nand not of extension, that is (by 2D1), it is not the body. This was\nthe first thing.\n\n\n\nNext, the motion and rest of a body must arise from another\nbody…whatever arises in the body must have arisen from God\ninsofar as he is considered to be affected by some mode of extension,\nand not insofar as he is considered to be affected by some mode of\nthinking (also 2P6), that is, it cannot arise from the mind, which (by\n2P11) is a mode of thinking. This was the second point. Therefore, the\nbody cannot determine the mind, and so on, q.e.d.\n\n", "\n\nAlthough this is reminiscent of Descartes in some respects, there\nis, of course, one crucial difference. For Descartes the fact that one\ncan conceive Thought distinctly from Extension is evidence for the\nexistence of two substances—mind and body. For Spinoza, this is\nnot the case, and this is the point he is making in this central\nproposition (1P10), namely, that although two attributes may be\nconceived independently—one without the other—this does\nnot imply that there are two substances existing separately.\nFor Spinoza there is only one substance with infinite attributes, and\nalthough each attribute is conceived independently from the other/s\nthey still are, nonetheless, all attributes of one and the same\nsubstance. It is possible then to conceive, think, or completely\nexplain the entire universe, or everything that exists, under each one\nof the attributes. That is, we can give a complete physical description\nof everything that exists, or alternatively explain, describe, or\nconceive everything as ideas or thought. Being able to explain the\nentire universe under the attribute of Extension is what allows Spinoza\nto preserve Descartes’ effort of providing room for progress in\nthe New Science (Cf. Appendix to Part One).", "\n\nSpinoza and Descartes agree about the epistemological separation\nbetween Thought and Extension, but not about the ontological one.\nDescartes calls the distinction between attributes of the same\nsubstance, and between a given attribute and its substance a\n“rational distinction,” (Principles, I, §62,\nCSM, I, p. 214, AT 30) and so, insofar as Thought and Extension belong\nto the same substance for Spinoza, they would be, in Descartes’\nterminology, rationally\n distinct.[8]\n Spinoza however, says\nthat they are “really distinct.” How exactly to\nunderstand the “reality” of the distinction among the\nattributes is a crucial interpretative matter and is discussed in\nSections 1.8.1–1.8.2." ], "subsection_title": "1.3 Real Distinction" }, { "content": [ "\n\nAnother claim that has to be taken into account in an analysis of\nSpinoza’s view on attributes is that God is his\nattributes: 1P4: “Therefore, there is nothing outside the\nintellect through which a number of things can be distinguished from\none another except substance, or what is the same (by 1D4),\ntheir attributes, and their affections” (italics added), 1P19:\n“God is eternal, or [sive] all God’s\nattributes are eternal,” 1P20Cor.: “It follows second, that\nGod, or [sive] all of God’s attributes, are\nimmutable.” Some might consider 1P29Schol to be making an\nidentity claim as well: “But by Natura Naturata I\nunderstand whatever follows from the necessity of God’s nature,\nor [sive] from any of God’s\nattributes…” Spinoza in these places seems to be claiming\nthat there is an identification of the substance with its attributes.\nHowever, this identification can be understood in several ways and in\nvarious degrees of strictness. How one reads this claim depends on\nother considerations discussed in\n Section 1.9.3." ], "subsection_title": "1.4 The Identification of Attributes with Substance" }, { "content": [ "\n\nOne of the important things that Spinoza does in the first two parts\nof the Ethics is to establish Extension as a divine attribute\n(elements of this view are evident already in KV I/25). Although\nSpinoza adopts many important aspects of Cartesian metaphysics, he\ncollapses\nthe divide between the infinite and created substances. This\nmeans that principal attributes that were at the “created\nsubstance” level in the Cartesian set-up are “moved\nup”, so to speak, to the infinite substance level for Spinoza.\nOne of these attributes is, of course, Extension. Spinoza has to\nexplain to a resistant audience how Extension can be considered a\ndivine attribute.", "\n\nThe important steps that will allow Spinoza to claim that Extension\ncan be an attribute of God are the following. He defines God as a\nsubstance consisting of infinite attributes\n (1D6).[9]\n He shows that\nsubstances cannot share attributes (1P5), that every substance is\ninfinite (1D8), that a single substance can have several attributes\n(1P10schol), and that an infinite substance exists (1P11). With an eye\ntowards specifically establishing Extension as a divine attribute, he\nclaims in 1P12: “No attribute of a substance can be truly\nconceived from which it follows that the substance can be\ndivided.” In 1P13, he states: “A substance which is\nabsolutely infinite is indivisible,” and in the corollary, he\nmakes the point especially clear with respect to Extension: “From\nthese propositions it follows that no substance, and consequently\nno corporeal substance, insofar as it is a substance, is\ndivisible.” In 1P14, he establishes that there is only one\nsubstance (or rather, that there are no created substances). Finally in\n1P15 he claims: “Whatever is, is in God, and nothing can be or be\nconceived without God.” With this, the stage is set for Extension\nbeing a divine attribute or applicable to God, if in fact it is a\ngenuine attribute (which is established only in Part Two).", "\n\nSpinoza is aware that this will be received with great resistance.\nThe possible objection he imagines is that since Extension is divisible\nby its very nature then, if Extension were an attribute of God, God\nwould be divisible. God, of course, cannot be divisible, for then he\nwould not be infinite. In the Scholium to 1P15 he shows the ensuing\ncontradictions if one holds Extension to be by its very nature\ndivisible. It is important for him to show that Extension cannot imply\ndivisibility in answer to possible objectors holding traditional\nviews. Moreover, he has just shown that there is only one\nsubstance, which is indivisible (1P12 and 1P13), and so whatever\nattributes it has, none of them can imply divisibility in the only\nsubstance. Spinoza then shows that if Extension is an attribute, it is\napplicable to God, and there is no danger of that implying any real\ndivision in the substance. One important result of this is that what\nappear to be individuated bodies cannot be really individuated in the\nCartesian sense of implying real distinction and the existence of\nmultiple substances. Rather, what appear to be individuated bodies are\nonly modes of substance under the attribute of\n Extension.[10]\n Only in\nPart Two does Spinoza show that Extension (as well as Thought) are in\nfact attributes of God: “Thought is an attribute of God,\nor [sive] God is a thinking thing” (2P1) and\n“Extension is an attribute of God, or [sive]\nGod is an extended thing” (2P2)." ], "subsection_title": "1.5 Extension as a Divine Attribute" }, { "content": [ "\n\nA very important characteristic regarding attributes is established\nin 2P7 and its scholium, which is sometimes referred to in the\nliterature as the “parallelism doctrine.” However, as will\nbe discussed in\n Section 1.9.2,\nthis\nnomenclature is laden with a significant amount of interpretative bias\nand the term is nowhere to be found in the Ethics itself. It\nis thus advisable to stay clear of it and simply refer to it\nas “the 2P7 Doctrine.” 2P7 states: “The order and\nconnection of ideas is the same as the order and connection of\nthings,” (“ordo, & connexio idearum idem est, ac\nordo & connexio rerum”). Spinoza explains this\nproposition in the scholium:", "\n\nFor example, a circle existing in Nature and the idea of the\nexisting circle, which is also in God, are one and the same thing,\nwhich is explained through different attributes…Therefore,\nwhether we conceive Nature under the attribute of extension, or under\nthe attribute of thought, or under any attribute, we shall find one and\nthe same order, or one and the same connection of causes, that is, that\nthe same things follow one another.", "\n\nSpinoza is claiming here that a mode X under the attribute of\nThought is one and the same as mode X under\nAttributey. A good way to get some intuitive sense\nof this is to see how this works with respect to ourselves. Under the\nattribute of Thought, I am a finite mode—an idea or mind. Under\nthe attribute of Extension, I am a finite mode, that is, a body. The\nclaim in 2P7 and its scholium is that my mind (a mode of Thought) and\nmy body (a mode of Extension) are one and the same. This is the case\nfor all modes. Furthermore, whatever causal relation my body, say,\nbears to other modes of Extension, my mind will bear to the other\nmodes of Thought. The understanding of this doctrine and its\nimplications in more depth depends, probably more than any other\ndoctrine, on how one construes other central elements of Spinoza’s\ntheory of attributes (e.g. the number of attributes). In Section\n1.9.2 different directions of interpretation are considered regarding\n2P7 and its scholium." ], "subsection_title": "1.6 The 2P7 Doctrine" }, { "content": [ "\n\nSpinoza famously claims that we, human minds, only know two\nattributes—Thought and Extension. This can be seen as arising\nfrom the axioms in Part Two: 2A2: “Man thinks,” 2A4:\n“We feel a certain body is affected in many ways,” 2A5:\n“We neither feel nor perceive any singular things, except bodies\nand modes of thinking,” as well as 2P13: “The object of the\nidea constituting the human mind is the body, or [sive] a\ncertain mode of extension which actually exists, and nothing\nelse” [italics added] (this is true already in KV, 1/27). In\nLetter 64 Spinoza tries to explain why we can only perceive these two\nattributes, and he does so by referring back to 2P13 and claims in the\nletter: “Therefore, the mind’s power of understanding\nextends only as far as that which this idea of the body contains within\nitself, or which follows therefrom. Now this idea of the body involves\nand expresses no other attributes of God than extension and\nthought.” Although some have found this line of argumentation\nunsatisfying (e.g. Bennett, 1984, 78–79) it is worth noting that\nSpinoza here is relying on axioms." ], "subsection_title": "1.7 The Two Known Attributes" }, { "content": [ "\n\nThe attempt to understand Spinoza’s doctrine regarding the attributes\nhas traditionally led interpreters in two main directions, although\nothers have been proposed (e.g. Lennon, 2005. 12–30; Shein,\n 2009).[11]\n The first is what is known as the “subjective”\ninterpretation which follows Hegel, and is given its paradigmatic\nexpression by Wolfson. More recently, Michael Della Rocca as been\nadvocating a more idealistic interpretation of the attributes, which\nshares certain important features with the subjectivist camp. The\nother, which has become the standard, is the “objective”\ninterpretation. These two principal avenues stem from some important\nambiguities in the definition of “attribute”: “By\nattribute I understand what the intellect perceives of substance as\nconstituting its essence”\n (1D4).[12] \nThe first term that is ambiguous is\n“intellect,” since it can refer either to the finite\nintellect or the infinite one (cf. diagram in Section 1). The second\nimportant ambiguity lies in the Latin term tanquam, since it\ncan mean either “as if, but not in fact,” or “as in\nfact.” The definition can therefore be read, either as stating\nthat attributes are what the intellect perceives of substance as\nconstituting its actual essence, or that attributes are what the\nintellect perceives only as if they are what constitute the\nessence but are not what in fact constitutes it or them. The\nsubjectivists accordingly claim that attributes are what the finite\nintellect perceives of substance as if constituting its\nessence. The objectivists, by and large, instead claim that it is the\ninfinite intellect that perceives the attribute as in fact\nconstituting the essence of substance. In the following sections the\ndifferent interpretative options are explained a grosso\nmodo. The ways in which the different interpretative avenues\naffect other Spinozistic doctrines are discussed in Sections\n1.9.1–1.9.4.", "\n\nAs is well known, Hegel, in various respects, considered himself to\nbe modifying Spinoza’s doctrine (“to be a follower of\nSpinoza is the essential commencement of all philosophy”) and his\ninterpretation of Spinoza was extremely\n influential.[13]\n In his Lectures on\nthe History of Philosophy, Hegel says that what has utmost reality\nfor Spinoza is the absolute (or the infinite substance) and that\nanything else (finite modes, in particular) are ways of negating this\nabsolute. He goes on to explain that the understanding [or\n“intellect”] grasps the reality of substance through\nattributes, but “it is only reality in view of the\nunderstanding.” He stresses that understanding in terms of\nattributes is due to the nature of the understanding and not because of\nthe nature of the absolute (or the infinite substance) as such. It is\nclear that he considers the understanding to be the understanding of\nfinite minds, because he goes on to explain that Spinoza’s claim\nthat there are “infinite attributes” has to be interpreted\nas “infinite in character” and not in number and that there\nare only the two attributes known to finite minds—Thought and\nExtension.", "\n\nWhat is referred to in the literature as the subjectivist reading,\nfollowing Hegel, holds that the intellect perceiving the attributes is\nthe finite intellect and that the attributes are projections of the\nfinite mind onto the infinite substance which it cannot fully\ncomprehend. In other words, according to the subjectivist\ninterpretation, the definition of attribute states that attributes are\nwhat the finite intellect perceives of substance as if (but not in\nfact) constituting its essence. In contrast, the objectivist\nreading takes the intellect in question to be the infinite one, and the\ntanquam to mean “as in fact,” and so it read the\ndefinition as claiming that attributes are what the infinite intellect\nperceives of substance as (in fact) constituting its essence.\nWolfson summarizes the difference between the two positions thus:", "\n\nAccording to the former interpretation [subjectivism], to be\nperceived by the mind means to be invented by the mind, for of\nthemselves the attributes have no independent existence at all but are\nidentical with the essence of the substance. According to the latter\ninterpretation [objectivism], to be perceived by the mind means only to\nbe discovered by the mind, for even of themselves the\nattributes have independent existence in the essence of substance\n(Wolfson, 1934, 146).", "\n\nOne of the motivations behind Wolfson’s view is that he\nconsiders Spinoza to be the last of the medieval Jewish rationalists,\nand in following with that tradition, Spinoza locates all multiplicity\nnot in the infinite substance (God), but rather in the human mind. That\nis, the fact that God has multiple attributes is explained not by his\nhaving multiple essences, natures, or aspects, but rather because of\nthe nature of the human mind. This is based on the conviction that\nGod’s true nature is simple and any multiplicity is merely\napparent but not real. It is because of the limitations of the finite\nmind that it attributes multiplicity to the infinite substance, when in\nreality the infinite substance is simple. In this view there is a gap\nbetween the attributes and the infinite substance. The infinite\nsubstance as it is in itself, so to speak, is unknowable to the finite\nmind. With respect to the “real distinction,” the\ndistinction between the attributes in this view is grounded in the\ndifferent ways the finite mind has of conceiving the infinite\nsubstance. That is, the distinction between the attributes is not based\non the nature of the infinite substance itself, but it reveals, in a\nway, something about the nature of finite perception. It is in these\nterms that the “reality” of the distinction is to be\nunderstood, i.e., as if but not in fact.", "\n\nTwo main objections have been brought forth against the subjectivist\ninterpretation. These are considered by most commentators to be\nforceful enough for rejecting subjectivism as a serious contender for\na satisfying interpretation of Spinoza’s theory of attributes. The\nfirst objection to subjectivism is that, finite minds can never have\ntrue knowledge of God, but only knowledge “as if.” All\nknowledge is rendered illusory. The reason for this is quite clear. In\nthe subjectivist interpretation the attributes are projections of the\nfinite mind, therefore the finite mind can never come to know the\ninfinite substance as it is in itself. This seems to contradict\nSpinoza’s claim that the finite mind can have adequate, that is,\nperfect knowledge of God’s essence (2P47). The second objection is\nthat this interpretation seems irreconcilable with those places in the\ntext where Spinoza identifies the attributes and God (cf. 1P4, 1P19\nand 1P20Cor.). Again, as projections of the finite intellect, the\nattributes do not properly pertain to the substance, and therefore\ncannot be identical to it. For these reasons, among others, the\nsubjective interpretation (understood in these terms) has fallen out\nof favor.[14]\nMichael Della Rocca, however, has been advocating more recently that\nattributes (and diversity more generally), are mind-dependent yet not\nillusory. Thus he aims to overcome some of the traditional objections\nto subjectivism (primarily “illusory knowledge” objections)\nwhile insisting on the mind-dependent status of attributes. He takes\nthe mind-dependant nature of diversity (be it of attribute or modes)\nto be an inevitable consequence of Spinoza’s adoption of the Principle\nof Sufficient Reason (cf. Della Rocca, 2012).", "\n\nIn light of these kinds of criticisms to the subjectivist\ninterpretation, commentators have turned towards what are known as\n“objectivist” accounts. Although the details of these\naccounts are quite diverse, there are a few key elements they\nshare—all related to the fact that they do not wish to be\nsubjectivist. The first of these characteristics is that they hold that\nknowledge in the system cannot be illusory. That is, knowledge through\nattributes must yield true, or adequate, knowledge. One way to do this\nis to claim that it is the infinite intellect that perceives the\nattributes, and so knowledge through attributes is the kind of\nknowledge the infinite intellect has, and therefore is not illusory\n(e.g. Bennett, 1984, 147; Delahunty, 1985, 116; Della Rocca 1996, 157;\nHaserot, 1972, 32–35). Therefore, the tanquam in the\ndefinition is to be read “as in fact” and not “as\nif.”", "\n\nAs opposed to subjectivism, which does not emphasize the\n“reality” of the distinction between the attributes, or\nrather, does not ground the distinction in the nature of the infinite\nsubstance, objectivist interpretations place ontological weight on the\n“real distinction” between the attributes. In other words,\nfor the multiplicity to have a certain reality and not be illusory, it\nmust somehow be grounded not in the perceiver but in the thing\nperceived, namely, the infinite substance. The danger of this kind of\ninterpretation is that if the distinction is stressed too strongly, the\nunity of the substance is lost. If the infinite substance has\n“really distinct” attributes, and this distinction is\ngrounded in, say, distinct natures or essences of the infinite\nsubstance, then there has to be an explanation of how a multiplicity of\nnatures or essences can be united to form one substance. (This issue is\naddressed in further detail in\n Section 1.9.4\nas it emerges in the discussion of the nature of the union of\nmind and body).", "\n\nAny interpretation of Spinoza must characterize the relation between\nany given attribute and the substance. As mentioned, in the\nsubjectivist account there is a problematic gap between the substance\nand any given attribute. The alternative is to deny this gap. For\nexample, Bennett claims the following:", "\n\nI think that here [Ep. 9] he is saying that substance differs from\nattribute only by the difference between a substance and an adjectival\npresentation of the very same content. If we look for how that\nwhich is extended (substance) differs from extension\n(attribute), we find that it consists only in the notion of that\nwhich has… extension or thought or whatever; and that,\nSpinoza thinks, adds nothing to the conceptual content of\nextension, but merely marks something about how the content is\nlogically structured. As I did in §12.7, he is rejecting the view\nthat a property bearer is an item whose nature qualifies it to have\nproperties, in favour of the view that the notion of a property bearer,\nof a thing which…, is a bit of formal apparatus, something which\norganizes conceptual content without adding to it. According to this\nview, there is an emptiness about the difference between substance and\nattribute (Bennett, 1984, 62–63).", "\n\nAlthough Bennett claims there is an emptiness about the distinction\nbetween the two, he does not consider it an absolute identity either.\nHe finds an identity claim to be irreconcilable with the claim that\nattributes are really distinct. Della Rocca has suggested\nintentionality as a way of denying the gap and treats “…\nis extended” and “… is thinking” as\nreferentially opaque. In other words, what is being picked out by the\ninfinite intellect in either instance is the same, but the way in which\nit is picked out is different. Yet another way of denying the gap is to\nclaim, along with Descartes, that the distinction between an attribute\nand the substance is only a rational distinction. That is, in\nreality there is no distinction, but in the finite mind we can\nseparate, contra natura, the attribute from the substance. Or\nin other words, the finite mind can abstract the attribute from the\nsubstance, but in reality they are not separated. This type of\nview must be supplemented by an account, then, of what is meant by the\n“real distinction” among the attributes." ], "subsection_title": "1.8 Ambiguities and Interpretative Directions" }, { "content": [ "\n\nAlthough Spinoza claims that there are infinite attributes, a\nquestion arises as to how many there are, because\n“infinity” may not necessarily refer to numeric\n infinity.[15]\n Bennett, among others, has made the case that infinity in early modern\nphilosophy means totality (Bennett, 1984, 75–79). Spinoza’s\nclaims, then, that the infinite substance has infinite attributes can\nbe understood as the claim that the infinite substance has all the\nattributes there are to be\n had.[16]\n This is consistent with\nthere being, say, only the two known attributes. There are sections in\nthe text, on the other hand, that seem to suggest that infinity means a\nnumerical infinity, and thus the infinite substance has as attributes\nThought and Extension, as well as infinitely many other unknown\nattributes. The places used as evidence for those wishing to claim\nthere are more than two attributes are the following:", "\n\n\n\n1D6: By God I understand a being absolutely infinite, that is, a\nsubstance consisting of an infinity of attributes, of which each one\nexpresses an eternal and infinite essence.\n\n\n\nExp.: I say absolutely infinite, not infinite in its own kind; for\nif something is only infinite in its own kind, we can deny infinite\nattributes of it; but if something is absolutely infinite, whatever\nexpresses essence and involves no negation pertains to its\nessence.\n\n\n\n2P7Schol: Therefore whether we conceive Nature under the attribute\nof Extension, or the attribute of Thought, or any other attribute, we\nshall find one and the same order, or one and the same connection of\ncauses, that is the same things follow one another.\n\n\n\nLetter 56: To your [Hugo Boxel] question as to whether I have as\nclear an idea of God as of a triangle, I reply in the affirmative. But\nif you ask me whether I have as clear a mental image of God as of a\ntriangle, I reply in the negative. We cannot imagine God, but we can\napprehend him by the intellect. Here it should also be observed that I\ndo not claim to have complete knowledge of God, but that I do\nunderstand some of his attributes—not indeed all of them, or the\ngreater part—and it is certain that my ignorance of very many\nattributes does not prevent me from having knowledge of some of them.\nWhen I was studying Euclid’s Elements, I understood\nearly on that the three angles of a triangle are equal to two right\nangles, and I clearly perceived this property of a triangle although I\nwas ignorant of many others.\n\n", "\n\nThis issue can be linked to the previous discussion regarding the\nambiguities in the definition of attribute, although this is not always\ndone. If one holds that it is the infinite intellect that is doing the\nrelevant perceiving, there seems to be no reason to limit the number of\nattributes it perceives. Conversely, it might be claimed that if the\ninfinite intellect perceives only two attributes, there must be a\nsufficient reason why there are only two, and why they are Thought and\nExtension and not other attributes. If, on the other hand, one holds\nthat it is the finite intellect that conceives the attributes, and it\nonly conceives Thought and Extension, then these are the only two\nattributes there are. In the literature, however, this line of\nreasoning is not always followed, and examples can be found of\ninterpreters who hold that it is the infinite intellect that does the\nperceiving, but that there need not be more than two attributes\n(Bennett, 1984, 75–76). At the same time, there are interpreters\nwho claim it is the finite intellect that perceives the attributes\nwhile there are infinitely many attributes (Wolfson, 1934, 226). How\nmany attributes there are affects how one reads another central\ndoctrine in Spinoza’s metaphysics, such as 2P7 and 2P7Schol, to\nwhich we turn next.", "\n\nA crucial role in Spinoza’s system is played by 2P7 and its\nscholium, since they lay the ground for solving, or rather dissolving,\nthe mind–body problem. Therefore, the understanding of the nature\nof the union of mind and body depends on one’s interpretation of\nSpinoza’s theory of attributes and 2P7 and its scholium in\nparticular. (For a discussion of the issues regarding the union of Mind\nand Body, see\n Section 1.9.4).\nThe\ninterpretation of the metaphysical structure of what is expressed in\n2P7 and its scholium is affected greatly by the number of attributes\none believes there are in Spinoza’s system and how one\nunderstands the relation between the attributes and the substance. The\ngeneral description of 2P7 and its scholium is discussed above in\n Section 1.6.", "\n\n2P7 and its scholium can be understood in very different ways. In\nwhat follows three types of interpretive directions are described. This\nis not meant to be exhaustive by any means, but it will provide a sense\nof the kinds of options that have been offered by commentators. Let us\nbegin with the simplest option first. If one holds that there are only\ntwo attributes, Thought and Extension, the metaphysical structure of\n2P7 and its scholium is quite straightforward. Every mode under the\nattribute of Thought is associated with a mode in Extension, and\nvice versa and the relations between modes in one attribute\nare mirrored in the other. Those that hold this kind of view must, of\ncourse, provide a convincing argument to the effect that there are only\ntwo attributes.", "\n\nHowever, if one takes there to be more than two attributes, the\nstructure gets quite a bit more complex. One option that has been\nadvanced is that Thought is a special attribute and encompasses ideas\nof all the modes in all the other attributes (Cf. for example Curley,\n1969, 146; and more recently, Melamed, 2009, Chapters 1–2).\nThought turns out to be “special” in this kind of\ninterpretation because there are many more modes (ideas) or facets of modes in Thought\nthan there are under any other attribute. Another way of expressing\nthis is by saying that 2P7 is not a biconditional. The requirement of\nan associated mode goes only in one direction from any mode in any\nattribute to a mode in Thought. The burden on this type of view is that\nit must account for the favoring of Thought over the other attributes,\nand perhaps also for the relation between all the non-Thought modes in\nthe other attributes.", "\n\nAnother option (or class of options) that is available is to claim\nthat attributes come in pairs: an object-like attribute coupled with a\nthought-like attribute (Curley entertains this option as well; Curley,\n1969, 146). Under this type of interpretation we would get Thought and\nExtension following the structure of the first alternative, that is,\neach idea in Thought is associated with (one and the same) a mode in\nExtension. Taking there to be more than just two attributes, we also\nget Thoughtx coupled with Extensionx in which\neach ideax is one and the same as bodyx under\nExtensionx, and Thoughty coupled with\nExtensiony, and so on. Letter 66 provides some support for\nthis view. This kind of account has to be supplemented, of course, with\nan account of the relations among these Thought-like / Extension-like\npairs of attributes.", "\n\nAs mentioned earlier, Spinoza identifies God, or the infinite\nsubstance with the attributes (1P4, 1P19 and 1P20Cor.). The nature of\nthis identification is also affected by one’s interpretative\nstance regarding the attributes. The traditional subjectivist view,\nsince it claims that the attributes are a projection of the finite mind\nonto the substance, cannot hold this identification to be strict.\nObjectivist views, which stress the distinctness of attributes, also\ncannot accept these claims literally (E.g., Bennett, 1984, 64; Curley,\n1988, 13; Gueroult, 1968, 50). The reason for this is as follows: if\nthe substance is strictly identical to any one of its attributes, then\nattributes will be identical to each other (by transitivity), and\ntherefore no longer distinct, as Spinoza claims. Different objectivist\ninterpretations address this issue differently. Curley, for example,\nholds that the identity is not one that holds between any given\nattribute and the substance, but rather between the totality of the\nattributes and the substance (Curley, 1988, 30). Bennett, on the other\nhand, believes Spinoza is simply overstating the case (Bennett, 1984,\n64).", "\n\nThis identity can be understood strictly if the distinction between\nthe attributes and the substance is taken to be only rationally\ndistinct, that is identical in reality, and at the same time\ntaking the distinction between attributes to be only epistemological\nand not ontological.", "\n\nAnother doctrine that is heavily affected by how one understands the\nattributes is the union of mind and body. For Descartes, the issue was\nhow to unite two really distinct created substances—uniting minds\nwith bodies. Descartes’ reply is that God unites these two\nsubstances, and we have tools by which to recognize that we are united\nin this way, i.e., sensory experience (Meditation Six).\nSpinoza, of course, cannot allude to God as creator to unite minds and\nbodies, since what is being united are not created substances\nbut finite modes. The possible problem can be\narticulated as follows: How can Spinoza claim, on the one hand, that\nthere are modes of really distinct attributes, e.g., my mind and my\nbody, and therefore there is a real distinction between my mind and my\nbody, and, on the other, claim in the Scholium to 2P7 that my mind and\nbody are one and the same?", "\n\nThis problem which arises for the objectivist interpretations has been\naddressed in a variety of ways. It is worth noting that this problem\ndoes not arise for subjectivist views. This possible tension in\nSpinoza does not present itself for the subjectivists, since they do\nnot claim that the “real distinction” between the\nattributes has ontological weight. That is, there are no two things\nthat have to be united. Commentators wishing to stress the\n“distinctness” of the attributes find themselves having to\nexplain the sense in which Spinoza can mean that the mind and the body\nare “one and the same.” A common strategy among\ncommentators has been to appeal to a structure that is\nattribute-neutral in order to account for the unity. To better\nunderstand this issue it is useful to consider a few examples.", "\n\nOne important example is Bennett, who claims that the unity is to be\nunderstood as a unity of properties, but not of the modes\nthemselves:", "\n\n…his [Spinoza’s] thesis about the identity of physical and\nmental particulars is really about the identity of properties. He\ncannot be saying that\nphysical P1=mental M1; that is\nimpossible because they belong to different attributes. His thesis is\nrather that if P1 is systematically linked with\nM1, then P1 is\nextension—and—F for some differentia F such that\nM1 is thought—and—F. What it\ntakes for an extended world to contain my body is exactly what it\ntakes for a thinking world to contain my mind (Bennett, 1984,\n141)", "\n\nThat is, Bennett thinks that there is some trans-attribute feature\n(what he calls “differentia F”) such that it can\nbe added to Extension to get extended-F, and added it to\nThought to get thinking-F. Bennett admits that nothing like\nthis is found anywhere in the text, but he believes that this way we\ncan make sense of Spinoza’s holding that the attributes are\n“really distinct” from each other and, at the same time,\nthat thinking-F and extended-F are one and the\nsame.", "\n\nDella Rocca, while holding a view different from that of Bennett\nregarding Spinoza’s theory of attributes, also finds himself\nhaving to account in some way for the unity of mind and body, and so he\nsuggests that modes are said to be numerically identical when they\nshare all of their neutral properties, where “neutral\nproperties” are those properties which do not involve being\nthought under any particular attributes. This is contrasted with\n“intentional properties” which are attribute-dependent such\nas “being of a certain volume.” As an example of a neutral\nproperty, Della Rocca offers “having five immediate\neffects.” He then claims that if modes share all of their neutral\nproperties, they are identical (that is, one and the same). Therefore,\nsince my mind and my body share all of their neutral properties, they\nare identical (Della Rocca, 1996, 133–38).", "\n\nThe final example that shall be considered is Gueroult’s\ninterpretation. Gueroult, in order to account for the professed\nidentity between modes of different attributes in 2P7 and its scholium,\nconsiders 1P28 which states:", "\n\nEvery singular thing, or any thing which is finite and has a\ndeterminate existence, can neither exist nor be determined to produce\nan effect unless it is determined to exist and produce an effect by\nanother cause, which is also finite and has a determinate existence;\nand again, this cause also can neither exist nor be determined to\nproduce an effect unless it is determined to exist and produce an\neffect by another, which is also finite and has a determinate\nexistence, and so on, to infinity.", "\n\nTo explain this proposition, Gueroult draws a distinction between\n“modes of substance” and “modes of attributes.”\nThe claim is that 1P28 treats only modes of substance and not\nattributes, and is therefore unique. In other words, the identity is\nthen understood in reference to “modes of substance” and\nnot “modes of attributes” (Gueroult, 1968, 338–39).\nAgain, we see an attribute-independent structure—the chain of\nmodes of substance—that is meant to account for the “one\nand the sameness” of modes of different attributes.", "\n\nIt has been pointed out, however, that this type of solution is not\nwithout serious problems (Shein, 2009). Briefly, the issue is as\nfollows: The main reason for rejecting the subjectivist view is that in\nthat type of interpretation, God, as he is in himself, remains\nunknowable, and this conflicts with Spinoza’s view that adequate\nknowledge is possible. However, as Spinoza makes clear in 1P10Schol,\nnature must be conceived under attributes. In light of this, an\nattribute-independent structure, by its very nature as\n“attribute-independent,” is unknowable as well. Therefore,\nin this view, knowledge of the union or the nature of the identity\nbetween mind and body, is in principle unknowable, and, in that\nrespect, does not provide any advantage over subjectivist views.", "\n\nAn alternative mentioned above that has been suggested is to deny\nthe gap between the attributes and the substance by claiming that,\nalong with Descartes, Spinoza holds there to be a rational distinction\nbetween them, that is, in reality they are identical (Shein,\n2009). This avoids the kind of problems that are raised for the\nsubjectivist view, since, in this interpretation to know the attributes\nis to know the substance. Since in this view the attributes are only\nrationally distinct from the substance, the “real\ndistinction” between the attributes, that Spinoza states in\n1P10Schol, is understood as being only an epistemological claim, as he\nstates in the text—“i.e., one may be conceived without the\nother” (1P10Schol). That is, it does not carry additional\nontological weight as the objectivists hold. This avoids having to\nimpose onto the Spinozistic system an attribute-independent structure\nto account for the unity which does not seem to fit with his\nepistemology." ], "subsection_title": "1.9 Implications of the Various Readings on Other Spinozistic Doctrines" } ] }, { "main_content": [ "\n\nIn the Short Treatise Spinoza develops ideas that will come\nto a full articulation later on in the Ethics, such as the\nidea that, strictly speaking, there are only two attributes through\nwhich we can properly come to have knowledge of God—Thought and\nExtension. However, unlike in the Ethics, he does not simply\ndismiss the more traditional attributes such as omnipotence,\neternality, immutability, and infinity. To maintain some sense of these\ntraditional divine attributes, Spinoza explains that they are not\nattributes strictly speaking, but rather propria of God. This\nis stated first clearly in the first footnote to Chapter III\n(“How God is the Cause of All Things”):", "\n\nThe following are called Propria because they are nothing\nbut Adjectives which cannot be understood without their\nSubstantives. I.e., without them God would indeed not be God;\nbut still, he is not God through them, for they do not make known\nanything substantial, and it is only through what is substantial that\nGod exists.", "\n\nSpinoza then, is distinguishing between that which gives us\nknowledge of God, or better yet, through which God can be\nknown—Thought and Extension—and things that can be said of\nGod, that is, adjectival, but give us no knowledge—what he terms\npropria. This is explained most explicitly in Chapter VII of\nthe Short Treatise. The difference Spinoza wishes to draw\nbetween these is that although these traditional divine attributes can\nbe said of God, they do not teach us anything about what God is really\nlike. An analysis of these traditional attributes (propria)\nshows them either to be said of God when considering all of the\nattributes or to be only modes of attributes. For example, Spinoza\nclaims that when statements such as that “God is one,”\n“eternal” and “immutable” are said of God, they\nare said “in consideration of all his attributes.” On the\nother hand, something like “omniscience” is only a mode of\nan attribute, since it is only said of God when he is conceived\nthrough, or considered under, the attribute of Thought. That is, only\nwhen God is thought of as a thinking thing, can he be said to be\nomniscient. Similarly, when God is said to be\n“omnipresent,” it is only when he is conceived of through\nExtension. In the Ethics though, Spinoza does away with the\ntalk of propria and does not accord them really any status as\nsuch." ], "section_title": "2. Attributes in the Short Treatise", "subsections": [] }, { "main_content": [ "\n\nWith the collapse of the divide between created substances and the\ninfinite substance, attributes play a new role for Spinoza; traditional\ndivine attributes are eliminated while attributes traditionally\nassociated with created substances (Extension in particular) are\nattributed to the infinite substance. Furthermore, with the elimination\nof this divide and the establishment of the infinite substance as the\nonly substance, Spinoza hopes that attributes account for variety in\nthe substance without jeopardizing its unity. All interpreters and\nreaders of Spinoza are forced to wrestle with making sense of this\ndouble role since it sits at the very core of his metaphysics. It is\nvital to realize that this endeavor is necessarily and beautifully\nlinked to other fundamental aspects of Spinoza’s metaphysics such\nas the “real distinction” between the attributes, the\nproclaimed identity of the substance and its attributes, the nature of\nthe conceiving intellect in the definition of ‘attribute’,\nthe nature of this intellect’s conceptions (illusory or not), the\nnumber of attributes, the structure of 2P7 and its scholium, and\nfinally the nature of the union of mind and body. These\ninter-connections are a reflection of the fully systematic nature of\nSpinoza’s metaphysics." ], "section_title": "3. Conclusion", "subsections": [] } ]

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[ "\n\nLudwig Boltzmann (1844–1906) is generally acknowledged as one of\nthe most important physicists of the nineteenth century. Particularly\nfamous is his statistical explanation of the second law of\nthermodynamics. The celebrated formula \\(S = k \\log W\\), expressing a\nrelation between entropy \\(S\\) and probability \\(W\\) has been engraved\non his tombstone (even though he never actually wrote this formula\ndown). Boltzmann's views on statistical physics continue to play an\nimportant role in contemporary debates on the foundations of that\ntheory.", "\n\nHowever, Boltzmann's ideas on the precise relationship between the\nthermodynamical properties of macroscopic bodies and their microscopic\nconstitution, and the role of probability in this relationship are\ninvolved and differed quite remarkably in different periods of his\nlife. Indeed, in his first paper in statistical physics of 1866, he\nclaimed to obtain a completely general theorem from mechanics that\nwould prove the second law. However, thirty years later he stated that\nthe second law could never be proved by mechanical means alone, but\ndepended essentially on probability theory. In his lifelong struggle\nwith the problem he employed a varying arsenal of tools and\nassumptions. (To mention a few: the so-called Stoßzahlansatz,\nthe ergodic hypothesis, ensembles, the combinatorial argument, the\nhypothesis of molecular disorder.) However, the exact role of these\nassumptions, and the results he obtained from them, also shifted in\nthe course of time. Particularly notorious are the role of the\nergodic hypothesis and the status of the so-called H-theorem.\nMoreover, he used ‘probability’ in four different\ntechnical meanings. It is, therefore, not easy to speak of a\nconsistent, single “Boltzmannian approach” to statistical physics. It\nis the purpose of this essay to describe the evolution of a selection\nof these approaches and their conceptual problems." ]

[ { "content_title": "1. Introduction", "sub_toc": [ "1.1 Popular perceptions of Boltzmann", "1.2 Debates and controversies", "1.3 Boltzmann's relevance for the foundations of statistical physics", "1.4 A concise chronography of Boltzmann's writings" ] }, { "content_title": "2. The ", "sub_toc": [ "2.1 Doubts about the ergodic hypothesis" ] }, { "content_title": "3. The H-theorem and the reversibility objection", "sub_toc": [ "3.1 1872: The Boltzmann equation and H-theorem", "3.2 Remarks and problems", "3.3 1877: The reversibility objection" ] }, { "content_title": "4. 1877b: The combinatorial argument", "sub_toc": [ "4.1 Remarks and problems" ] }, { "content_title": "5. Some later work", "sub_toc": [ "5.1 Return of the ergodic hypothesis", "5.2 Return of the reversibility objection", "5.3 The debate in Nature" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Introduction", "subsections": [ { "content": [ "\n\nBoltzmann's work met with mixed reactions during his lifetime, and\ncontinue to do so even today. It may be worthwhile, therefore, to\ndevote a few remarks to the perception and reception of his work.", "\n\nBoltzmann is often portrayed as a staunch defender of the atomic view\nof matter, at a time when the dominant opinion in the German-speaking\nphysics community, led by influential authors like Mach and Ostwald,\ndisapproved of this view. Indeed, the story goes, in the late\nnineteenth century any attempt at all to search for a hypothetical,\nmicrophysical underpinning of macroscopic phenomena was regarded as\nsuspicious. Further, serious criticism on his work was raised by\nLoschmidt and Zermelo. Various passages in Boltzmann's writing,\nespecially in the late 1890s, complain that his work was hardly\nnoticed (entitling one article “On some of my lesser-known papers on\ngas theory and their relation to the same” (1879b) or even about a\n“hostile attitude” (1898a, v) towards gas theory, and of his awareness\nof “being a powerless individual struggling against the currents of\nthe time” (ibid.).", "\n\nThus, the myth has arisen that Boltzmann was ignored or resisted by\nhis\n contemporaries.[1]\n Sometimes, his suicide in 1906 is attributed to the injustice he thus\nsuffered, The fact that his death occurred just at the dawn of the\ndefinitive victory of the atomic view in the works of Einstein,\nSmoluchowski, Perrin et al. adds a further touch of drama to this\npicture.", "\n\nAs a matter of fact, Boltzmann's reputation as a theoretical physicist\nwas actually widely known and well-respected. In 1888 he was offered\n(but declined, after a curious sequence of negotiations) a most\nprestigious chair in Berlin. Later, several universities (Vienna,\nMunich, Leipzig) competed to get him appointed, sometimes putting the\nsalaries of several professorships together in their effort (Lindley\n2001). He was elected to membership or honorary membership in many\nacademies (cf. Höflechner 1994, 192), received honorary doctorates,\nand was also awarded various medals. In short, there is no factual\nevidence for the claim that Boltzmann was ignored or suffered any\nunusual lack of recognition from his contemporaries. His suicide seems\nto have been due to factors in his personal life (depressions and\ndecline of health) rather than to any academic matters.\n" ], "subsection_title": "1.1 Popular perceptions of Boltzmann" }, { "content": [ "\n\nBoltzmann was involved in various disputes. But this is not to say\nthat he was the innocent victim of hostilities. In many cases he took\nthe initiative by launching a polemic attack on his colleagues. I will\nfocus below on the most important disputes: with Mach and Ostwald on\nthe reality of atoms; and with colleagues who criticized Boltzmann's\nown work in the form of the famous reversibility objection (Loschmidt)\nand the recurrence objection (Zermelo). For a wider sketch of how\ncontemporary scientists took position in the debate on the topics of\nmechanism and irreversibility I refer to (van Strien 2013). ", "\n\nOstwald and Mach clearly resisted the atomic view of matter (although\nfor different reasons). Boltzmann certainly defended and promoted this\nview. But he was not the naive realist or unabashed believer in the\nexistence of atoms that the more popular literature has made of\nhim. Instead, he stressed from the 1880s onwards that the atomic view\nyielded at best an analogy, or a picture or model of reality (cf. de\nRegt 1999). In his debate with Mach he advocated (1897c, 1897d) this\napproach as a useful or economical way to understand the thermal\nbehavior of gases. This means that his views were quite compatible\nwith Mach's views on the goal of \n science.[2]\n What divided them was more a\nstrategic issue. Boltzmann claimed that no approach in natural science\nthat avoids hypotheses completely could ever succeed. He argued that\nthose who reject the atomic hypothesis in favor of a continuum view of\nmatter were guilty of adopting hypotheses too. Ultimately, the choice\nbetween such views should depend on their fruitfulness, and here\nBoltzmann had no doubt that the atomic hypothesis would be\n more\n successful.[3]", "\n\nIn the case of Ostwald, and his ‘energetics’, Boltzmann\ndid become involved in a more heated dispute at a meeting in\nLübeck in 1895. Roughly speaking, energetics presented a\nconception of nature that took energy as the most fundamental physical\nentity, and thus represented physical processes as transformations of\nvarious forms of energy. It resisted attempts to comprehend energy, or\nthese transformations in terms of mechanical pictures.", "\n\nIt has been suggested that in the 1890s “the adherents of energetics\nreigned supreme in the German school and even throughout Europe”\n(Dugas 1959, 82). But this is surely a great exaggeration. It seems\ncloser to the truth to say that energetics represented a rather small\n(but vocal) minority in the physics community, that claimed to put\nforward a seemingly attractive conception of natural science, and\nbeing promoted in the mid-90s by reputed scientists, could no longer\nbe dismissed as the work of amateurs (cf. Deltete 1999).", "\n\nThe 1895 gathering of the Naturforscherversammlung in\nLübeck (the annual meeting of physicists, chemists, biologists\nand physicians) was programmed to devote special sessions to the state\nof the art of energetics. Boltzmann, who was member of the programme\ncommittee, had already shown interest in the development of energetics\nin private correspondence with Ostwald. Georg Helm was asked to\nprepare a report, and at Boltzmann's own suggestion, Ostwald also\ncontributed a lecture. All agreed that the meeting should follow the\n“British style”, i.e., manuscripts would be circulated beforehand and\nthere would be ample room for discussion, following the example of the\nBritish Association for the Advancement of Science meeting that\nBoltzmann had attended the previous year.", "\n\nBoth Helm and Ostwald, apparently, anticipated that they would have\nthe opportunity to discuss their views on energetics in an open-minded\natmosphere. But at the meeting Boltzmann surprised them with\ndevastating criticism. According to those who were present Boltzmann\nwas the clear winner of the\n debate.[4] \n Yet the energeticists experienced the confrontation as an ambush\n(Höflechner 1994, I, 169), for which he had not been\nprepared. Nevertheless, Boltzmann and Ostwald remained friends, and in\n1902 Ostwald made a great effort to persuade his home university in\nLeipzig to appoint Boltzmann (cf. Blackmore 1995, 61–65).", "\n\nNeither is there any hostile attitude in the famous\n‘reversibility objection’ by Loschmidt in 1875. Loschmidt\nwas Boltzmann's former teacher and later colleague at the University\nof Vienna, and a life-long friend. He had no philosophical\nreservations against the existence of atoms at all. (Indeed, he is\nbest known for his estimate of their size.) Rather, his main objection\nwas against the prediction by Maxwell and Boltzmann that a gas column\nin thermal equilibrium in a gravitational field has the same\ntemperature at all heights. His now famous reversibility objection\narose in his attempts to undermine this prediction. Whether Boltzmann\nsucceeded in refuting the objection or not is still a matter of\ndispute, as we shall see below (section 4.1).", "\n\nZermelo's opposition had a quite different background. When he put\nforward the recurrence objection in 1896, he was an assistant\nto Planck in Berlin. And like his mentor, he did not favor the\nmechanical underpinning of thermal phenomena. Yet his 1896 paper\n(Zermelo 1896a) is by no means hostile. It presents a careful logical\nargument that leads him to a dilemma: thermodynamics with its Second\nLaw on the one hand and gas theory (in the form as Zermelo understood\nit) on the other cannot both be literally true. By contrast, it is\nBoltzmann's (1896b) reaction to Zermelo, drenched in sarcasm and\nbitterness which (if anything) may have led to hostile feelings\nbetween these two authors. In any case, the tone of Zermelo's (1896b)\nis considerably sharper. Still, Zermelo maintained a keen, yet\ncritical, interest in gas theory and statistical physics, and\nsubsequently played an important role in making Gibbs' work known in\nGermany.", "\n\nIn fact, I think that Boltzmann's rather aggressive reactions to\nZermelo and Ostwald should be compared to other polemical exchanges in\nwhich he was involved, and sometimes initiated himself (e.g. against\nClausius, Tait, Planck, and Bertrand — not to mention his essay on\nSchopenhauer). It seems to me that Boltzmann enjoyed polemics, and the\nuse of sharp language for rhetorical \n effect.[5] \n Boltzmann's complaints in 1896–1898 about an hostile environment are,\nI think, partly explained by his love of polemic exaggerations, partly\nalso by his mental depression in that period. (See Höflechner\n1994, 198–202) for details.) Certainly, the debates with Ostwald\nand Zermelo might well have contributed to this personal crisis. But\nit would be wrong to interpret Boltzmann's plaintive moods as evidence\nthat his critics were, in fact, hostile.", "\n\nEven today, commentators on Boltzmann's works are divided in their\nopinion. Some praise them as brilliant and exceptionally clear. Often\none finds passages suggesting he possessed all the right answers all\nalong the way — or at least in his later writings, while his\ncritics were simply prejudiced, confused or misguided (von Plato,\nLebowitz, Kac, Bricmont, Goldstein). Others (Ehrenfests, Klein,\nTruesdell) have emphasized that Boltzmann's work is not always clear\nand that he often failed to indicate crucial assumptions or important\nchanges in his position, while friendly critics helped him in\nclarifying and developing his views.", "\n\nFans and critics of Boltzmann's work alike agree that he pioneered\nmuch of the approaches currently used in statistical physics, but also\nthat he did not leave behind a unified coherent theory. His scientific\npapers, collected in Wissenschaftliche Abhandlungen, contain\nmore than 100 papers on statistical physics alone. Some of these\npapers are forbiddingly long, full of tedious calculations and lack a\nclear coherent structure. Sometimes, vital assumptions, or even a\ncomplete change of approach, are stated only somewhere tucked away\nbetween the calculations, or at the very last page. Even Maxwell, who\nmight have been in the best position to appreciate Boltzmann's work,\nexpressed his difficulty with Boltzmann's longwindedness (in a letter\nto Tait, August 1873; see Garber, Brush, and Everett 1995,\n123).[6] But not\nall of his prose is cumbersome and heavy-going. Boltzmann at his best\ncould be witty, passionate and a delight to read. He excelled in such\nqualities in much of his popular work and some of his polemical\narticles." ], "subsection_title": "1.2 Debates and controversies" }, { "content": [ "\n\nThe foundations of statistical physics may today be characterized as a\nbattlefield between a dozen or so different schools, each firmly dug\ninto their own trenches, e.g.: ergodic theory, coarse-graining, the\napproaches of Markovianism, interventionism, BBKGY, or Jaynes,\nPrigogine, etc. Still, many of the protagonists of these schools,\nregardless of their disagreements, frequently express their debt to\nideas first formulated to Boltzmann. Even to those who consider the\nconcept of ensembles as the most important tool of statistical\nphysics, and claim Gibbs rather than Boltzmann as their champion, it\nhas been pointed out that Boltzmann introduced ensembles long before\nGibbs. And those who advocate Boltzmann while rejecting ergodic\ntheory, may similarly be reminded that the latter theory too\noriginated with Boltzmann himself.", "\n\nIt appears, therefore, that Boltzmann is the father of many\napproaches, even if these approaches are presently seen as conflicting\nwith each other. This is due to the fact that during his forty years of\nwork on the subject, Boltzmann pursued many lines of thought.\nTypically, he would follow a particular train of thought that he regarded\npromising and fruitful, only to discard it in the next paper for\nanother one, and then pick it up again years later. This meandering\napproach is of course not unusual among theoretical physicists but it\nmakes it hard to pin down Boltzmann on a particular set of rock-bottom\nassumptions, that would reveal his true colors in the modern debate on\nthe foundations of statistical physics. The Ehrenfests (1912) in their\nfamous Encyclopedia article, set themselves the task of constructing a\nmore or less coherent framework out of Boltzmann's legacy. But their\npresentation of Boltzmann was, as is rather well known, not\nhistorically adequate.", "\n\nWithout going into a more detailed description of the landscape of the\nbattlefield of the foundations of statistical physics, or a sketch of\nthe various positions occupied, it might be useful to mention only the\nroughest of distinctions. I use the term ‘statistical\nphysics’ as a deliberately vague term that includes at least two\nmore sharply distinguished theories: the kinetic theory of gases and\nstatistical mechanics proper.", "\n\nThe first theory aims to explain the properties of gases by assuming\nthat they consist of a very large number of molecules in rapid motion.\n(The term ‘kinetic’ is meant to underline the vital\nimportance of motion here, and to distinguish the approach from older\nstatic molecular gas models.) During the 1860s probability\nconsiderations were imported into this theory. The aim then became to\ncharacterize the properties of gases, in particular in thermal\nequilibrium, in terms of probabilities of various molecular\nstates. This is what the Ehrenfests call “kineto-statistics of the\nmolecule”. Here, molecular states, in particular their velocities, are\nregarded as stochastic variables, and probabilities are attached to\nsuch molecular states of motion. These probabilities themselves are\nconceived of as mechanical properties of the state of the total gas\nsystem. Either they represent the relative number of\nmolecules with a particular state, or the relative time\nduring which a molecule has that state.", "\n\nIn the course of time a transition was made to what the Ehrenfests\ncalled “kineto-statistics of the gas model”, or what is nowadays\nknown as statistical mechanics. In this latter approach, probabilities\nare not attached to the state of a molecule but of the entire gas\nsystem. Thus, the state of the gas, instead of determining the\nprobability distribution, now itself becomes a stochastic variable.", "\n\nA merit of this latter approach is that interactions between molecules\ncan be taken into account. Indeed, the approach is not restricted to\ngases, but also applicable to liquids or solids. The price to be paid,\nhowever, is that the probabilities themselves become more\nabstract. Since probabilities are attributed to the mechanical states\nof the total system, they are no longer determined by such mechanical\nstates. Instead, in statistical mechanics, the probabilities are\nusually determined by means of an ‘ensemble’, i.e., a\nfictitious collection of replicas of the system in question.", "\n\nIt is not easy to pinpoint this transition in the course of history,\nexcept to say that in Maxwell's work in the 1860s definitely belong to\nthe first category, and Gibbs' book of 1902 to the second. Boltzmann's\nown works fall somewhere in the middle. His earlier contributions\nclearly belong to the kinetic theory of gases (although his 1868 paper\nalready applies probability to an entire gas system), while his work\nof 1877 is usually seen as belonging to statistical\nmechanics. However, Boltzmann himself never indicated a clear\ndistinction between these two different theories, and any attempt to\ndraw a demarcation at an exact location in his work seems somewhat\narbitrary.", "\n\nFrom a conceptual point of view, the transition from kinetic gas\ntheory to statistical mechanics poses two main foundational questions.\nOn what grounds do we choose a particular ensemble, or the probability\ndistribution characterizing the system? Gibbs did not enter into a\nsystematic discussion of this problem, but only discussed special\ncases of equilibrium ensembles (i.e. canonical, micro-canonical\netc.). A second problem is to relate the ensemble-based probabilities\nwith the probabilities obtained in the earlier kinetic approach for a\nsingle gas model.", "\n\nThe Ehrenfests (1912) paper was the first to recognize these\nquestions, and to provide a partial answer: Assuming a certain\nhypothesis of Boltzmann's, which they dubbed the ergodic\nhypothesis, they pointed out that for an isolated system the\nmicro-canonical distribution is the unique stationary probability\ndistribution. Hence, if one demands that an ensemble of isolated\nsystems describing thermal equilibrium must be represented by a\nstationary distribution, the only choice for this purpose is the\nmicro-canonical one. Similarly, they pointed out that under the\nergodic hypothesis infinite time averages and ensemble averages were\nidentical. This, then, would provide a desired link between the\nprobabilities of the older kinetic gas theory and those of statistical\nmechanics, at least in equilibrium and in the infinite time limit. Yet\nthe Ehrenfests simultaneously expressed strong doubts about the\nvalidity of the ergodic hypothesis. These doubts were soon\nsubstantiated when in 1913 Rozenthal and Plancherel proved that the\nhypothesis was untenable for realistic gas models.", "\n\nThe Ehrenfests' reconstruction of Boltzmann's work thus gave a\nprominent role to the ergodic hypothesis, suggesting that it played a\nfundamental and lasting role in his thinking. Although this view\nindeed produces a more coherent view of his multifaceted work, it is\ncertainly not historically correct. Boltzmann himself also had grave\ndoubts about this hypothesis, and expressly avoided it whenever he\ncould, in particular in his two great papers of 1872 and 1877b. Since\nthe Ehrenfests, many other authors have presented accounts of\nBoltzmann's work. Particularly important are Klein (1973) and Brush\n(1976). Still, much confusion remains about what exactly his approach\nto statistical physics was, and how it developed. For a more elaborate\nattempt to sketch the general landscape, and Boltzmann's work in\nparticular,I refer to (Uffink 2007). " ], "subsection_title": "1.3 Boltzmann's relevance for the foundations of statistical physics" }, { "content": [ "\n\nRoughly speaking, one may divide Boltzmann's work in four periods. The\nperiod 1866–1871 is more or less his formative period. In his first\npaper (1866), Boltzmann set himself the problem of deriving the full\nsecond law from mechanics. The notion of probability does not appear\nin this paper. The following papers, from 1868 and 1871, were written\nafter Boltzmann had read Maxwell's work of 1860 and 1867. Following\nMaxwell's example, they deal with the characterization of a gas in\nthermal equilibrium, in terms of a probability distribution. Even\nthen, he was set on obtaining more general results, and extended the\ndiscussion to cases where the gas is subject to a static external\nforce, and might consist of poly-atomic molecules. He regularly\nswitched between different conceptions of probability: sometimes this\nreferred to a time average, sometimes a particle average or, in an\nexceptional paper (1871b), it referred to an ensemble average. The\nmain result of those papers is that from the so-called\nStoßzahlansatz (SZA), i.e. an assumption about the\nnumber of collisions (or a closely analogous assumption) the\nMaxwellian distribution function is stationary, and thus an\nappropriate candidate for the equilibrium state. In some cases\nBoltzmann also argued it was the unique such state.", "\n\nHowever, in this period he also presented a completely different\nmethod, which did not rely on the SZA but rather on the ergodic\nhypothesis. This approach led to a new form of the distribution\nfunction that, in the limit \\(N \\rightarrow \\infty\\) reduces to the\nMaxwellian form. In the same period, he also introduced the concept of\nensembles, but this concept would not play a prominent role in his\nthinking until the 1880s.", "\n\nThe next period is that of 1872–1878, in which he wrote his two most\nfamous papers: (1872) (Weitere Studien) and\n(1877b) (Über die Beziehung). The 1872\npaper contained the Boltzmann equation and the\nH-theorem. Boltzmann claimed that the H-theorem\nprovided the desired theorem from mechanics corresponding to the\nsecond law. However, this claim came under a serious objection due to\nLoschmidt's criticism of 1876. The objection was simply that no purely\nmechanical theorem could ever produce a time-asymmetrical\nresult. Boltzmann's response to this objection will be summarized\nlater.", "\n\nThe result was, however, that Boltzmann rethought the basis of his\napproach and in 1877b produced a conceptually very different analysis,\nwhich might be called the combinatorial argument, of\nequilibrium and evolutions towards equilibrium, and the role of\nprobability theory. The distribution function, which formerly\nrepresented the probability distribution, was now conceived of as a\nstochastic variable (nowadays called a macrostate) subject to a\nprobability distribution. That probability distribution was now\ndetermined by the size of the volume in phase space corresponding to\nall the microstates giving rise to the same macrostate, (essentially\ngiven by calculating all permutations of the particles in a given\nmacrostate). Equilibrium was now conceived of as the most probable\nmacrostate instead of a stationary macrostate. The evolution towards\nequilibrium could then be reformulated as an evolution from less\nprobable to more probable states.", "\n\nEven though all commentators agree on the importance of these two\npapers, there is still disagreement about what Boltzmann's claims\nactually were, and whether he succeeded (or indeed even attempted) in\navoiding the reversibility objection in this new combinatorial\nargument, whether he intended or succeeded to prove that most\nevolutions go from less probable to more probable states and whether\nor not he (implicitly) relied on the ergodic hypothesis in these\nworks. I shall comment on these issues in due course. (See Uffink\n(2007) for a more detailed overview.)", "\n\nThe third period is taken up by the papers Boltzmann wrote during\nthe 1880's have attracted much less attention. During this period, he\nabandoned the combinatorial argument, and went back to an approach that\nrelied on a combination of the ergodic hypothesis and the use of\nensembles. For a while Boltzmann worked on an application of this\napproach to Helmholtz's concept of monocyclic systems. However, after\nfinding that concept did not always provide the desired thermodynamical\nanalogies, he abandoned this topic again.", "\n\nNext, in the 1890s the reversibility problem resurfaced again, this\ntime in a debate in the columns of Nature. This time\nBoltzmann chose an entirely different line of counterargument than in\nhis debate with Loschmidt. A few years later, Zermelo presented\nanother objection, now called the recurrence objection. The same\nperiod also saw the publication of the two volumes of his Lectures\non Gas Theory. In this book, he takes the hypothesis of molecular\ndisorder (a close relative of the SZA) as the basis of his\napproach. The combinatorial argument is only discussed as an aside,\nand the ergodic hypothesis is not mentioned at all. His last paper is\nan Encyclopedia article with Nabl presenting a survey of kinetic\ntheory." ], "subsection_title": "1.4 A concise chronography of Boltzmann's writings" } ] }, { "main_content": [ "\n\nBoltzmann's first paper (1866) in statistical physics aimed to reduce\nthe second law to mechanics. Within the next two years he became\nacquainted with Maxwell's papers on gas theory of 1860 and 1867, which\nintroduced probability notions in the description of the gas. Maxwell\nhad studied specific mechanical models for a gas (as a system of hard\nspheres (1860) or of point particles exerting a mutual force on each\nother inversely proportional to the fifth power of their distance),\nand characterized the state of such a gas by means of a probability\ndistribution f over the various values of the molecular\nvelocities \\(\\vec{v}\\). For Maxwell, the probability\n\\(f(\\vec{v})d^3\\vec{v}\\) denoted the relative number of particles in\nthe gas with a velocity between \\(\\vec{v}\\) and \\(\\vec{v} +\nd^3\\vec{v}\\). In particular, he had argued that the state of\nequilibrium is characterized by the so-called Maxwell distribution\nfunction: ", "\n where \\(A\\) is a normalization constant and \\(B\\) is proportional to\nthe absolute temperature. ", "\n\nThe argument that Maxwell had given in 1860 to single out this\ndistribution relied on the fact that this is the only probability\ndistribution that is both spherically symmetric and factorizes into\nfunctions of the orthogonal components \\(v_x, v_y, v_z\\)\nseparately. In 1867, however he replaced these desiderata with the\nmore natural requirement that the equilibrium distribution should be\nstationary, i.e. it should not change shape as a result of the\ncontinual collisions between the particles. This called for a more\nelaborate argument, involving a detailed consideration of the\ncollisions between particles. The crucial assumption in this argument\nis what is now known as the SZA. Roughly speaking, it states that the\nnumber of particle pairs, \\(dN(\\vec{v}_1, \\vec{v}_2)\\) with initial\nvelocities between \\(\\vec{v}_1\\) and \\(\\vec{v}_1 + d^3\\vec{v}_1\\) and\nbetween \\(\\vec{v}_2\\) and \\(\\vec{v}_2 + d^3\\vec{v}_2\\) respectively,\nwhich are about to collide in a time span \\(dt\\) is proportional\nto", "\n where the proportionality constant depends on the geometry of the\ncollision and the relative velocity. For Maxwell, and Boltzmann later,\nthis assumption seemed almost self-evident. One ought to note,\nhowever, that by choosing the initial, rather than the final\nvelocities of the collision, the assumption introduced an explicit\ntime-asymmetric element. This, however, was not noticed until\n1895. Maxwell showed that, under the SZA, the distribution (1) is\nindeed stationary. He also argued, but much less convincingly, that it\nshould be the only stationary distribution.", "\n\nIn his (1868), Boltzmann set out to apply this argument to a variety\nof other models (including gases in a static external force field).\nHowever, Boltzmann started out with a somewhat different\ninterpretation of probability in mind than Maxwell. For him,\n\\(f(\\vec{v})d^3\\vec{v}\\) is introduced firstly as the relative time\nduring which a (given) particle has a velocity between \\(\\vec{v}\\) and\n\\(\\vec{v} + d^3\\vec{v}\\) (WA I, 50). But, in the same breath, he\nidentifies this with the relative number of particles with this\nvelocity. This equivocation between different meanings of probability\nreturned again and again in Boltzmann's\nwriting.[7] Either\nway, of course, whether we average over time or particles,\nprobabilities are defined here in strictly mechanical terms, and\ntherefore objective properties of the gas. Yet apart from this\nstriking difference in interpretation, the first section of the paper\nis a straightforward continuation of the ideas Maxwell had developed\nin his 1867. In particular, the main ingredient is always played by\nthe SZA, or a version of that assumption suitably modified for the\ncase discussed.", "\n\nBut in the last section of the paper he suddenly shifts course. He now\nfocuses on a general Hamiltonian system, i.e., a system of N\nmaterial points with an arbitrary interaction potential. The state of\nthis system may be represented as a phase point \\(x =\n(\\vec{p}_1,\\ldots,\\vec{p}_N,\\vec{q}_1,\\ldots,\\vec{q}_N)\\) in the\nmechanical phase space \\(\\Gamma\\). By the Hamiltonian equations of\nmotion, this point evolves in time, and thus describes a trajectory\n\\(x_t\\). This trajectory is constrained to lie on a given energy\nhypersurface \\(H(x) = E\\), where \\(H(x)\\) denotes the Hamiltonian\nfunction.", "\n\nNow consider an arbitrary probability density \\(\\rho(x)\\) over this\nphase space. He shows, by (what is now known as) Liouville's theorem,\nthat \\(\\rho\\) remains constant along a trajectory, i.e., \\(\\rho(x_0) =\n\\rho(x_t)\\). Assuming now for simplicity that all points in a given\nenergy hypersurface lie on a single trajectory, the probability should\nbe a constant over the energy hypersurface. In other words, the only\nstationary probability with fixed total energy is the microcanonical\ndistribution.", "where \\(\\delta\\) is Dirac's delta function.", "\n\nBy integrating this expression over all momenta but one, and dividing\nthis by the integral of \\(\\rho_{mc}\\) over all momenta, Boltzmann\nobtained the marginal probability density \\(\\rho_{mc}(\\vec{p}_1 \\mid\n\\vec{q}_1,\\ldots,\\vec{q}_N)\\) for particle 1's momentum,\nconditionalized on the particle positions\n\\(\\vec{q}_1,\\ldots,\\vec{q}_N\\). He then showed that this marginal\nprobability distribution tends to the Maxwell distribution when the\nnumber of particles tends to infinity.", "\n\nSome comments on this result.", "\n\nFirst, the difference between the approach relying on the ergodic\nhypothesis and that relying on the SZA is rather striking. Instead of\nconcentrating on a specific gas model, Boltzmann here assumes a much\nmore general model with an arbitrary interaction potential\n\\(V(\\vec{q}_1,\\ldots,\\vec{q}_N)\\). Moreover, the probability density\n\\(\\rho\\) is defined over phase space, instead of the space of\nmolecular velocities. This is the first occasion where probability\nconsiderations are applied to the state of the mechanical system as\nwhole, instead of its individual particles. If the transition between\nkinetic gas theory and statistical mechanics may be identified with\nthis caesura, (as argued by the Ehrenfests and by Klein) it would seem\nthat the transition has already been made right here in 1868, rather\nthan only in 1877. ", "\n\nBut of course, for Boltzmann the transition did not involve a major\nconceptual move, thanks to his conception of probability as a relative\ntime. Thus, the probability of a particular state of the total system\nis still identified with the fraction of time in which that state is\noccupied by the system. In other words, he had no need for ensembles or\nnon-mechanical probabilistic assumptions in this paper.", "\n\nHowever, note that the equivocation between relative times and\nrelative numbers, which was relatively harmless in the first section\nof the 1868 paper, is no longer possible in the interpretation of\n\\(\\rho\\). The probability \\(\\rho_{mc}(\\vec{p}_1 \\mid\n\\vec{q}_1,\\ldots,\\vec{q}_N) d^3\\vec{p}_1\\) gives us the relative time\nthat the total system is in a state for which particle 1 has a\nmomentum between \\(\\vec{p}_1\\) and \\(\\vec{p}_1 + d^3\\vec{p}_1\\), for\ngiven values of all positions. There is no route back to infer that\nthis has anything to do with the relative number of particles with\nthis momentum.", "\n\nSecond, and more importantly, these results open up a perspective of great\ngenerality. It suggests that the probability of the molecular\nvelocities for an isolated system in a stationary state will always\nassume the Maxwellian form if the number of particles tends to\ninfinity. Notably, this argument completely dispenses with any\nparticular assumption about collisions, or other details of the\nmechanical model involved, apart from the assumption that it is\nHamiltonian. Indeed it need not even represent a gas.", "\n\nThird, and most importanty, the main weakness of the present result is its\nassumption that the trajectory actually visits all points on the\nenergy hypersurface. This is what the Ehrenfests called the ergodic\n hypothesis.[8]\n Boltzmann returned to this issue on the final page of the paper\n(WA I, 96). He notes there that exceptions to his\ntheorem might occur, if the microscopic variables would not, in the\ncourse of time, take on all values compatible with the conservation of\nenergy. For example this would be the case when the trajectory is\nperiodic. However, Boltzmann observed, such cases would be immediately\ndestroyed by the slightest disturbance from outside, e.g., by the\ninteraction of a single external atom. He argued that these exceptions\nwould thus only provide cases of unstable equilibrium.", "\n\nStill, Boltzmann must have felt unsatisfied with his own argument.\nAccording to an editorial footnote in the collection of his scientific\npapers (WA I, 96), Boltzmann's personal copy of the paper contains a\nhand-written remark in the margin stating that the point was still\ndubious and that it had not been proven that, even including\ninteraction with an external atom, the trajectory would traverse all\npoints on the energy hypersurface." ], "section_title": "2. The Stoßzahlansatz and the ergodic hypothesis", "subsections": [ { "content": [ "\n\nHowever, his doubts were still not laid to rest. His next paper on gas\ntheory (1871a) returns to the study of a detailed mechanical gas\nmodel, this time consisting of polyatomic molecules, and explicitly avoids any\nreliance on the ergodic hypothesis. And when he did return to the\nergodic hypothesis in (1871b), it was with much more caution. Indeed, it is\nhere that he actually first described the worrying assumption as an\nhypothesis, formulated as follows:", "The great irregularity of the thermal motion and the\nmultitude of forces that act on a body make it probable that its atoms,\ndue to the motion we call heat, traverse all positions and velocities\nwhich are compatible with the principle of [conservation of] energy.\n(WA I, 284)", "\n Note that Boltzmann formulates this hypothesis for an arbitrary body,\ni.e., it is not restricted to gases. He also emphasizes, at the end of\nthe paper, that “the proof that this hypothesis is fulfilled for\nthermal bodies, or even is fullfillable, has not been provided” (WA I,\n287). ", "\n\nThere is a major confusion among modern commentators about the role\nand status of the ergodic hypothesis in Boltzmann's thinking. Indeed,\nthe question has often been raised how Boltzmann could ever have\nbelieved that a trajectory traverses all points on the energy\nhypersurface, since, as the Ehrenfests conjectured in 1911, and was\nshown almost immediately in 1913 by Plancherel and Rozenthal, this is\nmathematically impossible when the energy hypersurface has a dimension\nlarger than 1.", "\n\nIt is a fact that both (1868) [WA I, 96] and\n(1871b) [WA I, 284] mention external disturbances as an\ningredient in the motivation for the ergodic hypothesis. This might be\ntaken as evidence for ‘interventionalism’, i.e., the\nviewpoint that such external influences are crucial in the explanation\nof thermal phenomena (see Blatt 1959, Ridderbos & Redhead 1998).\nYet even though Boltzmann clearly expressed the thought that these\ndisturbances might help to motivate the ergodic hypothesis, he never\ntook the idea very seriously. The marginal note in the 1868 paper\nmentioned above indicated that, even if the system is disturbed, there\nis still no easy proof of the ergodic hypothesis, and all his further\ninvestigations concerning this hypothesis assume a system that is\neither completely isolated from its environment or at most acted upon\nby a static external force. Thus, interventionalism did not play a\nsignificant role in his\n thinking.[9] ", "\n\nIt has also been suggested, in view of Boltzmann's later habit of\ndiscretising continuous variables, that he somehow thought of the\nenergy hypersurface as a discrete manifold containing only finitely\nmany discrete cells (Gallavotti 1994). In this reading, obviously,\nthe mathematical no-go theorems of Rozenthal and Plancherel no longer\napply. Now it is definitely true that Boltzmann developed a preference\ntowards discretizing continuous variables, and would later apply this\nprocedure more and more (although usually adding that this was purely\nfor purposes of illustration and more easy understanding). However,\nthere is no evidence in the (1868) and (1871b) papers that Boltzmann\nimplicitly assumed a discrete structure of mechanical phase space or\nthe energy hypersurface.", "\n\nInstead, the context of his (1871b) makes clear enough how he intended\nthe hypothesis, as has already been argued by (Brush\n1976). Immediately preceding the section in which the hypothesis is\nintroduced, Boltzmann discusses trajectories for a simple example: a\ntwo-dimensional harmonic oscillator with potential \\(V(x,y) = ax^2 +\nby^2\\). For this system, the configuration point \\((x, y)\\) moves\nthrough the surface of a rectangle. See Figure 1 below. (See also\nCercignani 1998, 148.)\n", "\n He then notes that if \\(a/b\\) is rational, (actually: if\n\\(\\sqrt{a/b}\\) is rational) this motion is periodic. However, if this\nvalue is irrational, the trajectory will, in the course of time,\ntraverse “almählich die ganze Fläche” (WA I,\n271) of the rectangle. See Figure 2:", "\n He says in this case that \\(x\\) and \\(y\\) are independent,\nsince for each values of \\(x\\) an infinity of values for \\(y\\) in any\ninterval in its range are possible. The very fact that Boltzmann\nconsiders intervals for the values of \\(x\\) and \\(y\\) of arbitrary\nsmall sizes, and stressed the distinction between rational and\nirrational values of the ratio \\(a/b\\), indicates that he\ndid not silently presuppose that phase space was essentially\ndiscrete, where those distinctions would make no sense.", "\n\nNow clearly, in modern language, one should say in the second case\nthat the trajectory lies densely in the surface, but not that\nit traverses all points. Boltzmann did not possess this language. In\nfact, he could not have been aware of Cantor's insight that the\ncontinuum contains more than a countable infinity of points. Thus, the\ncorrect statement that, in the case that \\(\\sqrt{a/b}\\) is irrational,\nthe trajectory will traverse, for each value of \\(x\\), an infinity of\nvalues of \\(y\\) within any interval however small, could easily have\nlead him to believe (incorrectly) that all values of \\(x\\)\nand \\(y\\) are traversed in the course of time.", "\n\nIt thus seems eminently plausible, by the fact that this discussion\nimmediately precedes the formulation of the ergodic hypothesis, that\nthe intended reading of the ergodic hypothesis is really what the\nEhrenfests dubbed the quasi-ergodic hypothesis, namely, the\nassumption that the trajectory lies densely (i.e. passes arbitrarily\nclose to every point) on the energy\n hypersurface.[10]\n The quasi-ergodic hypothesis is not mathematically impossible in\nhigher-dimensional phase spaces. However, the quasi-ergodic hypothesis\ndoes not entail the desired conclusion that the only stationary\nprobability distribution over the energy surface is micro-canonical.\nOne might then still conjecture that if the system is quasi-ergodic,\nthe only continuous stationary distribution is microcanonical. But\neven this is fails in general (Nemytskii and Stepanov 1960). ", "\n\nNevertheless, Boltzmann remained skeptical about the validity of his\nhypothesis. For this reason, he attempted to explore different routes\nto his goal of characterizing thermal equilibrium in mechanics. Indeed,\nboth the preceding (1871a) and his next paper (1871c) present alternative\narguments, with the explicit recommendation that they avoid hypotheses.\nIn fact, he did not return to this hypothesis until the 1880s\n(stimulated by Maxwell's 1879 review of the last section of Boltzmann's\n1868 paper). At that time, perhaps feeling fortified by Maxwell's\nauthority, he would express much more confidence in the ergodic\nhypothesis (see Section 5). ", "\n\nSo what role did the ergodic hypothesis play? It seems that Boltzmann\nregarded the ergodic hypothesis as a special dynamical assumption that\nmay or may not be true, depending on the nature of the system, and\nperhaps also on its initial state. Its role was simply to help derive\na result of great generality: for any system for which the hypothesis\nis true, its unique equilibrium state is characterized by the\nmicrocanonical distribution (3), from which a form of the Maxwell\ndistribution may be recovered in the limit \\(N \\rightarrow \\infty\\),\nregardless of any details of the inter-particle interactions, or\nindeed whether the system represented is a gas, fluid, solid or any\nother thermal body. Note also that the microcanonical distribution\nimmediately implies that the probability of finding the system in any\nregion on the energy hypersurface is proportional to the size of that\nregion (as measured by the microcanonical measure). This idea would\nresurface in his 1877 combinatorial argument, although then without\nthe context of characterizing equilibrium thermal equilibrium.", "\n\nThe Ehrenfests have suggested that the ergodic hypothesis played a\nmuch more fundamental role. In particular they have pointed out that if\nthe hypothesis is true, averaging over an (infinitely) long time would\nbe identical to phase averaging with the microcanonical distribution.\nThus, they suggested that Boltzmann relied on the ergodic hypothesis in\norder to equate time averages and phase averages, or in other words, to\nequate two meaning of probability (relative time and relative volume in\nphase space.) There is however no evidence that Boltzmann ever followed\nthis line of reasoning. He simply never gave any justification for\nequivocating time and particle averages, or phase averages, at all.\nPresumably, he thought nothing much depended on this issue and that it\nwas a matter of taste." ], "subsection_title": "2.1 Doubts about the ergodic hypothesis" } ] }, { "main_content": [], "section_title": "3. The H-theorem and the reversibility objection", "subsections": [ { "content": [ "\n\nIn 1872 Boltzmann published one of his most important papers, its long\ntitle often abbreviated as Weitere Studien (Further\nstudies). It was aimed at something completely new, namely at\nshowing that whatever the initial state of a gas system was, it would\nalways tend to evolve to equilibrium. Thus, this paper is the first\nwork to deal with non-equilibrium theory. The paper contained two\ncelebrated results nowadays known as the Boltzmann equation and the\nH-theorem. The latter result was the basis of Boltzmann's\nrenewed claim to have obtained a general theorem corresponding to the\nsecond law. This paper has been studied and commented upon by numerous\nauthors. Indeed an integral translation of the text has been provided\nby (Brush 1966). Thus, for present purposes, a succinct summary\nof the main points might have been sufficient. However, there is still\ndispute among modern commentators about its actual content.", "\n\nThe issue at stake is the question whether the results obtained in\nthis paper are presented as necessary consequences of the mechanical\nequations of motion, or whether Boltzmann explicitly acknowledged that\nthey would allow for exceptions. Klein has written", " I can find no indication in his 1872 memoir that\nBoltzmann conceived of possible exceptions to the H-theorem,\nas he later called it. (Klein 1973, 73)", "\n Klein argues that Boltzmann only came to acknowledge the existence of\nsuch exceptions thanks to Loschmidt's critique in 1877. An opposite\nopinion is expressed by von Plato (1994). He argues that, already in\n1872, Boltzmann was well aware that his H-theorem had\nexceptions, and thus “already had a full hand against his future\ncritics”. Indeed, von Plato states that", "… contrary to a widely held opinion, Boltzmann is\nnot in 1872 claiming that the Second Law and the Maxwellian\ndistribution are necessary consequences of kinetic theory. (von Plato\n1994, 81) ", "\n It might be of some interest to try and settle this dispute. ", "\n The Weitere Studien starts with an\nappraisal of the role of probability theory in the context of gas\ntheory. The number of particles in a gas is so enormous, and their\nmovements are so swift that we can observe nothing but average values.\nThe determination of averages is the province of probability calculus.\nTherefore, “the problems of the mechanical theory of heat are really\nproblems in probability calculus” (WA I, 317). But, Boltzmann says, it\nwould be a mistake to believe that the theory of heat would therefore\ncontain uncertainties.", "\n\nHe emphasizes that one should not confuse incompletely proven\nassertions with rigorously derived theorems of probability theory. The\nlatter are necessary consequences from their premisses, as in any other\ntheory. They will be confirmed by experience as soon as one has\nobserved a sufficiently large number of cases. This last condition,\nhowever, should be no significant problem in the theory of heat because\nof the enormous number of molecules in macroscopic bodies. Yet, in this\ncontext, one has to make doubly sure that we proceed with the utmost\nrigor.", "\n\nThus, the message expressed in the opening pages of this paper seems\nclear enough: the results Boltzmann is about to derive are advertised\nas doubly checked and utterly rigorous. Of course, their relationship\nwith experience might be less secure, since any probability statement\nis only reproduced in observations by sufficiently large numbers of\nindependent data. Thus, Boltzmann would have allowed for exceptions in\nthe relationship between theory and observation, but not in the\nrelation between premisses and conclusion.", "\n\nHe continues by saying what he means by probability, and repeats its\nequivocation as a fraction of time and the relative number of particles\nthat we have seen earlier in 1868a:", "If one wants […] to build up an exact theory\n[…] it is before all necessary to determine the probabilities\nof the various states that one and the same molecule assumes in the\ncourse of a very long time, and that occur simultaneously for\ndifferent molecules. That is, one must calculate how the number of\nthose molecules whose states lie between certain limits relates to the\ntotal number of molecules (WA I, 317).", "\n This equivocation is not vicious however. For most of the paper the\nintended meaning of probability is always the relative number of\nmolecules with a particular molecular state. Only at the final stages\nof his paper (WA I, 400) does the time-average interpretation of\nprobability (suddenly) recur.", "\n\nBoltzmann says that both he and Maxwell had attempted the\ndetermination of these probabilities for a gas system but without\nreaching a complete solution. Yet, on a closer inspection, “it seems\nnot so unlikely that these probabilities can be derived on the basis\nof the equations of motion alone…” (WA I, 317). Indeed, he\nannounces, he has solved this problem for gases whose molecules\nconsist of an arbitrary number of atoms. His aim is to prove that\nwhatever the initial state in such a system of gas molecules, it must\ninevitably approach the state characterized by the Maxwell\ndistribution (WA I, 320).", "\n\nThe next section specializes to the simplest case of monatomic gases\nand also provides a more complete specification of the problem he aims\nto solve. The gas molecules are modelled as hard spheres, contained in\na fixed vessel with perfectly elastic walls (WA I, 320). Boltzmann\nrepresents the state of the gas by a time-dependent distribution\nfunction \\(f_t(\\vec{v})\\) which gives us, at each time \\(t\\), the\nrelative number of molecules with velocity\n\\(\\vec{v}\\).[11]\nHe also states three more special assumptions:", "\n After a few well-known manipulations, the result from these\nassumptions is a differentio-integral equation (the Boltzmann\nequation) that determines the evolution of the distribution function\n\\(f_t(v)\\) from any given initial form. ", "\n\nThere are also a few unstated assumptions that go into the derivation\nof this equation. First, the number of molecules must be large enough\nso that the (discrete) distribution of their velocities can be well\napproximated by a continuous and differentiable function\n\\(f\\). Secondly, \\(f\\) changes under the effect of binary collisions\nonly. This means that the density of the gas should be low (so that\nthree-particle collisions can be ignored) but not too low (so that\ncollisions would be too infrequent to change \\(f\\) at all. (The modern\nprocedure to put these requirements in a mathematically precise form\nis that of taking the so-called Boltzmann-Grad limit.) A final\ningredient is that all the above assumptions are not only valid at an\ninstant but remain true in the course of time.", "\nThe H-theorem. Assuming that the Boltzmann\nequation is valid for all times, one can prove without difficulty the\n“H-theorem”: the quantity \\(H\\) (that Boltzmann\nin this paper actually denotes as \\(E\\)), defined as ", "\n\ndecreases monotonically in time, i.e.,", "\n\nas well as its stationarity for the Maxwell distribution, i.e., ", "\n\nBoltzmann concludes this section of the paper as follows:", "\n It has thus been rigorously proved that whatever may have been the\ninitial distribution of kinetic energy, in the course of time it must\nnecessarily approach the form found by Maxwell. […] This\n[proof] actually gains much in significance because of its\napplicability on the theory of multi-atomic gas molecules. There too,\none can prove for a certain quantity \\(E\\) that, because of the\nmolecular motion, this quantity can only decrease or in the limiting\ncase remain constant. Thus, one may prove that, because of the atomic\nmovement in systems consisting of arbitrarily many material points,\nthere always exists a quantity which, due to these atomic movements,\ncannot increase, and this quantity agrees, up to a constant factor,\nexactly with the value that I found in [Boltzmann 1871c] for the\nwell-known integral \\(\\int dQ/T\\).\n\nThis provides an analytical proof of the Second Law in a way\ncompletely different from those attempted so far. Up till now, one has\nattempted to proof that \\(\\int dQ/T = 0\\) for reversible\n(umkehrbaren) cyclic[12] processes, which however does not prove\nthat for an irreversible cyclic process, which is the only one\nnote-that occurs in nature, it is always negative; the reversible\nprocess being merely an idealization, which can be approached more or\nless but never perfectly. Here, however, we immediately reach the\nresult that \\(\\int dQ/T\\) is in general negative and zero only in a\nlimit case… (WA I, 345)\n", "\n\nThus, as in his 1866 paper, Boltzmann claims to have a rigorous,\nanalytical and general proof of the Second Law." ], "subsection_title": "3.1 1872: The Boltzmann equation and H-theorem" }, { "content": [ "\n1. As we have seen, The H-theorem formed the basis of a\nrenewed claim by Boltzmann to have obtained a theorem corresponding to\nthe second law, at least for gases. A main difference with his\nprevious (1866) claim, is that he now strongly emphasized the role of\nprobability calculus in his derivation. Even so, it will be noted that\nhis conception of probability is still a fully mechanical one. Thus,\nthere is no conflict between his claims that on the one hand,\n“the problems of the mechanical theory of heat are really\nproblems in probability calculus” and that the probabilities\nthemselves are “derived on the basis of the equations of motion\nalone”, on the other hand. Indeed, it seems to me that\nBoltzmann's emphasis on the crucial role of probability is only\nintended to convey that probability theory provides a particularly\nuseful and appropriate language for discussing mechanical problems in\ngas theory. There is no indication in this paper yet that probability\ntheory could play a role by furnishing assumptions of a non-mechanical\nnature, i.e., independent of the equations of motion. However, see\nBadino (2006, Other Internet Resources) for a very different point of\nview. ", "\n\n2. Note that Boltzmann stresses the generality, rigor and\n“analyticity” of his proof. He put no emphasis on the special\nassumptions that go into the argument. Indeed,\nthe, Stoßzahlansatz commonly identified as the key\nassumption that is responsible for the time-asymmetry of the\nH-theorem, is announced as follows:", "The determination [of the number of collisions] can only\nbe obtained in a truly tedious manner, by consideration of the\nrelative velocities of both particles. But since this consideration\nhas, apart from its tediousness, not the slightest difficulty, nor any\nspecial interest, and because the result is so simple that one might\nalmost say it is self-evident I will only state this result. (WA I,\n323)", "This, is not an announcement that would alert his readers to the\ncrucial role of this assumption.", "\nStill, it thus seems natural that Boltzmann's contemporaries must have\nunderstood him as claiming that the H-theorem followed\nnecessarily from the dynamics of the mechanical gas model. Indeed this\nis exactly how Boltzmann's claims were understood. For example, the\nrecommendation written in 1888 for his membership of the Prussian\nAcademy of Sciences mentions as Boltzmann's main feat that had proven\nthat, whatever its initial state, a gas must necessarily approach the\nMaxwellian distribution (Kirsten and Körber 1975, 109). ", "\nIs there then no evidence at all for von Plato's reading of the\npaper? Von Plato quotes a passage from Section II, where Boltzmann\nrepeats the previous analysis by assuming that energy can take on only\ndiscrete values, and replacing all integrals by sums. He recovers, of\ncourse, the same conclusion, but now adds a side remark, which touches\nupon the case of non-uniform gases:", "Whatever may have been the initial distribution of states,\nthere is one and only one distribution which will be approached in the\ncourse of time. […] This statement has been proved for the case\nthat the distribution of states was already initially uniform. It must\nalso be valid when this is not the case, i.e. when the molecules are\ninitially distributed in such a way that in the course of time they\nmix among themselves more and more, so that after a very long time the\ndistribution of states becomes uniform. This will always be the case,\nwith the exception of very special cases, e.g., when all molecules\nwere initially situated along a straight line, and were reflected by\nthe walls onto this line. (WA I, 358)", "\n True enough, Boltzmann in the above quote indicates that there are\nexceptions. But he mentions them only in connection with an\nextension of his results to the case when the gas is not\ninitially uniform, i.e., when condition (b) above is dropped. There\ncan be no doubt that under the assumption of the conditions\n(a – c), Boltzmann claimed rigorous validity of the\nH-theorem.", "\n\n3. Note that Boltzmann misconstrues, or perhaps understates, the\nsignificance of his results. Both the Boltzmann equation and the\nH theorem refer to a body of gas in a fixed container that\nevolves in complete isolation from its environment. There is no\nquestion of heat being exchanged by the gas during a process, let\nalone in an irreversible cyclic process. His comparison with Clausius'\nintegral \\(\\int dQ/T\\) (i.e., \\(\\oint \\dbar Q/T\\) in modern notation)\nis therefore really completely out of place.", "\n\nThe true import of Boltzmann's results is rather that they provide a\ngeneralization of the entropy concept to non-equilibrium states, and a\nclaim that this non-equilibrium entropy \\(-kH\\) increases\nmonotonically as the isolated gas evolves from non-equilibrium towards\nan equilibrium state. The relationship with the second law is,\ntherefore, indirect. On the one hand, Boltzmann proves much more than\nwas required, since the second law does not speak of non-equilibrium\nentropy, nor of monotonic increase; on the other hand it proves also\nless, since Boltzmann does not consider more general adiabatic\nprocesses." ], "subsection_title": "3.2 Remarks and problems" }, { "content": [ "\n\nAccording to Klein (1973) Boltzmann seemed to have\nbeen satisfied with his treatments of 1871 and 1872 and turned his\nattention to other matters for a couple of years. He did come back to\ngas theory in 1875 to discuss an extension of the Boltzmann equation to\ngases subjected to external forces. But this paper does not present any\nfundamental changes of thought. However, the 1875 paper did contain a\nresult which, two years later, led to a debate with Loschmidt. It\nshowed that a gas in equilibrium in an external force field (such as\nthe earth's gravity) should have a uniform temperature, and therefore,\nthe same average kinetic energy at all heights. This conclusion\nconflicted with the intuition that rising molecules must do work\nagainst the gravitational field, and pay for this by having a lower\nkinetic energy at greater heights.", "\n\nNow Boltzmann (1875) was not the first to reach the contrary result,\nand Loschmidt was not the first to challenge it. Maxwell and Guthrie\nentered into a debate on the very same topic in 1873. But actually\ntheir main point of contention need not concern us very much. The\ndiscussion between Loschmidt and Boltzmann is important for quite\nanother issue which Loschmidt only introduced as a side remark:", "\n By the way, one should be careful about the claim that in\na system in which the so-called stationary state has been achieved,\nstarting from an arbitrary initial state, this average state can remain\nintact for all times. […] \n\nIndeed, if in the above case [i.e. starting in a state where one\nparticle is moving, and all the others lie still on the bottom], after\na time τ which is long enough to obtain the stationary state, one\nsuddenly assumes that the velocities of all atoms are reversed, we\nwould obtain an initial state that would appear to have the same\ncharacter as the stationary state. For a fairly long time this would\nbe appropriate, but gradually the stationary state would deteriorate,\nand after passage of the time τ we would inevitably return to our\noriginal state: only one atom has absorbed all kinetic energy of the\nsystem […], while all other molecules lie still on the bottom of the\ncontainer.\n\nObviously, in every arbitrary system the course of events\nmust be become retrograde when the velocities of all its elements are\nreversed. (Loschmidt 1876, 139)\n ", "\n\nPutting the point in more modern terms, the laws of (Hamiltonian)\nmechanics are such that for every solution one can construct another\nsolution by reversing all velocities and replacing \\(t\\) by\n\\(-t\\). Since \\(H[f]\\) is invariant under the velocity reversal, it\nfollows that if \\(H[f]\\) decreases for the first solution, it will\nincrease for the second. Accordingly, the reversibility objection is\nthat the H-theorem cannot be a general theorem for all\nmechanical evolutions of the gas.", "\n Boltzmann's response (1877a). Boltzmann's responses\nto the reversibility objection are not easy to make sense of, and\nvaried in the course of time. In his immediate response to Loschmidt\nhe acknowledges that certain initial states of the gas would lead to\nan increase of the \\(H\\) function, and hence a violation of the\nH-theorem. The crux of his rebuttal was that such initial\nstates were extremely improbable, and could hence safely be\nignored.", "\n\nThis argument shows that Boltzmann was already implicitly embarking\non an approach that differed from the context of the 1872 paper. Recall\nthat this paper used the concept of probability only in the guise of a\ndistribution function, giving the probability of molecular velocities.\nThere was no such thing in that paper as the probability of a state of\nthe gas as whole. This conceptual shift would become more explicit in\nBoltzmann's next paper (1877b).", "\n\nThis rebuttal of Loschmidt is far from satisfactory. Any reasonable\nprobability assignment to gas states is presumably invariant under the\nvelocity reversal of the molecules. If an initial state leading to an\nincrease of \\(H\\) is to be ignored on account of its small\nprobability, one ought to assume the same for the state from which it\nwas constructed by velocity reversal. In other words, any\nnon-equilibrium state would have to be ignored. But that in effect\nsaves the H-theorem by restricting it to those cases where it\nis trivially true, i.e., where \\(H\\) is constant.", "\n\nThe true source of the reversibility problem was only identified by\nBurbury (1894a) and Bryan1 (1894), by pointing out that already the\nStoßzahlansatz contained a time-asymmetric\nassumption. Indeed, if we replace the SZA by the assumption that the\nnumber of collisions is proportional to the product \\(f(\\vec{v}'_1)\nf(\\vec{v}'_2)\\) for the velocities \\(\\vec{v}'_1, \\vec{v}'_2\\) after\nthe collision, we would obtain, by a similar reasoning, \\(dH/dt \\le\n0\\). The question is now, of course, we would prefer one assumption\nabove the other, without falling into some kind of double\nstandards. One thing is certain, and that is that any such preference\ncannot be obtained from mechanics and probability theory alone." ], "subsection_title": "3.3 1877: The reversibility objection" } ] }, { "main_content": [ "\n\nBoltzmann’s begins the paper by stating that his goal is to\nelucidate the relationship between the Second Law and probability\ncalculus. He notes he has repeatedly emphasized that the Second Law is\nrelated to probability calculus. In particular he points out that the\n1872 paper confirmed this relationship by showing that a certain\nquantity [i.e. \\(H\\)] can only decrease, and must therefore obtain its\nminimum value in the state of thermal equilibrium. Yet, this\nconnection of the Second Law with probability theory became even more\napparent in his previous paper (1877a). Boltzmann states that he will\nnow solve the problem mentioned in that paper, of calculating the\nprobabilities of various distributions of state by determining the\nratio of their numbers.", "\nHe also announces that, when a system starts in an improbable state,\nit will always evolve towards more probable states, until it reaches\nthe most probable state, i.e. that of thermal equilibrium. When this\nis applied to the Second Law, he says, “we can identify that quantity\nwhich is usually called entropy, with the probability of the state in\nquestion.” And: “According to the present interpretation, [the Second\nLaw] states nothing else but that the probability of the total state\nof a composite system always increases” [W.A. II, pp. 165–6]. Exactly\nhow all this is meant, he says, will become clear later in the\narticle.", "\nSuccinctly, and rephrased in modern terms, the argument is as\nfollows. Apart from \\(\\Gamma\\), the mechanical phase space containing\nthe possible states x for the total gas system, we consider\nthe so-called \\(\\mu\\)-space, i.e., the state space of a single\nmolecule. For monatomic gases, this space is just a six-dimensional\nspace with \\((\\vec{p}, \\vec{q})\\) as coordinates. With each state\n\\(x\\) is associated a collection of \\(N\\) points in \\(\\mu\\)-space.", "\n\nWe now partition \\(\\mu\\) into \\(m\\) disjoint cells: \\(\\mu = \\omega_1\n\\cup \\ldots \\cup \\omega_m\\). These\n\ncells are taken to be rectangular in the position and momentum\ncoordinates and of equal size. Further, it is assumed we can\ncharacterize each cell in \\(\\mu\\) with a molecular energy\n\\(\\epsilon_i\\).", "\n\nFor each \\(x\\), henceforth also called the microstate, we define\nthe macrostate (Boltzmann's term was Komplexion) as\n\\(Z := (n_1,\\ldots,n_m)\\), where \\(n_i\\) is the number of particles\nthat have their molecular state in cell \\(\\omega_i\\). The relation\nbetween macro- and microstate is obviously non-unique since many\ndifferent microstates, e.g., obtained by permuting the molecules, lead\nto the same macrostate. One may associate with every given macrostate\n\\(Z_0\\) the corresponding set of microstates:", "\n The volume \\(\\lvert A_{Z_0} \\rvert\\) of this set is proportional to\nthe number of permutations that lead to this macrostate. Boltzmann\nproposes the problem to determine for which macrostate \\(Z\\) the\nvolume \\(\\lvert A_Z \\rvert\\) is maximal, under the constraints of a\ngiven total number of particles, and a given total energy:", "\n This problem can easily be solved with the Lagrange multiplier\ntechnique. Under the Stirling approximation for \\(n_i \\gg 1\\) we\nfind", "which is a discrete version of the Maxwell distribution. ", "\n\nMoreover, the volume of the corresponding set in \\(\\Gamma\\) is related\nto a discrete approximation of the H-function. Indeed, one\nfinds ", "\n In other words, if we take \\(-kNH\\) as the entropy of a macrostate,\nit is also proportional to the logarithm of the volume of the\ncorresponding region in phase space.", "\n\nBoltzmann also refers to these volumes as the “probability” of the\nmacrostate. He therefore now expresses the second law as a tendency to\nevolve towards ever more probable macrostates." ], "section_title": "4. 1877b: The combinatorial argument", "subsections": [ { "content": [ "\n\n1. No dynamical assumption is made; i.e., it is not relevant to the\nargument whether or how the particles collide. It might seem that this\nmakes the present argument more general than the previous one. Indeed,\nBoltzmann suggests at the end of the paper that the same argument might\nbe applicable also to dense gases and even to solids. ", "\n\nHowever, it should be noticed that the assumption that the total\nenergy can be expressed in the form \\(E = \\sum_i n_i\\epsilon_i\\) means\nthat the energy of each particle depends only on the cell in which it\nis located, and not the state of other particles. This can only be\nmaintained, independently of the number \\(N\\), if there is no\ninteraction at all between the particles. The validity of the argument\nis thus really restricted to ideal gases.", "\n\n2. The procedure of dividing \\(\\mu\\) space into cells is essential\nhere. Indeed, the whole prospect of using combinatorics would\ndisappear if we did not adopt a partition. But the choice to take all\ncells equal in size in position and momentum variables is not quite\nself-evident, as Boltzmann himself shows. In fact, before he develops\nthe argument above, his paper first discusses an analysis in which the\nparticles are characterized by their energy instead of position and\nmomentum. This leads him to carve up \\(\\mu\\)-space into cells of equal\nsize in energy. He then shows that this analysis fails to reproduce\nthe desired Maxwell distribution as the most probable state. This\nfailure is remedied by taking equally sized cells in position and\nmomentum variables. The latter choice is apparently\n‘right’, in the sense that leads to the desired\nresult. However, since the choice clearly cannot be relegated to a\nmatter of convention, it leaves the question for a justification.", "\n\n3. A crucial new ingredient in the argument is the distinction between\nmicro- and macrostates. Note in particular that where in the previous\nwork the distribution function \\(f\\) was identified with a probability\n(namely of a molecular state), in the present paper it, or its\ndiscrete analogy \\(Z\\) is a description of the macrostate of the\ngas. Probabilities are not assigned to the particles, but to the\nmacrostate of the gas as a whole. According to Klein (1973, 84), this\nconceptual transition in 1877b marks the birth of statistical\nmechanics. While this view is not completely correct (as we have seen,\nBoltzmann 1868 already applied probability to the total gas), it is\ntrue that (1877b) is the first occasion where Boltzmann identifies\nprobability of a gas state with relative volume in phase space, rather\nthan its relative time of duration.", "\n\nAnother novelty is that Boltzmann has changed his concept of\nequilibrium. Whereas previously the essential characteristic of an\nequilibrium state was always that it is stationary, in Boltzmann's new\nview it is conceived as the macrostate (i.e., a region in phase space)\nthat can be realized in the largest number of ways. As a result, an\nequilibrium state need not be stationary: in the course of time, the\nsystem may fluctuate in and out of equilibrium.", "4. But what about evolutions? Perhaps the most important\nissue is the question what exactly the relation is of the 1877b paper\nto Loschmidt’s objection and Boltzmann’s p reply to it (1877a)? The\nprimary reply can be read as an announcement of two subjects of\nfurther investigation:", "\nFrom the relative numbers of the various distributions of state, one\nmight even be able to calculate their probabilities. This could lead\nto an interesting method of determining thermal equilibrium (W.A. II,\np. 121)", "\nThis is a problem about equilibrium. The second announcement was that\nBoltzmann said: ", "\n “The case is completely analogous for the Second Law” (W.A.. II, p. 121).\n", "Because there are so very many more uniform than non-uniform\ndistributions, it should be extraordinarily improbable that a system\nshould evolve from a uniform distribution of states to a non-uniform\ndistribution of states. This is a problem about evolution. In other\nwords, one would like to see that something like the statistical\nH-theorem actually holds. Boltzmann’s (1877b) is widely read as a\nfollow-up to these announcements. Indeed, Boltzmann repeats the first\nquote above in the introduction of the paper (W.A. II, p. 165),\nindicating that he will address this problem. And so he does,\nextensively. Yet he also states:", "\nOur main goal is not to linger on a discussion of thermal equilibrium,\nbut to investigate the relations of probability with the Second Law of\nthermodynamics (W.A.. II, p. 166).\n", "\nThus, the main goal of 1877b is apparently to address the problem\nconcerning evolutions and to show how they relate to the Second\nLaw. Indeed, this is what one would naturally expect since the\nreversibility objection is, after all, a problem concerned with\nevolutions. Even so, a remarkable fact is that the 1877b paper hardly\never touches its self-professed “main goal” at all. For a sketch of\nhow different commentators on Boltzmann's (1877b) view his attitude on\nthis question I refer to Uffink (2007).", " To sum up this discussion of Boltzmann’s answer to the\nreversibility objection: it seems that on all above readings of his\ntwo 1877 papers, the lacuna between what Boltzmann had achieved and\nwhat he needed to do to answer Loschmidt satisfactorily –\ni.e. to address the issue of the evolution of distributions of state\nand to prove that non-uniform distributions tend, in some statistical\nsense, to uniform ones, or to prove any other reformulation of the\nH-theorem – remains striking." ], "subsection_title": "4.1 Remarks and problems" } ] }, { "main_content": [], "section_title": "5. Some later work", "subsections": [ { "content": [ "\n\nAs we have seen, the 1877 papers introduced some conceptual shifts in\nBoltzmann’ approach. Accordingly, this year is frequently seen as a\nwatershed in Boltzmann's thinking. Concurrent with that view, one would\nexpect his subsequent work to build on his new insights and turn away\nfrom the themes and assumptions of his earlier papers. Actually,\nBoltzmann's subsequent work in gas theory in the next decade and a half\nwas predominantly concerned with technical applications of his 1872\nBoltzmann equation, in particular to gas diffusion and gas friction.\nAnd when he did touch on fundamental aspects of the theory, he returned\nto the issues and themes raised in his 1868–1871 papers, in particular\nthe ergodic hypothesis and the use of ensembles. ", "\n\nThis step was again triggered by a paper of Maxwell, this time one\nthat must have pleased Boltzmann very much, since it was called “On\nBoltzmann's theorem” (Maxwell 1879) and dealt with the theorem\ndiscussed in the last section of his (1868). He pointed out that this\ntheorem does not rely on any collision assumption. But Maxwell also\nmade some pertinent observations along the way. He is critical about\nBoltzmann's ergodic hypothesis, pointing out that “it is manifest that\nthere are cases in which this does not take place” (Maxwell 1879,\n694). Apparently, Maxwell had not noticed that Boltzmann's later\npapers had also expressed similar doubts. He rejected Boltzmann'a\ntime-average view of probability and instead preferred to interpret\nρ as an ensemble density. Further, he states that any claim that\nthe distribution function obtained was the unique stationary\ndistribution “remained to be investigated” (Maxwell 1879,\n722). Maxwell's paper seems to have revived Boltzmann's interest in\nthe ergodic hypothesis, which he had been avoiding for a decade. This\nrenewed confidence is expressed, for example in Boltzmann\n(1887):", "Under all purely mechanical systems, for which equations\nexist that are analogous to the so-called second law of the mechanical\ntheory of heat, those which I and Maxwell have investigated …\nseem to me to be by far the most important. … It is likely that\nthermal bodies in general are of this kind [i.e., they obey the\nergodic hypothesis]", "\n However, he does not return to this conviction in later work. His\nLectures on Gas Theory (1896,1898), for example, does not\neven mention the ergodic hypothesis." ], "subsection_title": "5.1 Return of the ergodic hypothesis" }, { "content": [ "\n\nThe first occasion on which Boltzmann returned to the reversibility\nobjection is in (1887b). This paper delves into a discussion between\nTait and Burbury about the approach to equilibrium for a system\nconsisting of gas particles of two different kinds. The details of the\ndebate need not concern us, except to note that Tait raised the\nreversibility objection to show that taking any evolution approaching\nequilibrium one may construct, by reversal of the velocities, another\nevolution moving away from equilibrium. At this point Boltzmann\nentered the discussion:", "I remark only that the objection of Mr. Tait regarding the\nreversal of the direction of all velocities, after the special state\n[i.e., equilibrium] has been reached, […] has already been\nrefuted in my [(1877a)]. If one starts with an arbitrary non-special\nstate, one will get […] the to special state (of course,\nperhaps after a very long time). When one reverses the directions of\nall velocities in this initial state, then, going backwards, one will\nnot (or perhaps only during some time) reach states that are even\nfurther removed from the special state; instead, in this case too, one\nwill eventually again reach the special state. (WA III,\n304)", "\n This reply to the reversibility objection uses an entirely different\nstrategy from his (1877a). Here, Boltzmann does not exclude the\nreversed motions on account of their vanishing probability, but rather\nargues that, sooner or later, they too will reach the equilibrium\nstate. ", "\n\nNote how much Boltzmann's strategy has shifted: whereas previously the\nidea was that a gas system should approach equilibrium because of the\nH-theorem; Boltzmann's idea is now, apparently, that\nregardless of the behavior of \\(H\\) as a function of time,\nthere are independent reasons for assuming that the system approaches\nequilibrium. Boltzmann's contentions may of course very well be true.\nBut they do not follow from the H-theorem, or by ignoring its\nexceptions, and would have to be proven otherwise." ], "subsection_title": "5.2 Return of the reversibility objection" } ] } ]

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[ { "href": "../ernst-mach/", "text": "Mach, Ernst" }, { "href": "../physics-interrelate/", "text": "physics: intertheory relations in" }, { "href": "../probability-interpret/", "text": "probability, interpretations of" }, { "href": "../statphys-statmech/", "text": "statistical physics: philosophy of statistical mechanics" } ]

[ "\n[Editor’s Note: The following new entry by Roman Frigg and Charlotte Werndl replaces the\n former entry\non this topic by the previous author.]\n", "\nStatistical Mechanics is the third pillar of modern physics, next to\nquantum theory and relativity theory. Its aim is to account for the\nmacroscopic behaviour of physical systems in terms of dynamical laws\ngoverning the microscopic constituents of these systems and\nprobabilistic assumptions. Like other theories in physics, statistical\nmechanics raises a number of foundational and philosophical issues.\nBut philosophical discussions in statistical mechanics face an\nimmediate difficulty because unlike other theories, statistical\nmechanics has not yet found a generally accepted theoretical framework\nor a canonical formalism. In this entry we introduce the different\ntheoretical approaches to statistical mechanics and the philosophical\nquestion that attach to them." ]

[ { "content_title": "1. The Aims of Statistical Mechanics (SM)", "sub_toc": [] }, { "content_title": "2. The Theoretical Landscape of SM", "sub_toc": [] }, { "content_title": "3. Dynamical Systems", "sub_toc": [] }, { "content_title": "4. Boltzmannian Statistical Mechanics (BSM)", "sub_toc": [ "4.1 The Framework of BSM", "4.2 Defining Equilibrium: Boltzmann’s Combinatorial Argument", "4.3 Two Challenges: Reversibility and Recurrence", "4.4 The Ergodic Approach", "4.5 Typicality", "4.6 The Mentaculus and the Past-Hypothesis", "4.7 The Long-Run Residence Time Account", "4.8 Problems and Limitations" ] }, { "content_title": "5. The Boltzmann Equation", "sub_toc": [] }, { "content_title": "6. Gibbsian Statistical Mechanics (GSM)", "sub_toc": [ "6.1 The Framework of GSM", "6.2 Equilibrium: Why Does Phase Averaging Work?", "6.3 GSM and Approach to Equilibrium", "6.4 Coarse-Graining", "6.5 Interventionism", "6.6 The Epistemic Account", "6.7 The Relation between GSM and BSM" ] }, { "content_title": "7. Further Issues", "sub_toc": [ "7.1 The Interpretation of SM Probabilities", "7.2 Maxwell’s Demon and the Entropy Costs of Computation", "7.3 The Gibbs Paradox", "7.4 SM Beyond Physics", "7.5 Reductionism and Inter-Theory Relations" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nStatistical Mechanics (SM) is the third pillar of modern physics, next\nto quantum theory and relativity theory. Its aim is to account for the\nmacroscopic behaviour of physical systems in terms of dynamical laws\ngoverning the microscopic constituents of these systems and the\nprobabilistic assumptions made about them. One aspect of that\nbehaviour is the focal point of SM: equilibrium. Much of SM\ninvestigates questions concerning equilibrium, and philosophical\ndiscussions about SM focus on the foundational assumptions that are\nemployed in answers to these questions.", "\nLet us illustrate the core questions concerning equilibrium with a\nstandard example. Consider a gas confined to the left half of a\ncontainer with a dividing wall (see\n Figure 1a).\n The gas is in equilibrium and there is no manifest change in\nany of its macro properties like pressure, temperature, and volume.\nNow you suddenly remove the dividing wall (see\n Figure 1b),\n and, as result, the gas starts spreading through the entire available\nvolume. The gas is now no longer in equilibrium (see\n Figure 1c).\n The spreading of the gas comes to an end when the entire available\nspace is filled evenly (see\n Figure 1d).\n At this point, the gas has reached a new equilibrium. Since the\nprocess of spreading culminates in a new equilibrium, this process is\nan approach to equilibrium. A key characteristic of the\napproach to equilibrium is that it seems to be irreversible:\nsystems move from non-equilibrium to equilibrium, but not vice\nversa; gases spread to fill the container evenly, but they do not\nspontaneously concentrate in the left half of the container. Since an\nirreversible approach to equilibrium is often associated with\nthermodynamics, this is referred to as thermodynamic\nbehaviour. Characterising the state of equilibrium and accounting\nfor why, and how, a system approaches equilibrium is the core task for\nSM. Sometimes these two problems are assigned to separate theories (or\nseparate parts of a larger theory), which are then referred to as\nequilibrium SM and non-equilibrium SM,\nrespectively.", "\nWhile equilibrium occupies centre stage, SM of course also deals with\nother issues such as phase transitions, the entropy costs of\ncomputation, and the process of mixing substances, and in\nphilosophical contexts SM has also been employed to shed light on the\nnature of the direction of time, the interpretation of probabilities\nin deterministic theories, the state of the universe shortly after the\nbig bang, and the possibility of knowledge about the past. We will\ntouch on all these below, but in keeping with the centrality of\nequilibrium in SM, the bulk of this entry is concerned with an\nanalysis of the conceptual underpinnings of both equilibrium and\nnon-equilibrium SM.", "\nSometimes the aim of SM is said to provide a reduction of the laws of\nthermodynamics: the laws of TD provide a correct description of the\nmacroscopic behaviour of systems and the aim of SM is to account for\nthese laws in microscopic terms. We avoid this way of framing the aims\nof SM. Both the nature of reduction itself, and the question whether\nSM can provide a reduction of TD (in some specifiable sense) are\nmatters of controversy, and we will come back to them in\n Section 7.5." ], "section_title": "1. The Aims of Statistical Mechanics (SM)", "subsections": [] }, { "main_content": [ "\nPhilosophical discussions in SM face an immediate difficulty.\nPhilosophical projects in many areas of physics can take an accepted\ntheory and its formalism as their point of departure. Philosophical\ndiscussions of quantum mechanics, for instance, can begin with the\nHilbert space formulation of the theory and develop their arguments\nwith reference to it. The situation in SM is different. Unlike\ntheories such as quantum mechanics, SM has not yet found a generally\naccepted theoretical framework or a canonical formalism. What we\nencounter in SM is a plurality of different approaches and schools of\nthought, each with its own mathematical apparatus and foundational\nassumptions. For this reason, a review of the philosophy of SM cannot\nsimply start with a statement of the theory’s basic principles\nand then move on to different interpretations of the theory. Our task\nis to first classify different approaches and then discuss how each\nworks; a further question then concerns the relation between them.", "\nClassifying and labelling approaches raises its own issues, and\ndifferent routes are possible. However, SM’s theoretical\nplurality notwithstanding, most of the approaches one finds in it can\nbe brought under one of three broad theoretical umbrellas. These are\nknown as “Boltzmannian SM” (BSM), the “Boltzmann\nEquation” (BE), and “Gibbsian SM” (GSM). The label\n“BSM” is somewhat unfortunate because it might suggest\nthat Boltzmann, only (or primarily) championed this particular\napproach, whereas he has in fact contributed to the development of\nmany different theoretical positions (for an overview of his\ncontributions to SM see the entry on\n Boltzmann’s work in statistical physics;\n for detailed discussions see Cercignani (1998), Darrigol (2018), and\nUffink (2007)). These labels have, however, become customary and so we\nstick with “BSM” despite its historical infelicity. We\nwill now discuss the theoretical backdrop against which these\npositions are formulated, namely dynamical systems, and then introduce\nthe positions in\n §4,\n §5, and\n §6,\n respectively. Extensive synoptic discussion of SM can also be found\nin Frigg (2008b), Shenker (2017a, 2017b), Sklar (1993), and Uffink\n(2007)." ], "section_title": "2. The Theoretical Landscape of SM", "subsections": [] }, { "main_content": [ "\nBefore delving into the discussion of SM, some attention needs to be\npaid to the “M” in SM. The mechanical background theory\nagainst which SM is formulated can be either classical mechanics or\nquantum mechanics, resulting in either classical SM or quantum SM.\nFoundational debates are by and large conducted in the context of\nclassical SM. We follow this practice in the current entry, but we\nbriefly draw attention to problems and issues that occur when moving\nfrom a classical to a quantum framework\n (§4.8).\n From the point of view of classical mechanics, the systems of\ninterest in SM have the structure of dynamical system, a\ntriple \\((X,\\) \\(\\phi,\\) \\(\\mu).\\) \\(X\\) is the state space of the\nsystem (and from a mathematical point of view is a set). In the case\nof a gas with \\(n\\) molecules this space has \\(6n\\) dimensions: three\ncoordinates specifying the position and three coordinates specifying\nthe momentum of each molecule. \\(\\phi\\) is the time evolution\nfunction, which specifies how a system’s state changes over\ntime, and we write \\(\\phi_{t}(x)\\) to denote the state into which\n\\(x\\) evolves after time \\(t\\). If the dynamic of the system is\nspecified by an equation of motion like Newton’s or\nHamilton’s, then \\(\\phi\\) is the solution of that equation. If\nwe let time evolve, \\(\\phi_{t}(x)\\) draws a “line” in\n\\(X\\) that represents the time evolution of a system that was\ninitially in state \\(x\\); this “line” is called a\ntrajectory. Finally, \\(\\mu\\) is a measure on \\(X\\), roughly a\nmeans to say how large a part of \\(X\\) is. This is illustrated\nschematically in\n Figure 2.\n For a more extensive introductory discussion of dynamical systems see\nthe entry on\n the ergodic hierarchy, section on dynamical systems,\n and for mathematical discussions see, for instance, Arnold and Avez\n(1967 [1968]) and Katok and Hasselblatt (1995).", "\nIt is standard to assume that \\(\\phi\\) is deterministic, meaning, that\nevery state \\(x\\) has exactly one past and exactly one future, or, in\ngeometrical terms, that trajectories cannot intersect (for a\ndiscussion of determinism see Earman (1986)). The systems studied in\nBSM are such that the volume of “blobs” in the state space\nis conserved: if we follow the time evolution of a “blob”\nin state space, this blob can change its shape but not its volume.\nFrom a mathematical point of view, this amounts to saying that the\ndynamics is measure-preserving: \\(\\mu(A) = \\mu(\\phi_{t}(A))\\)\nfor all subsets \\(A\\) of \\(X\\) and for all times \\(t\\). Systems in SM\nare often assumed to be governed by Hamilton’s equations of\nmotion, and it is a consequence of Liouville’s theorem that the\ntime evolution of a Hamiltonian system is measure-preserving." ], "section_title": "3. Dynamical Systems", "subsections": [] }, { "main_content": [ "\nIn the current debate, “BSM” denotes a family of positions\nthat take as their starting point the approach that was first\nintroduced by Boltzmann in his 1877 paper and then presented in a\nstreamlined manner by Ehrenfest and Ehrenfest-Afanassjewa in their\n1911 [1959] review. In this section we discuss different contemporary\narticulations of BSM along with the challenges they face." ], "section_title": "4. Boltzmannian Statistical Mechanics (BSM)", "subsections": [ { "content": [ "\nTo articulate the framework of BSM, we distinguish between\nmicro-states and macro-states; for a discussion of the this framework\nsee, for instance, Albert (2000), Frigg (2008b), Goldstein (2001), and\nSklar (1993). The micro-state of a system at time \\(t\\) is\nthe state \\(x \\in X\\) in which the system is at time \\(t\\). This state\nspecifies the exact mechanical state of every micro-constituent of the\nsystem. As we have seen in the previous section, in the case of a gas\n\\(x\\) specifies the positions and momenta of every molecule in the\ngas. Intuitively, the macro-state \\(M\\) of a system at time\n\\(t\\) specifies the macro-constitution of the system at \\(t\\) in\nterms of variables like volume, temperature and other properties\nmeasurable, loosely speaking, at human scales, although, as we will\nsee in\n Section 4.8,\n reference to thermodynamic variables in this context must be taken\nwith a grain of salt. The configurations shown in\n Figure 1\n are macro-states in this sense.", "\nThe core posit of BSM is that macro-states supervene on\nmicro-states, meaning that any change in the system’s\nmacro-state must be accompanied by a change in the\nsystem’s micro-state: every micro-state \\(x\\) has exactly one\ncorresponding macro-state \\(M\\). This rules out that, say, the\npressure of a gas can change while the positions and momenta each of\nits molecules remain the same (see entry on\n supervenience).\n Let \\(M(x)\\) be the unique macro-state that corresponds to microstate\n\\(x\\). The correspondence between micro-states and macro-states\ntypically is not one-to-one and macro-states are multiply realisable.\nIf, for instance, we swap the positions and momenta of two molecules,\nthe gas’ macro-state does not change. It is therefore natural to\ngroup together all micro-states \\(x\\), that correspond to the same\nmacro-state \\(M\\):", "\n\\(X_{M}\\) is the macro-region of \\(M\\).", "\nNow consider a complete set of macro-states (i.e., a set that contains\nevery macro-state that the system can be in), and assume that there\nare exactly \\(m\\) such states. This complete set is \\(\\{\nM_{1},\\ldots,M_{m}\\}\\). It is then the case that the corresponding set\nof macro-regions, \\(\\{ X_{M_{1}},\\ldots,X_{M_{m}}\\}\\), forms a\npartition of \\(X\\), meaning that the elements of the set do not\noverlap and jointly cover \\(X\\). This is illustrated in\n Figure 3.", "\nThe figure also indicates that if the system under study is a gas,\nthen the macro-states correspond to different states of the gas we\nhave seen in\n Section 1.\n Specifically, one of the macro-states corresponds to the initial\nstate of the gas, and another one corresponds to its final equilibrium\nstate.", "\nThis raises two fundamental questions that occupy centre stage in\ndiscussions about BSM. First, what are macro-states and how is the\nequilibrium state identified? That is, where do we get the set\n\\(\\{M_{1},\\ldots,M_{m}\\}\\) from and how do we single out one member of\nthe set as the equilibrium macro-state? Second, as already illustrated\nin\n Figure 3,\n an approach to equilibrium takes place if the time evolution of the\nsystem is such that a micro-state \\(x\\) in a non-equilibrium\nmacro-region evolves such that \\(\\phi_{t}(x)\\) lies in the equilibrium\nmacro-region at a later point in time. Ideally one would want this to\nhappen for all \\(x\\) in any non-equilibrium macro-region, because this\nwould mean that all non-equilibrium states would eventually approach\nequilibrium. The question now is whether this is indeed the case, and,\nif not, what “portion” of states evolves differently.", "\nBefore turning to these questions, let us introduce the Boltzmann\nentropy \\(S_{B}\\), which is a property of a macro-state defined\nthrough the measure of the macro-states’ macro-region:", "\nfor all \\(i = 1,\\ldots, m\\), where \\(k\\) is the so-called Boltzmann\nconstant. Since the logarithm is a monotonic function, the larger the\nmeasure \\(\\mu\\) of a macro-region, the larger the entropy of the\ncorresponding macro-state.", "\nThis framework is the backbone of positions that self-identify as\n“Boltzmannian”. Differences appear in how the elements of\nthis framework are articulated and in how difficulties are\nresolved." ], "subsection_title": "4.1 The Framework of BSM" }, { "content": [ "\nAn influential way of defining equilibrium goes back to Boltzmann\n(1877); for contemporary discussion of the argument see, for instance,\nAlbert (2000), Frigg (2008b), and Uffink (2007). The approach first\nfocusses on the state space of one particle of the system, which in\nthe case of a gas has six dimensions (three for the particle’s\npositions in each spatial dimension and a further three for the\ncorresponding momenta). We then introduce a grid on this\nspace—an operation known as coarse-graining—and\nsay that two particles have the same coarse-grained\nmicro-state if they are in the same grid cell. The state of the\nentire gas is then represented by an arrangement, a\nspecification of \\(n\\) points on this space (one for each particle in\nthe gas). But for the gas’ macro-properties it is irrelevant\nwhich particle is in which state, meaning that the gas’\nmacro-state must be unaffected by a permutation of the particles. All\nthat the macro-state depends on is the distribution of\nparticles, a specification of how many particles are in each grid\ncell.", "\nThe core idea of the approach is to determine how many arrangements\nare compatible with a given distribution, and to define the\nequilibrium state as the one for which this number is maximal. Making\nthe strong (and unrealistic) assumption that the particles in the gas\nare non-interacting (which also means that they never collide) and\nthat the energy of the gas is preserved, Boltzmann offered a solution\nto this problem and showed that the distribution for which the number\nof arrangements is maximal is the so-called discrete Maxwell-Boltzmann\ndistribution:", "\nwhere \\(n_{i}\\) is the number of particles in cell \\(i\\) if the\ncoarse-graining, \\(E_{i}\\) is the energy of a particle in that cell,\nand \\(\\alpha\\) and \\(\\beta\\) are constants that depend on the number\nof particles and the temperature of the system (Tolman 1938 [1979]:\nCh. 4). From a mathematical point of view, deriving this distribution\nis a problem in combinatorics, which is why the approach is now known\nas the combinatorial argument.", "\nAs Paul and Tatiana Ehrenfest pointed out in their 1911 [1959] review,\nthe mathematical structure of the argument also shows that if we now\nreturn to the state space \\(X\\) of the entire system (which, recall,\nhas \\(6n\\) dimensions), the macro-region of the equilibrium state thus\ndefined is the largest of all macro-regions. Hence, the equilibrium\nmacro-state is the macro-state with the largest macro-region. In\ncontemporary discussions this is customarily glossed as the\nequilibrium macro-state not only being larger than any other\nmacro-state, but as being enormously larger and in fact taking up most\nof \\(X\\) (see, for instance, Goldstein 2001). However, as Lavis (2008)\npoints out, the formalism only shows that the equilibrium macro-region\nis larger than any other macro-region and it is not a general truism\nthat it takes up most of the state space; there are in fact systems in\nwhich the non-equilibrium macro-regions taken together are larger than\nthe equilibrium macro-region.", "\nSince, as we have seen, the Boltzmann entropy is a monotonic function\nof the measure of a macro-region, this implies that the equilibrium\nmicrostate is also the macro-state with the largest Boltzmann entropy,\nand the approach to equilibrium is a process that can be characterised\nby an increase of entropy.", "\nTwo questions arise: first, is this a tenable general definition of\nequilibrium, and, second, how does it explain the approach to\nequilibrium? As regards the first question, Uffink (2007) highlights\nthat the combinatorial argument assumes particles to be\nnon-interacting. The result can therefore be seen as a good\napproximation for dilute gases, but it fails to describe (even\napproximately) interacting systems like liquids and solids. But\nimportant applications of SM are to systems that are not dilute gases\nand so this is a significant limitation. Furthermore, from a\nconceptual point of view, the problem is that a definition of\nequilibrium in terms of the number of arrangements compatible with a\ndistribution makes no contact with the thermodynamic notion of\nequilibrium, where equilibrium is defined as the state to which an\nisolated system converges when left to itself (Werndl & Frigg\n2015b). Finally, this definition of equilibrium is completely\ndisconnected form the system’s dynamics, which has the odd\nconsequence that it would still provide an equilibrium state even if\nthe system’s time evolution was the identity function (and hence\nnothing ever changed and no approach to equilibrium took place). And\neven if one were to set thermodynamics aside, there is nothing truly\nmacro about the definition, which in fact directly constructs a\nmacro-region without ever specifying a macro-state.", "\nA further problem (still as regards the first question) is the\njustification of coarse-graining. The combinatorial argument does not\nget off the ground without coarse-grained micro-states, and so the\nquestion is what legitimises the use of such states. The problem is\naccentuated by the facts that the procedure only works for particular\nkind of coarse-graining (namely if the grid is parallel to the\nposition and momentum axes) and that the grid cannot be eliminated by\ntaking a limit which lets the grid size tend toward zero. A number of\njustificatory strategies have been proposed but none is entirely\nsatisfactory. A similar problem arises with coarse-gaining in Gibbsian\nSM, and we refer the reader to\n Section 6.5\n for a discussion.", "\nAs regards the second question, the combinatorial argument itself is\nsilent about why and how systems approach equilibrium and additional\ningredients must be added to the account to provide such an\nexplanation. Before discussing some of these ingredients (which is the\ntopic of much of the remainder of this section), let us discuss two\nchallenges that every explanation of the approach to equilibrium must\naddress: the reversibility problem and the recurrence problem." ], "subsection_title": "4.2 Defining Equilibrium: Boltzmann’s Combinatorial Argument" }, { "content": [ "\nIn\n Section 2\n we have seen that at bottom the physical systems of BSM have the\nstructure of a dynamical system \\((X,\\) \\(\\phi,\\) \\(\\mu)\\) where\n\\(\\phi\\) is deterministic and measure preserving. Systems of this kind\nhave two features that pose a challenge for an understanding of the\napproach to equilibrium.", "\nThe first feature is what is known as time-reversal\ninvariance. Intuitively you can think of the time-reversal of a\nprocess as what you get when you play a movie of a process backwards.\nThe dynamics of system is time-reversal invariant if every process\nthat is allowed to happen in one direction of time is also allowed to\nhappen the reverse direction of time. That is, for every process that\nis allowed by the theory it is that case that if you capture the\nprocess in a movie, then the process that you see when you play the\nmovie backwards is also allowed by the theory; for detailed and more\ntechnical discussions see, for instance, Earman (2002), Malament\n(2004), Roberts (2022), and Uffink (2001).", "\nHamiltonian systems are time-reversal invariant and so the most common\nsystems studied in SM have this property. A look at\n Figure 3\n makes the consequences of this for an understanding of the approach\nto equilibrium clear. We consider a system whose micro-state initially\nlies in a non-equilibrium macro-region and then evolves into a\nmicro-state that lies in the equilibrium macro-region. Obviously, this\nprocess ought to be allowed by the theory. But this means that the\nreverse process—a process that starts in the equilibrium\nmacro-region and moves back into the initial non-equilibrium macro\nregion—must be allowed too. In\n Section 1\n we have seen that the approach to equilibrium is expected to be\nirreversible, prohibiting systems like gases to spontaneously\nleave equilibrium and evolve into a non-equilibrium state. But we are\nnow faced with a contradiction: if the dynamics of the system is\ntime-reversal invariant, then the approach to equilibrium cannot be\nirreversible because the evolution from the equilibrium state to a\nnon-equilibrium state is allowed. This observation is known as\nLoschmidt's reversibility objection because it was first put\nforward by Loschmidt (1876); for a historical discussion of this\nobjection, see Darrigol (2021).", "\nThe second feature that poses a challenge is Poincaré\nrecurrence. The systems of interest in BSM are both\nmeasure-preserving and spatially bounded: they are gases in a box,\nliquids in a container and crystals on a laboratory table. This means\nthat the system’s micro-state can only access a finite region in\n\\(X\\). Poincaré showed that dynamical systems of this kind\nmust, at some point, return arbitrarily close to their initial state,\nand, indeed do so infinitely many times. The time that it takes the\nsystem to return close to its initial condition is called the\nrecurrence time. Like time-reversal invariance,\nPoincaré recurrence contradicts the supposed\nirreversibility of the approach to equilibrium: it implies that\nsystems will return to non-equilibrium states at some point. One just\nhas to wait for long enough. This is known as Zermelo’s\nrecurrence objection because it was first put forward by Zermelo\n(1896); for a historical discussion see Uffink (2007).", "\nAny explanation of the approach to equilibrium has to address these\ntwo objections." ], "subsection_title": "4.3 Two Challenges: Reversibility and Recurrence" }, { "content": [ "\nA classical explanation of the approach to equilibrium is given within\nergodic theory. A system is ergodic iff, in the long run (i.e., in the\nlimit of time \\(t \\rightarrow \\infty\\)), for almost all initial\nconditions it is the case that the fraction of time that the\nsystem’s trajectory spends in a region \\(R\\) of \\(X\\) is equal\nto the fraction that \\(R\\) occupies in \\(X\\) (Arnold & Avez 1967\n[1968]). For instance, if \\(\\mu(R)/\\mu(X) = 1/3,\\) then an ergodic\nsystem will, in the long run, spend 1/3 of its time in \\(R\\) (for a\nmore extensive discussion of ergodicity see entry on\n the ergodic hierarchy).", "\nIn\n Section 4.2\n we have seen that if the equilibrium macro-region is constructed with\nthe combinatorial argument, then it occupies the largest portion of\n\\(X\\). If we now also assume that the system is ergodic, it follows\nimmediately that the system spends the largest portion of time in\nequilibrium. This is then often given a probabilistic gloss by\nassociating the time that a system spends in a certain part of \\(X\\)\nwith the probability of finding the system in that part of \\(X\\), and\nso we get that we are overwhelmingly likely to find that system in\nequilibrium; for a discussion of this approach to probabilities see\nFrigg (2010) and references therein.", "\nThe ergodic approach faces a number of problems. First, being ergodic\nis a stringent condition that many systems fail to meet. This is a\nproblem because among those systems are many to which SM is\nsuccessfully applied. For instance, in a solid the molecules oscillate\naround fixed positions in a lattice, and as a result the phase point\nof the system can only access a small part of the energy hypersurface\n(Uffink 2007: 1017). The Kac Ring model and a system of anharmonic\noscillators behave thermodynamically but fail to be ergodic (Bricmont\n2001). And even the ideal gas—supposedly the paradigm system of\nSM—is not ergodic (Uffink 1996b: 381). But if core-systems of SM\nare not ergodic, then ergodicity cannot provide an explanation for the\napproach to equilibrium, at least not one that is applicable across\nthe board (Earman & Rédei 1996; van Lith 2001). Attempts\nhave been made to improve the situation through the notion of\nepsilon-ergodicity, where a system is epsilon-ergodic if it is ergodic\nonly on subset \\(Y \\subset X\\) where \\(\\mu(Y) \\geq 1 - \\varepsilon\\),\nfor small positive real number \\(\\varepsilon\\) (Vranas 1998). While\nthis approach deals successfully with some systems (Frigg & Werndl\n2011), it is still not universally applicable and hence remains silent\nabout large classes of SM systems.", "\nThe ergodic approach accommodates Loschmidt’s and\nZermelo’s objections by rejecting the requirement of strict\nirreversibility. The approach insists that systems, can, and actually\ndo, move away from equilibrium. What SM should explain is not strict\nirreversibility, but the fact that systems spend most of the time in\nequilibrium. The ergodic approach does this by construction, and only\nallows for brief and infrequent episodes of non-thermodynamic\nbehaviour (when the system moves out of equilibrium). This response is\nin line with Callender (2001) who argues that we should not take\nthermodynamics “too seriously” and see its strictly\nirreversible approach to equilibrium as an idealisation that is not\nempirically accurate because physical systems turn out to exhibit\nequilibrium fluctuations.", "\nA more technical worry is what is known as the measure zero\nproblem. As we have seen, ergodicity says that “almost all\ninitial conditions” are such that the fraction of time spent in\n\\(R\\) is equal to the fraction \\(R\\) occupies in \\(X\\). In technical\nterms this means that set of initial conditions for which this is not\nthe case has measure zero (with respect to \\(\\mu\\)). Intuitively this\nwould seem to suggest that these conditions are negligible. However,\nas Sklar (1993: 182–88) points out, sets of measure zero can be\nrather large (remember that set of rational numbers has measure zero\nin the real numbers), and the problem is to justify why a set of\nmeasure zero really is negligible." ], "subsection_title": "4.4 The Ergodic Approach" }, { "content": [ "\nAn alternative account explains the approach to equilibrium in terms\nof typicality. Intuitively something is typical if it happens\nin the “vast majority” of cases: typical lottery tickets\nare blanks, and in a typical series of a thousand coin tosses the\nratio of the number of heads and the number of tails is approximately\none. The leading idea of a typicality-based account of SM is to show\nthat thermodynamic behaviour is typical and is therefore to be\nexpected. The typicality account comes in different version, which\ndisagree on how exactly typicality reasoning is put to use; different\nversions have been formulated, among others, by Goldstein (2001),\nGoldstein and Lebowitz (2004), Goldstein, Lebowitz, Tumulka, and\nZanghì (2006), Lebowitz (1993a, 1993b), and Volchan (2007). In\nits paradigmatic version, the account builds on the observation\n(discussed in\n Section 4.2)\n that the equilibrium macro-region is so large that \\(X\\) consists\nalmost entirely of equilibrium micro-states, which means that\nequilibrium micro-states are typical in \\(X\\). The account submits\nthat, for this reason, a system that starts its time-evolution in a\nnon-equilibrium state can simply not avoid evolving into a typical\nstate—i.e., an equilibrium state—and staying there for\nvery long time, which explains the approach to equilibrium.", "\nFrigg (2009, 2011) and Uffink (2007) argue that from the point of view\nof dynamical systems theory this is unjustified because there is no\nreason to assume that micro-states in an atypical set have to evolve\ninto a typical set without there being any further dynamical\nassumptions in place. To get around this problem Frigg and Werndl\n(2012) formulate a version of the account that takes the dynamics of\nthe system into account. Lazarovici and Reichert (2015) disagree that\nsuch additions are necessary. For further discussions of the use of\ntypicality in SM, see Badino (2020), Bricmont (2022), Chibbaro,\nRondoni and Vulpiani (2022), Crane and Wilhelm (2020), Goldstein\n(2012), Hemmo and Shenker (2015), Luczak (2016), Maudlin (2020),\nReichert (forthcoming), and Wilhelm (2022). As far as\nLoschmidt’s and Zermelo’s objections are concerned, the\ntypicality approach has to make the same move as the ergodic approach\nand reject strict irreversibility as a requirement." ], "subsection_title": "4.5 Typicality" }, { "content": [ "\nAn altogether different approach has been formulated by Albert (2000).\nThis approach focusses on the internal structure of macro-regions and\naims to explain the approach to equilibrium by showing that the\nprobability for system in a non-equilibrium macro-state to evolve\ntoward a macro-state of higher Boltzmann entropy is high. The basis\nfor this discussion is the so-called statistical postulate.\nConsider a particular macro-state \\(M\\) with macro-region \\(X_{M}\\)\nand assume that the system is in macro-state \\(M\\). The postulate then\nsays that for any subset \\(A\\) of \\(X_{M}\\) the probability of finding\nthe system’s micro-state in \\(A\\) is \\({\\mu(A)/\\mu(X}_{M})\\). We\ncan now separate the micro-states in \\(X_{M}\\) into those that evolve\ninto a higher entropy macro-state and those that move toward\nmacro-states of lower entropy. Let’s call these sets\n\\(X_{M}^{+}\\) and \\(X_{M}^{-}\\). The statistical postulate then says\nthat the probability of a system in \\(M\\) evolving toward a higher\nentropy macro-state is \\({\\mu(X}_{M}^{+})/\\mu(X_{M})\\).", "\nFor it to be likely that system approaches equilibrium this\nprobability would have to be high. It now turns out that for purely\nmathematical reasons, if the system is highly likely to evolve toward\na macro-state of higher entropy, then it is also highly likely to have\nevolved into the current macro-state \\(M\\) from a macro-state of high\nentropy. In other words, if the entropy is highly likely to increase\nin the future, it is also highly likely to have decreased in the past.\nAlbert suggests solving this problem by regarding the entire universe\nas the system being studied and then conditionalizing on the\nPast-Hypothesis, which is the assumption that", "\n\n\nthat the world first came into being in whatever particular\nlow-entropy highly condensed big-bang sort of macrocondition it is\nthat the normal inferential procedures of cosmology will eventually\npresent to us. (2000: 96)\n", "\nLet \\(M_{p}\\) be the past state, the state in which the world\nfirst came into being according to the Past-Hypothesis, and let\n\\(I_{t} = \\phi_{t}(X_{M_{p}}) \\cap X_{M}\\) be the intersection of the\ntime-evolved macro-region of the past state and the current\nmacro-state. The probability of high entropy future is then\n\\({\\mu(I_{t} \\cap X}_{M}^{+})/\\mu(I_{t})\\). If we further assume\n“abnormal” states with low entropy futures are scattered\nall over \\(X_{M}\\), then a high entropy future can be highly likely\nwithout it a high entropy past also being highly likely.", "\nThis approach to SM is based on three core elements: the deterministic\ntime evolution of the system given by \\(\\phi_{t}\\), the\nPast-Hypothesis, and the statistical postulate. Together they result\nin the assignment of a probability to propositions about the history\nof a system. Albert (2015) calls this assignment the\nMentaculus. Albert regards the Mentaculus not only as an\naccount of thermodynamic phenomena, but as the backbone of a complete\nscientific theory of the universe because the Mentaculus assigns\nprobabilities to propositions in all sciences. This raises all kind of\nissues about the nature of laws, reduction, and the status of the\nspecial sciences, which are discussed, for instance, in Frisch (2011),\nHemmo and Shenker (2021) and Myrvold and others (2016).", "\nLike the ergodic approach, the Mentaculus must accommodate\nLoschmidt’s and Zermelo’s objections by rejecting the\nrequirement of strict irreversibility. Higher to lower entropy\ntransitions are still allowed, but they are rendered unlikely, and\nrecurrence can be tamed by noting that the recurrence time for a\ntypical SM system is larger than age of the universe, which means that\nwe won’t observe recurrence (Bricmont 1995; Callender 1999).\nYet, this amounts to admitting that entropy increase is not universal\nand the formalism is compatible with there being periods of decreasing\nentropy at some later point in the history of the universe.", "\nA crucial ingredient of the Mentaculus is the Past-Hypothesis. The\nidea of grounding thermodynamic behaviour in a cosmic low-entropy past\ncan be traced back to Boltzmann (Uffink 2007: 990) and has since been\nadvocated by prominent physicists like Feynman (1965: Ch. 5) and R.\nPenrose (2004: Ch. 27). This raises two questions: first, can the\nPast-Hypothesis be given a precise formulation that serves the purpose\nof SM, and, second, what status does the Past-Hypothesis have and does\nthe fact that the universe started in this particular state require an\nexplanation?", "\nAs regards the first question, Earman has cast the damning verdict\nthat the Past-Hypothesis is “not even false” (2006)\nbecause in cosmologies described in general relativity there is no\nwell-defined sense in which the Boltzmann entropy has a low value. A\nfurther problem is that in the Mentaculus the Boltzmann entropy is a\nglobal quantity characterising the entire universe. But, as Winsberg\npoints out, the fact that this quantity is low does not imply that the\nentropy of a particular small subsystem of interest is also low, and,\nworse just because the overall entropy of the universe increases it\nneed not be the case that the entropy in a small subsystem also\nincreases (2004a). The source of these difficulties is that the\nMentaculus takes the entire universe to be the relevant system and so\none might try get around them by reverting to where we started:\nlaboratory systems like gases in boxes. One can then take the the\npast state simply to be the state in which such a gas is prepared at\nthe beginning of a process (say in the left half of the container).\nThis leads to the so-called branch systems approach, because a system\nis seen as “branching off” from the rest of the universe\nwhen it is isolated from its environment and prepared in\nnon-equilibrium state (Davies 1974; Sklar 1993: 318–32). Albert\n(2000) dismisses this option for a number of reasons, chief among them\nthat it is not clear why one should regard the statistical postulate\nas valid for such a state (see Winsberg (2004b) for a discussion).", "\nAs regards the second question, Chen (forthcoming), Goldstein (2001),\nand Loewer (2001) argue that Past-Hypothesis has the status of a\nfundamental law of nature. Albert seems to regard it as something like\na Kantian regulative principle in that its truth must be assumed in\norder to make knowledge of the past possible at all. By contrast,\nCallender, Price, and Wald regard that the Past-Hypothesis a\ncontingent matter of fact, but they disagree on whether this fact\nstands in need of an explanation. Price (1996, 2004) argues that it\ndoes because the crucial question in SM is not why entropy increase,\nbut rather why it ever got to be low in the first place. Callender\n(1998, 2004a, 2004b) disagrees: the Past-Hypothesis simply specifies\ninitial conditions of a process, and initial conditions are not the\nkind of thing that needs to be explained (see also Sklar (1993:\n309–18)). Parker (2005) argues that conditionalising on the\ninitial state of the universe does not have the explanatory power to\nexplain irreversible behaviour. Baras and Shenker (2020) and Farr\n(2022) analysed the notion of explanation that is involved in this\ndebate and argue that different questions are in play that require\ndifferent answers." ], "subsection_title": "4.6 The Mentaculus and the Past-Hypothesis" }, { "content": [ "\nThe long-run residence time account offers a different perspective\nboth on the definition of equilibrium and the approach to it (Werndl\n& Frigg 2015a, 2015b). Rather than first defining equilibrium\nthrough combinatorial considerations (as in\n §4.2)\n and then asking why systems approach equilibrium thus\ndefined (as do the accounts discussed in\n §§4.4–4.6),\n the long-run residence time account defines equilibrium\nthrough thermodynamic behaviour. The account begins by characterising\nthe macro-states in the set \\(\\{ M_{1},\\ldots,M_{n}\\}\\) in purely\nmacroscopic terms, i.e., through thermodynamic variables like pressure\nand temperature, and then identifies the state in which a system\nresides most of the time as the equilibrium state: among the\n\\(M_{i}\\), the equilibrium macro-state is by definition the state in\nwhich a system spends most of its time in the long run (which gives\nthe account its name).", "\nThis definition requires no assumption about the size of the\nequilibrium macro-region, but one can then show that it is a property\nof the equilibrium macro-state that its macro-region is large. This\nresult is fully general in that it does not depend on assumptions like\nparticles being non-interacting (which makes it applicable to all\nsystems including liquids and solids), and it does not depend on\ncombinatorial considerations at the micro-level. The approach to\nequilibrium is built into the definition in the sense that if there is\nno macro-state in which the system spends most of its time, then the\nsystem simply has no equilibrium. This raises the question of the\ncircumstances under which an equilibrium exists. The account answers\nthis question by providing a general existence theorem which furnishes\ncriteria for the existence of an equilibrium state (Werndl & Frigg\nforthcoming-b). Intuitively, the existence theorem says that\nthere is an equilibrium just in case the system’s state space is\nsplit up into invariant regions on which the motion is ergodic and the\nequilibrium macro-state is largest in size relative to the other\nmacro-states on each such region.", "\nLike the account previously discussed, the long-run residence time\naccount accommodates Loschmidt’s and Zermelo’s objections\nby rejecting the requirement of strict irreversibility: it insists\nthat being in equilibrium most of the time is as much as one can\nreasonably ask for because actual physical systems show equilibrium\nfluctuations and equilibrium is not the dead and immovable state that\nthermodynamics says it is." ], "subsection_title": "4.7 The Long-Run Residence Time Account" }, { "content": [ "\nBSM enjoys great popularity in foundational debates due to its clear\nand intuitive theoretical structure. Nevertheless, BSM faces a number\nof problems and limitations.", "\nThe first problem is that BSM only deals with closed systems that\nevolve under their own internal dynamics. As we will see in\n Section 6,\n GSM successfully deals with systems that can exchange energy and even\nparticles with their environments, and systems of this kind play an\nimportant role in SM. Those who think that SM only deals with the\nentire universe can set this problem aside because the universe\n(arguably) is a closed system. However, those who think that the\nobjects of study in SM are laboratory-size systems like gases and\ncrystals will have to address the issues of how BSM can accommodate\ninteractions between systems and their environments, which is a\nlargely ignored problem.", "\nA second problem is that even though macro-states are ubiquitous in\ndiscussions about BSM, little attention is paid to a precise\narticulation of what these states are. There is loose talk about how a\nsystem looks from macroscopic perspective, or there is a vague appeal\nto thermodynamic variables. However, by the lights of thermodynamics,\nvariables like pressure and temperature are defined only in\nequilibrium and it remains unclear how non-equilibrium states, and\nwith them the approach to equilibrium, should be characterised in\nterms of thermodynamic variables. Frigg and Werndl (forthcoming-a)\nsuggest solving this problem by defining macro-states in terms of\nlocal field-variables, but the issue needs further attention.", "\nA third problem is that current formulations of BSM are closely tied\nto deterministic classical systems\n (§3).\n Some versions of BSM can be formulated based on classical stochastic\nsystem (Werndl & Frigg 2017). But the crucial question is whether,\nand if so how, a quantum version of BSM can be formulated (for a\ndiscussion see the entry on\n quantum mechanics).\n Dizadji-Bahmani (2011) discusses how a result due to Linden and\nothers (2009) can be used to construct an argument for the conclusion\nthat an arbitrary small subsystem of a large quantum system typically\ntends toward equilibrium. Chen (forthcoming) formulates a quantum\nversion of the Mentaculus, which he calls the Wentaculus (see\nalso his 2022). Goldstein, Lebowitz, Tumulka, and Zanghì (2020)\ndescribe a quantum analogue of the Boltzmann entropy and argue that\nthe Boltzmannian conception of equilibrium is vindicated also in\nquantum mechanics by recent work on thermalization of closed quantum\nsystems. These early steps have not yet resulted in comprehensive and\nwidely accepted formulation of quantum version of BSM, the formulation\nof a such a version of remains an understudied topic. Albert (2000:\nCh. 7) suggested that the spontaneous collapses of the so-called GRW\ntheory (for introduction see the entry on\n collapse theories),\n a particular approach quantum mechanics, could be responsible for the\nemergence of thermodynamic irreversibility. Te Vrugt, Tóth and\nWittkowski (2021) put this proposal to test in computer simulations\nand found that for initial conditions leading to anti-thermodynamic\nbehaviour GRW collapses do not lead to thermodynamic behaviour and\nthat therefore the GRW does not induce irreversible behaviour.", "\nFinally, there is no way around recognising that BSM is mostly used in\nfoundational debates, but it is GSM that is the practitioner’s\nworkhorse. When physicists have to carry out calculations and solve\nproblems, they usually turn to GSM which offers user-friendly\nstrategies that are absent in BSM. So either BSM has to be extended\nwith practical prescriptions, or it has to be connected to GSM so that\nit can benefit from its computational methods (for a discussion of the\nlatter option see\n §6.7)." ], "subsection_title": "4.8 Problems and Limitations" } ] }, { "main_content": [ "\nA different approach to the problem is taken by Boltzmann in his\nfamous (1872 [1966 Brush translation]) paper, which contains two\nresults that are now known as the Boltzmann Equation and the\nH-theorem. As before, consider a gas, now described through a\ndistribution function \\(f_{t}(\\vec{v})\\), which specifies what\nfraction of molecules in the gas has a certain velocity \\(\\vec{v}\\) at\ntime \\(t\\). This distribution can change over time, and\nBoltzmann’s aim was to show that as time passes this\ndistribution function changes so that it approximates the\nMaxwell-Boltzmann distribution, which, as we have seen in\n Section 4.2,\n is the equilibrium distribution for a gas.", "\nTo this end, Boltzmann derived an equation describing the time\nevolution of \\(f_{t}(\\vec{v})\\). The derivation assumes that the gas\nconsists of particles of diameter \\(D\\) that interact like hard\nspheres (i.e., they interact only when they collide); that\nall collisions are elastic (i.e., no energy is lost); that the number\nof particles is so large that their distribution, which in reality is\ndiscrete, can be well approximated by a continuous and differentiable\nfunction \\(f_{t}(\\vec{v})\\); and that the density of the gas is so low\nthat only two-particle collisions play a role in the evolution of\n\\(f_{t}(\\vec{v})\\).", "\nThe crucial assumption in the argument is the so-called\n“Stosszahlansatz”, which specifies how many\ncollisions of a certain type take place in certain interval of time\n(the German “Stosszahlansatz” literally means\nsomething like “collision number assumption”). Assume the\ngas has \\(N\\) molecules per unit volume and the molecules are equally\ndistributed in space. The type of collisions we are focussing on is\nthe one between a particle with velocity \\(\\vec{v}_{1}\\) and one with\nvelocity \\(\\vec{v}_{2}\\), and we want to know the number\n\\(N(\\vec{v}_{1}, \\vec{v}_{2})\\) of such collisions during a small\ninterval of time \\(\\Delta t\\). To solve this problem, we begin by\nfocussing on one molecule with \\(\\vec{v}_{1}\\). The relative velocity\nof this molecule and a molecule moving with \\(\\vec{v}_{2}\\) is\n\\(\\vec{v}_{2} - \\vec{v}_{1}\\) and the absolute value of that relative\nvelocity is \\(\\left\\| \\vec{v}_{2} - \\vec{v}_{1} \\right\\|\\). Molecules\nof diameter D only collide if their centres come closer than \\(D\\). So\nlet us look at a cylinder with radius \\(D\\) and height \\(\\left\\|\n\\vec{v}_{2} - \\vec{v}_{1} \\right\\|\\Delta t\\), which is the volume in\nspace in which molecules with velocity \\(\\vec{v}_{2}\\) would collide\nwith our molecule during \\(\\Delta t\\). The volume of this cylinder\nis", "\nIf we now make the strong assumption that the initial velocities of\ncolliding particles are independent, it follows that number of\nmolecules with velocity \\(\\vec{v}_{2}\\) in a unit volume of the gas at\ntime \\(t\\) is \\(Nf_{t}(\\vec{v}_{2})\\), and hence the number of such\nmolecules in our cylinder is", "\nThis is the number of collisions that the molecule we are focussing on\ncan be expected to undergo during \\(\\Delta t\\). But there is nothing\nspecial about this molecule, and we are interested in the number of\nall collisions between particles with velocities\n\\(\\vec{v}_{1}\\) and \\(\\vec{v}_{2}\\). To get to that number, note that\nthe number of molecules with velocity \\(\\vec{v}_{1}\\) in a unit volume\nof gas at time \\(t\\) is \\(Nf_{t}(\\vec{v}_{1})\\). That is, there are\n\\(Nf_{t}(\\vec{v}_{1})\\) molecules like the one we were focussing on.\nIt is then clear that the total number of collisions can be expected\nto be the product of the number of collisions for each molecule with\n\\(\\vec{v}_{1}\\) times the number of molecules with\n\\(\\vec{v}_{1}\\):", "\nThis is the Stosszahlansatz. For ease of presentation, we\nhave made the mathematical simplification of treating\n\\(f_{t}(\\vec{v})\\) as a fraction rather than as density in our\ndiscussion of the Stosszahlansatz; for a statement of the\nStosszahlansatz for densities see, for instance, Uffink\n(2007). Based on the Stosszahlansatz, Boltzmann derived what\nis now known as the Boltzmann Equation:", "\nwhere \\(\\vec{v}_{1}^{*}\\) and \\(\\vec{v}_{2}^{*}\\) are the velocities\nof the particles after the collision. The integration is over\nthe space of the box that contains the gas. This is a so-called\nintegro-differential equation. The details of this equation need not\nconcern us (and the mathematics of such equations is rather tricky).\nWhat matters is the overall structure, which says that the way the\ndensity \\(f_{t}(\\vec{v})\\) changes over time depends on the difference\nof the products of the densities of the incoming an of the outgoing\nparticles. Boltzmann then introduced the quantity \\(H\\),", "\nand proved that \\(H\\) decreases monotonically in time,", "\nand that \\(H\\) is stationary (i.e., \\(dH\\lbrack f_{t}(\\vec{v})\n\\rbrack/dt = 0\\)) iff \\(f_{t}(\\vec{v})\\) is the Maxwell-Boltzmann\ndistribution. These two results are the H-Theorem.", "\nThe definition of \\(H\\) bears formal similarities both to the\nexpression of the Boltzmann entropy in the combinatorial argument\n (§4.3)\n and, as we will see, to the Gibbs entropy\n (§6.3);\n in fact \\(H\\) looks like a negative entropy. For this reason the\nH-theorem is often paraphrased as showing that entropy\nincreases monotonically until the system reaches the equilibrium\ndistribution, which would provide a justification of thermodynamic\nbehaviour based on purely mechanical assumptions. Indeed, in his 1872\npaper, Boltzmann himself regarded it as a rigorous general proof of\nthe Second Law of thermodynamics (Uffink 2007: 965; Klein 1973:\n73).", "\nThe crucial conceptual questions at this point are: what exactly did\nBoltzmann prove with the H-theorem? Under which conditions is\nthe Boltzmann Equation valid? And what role do the assumptions, in\nparticular, the Stosszahlansatz play in deriving it? The\ndiscussion of these question started four years after the paper was\npublished, when Loschmidt put forward his reversibility objection\n (§4.3).\n This objection implies that \\(H\\) must be able to increase as well as\ndecrease. Boltzmann’s own response to Loschmidt’s\nchallenge and the question of the scope of the H-theorem is a\nmatter of much debate; for discussions see, for instance, Brown,\nMyrvold, and Uffink (2009), Cercignani (1998), Brush (1976), and\nUffink (2007). We cannot pursue this matter here, but the gist of\nBoltzmann’s reply would seem to have been that he admitted that\nthere exists initial states for which \\(H\\) decreases, but that these\nrarely, if ever, occur in nature. This leads to what is now known as a\nstatistical reading of the H-theorem: the H-theorem\nshows entropy increase to be likely rather universal.", "\nA century later, Lanford published a string of papers (1973, 1975,\n1976, 1981) culminating in what is now known as Lanford’s\ntheorem, which provides rigorous results concerning the validity of\nthe Boltzmann Equation. Lanford’s starting point is the question\nwhether, and if so in what sense, the Boltzmann equation is consistent\nwith the underlying Hamiltonian dynamics. To this end, note that every\npoint \\(x\\) in the state space \\(X\\) of a gas has a distribution\n\\(f_{x}(\\vec{r}, \\vec{v})\\) associated with it, where \\(\\vec{r}\\) and\n\\(\\vec{v}\\) are, respectively, the location and velocity of one\nparticle (recall from\n §3\n that \\(X\\) contains the position and momenta of all molecules). For a\nfinite number of particles \\(f_{x}(\\vec{r}, \\vec{v})\\) is not\ncontinuous, let alone differentiable. So as a first step, Lanford\ndeveloped a way to obtain a differentiable distribution function\ndistribution \\(f^{(x)}(\\vec{r}, \\vec{v})\\), which involves taking the\nso-called Boltzmann-Grad limit. He then evolved this distribution\nforward in time both under the fundamental Hamiltonian dynamics, which\nyields \\(f_{\\text{Ht}}^{(x)}(\\vec{r}, \\vec{v})\\), and under the\nBoltzmann Equation, which yields \\(f_{\\text{Bt}}^{(x)}(\\vec{r},\n\\vec{v})\\). Lanford’s theorem compares these two distributions\nand essentially says that for most points \\(x\\) in \\(X\\),\n\\(f_{\\text{Ht}}^{(x)}(\\vec{r}, \\vec{v})\\) and\n\\(f_{\\text{Bt}}^{(x)}(\\vec{r}, \\vec{v})\\) are close to each other for\ntimes in the interval \\(\\left\\lbrack 0, t^{*} \\right\\rbrack,\\) where\n\\(t^{*}\\) is a cut-off time (where “most” is judged by the\nso-called microcanonical measure on the phase space; for discussion of\nthis measure see\n §6.1).\n For rigorous statements and further discussions of the theorem see\nArdourel (2017), Uffink and Valente (2015), and Valente (2014).", "\nLanford's theorem is a remarkable achievement because it shows that a\nstatistical and approximate version of the Bolzmann Equation can be\nderived from the Hamiltonian mechanics and most initial conditions in\nthe Bolzmann-Grad limit for a finite amount of time. In this sense it\ncan be seen as a vindication of Boltzmann’s statistical version\nof the H-theorem. At the same time the theorem also\nhighlights the limitations of the approach. The relevant distributions\nare close to each other only up to time \\(t^{*}\\), and it turns out\nthat \\(t^{*}\\) is roughly two fifths of the mean time a particle moves\nfreely between two collisions. But this is a very short time! During\nthe interval \\(\\left\\lbrack 0, t^{*} \\right\\rbrack\\), which for a gas\nlike air at room temperature is in the order of microseconds, on\naverage 40% of the molecules in the gas will have been involved in one\ncollision and the other 60% will have moved freely. This is patiently\ntoo short to understand macroscopic phenomena like the one that we\ndescribed at the beginning of this article, which take place on a\nlonger timescale and will involve many collisions for all particles.\nAnd like Boltzmann's original results, Lanford's theorem also depends\non strong assumptions, in particular a measure-theoretic version of\nthe Stosszahlansatz and Valente (cf. Uffink & Valente\n2015).", "\nFinally, one of the main conceptual problems concerning\nLanford’s theorem is where the apparent irreversibility comes\nfrom. Various opinions have been expressed on this issue. Lanford\nhimself first argued that irreversibility results from passing to the\nBoltzmann-Grad limit (Lanford 1975: 110), but later changed his mind\nand argued that the Stosszahlansatz for incoming collision\npoints is responsible for the irreversible behaviour (1976, 1981).\nCercignani, Illner, and Pulvirenti (1994) and Cercignani (2008) claim\nthat irreversibility arises as a consequence of assuming a hard-sphere\ndynamics. Valente (2014) and Uffink and Valente (2015) argue that\nthere is no genuine irreversibility in the theorem because the theorem\nis time-reversal invariant. For further discussions on the role of\nirreversibility in Lanford’s theorem, see also Lebowitz (1983),\nSpohn (1980, 1991), and Weaver (2021, 2022)" ], "section_title": "5. The Boltzmann Equation", "subsections": [] }, { "main_content": [ "\nGibbsian Statistical Mechanics (GSM) is an umbrella term covering a\nnumber of positions that take Gibbs’ (1902 [1981]) as their\npoint of departure. In this section, we introduce the framework and\ndiscuss different articulations of it along with the issues they\nface." ], "section_title": "6. Gibbsian Statistical Mechanics (GSM)", "subsections": [ { "content": [ "\nLike BSM, GSM departs from the dynamical system \\((X,\\) \\(\\phi,\\)\n\\(\\mu)\\) introduced in\n Section 3\n (although, as we will see below, it readily generalises to quantum\nmechanics). But this is where the commonalities end. Rather than\npartitioning \\(X\\) into macro-regions, GSM puts a probability density\nfunction \\(\\rho(x)\\) on \\(X\\), often referred to as a\n“distribution”. This distribution evolves under the\ndynamics of the system through the law", "\nwhere \\(\\rho_{0}\\) is the distribution the initial time \\(t_{0}\\) and\n\\(\\phi_{- t}(x)\\) is the micro-state that evolves into \\(x\\) during\n\\(t\\). A distribution is called stationary if it does not change over\ntime, i.e., \\(\\rho_{t}(x)= \\rho_{0}(x)\\) for all \\(t\\). If the\ndistribution is stationary, Gibbs says that the system is in\n“statistical equilibrium”.", "\nAt the macro-level, a system is characterised by macro-variables,\nwhich are functions \\(f:X\\rightarrow \\mathbb{R}\\), where\n\\(\\mathbb{R}\\) are the real numbers. With the exception of entropy and\ntemperature (to which we turn below), GSM takes all physical\nquantities to be represented by such functions. The so-called\nphase average of \\(f\\) is", "\nThe question now is how to interpret this formalism. The standard\ninterpretation is in terms of what is known as an ensemble. An\nensemble is an infinite collection of systems of the same\nkind that differ in their state. Crucially, this is a collection of\ncopies of the entire system and not a collection of\nmolecules. For this reason, Schrödinger characterised an ensemble\nas a collection of “mental copies of the one system under\nconsideration” (1952 [1989: 3]). Hence the members of an\nensemble do not interact with each other; an ensemble is not a\nphysical object; and ensembles have no spatiotemporal existence. The\ndistribution can then be interpreted as specifying “how\nmany” systems in the ensemble have their state in certain region\n\\(R\\) of \\(X\\) at time \\(t\\). More precisely, \\(\\rho_{t}(x)\\) is\ninterpreted as giving the probability of finding a system in \\(R\\) at\n\\(t\\) when drawing a system randomly from the ensemble in much the\nsame way in which one draws a ball from an urn:", "\nWhat is the right distribution for a given physical situation? Gibbs\ndiscusses this problem at length and formulates three distributions\nwhich are still used today: the microcanonical distribution\nfor isolated systems, the canonical distribution for system\nwith fluctuating energy, and the grand-canonical distribution\nfor systems with both fluctuating energy and fluctuating particle\nnumber. For a discussion of the formal aspects of these distributions\nsee, for instance, Tolman (1938 [1979]), and for philosophical\ndiscussions see Davey (2008, 2009) and Myrvold (2016).", "\nGibbs’ statistical equilibrium is a condition on an\nensemble being in equilibrium, which is different from an\nindividual system being in equilibrium (as introduced in\n §1).\n The question is how the two relate, and what an experimenter who\nmeasures a physical quantity on a system observes. A standard answer\none finds in SM textbooks appeals to the averaging principle:\nwhen measuring the quantity \\(f\\) on a system in thermal equilibrium,\nthe observed equilibrium value of the property is the ensemble average\n\\(\\langle f\\rangle\\) of an ensemble in ensemble-equilibrium. The\npractice of applying this principle is often called phase\naveraging. One of the core challenges for GSM is to justify this\nprinciple." ], "subsection_title": "6.1 The Framework of GSM" }, { "content": [ "\nThe standard justification of phase averaging that one finds in many\ntextbooks is based on the notion of ergodicity that we have already\nencountered in\n Section 4.4.\n In the current context, we consider the infinite time\naverage \\(f^{*}\\)of the function \\(f\\). It is a mathematical fact\nthat ergodicity as defined earlier is equivalent to it being the case\nthat \\(f^{*} = \\langle f \\rangle\\) for almost all initial states. This\nis reported to provide a justification for phase averaging as follows.\nAssume we carry out a measurement of the physical quantity represented\nby \\(f\\). It will take some time to carry out the measurement, and so\nwhat the measurement device registers is the time average over the\nduration of the measurement. Indeed, the time needed to make the\nmeasurement is long compared to the time scale on which typical\nmolecular processes take place, the measured result is approximately\nequal to the infinite time average \\(f^{*}\\). By ergodicity, \\(f^{*}\\)\nis equal to \\(\\langle f\\rangle\\), which justifies the averaging\nprinciple.", "\nThis argument fails for several reasons (Malament & Zabell 1980;\nSklar 1993: 176–9). First, from the fact that measurements take\ntime it does not follow that what is measured are time averages, and\neven if one could argue that measurement devices output time averages,\nthese would be finite time averages and equating these finite\ntime averages with infinite time averages is problematic because\nfinite and infinite averages can assume very different values even if\nthe duration of the finite measurement is very long. Second, this\naccount makes a mystery of how we observe change. As we have seen in\n Section 1,\n we do observe how systems approach equilibrium, and in doing so we\nobserve macro-variables changing their values. If measurements\nproduced infinite time averages, then no change would ever be observed\nbecause these averages are constant. Third, as we already noted\nearlier, ergodicity is a stringent condition and many systems to which\nSM is successfully applied are not ergodic (Earman & Rédei\n1996), which makes equating time averages and phase averages\nwrong.", "\nA number of approaches have been designed to either solve or\ncircumvent these problems. Malament and Zabell (1980) suggest a method\nof justifying phase averaging that still invokes ergodicity but avoids\nan appeal to time averages. Vranas (1998) offers a reformulation of\nthis argument for systems that are epsilon-ergodic (see\n §4.4).\n This accounts for systems that are “almost” ergodic, but\nremains silent about systems that are far from being ergodic. Khinchin\n(1949) restricts attention to systems with a large number of degrees\nof freedom and so-called sum functions (i.e., functions that can are a\nsum over one-particle functions), and shows that for such systems\n\\(f^{*} = \\langle f\\rangle\\) holds on the largest part of \\(X\\); for a\ndiscussion of this approach see Batterman (1998) and Badino (2006).\nHowever, as Khinchin himself notes, the focus on sum-functions is too\nrestrictive to cover realistic systems, and the approach also has to\nrevert to the implausible posit that observations yield infinite time\naverages. This led to a research programme now known as the\n“thermodynamic limit”, aiming to prove\n“Khinchin-like” results under more realistic assumptions.\nClassic statements are Ruelle (1969, 2004); for a survey and further\nreferences see Uffink (2007: 1020–8).", "\nA different approach to the problem insists that one should take the\nstatus of \\(\\rho(x)\\) as a probability seriously and seek a\njustification of averaging in statistical terms. In this vein, Wallace\n(2015) insists that the quantitative content of statistical mechanics\nis exhausted by the statistics of observables (their expectation\nvalues, variances, and so on) and McCoy (2020) submits that\n\\(\\rho(x)\\) is the complete physical state of an individual\nstatistical mechanical system. Such a view renounces the association\nof measurement outcomes with phase averages and insists that\nmeasurements are “an instantaneous act, like taking a\nsnapshot” (O. Penrose 1970: 17–18): if a measurement of\nthe quantity associated with \\(f\\) is performed on a system at time\n\\(t\\) and the system’s micro-state at time \\(t\\) is \\(x(t)\\),\nthen the measurement outcome at time \\(t\\) will be \\(f(x(t))\\). An\nobvious consequence of this definition is that measurements at\ndifferent times can have different outcomes, and the values of\nmacro-variables can change over time. One can then look at how these\nvalues change over time. One way of doing this is to look at\nfluctuations away from the average:", "\nwhere \\(\\Delta(t)\\) is the fluctuation away from the average at time\n\\(t\\). One can then expect that a that the outcome of a measurement\nwill be \\(\\langle f\\rangle\\) if fluctuations turn out to be small and\ninfrequent. Although this would not seem to be the received textbook\nposition, something like it can be identified in some, for instance\nHill (1956 [1987]) and Schrödinger (1952 [1989]). A precise\narticulation will have to use \\(\\rho\\) to calculate the probability of\nfluctuations of a certain size, and this requires the system to meet\nstringent dynamical conditions, namely either the masking condition\nor the f-independence condition (Frigg & Werndl\n2021)." ], "subsection_title": "6.2 Equilibrium: Why Does Phase Averaging Work?" }, { "content": [ "\nAs discussed so far, GSM is an equilibrium theory, and this is also\nhow it is mostly used in applications. Nevertheless, a comprehensive\ntheory of SM must also account for the approach to equilibrium. To\ndiscuss the approach to equilibrium, it is common to introduce the\nGibbs entropy", "\nThe Gibbs entropy is a property of an ensemble characterised by a\ndistribution \\(\\rho\\). One might then try to characterise the approach\nto equilibrium as a process in which \\(S_{G}\\) increases monotonically\nto finally reach a maximum in equilibrium. But this idea is undercut\nimmediately by a mathematical theorem saying that \\(S_{G}\\) is a\nconstant of motion:", "\nfor all times \\(t\\). So not only does \\(S_{G}\\) fail to increase\nmonotonically; it does not change at all! This precludes a\ncharacterisation of the approach to equilibrium in terms of increasing\nGibbs entropy. Hence, either such a characterisation has to be\nabandoned, or the formalism has to be modified to allow \\(S_{G}\\) to\nincrease.", "\nA second problem is a consequence of the Gibbsian definition of\nstatistical equilibrium. As we have seen in\n §6.1,\n a system is in statistical equilibrium if \\(\\rho\\) is stationary. A\nsystem away from equilibrium would then have to be associated with a\nnon-stationary distribution and eventually evolve into the stationary\nequilibrium distribution. But this is mathematically impossible. It is\na consequence of the theory’s formalism of GSM that a\ndistribution that is stationary at some point in time has to be\nstationary at all times (past and future), and that a distribution\nthat is non-stationary at some point in time will always be\nnon-stationary. So an ensemble cannot evolve from non-stationary\ndistribution to stationary distribution. This requires either a change\nin the definition of equilibrium, or a change in the formalism that\nwould allow distributions to change in requisite way.", "\nIn what follows we discuss the main attempts to address these\nproblems. For alternative approaches that we cannot cover here see\nFrigg (2008b: 166–68) and references therein." ], "subsection_title": "6.3 GSM and Approach to Equilibrium" }, { "content": [ "\nGibbs was aware of the problems with the approach to equilibrium and\nproposed coarse-graining as a solution (Gibbs 1902 [1981]: Ch. 12).\nThis notion has since been endorsed by many practitioners (see, for\ninstance, Farquhar 1964 and O. Penrose 1970). We have already\nencountered coarse-graining in\n §4.2.\n The use of it here is different, though, because we are now\nputting a grid on the full state space \\(X\\) and not just on the\none-particle space. One can then define a coarse-grained density\n\\(\\bar{\\rho}\\) by saying that at every point \\(x\\) in \\(X\\) the\nvalue of \\(\\bar{\\rho}\\) is the average of \\(\\rho\\) over the grid cell\nin which \\(x\\) lies. The advantage of coarse-graining is that the\ncoarse-grained distribution is not subject to the same limitations as\nthe original distribution. Specifically, let us call the Gibbs entropy\nthat is calculated with the coarse-grained distribution the\ncoarse-grained Gibbs entropy. It now turns out that coarse-grained\nGibbs entropy is not a constant of motion and it is possible for the\nentropy to increase. This re-opens the avenue of understanding the\napproach to equilibrium in terms of an increase of the entropy. It is\nalso possible for the coarse-grained distribution to evolve so that it\nis spread out evenly over the entire available space and thereby comes\nto look like a micro-canonical equilibrium distribution. Such a\ndistribution is also known as the quasi-equilibrium equilibrium\ndistribution (Blatt 1959; Ridderbos 2002).", "\nCoarse-graining raises two questions. First, the coarse-grained\nentropy can increase and the system can approach a\ncoarse-grained equilibrium, but under what circumstances will it\nactually do so? Second, is it legitimate to replace standard\nequilibrium by quasi-equilibrium?", "\nAs regards the first question, the standard answer (which also goes\nback to Gibbs) is that the system has to be mixing.\nIntuitively speaking, a system is mixing if every subset of \\(X\\) ends\nup being spread out evenly over the entire state space in the long run\n(for a more detailed account of mixing see entry on\n the ergodic hierarchy).\n The problem is that mixing is a very demanding condition. In fact,\nbeing mixing implies being ergodic (because mixing is strictly\nstronger than ergodicity). As we have already noticed, many relevant\nsystems are not ergodic, and hence a fortiori not mixing.\nEven if a system is mixing, the mixed state is only achieved in the\nlimit for \\(t \\rightarrow \\infty\\), but real physical systems reach\nequilibrium in finite time (indeed, in most cases rather quickly).", "\nAs regards the second question, the first point to note is that a\nsilent shift has occurred: Gibbs initially defined equilibrium through\nstationarity while the above argument defines it through uniformity.\nThis needs further justification, but in principle there would seem to\nbe nothing to stop us from redefining equilibrium in this way.", "\nThe motivation for adopting quasi-equilibrium is that \\(\\bar{\\rho}\\)\nand \\(\\rho\\) are empirically indistinguishable. If the size of the\ngrid is below the measurement precision, no measurement will be able\nto tell the difference between the two, and phase averages calculated\nwith the two distributions agree. Hence, hence there is no reason to\nprefer \\(\\rho\\) to \\(\\bar{\\rho}\\).", "\nThis premise has been challenged. Blatt (1959) and Ridderbos and\nRedhead (1998) argue that this is wrong because the spin-echo\nexperiment (Hahn 1950) makes it possible to empirically discern\nbetween \\(\\rho\\) and \\(\\bar{\\rho}\\). The weight of this experiment\ncontinues to be discussed controversially, with some authors insisting\nthat it invalidates the coarse gaining approach (Ridderbos 2002) and\nothers insisting that coarse-graining can still be defended (Ainsworth\n2005; Lavis 2004; Robertson 2020). For further discussion see Myrvold\n(2020b)." ], "subsection_title": "6.4 Coarse-Graining" }, { "content": [ "\nThe approaches we discussed so far assume that systems are isolated.\nThis is an idealising assumption because real physical systems are not\nperfectly isolated from their environment. This is the starting point\nfor the interventionist programme, which is based on the idea that\nreal systems are constantly subject to outside perturbations, and that\nit is exactly these perturbations that drive the system into\nequilibrium. In other words, it’s these interventions from\noutside the system that are responsible for its approach to\nequilibrium, which is what earns the position the name\ninterventionism. This position has been formulated by Blatt\n(1959) and further developed by Ridderbos and Redhead (1998). The key\ninsight behind the approach is that two challenges introduced in\n Section 6.3\n vanish once the system is not assumed to be isolated: the entropy can\nincrease, and a non-stationary distribution can be pushed toward a\ndistribution that is stationary in the future.", "\nThis approach accepts that isolated systems do not approach\nequilibrium, and critics wonder why this would be the case. If one\nplaces a gas like the one we discussed in\n Section 1\n somewhere in interstellar space where it is isolated from outside\ninfluences, will it really sit there confined to the left half of the\ncontainer and not spread? And even if this were the case, would adding\njust any environment resolve the issue? Interventionist\nsometimes seem to suggest that this is the case, but in an unqualified\nform this claim cannot be right. Environments can be of very different\nkinds and there is no general theorem that says that any environment\ndrives a system to equilibrium. Indeed, there are reasons to assume\nthat there is no such theorem because while environments do drive\nsystems, they need not drive them to equilibrium. So it remains an\nunresolved question under what conditions environments drive systems\nto equilibrium.", "\nAnother challenge for interventionism is that one is always free to\nconsider a larger system, consisting of our original system plus its\nenvironment. For instance, we can consider the “gas + box”\nsystem. This system would then also approach equilibrium because of\noutside influences, and we can then again form an even larger system.\nSo we get into a regress that only ends once the system under study is\nthe entire universe. But the universe has no environment that could\nserve as a source of perturbations which, so the criticism goes, shows\nthat the programme fails.", "\nWhether one sees this criticism as decisive depends on one’s\nviews of laws of nature. The argument relies on the premise that the\nunderlying theory is a universal theory, i.e., one that applies to\neverything that there is without restrictions. The reader can find an\nextensive discussion in the entry on\n laws of nature.\n At this point we just note that while universality is widely held,\nsome have argued against it because laws are always tested in highly\nartificial situations. Claiming that they equally apply outside these\nsettings involves an inductive leap that is problematic; see for\ninstance Cartwright (1999) for a discussion of such a view. This, if\ntrue, successfully undercuts the above argument against\ninterventionism." ], "subsection_title": "6.5 Interventionism" }, { "content": [ "\nThe epistemic account urges a radical reconceptualization of SM. The\naccount goes back to Tolman (1938 [1979]) and has been brought to\nprominence by Jaynes in a string of publications between 1955 and\n1980, most of which are gathered in Jaynes (1983). On this approach,\nSM is about our knowledge of the world and not about the\nworld itself, and the probability distributions in GSM represents our\nstate of knowledge about a system and not some matter of fact. The\ncentre piece of this interpretation is the fact that the Gibbs entropy\nis formally identical to the Shannon entropy in information theory,\nwhich is a measure for the lack of information about a system: the\nhigher the entropy, the less we know (for a discussion of the Shannon\nentropy see the entry on\n information, §4.2).\n The Gibbs entropy can therefore be seen as quantifying our lack of\ninformation about a system. This has the advantage that ensembles are\nno longer needed in the statement of GSM. On the epistemic account,\nthere is only one system, the one on which we are performing our\nexperiments, and \\(\\rho\\) describes what we know about it. This also\noffers a natural criterion for identifying equilibrium distributions:\nthey are the distributions with the highest entropy consistent with\nthe external constraints on the system because such distributions are\nthe least committal distributions. This explains why we expect\nequilibrium to be associated with maximum entropy. This is known as\nJaynes’ maximum entropy principle (MEP).", "\nMEP has been discussed controversially, and, to date, there is no\nconsensus on its significance, or even cogency. For discussions see,\nfor instance, Denbigh and Denbigh (1985), Howson and Urbach (2006),\nLavis (1977), Lavis and Milligan (1985), Seidenfeld (1986), Shimony\n(1985), Uffink (1995, 1996a), and Williamson (2010). The epistemic\napproach also assumes that experimental outcomes correspond to phase\naverages, but as we have seen, this is a problematic assumption\n (§6.1).\n A further concern is that the system’s own dynamics plays no\nrole in the epistemic approach. This is problematic because if the\ndynamics has invariant quantities, a system cannot access certain\nparts of the state space even though \\(\\rho\\) may assign a non-zero\nprobability to it (Sklar 1993: 193–4).", "\nThe epistemic account’s explanation of the approach to\nequilibrium relies on making repeated measurements and\nconditionalizing on each measurement result; for a discussion see\nSklar (1993: 255–257). This successfully gets around the problem\nthat the Gibbs entropy is constant, because the value assignments now\ndepend not only on the system’s internal dynamics, but also on\nthe action of an experimenter. The problem with this solution is that\ndepending on how exactly the calculations are done, either the entropy\nincrease fails to be monotonic (indeed entropy decreases are possible)\nor the entropy curve will become dependent on the sequence of instants\nof time chosen to carry out measurements (Lavis & Milligan\n1985).", "\nHowever, the most fundamental worry about the epistemic approach is\nthat it fails to realise the fundamental aim of SM, namely to explain\nhow and why processes in nature take place because these processes\ncannot possibly depend on what we know about them. Surely, so the\nargument goes, the boiling of kettles or the spreading of gases has\nsomething to do with how the molecules constituting these systems\nbehave and not with what we happen (or fail) to know about them\n(Redhead 1995; Albert 2000; Loewer 2001). For further discussions of\nthe epistemic approach see Anta (forthcoming-a, forthcoming-b),\nShenker (2020), and Uffink (2011)." ], "subsection_title": "6.6 The Epistemic Account" }, { "content": [ "\nA pressing and yet understudied question in the philosophy of SM\nconcerns the relation between the GSM and BSM. GSM provides the tools\nand methods to carry out a wide range of equilibrium calculations, and\nit is the approach predominantly used by practitioners in the field.\nWithout it, the discipline of SM would not be able to operate (Wallace\n2020). BSM is conceptually neat and is preferred by philosophers when\nthey give foundational accounts of SM. So what we’re facing is a\nschism whereby the day-to-day work of physicists is in one framework\nand foundational accounts and explanations are given in another\nframework (Anta 2021a). This would not be worrisome if the frameworks\nwere equivalent, or at least inter-translatable in relatively clear\nway. As the discussion in the previous sections has made clear, this\nis not the case. And what is more, in some contexts the formalisms do\nnot even give empirically equivalent predictions (Werndl & Frigg\n2020b). This raises the question of how exactly the two approaches are\nrelated. Lavis (2005) proposes a reconciliation of the two frameworks\nthrough giving up on the binary property of the system being or not\nbeing in equilibrium, which should be replaced by the continuous\nproperty of commonness. Wallace (2020) argues that GSM is a\nmore general framework in which the Boltzmannian approach may be\nunderstood as a special case. Frigg and Werndl suggest that BSM is a\nfundamental theory and GSM is an effective theory that offers means to\ncalculate values defined in BSM (Frigg & Werndl 2019; Werndl &\nFrigg 2020a). Goldstein (2019) plays down their difference and argues\nthat the conflict between them is not as great as often imagined.\nFinally, Goldstein, Lebowitz, Tumulka, and Zanghì (2020)\ncompare the Boltzmann entropy and the Gibbs entropy and argue that the\ntwo notions yield the same (leading order) values for the entropy of a\nmacroscopic system in thermal equilibrium." ], "subsection_title": "6.7 The Relation between GSM and BSM" } ] }, { "main_content": [ "\nSo far we have focussed on the questions that arise in the\narticulation of the theory itself. In this section we discuss some\nfurther issue that arise in connection with SM, explicitly excluding a\ndiscussion of the direction of time and other temporal asymmetries,\nwhich have their own entry in this encyclopedia (see the entry on\n thermodynamic asymmetry in time)." ], "section_title": "7. Further Issues", "subsections": [ { "content": [ "\nHow to interpret probabilities is a problem with a long philosophical\ntradition (for a survey of different views see the entry on\n interpretations of probability).\n Since SM introduces probabilities, there is a question of how these\nprobabilities should be interpreted. This problem is particularly\npressing in SM because, as we have seen, the underlying mechanical\nlaws are deterministic. This is not a problem so long as the\nprobabilities are interpreted epistemically as in Jaynes’\naccount\n (§6.6).\n But, as we have seen, a subjective interpretation seems to clash with\nthe realist intuition that SM is a physical theory that tells us how\nthings are independently of what we happen to know about them. This\nrequires probabilities to be objective.", "\nApproaches to SM that rely on ergodic theory tend to interpret\nprobabilities as time-averages, which is natural because ergodicity\nprovides such averages. However, long-run time averages are not a good\nindicator for how a system behaves because, as we have seen, they are\nconstant and so do not indicate how a system behaves out of\nequilibrium. Furthermore, interpreting long-run time averages as\nprobabilities is motivated by the fact the that these averages seem to\nbe close cousins of long-run relative frequencies. But this\nassociation is problematic for a number of reasons (Emch 2005;\nGuttmann 1999; van Lith 2003; von Plato 1981, 1982, 1988,\n1994). An alternative is to interpret SM probabilities as\npropensities, but many regard this as problematic because\npropensities would ultimately seem to be incompatible with a\ndeterministic underlying micro theory (Clark 2001).", "\nLoewer (2001) suggested that we interpret SM probabilities as Humean\nobjective chances in Lewis’ sense (1980) because the Mentaculus\n(see\n §4.6)\n is a best system in Lewis’ sense. Frigg (2008a) identifies some\nproblems with this interpretation, and Frigg and Hoefer (2015)\nformulate an alternative Humean account that is designed to overcome\nthese issues. For further discussion of Humean chances in SM, see\nBeisbart (2014), Dardashti, Glynn, Thébault, and Frisch (2014),\nHemmo and Shenker (2022),  Hoefer (2019), and Myrvold (2016,\n2021)." ], "subsection_title": "7.1 The Interpretation of SM Probabilities" }, { "content": [ "\nConsider the following scenario, which originates in a letter that\nMaxwell wrote in 1867 (see Knott 1911). Recall the vessel with a\npartition wall that we have encountered in\n Section 1,\n but vary the setup slightly: rather than having one side empty, the\ntwo sides of the vessel are filled with gases of different\ntemperatures. Additionally, there is now a shutter in the wall which\nis operated by a demon. The demon carefully observes all the\nmolecules. Whenever a particle in the cooler side moves towards the\nshutter the demon checks its velocity, and if the velocity of the\nparticle is greater than the mean velocity of the particles on the\nhotter side of the vessel he opens the shutter and lets the particle\npass through to the hotter side. The net effect of the demon’s\nactions is that the hotter gas becomes even hotter and that the colder\ngas becomes even colder. This means that there is a heat transfer from\nthe cooler to the hotter gas without doing any work because the heat\ntransfer is solely due to the demon’s skill and intelligence in\nsorting the molecules. Yet, according to the Second Law of\nthermodynamics, this sort of heat transfer is not allowed. So we\narrive at the conclusion that the demons’ action result in a\nviolation of the Second Law of thermodynamics.", "\nMaxwell interpreted this scenario as a thought experiment that showed\nthat the Second Law of thermodynamics is not an exceptionless law and\nthat it has only “statistical certainty” (see Knott 1911;\nHemmo & Shenker 2010). Maxwell’s demon has given rise to a\nvast literature, some of it in prestigious physics journals. Much of\nthis literature has focused on exorcising the demon, i.e., on showing\nthat a demon would not be physically possible. Broadly speaking, there\nare two approaches. The first approach is commonly attributed to\nSzilard (1929 [1990]), but also goes also back to von Neumann (1932\n[1955]) and Brillouin (1951 [1990]). The core idea of this approach is\nthat gaining information that allows us to distinguish between \\(n\\)\nequally likely states comes at a necessary minimum cost in\nthermodynamic entropy of \\(k \\log(n)\\), which is the entropy\ndissipated by the system that gains information. Since the demon has\nto gain information to decide whether to open the shutter, the second\nlaw of thermodynamics is not violated. The second approach is based on\nwhat is now called Landauer’s principle, which states\nthat in erasing information that can discern between \\(n\\) states, a\nminimum thermodynamic entropy of \\(k \\log(n)\\) is dissipated (Landauer\n1961 [1990]). Proponents of the principle argue that because a demon\nhas to erase information on memory devices, Landauer’s principle\nprohibits a violation of the second law of thermodynamics.", "\nIn two influential articles Earman and Norton (1998, 1999) lament that\nfrom the point of view of philosophy of science the literature on\nexorcising the demon lacks rigour and reflection on what the goals the\nenterprise are, and that the demon has been discussed from various\ndifferent perspectives, often leading to confusion. Earman and Norton\nargue that the appeal to information theory has not resulted in a\ndecisive exorcism of Maxwell’s demon. They pose a dilemma for\nthe proponent of an information theoretic exorcism of Maxwell’s\ndemon. Either the combined system of the vessel and the demon are\nalready assumed to be subject to the second law of thermodynamics, in\nwhich case it is trivial that the demon will fail. Or, if this is not\nassumed, then proponents of the information theoretic exorcism have to\nsupply new physical principles to guarantee the failure of the demon\nand they have to give independent grounds for it. Yet, in Earman and\nNorton’s view, such independent grounds have not been\nconvincingly established.", "\nBub (2001) and Bennett (2003) responded to Earman and Norton that if\none assumes that the demon is subject to the Second Law of\nthermodynamics, the merit of Landauer’s principle is that it\nshows where the thermodynamic costs arise. Norton (2005, 2017) replies\nthat no general precise principle is stated how erasure and the\nmerging of computational paths necessarily lead to an increase in\nthermodynamic entropy. He concludes that the literature on\nLandauer’s principle is too fragile and too tied to a few\nspecific examples to sustain general claims about the failure of\nMaxwell’s demons. Maroney (2005) argues that thermodynamic\nentropy and information-theoretic entropy are conceptually different,\nand that hence, in general, Landauer’s principle fails.", "\nThe discussions around Maxwell’s demon are now so extensive that\nthey defy documentation in an introductory survey of SM. Classical\npapers on the matter are collected in Leff and Rex (1990). For more\nrecent discussion see, for instance, Anta (2021b), Hemmo and Shenker\n(2012; 2019), Ladyman and Robertson (2013, 2014), Leff and Rex (1994),\nMyrvold (forthcoming), Norton (2013), and references therein." ], "subsection_title": "7.2 Maxwell’s Demon and the Entropy Costs of Computation" }, { "content": [ "\nSo far, we have considered how one gas evolves. Now let’s look\nat what happens when we mix two gases. Again, consider a container\nwith a partition wall in the middle, but now imagine that there are\ntwo different gases on the left and on the right (for\ninstance helium and hydrogen) where both gases have the same\ntemperature. We now remove the shutter, and the gases start spreading\nand get mixed. If we then calculate the entropy of the initial and the\nfinal state of the two gases, we find that the entropy of the mixture\nis greater than the entropy of the gases in their initial\ncompartments. This is the result that we expect. The paradox arises\nfrom the fact that the calculations do not depend on the fact\nthat the gases are different: if we assume that we have air of the\nsame temperature on both sides of the barrier the calculations still\nyield an increase in entropy when the barrier is removed. This seems\nwrong because it would imply that the entropy of a gas depends on its\nhistory and cannot be a function of its thermodynamic state alone (as\nthermodynamics requires). This is known as the Gibbs\nParadox.", "\nThe standard textbook resolution of the paradox is that classical SM\ngets the entropy wrong because it counts states that differ only by a\npermutation of two indistinguishable particles as distinct, which is a\nmistake (Huang 1963). So the problem is rooted in the notion of\nindividuality, which is seen as inherent to classical mechanics.\nTherefore, so the argument goes, the problem is resolved by quantum\nmechanics, which treats indistinguishable particles in the right way.\nThis argument raises a number of questions concerning the nature of\nindividuality in classical and quantum mechanics, the way of counting\nstates in both the Boltzmann and the Gibbs approach, and the relation\nof SM to thermodynamics. Classical discussions include Denbigh and\nDenbigh (1985: Ch. 4), Denbigh and Redhead(1989), Jaynes (1992),\nLandé (1965), Rosen (1964), and van Kampen (1984). For more\nrecent discussions, see, for instance, Huggett (1999), Saunders\n(2006), and Wills (forthcoming), as well as the contributions to Dieks\nand Saunders (2018) and references therein." ], "subsection_title": "7.3 The Gibbs Paradox" }, { "content": [ "\nIncreasingly, the methods of SM are used to address problems outside\nphysics. Costantini and Garibaldi (2004) present a generalised version\nof the Ehrenfest flea model and show that it can be used to describe a\nwide class of stochastic processes, including problems in population\ngenetics and macroeconomics. Colombo and Palacios (2021) discuss the\napplication of the free energy principle in biology. The most prolific\napplication of SM methods outside physics are in economics and\nfinance, where an entire field is named after them, namely\neconophysics. For discussions of different aspects of econophysics see\nJhun, Palacios, and Weatherall (2018); Kutner et al. (2019),\nRickles (2007, 2011), Schinckus (2018), Thébault, Bradley, and\nReutlinger (2017), and Voit (2005)." ], "subsection_title": "7.4 SM Beyond Physics" } ] } ]

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[ "\nWe sometimes think about the ethical significance of merely possible\ncircumstances. People sometimes wonder, for example, if it would have\nbeen wrong to break certain promises that they in fact kept. Examples\nlike this do not exhaust the significance of possibility—or\nmodality more generally—in our ethical thinking. Rather, we also\nseem to be committed to a certain modal structure in our ethical\ncommitments. To see this, consider an example. Suppose that a bank\nmanager wrongfully embezzles their client’s money. If we imagine\nholding fixed how much the bank manager stole, and how; the trust\ntheir customers placed in them; what they did with the money; all of\nthe short- and long-term consequences of their actions; and so on, it\nseems that there could not be a second action that perfectly resembled\nthis embezzlement, except that the second action was right rather than\nwrong. Cases like this one seem to show a necessary\nconnection: they suggest that the ethical character of the bank\nmanager’s act cannot vary without some other facts varying as\nwell.", "\nWhile the embezzling bank manager example concerns a specific\nnecessary connection, many philosophers also find it plausible that\nthere are general necessary connections between ethical\nproperties and certain other properties. For example, many\nphilosophers have been inclined to accept:", "\nFollowing R. M. Hare (1952), claims of such general necessary\nconnection are called ethical supervenience theses. Such\ntheses have played a key role in arguments for and against a variety\nof influential views about ethics. This entry aims to introduce the\nidea of ethical supervenience and its philosophical significance. The\nentry considers ways of making more precise the claim that the ethical\nsupervenes, and what case can be made for the supervenience of the\nethical. It then considers arguments that use ethical supervenience as\na premise, and doubts that ethical supervenience has the sort of\nsignificance suggested by these arguments." ]

[ { "content_title": "1. Theorizing Ethical Supervenience", "sub_toc": [ "1.1 What does the ethical supervene on?", "1.2 The structure of ethical supervenience", "1.3 The modal strength of ethical supervenience", "1.4 Ontological and ascriptive supervenience" ] }, { "content_title": "2. Arguments for Ethical Supervenience", "sub_toc": [] }, { "content_title": "3. Arguments from Ethical Supervenience", "sub_toc": [ "3.1 Arguments against realism", "3.2 Arguments against non-reductive realism", "3.3 Supervenience and anti-realism", "3.4 Supervenience and moral epistemology", "3.5 Supervenience and the existence of ethical principles" ] }, { "content_title": "4. Metaphysical Supervenience and Ethical Realism", "sub_toc": [ "4.1 Reductive explanations of ethical supervenience", "4.2 Functionalist explanations of ethical supervenience", "4.3 Grounding explanations of ethical supervenience", "4.4 Analytic and conceptual explanations of ethical supervenience", "4.5 Ethical explanations of ethical supervenience" ] }, { "content_title": "5. Arguments against Ethical Supervenience, or its Significance", "sub_toc": [ "5.1 Arguments against supervenience from thick ethical concepts", "5.2 Arguments against the epistemic credentials of ethical supervenience", "5.3 Arguments against the strong metaphysical supervenience of the ethical", "5.4 Arguments against the dialectical significance of ethical supervenience" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] }, { "content_title": "Acknowledgments", "sub_toc": [] } ]

[ { "main_content": [ "\nMany philosophers hope to make significant arguments about ethics\nusing ethical supervenience as a premise. However, there are many\ndistinct ethical supervenience theses that philosophers might be\ninterested in. Understanding the differences between these theses can\nhelp to clarify which of them deserve our allegiance. It is also\nimportant because different supervenience theses will support quite\ndifferent arguments about ethics.", "\nTo begin, it is worth briefly characterizing certain core features of\nsupervenience relations, as they are now standardly understood in\nmetaphysics (see, e.g., the entry on\n supervenience).\n Supervenience relations are typically understood as relations between\npairs of classes of properties. Consider the claim that a certain\nclass of properties—the A-properties—cannot vary\nwithout the B-properties also varying. In this claim, we can\ncall the A-properties the supervening properties,\nand the B-properties the subvening or base\nproperties.", "\nSupervenience relations are covariance relations that have\nthree logical features: they are reflexive, transitive, and\nnon-symmetric. The claim that supervenience is reflexive\nmeans that every set of properties supervenes on itself: for any class\nof properties A, there can be no difference in the\nA-properties without a difference in the\nA-properties. The claim that supervenience is\ntransitive means that: if the A-properties supervene\non the B-properties, and the B-properties supervene\non the C-properties, then the A-properties supervene\non the C-properties. The claim that supervenience is\nnon-symmetric means that supervenience is compatible with\neither symmetry (A supervenes on B and B\nsupervenes on A; as in the case of the ethical and itself) or\nasymmetry (A supervenes on B but B does not\nsupervene on A; as may be the case between the biological and\nthe microphysical).", "\nThese claims reflect how use of the word ‘supervenience’\nhas come to be usefully regimented in contemporary metaphysics. It is\nworth emphasizing this point, because there is a significant history\nof the word being used in ways that depart from this contemporary\northodoxy. For example, for a time it was quite common both in\nmetaphysics and in ethics for ‘supervenience’ to be used\nto mark an asymmetrical dependence relation. Such uses are, however,\ninconsistent with the contemporary regimentation. This is a point\nabout terminological clarity, not a substantive barrier to discussing\nsuch asymmetric relations. For example, one could name the asymmetric\nrelation that holds when A supervenes on B but\nB does not supervene on A. Or one could name the\nrelation that holds when the supervenience of A on B\nis accompanied by an adequate explanation. One influential variant of\nthe latter sort of explanatory relation has been dubbed\n‘superdupervenience’ (Horgan 1993, 566). More recently,\nmany philosophers have suggested that a certain asymmetric dependence\nrelation—grounding—is of central importance to\nour metaphysical theorizing. (For discussion, see the entry on\n metaphysical grounding.)", "\nGiven the standard contemporary regimentation, however, supervenience\nclaims state a certain pattern of covariation between classes\nof properties, they do not purport to explain that pattern,\nas a grounding or superdupervenience thesis would (compare DePaul\n1987). This point is crucial to several arguments from ethical\nsupervenience, as we will see below.", "\nThese clarifying remarks put us in a position to introduce four\ncentral questions that can be used to develop alternative\nsupervenience theses:", "\nThe next four subsections consider these questions in turn. Before\nturning to these questions, it is worth briefly highlighting a\ndifferent issue: which class of supervening properties to focus on? A\nsurvey of the literature provides a variety of suggestions: relevant\nsupervening properties are characterized as ethical,\nmoral, evaluative, or normative. The nature\nof each of these categories, and the relationship between them, are\nboth controversial. For example, some philosophers will question the\nnormative authority of morality, while others will think of\nnormativity as a very broad tent, including any rule- or\nconvention-governed activity, such as chess or etiquette. This entry\nwill not explore these interesting issues (see Baker 2017 for\ndiscussion). Instead, it will provisionally assume that the\nsignificance of supervenience is similar for each of these classes of\nproperties. For the sake of uniformity, the entry will focus on\nethical properties throughout." ], "section_title": "1. Theorizing Ethical Supervenience", "subsections": [ { "content": [ "\nSomewhat surprisingly, the idea of ethical supervenience can be made\nto seem plausible despite the fact that it is difficult to provide a\ncharacterization of what the ethical supervenes on that is at\nonce uncontroversial and theoretically interesting (see\n Section 5.4\n for further discussion of this point). This section briefly sketches\nthe options for characterizing what the ethical supervenes on, and\nsome difficulties that these options face.", "\nThe thesis used to introduce supervenience\nabove—Initial—suggested that the ethical supervenes on the\nnatural properties. This is the most common way of\ncharacterizing ethical supervenience in the literature. However, there\nare at least two difficulties with this idea. The first difficulty is\nambiguity: the term ‘natural’ has been characterized in\nwildly varying terms in metaethics (see the introductory section of\nthe entry on\n moral non-naturalism\n for a brief survey of characterizations of the natural; see McPherson\n2015, §3–4 for one constructive proposal). The second\ndifficulty is that on many conceptions of the natural there will be\ncounterexamples to Initial. For example, many philosophers want to\ncontrast natural properties with supernatural\nproperties. Even if we assume that there are no actually instantiated\nsupernatural properties, we might allow that such entities are\npossible. But this might in turn seem to suggest that two\npossible states of affairs could be naturalistically identical, but\nethically different. For example, they might be different because of\nethically significant interactions between supernatural beings (Klagge\n1984, 374–5; for some complications see McPherson 2015,\n134–5).", "\nThis sort of worry might lead one to reject the common assumption that\nthe ethical supervenes on the natural as misguided; instead,\none might propose that the ethical supervenes on the\nnon-ethical. This might seem promising: the point of the\nembezzling bank manager case might seem to be that there would need to\nbe some non-ethical difference between cases—natural or\nnot—in order for there to be an ethical difference in the bank\nmanager’s actions. However, there is an important worry about\nthis way of characterizing the supervenience base (compare Sturgeon\n2009, 70–72), which can be brought out briefly by example. Some\nphilosophers are sympathetic to ambitious reductive hypotheses about\nethics. On one such example, the ethical property of goodness is just\nidentical to the property of pleasantness. Because identicals have all\nof the same properties, this would entail that pleasantness is an\nethical property. Some philosophers also think that certain\nexperiential or “phenomenal” properties, such as\npleasantness, are metaphysically fundamental, such that two possible\ncircumstances could differ only in how much pleasantness they\ncontained. Together, the points entail the conclusion that two worlds\ncould differ from each other solely in an ethical respect: how much\ngoodness/pleasantness they include. This is inconsistent with the\nsupervenience of the ethical on the non-ethical, but it is not clear\nthat we should be prepared to dismiss out of hand the assumptions that\ngenerate this conclusion. This might in turn lead us to think that\nthere can at least be reasonable controversy concerning the\nsupervenience of the ethical on the non-ethical.", "\nOne can avoid this problem by proposing that the ethical supervenes on\nthe distribution of all of the properties. But this\nformulation purchases plausibility at the price of triviality. Ethical\ndifferences are differences, so there can obviously be no ethical\ndifference without some difference. In light of its\ntriviality, this sort of supervenience thesis fails to identify\nanything in ethical supervenience that is of philosophical\ninterest.", "\nAn influential alternative way of characterizing what the ethical\nsupervenes on begins with a distinction in language. Some philosophers\nthink that we can intuitively distinguish between broadly\nevaluative predicates (like ‘is right’, ‘is\ngood’, ‘is virtuous’, etc.) from\ndescriptive predicates (like ‘is round’,\n‘is accelerating’, ‘is a badger’ etc.). We can\nthen ask about the relationship between the properties that are picked\nout by these two sets of predicates. Frank Jackson has argued that\nthis allows us to state an ethical supervenience thesis: there is no\npossible difference that can be stated using evaluative predicates\nbetween states that are identical with respect to all properties\npicked out by descriptive predicates (1998, 118–125).", "\nJackson’s proposal seemingly avoids triviality, because\nevaluative and descriptive predicates appear to be distinct. However,\nthe detour through language faces significant challenges. One\nchallenge concerns the expressive power of a language like ours: if it\nis limited, then there seemingly might be ethical differences between\nstates of affairs that are not correlated with descriptive differences\nexpressible in a language like ours (for related worries, see Sturgeon\n2009, 73–79). A second challenge questions whether the\ndistinction between description and evaluation is characteristically a\ndistinction in the semantic properties of predicates, as Jackson\nassumes. On one contrasting view, evaluation might instead\ncharacteristically be a pragmatic property of whole speech acts (see\nVäyrynen 2013b for extended defense of this idea for the case of\n“thick” evaluation.)", "\nIn the face of these difficulties, some philosophers have sought to\ndevelop accounts of the class of properties which subvene the ethical\nwhich are substantive enough for ethical supervenience to do\ndialectical work, but avoid some of the difficulties just sketched.\nFor example, it has been proposed that the ethical supervenes on the\ndisjunctive class of non-ethical or descriptive properties\n(Ridge 2007). In the context of discussing arguments concerning\nsupervenience and non-naturalism, it has been proposed that the\nethical supervenes on the set of properties that are not ethical\nproperties as those are understood by the non-naturalist (McPherson\n2012).", "\nThere is a cross-cutting distinction that may be important for our\nthinking about the supervenience of the ethical. Most properties are\nrepeatable, in the sense that they can be possessed by\ndistinct possible individuals. But some properties are not repeatable.\nFor example, the property of being identical to Emad Atiq is\nnot repeatable: it can only be borne by a single individual, across\nmodal space. It appears plausible that the ethical properties\nsupervene on a set of repeatable properties (Atiq forthcoming).", "\nAs this brief survey makes clear, it is not obvious how to\ncharacterize what the ethical supervenes on, in a way that makes an\nethical supervenience thesis both plausible and theoretically\ninteresting. Now that the difficulties here have been made clear\n(especially by Sturgeon 2009), this is an important potential locus\nfor future research. The following discussion largely sets aside these\ndebates, speaking of the supervenience of the ethical properties on\nthe base properties,where ‘base’ serves as a\nplaceholder for a more illuminating characterization of the class of\nproperties that subvene the ethical." ], "subsection_title": "1.1 What does the ethical supervene on?" }, { "content": [ "\nThere are many possible structures of covariation that have been\ncalled supervenience theses in the metaphysics literature. For our\npurposes, it will be convenient to distinguish four of the most\ninfluential formulations. (The literature on supervenience contains\nseveral other variations; see the entry on\n supervenience\n for an excellent introduction, from which this entry adopts some of\nthe formulations below. That entry also has very helpful discussion of\nthe contrast between supervenience and certain other metaphysical\nrelations with which it is often associated. The contrast between\nsupervenience and the closely-related notion of entailment, discussed\nin section 3.2 of the entry on\n supervenience,\n is especially germane to the topic of this subsection.)", "\nOne important structural distinction concerns whether a thesis makes\nclaims about the properties of individuals (individual\nsupervenience theses), or is cast in terms of the character of whole\npossible worlds (global supervenience theses). The ethical\nproperties globally supervene on the base properties just in\ncase:", "\nGlobal\n\nEvery pair of possible worlds that has exactly the same world-wide\npattern of distribution of base properties, also has exactly the same\nworld-wide pattern of distribution of ethical properties (cf. the\nentry on\n supervenience).\n ", "\nIndividual supervenience theses are so-called because they explicitly\nstate patterns of instantiation of properties by individuals\n(rather than across whole possible worlds). There are two prominent\nsorts of individual supervenience theses in the literature. The\nethical properties weakly supervene on the base properties\njust in case:", "\nWeak\n\nNecessarily, if anything x has some ethical property\nF, then there is at least one base property G such\nthat x has G, and everything that has G has\nF (cf. the entry on\n supervenience).\n ", "\nThe ethical properties strongly supervene on the base\nproperties just in case:", "\nStrong\n\nNecessarily, if anything x has some ethical property\nF, then there is at least one base property G such\nx has G, and necessarily everything\nthat has G has F (cf. the entry on\n supervenience).\n ", "\nThe crucial difference between Strong and Weak supervenience is the\nsecond necessity operator in Strong. An example will make the\ndifference here vivid: weak ethical supervenience is compatible with\nit being a brute fact that there are both “utilitarian”\npossible worlds where rightness covaries uniformly with happiness\nmaximization, and “Kantian” possible worlds, where\nrightness covaries uniformly with satisfying the categorical\nimperative. By contrast, strong supervenience denies this\npossibility.", "\nIt is generally agreed that strong supervenience entails global\nsupervenience and weak supervenience; there is considerable\ncontroversy about whether global supervenience entails strong\nsupervenience (see §4.3 of the entry on\n supervenience).", "\nConsider another important individual ethical supervenience relation,\ninspired by Brian McLaughlin (1995, 24) but stated less\ntechnically:", "\nStrong Intuitive\n\nIf two possible entities are alike in all base respects, they are\nalike in all ethical respects.\n", "\nIf we interpret ‘possible’ here as representing\nmetaphysical modality, both McLaughlin and Jaegwon Kim (1993, 81) note\nthat the Strong and Strong Intuitive supervenience relations are\nequivalent. However,\n Section 2\n below will show that if we reinterpret the modalities involved, these\ntheses will no longer be equivalent." ], "subsection_title": "1.2 The structure of ethical supervenience" }, { "content": [ "\nSo far this entry has talked freely of necessity, possibility, and\npossible worlds. However, one can use such talk to discuss importantly\ndifferent modal standards: for example, philosophers talk of\nlogical necessity, conceptual necessity,\nmetaphysical necessity, nomic necessity, and\nnormative necessity. The aim of this section is to briefly\norient readers to each of these notions. To begin, consider some\nexamples:", "\nOn one traditional gloss, a sentence is logically necessary\nif it would remain true given any uniform and grammatically legitimate\nreinterpretation of the non-logical expressions of that sentence.\nSentence (1) is a promising example: the only non-logical word in (1)\nis ‘bachelor’, and any uniform and grammatically\nappropriate interpretation of ‘bachelor’ in (1) will\nresult in a true sentence. (For more on logical truths, see the entry\non\n logical truth.\n Section 1.1 of that entry discusses the alleged modal force of\nlogical truths.)", "\nBy contrast, (2) is not a logical truth: one could easily hold fixed\nits logical structure, but vary the meaning of ‘bachelor’\nor ‘unmarried’ and thereby produce a false sentence.\nHowever, (2) is a promising candidate to be conceptually necessary. On\none gloss, a sentence is conceptually necessary (or\n“analytically true”) if it is true solely in virtue of the\nmeanings or concepts involved in the sentence. Sentence (2) is a\ntraditional example. If ‘bachelor’ means unmarried\nmale, then the meaning of the sentence suffices to explain why it\nis true. (The notion of analyticity is famously controversial; for\ndiscussion, see the entry on the\n analytic-synthetic distinction.)", "\nTwo notes are relevant here. First, some philosophers will talk of\n‘logical’ necessity or supervenience as a way of\ndiscussing what this entry is calling conceptual necessity or\nsupervenience. Here, as elsewhere, it is important to keep track of\nwhat exactly an author intends to express by their terms. Second, some\nproponents of analytic truth will nonetheless reject the idea of a\ndistinct conceptual modality (e.g. Jackson 1998, Ch. 3). Such\nphilosophers can, however, capture importantly related phenomena by\ndiscussing modal claims formulated in terms of sentences and their\nintensions.", "\nNext consider (3): this does not seem to be true simply because of the\nconcepts it expresses. Rather, if it is true, it seems to reflect an\nimportant law of nature: a deep and non-accidental pattern in our\nuniverse. Some philosophers think that such laws underwrite a\ndistinctive sort of modality: a proposition is nomically\nnecessary just in case its falsity is incompatible with the laws\nof nature. On this view, (3) is nomically necessarily true, because it\nfollows from the laws governing the speed of light.", "\nNow consider (4). It is commonly thought that (4) is necessarily true.\nFor example: a substance composed overwhelmingly of atoms that do not\ncontain 79 protons in their nuclei could not be gold. But (4) does not\non its face look like a conceptual truth: it was a substantive\ndiscovery that there were protons at all, let alone how many protons\nan atom of gold characteristically possesses. Further (4) does not\nseem like it reflects a law of nature in the way that (3) does:\nrather, (4) seems to follow immediately from facts about what it is to\nbe gold. Examples like (4) thus purport to give us an initial grasp on\nmetaphysical modality as distinct from the other modalities considered\nthus far.", "\nStill more controversial is the notion of normative necessity\n(Fine2002, Rosen 2020). One way of understanding this idea appeals to\nan analogy with nomic modality. We can think of nomically necessary\nfacts as those which follow from facts about the laws of nature. For\nexample, the nomic impossibility of something traveling faster than\nlight is a direct consequence of it being a law of nature that that\nnothing can travel faster than light. Someone might similarly claim\nthat there are fundamental normative laws or principles.\nSuppose that (5) stated one of those laws. Then the normative\nimpossibility of a state’s being good just because it is painful\ncould be understood as expressing a consequence of that underlying\nnormative law.", "\nThere is enormous controversy about each of these alleged varieties of\nmodality. For each of logical, conceptual, nomic, metaphysical and\nnormative flavors of modality, some philosophers have raised important\nchallenges to whether that flavor of modality is well-regimented,\ntheoretically useful, or genuinely distinct from others on the list.\nThis entry will not enter seriously into those debates. (For\ndiscussion of some of the issues, see the entry on\n varieties of modality.)\n If we instead provisionally assume that each of these notions is\nlegitimate, this will put us in a position to ask (in\n Section 2,\n below): what is the modal strength of the supervenience thesis that\nwe should accept?" ], "subsection_title": "1.3 The modal strength of ethical supervenience" }, { "content": [ "\nThe ethical supervenience theses discussed thus far are\nontological: they propose various covariance relationships\nbetween ethical properties and certain other properties. However,\nJames Klagge (1988) has helpfully regimented an important alternative\nway of understanding ethical supervenience. Call two circumstances\nthat a thinker believes to be identical in all base respects\napparently base-identical. Now consider the following\nclaim:", "\nAscriptive\n\nAnyone who treats apparently base-identical circumstances as ethically\ndifferent from each other thereby makes a mistake.\n", "\nUnlike the supervenience theses encountered so far, Ascriptive is\nfundamentally a claim about ethical judgments: it is a claim\nthat someone who makes a certain pair of such judgments thereby makes\na mistake. Klagge usefully dubs claims like this ascriptive\nsupervenience theses.", "\nA fully informative ascriptive supervenience thesis would explain how\nwe should understand the mistake claimed by Ascriptive. There\nare several possibilities, of which four are worth emphasizing. The\nclaimed mistake could be alethic, consisting in having made\nat least one judgment with a false content. Or it might be\nepistemic: consisting in making at least one epistemically\nunjustified judgment. It could be conceptual, consisting in\njudging in a way that is inconsistent with the meanings of ethical\nwords. Finally, it might be characterized as ethical,\nconsisting in making a judgment in a way that is vicious or ethically\nobjectionable. (Note that the relevant judgment might be mistaken in\nmore than one of these ways.)", "\nBecause ascriptive supervenience theses are about judgments rather\nthan relations between classes of properties, they are quite different\nfrom the ontological supervenience theses we have considered thus far.\nOne way to bring this out is to notice that one could potentially\naccept Ascriptive without thereby having any views about whether there\nare ethical properties. On the other hand, there are interesting\nconnections between certain ascriptive and ontological supervenience\ntheses. For example, anyone who accepts Strong Intuitive seems to be\ncommitted to a version of Ascriptive, with an alethic gloss on\n‘mistake’.", "\nThis entry began with the suggestion that it is plausible that the\nethical supervenes. This section has aimed to clarify some of our\noptions for understanding that idea. The various interpretive options\nwe have explored together suggest a dizzying space of possible ethical\nsupervenience theses. This in turn raises a pressing question: which\nof these theses (if any) best articulate the plausibility and\nsignificance that philosophers have often taken ethical supervenience\nto have? One thing that might help to answer this question is to\nconsider the arguments that we can give for supervenience: these\narguments might favor some of these theses over others." ], "subsection_title": "1.4 Ontological and ascriptive supervenience" } ] }, { "main_content": [ "\nIt is common for philosophers to endorse ethical supervenience without\nmuch argument (an important exception is Smith 2004; for critical\ndiscussion of a variety of the arguments that have been offered, see\nRoberts 2018, 10–18). Part of the reason for this is that\nethical supervenience is taken to be both obvious and uncontroversial.\n(Rosen 2020 calls it “The least controversial thesis in\nmetaethics”.) Further, ethical supervenience is often claimed or\nassumed to be an obvious conceptual truth, doubts about which are\nsupposed to reveal conceptual incompetence. The discussion just\ncompleted, however, suggests reason to worry about this assumption:\nthere is not one ethical supervenience thesis but instead a complex\nvariety of such theses. It is far from clear that we should accept all\nof these theses, and a substantive question how to assess each of\nthem. Given that supervenience claims are modal claims, those seeking\nto evaluate supervenience claims might begin by considering the\ngeneral question of how we can know modal facts (see the entry\n modality-epistemology/).", "\nThis section sets aside this broad question. Instead, it begins by\nsetting out a general strategy for arguing for ethical supervenience.\nIt then explores the implications of that strategy for the\ncontroversies introduced in the previous section.", "\nThe general argumentative strategy has two elements. The first element\ndefends ethical supervenience as a plausible generalization from\ncases. Thus, consider our orienting case of the embezzling bank\nmanager. This case provides us with a specific ethical\nsupervenience thesis: it suggests that the ethical quality of the\nmanager’s action cannot vary without something else varying as\nwell (compare Horgan and Timmons 1992, 226 on specific\nsupervenience facts). Next, notice that there is nothing special\nin this respect about the bank manager case: we can identify specific\nsupervenience facts about anything from genocide to insulting your\nneighbor’s hat. Each such fact is constituted by an interesting\nnecessary connection between ethical properties and some base\nproperties. It is theoretically unattractive to rest satisfied with a\nlong list of such necessary connections. Instead, we should look for a\nsingle thesis that unifies all of these specific theses into a single\npattern. This pattern can be captured by a general ethical\nsupervenience thesis such as Initial (compare McPherson 2012,\n211).", "\nThe second element of the general strategy for arguing for ethical\nsupervenience emphasizes the independent credibility of such a general\nsupervenience thesis. This element takes inspiration from a comment by\nHenry Sidgwick:", "\nIn the variety of coexistent physical facts we find an accidental or\narbitrary element in which we have to acquiesce…. But within\nthe range of our cognitions of right and wrong, it will be generally\nagreed that we cannot admit a similar unexplained variation. (1907,\n209)\n", "\nIt is plausible to interpret Sidgwick as suggesting that although we\nseek explanatory power when we develop our account of the physical\nworld, we need to be prepared to admit brute contingency: the\npossibility that our best theories or explanations include claims like\n“and these just happened to be the initial conditions”, or\n(to be anachronistic) “it is a brute fact that the quantum wave\nfunction collapsed this way”. By contrast, we cannot\nadmit the analogous idea that it is a brute contingent fact that a\ncertain ethical property just happens to covary with the base\nproperties that are instantiated around here. Because of their modal\nscope, ethical supervenience theses reflect this ban on brute ethical\ncontingency (compare also Shafer-Landau 2003, 78; Smith 2004,\n225).", "\nThe two parts of the strategy complement each other: The first part of\nthe strategy defends general ethical supervenience on the basis of\nunification, which is a familiar and domain-general theoretical\nvirtue. The second part of the strategy suggests that we have further\nreasons to accept such a general thesis that stem from a feature of\nour understanding of the ethical domain specifically.", "\nWhile Initial is a general supervenience thesis, it is silent on many\nof the issues broached in\n Section 1.\n The next task is thus to extend the strategy just introduced to\ndiscuss those issues. Before doing so, it is important to emphasize\nthat many of the options considered in that section are\ncompatible: for example, supervenience on the natural\nproperties entails supervenience on all of the properties. Because of\nthis, an argument for the former thesis is not an argument against the\nlatter thesis. Because stronger ethical supervenience theses are\npotentially both more illuminating and more dialectically significant,\nthis section will focus on examining competing cases concerning what\nthe strongest well-supported ethical supervenience thesis\nis.", "\nThe general strategy just canvassed has two stages: the first stage\ncarefully examines cases, and the second appeals to our more general\nunderstanding of the ethical. Both parts of the strategy can be useful\nin addressing the question of what the ethical supervenes on. For\nexample,\n Section 1.1\n appealed to possible cases involving supernatural beings as part of\nan argument against the idea that the ethical supervenes on the\nnatural. In terms of the first part of the strategy, this suggests\nthat once we make salient the possibility of supernatural beings,\nethical supervenience theses that posit a naturalistic base become\nmore doubtful. In terms of the second part of the strategy, the same\ncases fit nicely with the Sidgwickian thesis: if an ethical claim were\ntrue in part because of some supernatural truth, it would thereby not\nbe brutely true. As noted in\n Section 1.1,\n characterizing what the ethical supervenes on is an open challenge.\nThis merely illustrates how the strategy can be applied to make\nprogress on that challenge.", "\nThe general strategy can also be applied to the structural question:\nfor example,\n Section 1.2\n noted that weak supervenience is compatible with the idea that a\nutilitarian ethical principle is a fundamental truth in some possible\nworlds, but is false in others. Strong ethical supervenience, by\ncontrast, is incompatible with this idea. Many philosophers believe\nthat the fundamental ethical principles could not vary contingently in\nthis way, because this would again threaten to entail that some\nfundamental ethical truths are brute contingencies. If correct, this\nsupports the idea that ethical supervenience is a strong supervenience\nthesis. On the other hand, assessing whether ethical supervenience is\nstrong or global (or both) might require adjudicating live\nmetaphysical controversies concerning the relationship between strong\nand global supervenience (for discussion of these controversies, see\nsection 4.3.1 of the entry on\n supervenience).", "\nWhat about the modality of ethical supervenience? One might\nthink of this question as seeking to clarify what sort of\nnon-contingency the Sidgwickian commitment requires. If we distinguish\nlogical from conceptual necessity, it is easy to see that the\nlogical supervenience of the ethical is a non-starter. The\ntruth of ‘pain is bad’, e.g., is not secured simply by the\nlogical vocabulary and the syntax of the sentence, in the way that the\ntruth of ‘all bachelors are bachelors’ seemingly is.", "\nThe most common view in the literature is that the supervenience of\nthe ethical is a conceptual truth. Here we cannot simply adapt the\ngeneral strategy used so far, since neither the cases nor the\ninference to the best explanation from those cases seems to settle the\nmatter. Consider three reasons to think that ethical supervenience is\na conceptual truth.", "\nFirst, to adapt R. M. Hare’s canonical example (1952,\n§5.2), if I mentioned to you that one possible act was right, and\nanother wrong, despite these acts being exactly alike in all other\nrespects, your initial reaction would be puzzlement, and if I\npersisted in my view upon interrogation, you might start to worry that\nI was simply confused or misusing words. Second, the crucial cases\nused to support supervenience—like the embezzling banker\ncase—seem to involve conceivability reasoning: we are\nasked to consider two circumstances that are identical in all base\nrespects, and notice that we cannot make sense of the idea that they\ndiffer in ethical respects. Some philosophers find it natural to think\nthat conceivability reasoning first and foremost reveals facts about\nconceptual possibility and necessity. This can be bolstered by a third\n(much more controversial) thought. Conceivability reasoning appears to\nbe a priori. But if such reasoning fundamentally concerned the world\nrather than our concepts, then we would seemingly have a priori access\nto substantive facts about the world, which many philosophers have\nfound deeply mysterious.", "\nEach of the sorts of reasons just offered is controversial. Consider\nthree examples of this controversy. First, it is controversial whether\nthe sorts of puzzlement reactions identified by Hare must signal\nconceptual confusion or misuse (Kramer 2009, Harrison 2013). For\nexample, perhaps we take ethical supervenience claims to be so obvious\nthat when someone appears to deny them, we are inclined to treat\nconceptual confusion or difference as a charitable hypothesis. One\npotential piece of evidence for this is that when denial of ethical\nsupervenience is based upon reasoned arguments, such as those\nmentioned in\n Section 5\n below, a diagnosis of conceptual confusion or difference arguably\nbecome less plausible diagnosis.", "\nSecond, philosophers unafraid of the ‘synthetic a priori’\ncan reject the inference from conceivability reasoning to conceptual\nstatus. It is notable here that a great deal of work in contemporary\nmetaphysics appeals to something like conceivability reasoning to\nargue directly for claims about the nature of reality. Third, the very\nnotion of conceptual truth is hotly contested: many philosophers have\nbecome convinced that there is no notion of conceptual truth that is\nboth coherent and philosophically interesting (for discussion, see the\nentry on the\n analytic-synthetic distinction).", "\nSet aside these challenges for the moment, and consider how we should\ninterpret the idea that ethical supervenience is a conceptual truth.\nWe saw above that there is some support for thinking that ethical\nsupervenience is a strong supervenience thesis. But combining this\nidea with the idea that the modality of supervenience is conceptual\nleads to complications. To see the issue, recall the schema for Strong\nSupervenience:", "\nStrong\n\nNecessarily, if anything x has some ethical property\nF, then there is at least one base property G such\nthat x has G, and necessarily everything\nthat has G has F.\n", "\nIf we interpret the claim that ethical supervenience is conceptual by\nreplacing ‘Necessarily’ in the schema with ‘it is a\nconceptual truth that’. The result is:", "\nStrong Conceptual\n\nIt is a conceptual truth that if anything x has some\nethical property F, then there is some base property\nG such that x has G, and it is a\nconceptual truth that everything that has G also has\nF.\n", "\nOne central problem with Strong Conceptual is that it claims that for\nevery instantiated ethical property, there is a base property such\nthat: it is a conceptual truth that anything that has this base\nproperty also has the ethical property. And this consequence will seem\ndefensible only on certain very controversial views about ethics and\nconceptual analysis.", "\nThe implausibility of Strong Conceptual may explain why two of the\nmost influential philosophers who discussed supervenience in ethics\n—R. M. Hare (1984, 4) and Simon Blackburn (cf. 1985, 134, and\nthe contrast between ‘supervenience’ and\n‘necessity’ in 1984, 183–4.)—seemed to accept\nsomething like weak but not strong conceptual supervenience of the\nethical.", "\nHowever, as noted above, it appears that we have reason to accept\nsomething stronger than weak ethical supervenience (Shoemaker 1987,\n440–1; for dissent see Miller 2017). It is thus worth\nconsidering alternatives that capture that strength without succumbing\nto the difficulties facing Strong Conceptual. One way to avoid the\nproblem is to interpret the first necessity operator in Strong as\nconceptual, while leaving the second operator as metaphysical:", "\nStrong Mixed\n\nIt is a conceptual truth that if anything x has some ethical\nproperty F, then there is some base property G such that\nx has G, and it is metaphysically necessary\nthat everything that has G also has F (compare\nDreier 1992, 15).\n", "\nThis avoids the implausible implications that Strong Conceptual has:\nStrong Mixed says only that it is a conceptual truth that a certain\nbase property (we may not know which) covaries with each ethical\nproperty.", "\nNote that Strong Mixed is only one possible mixed-modality\nsupervenience thesis: one could reinterpret either necessity operator,\nto produce one of a wide variety of possible mixed ethical\nsupervenience theses. For example, the second necessity operator could\nbe interpreted as normative (rather than metaphysical) necessity. Such\nmixed modality theses have not yet been seriously explored.", "\nAnother option is to offer a conceptual version of the Strong\nIntuitive supervenience thesis mentioned in\n Section 1.2:", "\nIntuitive Conceptual\n\nIf two conceptually possible entities are alike in all base respects,\nthey are alike in all ethical respects.\n", "\nBecause it does not posit known relations between specific ethical and\nbase properties, Intuitive Conceptual does not face the difficulties\nof Strong Conceptual. Intuitive Conceptual also has an advantage over\nStrong Mixed: the latter commits one to metaphysical as well as\nconceptual modality. Intuitive Conceptual is a plausible option for\nphilosophers who take there to be a stronger alternative to weak\nethical supervenience, but who are suspicious of the notion of\nmetaphysical modality.", "\nAmong philosophers who reject the idea that ethical supervenience is a\nconceptual truth, many will insist that the supervenience of the\nethical is at least metaphysically necessary. Most such philosophers\nappear happy to accept the strong metaphysical supervenience of the\nethical. Such philosophers might defend the metaphysical supervenience\nof the ethical by applying the general strategy suggested at the\nbeginning of this section, while rejecting the case for thinking this\nstrategy has specifically conceptual implications. Other philosophers\nwill reject the idea that we should begin with the sorts of judgments\nabout cases that drove the general strategy. They can instead argue\nthat the metaphysical supervenience of the ethical is supported as an\nabstract consequence of the best overall empirical theory concerning\nethical facts (e.g. Sturgeon 2009, 61).", "\nOther philosophers reject the conceptual and metaphysical\nsupervenience of the ethical, but claim that the ethical supervenes\nnomically or normatively. In general, such supervenience theses are\ntoo weak to support the sorts of arguments from ethical supervenience\nthat philosophers have made. Because of this, arguments for these\ntheses will be discussed in\n Section 5.4,\n which concerns doubts about ethical supervenience.", "\nFinally, how should we decide between ontological and ascriptive\nsupervenience theses? Proponents of ascriptive supervenience take on\nthe obligation of making precise the sort of mistake that\n‘supervenience-violators’ are allegedly making, and\ndefending the idea that this is a mistake. The most prominent approach\ntakes the mistake to be conceptual, which involves commitments similar\nto those taken on by defenders of the conceptual supervenience theses\njust discussed.", "\nOne reason to focus on ascriptive supervenience theses is that some\nphilosophers deny that our ethical thought and talk commits us to the\nexistence of ethical facts and properties. Such philosophers can still\ngrant that if we interpret supervenience in an ascriptive way, it\nprovides important insights into ethics. Further, philosophers who\naccept that there are ethical facts and properties can also accept\nascriptive supervenience theses about ethical thought. Indeed, if we\nunderstand Ascriptive as a conceptual claim, then together with\nrealism it could provide the basis for accepting a conceptual-strength\nethical supervenience thesis. This means that ascriptive ethical\nsupervenience theses have the potential to be a point of significant\ncommon ground between philosophers with widely differing views about\nthe nature of ethical thought and talk. And this might make them\nespecially dialectically powerful in arguments that appeal to ethical\nsupervenience." ], "section_title": "2. Arguments for Ethical Supervenience", "subsections": [] }, { "main_content": [ "\nThis section examines arguments in and about ethics that philosophers\nhave made which appeal centrally to ethical supervenience as a\npremise. The bulk of the section discusses the most influential\nsupervenience arguments in ethics, which have concerned realism and\nreduction, before considering the significance of ethical\nsupervenience for the epistemology of ethics, and for debates about\nthe existence of ethical principles." ], "section_title": "3. Arguments from Ethical Supervenience", "subsections": [ { "content": [ "\nThe earliest influential discussions of what we now call supervenience\nin ethics focused on its significance for substantive ethical\ninvestigation. Henry Sidgwick draws from it what he takes to be a\n“practical rule of some value” for such investigation\n(1907, 208–9). And G. E. Moore (1922) used the idea as part of\nhis attempt to explain the idea of intrinsic value. Given that Moore\nand Sidgwick were both ethical realists, it is perhaps striking that\nthe most influential philosophical use of ethical supervenience has\nbeen in arguments against ethical realism.", "\nIn his argument for error theory, J. L. Mackie briefly claims that\nsupervenience makes trouble for the realist. His quick argument can\nusefully serve as a prelude to the more detailed discussion to come.\nMackie suggests that we think that actions have their ethical\nproperties because they have some natural features. For\nexample, we think a certain action wrong because it is cruel. He\ndenies that this ‘because’ references a conceptual\nentailment, and thinks this raises two questions: (1) what sort of\nrelation is the connection being referred to? And (2) how do\nwe come to know that actions stand in this relation? (1977, 41). As it\nstands, Mackie’s questions serve more as a research agenda than\nan argument (for important recent discussion, see Olson 2014,\n§5.1). It appears plausible that realists should aim to have\nsomething illuminating to say both about the nature of the relation\nbetween the ethical and base properties, and a credible epistemology\nfor how we come to know such relations. But Mackie’s questions\ndo not yet constitute an argument that realists cannot achieve these\naims.", "\nSimon Blackburn developed a more substantial supervenience argument\nagainst realism. The details of Blackburn’s various\npresentations of his argument (1971, 1984, and 1985) are complex and\nraise difficult interpretive questions; the reconstruction that\nfollows is a rather free interpretation of Blackburn’s (1984,\n183–4; for sympathetic discussion, see Mabrito 2005 and Mitchell\n2017). The argument starts with two claims:", "\nNow consider an act of happiness-maximizing promise-breaking. It\nfollows from (2) that is conceptually possible that the world is\nbase-identical to the actual world, and this act is wrong, but it is\nalso conceptually possible that the world is base-identical to the\nactual world, and this act is not wrong. But from (1), we can notice\nthat it is not conceptually possible that there are two\nbase-identical acts, one of which is wrong and one of which is\nnot.", "\nThis combination is supposed to be difficult for the realist to\nexplain. For (2) seems to show that there is no conceptual link\nbetween ethical concepts like ‘wrong’ and any one of our\nnaturalistic concepts. And if ethical concepts function to pick out\nproperties (as the realist claims), then given this conceptual\nseparation, it seems that we should be able to identify conceptual\npossibilities by arbitrarily “mixing and matching”\ndistributions of naturalistic and ethical properties. Ethical\nsupervenience precisely functions to limit such mixing and\nmatching.", "\nConsider four possible ways that the realist might reply. First, the\nrealist could seek to debunk the challenge. For example, she might do\nthis by denying that the ethical supervenes with conceptual necessity\n(see\n the previous section\n for discussion). Or she might reject the supervenience of the ethical\non the natural (see\n Section 1.1),\n and challenge Blackburn to identify a supervenience base for which\nthe argument remains potent.", "\nSecond, the realist might seek to explain the pattern of individual\nconceptual possibility without conceptual co-possibility. For example,\nif it were a conceptual truth that ethical properties were natural\nproperties, then this would explain the pattern of knowledge suggested\nhere (Dreier 1992, 20). An analogy may help to make this vivid: it\nmight be a conceptual truth that physical properties are natural\nproperties (compare Kim 2011). But which total naturalistic patterns\nin the world the physical properties covary with is arguably an\nempirical question. One might take these examples to illustrate a\ngeneral reply: the pattern is not puzzling, because it simply reflects\nthe limitation of our conceptually-based insight into reality\n(Shafer-Landau 2003, 86).", "\nThird, some realists are prepared to claim more ambitiously that we\ncan give a conceptual analysis of rightness in base terms\n(e.g. Jackson 1998, Ch. 5). Such philosophers can thereby deny (2),\ncutting the argument off at the knees. (Dreier 1992, 17–18\nsuggests that Blackburn’s argument simply begs the question\nagainst this sort of reductive realist.) Such realists take on the\nburden of rejecting the most famous argument in metaethics: G. E.\nMoore’s “open question argument” (1903, Ch. 1).\nHowever, it is a hotly contested question what—if\nany—probative value this argument has (for discussion, see\nsection 2 of the entry on\n moral non-naturalism).", "\nA fourth reply would be to shrug off the alleged explanatory\nchallenge. However allegedly puzzling the combination of the features\ndescribed by (1) and (2) are, they are consistent features of a\nconcept. This means that we could choose to introduce a concept that\nexemplified those features. It might thus be suggested that\nBlackburn’s argument shows only that we have chosen to do so\nwith our ethical concepts (compare Olson 2014, 89–90). One might\nreply to this last point that it is precisely this choice that needs\nto be explained. Blackburn argues that the non-cognitivist has a\nsmooth functionalist explanation for why our ethical thought and talk\nincludes the ban on mixed worlds (see\n Section 3.3\n below for discussion), while for the realist, this might just be an\nunexplained peculiarity of our choice of concepts." ], "subsection_title": "3.1 Arguments against realism" }, { "content": [ "\nAs was just noted, a certain kind of reductive naturalist seems to\nhave an easy reply to Blackburn’s argument. In light of this, it\nis perhaps unsurprising that several philosophers have argued that\nethical supervenience theses support reductionist forms of ethical\nrealism against non-reductive forms. Consider a few important variants\nof such arguments.", "\nThe first is a simplified version of arguments due to Frank Jackson\n(1998, Ch. 5; see also related arguments by Brown 2011 and Streumer\n2017, Ch.s 2–3). The argument has two steps. The first step is an\nargument that if the ethical properties strongly (or globally)\nmetaphysically supervene on the base properties, then there is no\nmetaphysically possible ethical difference between states that does\nnot have a correlated base difference between the same states. If we\nmake some liberal assumptions about property types, this entails in\nturn that there is a base property that is necessarily coextensive\nwith every ethical property.", "\nThe second step of the argument is the claim that necessarily\ncoextensive properties are identical. Brown offers a nice motivation\nfor this thesis: we should commit ourselves to the existence of a\nproperty only insofar as it can do explanatory work, and the only way\nfor a property to do explanatory work is for it to distinguish\nmetaphysical possibilities (2011, 213). If we assume that identity is\nsufficient for reduction, these two steps together entail the\nreduction of the ethical.", "\nWhile both steps of the argument are controversial, the second stage\nhas come in for especially heavy fire. (For a careful discussion of\nthe dialectic, see Suikkanen 2010; for an ingenious argument against\nJackson that identity with descriptive properties is\ncompatible with ethical non-naturalism, see Dunaway 2017). One\nimportant general basis for doubt is that many contemporary\nphilosophers question whether modality constitutes the fundamental\nexplanatory currency of metaphysics, as Jackson and Brown seem to\npresuppose (for an especially influential challenge see Fine 1994, for\nan especially radical challenge, see Sider 2011, Ch. 12).", "\nThe argument for reduction from metaphysical supervenience can,\nhowever, be prosecuted within frameworks that reject Jackson’s\nand Brown’s core assumptions. Consider two examples. First, one\nmight deny that necessary coextension entails identity, but\nnonetheless argue that the best explanation of ethical supervenience\nis a grounding relation that suffices to ensure that ethical\nproperties are identical to some of the base properties (Bader 2017).\nSecond, you might deny that reduction requires identity. Of course,\nidentifying non-obvious identities is a powerful model of reduction.\nFor example, a standard way of characterizing the physicalistic\nreduction of heat is that the heat in a volume of gas is\nidentical to the mean molecular kinetic energy of that volume\nof gas, which is a physical property. However, there is no consensus\nconcerning how to understand reduction as a metaphysical relation (for\na taste of the controversy, see McPherson 2015, §3, and the entry\non\n scientific reduction\n and the discussion of reduction in the entry on\n David Lewis).", "\nThe core idea at stake in debates over reduction is that commitment to\nthe existence of the reduced properties should constitute no\nontological commitment “over and above” commitment to the\nreducing properties. Some philosophers have sought to spell out this\nidea by appealing to essence rather than to identity.\nConsider an essentialist account of reduction (cf. Rosen 2017b, 163),\non which the A properties reduce to the B-properties\njust in case:", "\n\n\n(i) it is necessary and sufficient for each A property to be\ninstantiated that some B property is instantiated; and\n\n\n(ii) these modal facts follow from the essences of the\nA-properties.\n", "\nThe idea is that if what it is to be each A property entails\nthat the A-properties are uniquely realized by the B-properties, this\namounts to a kind of reducibility of the A-properties. Consider an\nexample: one might take oneself to have offered a reduction of the\nnumber one, in claiming that: what it is to be the number one\nis just to be the successor of zero. One important contrast with the\nidentity conception is that on the essentialist conception, successful\nreductions reveal metaphysical structure. Thus, one might say in our\nexample that the number one is ‘built out of’ the number\nzero and the successor function.", "\nOn an influential essentialist account of metaphysical\nmodality, all necessities are to be explained by facts about the\nessences of things. Ralph Wedgwood (2007) and Gideon Rosen (2020)\nargue that on this sort of view, the strong metaphysical supervenience\nof the ethical would entail that the ethical possibilities are fully\nexplained by the essences of the base entities.", "\nInterestingly, both Rosen and Wedgwood reject this reductive\nconclusion. Wedgwood argues that some necessary truths (including\nethical supervenience theses) can be explained by certain contingent\ntruths, together with facts about essences, and that this sort of\nexplanation does not have reductive implications (2007, §9.3; for\ncritical discussion of this response, see McPherson 2009, Sec 3, and\nespecially Schmitt and Schroeder 2011). Rosen responds by rejecting\nthe strong metaphysical supervenience of the ethical (see\n Section 5.3\n below)." ], "subsection_title": "3.2 Arguments against non-reductive realism" }, { "content": [ "\nAs\n Section 3.1\n explained, supervenience arguments were initially used by Mackie and\nBlackburn to raise doubts about ethical realism. Indeed, it has been\nwidely assumed that the realist faces a challenge here that the\nanti-realist does not. The issues here are complicated, and it will be\nhelpful to consider common varieties of ethical anti-realism\nseparately.", "\nFirst, consider ethical nihilism, the thesis that there are\nno ethical properties. The ethical nihilist might seem to have an easy\ntime explaining the metaphysical supervenience of the ethical: if\nthere are no ethical properties, there are, trivially, no ethical\ndifferences. And if there are no ethical differences, there are no\nethical differences without base differences.", "\nThis line of reasoning is too quick as it stands. Supervenience is a\nmodal claim, so contingent ethical nihilism—the thesis\nthat there are no actually instantiated ethical\nproperties—cannot explain ethical supervenience. Indeed, as\nChristian Coons (2011) has shown, it is possible to use supervenience\nto construct an interesting argument against contingent\nnihilism. A crucial question here is: what is the modality of the\nsupervenience thesis to be accounted for? If the supervenience thesis\nwe need to explain is conceptual, then even the truth of\nnon-contingent nihilism—the thesis that it is\nmetaphysically impossible for ethical properties to be\ninstantiated—would not do the relevant explanatory work. Only\nthe thesis that the instantiation of ethical properties is\nconceptually impossible would suffice. (Note that the\nnihilist might be able to adapt one of the realist replies to\nBlackburn discussed in\n Section 3.1,\n but in this case it would not be easier for the nihilist to\nexplain supervenience, than it is for the realist who adopts the same\nreply.)", "\nThe nihilist imagined above does not question the assumption that\nordinary ethical thought and talk commits us to ontological claims.\nOther ethical anti-realists, however, will deny this assumption (for\ndiscussion, see the entries on\n moral anti-realism\n and\n moral cognitivism vs. non-cognitivism).\n Consider two examples of such views.", "\nFirst, hermeneutic fictionalists about ethical thought and\ntalk argue that such thought and talk is to be understood as a form of\npretense or fictional discourse (see Kalderon 2005 for discussion and\ndefense). It will be natural for the hermeneutic fictionalist to\nreject ordinary ethical supervenience claims as misleading. However,\nthey will presumably still need to account for the considerations that\nlead other philosophers to accept ethical supervenience claims. The\nissues concerning ethical fictionalism and supervenience are\ncomparatively unexplored; see (Nolan, Restall, and West 2005,\n325–327) for important preliminary discussion.", "\nSecond (and much more influentially) some non-cognitivists\nabout ethical thought and talk deny that our ethical claims express\nbeliefs about the ethical nature of the world, suggesting instead that\nthey express desire-like mental states. Such a view may make\nontological supervenience claims about ethics appear misleading at\nbest. More interesting is the question of what non-cognitivists can\nsay about the sort of ascriptive supervenience thesis discussed in\n Section 1.4:", "\nAscriptive\n\nAnyone who treats apparently base-identical circumstances as ethically\ndifferent from each other thereby makes a mistake.\n", "\nThis thesis is an alleged correctness constraint on ethical thought\nand talk. Prominent philosophers in the non-cognitivist tradition\n(broadly understood) have characteristically claimed that their views\nenabled them to explain theses like Ascriptive.", "\nConsider a representative sample of these explanations. R. M. Hare\nclaims that ascriptive supervenience holds because a significant part\nof the function of moralizing is to teach others our ethical\nstandards, and the only way to do that is to get our audience to see\nthe recognizable pattern that we are prescribing that they follow\n(1952, 134). According to Simon Blackburn, the presumption of\nascriptive supervenience is required by the idea that our ethical\nattitudes are supposed to be practical guides to decision-making\n(1984, 186). According to Allan Gibbard (2003, Ch. 5), ascriptive\nsupervenience for ethical thought is explained by a consistency norm\non planning states.", "\nCritics of non-cognitivism (e.g. Zangwill 1997, 110–11; Sturgeon\n2009) have challenged the rationales offered by Hare and Blackburn.\nSuppose that we grant that consistency is useful, given the various\nfunctions of ethical discourse. It is unclear why this usefulness\nshould force on us a conceptual truth about moral discourse.\nFurther, it is arguable that all that is required for these practical\npurposes is consistency within worlds that are very similar to the\nactual world. So the idea that such consistency is required over every\npossible world (as seems to be the case for ethical supervenience)\nseems like considerably more than the practical considerations\nrequire. Gibbard’s rationale has faced related criticism: why\nmust planners be committed to consistency in the sweeping way that\nGibbard envisions (Chrisman 2005, 411–12; Sturgeon 2009,\n84–87)? If these critics are right, it is not clear that the\nnon-cognitivist has an especially compelling explanation of ethical\nsupervenience. And if they do not, this will complicate their efforts\nto claim that explaining ethical supervenience is a dialectical\nadvantage against cognitivism. It is also worth bearing in mind that\nthe details of which ethical supervenience thesis we need to explain\ncan affect how promising the non-cognitivist explanations will be. For\nan important illustration of this point, see (Atiq 2019).", "\nA further complication arises from the fact that leading contemporary\nheirs of non-cognitivism (such as Blackburn and Gibbard) have\nabandoned anti-realism. Instead, they have adopted what Simon\nBlackburn (e.g. 1993) has dubbed the ‘quasi-realist’\nprogram. This involves the claim that one can, while beginning with\nthe non-cognitivist’s framework, “earn the right” to\nrealist-sounding claims about ethical truth and objectivity (for\nfurther discussion see the section on noncognitivism in the entry on\n moral anti-realism).", "\nNow consider an ontological supervenience claim: that there can be no\ndifference in ethical properties without a difference in base\nproperties. The quasi-realist program can seem to commit the\nquasi-realist to accepting this claim. Dreier (2015) argues that this\nleads to a further challenge to the non-cognitivist: even if\nshe can explain ascriptive supervenience, it is not clear that she can\nexplain ontological supervenience. If this is the case, the most\ninfluential contemporary non-cognitivists may find that supervenience\nis a dialectical burden rather than benefit." ], "subsection_title": "3.3 Supervenience and anti-realism" }, { "content": [ "\nSo far, this entry has focused on the significance of supervenience\nfor claims about the nature of ethical thought, talk, and metaphysics.\nHowever, influential early discussions of this sort of thesis seemed\nto have something else in mind. For example,\n Section 2\n above quoted an evocative passage from Henry Sidgwick. But\nSidgwick’s point was not to argue about the metaphysics of\nethics. Rather, he was proposing a supervenience-like idea as an\nepistemological corrective to ad hoc special pleading in one’s\nethical reasoning (1907, 209).", "\nThe mere fact of supervenience could not play this sort of role: after\nall, the supervenience of the ethical is compatible with the idea that\neveryone ought always to do what I want them to do. However, Sidgwick\npoints to an important idea: that we expect there to be a rational\nexplanation for any ethical fact. One ambitious way of developing this\nidea has been suggested by Nick Zangwill (2006). According to\nZangwill, a central conceptual constraint on ethical reasoning is the\n“because constraint”: when we judge something to be wrong\n(or to have another ethical property), we are committed to its having\nthis property because it has some other property. Zangwill\nclaims that this principle “either is, or explains”\nethical supervenience (2006, 273). And Zangwill goes on to argue that\nthis constraint has striking epistemological implications: he claims\nthat it entails that our only epistemic access to facts about\nthe distribution of ethical properties is by knowing about the\ndistribution of base properties, and knowing ethical principles that\nlink the presence of base properties to ethical properties. He then\nargues that our knowledge of these ethical principles could itself\nonly be a priori (2006, 276). If Zangwill is right about this, then\nthe a priori character of moral epistemology can be derived from\nclaims about the supervenience of the ethical.", "\nOne worry about this argument is that it might overgeneralize. The\n“because” structure seems to be shared by other normative\ndomains: it would be very odd to claim that a particular chess move\nwas winning, or that a particular action was illegal, without being\ncommitted to their being some general explanation in terms of the\nrules of chess, or the relevant laws, that explains this particular\nfact. But our knowledge of the law and the rules of chess is\nempirical. So one might wonder what precisely prevents our knowledge\nof ethical principles being empirical as well." ], "subsection_title": "3.4 Supervenience and moral epistemology" }, { "content": [ "\nOne traditional assumption about ethics is that our ethical\nobligations can be expressed by general ethical principles. This\nassumption has recently been challenged by ethical\nparticularists, who claim that our ethical reasons and\nobligations cannot be codified into principles. Supervenience might\nseem to be relevant to this debate. For as\n Section 3.2\n above showed, some philosophers argue that the strong metaphysical\nsupervenience of the ethical entails that for every ethical property,\nthere will be a base property that is necessarily coextensive with it.\nFocusing on wrongness, this in turn has the apparent consequence that\nthere is a base property B such that:", "\nEntailment\n\nIt is metaphysically necessary that an action is wrong just in case\nthat action is B.\n", "\nOne might think that Entailment just is the schema for an ethical\nprinciple concerning wrongness: for example, if we substitute\n‘fails to maximize happiness’ for ‘is\nB’ we seem to get a clear statement of a utilitarian\nethical principle. And this in turn might seem to cast doubt on the\ncoherence of particularism.", "\nThis reasoning, however, is too quick. To see this, note that\nsupervenience itself in no way guarantees that B will be some\nelegant base property like failing to maximize happiness. B\nmight instead be enormously complicated: at the limit, supervenience\nis compatible with B simply being a disjunction of an\ninfinitely long list of complete base specifications of various\npossible worlds. Call an instance of Entailment with such a base a\ngruesome entailment. It is not clear that such entailments\nconstitute principles that are incompatible with particularism. One\nreason to think that they do not is that genuine ethical principles\narguably have explanatory power. Margaret Little argues that\nthe “radical over-specificity” of gruesome entailments\nrenders them non-explanatory, and hence inapt to be principles (2000,\n286). Another reason to doubt that gruesome entailments are principles\nis that we ordinarily assume that ethical principles would be usable\nby agents (Dancy 2004, 87–8), but a gruesome\n“principle” is clearly not. (For a relevant argument that\nthe true instance of Entailment could not be gruesome,\nbecause it would need to be learnable by ordinary speakers, see\nJackson, Pettit, and Smith 2000)." ], "subsection_title": "3.5 Supervenience and the existence of ethical principles" } ] }, { "main_content": [ "\nThe Blackburn-inspired argument against ethical realism relies\ncrucially on the assumption that ethical supervenience is a conceptual\ntruth. For thesis (2) was crucial to that argument:", "\n2. No specific naturalistic description of an action\nconceptually entails an ethical description….\n", "\nWhile many find (2) plausible, fewer would be prepared to accept a\npurely metaphysical version of this thesis, such as:", "\n2*. No base way a world could be metaphysically\nnecessitates that world being a certain ethical way.\n", "\nThis is precisely because thesis (2*) is inconsistent with the strong\nmetaphysical supervenience of the ethical, which very many\nphilosophers accept. This means that a purely metaphysical variant of\nBlackburn’s argument will not be plausible.", "\nThis does not mean, however, that treating ethical supervenience as a\nnon-conceptual truth renders it dialectically inert. This section\nconsiders the significance of metaphysical supervenience for ethical\nrealism: does it pose a challenge to ethical realism? If so, how can\nwe best understand this challenge? And what resources do different\nsorts of ethical realist have to meet the challenge?", "\nTo focus our discussion, assume this metaphysical variant of Strong\nIntuitive (cf. Rosen 2020):", "\nIntuitive Metaphysical\n\nIf two metaphysically possible entities are alike in all base\nrespects, they are alike in all ethical respects.\n", "\nIntuitive Metaphysical might pose a challenge to the ethical realist\nin light of one of at least two background ideas. First, some\nphilosophers have argued that there are no necessary connections\nbetween “distinct existences,” a claim that is sometimes\ncalled Hume’s dictum. If Hume’s dictum is correct, then\nthe ethical realist will be committed to the ethical not being\ndistinct in the relevant sense from what it supervenes on. The\nmetaphysical use of Hume’s dictum faces at least two formidable\nchallenges. The first is to clarify the dictum in such a way that it\nis both interesting and a plausible candidate for truth. To see this,\nnote that many non-identical properties are necessarily connected: for\nexample, a surface’s being scarlet entails that it is red, but\nbeing scarlet is not identical to being red. Red and scarlet, then,\nmust not count as distinct in the sense relevant to a plausible form\nof the dictum. This raises the question: what does distinctness amount\nto? If we use necessary connection as a criterion, then Hume’s\ndictum turns out to be a trivial way of tracking this way of using the\nword ‘distinct’. Second, Hume’s dictum is usually\ndefended on directly intuitive grounds. This raises a deep\nmethodological question: if we notice a conflict between Hume’s\ndictum and another intuitively plausible claim, why should we retain\nHume’s dictum and jettison the other claim? (For helpful\ndiscussion of Hume’s Dictum, see Wilson 2010).", "\nConsider a second way of developing a challenge to the ethical\nrealist, inspired by the Sidgwickian motivation for accepting ethical\nsupervenience, introduced in\n Section 2.\n According to this motivation, we should accept an ethical\nsupervenience thesis because doing so rules out the implausible\nhypothesis of brute ethical contingency. Intuitive Metaphysical\nclearly satisfies this motivation: it permits no brutely contingent\nethical variation. However, suppose that it was not possible to\nexplain why the ethical properties supervene on the base properties.\nThen the very thesis that we used to explain why there was no brute\nethical contingency would turn out to be something arguably even more\npeculiar. It would be a metaphysically necessary connection that\nnonetheless has what Sidgwick might call an “arbitrary element\nin which we have to acquiesce;” in a slogan: a brute\nnecessity.", "\nA natural way of thinking about the significance of brute necessity\nbegins with the assumption that we are entitled to a default\ncombinatorial assumption about modality: that for any pair of\nproperties F and G, it is possible that there is an\nx that is both F and G, that x is\nonly one and not the other, and that there is an x that is\nneither F nor G. The next step is to suggest that\nthis default assumption can be defeated. Consider red and scarlet: on\none view, to be red just is to be scarlet or crimson or cherry red\nor… The thesis that this is what it is to be red, if true,\nwould provide a straightforward explanation of why the combinatorial\nassumption is defeated here: it is not possible for something to be\nscarlet but not red precisely because of what it is to be red. Where\nwe take there to be no such explanation however, we should be loathe\nto accept an alleged necessary connection (cf. McPherson (2012); for a\nsimilar idea in a different context, compare Levine and Trogdon 2009).\nCall this constraint on our metaphysical theorizing\nanti-brutalism.", "\nBoth Hume’s dictum and anti-brutalism put us in a position to\npose a conditional challenge to the ethical realist. If the realist\nthinks that the ethical properties are distinct from the base\nproperties, they must reject either metaphysical supervenience or\nHume’s dictum. And if they think the supervenience of the\nethical is a brute necessity, they need to explain why such brutalism\nis not objectionable. Different variants of ethical realism have\ndifferent resources available to address this challenge. The remainder\nof this section examines some of these resources." ], "section_title": "4. Metaphysical Supervenience and Ethical Realism", "subsections": [ { "content": [ "\nAs\n Section 3.2\n explained, some philosophers have argued that the supervenience of\nthe ethical entails that the ethical can be reduced. These arguments\nare quite controversial, but it is perhaps less controversial that a\nsuccessful reduction of the ethical properties would suffice to\nexplain the metaphysical supervenience of the ethical.", "\nConsider first a reductive account that identifies the ethical\nproperties with some natural or supernatural property. Assuming that\nnatural and supernatural properties are among the base properties, the\nsupervenience of rightness on the base properties would be easily\nexplained on this view: because rightness is identical to a base\nproperty, on this view, there clearly cannot be a difference in\nrightness without some difference in base properties.", "\nIf essentialist explanations are legitimate, essentialist reduction\nagain appears to be a straightforward way of explaining the\nsupervenience of the ethical. Part of the idea of essence is that\nnecessarily, nothing can survive the loss of one of its essential\nproperties. So if rightness had an essentialist real definition purely\nin terms of base properties, then it would be clear why there could be\nno difference in rightness without a difference in base\nproperties.", "\nIn light of this, neither Hume’s dictum nor anti-brutalism\nappear to cast doubt on either sort of reductive theory, for both\ntheories are able to explain supervenience, and hence avoid commitment\nto a brute necessary connection between the ethical properties and the\nbase properties.", "\nTerence Horgan and Mark Timmons claim that even if the ethical realist\nendorses reduction, they face a further explanatory burden before they\ncan fully explain supervenience: “Even if goodness, for\ninstance, is identical to some specific natural property, there\nremains the task of explaining why this natural property,\nrather than any other one(s), counts as the correct referent of the\nterm ‘goodness’” (1992, 230; emphasis in original).\nThis is a fair explanatory demand, if we interpret it as the familiar\nchallenge to provide a plausible theory of reference for ethical terms\n(a demand that Horgan and Timmons have pressed incisively). However\nthis challenge does not appear to have anything distinctive to do with\nsupervenience. Either the reductive naturalistic realist can explain\nthe reference of ‘wrong,’ in which case she can also\nexplain supervenience, or she cannot explain the reference of\n‘wrong,’ in which case her view is implausible for reasons\nthat have nothing to do with supervenience." ], "subsection_title": "4.1 Reductive explanations of ethical supervenience" }, { "content": [ "\nOne influential account of metaphysical structure, especially in the\nphilosophy of mind, has been functionalism. Here is a simplified toy\nexample of a functional analysis: any system that takes some money as\nan input, and reliably produces a candy as an output, thereby counts\nas a candy machine. On this account, the kind candy machine\nis individuated by input-output relations. A functional kind\nis any kind that can be individuated in this way. Because functional\nkinds are not individuated by the nature of the stuff that realizes\nthe functional relations, they are often claimed to be\nparadigmatically friendly to multiple realization. Thus,\ngiven my characterization of candy machines, such a machine could be\nrealized by a structure composed of metal or of plastic or perhaps\neven of spooky supernatural stuff. In light of this possibility of\nmultiple realization, the relationship of functionalism to reduction\nis controversial: many philosophers have taken multiple realizability\nto constitute a barrier to reduction, but others disagree. (See the\nentries on\n functionalism\n and\n multiple realization\n for useful discussion).", "\nNow consider a version of ethical realism that takes ethical\nproperties to be functional properties. Such a view, like the\nreductionist view, appears well-placed to explain the metaphysical\nsupervenience of the ethical. This is because functional properties\nnecessarily covary with the class of properties that are their\npossible realizers. If, for example, every complex property that could\nrealize a candy machine is a natural property, then there could be no\n“candy machine difference” without a naturalistic\ndifference. Similarly, if ethical properties are functional properties\nthat could only be realized by certain of the base properties, then\nthe supervenience of the ethical on the base properties would be\nsmoothly explained." ], "subsection_title": "4.2 Functionalist explanations of ethical supervenience" }, { "content": [ "\nThe strategies for explaining ethical supervenience discussed in the\npreceding two sections are useful to reductionist and\nfunctionalist ethical realists. However, many contemporary\nethical realists reject both functionalism and reductionism about\nethical properties. Most strikingly, several contemporary ethical\nrealists are non-naturalists, claiming that the ethical\nproperties are a distinct and irreducible class of properties (see the\nentry on\n moral non-naturalism\n for discussion). Several philosophers have argued that ethical\nsupervenience poses a distinctive problem for the non-naturalist\n(Dreier 1992, 2019 ; Ridge 2007; McPherson 2012; Väyrynen 2017).\nSo it is worth asking what metaphysical resources non-naturalists\nmight have for explaining the supervenience of the ethical.", "\nA salient place to begin is with the grounding relation. As\nwas noted in\n Section 1,\n grounding has recently been theorized as an asymmetrical explanatory\nmetaphysical relationship (For an introduction to grounding, see the\nentry on\n metaphysical grounding;\n for a useful discussion of relevant issues in the context of ethics,\nsee Väyrynen 2013a). It is thus natural to ask whether the\nnon-naturalist could explain the supervenience of the ethical on the\nbase properties by appealing to the fact that: certain facts about the\ninstantiation of the base properties fully ground all facts\nabout the instantiation of the ethical properties.", "\nA natural question at this point concerns why such a\ngrounding relationship holds. An influential answer is that all\ngrounding facts are themselves explained in essentialist terms (Fine\n1994, Rosen 2010). As\n Section 4.1\n suggested, these essentialist explanations can appear to have\nreductionist implications. If so, essentialist explanations are no\nhelp to the non-naturalist.", "\nStephanie Leary has offered an ingenious proposal within the\nessentialist framework: she posits a class of “hybrid”\nproperties, whose essences entail (i) that they are instantiated just\nin case certain base properties are instantiated, and (ii) that\nethical properties are instantiated whenever they are instantiated,\nand argues that these relations do not suffice for essentialist\nreduction of the ethical (Leary 2017; for critical discussion see\nFaraci 2017 and Toppinen 2018).", "\nA recently influential alternative to the essentialist account of\ngrounding proposes that we can explain the grounding of the ethical in\nterms of metaphysical laws. Here is the basic idea. One class\nof ethical facts are facts which state the instantiation of some\nethical property. An example of such an ethical instantiation fact\nwould be: Alice’s current state is intrinsically bad.\nOne explanation of why the ethical supervenes is that such facts are\nalways grounded in certain base facts, such as: Alice is currently\nin pain. The proponent of law-mediated ethical grounding denies\nthat the latter base fact provides a complete grounding explanation\nfor the former ethical fact. Rather, a complete grounding explanation\nwill take this form:", "\n\n\nIt requires a base fact (e.g. Alice is currently in pain) and\nan ethical law (e.g. Pain grounds badness), in order to fully\nground any ethical instantiation fact (e.g. Alice’s current\nstate is intrinsically bad).\n", "\nSuppose that, necessarily, every possible ethical instantiation fact\nis grounded by the combination of a base fact and an ethical law, as\nin this example. Then, (i) this would provide a complete explanation\nfor supervenience: this grounding structure would explain why the\ninstantiation of ethical properties must covary with thew\ninstantiation of base properties. And (ii) this might look like a\npromising explanation on behalf of the non-naturalist, since the\nethical laws could be metaphysically fundamental ethical entities. If\nethical laws such as the one mentioned here are metaphysically\nfundamental, then one might think that this would secure\nnon-naturalism (For this reason, Gideon Rosen calls such\nmetaphysically fundamental laws ‘Moorean connections’\n(2010, §13).", "\nThe appeal to fundamental laws may seem to raise the same concerns\nthat a brute supervenience relation did, however: Why is there a\nmetaphysical law linking these distinct properties? The contrast with\nessentialist explanations is striking: in the latter case, facts about\nthe natures of the related properties explain the links between them.\nHowever, some have argued that metaphysical grounding relations are\neither commonly, or even universally, law-mediated (e.g. Kment 2014,\n§6.2.3; Wilsch 2015). For a taste of the currently flowering\nliterature on the explanatory role of ethical laws or principles, see\n(Eliot 2014; Scanlon 2014, Ch. 2; Schroeder 2014; Skarsaune 2015;\n§7; Rosen 2017a; 2017c; Berker forthcoming; and Morton\nforthcoming).", "\nThis brief sketch of possible types of metaphysical explanations of\nsupervenience barely scratches the surface. Among the many other\noptions, replies grounded in appeals to tropes or universals have\ngarnered explicit attention (Ridge 2007, Suikkanen 2010). As with the\nappeal to grounding, a central question about such strategies is\nwhether they constitute genuine explanatory progress, or whether they\nsimply explain one necessity by appealing to some further brute\nnecessity." ], "subsection_title": "4.3 Grounding explanations of ethical supervenience" }, { "content": [ "\nThis and the next subsection consider attempts to explain the\nmetaphysical supervenience of the ethical by appealing to conceptual\nor ethical premises.", "\nThe first such strategy appeals to analytic or conceptual truths.\nSuppose that an ethical realist accepts the popular view that ethical\nsupervenience is an analytic truth. She might put her view this\nway:", "\nAnalytic\n\nIt is an analytic truth that: if two metaphysically possible entities\nare alike in all base respects, they are alike in all ethical\nrespects.\n", "\nThe core idea is that the truth of Analytic explains the truth of the\nsupervenience thesis that it embeds (Intuitive Metaphysical). On this\naccount, the ethical and the base properties covary because it is\ndefinitional of ‘ethical’ that nothing could\ncount as an ethical property unless it covaried in this way. This\nstrategy claims to meet the bruteness challenge: the necessary\nconnection is explained by the way a property would have to be, in\norder to be what we talk about when we talk about ethical properties\n(cf. Stratton-Lake and Hooker 2006).", "\nConsider three brief worries about this strategy. The first is that on\nsome influential contemporary accounts of analyticity, analyticity\ndoes not guarantee truth. For example, one account of analyticity is\nthat for a sentence ‘S’ to be analytic in a language L is\nfor competence with L to dispose a speaker to accept ‘S’.\nAnd some philosophers (e.g. Eklund 2002) have argued that there are\ninconsistent sets of sentences that satisfy this condition. If this is\nright, Intuitive Metaphysical’s being analytic in\nEnglish would not guarantee its being true.", "\nThe second worry is broadly intuitive. Analytic alone does not appear\nto guarantee that the supervenience of the ethical follows\nfrom the other aspects of the nature of ethical properties. And this\nsuggests that, for all Analytic says, we can conceive of ethical*\nproperties, which have every feature characteristic of ethical\nproperties, except that they do not supervene. But this may lead us to\nwonder: why give the ethical properties the role in our lives that we\ndo, and ignore the ethical* properties, just because they do not\nsupervene? (For a related point, see the end of Mabrito 2005.)", "\nThe third worry is that even if the truth of Analytic entails the\ntruth of Intuitive Metaphysical, it nonetheless arguably does nothing\nto explain why the supervenience relationship holds. Consider\nan analogy: suppose that the infallible oracle tells you that a\ncertain ethical supervenience thesis holds. This testimony does\nnothing to explain why that supervenience thesis holds (compare\nMcPherson 2012, 221–222, and Dreier 2015, 2019). Like the\noracle’s testimony, one might think that learning the truth of\nAnalytic would simply reinforce our confidence in the very thesis\n(Intuitive Metaphysical) that we were hoping to explain.", "\nMy exposition of these three worries (like the rest of this entry thus\nfar) has followed the common practice of lumping together the notions\nof analytic truth and conceptual truth. Terence\nCuneo and Russ Shafer-Landau (2014) have argued that distinguishing\nthese two notions permits them to develop an attractive form of moral\nrealism, and also enables them to explain the supervenience of the\nmoral properties. They distinguish analytic and conceptual truth as\nfollows: for a sentence to be analytically true is for it to\nbe true in virtue of the meanings of the terms that constitute it. By\ncontrast, for a proposition to be a conceptual truth is for\nit to be true wholly in virtue of the essences of its constituent\nconcepts (ibid., 410–11). Concepts, in turn, are to be\nunderstood as abstract non-mental objects. One has a propositional\nthought in virtue of being appropriately related to some of these\nobjects.", "\nCuneo and Shafer-Landau then offer what they call a ‘reversal\nargument’, which entails that some conceptual truths about\nmorality are ‘fact-makers’: that is, some of the facts\nabout the distribution of moral properties are grounded in facts about\nmoral concepts (ibid., 418–421). This puts them in a position to\navoid the complaint that I just made about Analytic: on their view,\nconceptual truths really do metaphysically explain (some) of the\nrelations between the moral and the base properties. They then propose\nthat such connections quite generally explain the supervenience of the\nmoral.", "\nIt is worth emphasizing the commitments of this ingenious proposal.\nConsider one central issue. Cuneo and Shafer-Landau argue for the\nexistence of several substantive-seeming conceptual truths about\nmorality. As they admit, their view is quite heterodox in virtue of\nthis. However, they nowhere claim that all necessary moral\ntruths can be explained as conceptual truths. That, of course, would\nbe a much stronger claim, and much harder to motivate. However,\nIntuitive Metaphysical is a quite general modal covariance thesis, and\nin light of this, only the stronger claim would suffice to explain its\ntruth." ], "subsection_title": "4.4 Analytic and conceptual explanations of ethical supervenience" }, { "content": [ "\nSeveral philosophers have suggested that we can offer ethical\nexplanations of the supervenience relation (Kramer 2009, Ch. 10; Olson\n2014, §5.1, Scanlon 2014, 38ff; other philosophers, such as\nDworkin 1996 and Blackburn 1998, 311 also appear committed to this\nidea; for discussion see Tiefensee 2014). For example, one might think\nthat the dictum treat like cases alike! is an ethical\nrequirement of ethical reasoning. Or one might think that all ethical\ntruths are grounded in certain fundamental ethical truths that are\nrelational: for example, a fundamental truth might be that it is wrong\nto torture someone purely for fun. This truth states a relationship\nbetween ethical and non-ethical properties. If all ethical facts are\nexplained by such fundamental ethical truths, then these truths could\nseemingly explain why there are supervenience relations between\nethical and base properties.", "\nOne worry about this strategy is that one might take a mark of ethical\nrealism to be commitment to a truthmaker thesis, according to which\nethical truths are metaphysically explained by (or grounded in) the\npatterns of instantiation of ethical properties. The ethical\nexplanation strategy seems to invert this intuitive order of\nexplanation, by having the distribution of ethical properties\nexplained by ethical truths.", "\nSuppose that we rejected this idea in an especially radical way,\ninsisting instead on the reverse order of metaphysical explanation\neverywhere. The nature of every property, we might say, is wholly\ngrounded in some relevant subset of the true propositions. Provided\nthat we can recover the idea of metaphysical explanation within this\nframework, we will be able to isolate the set of propositions that\nstate metaphysically unexplained necessary connections. And it is\nnatural to think that the brute necessities worry could be expressed\nwithin this framework as objecting to accepting such propositions. The\nproblem is that fundamental normative principles, as invoked\nin the ‘ethical explanation’ strategy, would seem to be of\nexactly the objectionable sort." ], "subsection_title": "4.5 Ethical explanations of ethical supervenience" } ] }, { "main_content": [ "\nAs the preceding sections have shown, philosophers have tried to\nextract a number of striking conclusions using ethical supervenience\nas a premise. Part of the motivation for these attempts is that\nethical supervenience is widely assumed to be a powerful dialectical\nweapon, such that if your view is incompatible with ethical\nsupervenience, it is in trouble. This section considers challenges to\nthis status." ], "section_title": "5. Arguments against Ethical Supervenience, or its Significance", "subsections": [ { "content": [ "\nIt is now common to distinguish thick ethical concepts—like\ncourage—from thin ethical concepts—like\nought or good (for an introduction to thick ethical\nconcepts, see Roberts 2017). Courage seems like an ethical concept: we\nexpect each other to treat courage as a virtue and not a vice.\nHowever, competent use of thick ethical concepts seems to require\nrecognition that only certain sorts of grounds make an ascription of\nsuch a concept apt. To adapt Monty Python’s example, it seems\nconceptually inapt to say that Sir Robin was courageous in\nlight of running away from battle, even if we think that is what he\nought to have done.", "\nJonathan Dancy (1995, 278–9) and Debbie Roberts (2018) have\nsuggested that attention to thick ethical concepts casts doubt on\nethical supervenience. The core idea is this: it is true that there\nare no thin ethical differences between otherwise identical\ncircumstances. However, it is suggested that sometimes the thin\nethical properties of an action or event are best explained by citing\nthick ethical properties. And it is claimed that it is not at all\nclear that these thick ethical properties can always be explained in\npurely base terms (see especially Roberts 2017a).", "\nA natural objection to this strategy is to point out that the\nsupervenience of the thick on the base properties is, if anything, far\nmore plausible than the supervenience of the thin. For example, it is\nvery hard to believe that two possible worlds could be wholly\nbase-identical, but be such that Doris’s action is brave in the\nfirst world, but not brave in the second." ], "subsection_title": "5.1 Arguments against supervenience from thick ethical concepts" }, { "content": [ "\n\n Section 2\n noted that there are few extended defenses of ethical supervenience.\nThis might suggest that the evidence for the supervenience is\noverwhelming. However, it might instead be a sign that supervenience\nis a dogma, accepted without adequate critical examination. This\nsection briefly explains two challenges to the epistemic credentials\nof ethical supervenience.", "\nJoseph Raz briefly suggests that the supervenience of the ethical does\nnot purport to explain much. And he suggests that this explanatory\npoverty gives us reason to doubt whether the ethical supervenes.\nAccording to Raz, ethical supervenience neither provides more specific\ntheses that allow us to concretely explain the ethical features of\nreality, nor guarantees that we can find such explanatory theses\n(2000, 54–5). If we assume that we should accept only those\ntheoretical claims that do substantial explanatory work, then this\ncasts doubt on ethical supervenience as a theoretical claim.", "\n\n Section 2\n suggested a different explanatory case for supervenience than the one\nRaz considers: general ethical supervenience theses serve to explain\nthe host of specific ethical supervenience facts that we notice. These\nfacts are perhaps not themselves explanatory. But they may seem\ndifficult to intelligibly deny, at least pending a developed moral\nepistemology that might adjudicate their epistemic credentials.", "\nAlison Hills (2009) argues that we can undermine the case for ethical\nsupervenience by granting that in many cases ethical difference\nwithout naturalistic difference seems inconceivable, and\narguing that we should not take inconceivability here to be a good\nguide to impossibility. She suggests that the appearance of\ninconceivability may be grounded in our unwillingness to engage in\ncertain distasteful imaginative exercises.", "\nHills bolsters this case by arguing that if we consider a\ncontroversial and low-stakes case—say, whether a certain lie\nmade with benevolent motives is permissible—we are able to\nconceive of such a lie being either permissible or impermissible. But,\nshe suggests, if we can conceive of it as being permissible, and as\nbeing impermissible, we have shown that we are able to conceive of two\nethically inconsistent possible worlds. Further, this low-stakes case\nis easier to conceive of than the possibility of Hitler being a moral\nparagon, and Hills suggests that this supports the idea that\nconceivability is grounded in our willingness to imagine certain\npossibilities, for we presumably have a stronger desire to avoid\nimagining Hitler as a moral paragon than we do to avoid imagining the\nlower-stakes case." ], "subsection_title": "5.2 Arguments against the epistemic credentials of ethical supervenience" }, { "content": [ "\n\n Section 1.3\n showed that one of the crucial choice-points in theorizing ethical\nsupervenience is the strength of the modality of the supervenience\nrelation (conceptual? metaphysical? etc.). And\n Section 3\n and\n Section 4\n showed that the claim that the ethical supervenes with conceptual or\nmetaphysical necessity is the starting point for several influential\narguments. Gideon Rosen’s (2020) develops a view of the modal\nstrength of ethical supervenience that is intended to be strong enough\nto accommodate the intuitive appearances, while weak enough to be\ndialectically inert.", "\nThe heart of Rosen’s challenge is an argument that we can\ncharacterize and clearly regiment a notion of normative\nnecessity, which falls short of metaphysical necessity (i.e. at least\nsome normative necessities are metaphysically contingent), while still\nbeing quite strong, in the sense that in any counterfactual where one\nconsiders how things would be if we altered some non-normative fact,\nwe hold fixed the normative necessities. Rosen proposes that normative\nnecessity is the appropriate modality for ethical supervenience. If he\nis correct about this, most of the arguments from supervenience\ndiscussed so far would fail, as they tend to require ethical\nsupervenience to have either metaphysical or conceptual strength.", "\nEven with this alternative clearly stated, the strong metaphysical\nsupervenience of the ethical may seem especially plausible. But with\nhis account of normative necessity in hand, Rosen can make two points:\n(i) when we consider possibilities that violate the strong\nmetaphysical supervenience of the ethical, we are considering very\ndistant possibilities, where our modal judgments may not be\nparticularly trustworthy, and (ii) our judgments of metaphysical\nimpossibility of these scenarios might be explained by implicit\nconfusion derived from the fact that while these scenarios may be\nmetaphysically possible, they are normatively impossible.", "\nBy rejecting strong metaphysical supervenience, Rosen must reject the\nSidgwickian explanatory idea suggested in\n Section 2:\n that ethical supervenience reflects a commitment to rejecting brute\nethical contingency. One worry about Rosen’s strategy is that by\nembracing such contingency one permits an especially objectionable\nform of moral luck (Dreier, 2019). On Rosen’s view, there may be\na world that is relevantly non-ethically identical to this one in\nwhich my counterpart is ethically quite different: in the\nextreme case, it raises the specter that the specific loving attitudes\nthat I bear towards my child might have been evil, or even\njust a matter of utter ethical indifference. But it is hard to believe\nthat I am lucky that the very attitudes that I possess count\nas commendable rather than awful. (See Lange 2018 for another\nimportant challenge to Rosen’s argument).", "\nAnandi Hattiangadi (2018) offers a conceivability argument against the\nidea that the ethical supervenes with conceptual or metaphysical\nnecessity. The core idea is this. Mutually inconsistent ethical\nprinciples each appear to be perfectly conceivable. And in general,\nconceivability is a good guide to possibility. But if utilitarianism\nand Kantianism, say, are both true in some possible world otherwise\nlike ours, then the supervenience of the ethical fails.", "\nOne worry for Hattiangadi’s argument is that there seems to be a\nstraightforward way to contextualize the relevant conceivability\njudgments. Consider an analogy. I cannot remember the atomic number of\nplutonium. So it is conceivable to me that plutonium atoms have any of\na fairly wide range of numbers of protons. But I do not think\nthat it is possible both that one plutonium atom has 100 protons, and\nthat some other possible plutonium atom has 110 protons. If any\nplutonium atom has 100 protons, they all do. (This stems from my\nempirically-derived belief that number of protons is essential to the\nnature of plutonium). Similarly, I can entertain the possibility that\nutilitarianism is true, or that it is false. But what is hard to wrap\none’s head around is the idea that there might be worlds just\nlike this one in all base respects, which vary with respect to whether\nutilitarianism is true." ], "subsection_title": "5.3 Arguments against the strong metaphysical supervenience of the ethical" } ] } ]

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M., 1952, The Language of Morals, Oxford: Oxford\nUniversity Press.", "–––, 1984, “Supervenience”,\nProceedings of the Aristotelian Society (Supplementary\nVolume), 58: 1–16.", "Harrison, Gerald, 2013, “The Moral Supervenience Thesis is\nnot a Conceptual Truth”, Analysis, 73:\n62–68.", "Hattiangadi, Anandi, 2018, “Moral Supervenience”,\nCanadian Journal of Philosophy, 48(3-4): 592–615.", "Hills, Alison, 2009, “Supervenience and Moral\nRealism”, in Heike Alexander and Leitgeb Hannes (eds.),\nReduction, Abstraction, and Analysis, Frankfurt: Ontos\nVerlag, pp. 163–178.", "Horgan, Terence, 1993, “From Supervenience to\nSuperdupervenience: Meeting the Demands of a Material World”,\nMind, 102: 555–86.", "–––, and Mark Timmons, 1992, “Troubles on\nMoral Twin Earth: Moral Queerness Revived”, Synthese,\n92(2): 221–260.", "Jackson, Frank, 1998, From Metaphysics to Ethics, Oxford:\nOxford University Press.", "–––, Philip Pettit, and Michael Smith, 2000,\n“Ethical Particularism and Patterns”, in Brad Hooker and\nMargaret Olivia Little (eds.), Moral Particularism, Oxford:\nOxford University Press, pp. 79–99.", "Kalderon, Mark, 2005, Moral Fictionalism, Oxford: Oxford\nUniversity Press.", "Kim, Jaegwon, 1993, Supervenience and Mind, Cambridge:\nCambridge University Press.", "–––, 2011, “From Naturalism to\nPhysicalism: Supervenience Redux”, Proceedings of the\nAmerican Philosophical Association, 85(2): 109–134.", "Klagge, James, 1984, “An Alleged Difficulty Concerning Moral\nProperties”, Mind, 93: 370–380.", "–––, 1988, “Supervenience: Ontological or\nAscriptive”, Australasian Journal of Philosophy, 66:\n461–470.", "Kment, Boris, 2014, Modality and Explanatory Reasoning,\nOxford: Oxford University Press.", "–––, 2015, “Modality, Metaphysics, and\nMethod”, in Christopher Daly (ed.), Palgrave Handbook of\nPhilosophical Methods, Palgrave, pp. 179–207.", "Kramer, Matthew, 2009, Moral Realism as a Moral Doctrine,\nOxford: Blackwell.", "Lange, Marc, 2018, “What Would Normative Necessity\nBe”, Journal of Philosophy, 115(4): 169–186.", "Leary, Stephanie, 2017, “Non-Naturalism and Normative\nNecessities”, in Russ Shafer-Landau (ed.), Oxford Studies in\nMetaethics (Volume 12), Oxford: Oxford University Press, pp.\n76–105.", "Levine, Joseph, and Kelly Trogdon, 2009, “The Modal Status\nof Materialism”, Philosophical Studies, 145:\n351–362.", "Little, Margaret Olivia, 2000, “Moral Generalities\nRevisited”, in Brad Hooker and Margaret Olivia Little (eds.),\nMoral Particularism, Oxford: Oxford University Press, pp.\n276–304.", "Mabrito, Robert, 2005, “Does Shafer-Landau have a Problem\nwith Supervenience?”, Philosophical Studies, 126:\n297–311.", "Mackie, J. L., 1977, Ethics: Inventing Right and Wrong,\nHarmondsworth: Penguin.", "McLaughlin, Brian, 1995, “Varieties of Supervenience”,\nin Elias Savellos and Umit Yalcin (eds.), Supervenience: New\nEssays, Cambridge: Cambridge University Press, pp.\n16–59.", "McPherson, Tristram, 2009, “Unnatural Normativity?”,\nPhilosophical Books, 50: 63–82.", "–––, 2012, “Ethical Non-Naturalism and the\nMetaphysics of Supervenience”, in Russ Shafer-Landau (ed.),\nOxford Studies in Metaethics (Volume 7), Oxford: Oxford\nUniversity Press, pp. 205–234.", "–––, 2015, “What is at Stake in Debates\namong Normative Realists?” Noûs, 49:\n123–146.", "Miller, Alexander, 2017, “Moral Supervenience: A Defence of\nBlackburn’s argument ”, Dialectica, 71:\n581–601.", "Mitchell, Cole, 2017, “Mixed-Up about Mixed Worlds?”,\nPhilosophical Studies, 174: 2903–2925.", "Moore, G. 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Unbelievable Errors, Oxford: Oxford\nUniversity Press.", "Sturgeon, Nicholas, 2009, “Doubts about the Supervenience of\nthe Evaluative”, in Russ Shafer-Landau (ed.), Oxford Studies\nin Metaethics (Volume 4), Oxford: Oxford University Press, pp.\n53–92.", "Suikkanen, Jussi, 2010, “Non-Naturalism: The Jackson\nChallenge”, in Russ Shafer-Landau (ed.), Oxford Studies in\nMetaethics (Volume 5), Oxford: Oxford University Press, pp.\n87–110.", "Tiefensee, Christine, 2014, “Expressivism,\nAnti-Archimedeanism, and Supervenience”, Res Publica,\n20: 163–181.", "Toppinen, Teemu, 2018, “Essentially Grounded Non-Naturalism\nand Normative Supervenience”, Topoi, 37:\n645–653.", "Väyrynen, Pekka, 2013a, “Grounding and Normative\nExplanation”, Proceedings of the Aristotelian Society\n(Supplementary Volume), 87(1): 155–178.", "–––, 2013b, The Lewd, the Rude, and the\nNasty, Oxford: Oxford University Press.", "–––, 2017, “The Supervenience Challenge to\nNon-naturalism”, in Tristram McPherson and David Plunkett\n(eds.), Routledge Handbook of Metaethics, New York:\nRoutledge, pp. 170–184.", "Wedgwood, Ralph, 2007, The Nature of Normativity, Oxford:\nOxford University Press.", "Wilsch, Tobias, 2015, “The Nomological Account of\nGround”, Philosophical Studies, 172(12):\n3293–3312.", "Zangwill, Nick, 1997, “Explaining Supervenience: Moral and\nMental”, Journal of Philosophical Research, 22:\n509–18.", "–––, 2006, “Moral Epistemology and the\nBecause Constraint”, in James Dreier (ed.), Contemporary\nDebates in Moral Theory, Oxford: Blackwell: pp.\n263–281." ]

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[ "\nIn 1933 the Polish logician Alfred Tarski published a paper in which\nhe discussed the criteria that a definition of ‘true\nsentence’ should meet, and gave examples of several such\ndefinitions for particular formal languages. In 1956 he and his\ncolleague Robert Vaught published a revision of one of the 1933 truth\ndefinitions, to serve as a truth definition for model-theoretic\nlanguages. This entry will simply review the definitions and make no\nattempt to explore the implications of Tarski’s work for\nsemantics (natural language or programming languages) or for the\nphilosophical study of truth. (For those implications, see the entries\non\n truth\n and\n Alfred Tarski.)" ]

[ { "content_title": "1. The 1933 programme and the semantic conception", "sub_toc": [ "1.1 Object language and metalanguage", "1.2 Formal correctness", "1.3 Material adequacy" ] }, { "content_title": "2. Some kinds of truth definition on the 1933 pattern", "sub_toc": [ "2.1 The standard truth definitions", "2.2 The truth definition by quantifier elimination" ] }, { "content_title": "3. The 1956 definition and its offspring", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nIn the late 1920s Alfred Tarski embarked on a project to give rigorous\ndefinitions for notions useful in scientific methodology. In 1933 he\npublished (in Polish) his analysis of the notion of a true sentence.\nThis long paper undertook two tasks: first to say what should count as\na satisfactory definition of ‘true sentence’ for a given\nformal language, and second to show that there do exist satisfactory\ndefinitions of ‘true sentence’ for a range of formal\nlanguages. We begin with the first task; Section 2 will consider the\nsecond.", "\nWe say that a language is fully interpreted if all its\nsentences have meanings that make them either true or false. All the\nlanguages that Tarski considered in the 1933 paper were fully\ninterpreted, with one exception described in Section 2.2 below. This\nwas the main difference between the 1933 definition and the later\nmodel-theoretic definition of 1956, which we shall examine in Section\n3.", "\nTarski described several conditions that a satisfactory definition of\ntruth should meet." ], "section_title": "1. The 1933 programme and the semantic conception", "subsections": [ { "content": [ "\nIf the language under discussion (the object language) is\n\\(L\\), then the definition should be given in another language known\nas the metalanguage, call it \\(M\\). The metalanguage should\ncontain a copy of the object language (so that anything one can say in\n\\(L\\) can be said in \\(M\\) too), and \\(M\\) should also be able to talk\nabout the sentences of \\(L\\) and their syntax. Finally Tarski allowed\n\\(M\\) to contain notions from set theory, and a 1-ary predicate symbol\nTrue with the intended reading ‘is a true sentence of\n\\(L\\)’. The main purpose of the metalanguage was to formalise\nwhat was being said about the object language, and so Tarski also\nrequired that the metalanguage should carry with it a set of axioms\nexpressing everything that one needs to assume for purposes of\ndefining and justifying the truth definition. The truth definition\nitself was to be a definition of True in terms of the other\nexpressions of the metalanguage. So the definition was to be in terms\nof syntax, set theory and the notions expressible in \\(L\\), but not\nsemantic notions like ‘denote’ or ‘mean’\n(unless the object language happened to contain these notions).", "\nTarski assumed, in the manner of his time, that the object language\n\\(L\\) and the metalanguage \\(M\\) would be languages of some kind of\nhigher order logic. Today it is more usual to take some kind of\ninformal set theory as one’s metalanguage; this would affect a\nfew details of Tarski’s paper but not its main thrust. Also\ntoday it is usual to define syntax in set-theoretic terms, so that for\nexample a string of letters becomes a sequence. In fact one must use a\nset-theoretic syntax if one wants to work with an object language that\nhas uncountably many symbols, as model theorists have done freely for\nover half a century now." ], "subsection_title": "1.1 Object language and metalanguage" }, { "content": [ "\nThe definition of True should be ‘formally\ncorrect’. This means that it should be a sentence of the\nform", "\nFor all \\(x\\), True\\((x)\\) if and only if \\(\\phi(x)\\), ", "\nwhere True never occurs in \\(\\phi\\); or failing this, that\nthe definition should be provably equivalent to a sentence of this\nform. The equivalence must be provable using axioms of the\nmetalanguage that don’t contain True. Definitions of\nthe kind displayed above are usually called explicit, though\nTarski in 1933 called them normal." ], "subsection_title": "1.2 Formal correctness" }, { "content": [ "\nThe definition should be ‘materially adequate’\n(trafny – a better translation would be\n‘accurate’). This means that the objects satisfying\n\\(\\phi\\) should be exactly the objects that we would intuitively count\nas being true sentences of \\(L\\), and that this fact should be\nprovable from the axioms of the metalanguage. At first sight this is a\nparadoxical requirement: if we can prove what Tarski asks for, just\nfrom the axioms of the metalanguage, then we must already have a\nmaterially adequate formalisation of ‘true sentence of\n\\(L\\)’ within the metalanguage, suggesting an infinite regress.\nIn fact Tarski escapes the paradox by using (in general) infinitely\nmany sentences of \\(M\\) to express truth, namely all the sentences of\nthe form", "\nwhenever \\(s\\) is the name of a sentence \\(S\\) of \\(L\\) and \\(\\psi\\)\nis the copy of \\(S\\) in the metalanguage. So the technical problem is\nto find a single formula \\(\\phi\\) that allows us to deduce all these\nsentences from the axioms of \\(M\\); this formula \\(\\phi\\) will serve\nto give the explicit definition of True.", "\nTarski’s own name for this criterion of material adequacy was\nConvention T. More generally his name for his approach to\ndefining truth, using this criterion, was the semantic conception\nof truth.", "\nAs Tarski himself emphasised, Convention \\(T\\) rapidly leads to the\nliar paradox if the language \\(L\\) has enough resources to talk about\nits own semantics. (See the entry on\n the revision theory of truth.)\n Tarski’s own conclusion was that a truth definition for a\nlanguage \\(L\\) has to be given in a metalanguage which is essentially\nstronger than \\(L\\).", "\nThere is a consequence for the foundations of mathematics. First-order\nZermelo-Fraenkel set theory is widely regarded as the standard of\nmathematical correctness, in the sense that a proof is correct if and\nonly if it can be formalised as a formal proof in set theory. We would\nlike to be able to give a truth definition for set theory; but by\nTarski’s result this truth definition can’t be given in\nset theory itself. The usual solution is to give the truth definition\ninformally in English. But there are a number of ways of giving\nlimited formal truth definitions for set theory. For example Azriel\nLevy showed that for every natural number \\(n\\) there is a\n\\(\\Sigma_n\\) formula that is satisfied by all and only the\nset-theoretic names of true \\(\\Sigma_n\\) sentences of set theory. The\ndefinition of \\(\\Sigma_n\\) is too technical to give here, but three\npoints are worth making. First, every sentence of set theory is\nprovably equivalent to a \\(\\Sigma_n\\) sentence for any large enough\n\\(n\\). Second, the class of \\(\\Sigma_n\\) formulas is closed under\nadding existential quantifiers at the beginning, but not under adding\nuniversal quantifiers. Third, the class is not closed under negation;\nthis is how Levy escapes Tarski’s paradox. (See the entry on\n set theory.)\n Essentially the same devices allow Jaakko Hintikka to give an\ninternal truth definition for his\n independence friendly logic;\n this logic shares the second and third properties of Levy’s\nclasses of formulas." ], "subsection_title": "1.3 Material adequacy" } ] }, { "main_content": [ "\nIn his 1933 paper Tarski went on to show that many fully interpreted\nformal languages do have a truth definition that satisfies his\nconditions. He gave four examples in that paper. One was a trivial\ndefinition for a finite language; it simply listed the finitely many\ntrue sentences. One was a definition by quantifier elimination; see\nSection 2.2 below. The remaining two, for different classes of\nlanguage, were examples of what people today think of as the standard\nTarski truth definition; they are forerunners of the 1956\nmodel-theoretic definition." ], "section_title": "2. Some kinds of truth definition on the 1933 pattern", "subsections": [ { "content": [ "\nThe two standard truth definitions are at first glance not definitions\nof truth at all, but definitions of a more complicated relation\ninvolving assignments \\(a\\) of objects to variables:", "\n(where the symbol ‘\\(F\\)’ is a placeholder for a name of a\nparticular formula of the object language). In fact satisfaction\nreduces to truth in this sense: \\(a\\) satisfies the formula \\(F\\) if\nand only if taking each free variable in \\(F\\) as a name of the object\nassigned to it by \\(a\\) makes the formula \\(F\\) into a true sentence.\nSo it follows that our intuitions about when a sentence is true can\nguide our intuitions about when an assignment satisfies a formula. But\nnone of this can enter into the formal definition of truth, because\n‘taking a variable as a name of an object’ is a semantic\nnotion, and Tarski’s truth definition has to be built only on\nnotions from syntax and set theory (together with those in the object\nlanguage); recall Section 1.1. In fact Tarski’s reduction goes\nin the other direction: if the formula \\(F\\) has no free variables,\nthen to say that \\(F\\) is true is to say that every assignment\nsatisfies it.", "\nThe reason why Tarski defines satisfaction directly, and then deduces\na definition of truth, is that satisfaction obeys recursive\nconditions in the following sense: if \\(F\\) is a compound\nformula, then to know which assignments satisfy \\(F\\), it’s\nenough to know which assignments satisfy the immediate constituents of\n\\(F\\). Here are two typical examples:", "\nWe have to use a different approach for atomic formulas. But for\nthese, at least assuming for simplicity that \\(L\\) has no function\nsymbols, we can use the metalanguage copies \\(\\#(R)\\) of the predicate\nsymbols \\(R\\) of the object language. Thus:", "\n(Warning: the expression \\(\\#\\) is in the metametalanguage, not in the\nmetalanguage \\(M\\). We may or may not be able to find a formula of\n\\(M\\) that expresses \\(\\#\\) for predicate symbols; it depends on\nexactly what the language \\(L\\) is.)", "\nSubject to the mild reservation in the next paragraph, Tarski’s\ndefinition of satisfaction is compositional, meaning that the\nclass of assignments which satisfy a compound formula \\(F\\) is\ndetermined solely by (1) the syntactic rule used to construct \\(F\\)\nfrom its immediate constituents and (2) the classes of assignments\nthat satisfy these immediate constituents. (This is sometimes phrased\nloosely as: satisfaction is defined recursively. But this formulation\nmisses the central point, that (1) and (2) don’t contain any\nsyntactic information about the immediate constituents.)\nCompositionality explains why Tarski switched from truth to\nsatisfaction. You can’t define whether ‘For all\n\\(x, G\\)’ is true in terms of whether \\(G\\) is true, because in\ngeneral \\(G\\) has a free variable \\(x\\) and so it isn’t either\ntrue or false.", "\nThe reservation is that Tarski’s definition of satisfaction in\nthe 1933 paper doesn’t in fact mention the class of assignments\nthat satisfy a formula \\(F\\). Instead, as we saw, he defines the\nrelation ‘\\(a\\) satisfies \\(F\\)’, which determines what\nthat class is. This is probably the main reason why some people\n(including Tarski himself in conversation, as reported by Barbara\nPartee) have preferred not to describe the 1933 definition as\ncompositional. But the class format, which is compositional on any\nreckoning, does appear in an early variant of the truth definition in\nTarski’s paper of 1931 on definable sets of real numbers. Tarski\nhad a good reason for preferring the format ‘\\(a\\) satisfies\n\\(F\\)’ in his 1933 paper, namely that it allowed him to reduce\nthe set-theoretic requirements of the truth definition. In sections 4\nand 5 of the 1933 paper he spelled out these requirements\ncarefully.", "\nThe name ‘compositional(ity)’ first appears in papers of\nPutnam in 1960 (published 1975) and Katz and Fodor in 1963 on natural\nlanguage semantics. In talking about compositionality, we have moved\nto thinking of Tarski’s definition as a semantics, i.e. a way of\nassigning ‘meanings’ to formulas. (Here we take the\nmeaning of a sentence to be its truth value.) Compositionality means\nessentially that the meanings assigned to formulas give at\nleast enough information to determine the truth values of\nsentences containing them. One can ask conversely whether\nTarski’s semantics provides only as much information as we\nneed about each formula, in order to reach the truth values of\nsentences. If the answer is yes, we say that the semantics is\nfully abstract (for truth). One can show fairly easily, for\nany of the standard languages of logic, that Tarski’s definition\nof satisfaction is in fact fully abstract.", "\nAs it stands, Tarski’s definition of satisfaction is not an\nexplicit definition, because satisfaction for one formula is defined\nin terms of satisfaction for other formulas. So to show that it is\nformally correct, we need a way of converting it to an explicit\ndefinition. One way to do this is as follows, using either higher\norder logic or set theory. Suppose we write \\(S\\) for a binary\nrelation between assignments and formulas. We say that \\(S\\) is a\nsatisfaction relation if for every formula \\(G, S\\) meets the\nconditions put for satisfaction of \\(G\\) by Tarski’s definition.\nFor example, if \\(G\\) is ‘\\(G_1\\) and \\(G_2\\)’,\n\\(S\\) should satisfy the following condition for every assignment\n\\(a\\):", "\nWe can define ‘satisfaction relation’ formally, using the\nrecursive clauses and the conditions for atomic formulas in\nTarski’s recursive definition. Now we prove, by induction on the\ncomplexity of formulas, that there is exactly one satisfaction\nrelation \\(S\\). (There are some technical subtleties, but it can be\ndone.) Finally we define", "\n\\(a\\) satisfies \\(F\\) if and only if: there is a satisfaction relation\n\\(S\\) such that \\(S(a,F)\\). ", "\nIt is then a technical exercise to show that this definition of\nsatisfaction is materially adequate. Actually one must first write out\nthe counterpart of Convention \\(T\\) for satisfaction of formulas, but\nI leave this to the reader." ], "subsection_title": "2.1 The standard truth definitions" }, { "content": [ "\nThe remaining truth definition in Tarski’s 1933 paper –\nthe third as they appear in the paper – is really a bundle of\nrelated truth definitions, all for the same object language \\(L\\) but\nin different interpretations. The quantifiers of \\(L\\) are assumed to\nrange over a particular class, call it \\(A\\); in fact they are second\norder quantifiers, so that really they range over the collection of\nsubclasses of \\(A\\). The class \\(A\\) is not named explicitly in the\nobject language, and thus one can give separate truth definitions for\ndifferent values of \\(A\\), as Tarski proceeds to do. So for this\nsection of the paper, Tarski allows one and the same sentence to be\ngiven different interpretations; this is the exception to the general\nclaim that his object language sentences are fully interpreted. But\nTarski stays on the straight and narrow: he talks about\n‘truth’ only in the special case where \\(A\\) is the class\nof all individuals. For other values of \\(A\\), he speaks not of\n‘truth’ but of ‘correctness in the domain\n\\(A\\)’.", "\nThese truth or correctness definitions don’t fall out of a\ndefinition of satisfaction. In fact they go by a much less direct\nroute, which Tarski describes as a ‘purely accidental’\npossibility that relies on the ‘specific peculiarities’ of\nthe particular object language. It may be helpful to give a few more\nof the technical details than Tarski does, in a more familiar notation\nthan Tarski’s, in order to show what is involved. Tarski refers\nhis readers to a paper of Thoralf Skolem in 1919 for the\ntechnicalities.", "\nOne can think of the language \\(L\\) as the first-order language with\npredicate symbols \\(\\subseteq\\) and =. The language is interpreted as\ntalking about the subclasses of the class \\(A\\). In this language we\ncan define:", "\nNow we aim to prove: ", "\nLemma. Every formula \\(F\\) of \\(L\\) is equivalent to (i.e. is\nsatisfied by exactly the same assignments as) some boolean combination\nof sentences of the form ‘There are exactly \\(k\\) elements in\n\\(A\\)’ and formulas of the form ‘There are exactly \\(k\\)\nelements that are in \\(v_1\\), not in \\(v_2\\), not in \\(v_3\\) and in\n\\(v_4\\)’ (or any other combination of this type, using only\nvariables free in \\(F)\\). ", "\nThe proof is by induction on the complexity of formulas. For atomic\nformulas it is easy. For boolean combinations of formulas it is easy,\nsince a boolean combination of boolean combinations is again a boolean\ncombination. For formulas beginning with \\(\\forall\\), we take the\nnegation. This leaves just one case that involves any work, namely the\ncase of a formula beginning with an existential quantifier. By\ninduction hypothesis we can replace the part after the quantifier by a\nboolean combination of formulas of the kinds stated. So a typical case\nmight be:", "\n\\(\\exists z\\) (there are exactly two elements that are in \\(z\\) and\n\\(x\\) and not in \\(y)\\). ", "\nThis holds if and only if there are at least two elements that are in\n\\(x\\) and not in \\(y\\). We can write this in turn as: The number of\nelements in \\(x\\) and not in \\(y\\) is not 0 and is not 1; which is a\nboolean combination of allowed formulas. The general proof is very\nsimilar but more complicated.", "\nWhen the lemma has been proved, we look at what it says about a\nsentence. Since the sentence has no free variables, the lemma tells us\nthat it is equivalent to a boolean combination of statements saying\nthat \\(A\\) has a given finite number of elements. So if we know how\nmany elements \\(A\\) has, we can immediately calculate whether the\nsentence is ‘correct in the domain \\(A\\)’.", "\nOne more step and we are home. As we prove the lemma, we should gather\nup any facts that can be stated in \\(L\\), are true in every domain,\nand are needed for proving the lemma. For example we shall almost\ncertainly need the sentence saying that \\(\\subseteq\\) is transitive.\nWrite \\(T\\) for the set of all these sentences. (In Tarski’s\npresentation \\(T\\) vanishes, since he is using higher order logic and\nthe required statements about classes become theorems of logic.) Thus\nwe reach, for example:", "\nTheorem. If the domain \\(A\\) is infinite, then a sentence\n\\(S\\) of the language \\(L\\) is correct in \\(A\\) if and only if \\(S\\)\nis deducible from \\(T\\) and the sentences saying that the number of\nelements of \\(A\\) is not any finite number. ", "\nThe class of all individuals is infinite (Tarski asserts), so\nthe theorem applies when \\(A\\) is this class. And in this case Tarski\nhas no inhibitions about saying not just ‘correct in\n\\(A\\)’ but ‘true’; so we have our truth\ndefinition.", "\nThe method we have described revolves almost entirely around removing\nexistential quantifiers from the beginnings of formulas; so it is\nknown as the method of quantifier elimination. It is not as\nfar as you might think from the two standard definitions. In all cases\nTarski assigns to each formula, by induction on the complexity of\nformulas, a description of the class of assignments that satisfy the\nformula. In the two previous truth definitions this class is described\ndirectly; in the quantifier elimination case it is described in terms\nof a boolean combination of formulas of a simple kind.", "\nAt around the same time as he was writing the 1933 paper, Tarski gave\na truth definition by quantifier elimination for the first-order\nlanguage of the field of real numbers. In his 1931 paper it appears\nonly as an interesting way of characterising the set of relations\ndefinable by formulas. Later he gave a fuller account, emphasising\nthat his method provided not just a truth definition but an algorithm\nfor determining which sentences about the real numbers are true and\nwhich are false." ], "subsection_title": "2.2 The truth definition by quantifier elimination" } ] }, { "main_content": [ "\nIn 1933 Tarski assumed that the formal languages that he was dealing\nwith had two kinds of symbol (apart from punctuation), namely\nconstants and variables. The constants included logical constants, but\nalso any other terms of fixed meaning. The variables had no\nindependent meaning and were simply part of the apparatus of\nquantification.", "\n\n Model theory\n by contrast works with three levels of symbol. There are the logical\nconstants \\((=, \\neg\\), & for example), the variables (as before),\nand between these a middle group of symbols which have no fixed\nmeaning but get a meaning through being applied to a particular\nstructure. The symbols of this middle group include the nonlogical\nconstants of the language, such as relation symbols, function symbols\nand constant individual symbols. They also include the quantifier\nsymbols \\(\\forall\\) and \\(\\exists\\), since we need to refer to the\nstructure to see what set they range over. This type of three-level\nlanguage corresponds to mathematical usage; for example we write the\naddition operation of an abelian group as +, and this symbol stands\nfor different functions in different groups.", "\nSo one has to work a little to apply the 1933 definition to\nmodel-theoretic languages. There are basically two approaches: (1)\nTake one structure \\(A\\) at a time, and regard the nonlogical\nconstants as constants, interpreted in \\(A\\). (2) Regard the\nnonlogical constants as variables, and use the 1933 definition to\ndescribe when a sentence is satisfied by an assignment of the\ningredients of a structure \\(A\\) to these variables. There are\nproblems with both these approaches, as Tarski himself describes in\nseveral places. The chief problem with (1) is that in model theory we\nvery frequently want to use the same language in connection with two\nor more different structures – for example when we are defining\nelementary embeddings between structures (see the entry on\n first-order model theory).\n The problem with (2) is more abstract: it is disruptive and bad\npractice to talk of formulas with free variables being\n‘true’. (We saw in Section 2.2 how Tarski avoided talking\nabout truth in connection with sentences that have varying\ninterpretations.) What Tarski did in practice, from the appearance of\nhis textbook in 1936 to the late 1940s, was to use a version of (2)\nand simply avoid talking about model-theoretic sentences being true in\nstructures; instead he gave an indirect definition of what it is for a\nstructure to be a ‘model of’ a sentence, and apologised\nthat strictly this was an abuse of language. (Chapter VI of Tarski\n1994 still contains relics of this old approach.)", "\nBy the late 1940s it had become clear that a direct model-theoretic\ntruth definition was needed. Tarski and colleagues experimented with\nseveral ways of casting it. The version we use today is based on that\npublished by Tarski and Robert Vaught in 1956. See the entry on\n classical logic\n for an exposition.", "\nThe right way to think of the model-theoretic definition is that we\nhave sentences whose truth value varies according to the situation\nwhere they are used. So the nonlogical constants are not variables;\nthey are definite descriptions whose reference depends on the context.\nLikewise the quantifiers have this indexical feature, that the domain\nover which they range depends on the context of use. In this spirit\none can add other kinds of indexing. For example a Kripke structure is\nan indexed family of structures, with a relation on the index set;\nthese structures and their close relatives are fundamental for the\nsemantics of modal,\n temporal\n and\n intuitionist\n logic.", "\nAlready in the 1950s model theorists were interested in formal\nlanguages that include kinds of expression different from anything in\nTarski’s 1933 paper. Extending the truth definition to\ninfinitary logics was no problem at all. Nor was there any serious\nproblem about most of the generalised quantifiers proposed at the\ntime. For example there is a quantifier \\(Qxy\\) with the intended\nmeaning:", "\n\\(QxyF(x,y)\\) if and only if there is an infinite set \\(X\\) of\nelements such that for all \\(a\\) and \\(b\\) in \\(X, F(a,b)\\). ", "\nThis definition itself shows at once how the required clause in the\ntruth definition should go.", "\nIn 1961 Leon Henkin pointed out two sorts of model-theoretic language\nthat didn’t immediately have a truth definition of\nTarski’s kind. The first had infinite strings of\nquantifiers:", "\nThe second had quantifiers that are not linearly ordered. For ease of\nwriting I use Hintikka’s later notation for these:", "\nHere the slash after \\(\\exists v_4\\) means that this quantifier is\noutside the scope of the earlier quantifier \\(\\forall v_1\\) (and also\noutside that of the earlier existential quantifier).", "\nHenkin pointed out that in both cases one could give a natural\nsemantics in terms of Skolem functions. For example the second\nsentence can be paraphrased as", "\nwhich has a straightforward Tarski truth condition in second order\nlogic. Hintikka then observed that one can read the Skolem functions\nas winning strategies in a game, as in the entry on\n logic and games.\n In this way one can build up a compositional semantics, by assigning\nto each formula a game. A sentence is true if and only if the player\nMyself (in Hintikka’s nomenclature) has a winning strategy for\nthe game assigned to the sentence. This game semantics agrees with\nTarski’s on conventional first-order sentences. But it is far\nfrom fully abstract; probably one should think of it as an operational\nsemantics, describing how a sentence is verified rather than whether\nit is true.", "\nThe problem of giving a Tarski-style semantics for Henkin’s two\nlanguages turned out to be different in the two cases. With the first,\nthe problem is that the syntax of the language is not well-founded:\nthere is an infinite descending sequence of subformulas as one strips\noff the quantifiers one by one. Hence there is no hope of giving a\ndefinition of satisfaction by recursion on the complexity of formulas.\nThe remedy is to note that the explicit form of\nTarski’s truth definition in Section 2.1 above didn’t\nrequire a recursive definition; it needed only that the conditions on\nthe satisfaction relation \\(S\\) pin it down uniquely. For\nHenkin’s first style of language this is still true, though the\nreason is no longer the well-foundedness of the syntax.", "\nFor Henkin’s second style of language, at least in\nHintikka’s notation (see the entry on\n independence friendly logic),\n the syntax is well-founded, but the displacement of the quantifier\nscopes means that the usual quantifier clauses in the definition of\nsatisfaction no longer work. To get a compositional and fully abstract\nsemantics, one has to ask not what assignments of variables satisfy a\nformula, but what sets of assignments satisfy the formula\n‘uniformly’, where ‘uniformly’ means\n‘independent of assignments to certain variables, as shown by\nthe slashes on quantifiers inside the formula’. (Further details\nof revisions of Tarski’s truth definition along these lines are\nin the entry on\n dependence logic.)\n Henkin’s second example is of more than theoretical interest,\nbecause clashes between the semantic and the syntactic scope of\nquantifiers occur very often in natural languages." ], "section_title": "3. The 1956 definition and its offspring", "subsections": [] } ]

[ "Feferman, S., 2004, “Tarski’s conceptual analysis of\nsemantical notions”, in Sémantique et\nÉpistémologie, ed. Ali Benmakhlouf, Casablanca:\nEditions Le Fennec, 79–108; reprinted in Patterson 2008.", "Henkin, L., 1961, “Some remarks on infinitely long\nformulas”, in Infinitistic methods: Proceedings of the\nsymposium on foundations of mathematics, Oxford: Pergamon Press,\n167–183.", "Hintikka, J., 1996, The Principles of Mathematics\nRevisited, Cambridge: Cambridge University Press.", "Hodges, W., 1997, “Compositional semantics for a language of\nimperfect information”, Logic Journal of the IGPL, 5:\n539–563.", "–––, 2008, “Tarski’s theory of\ndefinition”, in Patterson 2008, pp. 94–132.", "Katz, J. and Fodor, J., 1963, “The structure of a semantic\ntheory”, Language, 39: 170–210.", "Levy, A., 1965, A hierarchy of formulas in set theory,\n(Memoirs of American Mathematical Society 57), Providence: American\nMathematical Society.", "Patterson, D. (ed.), 2008, New Essays on Tarski and\nPhilosophy, Oxford: Oxford University Press.", "Putnam, H., 1975, “Do true assertions correspond to\nreality?”, in Mind, Language and Reality (Philosophical\nPapers: Volume 2), Cambridge: Cambridge University Press,\n70–84.", "Skolem, T., 1919, “Untersuchungen über die Axiome des\nKlassenkalküls und über Produktations- und\nSummationsprobleme, welche gewisse Klassen von Aussagen\nbetreffen”, Videnskapsselskapets Skrifter, I. Matem.-naturv.\nklasse, 3; reprinted in T. Skolem, Selected Works in\nLogic, J. E. Fenstad (ed.), Oslo: Universitetforlaget, pp.\n67–101.", "Tarski, A., 1931, “Sur les ensembles définissables de\nnombres réels. I”, Fundamenta Mathematicae, 17:\n210–239.", "–––, 1933, “The concept of truth in the\nlanguages of the deductive sciences” (Polish), Prace\nTowarzystwa Naukowego Warszawskiego, Wydzial III Nauk\nMatematyczno-Fizycznych 34, Warsaw; reprinted in Zygmunt 1995,\npp. 13–172; expanded English translation in Tarski 1983 [1956],\npp. 152–278.", "–––, 1944, “The semantic conception of\ntruth”, Philosophy and Phenomenological Research, 4\n(3): 341–376.", "–––, 1983 [1956], Logic, Semantics,\nMetamathematics: Papers from 1923 to 1938, 2nd edition,\nJohn Corcoran (ed.), Indianapolis: Hackett Publishing Company; 1st\nedition, Oxford: Oxford University Press, 1956.", "–––, 1994 [1936], Introduction to Logic and\nto the Methodology of the Deductive Sciences, 4th edition, Jan\nTarski (ed.), Oxford: Oxford University Press; originally published as\nO logice matematycznej i metodzie dedukcyjnej (On\nMathematical Logic and the Deductive Method), Lwów, Warsaw:\nKsiążnica-Atlas, 1936; German translation,\nEinführung in die mathematische Logik und in die Methodologie\nder Mathematik, Vienna: Julius Springer-Verlag; first English\nedition, Oxford: Oxford University Press, 1941; 2nd edition, 1946; 3rd\nedition, 1985. ", "Tarski, A. and Vaught, R., 1956, “Arithmetical extensions of\nrelational systems”, Compositio Mathematica, 13:\n81–102.", "Wole&nacute;ski, J., 2019, Semantics and Truth,\nCham: Springer.", "Zygmunt, J. (ed.), 1995, Alfred Tarski, Pisma\nLogiczno-Filozoficzne, 1 Prawda, Warsaw: Wydawnictwo Naukowe\nPWN." ]

[ { "href": "../compositionality/", "text": "compositionality" }, { "href": "../logic-games/", "text": "logic: and games" }, { "href": "../logic-dependence/", "text": "logic: dependence" }, { "href": "../logic-if/", "text": "logic: independence friendly" }, { "href": "../logic-infinitary/", "text": "logic: infinitary" }, { "href": "../logic-intuitionistic/", "text": "logic: intuitionistic" }, { "href": "../logic-higher-order/", "text": "logic: second-order and higher-order" }, { "href": "../logic-temporal/", "text": "logic: temporal" }, { "href": "../meaning/", "text": "meaning, theories of" }, { "href": "../model-theory/", "text": "model theory" }, { "href": "../modeltheory-fo/", "text": "model theory: first-order" }, { "href": "../tarski/", "text": "Tarski, Alfred" }, { "href": "../truth/", "text": "truth" }, { "href": "../truth-axiomatic/", "text": "truth: axiomatic theories of" }, { "href": "../truth-deflationary/", "text": "truth: deflationation about" }, { "href": "../truth-revision/", "text": "truth: revision theory of" } ]

[ "\nSo much of what we know about the world, e.g., history, science,\npolitics, one another, etc., comes from the testimony of others. But\nwhile testimony is clearly an indispensable source of knowledge,\nspecifying exactly how it is that we are able to learn from a\nspeaker’s say-so has proven to be a difficult task.", "\nTo this end, a lot (but certainly not all) of the interest in the\nepistemology of testimony has centered on the following questions:", "\nThe aim of this article is to provide an overview of the major debates\nsurrounding these issues.", "\nBefore moving on, it is important to note that these are certainly not\nthe only important questions about testimony. For instance, there is a\ngrowing literature about how failing to give a testifier the credit\nthey deserve gives rise to a form of epistemic injustice\n(e.g., M. Fricker\n 2007).[1]\n Moreover, there are many interesting questions about eyewitness\ntestimony and the law (e.g., Wells & Olson 2003 and Burroughs\n& Tollefsen 2016), as well as important questions about the\nrelationship between testimony and assertion (e.g., Pagin 2007\n[2016]). And there are also growing literatures about moral\n testimony[2]\n and aesthetic\n testimony,[3]\n e.g., while it is uncontroversial that you can acquire justification\nfor believing that the taco truck is open by relying on your\nfriend’s say-so, it is far less clear that you can acquire\njustification for believing that eating carne asada is morally wrong\nor that the mural on the taco truck is beautiful, solely on the basis\nof what your friend tells you. For reasons only having to do with\nspace, though, this article will focus exclusively on the seven\nquestions above." ]

[ { "content_title": "1. Reductionism and Non-Reductionism", "sub_toc": [ "1.1 Reductionism", "1.2 Non-Reductionism", "1.3 Hybrid Views" ] }, { "content_title": "2. Knowledge Transmission and Generation", "sub_toc": [ "2.1 The Transmission View", "2.2 The Generation View" ] }, { "content_title": "3. Testimony and Evidence", "sub_toc": [ "3.1 Evidential Views", "3.2 Non-Evidential Views", "3.3 Hybrid Views" ] }, { "content_title": "4. Individualism and Anti-Individualism", "sub_toc": [ "4.1 Individualism", "4.2 Anti-Individualism" ] }, { "content_title": "5. Authoritative Testimony", "sub_toc": [] }, { "content_title": "6. Group Testimony", "sub_toc": [] }, { "content_title": "7. The Nature of Testimony Itself", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nConsider this scenario: Your friend testifies to you that your\nfavorite team won last night’s game (= p). Because you\nknow that your friend is a highly reliable sports reporter, and\nbecause you have no reason to doubt what she says on this occasion,\nyou believe what you are told. In this case, your belief that p\nis clearly justified.", "\nNow, contrast that scenario with this one: You run into a stranger\nwhom you have never met and they tell you that your favorite team won\nlast night’s game (= p). Even though you don’t know\nif this person often speaks the truth, you also don’t have any\ngood reason to doubt what they are telling you. Thus, you decide to\nbelieve what you are told. Whether or not your belief that p is\njustified in this case is a lot less clear.", "\nThinking about the difference between cases like these helps motivate\nthe debate about the following question:", "\n\n\nFirst Big Question: Is testimony a basic source of\njustification, or can testimonial justification be reduced to a\ncombination of other epistemic sources?\n", "\nThose who defend answers to this question tend to endorse one of three\nmain positions: Reductionism, Non-Reductionism, and\nHybrid Views." ], "section_title": "1. Reductionism and Non-Reductionism", "subsections": [ { "content": [ "\nReductionists maintain that in order to acquire testimonial\njustification, one must have positive reasons for thinking that the\nspeaker in question is a reliable testifier. More specifically,\nReductionists endorse", "\n\n\nPositive Reasons: A hearer is justified in believing what a\nspeaker says if, and only if, they (a) have positive reasons for\nthinking that the speaker’s testimony is reliable, where these\nreasons are not themselves ultimately based on testimony, and (b) do\nnot have any undefeated\n defeaters[4]\n that indicate that the speaker’s testimony is false or unlikely\nto be true.\n", "\nReductionist views trace at least as far back as David Hume’s\n(1740, 1748)—see Traiger (1993, 2010), Faulkner (1998), Root\n(2001), Fogelin (2005), van Cleve (2006), Gelfert (2010), and Shieber\n(2015) for more on Hume’s view in particular. More recently,\nother Reductionist views have been defended by E. Fricker (1987, 1994,\n1995, 2002, 2006a, 2006b), Adler (1994, 2002), Lyons (1997), Lipton\n(1998), Shogenji (2006), Sutton (2007), Malmgren (2006), and Kenyon\n(2013).", "\nOne of the primary motivations for Reductionism stems from concerns\nhaving to do with gullibility; that is, many reductionists\nmaintain that if we could justifiably accept a speaker’s\ntestimony without having positive reasons for thinking that they\ntypically speak the truth, then we would be justified in accepting\ntestimony in cases in which doing so would be clearly irresponsible.\nSo for example, if a hearer does not need positive reasons for\nthinking that the speaker’s testimony is reliable, then one\ncould be justified in believing the say-so of a random blogger on an\narbitrary website so long as one did not have any reasons for doubting\nthe testimony in question.", "\nNow, while all Reductionists endorse Positive Reasons, there is\ndisagreement over exactly how this thesis should be understood. For\nthis reason, Reductionists fall into one of two camps: Global\nReductionists and Local Reductionists.", "\nAccording to Global Reductionism, in order to be justified in\naccepting a speaker’s testimony, you need to have positive\nreasons for believing that testimony is generally reliable, i.e., that\naccepting the reports of others is a reliable way of forming true\nbeliefs. For instance, suppose that your friend tells you that he got\na puppy. Global Reductionists maintain that you are only justified in\naccepting this report if you have positive reasons that support\ninferences like the following:", "\nIt is in this sense that Global Reductionists think that testimonial\njustification can be reduced to a combination of perceptual, memorial,\nand inferential justification. That is, testimonial justification can\nbe reduced to a combination of other epistemic sources because it only\ninvolves you (i) perceiving that the speaker made an utterance (ii)\nremembering that when people have told you things in the past, they\nturned out to be right most of the time and (iii) inferring on this\nbasis that what you were told on this occasion is likely to be\ntrue.", "\nHistorically, Global Reductionism has been saddled with three\nobjections. First, opponents have argued that any attempt to acquire\nnon-testimonially based reasons for thinking that testimony is\ngenerally reliable will either be viciously circular or else involve\nan insurmountable regress. For instance, in order to know that people\ngenerally speak the truth, I might need to rely on Bill’s\ntestimony to confirm that what Alice said was true. But in order to\nknow that Bill can be trusted, I might need to rely on Carly to\nconfirm that he usually says true things. But to ensure that Carly\ntypically speaks the truth, I will either need to rely on Alice or\nBill to confirm this for me (hence the vicious circle), or else I will\nneed to rely on on a fourth person like Donald (and hence the regress\nwill continue). Thus, because there is no good way to acquire the\nnon-testimonially based reasons in question, Global Reductionism\nproblematically entails that we are rarely (if ever) justified in\naccepting what people tell us. See Coady (1992) for this worry, and\nsee Wright (2016a, 2019) for an importantly different kind of\ncircularity worry for all Reductionist views.", "\nSecond, and relatedly, opponents have argued that in order to acquire\nnon-testimonially based reasons for thinking that testimony is\ngenerally reliable, we would need to be exposed to loads and loads of\nfacts that correspond to the things that we receive testimony about,\ni.e., in order to check if testimony about history, medicine, biology,\netc., is generally reliable, we would need to have confirmed many of\nthese facts for ourselves. However, most (if not all) of us simply\nlack the time and resources to confirm such things. Thus, Global\nReductionism seems to problematically entail that we are rarely (if\never) justified in accepting what other people tell us. See, e.g.,\nCoady (1992).", "\nTo see the third worry with Global Reductionism, notice that Global\nReductionists treat testimony as if it is a unified, homogeneous\ncategory, i.e., according to Global Reductionists, testimony in\ngeneral can be a more or less reliable source of knowledge. The\nproblem here is that we frequently receive testimony about wildly\ndifferent topics, e.g., quantum mechanics, politics, one’s own\nmusic preferences, etc. And clearly testimony about some of these\nthings is highly reliable (e.g., all of your friends are probably very\ngood at speaking truly about what kinds of music they like), whereas\ntestimony about other topics is less so (e.g., if your friends are\nlike mine, then at least a few of them are probably a lot less\nreliable at speaking truly about politics). Thus, contra Global\nReductionism, it is a mistake to treat testimony as a unified source\nof knowledge; that is, instead of thinking about testimony in general,\nwe should think about the various categories of testimony in\nparticular, e.g., categories differentiated by subject matter. For it\nis only when we think of testimony as being disaggregated in this way\nthat it make sense to ask about whether receiving testimony about a\nparticular category is a reliable source of knowledge. See, e.g., E.\nFricker (1994).", "\nAccording to Local Reductionism, in order to be justified in accepting\na speaker’s testimony, the hearer needs to have\nnon-testimonially based reasons for thinking that the speaker in\nquestion is a reliable testifier on this occasion (as opposed to\nhaving positive reasons for thinking that testimony in general is\nreliable). For instance, suppose your friend tells you that he got a\npuppy and that you make the following inference:", "\nLocal Reductionists maintain that you are only justified in accepting\nwhat you are told on this occasion if you have non-testimonially based\nreasons that support (1) and (2). For instance, perhaps you know that\nyour friend usually speaks the truth about these sorts of things\nbecause you have known them for a long time. Or perhaps it is because\nyou know that, generally speaking, anyone who takes the time to talk\nto you about their pets is probably telling the truth. Or perhaps it\nis because you know that when you ask people about their pets in this\nkind of context, it is highly likely that you will get an honest\nanswer.", "\nRegardless of how these non-testimonially based reasons are acquired,\nit is in this sense that Local Reductionists also think that\ntestimonial justification can be reduced to a combination of\nperceptual, memorial, and inferential justification, i.e., testimonial\njustification only consists in you perceiving that the speaker made an\nutterance and then inferring on this basis that what the speaker said\non this occasion is likely to be true.", "\nLocal Reductionists are well positioned to avoid the problems that\nplague Global Reductionism. This is because they are not committed to\nthe claim that testimony is a unified category, i.e., instead of\nthinking about the reliability of testimony in general, we only need\nto think about the reliability of each piece of testimony that we are\noffered on a given occasion. Moreover, Local Reductionists do not\nmaintain that in order to be justified in accepting a speaker’s\nsay-so, one needs positive reasons for thinking that testimony in\ngeneral is a reliable source of knowledge. Thus, even if you lack the\nresources to confirm that most people generally speak the truth, you\ncan still have non-testimonially based reasons for thinking that what\nthe speaker said is likely to be true on this occasion. For instance,\nif your relationship is long enough, you can come to know that your\nfriend has a great track record of saying true things about getting\nnew pets, since anytime they say this, you can just go over to their\nplace and see their new puppy for yourself. And because you\ndon’t need to rely on the testimony of a third party to acquire\nthese positive reasons, there is no worry of running into the kinds of\nvicious circles or insurmountable regresses that Global Reductionists\nneed to explain away.", "\nHistorically, though, there are at least three problems that cause\ntrouble for Local Reductionists. First, opponents have objected to\nLocal Reductionism on the grounds that it problematically excludes\nyoung children (e.g., 3-year-olds) from justifiably accepting what\ntheir parents tell them. For if Local Reductionism is true, then in\norder to be justified in accepting a parent’s testimony, a young\nchild would need non-testimonially based reasons for thinking that\nthis parent is a reliable testifier. But youngsters simply lack the\nworldly experience to have good reasons for thinking that their\nparents’ reports are usually true, i.e., they have not been\naround long enough to have confirmed enough of these reports for\nthemselves. Thus, Local Reductionism problematically precludes young\nchildren from being able to learn from the say-so of their parents.\nSee, e.g., Audi (1997), and see also Harris (2002), Harris and\nCorriveau (2011) and Koenig and Harris (2007) for empirical results\nabout children accepting the testimony of others. (Note: This\nobjection poses a worry for Global Reductionists as well).", "\nSecond, opponents have objected to Local Reductionism on the grounds\nthat we can be justified in believing a speaker, S’s,\ntestimony that p even if we lack the relevant non-testimonially\nbased reasons to support the inference from “S said that\np” to “p”. (See, e.g., Webb [1994:\n263–264], Strawson [1994: 25], Schmitt [1999: 360] and Lackey\n[2008: 180]). For instance, suppose you arrive in a new country and\nspot someone on the street. And suppose that you approach this person\nand ask them for directions. Now, if that person tells you that your\nhotel is three blocks down the road, then it seems like you are\njustified in accepting their testimony that this is the case. But\nLocal Reductionism cannot accommodate this result. For insofar as the\nonly thing that justifies your belief is your inference from\n“This person said that my hotel is just down the road” to\n“My hotel is just down the road”, then since you know next\nto nothing about this stranger, and since you also know very little\nabout whether anyone in this area is likely to answer this sort of\nquestion honestly, it is hard to see how your non-testimonially based\nreasons for accepting this person’s testimony are strong enough\nto justify you in believing what you are told on this occasion. (But\nsee, e.g., Kenyon [2013], who defends Local Reductionism from this\nworry by arguing that even if a hearer knows very little about the\nspeaker in question, they can still appeal to other contextual\ninformation to support their inference).", "\nThird, others have argued that given the current results in social\npsychology, there is good reason to reject Local Reductionism on the\ngrounds that it makes testimonial justification too hard to come by.\nThe worry here is that the evidence from social psychology suggests\nthat humans are not very good at determining when a particular\ninstance of testimony is false or unlikely to be true. Thus, insofar\nas Local Reductionists maintain that hearers need to be good at\nmonitoring for these signs of falsehood and unreliability in order to\nhave positive reasons for thinking that a particular instance of\ntestimony is worth accepting, Local Reductionism problematically\nentails that we have way less testimonial justification than we\npreviously thought. See Michaelian (2010, 2013) and Shieber (2012,\n2015) for more on this style of objection, and see Sperber (2013) and\nHarris et al. (2018) for an empirical arguments to the contrary.\n(Note: This objection is not meant to just target Local Reductionism,\nbut Reductionist views more generally).", "\nReductionists have offered responses to all of the worries mentioned\nabove. For instance, see Owen (1987), Sobel (1987), and Alvin Goldman\n(1999: Ch. 4) for a Bayesian analysis of how a hearer can acquire\npositive reasons for accepting a speaker’s testimony. See also\nE. Fricker (1995), Lipton (1998, 2007), Schiffer (2003), and Malmgren\n(2006) for more on how hearers can acquire these positive reasons via\ninference to the best explanation. And for more on debates surrounding\nReductionism in general, see Faulkner (2000), Elgin (2002), Lackey\n(2005a, 2006), Goldberg and Henderson (2006), Kenyon (2013) and Graham\n(2018). Whether or not these responses succeed remains an open\nquestion." ], "subsection_title": "1.1 Reductionism" }, { "content": [ "\nAccording to Non-Reductionists, Positive Reasons is false, i.e., we\ndon’t need positive reasons for thinking that a speaker’s\ntestimony is reliable in order to be justified in believing what we\nare told. Instead, we have a defeasible but presumptive right to\nbelieve what people tell us. More specifically, Non-Reductionists\nendorse", "\n\n\nPresumptive Right: A hearer is justified (or\n warranted[5])\n in believing what a speaker says if they do not have an undefeated\ndefeater that indicates that the speaker’s testimony is false or\nunlikely to be true. (Some Non-Reductionists (e.g., Goldberg &\nHenderson 2006) maintain that in addition to simply lacking any\nrelevant undefeated defeaters, the hearer must also be\ncounterfactually sensitive to, or on the lookout for, the\npresence of defeaters in their environment).\n", "\nNon-Reductionism traces at least as far back as Thomas Reid’s\n(IE [1983, 94–95])—see Wolterstorff (2001) for more on\nReid’s view. More recently, various versions of Non-Reductionism\nhave been defended by Austin (1946 [1979]), Welbourne (1979, 1981,\n1986, 1994), Evans (1982), A. Ross (1986), Hardwig (1985, 1991), Coady\n(1992, 1994), Burge (1993, 1997, 2013), Plantinga (1993), Stevenson\n(1993), Webb (1993), Dummett (1994), Foley (1994), McDowell (1994),\nStrawson (1994), Williamson (1996, 2000), Millgram (1997), Alvin\nGoldman (1999), Schmitt (1999), Insole (2000), Owens (2000), Rysiew\n(2000), Weiner (2003), Graham (2006a), Sosa (2006), McMyler (2011) and\nBaker and Clark (2018). See also Audi (1997, 1998, 2004, 2006), who\ndefends Non-Reductionism about testimonial knowledge but not about\ntestimonial justification.", "\nOne motivation for Non-Reductionism stems from the desire to avoid the\nproblems associated with the various forms of Reductionism, e.g., if\nhearers are not required to have positive reasons for thinking that\nthe speaker’s testimony is reliable on this occasion,\ntestimonial knowledge will not be too hard to acquire. Another\nmotivation (i.e., Reid IE [1983, 94–95]) is rooted in the following\nidea: Whatever reason we have for thinking that perception is a basic\nsource of justification, we have an analogous reason for thinking that\ntestimony is a basic source of justification too. For instance, we can\nrely on a speaker’s testimony unless we have a good reason not\nto because humans are endowed—perhaps by God or just by\nnature—with the disposition to (a) tell the truth (b) believe\nwhat they are told and (c) have some sense of when a speaker is not to\nbe trusted.", "\nHowever, because Non-Reductionists reject Positive Reasons, opponents\nhave objected to the view on the grounds that it permits hearers to be\nirrationally gullible. For instance, recall the case in which you read\na bit of testimony from an anonymous blogger on an arbitrary website\n(i.e., E. Fricker 2002). Or consider this situation: While on your way\nhome from work you see a group of aliens from another planet drop a\nnotebook written in what appears to be English. Upon reading the\nnotebook, you see that the aliens seem to have testified that hungry\ntigers have eaten some of their friends (i.e., Lackey 2008:\n168–169). While these cases are different in certain respects,\nthey are related by the fact that while you do not have any defeaters\nthat indicate that the testimony in question is false or unlikely to\nbe true, you also do not have any positive reasons for accepting what\nthe speaker says. Opponents of Non-Reductionism argue that because it\nwould be irrational for you to accept either of these reports, these\ncases show that Non-Reductionism is false and that in order to be\njustified in believing what a speaker says, you really do need\npositive reasons for thinking that the speaker’s testimony is\nlikely to be true." ], "subsection_title": "1.2 Non-Reductionism" }, { "content": [ "\nFinally, some epistemologists reject both Reductionism and\nNon-Reductionism in favor of various hybrid views. The primary\nmotivation for these hybrid views is to capture what seems promising\nabout the Reductionist and Non-Reductionist approaches while also\navoiding the objections discussed above.", "\nFor instance, instead of endorsing Reductionism and requiring that\nall hearers must possess strong, non-testimonially based\npositive reasons for thinking that the speaker in question is\nreliable, one might opt for a qualified hybrid view according to which\n(a) adults need to possess these positive reasons but (b) youngsters\nin the developmental phase do not, i.e., children are justified in\nbelieving a speaker’s testimony so long as they do not have any\nreasons to not do so. One upshot of this hybrid view is that unlike\nstandard versions of Reductionism, it is possible for young children\nto be justified in believing what their parents tell them. See, e.g.,\nE. Fricker (1995).", "\nOr, one might opt for a hybrid view according to which the hearer and\nthe speaker both have an important role to play in the hearer’s\nability to acquire testimonial justification, i.e., it takes two\nto tango, so to speak. For instance, perhaps a hearer does need\nto possess at least some non-testimonially based reasons for thinking\nthat the speaker in question is a reliable testifier on this occasion.\nBut insofar as the hearer’s inference from “S said\nthat p” to “P” is not the only thing\nthat justifies the hearer’s belief, these reasons do not need to\nbe nearly as strong as standard Reductionists have made them out to\nbe; that is, so long as the hearer’s non-testimonially based\nreasons render it not irrational to rely on the speaker’s\nsay-so, then this is good enough. And this is because, in addition to\nthe hearer having these weaker kinds of positive reasons, the speaker\nin question needs to actually be a reliable reporter. The hope here is\nthat by requiring contributions from both the speaker and the hearer,\nall of the worries associated with standard versions of Reductionism\nand Non-reductionism can be avoided. For instance, by requiring that\nthe speaker has these weaker kinds of positive reasons, this hybrid\nview can explain how young children can acquire testimonial\njustification while also avoiding the worries associated with\ngullibility. See, e.g., Lackey (2008). And for defenses of other\nhybrid views, see E. Fricker (2006b), Faulkner (2000), Lehrer (2006),\nand Pritchard (2006).", "\nWhether any of these hybrid views will ultimately succeed is still\nvery much an open debate. However, opponents have worried that at\nleast some of these accounts either run into the same objections that\nplagued standard versions of Reductionism and Non-Reductionism, or\nthat they incur entirely new problems of their own, e.g., Insole\n(2000), Weiner (2003) and Lackey (2008)." ], "subsection_title": "1.3 Hybrid Views" } ] }, { "main_content": [ "\nConsider this scenario: Gretchen knows that the bakery is closed. If\nGretchen tells you that this is the case, and if all goes well, then\nit is uncontroversial that you can acquire testimonial knowledge that\nthe bakery is closed too.", "\nNow, contrast that scenario with this one: Gretchen does not know that\nthe bakery is closed (perhaps because she simply lacks any\njustification for believing this). Nevertheless, she testifies to you\nthat the bakery is closed anyway. If you come to believe that the\nbakery is closed on the basis of Gretchen’s testimony, and if\nthe bakery really is closed, then is it possible for your belief to\namount to knowledge?", "\nDepending on how the details are filled in, things are much more\ncontroversial in this second scenario. The controversy centers on the\nfollowing question:", "\n\n\nSecond Big Question: Can testimony generate knowledge, or can\nit merely transmit it?\n", "\nOtherwise put, can a hearer acquire testimonial knowledge that\np from a speaker who does not know that p\nthemselves?", "\nBefore moving on, two clarification points are in order. First, while\nmuch of the debate about the Transmission View has centered on whether\ntestimony can only transmit knowledge, there is also some\ndebate about whether testimony can transmit justification.\n(See, e.g., Audi [1997] who maintains that while testimony can\ngenerate justification, it can only transmit knowledge. See also\nWright 2016a for a recent discussion of other views according to which\ntestimony transmits knowledge but generates justification). Second,\ndebates about knowledge transmission bear on debates about the\nInheritance View\n (Section 3.1.2)\n and on the Individualism vs. Non-Individualism debate\n (Section 4)." ], "section_title": "2. Knowledge Transmission and Generation", "subsections": [ { "content": [ "\nAccording to the Transmission View, testimonial knowledge can only be\ntransmitted from a speaker to a hearer. Here is one (but not the only)\nway of formulating this view in terms of necessity and\nsufficiency:", "\n\n\nTV-S: For every speaker, A, and hearer,\nB, if\n\n\n\nA knows that p,\n\nB comes to believe that p on the basis of\nA’s testimony and\n\nB has no undefeated defeaters for believing that p,\nthen B comes to know that p too.\n\n\n\n(See Austin 1946 [1979]; Welbourne 1979, 1981, 1986, 1994; Evans 1982;\nE. Fricker 1987; Coady 1992; McDowell 1994; Adler 1996, 2002; Owens\n2000, 2006; Burge 1993; Williamson 1996, 2000; and Audi 1997).\n\n\nTV-N: For every speaker, A, and hearer,\nB, B knows that p on the basis of\nA’s testimony only if A knows that p\ntoo.\n\n\n(See Welbourne 1979, 1981, 1986, 1994; Hardwig 1985, 1991; A. Ross\n1986; Burge 1993, 1997; Plantinga 1993; Williamson 1996, 2000; Audi\n1997, 1998, 2006; Owens 2000, 2006; Reynolds 2002; Adler 2002;\nFaulkner 2006; Schmitt 2006).\n", "\nOne of the main motivations for the Transmission View comes from an\nalleged analogy between testimony and memory: Just as I cannot acquire\nmemorial knowledge that p today if I did not know that p\nat some earlier point in time, I cannot acquire testimonial knowledge\nthat p from you today if you do not know that p\nyourself. (But see Barnett 2015 for a recent discussion of the\nimportant differences between memory and testimony, and see Lackey\n2005b for why memory can generate knowledge.)", "\nDespite the intuitive and theoretical appeal, the Transmission View\nhas challenged in a variety of ways." ], "subsection_title": "2.1 The Transmission View" }, { "content": [ "\nOpponents have raised two importantly different kinds of arguments\nagainst TV-N. First, suppose that there is a creationist teacher,\nStella, who does not believe, and thus fails to know, that homo\nsapiens evolved from homo erectus (= p). That is,\nwhile Stella has read the relevant text books on evolutionary theory,\nher creationist commitments prevent her from believing that p\nis true. Now, suppose that during one of her biology lessons Stella\ntells her fourth grade students that p, and suppose that her\nstudents come to believe that p on the basis of Stella’s\ntestimony.", "\nThe argument here is that the fourth graders can come to know that\np on the basis of Stella’s testimony even though Stella\nherself does not believe, and thus does not know, that p is\ntrue. Thus, TV-N is false, i.e., testimonial knowledge can be\ngenerated from a speaker who lacks the knowledge in question.\n(This Creationist Teacher case comes from Lackey (2008). Other school\nteacher cases have been discussed in Graham (2006a) and Carter and\nNickel (2014). Goldberg (2005) and Pelling (2013) also give cases in\nwhich a speaker’s belief is unsafe and does not amount to\nknowledge even though the hearer’s belief\n does).[6]", "\nWhile this first case involved a speaker who did not know that\np because they did not believe it, the second type of objection\nto TV-N involves a speaker who does not know that p because\nthey are not justified in believing it. For instance, consider Persia,\nwho is a persistent believer in the following sense: Persia goes to\nher eye doctor, Eyal, who tells her that the eye drops she was just\ngiven will make her vision unreliable for the next three hours. While\nEyal is a highly reliable testifier, he is wrong on this occasion,\ni.e., for some strange reason, the drops did not have this side-effect\non Persia. However, while Persia has no reason to distrust Eyal, she\nignores him on this occasion, walks out of his office, and sees a\nBadger in the parking lot. Because Persia is a persistent believer,\nshe forms the true belief that there is a badger in the parking lot\ndespite Eyal’s (misleading) testimony about the unreliability of\nher visual faculties. Later that day Persia runs into her friend,\nFred, and tells him that there was a badger in the parking lot (=\np).", "\nThe argument here is that Eyal’s testimony constitutes an\nundefeated defeater that defeats Persia’s justification for\nbelieving that p. However, since Fred is completely unaware\nthat Persia has the defeater, and because he has positive reasons for\nthinking that his friend is a reliable testifier, he does come to know\nthat p on the basis of Persia’s say-so. Thus, TV-N is\nfalse (This Persistent Believer case comes from Lackey [2008]. It is\nworth noting that this case purports to show that testimonial\njustification can also be generated, i.e., Fred can acquire\ntestimonial justification for believing p via Persia’s\ntestimony even though Persia was not justified in believing p\nherself).", "\nIn addition to targeting TV-N, opponents of the Transmission View have\nalso targeted TV-S. Consider for instance, Quinn, who is so infatuated\nwith his friend, Kevin, that he is compulsively trusting, i.e., Quinn\nbelieves anything that Kevin says, regardless of how outrageous\nKevin’s claim may be. One day Kevin testifies to Quinn that he\nis moving to Brooklyn (= p). Kevin is being truthful, and he\nhas terrific evidence that p is true (he is the one who is\nmoving, after all). Unsurprisingly, Quinn believes what Kevin says.\nHowever, Quinn would also have believed Kevin even if he had massive\namounts of evidence that Kevin was lying, or joking, or whatever.", "\nOpponents argue that while Kevin knows that p, Quinn does not,\ni.e., because of his compulsively trusting nature, Quinn’s\nattitude is insensitive to counterevidence in a way that precludes his\nbelief from being amounting to knowledge. Thus, TV-S is false. (This\nCompulsively Trusting case comes from Lackey 2008. See also Graham\n2000b).", "\nMuch of the recent work on whether testimony generates or transmits\nknowledge concerns carefully distinguishing between different versions\nof TV-N and TV-S, and arguing that while some versions may face the\nproblems mentioned here, others do not. See, e.g., Wright (2016a)." ], "subsection_title": "2.2 The Generation View" } ] }, { "main_content": [ "\nConsider this scenario: Your friend testifies to you that the taco\ntruck is open. Because you know that your friend is almost always\nright about this kind of thing, and because you have no reason to\ndoubt what they are telling you on this occasion, you believe what you\nare told.", "\nWhile it is uncontroversial that your belief is justified in this\ncase, scenarios like this one have generated lots of debate about the\nfollowing question:", "\n\n\nThird Big Question: When a hearer is justified in believing\nthat p on the basis of a speaker’s testimony, is the\nhearer’s belief justified by evidence? And if the hearer’s\nbelief is justified by evidence, where does this evidence come\nfrom?\n" ], "section_title": "3. Testimony and Evidence", "subsections": [ { "content": [ "\nSome epistemologists maintain that our testimonially based beliefs are\njustified by evidence. However, there is disagreement about where\nexactly this evidence comes from. On the one hand, some maintain that\nthis evidence must be supplied by the hearer. On the other hand, some\nmaintain that this evidence must be supplied by the speaker. Let us\nconsider these two views in turn.", "\nAs we saw in\n Section 1,\n Reductionists maintain that because a hearer must have positive\nreasons for accepting a speaker’s testimony, testimonial\njustification can be reduced to a combination of other epistemic\nresources that the hearer possesses, i.e., the hearer’s\nmemorial, perceptual, and inferential capacities. For this reason,\nReductionists can maintain that a hearer’s testimonial-based\nbeliefs are justified by evidence, where this evidence comes from the\nhearer’s inferences, i.e., inferences from the premise that the\nspeaker said that p, to the conclusion that p is\ntrue.", "\nHowever, as we also saw in\n Section 1,\n Reductionists face a number of difficult challenges. For this reason,\nthose who are sympathetic with an evidential approach to testimonial\njustification have offered an alternative account of how our\ntestimonially based beliefs are justified.", "\nInstead of thinking about testimonial justification in terms of the\nevidence that a hearer possesses, some have offered an alternative\naccount in which the hearer’s belief is justified by evidence\nthat is supplied by the speaker. More specifically, consider", "\n\n\nThe Inheritance\n View:[7]\n If a hearer acquires testimonial justification for believing that\np on the basis of a speaker’s testimony, then the\nhearer’s belief that p is justified by whatever evidence\nis justifying the speaker’s belief that p. (See, e.g.,\nBurge 1993,\n 1997;[8]\n McDowell 1994; Owens 2000, 2006; Schmitt 2006; Faulkner 2011; and\nWright 2015, 2016b, 2016c,\n 2019[9]).\n ", "\n(It is worth nothing that while this debate about evidence and\njustification is importantly different from the debate between\nReductionists and Anti-Reductionists, some of the biggest proponents\nof the Inheritance View also endorse Anti-Reductionism, e.g., Burge\n1993, 1997.)", "\nTo begin to get a handle on the Inheritance View, suppose that you are\njustified in believing that the taco truck is busy because your friend\njust told you so. And suppose that your friend’s belief is\njustified by some excellent evidence, i.e., they are standing in front\nof the truck and can see the long lineup. According to the Inheritance\nview, the evidence that justifies your belief comes from, or is based\non, the very same evidence that justifies your friend’s belief,\ni.e., your belief is based on your friend’s perception of a huge\ngroup of people waiting to order tacos.", "\nOr, consider this example from David Owens (2006: 120): Suppose that\nyou are justified in believing that some math theorem, T, is true\nbecause you just proved it yourself on the basis of some impeccable\na priori reasoning. If you testify to me that T is true such\nthat I come to acquire testimonial justification for believing that\nthis is the case, then according to the Inheritance View, my belief is\nalso based on your impeccable a priori\n reasoning.[10]", "\nNow, while many epistemologists are sympathetic to the idea that your\ntestimonial-based beliefs are justified by evidence, they disagree\nthat the evidence in question is literally inherited from the speaker.\nHere are two reasons why.", "\nThe first objection starts with the observation that a hearer can\nacquire testimonial justification for believing p even though\nthe speaker’s evidence does not justify them in believing\np. For instance, suppose that after an eye exam your\noptometrist tells you that your eyes will be dilated for a few hours\nand that your visual faculties will be unreliable during this time.\nSuppose also that as you are walking home it appears to you that there\nis a small puppy playing fetch in a field (= p). Thus, because\nyou decide to completely and irrationally ignore what your doctor\nsaid, you decide to believe that p. Finally, suppose that\nunbeknownst to you, your doctor was a bit off and the effects of the\neye medication have worn off such that your eyes are now functioning\nin a highly reliable way.", "\nHere it seems like your total evidence does not justify you in\nbelieving p. After all, given what your doctor said, you ought\nto think that your vision is still unreliable, i.e., your\ndoctor’s testimony provides you with a defeater that makes it\nirrational for you to believe that what you are looking at is a small\npuppy (as opposed to, say, a really big kitten or an average sized\nraccoon).", "\nBut, suppose that you decide to call and tell me that p anyway.\nInsofar as your visual faculties are actually working great, and\ninsofar as I have no reason to think that your vision is screwed up,\nit does seem like I can acquire testimonial justification for\nbelieving that p on the basis of your say-so.", "\nAnd herein lies the problem. For if the Inheritance View is true, then\nI could not acquire testimonial justification on the basis of what you\ntold me. After all, if your total evidence does not justify you in\nbelieving p, and if my belief is literally based on the\nevidence that you have, then I could not be justified in believing\np either. But since I do seem to acquire testimonial\njustification for believing that p in this case, the\nInheritance View is false. (This objection comes from Lackey’s\n[2008] Persistent Believer case. Graham (2006b) gives a similar\nobjection, and Pelling (2013) offers a case in which a hearer seems to\nacquire testimonial justification from a speaker who has no good\nreason to believe what they say, but does so anyway on the basis of an\nirrational hunch.)", "\nTo see the second problem with the Inheritance View, notice that a\nhearer can receive testimony from multiple speakers who each have\nexcellent evidence for believing that p, but where their\nevidence conflicts in an important sense. For instance, suppose that\ntwo detectives are investigating who stole the curry from\nSonya’s restaurant. And suppose that the first detective, Dell,\nhas excellent evidence that justifies him in believing that that Steph\nis the only one who committed the crime. Thus, Dell infers that there\nis exactly one culprit. Moreover, suppose that the second detective,\nDoris, has excellent evidence that justifies her in believing that\nSeth is the only one who committed the crime. Thus, Doris also infers\nthat there is exactly one culprit.", "\nNow, suppose that while Dell does testify to you that there is exactly\none thief, he does not fill you in on the evidence that he has for\nthinking this. And suppose while Doris also tells you that there is\nexactly one thief, she does not fill you in on the evidence that she\nhas for thinking this either. Even so, it seems like you are clearly\njustified in believing that there is exactly one culprit on the basis\nof what these detectives have told you. However—and herein lies\nthe problem—if the Inheritance View is true, then it is hard to\nsee how you could be justified in believing this. After all, you have\ninherited Dell’s evidence for believing that there is exactly\none culprit (i.e., his evidence for thinking that Steph is guilty),\nand you have also inherited Doris’ evidence for thinking that\nthere is exactly one culprit (i.e., her evidence for thinking that\nSeth is guilty). But taken together, your combined body of evidence\nconflicts in the sense that it does not justify you in thinking that\nthere is exactly one thief. Thus, the Inheritance View is false. See\nLeonard\n (2018).[11]" ], "subsection_title": "3.1 Evidential Views" }, { "content": [ "\nInstead of further developing these evidential views, some\nepistemologists maintain that our testimonial-based beliefs are not\njustified by evidence. More specifically, some argue that testimonial\njustification should be understood in terms of non-evidential\nassurances, while others contend that it should be understood in terms\nof the reliability of the processes that produced the belief in\nquestion. Let us consider both of these positions in turn.", "\nAccording to proponents of the Assurance View (also called the\nInterpersonal View), the problem with all of the theories discussed\nabove is that they do not appreciate the epistemological significance\nof the interpersonal relationship that obtains between a speaker and\ntheir audience in a testimonial exchange. More specifically,\nconsider", "\n\n\nThe Assurance View: Because of the interpersonal relationship\nthat obtains in a testimonial exchange, if a hearer acquires\ntestimonial justification for believing that p on the basis of\na speaker’s say-so, then the hearer’s belief is justified,\nat least in\n part,[12]\n by the speaker’s assurance, where this assurance is\nnon-evidential in nature. (A. Ross 1986; Hinchman 2005, 2014;\nMoran 2005, 2018; Faulkner 2007, 2011; Zagzebski 2012; and McMyler\n2011).\n", "\nIn order to get a handle on this view, there are two things that need\nunpacking here. First, how should we understand the nature of the\ninterpersonal relationship that is said to obtain in a testimonial\nexchange? And second, why is testimonial justification non-evidential\nin nature? Let us consider these questions in turn.", "\nFirst, proponents of the Assurance View maintain that the speech act\nof telling is key to understanding the relationship that a\nspeaker has with their audience. This is because when a speaker\ntells their audience that p is true, she is doing much\nmore than merely uttering p. Rather, she is inviting her\naudience to trust her that p is true; that is, she is assuring,\nor guaranteeing her audience that p is the case. More\nspecifically, in order for a hearer to acquire testimonial\njustification, the speaker must tell them that p is true, where\ntelling is understood along the following lines:", "\n\n\nTelling: S tells A that p iff\n\n\n\nA recognizes that S, in asserting that p,\nintends:\n\nthat A gain access to an epistemic reason to believe that\np,\n\nthat A recognize S’s (ii)-intention, and\n\nthat A gain access to the epistemic reason to believe that\np as a direct result of A’s recognition of\nS’s (ii)-intention (Hinchman 2005: 567).\n\n", "\nThe idea is that when your friend testifies to you that the ice cream\nshop is open (= p), they are not merely uttering something;\nrather, they are telling you that p. And by telling\nyou that p, they are thereby assuring you that this\nreally is the\n case.[13]", "\nThus, when your friend tells you that p, i.e., when conditions\n(i)–(iv) are satisfied, they have established an important,\ninterpersonal relationship with you, and you alone. This is because\nyou are the only one that has been assured by your friend that\np is true.", "\nIt is in this sense, then, that proponents of the Assurance View\nmaintain that there is an important interpersonal relationship that\nobtains between a speaker and their audience.", "\nThis brings us to the second key question about the Assurance View:\nEven if testimony should be understood in terms of the speech act of\ntelling, why does this mean that testimonial justification cannot be\nunderstood in terms of evidence?", "\nThe idea here is that when your friend tells you that p, they\nare assuring you that p is true, and that this assurance is\nwhat is justifying your belief. Moreover—and this is the\nkey—these assurances are non-evidential in nature.", "\nHere is one way that proponents of the Assurance View have argued for\nthis claim: a piece of evidence, e, counts in favor of a proposition,\np, regardless of what anyone intends (e.g., my fingerprint at\nthe ice cream shop is evidence that I was there regardless of whether\nI wanted to leave the print behind); but a speaker’s assurance\nthat p only counts in favor of p because they intended\nit to, i.e., a speaker cannot unintentionally assure you of anything;\nthus, the assurances that justify your testimonial-based beliefs are\nnon-evidential in\n nature.[14]", "\nIt is for this reason, then, that proponents of the Assurance View\nmaintain that testimonial justification cannot be understood in terms\nof evidence.", "\nHowever, the Assurance View is not without problems of its own. One\nobjection is that it is unclear how these non-evidential assurances\ncan actually justify one’s belief. For instance, suppose that\nonce again your friend tells you that the ice cream shop is\nopen (= p). But suppose that unbeknownst to both of you, Evelyn\nis eavesdropping on the conversation. Thus, while your friend does not\nissue Evelyn an assurance (namely because they do not intend for her\nto believe what they say and thus fail to satisfy conditions\n(i)–(iv) in Telling), Evelyn clearly hears what your\nfriend says. Finally, suppose that you and Evelyn are equally reliable\nconsumers of testimony, that both of have the same background\ninformation about your friend, and that neither of you have any reason\nto doubt what your friend says on this occasion.", "\nThe key question here is this: Insofar as you and Evelyn both believe\nthat p because of what your friend said, epistemically\nspeaking, is there any sense in which your belief is better off than\nEvelyn’s?", "\nGiven the details of the case, it is hard to see what the important\ndifference could be. Thus—and herein lies the problem—even\nthough you were issued an assurance and Evelyn was not, the assurance\nin question seems epistemically superfluous, i.e., it makes no\ndifference to the epistemic status of one’s belief. Thus,\nproponents of the Assurance View must explain how assurances can\njustify one’s beliefs, given that they seem epistemically inert.\n(This case comes from Lackey 2008. Owens 2006 and Schmitt 2010 raise\nsimilar worries).", "\nA second problem is that in order to make the case that testimonial\njustification is non-evidential in nature, proponents of the Assurance\nView have over-cognized what is involved in a testimonial\nexchange.", "\nTo see why, notice that Telling requires that the speaker and\nthe hearer both have the cognitive capacity to recognize that other\npeople have higher-order mental states, i.e., both parties\nmust be cognitively capable of recognizing that people have mental\nstates about other people’s mental states. For instance, in\norder for you to satisfy all of the conditions in Telling,\nyou must believe (that your friend intends [that you\nbelieve (that your friend is intending [that you\nacquire an epistemic reason for belief because you recognizes that you\nfriend is intending to offer one)]). But decades of literature in\ndevelopmental psychology suggest that for neuro-typical children, the\nability to recognize that people have higher order mental states is\nnot acquired until around five or six years old. Moreover, this\nliterature also suggests that for people with autism, the ability to\ndo this is not acquired until much later in life, if it is acquired at\nall. Thus, insofar as young children and people with autism can\nacquire testimonial justification from their parents, say, then the\nAssurance View should be rejected on the grounds that it\nproblematically excludes these people from acquiring something of\nepistemic importance. See Leonard (2016).", "\nTestimonial Reliabilists also deny that our testimonial-based beliefs\nare justified by evidence. But instead of claiming that they are\njustified by non-evidential assurances, the idea is that:", "\n\n\nTestimonial\n Reliabilism:[15]\n A hearer’s testimonial justification consists in the\nreliability of the processes involved in the production of the\nhearer’ testimonially-based belief. (See, e.g., Graham 2000a,\n2000b,\n 2006a;[16]\n Goldberg 2010a; and Sosa 2010).\n", "\nTo get a better handle on this view, suppose that your friend tells\nyou that the concert starts in an hour and that you thereby acquire\ntestimonial justification for believing that this is the case. In very\nbroad strokes, Testimonial Reliabilists can explain the nature of your\njustification as follows: When it comes to concerts, your friend\ntestifies truly almost all of the time; moreover, you are great at\ndifferentiating cases in which your friend is speaking honestly and\nwhen she is trying to deceive you; thus, you have testimonial\njustification in this case because the processes involved in the\nproduction and consumption of the testimony in question are highly\nreliable.", "\nIt is worth noting that there are at least two important processes\ninvolved in a testimonial exchange. First, there are the processes\ninvolved in the production of the speaker’s testimony, i.e., the\nprocesses that are relevant to the likelihood that the testifier\nspeaks the truth. Second, there are the processes involved in the\nhearer’s consumption of the testimony, i.e., the processes\ninvolved in the hearer being able to monitor for signs that what the\nspeaker says is false or unlikely to be true. For this reason,\nTestimonial Reliabilism can be developed in a number of importantly\ndifferent ways. For instance, one could opt for a view according to\nwhich a hearer’s testimonial justification for believing that\np is only a matter of the reliability of the processes involved\nin the production of the speaker’s say-so. Or, one could opt for\na view according to which testimonial justification only amounts to\nthe reliability of the processes involved in the hearer’s\nconsumption of the speaker’s testimony. Or, one could also opt\nfor a view according to which all of the relevant processes matter.\nSee Graham (2000a, 2000b, 2006a), Goldberg (2010a), and Sosa (2010)\nfor recent defenses of Testimonial Reliabilism, and see\n Section 4\n for additional versions of this view as well.", "\nTestimonial Reliabilism is motivated by the considerations that\nsupport Reliabilist theories of justification more generally, as well\nas its ability to avoid the problems that plague the views discussed\nabove. Nevertheless, opponents have argued that Testimonial\nReliabilism faces at least two problems of its own.", "\nFirst, insofar as there are at least two processes involved in a\ntestimonial exchange, Testimonial Reliabilists are faced with the\nsubstantial challenge of specifying which of these processes are\nrelevant to the hearer’s testimonial justification, i.e.,\nTestimonial Reliabilists must give an account of which processes are\nrelevant here, and they must do so in a way that captures every\ninstance in which a hearer intuitively acquires testimonial\njustification from a speaker. (See Wright 2019, who argues that this\nis not merely an instance of the generality problem that poses a worry\nfor Reliabilist views of justification more generally).", "\nSecond, consider cases that involve one hearer and two\nsources of information. For instance, suppose that Rebecca, who\nis in fact a reliable testifier, tells you that traffic on I405 is\nbad. And suppose also that Umar, who is in fact an unreliable\ntestifier, tells you that traffic on I90 is all clear. Finally,\nsuppose that you do not have any reason to prefer one source of\ninformation over the other, i.e., for all you know, Rebecca and Umar\nare equally reliable testifiers.", "\nNow, consider the versions of Testimonial Reliabilism according to\nwhich the processes that are relevant to acquisition of testimonial\njustification are those that are involved in the speaker’s\nproduction of the testimony in question, as well as the hearer’s\nability to discern when the speaker is being sincere. It seems that\nthese Testimonial Reliabilists are committed to giving an\nasymmetric verdict in this case; that is, because the\nprocesses involved in the production of your belief based on\nRebecca’s testimony are reliable, and because the processes\ninvolved in the production of your belief based on Umar’s\ntestimony are not, this version of Testimonial Reliabilism is\ncommitted to the claim that while you do have testimonial\njustification for believing that the traffic on 1405 is bad, you do\nnot have testimonial justification for believing that I90 is all\nclear.", "\nHowever, opponents have argued that this verdict is highly\ncounterintuitive. After all, how could you possibly be justified in\nbelieving Rebecca’s testimony but not Umar’s, given that\nyou have no reason to think that the former is in any way better than\nthe latter? Thus, this version of Testimonial Reliabilism should be\nrejected. See Barnett (2015)." ], "subsection_title": "3.2 Non-Evidential Views" }, { "content": [ "\nWe have seen that the evidential and non-evidential views discussed\nabove offer very different takes on how our testimonial-based beliefs\nare justified. We have also seen that while these views have their\nadvantages, they face some serious problems as well. Consequently,\nsome epistemologists have argued that testimonial justification cannot\nbe explained in a unified way. Instead, the strategy has been to offer\nhybrid views that combine various components of the accounts discussed\nabove.", "\nFor instance, some have tried to combine Reductionist and Reliabilist\ninsights such that testimonial justification consists partly in the\nhearer’s evidence for accepting the speaker’s testimony,\nand partly in terms of the speaker’s and hearer’s\nreliability at producing and consuming testimony respectively, e.g.,\nLackey (2008). Others have tried to combine insights from\nReductionism, Reliabilism and the Inheritance View such that a\nhearer’s belief can be justified by their own evidence for\naccepting what the speaker says, or by the reliability of the\nspeaker’s testimony, or by inheriting the evidence that is\npossessed by the speaker, e.g., Wright (2019). (For other hybrid\nviews, see Gerken 2013 and Faulkner 2000).", "\nMuch of the recent work on testimonial justification concerns whether\nthese hybrid views ultimately succeed, or whether they run into\nproblems of their own." ], "subsection_title": "3.3 Hybrid Views" } ] }, { "main_content": [ "\nConsider", "\n\n\nFourth Big Question: Should testimonial justification be\nunderstood individualistically, or anti- individualistically?\n", "\nSome epistemologists endorse", "\n\n\nIndividualism: A complete account of testimonial\njustification can be given by appealing to features that only have to\ndo with the hearer.\n", "\nOther epistemologists endorse", "\n\n\nAnti-Individualism: A complete account of testimonial\njustification cannot be given by only appealing to features that have\nto do with the hearer.\n", "\nFor instance, according to some Anti-Individualists, acquiring\ntestimonial justification involves features having to do with both the\nhearer and the speaker. And according to other Anti-Individualists,\nacquiring testimonial justification involves features having to do\nwith both the hearer and the other speakers in the hearer’s\nlocal environment. For various defenses of Anti-Individualism, see,\ne.g., Graham (2000b), Lackey (2008), Goldberg (2010a), Kallestrup and\nPritchard (2012), Gerken (2013), Pritchard (2015), and Palermos\n(forthcoming).", "\n(Note: In formulating these two views, I am being deliberately\nopen-ended about how the “features” in question should be\nunderstood. As we will see below, this is because the debate between\nIndividualists and Anti-Individualists cuts across the other debates\nabout testimonial justification that we have explored above.\nConsequently, different members of each camp will want to give\nimportantly different takes on what these features amount to.)" ], "section_title": "4. Individualism and Anti-Individualism", "subsections": [ { "content": [ "\nSuppose that Amanda tells Scott that the roller rink is open (=\np) and that Scott thereby acquires testimonial justification\nfor believing that p.", "\nTo get a grip on one version of Individualism, recall the Reductionist\nviews discussed in\n Section 1.1.\n According to Reductionists, testimonial justification consists in an\ninference that the hearer makes, i.e., the hearer’s inference\nfrom the claim that (a) the speaker said that p to the\nconclusion that (b) p is true. Thus, Reductionists are\nIndividualists in the following sense: they maintain that whether or\nnot a hearer acquires testimonial justification for believing p\ndepends entirely on features having to do with the hearer, where these\nfeatures include, e.g., the hearer’s perception of the speaker\nuttering p, the hearer remembering that testimony is generally\nreliable, and the hearer inferring on these grounds that what the\nspeaker said on this occasion is likely to be true.", "\nTo see a second version of Individualism, recall the our discussion of\nTestimonial Reliabilism in\n Section 3.2.2.\n According to some (but certainly not all) Testimonial Reliabilists,\ntestimonial justification should be understood Individualistically\nbecause it consists only in the reliability of the cognitive processes\nthat are internal to the hearer, i.e., the cognitive processes that\ntake place exclusively in the mind of the hearer herself. See Alvin\nGoldman (1979, 1986) and Alston (1994, 1995).", "\nWhile we have seen a variety of problems for both of these views\nabove, it is worth considering one challenge to this individualistic\nversion of Testimonial Reliabilism in particular. Doing so will not\nonly help shed light on why some Testimonial Reliabilists opt for an\nanti-individualistic view, it will also help illustrate how the debate\nabout Individualism and Anti-Individualism cuts across the other\ndebates we have considered above.", "\nTo begin, consider these two cases from Goldberg (2010a):", "\n\n\nGood: Wilma has known Fred for a long time; she knows\nthat he is a highly reliable speaker. So when Fred tells her that\nBarney has been at the stonecutters’ conference all day, Wilma\nbelieves him. (Fred appeared to her as sincere and competent as he\nnormally does, and she found nothing remiss with the testimony.) In\npoint of fact, Fred spoke from knowledge.\n\n\nBad: Wilma has known Fred for a long time; she knows\nthat he is a highly reliable speaker. So when Fred tells her that\nBarney has been at the stonecutters’ conference all day, Wilma\nbelieves him. (Fred appeared to her as sincere and competent as he\nnormally does, and she found nothing remiss with the testimony.)\nHowever, in this case, Fred did not speak from knowledge. Instead, he\nwas just making up a story about Barney, having had ulterior motives\nin getting Wilma to believe this story. (Fred has never done this\nbefore; it is out of his normally reliable character to do such a\nthing.) Even so, Fred’s speech contribution struck Wilma here,\nas in the good scenario, as sincere and competent; and she was not\nepistemically remiss in reaching this verdict… As luck would\nhave it, though, Barney was in fact at the conference all day (though\nFred, of course, did not know this).\n", "\nContrasting these two cases motivates the following line of thought:\nIt seems like Wilma knows that Barney was at the stonecutters’\nconference (= p) in Good but not in\nBad. It also seems like the cognitive processes that\nare internal to Wilma are the same across both cases. Thus, insofar as\njustification is what turns an unGettiered, true belief into\nknowledge, and insofar as Wilma’s unGettiered, true belief that\np amounts to knowledge in Good but not in\nBad, the cognitive processes involved in the\nacquisition of testimonial justification cannot just be the ones that\nare internal to Wilma. Thus, Testimonial Reliabilists should not\nendorse Individualism. See Goldberg (2010a) for this argument." ], "subsection_title": "4.1 Individualism" }, { "content": [ "\nContrasting the Good and Bad cases\nhas motivated some Testimonial Reliabilists to endorse one version of\nAnti-Individualism. The core idea here is that insofar as testimonial\njustification should be understood in terms of the cognitive processes\nimplicated in the production of the hearer’s belief that\np, the relevant processes must include both (a) the processes\ninvolved in the production of the speaker’s testimony and (b)\nthe processes involved in the hearer’s consumption of what the\nspeaker said. For instance, the cognitive processes internal to Wilma\nwere the highly reliable in both Good and\nBad, e.g., in both cases she was equally good at\nmonitoring for signs that Barney was being insincere. However, the\nprocesses internal to Barney that were implicated in his utterance\nthat p were reliable in Good (i.e., Barney\nspoke from knowledge) but unreliable in Bad (i.e.,\nBarney uttered that p in an attempt to be deceptive). Thus, by\ngiving an account of testimonial justification that requires both the\nspeaker and hearer to be reliable producers and consumers of testimony\nrespectively, Testimonial Reliabilists who endorse this\nAnti-Individualistic approach can explain why Wilma’s belief\nseems better off in Good than it is in\nBad. (Goldberg [2010a] defends Anti-Individualism on\nthese grounds, and Graham (2000b) and Lackey (2008) also defend\nAnti-Individualistic views by requiring that in order for a hearer to\nacquire testimonial justification, not only does the hearer need to be\na reliable consumer of testimony, the speaker needs to be a reliable\ntestifier as well. Finally, Kallestrup and Pritchard (2012), Gerken\n(2013), Pritchard (2015), and Palermos (forthcoming) have recently\ndefended versions of Anti-Individualism according to which the\ntestifiers in the hearer’s local environment need to be reliable\nin order for the hearer to acquire testimonial knowledge from the\nparticular speaker in question).", "\nTo see a second and importantly different version of\nAnti-Individualism, recall the Inheritance View from\n Section 3.1.2.\n On this view, when a hearer acquires testimonial justification for\nbelieving p, this is because they literally inherit the\njustification that the speaker has for believing p. Thus,\nproponents of the Inheritance View are Anti-Individualists in the\nfollowing sense: they maintain that whether or not a hearer acquires\ntestimonial justification for believing p crucially depends on\nfeatures having to do with the speaker, i.e., whether the speaker has\nany justification for the hearer to inherit.", "\nWhether or not either of these Anti-Individualistic approaches will\nultimately succeed is a topic of current debate.", "\nBefore moving on, it is worth noting that while we have been focusing\non testimonial justification, similar debates between\nIndividualists and Anti-Individualists can be had about testimonial\nknowledge. While many epistemologists endorse Individualism\n(Anti-Individualism) about both justification and knowledge, one need\nnot do so. For instance, Audi (1997) endorses Reductionism about\njustification and the Transmission View about knowledge. On this\npicture, then, Individualism is true with respect to justification\nbecause whether or not a hearer acquires testimonial justification\ndepends solely on the inferences that they make. However,\nAnti-Individualism is true with respect to knowledge because in order\nfor a hearer to acquire testimonial knowledge that p, the\nspeaker must also know that p. Keeping these distinctions in\nmind further illustrates how the debate between Individualists and\nAnti-Individualists cuts across so many of the other debates we have\nseen above." ], "subsection_title": "4.2 Anti-Individualism" } ] }, { "main_content": [ "\nHere is a conversation that we might have:", "\n\n\n\nYou: This plant is Pacific Poison Oak. Don’t touch it!\n\nMe: How do you know that?\n\nYou: Suneet told me. He lives in this area a knows a little bit\nabout plants.\n\n", "\nAnd here is another:", "\n\n\n\nYou: This plant is Pacific Poison Oak. Don’t touch it!\n\nMe: How do you know that?\n\nYou: Margae told me. She has a PhD in plant biology and studies\nthis plant in particular.\n\n", "\nIn both cases you have acquired testimonial knowledge. But in the\nsecond case it seems like your belief is better off, epistemically\nspeaking. This is because in the first case your belief is based on\nthe testimony of a layman who is somewhat knowledgeable about the\ntopic at hand, whereas in the second case your belief is based on the\ntestimony of an epistemic authority (or, someone who is both\nyour epistemic superior and an expert about the domain in question).\n(See Zagzebski 2012; Jäger 2016; Croce 2018; and Constantin &\nGrundmann 2020 for more on how the notion of an epistemic authority\nshould be understood.)", "\nBut how exactly should the difference between epistemic authorities\nand everyone else be accounted for?", "\nBroadly speaking, those working on the epistemology of authoritative\ntestimony endorse one of two accounts: Preemptive Accounts\nand Non-Preemptive Accounts. Those who endorse a Preemptive\nAccount of authoritative testimony accept", "\n\n\nPreemption: The fact that an authority… [testifies]\nthat p is a reason for me to believe that p which\nreplaces my other reasons relevant to p and is not simply added\nto them. (Zagzebski 2012: 107)\n", "\nThe key idea here is that when you get testimony from an authority\nthat p, the authority’s testimony is now the only reason\nthat you have for believing p, i.e., any other reasons you may\nhave had are now preempted in the sense that they no longer count for\nor against p. Proponents of the Preemptive Account, then,\nexplain the difference between authoritative and non-authoritative\ntestimony as follows: Authoritative testimony can provide you with a\npreemptive reason for belief, whereas non-authoritative testimony\ncannot. For defenses of various versions of the Preemptive Account,\nsee Zagzebski (2012, 2014, 2016), Keren (2007, 2014a, 2014b), Croce\n(2018) and Constantin and Grundmann (2020). See Anderson (2014),\nDougherty (2014), Jäger (2016), Dormandy (2018), and Lackey\n(2018a) for some worries with this view.", "\nThose who endorse a Non-Preemptive Account of authoritative testimony\nargue that Preemption has wildly unintuitive consequences, e.g., if\nPreemption is true, then you can be justified in believing your pastor\n(who is otherwise reliable) when he tells you that women are\ninherently inferior to men (see, e.g., Lackey 2018a). Instead of\nthinking about authoritative testimony as providing preemptive reasons\nfor belief, proponents of the Non-Preemptive Account take an\nauthority’s testimony that p to provide a very strong\nreason to believe that p, where this reason is to be added to,\nor combined with, all of the other reasons that you have related to\nthe proposition in question. See Dormandy (2018) and Lackey (2018a)\nfor defenses of Non-Preemptive Accounts.", "\nFor related debates about testimony and expertise, see Hardwig’s\n(1985) seminal paper on expert testimony in general, Alvin\nGoldman’s (2001) paper on determining which experts to trust\nwhen there is disagreement amongst them, and Goldberg’s (2009)\npaper that links issues in epistemology and philosophy of language by\ndiscussing how expert testimony bears on the semantics of technical\nterms. See also Kitcher (1993), Walton (1997), Brewer (1998) and\nGolanski (2001) for a discussion of expert testimony in the scientific\nsetting, and for discussion of expert testimony in a legal setting,\nsee Wells and Olson (2003)." ], "section_title": "5. Authoritative Testimony", "subsections": [] }, { "main_content": [ "\nWhile much attention has been paid to issues surrounding\nindividual testimony, i.e., cases in which one speaker tells\nsomeone that p is true, recently epistemologists have started\nexploring a number of related questions regarding group\ntestimony, i.e., cases in which a group testifies to someone that\np is true. Here is one case that motivates this line of\nresearch.", "\n\n\nPopulation Commission: Consider the UN Population\nCommission that was established by the Economic and Social Council of\nthe United Nations in 1946. The Commission was designed to assist the\ncouncil by arranging studies and advising the council on population\nissues, trends, developments, policies, and so on. It is also charged\nwith monitoring the implementation of policies designed by the United\nNations to regulate population and to provide recommendations to the\ncouncil and United Nations as a whole. The commission is composed of\n47 members with a representative from almost every country in the\nUnited Nations. In 2002, the Commission released a report entitled\nCharting the Progress of Populations that provides information on 12\nsocio-economic indicators, including total population, maternal\nmortality, infant mortality, and so on. (Tollefsen 2007:\n300–301)\n", "\nThere are three things to notice here. First, consider a particular\nclaim in the Charting the Progress of Populations report. For\ninstance, let p be the claim that", "\n\n\nWhile the population in North America has risen, the population in\nCentral America has stayed the same, and the population in South\nAmerica has declined.\n", "\nAt the time the report was released, no single member of the UN\nPopulation committee believed p. That is, none of the committee\nmembers were aware that p was true until the report was\nreleased and they read it for themselves.", "\nSecond, and relatedly, before the report was released, none of the\ncommittee members had any evidence, or justification, for believing\np. That is, while some members might have justifiably believed\nthat the population in North America was on the rise, and while others\nmight have justifiably believed that the population in South America\nwas on the decline, and while others still might have justifiably\nbelieved that the population in Central America had stayed the same,\ngiven the way in which the labor was divided amongst the researchers,\ni.e., given that none of them had communicated their findings with one\nanother, nobody had justification for thinking that p itself\nwas true until after the report came out.", "\nThird, and finally, the UN Commission did seem to testify that\np, i.e., their report did contain the group’s testimony\nabout the population changes in the Americas.", "\n(Of course, this is not the only case that motivates the need for an\nepistemology of group testimony. Wikipedia, for instance,\npresents a number of interesting questions about what it would take\nfor a group to testify, and when and why we should accept what a group\nsays. See, e.g., Tollefsen 2009; Wray 2009; and Fallis 2008. Cases\ninvolving testimony from scientific groups also raise similar issues.\nSee, e.g., Hardwig 1985 and Faulkner 2018).", "\nCases like this give rise to at least five important questions. First,\nconsider", "\n\n\nHow should we understand the relationship between a group’s\ntestimony that p and the testimony of the group’s\nindividual members?\n", "\nOn the one hand, Summativists maintain that a group’s\ntestimony that p should be understood in terms of the testimony\nof some (or most, or all) of its members. On the other hand,\nNon-Summativists maintain that it is possible for a group to\ntestify that p even if none of its members do. (See Tollefsen\n(2007) and Lackey (2014) for a defense of different Non-Summative\npositions).", "\nRelatedly, Deflationists maintain to a group’s\ntestimony that p can be reduced to some individual’s\ntestimony that p (regardless of whether those individuals are\nmembers of the group, or just mere spokesmen), whereas\nInflationists maintain that a group itself can be a\ntestifier. (See Tollefsen (2007) for a defense of the latter, and see\nLackey’s (2014) for a deflationary account of the epistemology\nof group testimony and her (2018a) for an inflationary account of the\nnature of group assertion).", "\nSecond, consider", "\n\n\nUnder what conditions is a hearer justified in believing a\ngroup’s testimony that p?\n", "\nThe debate surrounding this question is analogous to the\nReductionist/Anti-reductionist debate about individual testimony in\n Section 1.\n See Tollefsen (2007) for a defense of a reductionist view.", "\nThird, consider", "\n\n\nIf you are justified in believing that p on the basis of a\ngroup’s testimony, is your belief justified by\nevidence?\n", "\nThe debate surrounding this question is analogous to the debates about\nindividual testimony discussed in\n Section 3.\n For instance, suppose that you are justified in believing that\np on the basis of a group’s testimony that p.\nMiranda Fricker (2012) defends an Assurance View according to which\nyour belief is justified by the group’s assurance that p\n(but see Faulkner (2018) for a criticism of this view). Lackey (2014)\ndefends a reliabilist account according to which your belief is\njustified by the reliability (or truth conduciveness) of the\ngroup’s statement that p (but see Faulkner (2018) for a\ncriticism of this view too). Finally, Faulkner (2018) defends a\nqualified Inheritance View according to which your belief that\np can be justified by the justification that the group has (or\nat least has access to).", "\nFourth, consider,", "\n\n\nCan group testimony generate knowledge, or can it merely transmit\nit?\n", "\nThe debate surrounding this question is analogous to the debates about\nindividual testimony in\n Section 2.\n On the one hand, Faulkner (2018) defends a qualified Transmission\nView according to which you can only acquire testimonial knowledge and\njustification from a group’s testimony that p if that\ngroup has, or at least has access to, a body of justification\nthat supports p. On the other hand, Lackey (2014) defends a\nview that is compatible with a group’s testimony generating\nknowledge and justification.", "\nFifth, and finally, consider,", "\n\n\nWhat, if anything, does a group’s testimony that p\nentail about that group’s knowledge (and thus belief) that\np?\n", "\nMore specifically, suppose that a group testifies that p and\nthat you come to know that p on this basis. Does the fact that\nyou acquired testimonial knowledge in this case entail that groups\nthemselves can be knowers (and thus believers)?", "\nOn the one hand, John Hardwig (1985) argues for a positive answer\nhere. That is, Hardwig argues that if we acknowledge that groups can\ntestify, we should also acknowledge that groups themselves can be\nknowers, and thus believers too (see also Lackey (2016) for an\nargument to the effect that groups can possess justified beliefs). On\nthe other hand, Faulkner (2018) argues against this line of thought\nand suggests that even if groups can testify, this does not entail\nthat they possess any mental states.", "\nOf course, there is much more work that can, and should, be done about\nthe epistemological significance of receiving testimony from\ngroups." ], "section_title": "6. Group Testimony", "subsections": [] }, { "main_content": [ "\nUntil now we have been operating with an intuitive but inexact notion\nof what counts as testimony, i.e., for the most part, we have just\nbeen looking at cases in which speakers say stuff. But how exactly\nshould the speech act of testimony be understood? That is, how should\ntestimony be individuated from the other things that one can do with\ntheir words?", "\nOne answer is that testimony should simply be identified with\nassertion, i.e., one testifies that p if, and only if, one\nasserts that p. (E. Fricker 1987 and Sosa (1994) offer passing\nremarks in defense of this position). But while it is widely accepted\nthat one must assert that p in order to testify that p,\nthere is much debate about whether asserting that p is\nsufficient for testifying that p. (See Goldberg 2010b, though,\nwho argues that asserting that p is not even necessary for\ntestifying that p, and see the entry on Assertion for more\nabout how this speech act should be understood).", "\nFor instance, in addition to asserting that p, one influential\naccount maintains that in order to testify that p, the\nfollowing conditions must also be met:", "\n\n\nTestimony: S testifies by making some statement that p\nif and only if:\n\n\n(T1)\nS’s stating that p is evidence that p\nand is offered as evidence that p.\n(T2)\nS has the relevant competence, authority, or credentials to\nstate truly that p.\n(T3)\nS’s statement that p is relevant to some\ndisputed or unresolved question (which may or may not be whether\np) and is directed to those who are in need of evidence on the\nmatter. (Coady 1992: 42).\n\n", "\nHowever, opponents have objected to each of T1–T3. Here is just\none example. Some have rejected T1 on the grounds that one can testify\nthat p even though the testimony itself does not provide the\nhearer with any evidence that p is true, e.g., if I tell you\nthat humans spontaneously combust all the time, and insofar as you\nknow that I am wildly unreliable about this issue, it seems like I\nhave testified to you even though my testimony provides no evidence\nwhatsoever for the proposition in question. (See E. Fricker (1995) and\nLackey (2008). See Lackey (2008: Ch. 1) for a discussion of other\nproblems with this view).", "\nIn light of worries like these, many authors have offered alternative\ntakes on how testimony should be characterized. For instance, E.\nFricker (1995: 396–7) argues that testimony should just be\nunderstood in a very general sense, with “no restrictions either\non the subject matter, or on the speaker’s epistemic relation to\nit.” (See also Audi (1997) and Sosa (1991) for views in this\nballpark). And, as we saw in\n Section 3.2.1,\n proponents of the Assurance View understand testimony in terms of\nTelling.", "\nGraham (1997: 227) offers a different account of testimony based on\nconveying information, i.e., a speaker, S, testifies that\np if, and only if, (i) S’s stating that p\nis offered as evidence that p (ii) S intends that his\naudience believe that he has the relevant competence, authority, or\ncredentials to state truly that p and (iii) S’s\nstatement that p is believed by S to be relevant to some\nquestion that he believes is disputed or unresolved (which may or may\nnot be whether p) and is directed at those whom he believes to\nbe in need of evidence on the matter. (J. Ross 1975 and Elgin (2002)\nalso offer accounts that crucially hinge on the speaker’s\nstatement purporting to convey information).", "\nAnd Lackey (2008: 30–32) offers a disjunctive account of\ntestimony according to which we need to distinguish between\nspeaker testimony and hearer testimony as\nfollows.", "\n\n\nSpeaker Testimony: S s-testifies that p by\nperforming an act of communication a if and only if, in\nperforming a, S reasonably intends to convey the\ninformation that p (in part) in virtue of a’s\ncommunicable content.\n\n\nHearer Testimony: S h-testifies that p by\nmaking an act of communication a if and only if H,\nS’s hearer, reasonably takes a as conveying the\ninformation that p (in part) in virtue of a’s\ncommunicable content.\n", "\nOne upshot of this disjunctive account is that it captures the sense\nin which testimony is often an intentional act performed by the\nspeaker, as well as the sense in which testimony is a source of\nknowledge and justified belief regardless of what the speaker intended\nto say.", "\nRegardless of how testimony itself should be understood, all of these\nauthors agree that it is possible to learn from the testimony of\nothers. As we have seen, though, explaining how it is that we can\nlearn from what other people tell us has proven to be a difficult\ntask." ], "section_title": "7. The Nature of Testimony Itself", "subsections": [] } ]

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[ "\nWe see colours, hear sounds and feel textures. Some aspects of the\nworld, it seems, are perceived through a particular sense. Others,\nlike shape, are perceived through more than one sense. But what sense\nor senses do we use when perceiving time? It is certainly not\nassociated with one particular sense. In fact, it seems odd to say\nthat we see, hear or touch time passing. And indeed, even if all our\nsenses were prevented from functioning for a while, we could still\nnotice the passing of time through the changing pattern of our\nthought. Perhaps, then, we have a special faculty, distinct from the\nfive senses, for detecting time. Or perhaps, as seems more likely, we\nnotice time through perception of other things. But how?", "\nTime perception raises a number of intriguing puzzles, including what\nit means to say we perceive time. In this article, we shall\nexplore the various processes through which we are made aware of time,\nand which influence the way we think time really is. Inevitably, we\nshall be concerned with the psychology of time perception, but the\npurpose of the article is to draw out the philosophical issues, and in\nparticular whether and how aspects of our experience can be\naccommodated within certain metaphysical theories concerning the\nnature of time and causation." ]

[ { "content_title": "1. What is ‘the perception of time’?", "sub_toc": [] }, { "content_title": "2. Kinds of temporal experience", "sub_toc": [] }, { "content_title": "3. Duration", "sub_toc": [] }, { "content_title": "4. The specious present", "sub_toc": [] }, { "content_title": "5. Past, present and the passage of time", "sub_toc": [] }, { "content_title": "6. Time order", "sub_toc": [] }, { "content_title": "7. The metaphysics of time perception", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThe very expression ‘the perception of time’ invites\nobjection. Insofar as time is something different from events, we do\nnot perceive time as such, but changes or events in\ntime. But, arguably, we do not perceive events only, but also their\ntemporal relations. So, just as it is natural to say that we perceive\nspatial distances and other relations between objects (I see the\ndragonfly as hovering above the surface of the water), it seems\nnatural to talk of perceiving one event following another (the\nthunderclap as following the flash of lightning), though even here\nthere is a difficulty. For what we perceive, we perceive as\npresent—as going on right now. Can we perceive a\nrelation between two events without also perceiving the events\nthemselves? If not, then it seems we perceive both events as present,\nin which case we must perceive them as simultaneous, and so not as\nsuccessive after all. There is then a paradox in the notion of\nperceiving an event as occurring after another, though one that\nperhaps admits of a straightforward solution. When we perceive B as\ncoming after A, we have, surely, ceased to perceive A. In which case,\nA is merely an item in our memory. Now if we wanted to construe\n‘perceive’ narrowly, excluding any element of memory, then\nwe would have to say that we do not, after all, perceive B as\nfollowing A. But in this article, we shall construe\n‘perceive’ more broadly, to include a wide range of\nexperiences of time that essentially involve the senses. In this wide\nsense, we perceive a variety of temporal aspects of the world. We\nshall begin by enumerating these, and then consider accounts of how\nsuch perception is possible." ], "section_title": "1. What is ‘the perception of time’?", "subsections": [] }, { "main_content": [ "\nThere are a number of what Ernst Pöppel (1978) calls\n‘elementary time experiences’, or fundamental aspects of\nour experience of time. Among these we may list the experience of (i)\nduration; (ii) non-simultaneity; (iii) order; (iv) past and present;\n(v) change, including the passage of time. It might be thought that\nexperience of non-simultaneity is the same as experience of time\norder, but it appears that, when two events occur very close together\nin time, we can be aware that they occur at different times without\nbeing able to say which one came first (see Hirsh and Sherrick 1961).\nWe might also think that perception of order was itself explicable in\nterms of our experience of the distinction between past and present.\nThere will certainly be links here, but it is a contentious question\nwhether the experience of tense—that is, experiencing\nan event as past or present—is more fundamental than the\nexperience of order, or vice versa, or whether indeed there is such a\nthing as the experience of tense at all. This issue is taken up below.\nFinally, we should expect to see links between the perception of time\norder and the perception of motion if the latter simply involves\nperception of the order of the different spatial positions of an\nobject. This is another contentious issue that is taken up below." ], "section_title": "2. Kinds of temporal experience", "subsections": [] }, { "main_content": [ "\nOne of the earliest, and most famous, discussions of the nature and\nexperience of time occurs in the autobiographical Confessions\nof St Augustine. Augustine was born in Numidia (now Algeria) in 354\nAD, held chairs in rhetoric at Carthage and Milan, and become Bishop\nof Hippo in 395. He died in 430. As a young adult, he had rejected\nChristianity, but was finally converted at the age of 32. Book XI of\nthe Confessions contains a long and fascinating exploration\nof time, and its relation to God. During the course of it Augustine\nraises the following conundrum: when we say that an event or interval\nof time is short or long, what is it that is being described as of\nshort or long duration? It cannot be what is past, since that has\nceased to be, and what is non-existent cannot presently have any\nproperties, such as being long. But neither can it be what is present,\nfor the present has no duration. (For the reason why the present must\nbe regarded as durationless, see the section on the specious present,\nbelow.) In any case, while an event is still going on, its duration\ncannot be assessed.", "\nAugustine’s answer to this riddle is that what we are measuring,\nwhen we measure the duration of an event or interval of time, is in\nthe memory. From this he derives the radical conclusion that past and\nfuture exist only in the mind. While not following Augustine all the\nway to the mind-dependence of other times, we can concede that the\nperception of temporal duration is crucially bound up with memory. It\nis some feature of our memory of the event (and perhaps specifically\nour memory of the beginning and end of the event) that allows us to\nform a belief about its duration. This process need not be described,\nas Augustine describes it, as a matter of measuring something wholly\nin the mind. Arguably, at least, we are measuring the event or\ninterval itself, a mind-independent item, but doing so by means of\nsome psychological process.", "\nWhatever the process in question is, it seems likely that it is\nintimately connected with what William Friedman (1990) calls\n‘time memory’: that is, memory of when some particular\nevent occurred. That there is a close connection here is entailed by\nthe plausible suggestion that we infer (albeit subconsciously) the\nduration of an event, once it has ceased, from information about how\nlong ago the beginning of that event occurred. That is, information\nthat is metrical in nature (e.g. ‘the burst of sound\nwas very brief’) is derived from tensed information,\nconcerning how far in the past something occurred. The question is how\nwe acquire this tensed information. It may be direct or indirect, a\ncontrast we can illustrate by two models of time memory described by\nFriedman. He calls the first the strength model of time\nmemory. If there is such a thing as a memory trace that persists over\ntime, then we could judge the age of a memory (and therefore how long\nago the event remembered occurred) from the strength of the trace. The\nlonger ago the event, the weaker the trace. This provides a simple and\ndirect means of assessing the duration of an event. Unfortunately, the\ntrace model comes into conflict with a very familiar feature of our\nexperience: that some memories of recent events may fade more quickly\nthan memories of more distant events, especially when those distant\nevents were very salient ones (visiting a rarely seen and frightening\nrelative when one was a child, for instance.) A contrasting account of\ntime memory is the inference model. According to this, the\ntime of an event is not simply read off from some aspect of the memory\nof it, but is inferred from information about relations between the\nevent in question and other events whose date or time is known.", "\nThe inference model may be plausible enough when we are dealing with\ndistant events, but rather less so for much more recent ones. In\naddition, the model posits a rather complex cognitive operation that\nis unlikely to occur in non-human animals, such as the rat. Rats,\nhowever, are rather good at measuring time over short intervals of up\nto a minute, as demonstrated by instrumental conditioning experiments\ninvolving the ‘free operant procedure’. In this, a given\nresponse (such as depressing a lever) will delay the occurrence of an\nelectric shock by a fixed period of time, such as 40 seconds,\ndescribed as the R-S (response-shock) interval. Eventually, rate of\nresponding tracks the R-S interval, so that the probability of\nresponding increases rapidly as the end of the interval approaches.\n(See Mackintosh 1983 for a discussion of this and related\nexperiments.) It is hard to avoid the inference here that the mere\npassage of time itself is acting as a conditioned stimulus: that the\nrats, to put it in more anthropocentric terms, are successfully\nestimating intervals of time. In this case, the strength model seems\nmore appropriate than the inference model." ], "section_title": "3. Duration", "subsections": [] }, { "main_content": [ "\nThe term ‘specious present’ was first introduced by the\npsychologist E.R. Clay, but the best known characterisation of it was\ndue to William James, widely regarded as one of the founders of modern\npsychology. He lived from 1842 to 1910, and was professor both of\npsychology and of philosophy at Harvard. His definition of the\nspecious present goes as follows: ‘the prototype of all\nconceived times is the specious present, the short duration of which\nwe are immediately and incessantly sensible’ (James 1890). How\nlong is this specious present? Elsewhere in the same work, James\nasserts ‘We are constantly aware of a certain duration—the\nspecious present—varying from a few seconds to probably not more\nthan a minute, and this duration (with its content perceived as having\none part earlier and another part later) is the original intuition of\ntime.’ This surprising variation in the length of the specious\npresent makes one suspect that more than one definition is hidden in\nJames’ rather vague characterisation. ", "\nThere are two sources of ambiguity here. One is over whether\n‘the specious present’ refers to the object of the\nexperience, namely a duration in time, or the way in which that object\nis presented to us. The second is over how we should interpret\n‘immediately sensible’. James’ words suggest that\nthe specious present is the duration itself, picked out as the object\nof a certain kind of experience. But ‘ immediately\nsensible’admits of a number of disambiguations. So we could\ndefine the specious present as:", "\nIf James means the first of these, that would certainly explain his\nsuggestion that it could last up to a minute. But this does not seem\nto have much to do specifically with the experience of\npresentness, since we can certainly hold something in the\nshort-term memory and yet recognise it as past. James may be thinking\nof cases where we are listening to a sentence: if we did not somehow\nhold all the words in our conscious mind, we would not understand the\nsentence as a whole. But it is clear that the words are not\nexperienced as simultaneous, for then the result would be an\nunintelligible jumble of sounds. (2) is illustrated by the familiar\nfact that some movements are so fast that we see them as a blur, such\nas when we look at a fan. What is in fact taking place at different\ntimes is presented as happening in an instant. But this is not\nstandardly what is meant by the specious present. (3) is a construal\nthat is found in the literature (see, e.g., Kelly 2005), but it is not\nobvious that that is what James had in mind, since James is concerned\nwith the phenomenology of time perception, and whether or not an\nexperience constitutes a direct or indirect perception of an interval\ndoes not seem to be a phenomenological matter. (Besides which, as\nKelly points out, we might think it odd to suppose that past parts of\nthe interval could be directly perceived.)", "\nThat leaves us with (4): a duration which is perceived both as present\nand as temporally extended. This present of experience is\n‘specious’ in that, unlike the objective present (if there\nis such a thing — see\n The metaphysics of time perception\n below) it is an interval and not a durationless instant. The real or\nobjective present must be durationless for, as Augustine argued, in an\ninterval of any duration, there are earlier and later parts. So if any\npart of that interval is present, there will be another part that is\npast or future.", "\nBut is it possible to perceive something as extended and as present? If\nwe hear a short phrase of music, we seem to hear the phrase as\npresent, and yet — because it is a phrase rather than a single\nchord — we also hear the notes as successive, and therefore as\nextending over an interval. If this does not seem entirely convincing,\nconsider the perception of motion. As Broad (1923) puts it, ‘to\nsee a second-hand moving is quite a different thing from \"seeing\" that\na hour-hand has moved.’ It is not that we see the current\nposition of the second hand and remember where it was a second ago: we\njust see the motion. That leads to the following argument:", "\nStill, there is more than an air of paradox about this. If successive\nparts of the motion (or musical phrase, or whatever change we\nperceive) are perceived as present, then surely they are perceived as\nsimultaneous. But if they are perceived as simultaneous, then the\nmotion will simply be a blur, as it is in cases where it is too fast\nto perceive as motion. The fact that we do not see it as motion\nsuggests that we do not see the successive parts of it as\nsimultaneous, and so do not see them as present. But then how do we\nexplain the distinction to which Broad directs our attention?", "\nOne way out of this impasse is to suggest that two quite distinct\nprocesses are going on in the perception of motion (and other kinds of\nchange). One is the perception of successive states as successive, for\nexample the different positions of the second hand. The other is the\nperception of pure movement. This second perception, which may involve\na more primitive system than the first, does not contain as part the\nrecognition of earlier and later elements. (Le Poidevin 2007, Chapter\n5.) Alternatively, we might attempt to explain the phenomena of temporal experience without appeal to the notion of the specious present at all (see Arstila, 2018)." ], "section_title": "4. The specious present", "subsections": [] }, { "main_content": [ "\nThe previous section indicated the importance of distinguishing\nbetween perceiving the present and perceiving something as\npresent. We may perceive as present items that are past. Indeed, given\nthe finite speed of the transmission of both light and sound (and the\nfinite speed of transmission of information from receptors to brain),\nit seems that we only ever perceive what is past. However, this does\nnot by itself tell us what it is to perceive something as present,\nrather than as past. Nor does it explain the most striking feature of\nour experience as-of the present: that it is constantly changing. The\npassage (or apparent passage) of time is its most striking feature,\nand any account of our perception of time must account for this aspect\nof our experience.", "\nHere is one attempt to do so. The first problem is to explain why our\ntemporal experience is limited in a way in which our spatial\nexperience is not. We can perceive objects that stand in a variety of\nspatial relations to us: near, far, to the left or right, up or down,\netc. Our experience is not limited to the immediate vicinity (although\nof course our experience is spatially limited to the extent that\nsufficiently distant objects are invisible to us). But, although we\nperceive the past, we do not perceive it as past, but as present.\nMoreover, our experience does not only appear to be temporally\nlimited, it is so: we do not perceive the future, and we do not\ncontinue to perceive transient events long after information from them\nreached our senses. Now, there is a very simple answer to the question\nwhy we do not perceive the future, and it is a causal one. Briefly,\ncauses always precede their effects; perception is a causal process,\nin that to perceive something is to be causally affected by it;\ntherefore we can only perceive earlier events, never later ones. So\none temporal boundary of our experience is explained; what of the\nother?", "\nThere seems no logical reason why we should not directly\nexperience the distant past. We could appeal to the principle that\nthere can be no action at a temporal distance, so that something\ndistantly past can only causally affect us via more proximate events.\nBut this is inadequate justification. We can only perceive a spatially\ndistant tree by virtue of its effects on items in our vicinity (light\nreflected off the tree impinging on our retinas), but this is not seen\nby those who espouse a direct realist theory of perception as\nincompatible with their position. We still see the tree, they\nsay, not some more immediate object. Perhaps then we should look for a\ndifferent strategy, such as the following one, which appeals to\nbiological considerations. To be effective agents in the world, we\nmust represent accurately what is currently going on: to be constantly\nout of date in our beliefs while going about our activities would be\nto face pretty immediate extinction. Now we are fortunate in that,\nalthough we only perceive the past it is, in most cases, the very\nrecent past, since the transmission of light and sound, though finite,\nis extremely rapid. Moreover, although things change, they do so,\nagain in most cases, at a rate that is vastly slower than the rate at\nwhich information from external objects travels to us. So when we form\nbeliefs about what is going on in the world, they are largely accurate\nones. (See Butterfield 1984 for a more detailed account along these\nlines.) But, incoming information having been registered, it needs to\nmove into the memory to make way for more up to date information. For,\nalthough things may change slowly relative to the speed of light or of\nsound, they do change, and we cannot afford to be simultaneously\nprocessing conflicting information. So our effectiveness as agents\ndepends on our not continuing to experience a transient state of\naffairs (rather in the manner of a slow motion film) once information\nfrom it has been absorbed. Evolution has ensured that we do not\nexperience anything other than the very recent past (except when we\nare looking at the heavens).", "\nTo perceive something as present is simply to perceive it: we do not\nneed to postulate some extra item in our experience that is ‘the\nexperience of presentness.’ It follows that there can be no\n‘perception of pastness’. In addition, if pastness were\nsomething we could perceive, then we would perceive\neverything in this way, since every event is past by the time\nwe perceive it. But even if we never perceive anything as past (at the\nsame time as perceiving the event in question) we could intelligibly\ntalk more widely of the experience of pastness: the experience we get\nwhen something comes to an end. And it has been suggested that\nmemories—more specifically, episodic memories, those of\nour experiences of past events—are accompanied by a feeling of\npastness (see Russell 1921). The problem that this suggestion is\nsupposed to solve is that an episodic memory is simply a memory of an\nevent: it represents the event simpliciter, rather than the\nfact that the event is past. So we need to postulate something else\nwhich alerts us to the fact that the event remembered is past. An\nalternative account, and one which does not appeal to any\nphenomenological aspects of memory, is that memories dispose us to\nform past-tensed beliefs, and is by virtue of this that they represent\nan event as past.", "\nWe have, then, a candidate explanation for our experience of being\nlocated at a particular moment in time, the (specious) present. And as\nthe content of that experience is constantly changing, so that\nposition in time shifts. But there is still a further puzzle. Change\nin our experience is not the same thing as experience of change. We\nwant to know, not just what it is to perceive one event after another,\nbut also what it is to perceive an event as occurring after another.\nOnly then will we understand our experience of the passage of time. We\nturn, then, to the perception of time order." ], "section_title": "5. Past, present and the passage of time", "subsections": [] }, { "main_content": [ "\nHow do we perceive precedence amongst events? A temptingly simple\nanswer is that the perception of precedence is just a sensation caused\nby instances of precedence, just as a sensation of red is caused by\ninstances of redness. Hugh Mellor (1998), who considers this line,\nrejects it for the following reason. If this were the correct\nexplanation, then we could not distinguish between x being\nearlier than y, and x being later\nthan y, for whenever there is an instance of one relation,\nthere is also an instance of the other. But plainly we are able to\ndistinguish the two cases, so it cannot simply be a matter of\nperceiving a relation, but something to do with our perception of the\nrelata. But mere perception of the relata cannot be all there is to\nperceiving precedence. Consider again Broad’s point about the\nsecond hand and the hour hand. We first perceive the hour hand in one\nposition, say pointing to 3 o’clock, and later we perceive it in\na different position, pointing to half-past 3. So I have two\nperceptions, one later than the other. I may also be aware of the\ntemporal relationship of the two positions of the hand. Nevertheless,\nI do not perceive that relationship, in that I do not see the hand\nmoving. In contrast, I do see the second hand move from one position\nto another: I see the successive positions as successive.", "\nMellor’s proposal is that I perceive x precede\ny by virtue of the fact that my perception of x\ncausally affects my perception of y. As I see the second hand\nin one position, I have in my short-term memory an image (or\ninformation in some form) of its immediately previous position, and\nthis image affects my current perception. The result is a perception\nof movement. The perceived order of different positions need not\nnecessarily be the same as the actual temporal order of those\npositions, but it will be the same as the causal order of the\nperceptions of them. Since causes always precede their\neffects, the temporal order perceived entails a corresponding temporal\norder in the perceptions. Dainton (2001) has objected to this that, if\nthe account were right, we should not be able to remember perceiving\nprecedence, since we only remember what we can genuinely perceive. But\nthere seems no reason to deny that, just because perception of\nprecedence may involve short-term memory, it does not thereby count as\ngenuine perception.", "\nThere is a further disanalogy between perception of colour and\nperception of time order. What is perceived in the case of colour is\nsomething that has a definite spatio-temporal location. The relation\nof precedence, in contrast, is not something that has any obvious\nlocation. But causes do have locations, so the perception of\nprecedence is rather harder to reconcile with the causal theory of\nperception than the perception of colour (Le Poidevin 2004, 2007).", "\nIn effect, Mellor’s idea is that the brain represents time by\nmeans of time: that temporally ordered events are represented by\nsimilarly temporally ordered experiences. This would make the\nrepresentation of time unique. (For example, the brain does not\nrepresent spatially separated objects by means of spatially separated\nperceptions, or orange things by orange perceptions.) But why should\ntime be unique in this respect? In other media, time can be\nrepresented spatially (as in cartoons, graphs, and analogue clocks) or\nnumerically (as in calendars and digital clocks). So perhaps the brain\ncan represent time by other means. One reason to suppose that it must\nhave other means at its disposal is that time needs to be represented\nin memory (I recall, both that a was earlier than\nb, and also the experience of seeing a occur before b) and\nintention (I intend to F after I G), but\nthere is no obvious way in which Mellor’s ‘representation\nof time by time’ account can be extended to these.", "\nOn Mellor’s model, the mechanism by which time-order is\nperceived is sensitive to the time at which perceptions\noccur, but indifferent to their content (what the perceptions\nare of). Daniel Dennett (1991) proposes a different model, on which\nthe process is time-independent, but content-sensitive. For example,\nthe brain may infer the temporal order of events by seeing which\nsequence makes sense of the causal order of those events. One of the\nadvantages of Dennett’s model is that it can account for the\nrather puzzling cases of ‘backwards time referral’, where\nperceived order does not follow the order of perceptions. (See Dennett\n1991 for a discussion of these cases, and also Roache 1999 for an\nattempt to reconcile them with Mellor’s account.)" ], "section_title": "6. Time order", "subsections": [] }, { "main_content": [ "\nIn giving an account of the various aspects of time perception, we\ninevitably make use of concepts that we take to have an objective\ncounterpart in the world: the past, temporal order, causation, change,\nthe passage of time and so on. But one of the most important lessons\nof philosophy, for many writers, is that there may be a gap, perhaps\neven a gulf, between our representation of the world and the world\nitself, even on a quite abstract level. (It would be fair to add that,\nfor other writers, this is precisely not the lesson\nphilosophy teaches.) Philosophy of time is no exception to this.\nIndeed, it is interesting to note how many philosophers have taken the\nview that, despite appearances, time, or some aspect of time, is\nunreal. In this final section, we will take a look at how three\nmetaphysical debates concerning the nature of the world interact with\naccounts of time perception.", "\nThe first debate concerns the reality of tense, that is, our division\nof time into past, present and future. Is time really divided in this\nway? Does what is present slip further and further into the past? Or\ndoes this picture merely reflect our perspective on a reality in which\nthere is no uniquely privileged moment, the present, but simply an\nordered series of moments? A-theorists say that our ordinary\npicture of the world as tensed reflects the world as it really is: the\npassage of time is an objective fact. B-theorists deny this.\n(The terms A-theory and B-theory derive from McTaggart’s (1908)\ndistinction between two ways in which events can be ordered in time,\neither as an A-series—that is in terms of whether they are past,\npresent or future — or as a B-series—that is according to\nwhether they are earlier than, later than, or simultaneous with other\nevents.)", "\nFor B-theorists, the only objective temporal facts concern relations\nof precedence and simultaneity between events. (I ignore here the\ncomplications introduced by the Special Theory of Relativity, since\nB-theory—and perhaps A-theory also—can be reformulated in\nterms which are compatible with the Special Theory.) B-theorists do\nnot deny that our tensed beliefs, such as the belief that a cold front\nis now passing, or that Sally’s wedding was two\nyears ago, may be true, but they assert that what makes such\nbeliefs true are not facts about the pastness, presentness or futurity\nof events, but tenseless facts concerning precedence and simultaneity\n(see Mellor 1998, Oaklander and Smith 1994). On one version of the\nB-theory, for example, my belief that there is a cold front now\npassing is true because the passing of the front is simultaneous\nwith my forming the belief. Now one very serious challenge to the\ntenseless theorist is to explain why, if time does not pass in\nreality, it appears to do so. What, in B-theoretic terms, is the basis\nfor our experience as-of the passage of time?", "\nThe accounts we considered above, first of the temporal restrictions\non our experience, and secondly of our experience of time order, did\nnot explicitly appeal to tensed, or A-theoretic notions. The facts we\ndid appeal to look like purely B-theoretic ones: that causes are\nalways earlier than their effects, that things typically change slowly\nin relation to the speed of transmission of light and sound, that our\ninformation-processing capacities are limited, and that there can be\ncausal connections between memories and experiences. So it may be that\nthe tenseless theorist can discharge the obligation to explain why\ntime seems to pass. But two doubts remain. First, perhaps the A-\ntheorist can produce a simpler explanation of our experience. Second,\nit may turn out that supposedly B-series facts are dependent upon\nA-series ones, so that, for example, a and b are\nsimultaneous by virtue of the fact that both are present.", "\nWhat is clear, though, is that there is no direct argument from\nexperience to the A-theory, since the present of experience, being\ntemporally extended and concerning the past, is very different from\nthe objective present postulated by the A-theory. Further, it cannot\nbe taken for granted that the objective passage of time would explain\nwhatever it is that the experience as-of time’s passage is\nsupposed to amount to. (See Prosser 2005, 2007, 2012, 2016, 2018.)", "\nThe second metaphysical issue that has a crucial bearing on time\nperception is connected with the A/B-theory dispute, and that is the\ndebate between presentists and eternalists. Presentists hold that only\nthe present exists (for an articulation of various kinds of\npresentism, and the challenges they face, see Bourne 2006), whereas\neternalists grant equal reality to all times. the two debates, A-\nversus B-theory and presentism versus eternalism, do not map precisely\nonto each other. Arguably, B-theory is committed to eternalism, but\nA-theorists may not necessarily endorse presentism (though Bourne\nargues that they should).", "\nHow might his be connected to perception? According to the indirect\n(or, as it is sometimes called, representative) theory of perception,\nwe perceive external objects only by perceiving some intermediate\nobject, a sense datum. According to the direct theory, in contrast,\nperception of external objects involves no such intermediary. Now,\nexternal objects are at varying distances from us, and, as noted\nabove, since light and sound travel at finite speeds, that means that\nthe state of objects that we perceive will necessarily lie in the\npast. In the case of stars, where the distances are very considerable,\nthe time gap between light leaving the star and our perceiving it may\nbe one of many years. The presentist holds that past states, events\nand objects are no longer real. But if all that we perceive in the\nexternal world is past, then it seems that the objects of our\nperception (or at least the states of those objects that we perceive)\nare unreal. It is hard to reconcile this with the direct theory of\nperception. It looks on the face of it, therefore, that presentists\nare committed to the indirect theory of perception. (See Power 2010a,\n2010b, 2018, Le Poidevin 2015b.)", "\nThe third and final metaphysical issue that we will discuss in the\ncontext of time perception concerns causal asymmetry. The account of\nour sense of being located at a time which we considered under\n Past, present and the passage of time\n rested on the assumption that causation is asymmetric. Later events,\nit was suggested, cannot affect earlier ones, as a matter of\nmind-independent fact, and this is why we do not perceive the future,\nonly the past. But attempts to explain the basis of causal asymmetry,\nin terms for example of counterfactual dependence, or in probabilistic\nterms, are notoriously problematic. One moral we might draw from the\ndifficulties of reducing causal asymmetry to other asymmetries is that\ncausal asymmetry is primitive, and so irreducible. Another is that\nthat the search for a mind-independent account is mistaken. Perhaps\ncausation in intrinsically symmetric, but some feature of our\npsychological constitution and relation to the world makes causation\nappear asymmetric. This causal perspectivalism is the line\ntaken by Huw Price (1996). That causal asymmetry should be explained\nin part by our psychological constitution, in a way analogous to our\nunderstanding of secondary qualities such as colour, is a radical\nreversal of our ordinary assumptions, but then our ordinary\nunderstanding of a number of apparently objective features of the\nworld—tense, absolute simultaneity—have met with similarly\nradical challenges. Now, if causal asymmetry is mind-dependent in this\nway, then we cannot appeal to it in accounting for our experience of\ntemporal asymmetry—the difference between past and future.", "\nFurther, it is not at all clear that perspectivalism can account for\nthe perception of time order. The mechanism suggested by Mellor (see\n Time Order)\n exploited the asymmetry of causation: it is the fact that the\nperception of A causally influences the perception of B, but not vice\nversa, that gives rise to the perception of A’s being followed\nby B. We can represent this schematically as follows (where the arrow\nstands for an asymmetric causal relation):", "\nP(A)→P(B)→P(A<B)\n", "\nBut if there is no objective asymmetry, then what is the explanation?\nOf course, we can still define causal order in terms of a causal\nbetweenness relation, and we can say that the perceived order follows\nthe objective causal order of the perceptions, in this sense: on the one hand, where A\nis perceived as being followed by B, then the perception of B is\nalways causally between the perception of A and the perception of\nA’s being followed by B (the dash represents a symmetric causal\nrelation):", "\nP(A) – P(B) – P(A<B)\n", "\nOn the other hand, where B is perceived as being followed by A, the perception\nof A is always causally between the perception of B and the perception\nof B’s being followed by A:", "\nP(B) – P(A)) – P(B<A)\n", "\nBut what, on the causal perspectivalist view, would rule out the\nfollowing case?", "\nP(B<A) – P(A) – P(B) – P(A<B)\n", "\nFor such a case would satisfy the above constraints. But it is a case\nin which A is perceived by an observer both as following, and as being\nfollowed by, B, and we know that such a case never occurs in\nexperience. ‘Is perceived by x as followed by’ is\nan asymmetric relation (assuming we are dealing with a single sense\nmodality), and so one that can be grounded in the causal relation only\nif the causal relation is itself asymmetric. Now if perspectivalism\ncannot meet the challenge to explain why, when B is perceived as\nfollowing A, A is never perceived by the same observer as following B,\nit seems that our experience of time order, insofar as it has a causal\nexplanation, requires causation to be objectively asymmetric.", "\nOne strategy the causal perspectivalist could adopt (indeed, the only\none available) is to explain the asymmetric principle above in terms\nof some objective non-causal asymmetry. Price, for example, allows an\nobjective thermodynamic asymmetry, in that an ordered series of states\nof the universe will exhibit what he calls a thermodynamic gradient:\nentropy will be lower at one end of the series than at the end. We\nshould resist the temptation to say that entropy increases, for that\nwould be like asserting that a road goes uphill rather than downhill\nwithout conceding the perspectival nature of descriptions like\n‘uphill’. Could such a thermodynamic asymmetry explain the\nperception of time order? That is a question for the reader to\nponder." ], "section_title": "7. The metaphysics of time perception", "subsections": [] } ]

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[ "\nThe thermodynamic time asymmetry is one of the most salient and\nconsequential features of the physical universe. Heat flows from hot\nto cold, never the reverse. The smell of coffee spreads throughout its\navailable volume, never the reverse. Car engines convert fuel energy\ninto work and thermal energy, never the reverse. And so on. The\nscience of thermodynamics is able to capture these generalizations as\nconsequences of its claim that systems spontaneously evolve to future\nequilibrium states but do not spontaneously evolve away from\nequilibrium states. This generalization covers an amazing amount of\nmacroscopic physics and is rightly celebrated as one of the great laws\nof physics.", "\nDespite its familiarity, however, the thermodynamic arrow of time\nraises many deep questions relevant to both philosophy and the\nfoundations of physics. This entry concentrates on two of them. In\ncontemporary parlance, they are each questions about grounding. (1)\nWhat grounds the thermodynamic asymmetry in time? In a world possibly\ngoverned at bottom by time-symmetric laws, how do the time-asymmetric\nlaws of thermodynamics arise? (2) Does the thermodynamic time\nasymmetry ground any other temporal asymmetries? Does it account, for\ninstance, for the fact that we know more about the past than the\nfuture? The discussion thus divides between thermodynamics being an\nexplanandum or explanans. What grounds the thermodynamic asymmetry,\nand given the asymmetry, what does it ground?" ]

[ { "content_title": "1. Thermodynamic Time Asymmetry: A Brief Guide", "sub_toc": [] }, { "content_title": "2. The Problem of the Direction of Time I", "sub_toc": [ "2.1 Past Hypothesis", "2.2 Electromagnetism", "2.3 Cosmology", "2.4 Quantum Cosmology", "2.5 Time Itself", "2.6 Interventionism", "2.7 Quantum Mechanics", "2.8 Lawlike Initial Conditions?" ] }, { "content_title": "3. The Problem of the Direction of Time II", "sub_toc": [ "3.1 The Thermodynamic Reduction", "3.2 The Statistical Mechanical Reduction" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nFirst developed in Sadi Carnot’s Reflections on the Motive\nPower of Fire 1824, the science of classical thermodynamics is\nintimately associated with the industrial revolution. Most of the\nresults responsible for the science originated from the practice of\nengineers trying to improve steam engines. Originating in France and\nEngland in the late eighteenth and early nineteenth centuries, the\nscience quickly spread throughout Europe. By the mid-nineteenth\ncentury, Rudolf Clausius in Germany and William Thomson (later Lord\nKelvin) in England had developed the theory in great detail. Once\ndeveloped, its scope grew from steam engines and the like to arguably\nall macroscopic processes.", "\nThermodynamics is a “phenomenal” science. That means that\nits variables range over macroscopic parameters such as temperature,\npressure and volume. These are properties that hold at equilibrium,\ni.e., when the values of the macroscopic variables remain\napproximately stable. Whether the microphysics underlying these\nvariables are motive atoms in the void or an imponderable fluid is\nlargely irrelevant to this science. The developers of the theory both\nprided themselves on this fact and at the same time worried about it.\nClausius, for instance, was one of the first to speculate that heat\nconsisted solely of the motion of particles (without an ether), for it\nmade the equivalence of heat with mechanical work less surprising.\nHowever, as was common, he kept his “ontological” beliefs\nseparate from his official statement of the principles of\nthermodynamics because he didn’t wish to (in his words)\n“taint” the latter with the speculative character of the\n former.[1]", "\nA treatment of thermodynamics naturally begins with the statements it\ntakes to be laws of nature. These laws are founded upon observations\nof relationships between particular macroscopic parameters and they\nare justified by the fact they are empirically adequate. No further\njustification of these laws is to be found—at this\nstage—from the details of microphysics. Rather, stable,\ncounterfactual-supporting generalizations about macroscopic features\nare enshrined as law. The typical textbook treatment of thermodynamics\ndescribes some basic concepts, states the laws in a more or less rough\nway and then proceeds to derive the concepts of temperature and\nentropy and the various thermodynamic equations of state. It is worth\nremarking, however, that in the last fifty years the subject has been\npresented with a degree of mathematical rigor not previously achieved.\nOriginating from the early axiomatization by Carathéodory in\n1909, the development of “rational thermodynamics” has\nclarified the concepts and logic of classical thermodynamics to a\ndegree not generally appreciated. There now exist many quite\ndifferent, mathematically exact approaches to thermodynamics, each\nstarting with different primitive kinds and/or observational\nregularities as axioms. (For a popular presentation of a recent\naxiomatization, see Lieb and Yngvason 2000.)", "\nIn the traditional approach classical thermodynamics has two laws, the\nFirst and Second\n Laws.[2]\n The First Law expresses the conservation of energy and is founded\nupon the impossibility of creating a machine that can create energy.\nThe law uses the concept of the internal energy of a system, \\(U\\),\nwhich is a function of the system’s macroscopic variables, e.g.,\ntemperature, volume. For thermally isolated (adiabatic)\nsystems—think of systems such as coffee in a thermos—the\nlaw states that this function, \\(U\\), is such that the work \\(W\\)\ndelivered to a system’s surroundings is compensated by a loss of\ninternal energy, i.e., \\(dW = -dU\\). When James Joule and others\nshowed that mechanical work and heat were interconvertible,\nconsistency with the principle of energy conservation demanded that\nheat, \\(Q\\), considered as a different form of energy, be taken into\naccount. For non-isolated systems we extend the law as \\(dQ = dU +\ndW\\), where \\(dQ\\) is the differential of the amount of heat added to\nthe system (in a reversible manner).", "\nThe conservation of energy tells us nothing about temporally\nasymmetric behavior. It doesn’t follow from the First Law that\ninteracting systems quickly tend to approach equilibrium, and once\nachieved, never leave this state. It is perfectly consistent with the\nFirst Law that systems in equilibrium leave equilibrium. In\nparticular, no limitations are placed on transforming energy from one\nform into another, so the Law permits the possibility of machines that\nremove heat from their environment and turn it into work (a so-called\nperpetual mobile of the second kind). To rule out such machines, and\nmore generally, to capture the amazingly general temporally asymmetric\nbehavior we find, another law is needed. Although Carnot was the first\nto state it, the formulations of Kelvin and Clausius are standard:", "\nKelvin’s version is essentially the same as the version arrived\nat by both Carnot and Planck, whereas Clausius’ version differs\nfrom these in a few\n ways.[3]", "\nClausius’ version transparently rules out anti-thermodynamic\nbehavior such as a hot iron bar extracting heat from a neighboring\ncold iron bar. The cool bar cannot give up a quantity of heat to the\nwarmer bar (without something else happening). Kelvin’s\nstatement is perhaps less obvious. It originates in an observation\nabout steam engines, namely, that heat energy is a “poor”\ngrade of energy. Consider a gas-filled cylinder with a frictionless\npiston holding the gas down at one end. If we put a flame under the\ncylinder, the gas will expand and the piston can perform work, e.g.,\nit might move a ball. However, we can never convert the heat energy\nstraight into work without some other effect occurring. In this case,\nthe gas occupies a larger volume.", "\nIn 1854, Clausius introduced the notion of the “equivalence\nvalue” of a transformation, a concept that is the ancestor of\nthe modern day concept of entropy. Later in 1865 Clausius coined the\nterm “entropy” for a similar concept (the word derives\nfrom the Greek word for transformation). The entropy of a state \\(A\\),\n\\(S(A)\\) is defined as the integral \\(S(A) = \\int^{A}_{O} dQ/T\\) over\na reversible transformation, where \\(O\\) is some arbitrary fixed\nstate. For \\(A\\) to have an entropy, the transformation from \\(O\\) to\n\\(A\\) must be quasi-static, i.e., a succession of equilibrium states.\nContinuity considerations then imply that the initial and final states\n\\(O\\) and \\(A\\) must also be equilibrium states. Put in the language\nof entropy, the Second Law states that in a transformation from\nequilibrium state \\(A\\) to equilibrium state \\(B\\), the inequality\n\\(S(B) - S(A)\\) is greater than or equal to the \\(\\int^{A}_{B} dQ/T\\).\nLoosely put, for realistic systems, this implies that in the\nspontaneous evolution of a thermally closed system the entropy can\nnever decrease and that it attains its maximum value at equilibrium.\nWe are invited to think of the Second Law as driving the system to its\nnew, higher entropy equilibrium state.", "\nWith the Second Law thermodynamics is able to characterize an\nextraordinary range of phenomena under one simple law. Remarkably,\nwhether they are gases filling their available volumes, iron bars in\ncontact coming to the same temperature, vinegar and oil separating, or\nmilk mixing in your coffee, they all have an observable property in\ncommon: their entropy increases. Coupled with the First Law, the\nSecond Law is remarkably powerful. It appears that all classical\nthermodynamical behavior can be derived from these two simple\nstatements (O. Penrose 1970).", "\nThe above sketch represents the conventional way of describing\nthermodynamics and its Second Law. Let me mention a few questions that\nit raises.", "\nFirst, what is the precise location of the time-asymmetry? Almost all\ncommentators claim that it lay in the Second Law. If Uffink (2001) and\nBrown and Uffink (2001) are correct, however, then this\n“static” Second Law does not encode any time asymmetry at\nall. It is, after all, simply a relation between a few variables at\nequilibrium. While that may be right, there is no question that\nthermodynamics, if not its Second Law, makes time-asymmetric\nclaims. The spontaneous movement from non-equilibrium to equilibrium\nhappens and is assumed throughout the field. The only question is\nwhether it must be regarded as a separate assumption (perhaps\ndemanding its own name) or can somehow be derived from existing\nprinciples. It’s also worth remarking that many other principles\nof thermodynamics are time-asymmetric, e.g., the classical heat\nequation.", "\nSecond, what is the scope of the Second Law? There are two issues\nhere. First, does it apply to the universe as a whole, so that we can\nsay the universe’s entropy is increasing, or does it only apply\nto select sub-systems of the universe? (See Uffink 2001 for an\ninteresting historical discussion of this topic.) Many philosophers\nand physicists have balked at the idea that the universe itself has an\nentropy. As one might expect, those in the grip of an operationalist\nphilosophy are especially prone to deny that the universe as a whole\nhas an entropy. Second, what sub-systems of the universe does it\ngovern? Are the principles of thermodynamics responsible for\ngeneralizations about black holes? The field of black hole\nthermodynamics assumes it is (see the section on black hole\nthermodynamics in the entry on\n singularities and black holes,\n for discussion and references), although not all are convinced\n(Dougherty & Callender forthcoming). What about the\nmicro-realm?", "\nThird, how are these laws framed in a relativistic universe? They were\ndeveloped in the nineteenth century with a classical spacetime\nbackground in mind. How do we write the theory in a modern\nformulation? Surprisingly, the issue is as much conceptual as\ntechnical. The correct (special) relativistic transformation rules for\nthermodynamic quantities are controversial. Do Lorentz boosted gases\nappear hotter or colder in the new inertial frame? Albert Einstein\nhimself answered the question about the gas differently throughout his\nlife! With all the current activity of physicists being focused on the\nthermodynamics of black holes in general relativity and quantum\ngravity, it is amusing to note that special relativistic\nthermodynamics is still a field with many open questions, both\nphysically and philosophically (see Earman 1981 and Liu 1994).", "\nFourth, another important question concerns the reduction of\nthermodynamic concepts such as entropy to their mechanical, or\nstatistical mechanical, basis. As even a cursory glance at statistical\nmechanics reveals, there are many candidates for the statistical\nmechanical entropy, each the center of a different program in the\nfoundations of the field. Surprisingly, there is no consensus as to\nwhich entropy is best suited to be the reduction basis of the\nthermodynamic entropy (see, for example, Sklar 1993; Callender 1999;\nLavis 2005; Frigg 2008; Robertson forthcoming). Consequently, there is\nlittle agreement about what grounds the Second Law in statistical\nmechanics.", "\nDespite the worthiness of all of these issues, this article focuses on\ntwo distinct problems associated with the direction of time." ], "section_title": "1. Thermodynamic Time Asymmetry: A Brief Guide", "subsections": [] }, { "main_content": [ "\nThe first “problem of the direction of time” is: what\naccounts for the time asymmetry of thermodynamics? Thermodynamics is\nnot a fundamental physical science. Hence it must inherit its massive\ntime asymmetry from the microworld. But where? In virtue of what,\nfundamentally, is thermodynamics time asymmetric? The puzzle is\nusually said to arise due to fundamental physics being time symmetric,\nor more precisely, time reversal invariant. (A theory is time reversal\ninvariant, loosely speaking, if its laws don’t care about the\ndirection of time.) No asymmetry in, no asymmetry out; therefore there\nis a puzzle over where the asymmetry enters. However, even if\nfundamental physics is time asymmetric one can and should still demand\nan answer to the question of what accounts for thermodynamics time\nasymmetry. The answer could be non-trivial because the time asymmetry\nof fundamental physics may have nothing to do with the time asymmetry\nof thermodynamics. This situation actually appears to be the case, as\nweak interactions between quarks and leptons can violate time symmetry\nyet these violations don’t appear to be responsible for\nthermodynamic behavior.", "\nHistorically the problem arose in a wonderful series of debates and\narguments between the great physicist Ludwig Boltzmann and some of his\ncontemporaries, notably, Johann Loschmidt, Ernst Zermelo and Edward\nCulverwell. Boltzmann was one of the founders and most influential\ndevelopers of the field of statistical mechanics, as well as (later in\nlife) a philosopher. While seeking a mechanical underpinning of the\nSecond Law, he discovered a particularly ingenious explanation for why\nsystems tend toward equilibrium.", "\nIgnoring historical details (Brush 1976, Frigg & Werndl 2011,\nSklar 1993, Uffink 2006), here is the core idea loosely reconstructed\nfrom Boltzmann’s later writings. Consider an isolated gas of\n\\(N\\) particles in a box, where \\(N\\) is large enough to make the\nsystem macroscopic \\((N \\approx 10^{23}+)\\). For the sake of\nfamiliarity we will work with classical mechanics. We can characterize\nthe gas by the coordinates and momenta \\(x_{in}, p_{in}\\) of each of\nits particles and represent the whole system by a point \\(X = (q,p)\\)\nin a \\(6N\\)-dimensional phase space known as \\(\\Gamma\\), where \\(q =\n(q_1 \\ldots q_{3N})\\) and \\(p = (p_1 \\ldots p_{3N})\\).\nBoltzmann’s great insight was to see that the thermodynamic\nentropy arguably “reduced” to the volume in \\(\\Gamma\\)\npicked out by the macroscopic parameters of the system. The key\ningredient is partitioning \\(\\Gamma\\) into compartments, such that all\nof the microstates \\(X\\) in a compartment are macroscopically (and\nthus thermodynamically) indistinguishable. To each macrostate \\(M\\),\nthere corresponds a volume of \\(\\Gamma\\), \\(\\lvert\\Gamma_M\\rvert\\),\nwhose size will depend on the macrostate in question. For\ncombinatorial reasons, almost all of \\(\\Gamma\\) corresponds to a state\nof thermal equilibrium. There are simply many more ways to be\ndistributed with uniform temperature and pressure than ways to be\ndistributed with nonuniform temperature and pressure. There is a vast\nnumerical imbalance in \\(\\Gamma\\) between the states in thermal\nequilibrium and the states in thermal nonequilibrium.", "We now introduce Boltzmann’s famous formula (up to an additive constant) for what we might call the “Boltzmann entropy” \\(S_B\\): \\[ S_B (M(X)) = k \\log \\lvert\\Gamma_M\\rvert \\] where \\(\\lvert\\Gamma_M\\rvert\\) is the volume in \\(\\Gamma\\) associated with the macrostate \\(M\\), \\(X\\) is the microstate of the system, and \\(k\\) is Boltzmann’s constant. \\(S_B\\) provides a relative measure of the amount of \\(\\Gamma\\) corresponding to each \\(M\\).", "\nGiven the mentioned asymmetry in \\(\\Gamma\\), almost all microstates\nrealizing non-equilibrium macrostates are such that their\nentropy value is overwhelmingly likely to increase with time. When the\nconstraints are released on systems initially confined to small\nsections of \\(\\Gamma\\), typical systems will evolve into\nlarger compartments. Since the new equilibrium distribution occupies\nalmost all of the newly available phase space, nearly all of\nthe microstates originating in the smaller volume will tend toward\nequilibrium. Except for those incredibly rare microstates conspiring\nto stay in small compartments, microstates will evolve in such a way\nas to have \\(S_B\\) increase. Substantial questions can be raised about\nthe details of this approach. What justifies, for instance, the\nstandard probability measure on \\(\\Gamma\\)? Nonetheless, the\nBoltzmannian explanation seems to offer a plausible and powerful\nframework for understanding why the entropy of systems tends\nto increase with time. (For further explanation and discussion see\nBricmont 1995; Frigg 2008, 2009; Goldstein 2001; Hemmo & Shenker\n2012; Klein 1973; Lavis 2005; Lebowitz 1993; Uffink 2006.)", "\nTrouble looms over this explanation of time asymmetry (see Brown,\nMyrvold, & Uffink 2009). Before Boltzmann explained entropy\nincrease as described above, he proposed a now notorious\n“proof” known as the “\\(H\\)-theorem” to the\neffect that entropy must always increase. Loschmidt 1876/1877 and\nZermelo 1896 launched objections to the \\(H\\)-theorem. If we take as\npremises classical mechanical dynamics, they pointed out, it’s\nimpossible to get any function of the classical state to monotonically\nincrease. Loschmidt focused on the time reversal invariance of the\nclassical dynamics and Zermelo on its recurrence property (roughly,\nthat a bounded system, left to itself, will eventually return\narbitrarily close to its initial state, for any given initial state).\nThey were right: time reversal means that for every entropy-increasing\nsolution to the classical equations there is a mirror\nentropy-decreasing solution; and recurrence means that every solution\nwill at some point have its entropy decrease if we wait long enough.\nSome time asymmetric ingredient that had not been properly announced\nhad been smuggled into the theorem.", "\nThe reader can find this story in many textbooks and in many\nreferences cited above. An objection in their spirit (specifically,\nLoschmidt’s) can also be advanced against Boltzmann’s\nlater view sketched above. Loosely put, because the classical\nequations of motion are time reversal invariant, nothing in the\noriginal explanation necessarily referred to the direction of time\n(see Hurley 1986). Although we just stated the Boltzmannian account of\nentropy increase in terms of entropy increasing into the future, the\nexplanation can be turned around and made for the past\ntemporal direction as well. Given a gas in a box that is in a\nnonequilibrium state, the vast majority of microstates that are\nantecedents of the dynamical evolution leading to the present\nmacrostate correspond to a macrostate with higher entropy\nthan the present one. Therefore, not only is it highly likely that\ntypical microstates corresponding to a nonequilibrium state will\nevolve to higher entropy states, but it is also highly likely\nthat they evolved from higher entropy states.", "\nConcisely put, the problem is that given a nonequilibrium state at\ntime \\(t_2\\), it is overwhelmingly likely that", "\nbut that due to the reversibility of the dynamics it is also\noverwhelmingly likely that", "\nwhere \\(t_1 \\lt t_2 \\lt t_3\\). However, transitions described by\n (2)\n do not seem to occur; or phrased more carefully, not both\n (1)\n and\n (2)\n occur. However we choose to use the terms “earlier” and\n“later”, clearly entropy doesn’t increase in both\ntemporal directions. For ease of exposition let us dub\n (2)\n the culprit.", "\nThe traditional problem is not merely that nomologically possible\n(anti-thermodynamic) behavior does not occur when it could. That is\nnot straightforwardly a problem: all sorts of nomologically\nallowed processes do not occur. Rather, the problem is that\nstatistical mechanics seems to make a prediction that is falsified,\nand that is a problem according to anyone’s theory of\nconfirmation.", "\nMany solutions to this problem have been proposed. Generally speaking,\nthere are two ways to solve the problem: eliminate transitions of type\n (2)\n either with special boundary conditions or with laws of nature. The\nformer method works if we assume that earlier states of the\nuniverse are of comparatively low-entropy and that\n(relatively) later states are not also low-entropy states.\nThere are no high-to-low-entropy processes simply because earlier\nentropy was very low. Alternatively, the latter method works if we can\nsomehow restrict the domain of physically possible worlds to those\nadmitting only low-to-high transitions. The laws of nature are the\nstraightjacket on what we deem physically possible. Since we need to\neliminate transitions of type\n (2)\n while keeping those of type\n (1)\n (or vice versa), a necessary condition of the laws doing this job is\nthat they be time reversal noninvariant. Our choice of strategy boils\ndown to either assuming temporally asymmetric boundary conditions or\nof adding (or changing to or restricting to) time reversal\nnoninvariant laws of nature that make entropy increase likely. Many\napproaches to this problem have thought to avoid this dilemma, but a\nlittle analysis of any proposed “third way” arguably\nproves this to be false.", "\nMotivations for restrictions of type\n (2)\n transitions originate in both philosophy and in particular physical\ntheories. The rest of this section describes some of the wide range of\nviews found on the issue." ], "section_title": "2. The Problem of the Direction of Time I", "subsections": [ { "content": [ "\nWithout proclaiming the laws of nature time asymmetric, there is no\nway to eliminate as impossible transitions\n (2)\n in favor of\n (1).\n Nevertheless, appealing to temporally asymmetric boundary conditions\nallows us to describe a world wherein\n (1)\n but not\n (2)\n occur. A cosmological hypothesis claiming that in the very distant\npast entropy was much lower will work. Boltzmann, as well as many of\nthis century’s greatest scientists, e.g., Einstein, Richard\nFeynman, and Erwin Schroedinger, saw that this hypothesis is necessary\ngiven our (mostly) time asymmetric laws. (Boltzmann, however,\nexplained this low-entropy condition by treating the observable\nuniverse as a natural statistical fluctuation away from equilibrium in\na vastly larger universe.) Earlier states do not have higher entropy\nthan present states because we make the cosmological posit that the\nuniverse began in an extremely tiny section of its available phase\nspace. Albert (2000) calls this the “Past Hypothesis” and\nargues that it solves both this problem of the direction of time and\nalso the one to be discussed below. Note that classical mechanics is\nalso compatible with a “Future Hypothesis”: the claim that\nentropy is very low in the distant future. The restriction to\n“distant” is needed, for if the near future were of\nlow-entropy, we would not expect the thermodynamic behavior that we\nsee—see Cocke 1967, Price 1996, and Schulman 1997 for discussion\nof two-time boundary conditions.", "\nThe Past Hypothesis offers an elegant solution to the problem of the\ndirection of time. However, there are some concerns.", "\nFirst, some find it incredible that (e.g.) gases everywhere for all\ntime should expand through their available volumes due to special\ninitial conditions. The common cause of these events is viewed as\nitself monstrously unlikely. Expressing this feeling, R. Penrose\n(1989) estimates that the probability, given the standard measure on\nphase space, of the universe starting in the requisite state is\nastronomically small. In response, one may hold that the Past\nHypothesis is lawlike. If so, then the probability for this state, if\nsuch exists, is one! Even if one doesn’t go down this path, one\nmay have other problems with claiming that the initial condition of\nthe universe needs further explanation. See Callender 2004a,b for such\na view and Price 1996, 2004 for the contrary position.", "\nSecond, another persistent line of criticism might be labeled the\n“subsystem” worry. It’s consistent with the Past\nHypothesis, after all, that none of the subsystems on Earth ever\ndisplay thermodynamically asymmetric behavior. How exactly does the\nglobal entropy increase of the universe imply local\nentropy increase among the subsystems (which, after all, is what\ncauses us to posit the Second Law in the first place)? See Winsberg\n2004 for this objection and Callender 2011a, Frisch 2010, and North\n2011 for discussion.", "\nThird, what exactly does the Past Hypothesis say in the context of our\nbest and most recent physics? While not denying that temporally\nasymmetric boundary conditions are needed to solve the problem, Earman\n(2006) is very critical of the Past Hypothesis, concluding that it\nisn’t even coherent enough to be false. The main problem Earman\nsees is that we cannot state the Past Hypothesis in the language of\ngeneral relativity. Callender (2010, 2011b) and Wallace (2010) discuss\nthe related question of stating the Past Hypothesis when\nself-gravitation is included. One may also consider the question in\nthe context of quantum theory (see Wallace 2013)." ], "subsection_title": "2.1 Past Hypothesis" }, { "content": [ "\nIf we place an isolated concentrated homogeneous gas in the middle of\na large empty volume, we would expect the particles to spread out in\nan expanding sphere about the center of the gas, much as waves of\nradiation spread out from concentrated charge sources. It is therefore\ntempting to think that there is a relationship between the\nthermodynamic and electromagnetic arrows of time. In a debate in 1909,\nAlbert Einstein and Walther Ritz apparently disagreed about the nature\nof this relationship, although the exact points of dispute remain a\nbit unclear. The common story told is that Ritz took the position that\nthe asymmetry of radiation had to be judged lawlike and that the\nthermodynamic asymmetry could be derived from this law.\nEinstein’s position is instead that “irreversibility is\nexclusively based on reasons of probability” (Ritz and Einstein\n1909, English translation from Zeh 1989: 13). It is unclear whether\nEinstein meant probability plus the right boundary conditions, or\nsimply probability alone. In any case, Ritz is said to believe that\nthe radiation arrow causes the thermodynamic one, whereas Einstein is\nsaid to hold something closer to the opposite position. The real story\nis far more complicated, as Ritz had a particle-based ontology in mind\nas well as many additional considerations (see Frisch and Pietsch 2016\nfor subtleties of the actual historical debate).", "\nIf this common tale is correct—and there is reason to\nthink it isn’t the full story—then it seems that Einstein\nmust be closer to being correct than Ritz. Ritz’ position\nappears implausible if only because it implies gases composed of\nneutral particles will not tend to spread out. That aside,\nEinstein’s position is attractive if we concentrate on the wave\nasymmetry mentioned above. Using Popper 1956’s famous mechanical\nwave example as an analogy, throwing a rock into a pond so that waves\non the surface spread out into the future requires every bit the\nconspiracy that is needed for waves to converge on a point in order to\neject a rock from the bottom. However, here it does seem clear that\none process is favored thermodynamically and the other disfavored once\nwe have a thermodynamic arrow in hand. Given a solution to the\nthermodynamic arrow, impulses directed toward the center of a pond\nsuch as to eject a rock are unlikely, whereas a rock triggering\nspherical waves diverging from the point of impact are likely. Here\nthe radiation arrow seems plausibly connected to and perhaps even\nderivable from the thermodynamic arrow. The main interesting\ndifference is that Popper’s time-reversed pond seems\napproximately attainable whereas anti-thermodynamic processes seem\nmore absolutely forbidden (or at least dramatically harder to engine,\nrequiring a so-called Maxwell Demon).", "\nIf the wave asymmetry were the only electromagnetic arrow, then the\nabove sketch would plausibly capture the core connection between the\nthermodynamic and electromagnetic arrows of time. We would have reason\nto think that whatever causes the thermodynamic arrow also is\nresponsible for the electromagnetic arrow. That may ultimately be\ncorrect. However, it’s too early to conclude that, for\nelectromagnetism is chock full of arrows of time besides the wave\nasymmetry.", "Maxwell’s equations are well-known to include both “advanced” and “retarded” solutions. The retarded solution \\[ \\phi_{\\text{ret}}(r,t) = \\int dr' \\rho\\frac{(r', t- \\frac{\\lvert r'-r\\rvert}{c})}{\\lvert r'-r\\rvert} \\] gives the field amplitude \\(\\phi_{\\text{ret}}\\) at \\(r,t\\) by finding the source density \\(r\\) at \\(r'\\) at earlier times. The advanced solution \\[ \\phi_{\\text{adv}}(r,t) = \\int dr' \\rho\\frac{(r', t+ \\frac{\\lvert r'-r\\rvert}{c})}{\\lvert r'-r\\rvert} \\] gives the field amplitude in terms of the source density at \\(r'\\) at later times. Physicists routinely discard the advanced solutions for reasons of “causality”. It is not so clear thermodynamic considerations are behind this rejection of solutions, an asymmetry made all the harder to see given the freedom electromagnetism has to rewrite retarded fields in terms of advanced fields and outgoing sourceless radiation (and vice versa). Electromagnetism is also said to be allow emissions and not absorptions. Accelerating charges are also damped and not anti-damped by the field. With so many arrows besides the wave asymmetry—emission/absorption, in/out, retarded/advanced, damped/anti-damped—it’s premature to say that the thermodynamic arrow is the one arrow to rule them all. Most agree that the wave asymmetry is ultimately “thermodynamic” but after that matters are contested.", "\nFor further discussion of these controversial points, see the\narticles/chapters by Allori 2015; Arntzenius 1994; Atkinson 2006;\nEarman 2011; Frisch 2000, 2006; Frisch and Pietsch 2016; North 2003;\nPrice 1996, 2006; Rohrlich 2006; and Zeh 1989." ], "subsection_title": "2.2 Electromagnetism" }, { "content": [ "\nCosmology presents us with a number of apparently temporally\nasymmetric mechanisms. The most obvious one is the inexorable\nexpansion of the universe. The spatial scale factor \\(a(t)\\), which we\nmight conceive roughly as the radius of the universe (it gives the\ndistance between co-moving observers), is increasing. The universe\nseems to be uniformly expanding relative to our local frame. Since\nthis temporal asymmetry occupies a rather unique status it is natural\nto wonder whether it might be the “master” arrow.", "\nThe cosmologist Thomas Gold 1962 proposed just this. Believing that\nentropy values covary with the size of the universe, Gold asserts that\nat the maximum radius the thermodynamic arrow will “flip”\ndue to the re-contraction. However, as Richard Tolman 1934 has shown\nin some detail, a universe filled with non-relativistic particles will\nnot suffer entropy increase due to expansion, nor will an expanding\nuniverse uniformly filled with blackbody radiation increase its\nentropy either. Interestingly, Tolman demonstrated that more realistic\nuniverses containing both matter and radiation will change\ntheir entropy contents. Coupled with expansion, various processes will\ncontribute to entropy increase, e.g., energy will flow from the\n“hot” radiation to the “cool” matter. So long\nas the relaxation time of these processes is larger than the expansion\ntime scale, they should generate entropy. We thus have a purely\ncosmological method of entropy generation.", "\nOthers (e.g., Davies 1994) have thought inflation provides a kind of\nentropy-increasing behavior—again, given the sort of matter\ncontent we have in our universe. The inflationary model is an\nalternative of sorts to the standard big bang model, although by now\nit is so well entrenched in the cosmology community that it really\ndeserves the tag “standard”. In this scenario, the\nuniverse is very early in a quantum state called a “false\nvacuum”, a state with a very high energy density and negative\npressure. Gravity acts like Einstein’s cosmological constant, so\nthat it is repulsive rather than attractive. Under this force the\nuniverse enters a period of exponential inflation, with geometry\nresembling de Sitter space. When this period ends any initial\ninhomogeneities will have been smoothed to insignificance. At this\npoint ordinary stellar evolution begins. Loosely associating\ngravitational homogeneity with low-entropy and inhomogeneity with\nhigher entropy, inflation is arguably a source of a low entropy\n“initial” condition.", "\nThere are other proposed sources of cosmological entropy generation,\nbut these should suffice to give the reader a flavor of the idea. We\nshall not be concerned with evaluating these scenarios in any detail.\nRather, our concern is about how these proposals explain time’s\narrow. In particular, how do they square with our earlier claim that\nthe issue boils down to either assuming temporally asymmetric boundary\nconditions or of adding time reversal non-invariant laws of\nnature?", "\nThe answer is not always clear, owing in part to the fact that the\nseparation between laws of nature and boundary conditions is\nespecially slippery in the science of cosmology. Advocates of the\ncosmological explanation of time’s arrow typically see\nthemselves as explaining the origin of the needed low-entropy\ncosmological condition. Some explicitly state that special initial\nconditions are needed for the thermodynamic arrow, but differ with the\nconventional “statistical” school in deducing the origin\nof these initial conditions. Earlier low-entropy conditions are not\nviewed as the boundary conditions of the spacetime. They came about,\naccording to the cosmological schools, about a second or more after\nthe big bang. But when the universe is the size of a small particle, a\nsecond or more is enough time for some kind of cosmological mechanism\nto bring about our low-entropy “initial” condition. What\ncosmologists (primarily) differ about is the precise nature of this\nmechanism. Once the mechanism creates the “initial”\nlow-entropy we have the same sort of explanation of the thermodynamic\nasymmetry as discussed in the previous section. Because the proposed\nmechanisms are supposed to make the special initial conditions\ninevitable or at least highly probable, this maneuver seems like the\nalleged “third way” mentioned above.", "\nThe central question about this type of explanation, as far as\nwe’re concerned, is this: Is the existence of the low\n“initial” state a consequence of the laws of nature alone\nor the laws plus boundary conditions? In other words, first, does the\nproposed mechanism produce low-entropy states given any\ninitial condition, and second, is it a consequence of the\nlaws alone or a consequence of the laws plus initial\nconditions? We want to know whether our question has merely been\nshifted back a step, whether the explanation is a disguised appeal to\nspecial initial conditions. Though we cannot here answer the question\nin general, we can say that the two mechanisms mentioned are not\nlawlike in nature. Expansion fails on two counts. There are boundary\nconditions in expanding universes that do not lead to an entropy\ngradient, i.e., conditions without the right matter-radiation content,\nand there are boundary conditions that do not lead to expansion in\nwhich entropy nonetheless increases, e.g., matter-filled Friedmann\nmodels that do not expand. Inflation fails at least on the second\ncount. Despite advertising, arbitrary initial conditions will not give\nrise to an inflationary period. Furthermore, it’s not clear that\ninflationary periods will give rise to thermodynamic asymmetries\n(Price 1996: ch. 2). The cosmological scenarios do not seem to make\nthe thermodynamic asymmetries a result of nomic necessity. The\ncosmological hypotheses may be true, and in some sense, they may even\nexplain the low-entropy initial state. But they do not appear to\nprovide an explanation of the thermodynamic asymmetry that makes it\nnomologically necessary or even likely.", "\nAnother way to see the point is to consider the question of whether\nthe thermodynamic arrow would “flip” if (say) the universe\nstarted to contract. Gold, as we said above, asserts that at the\nmaximum radius the thermodynamic arrow must “flip” due to\nthe re-contraction. Not positing a thermodynamic flip while\nmaintaining that entropy values covary with the radius of the universe\nis clearly inconsistent—it is what Price (1996) calls the\nfallacy of a “temporal double standard”. Gold does not\ncommit this fallacy, and so he claims that the entropy must decrease\nif ever the universe started to re-contract. However, as Albert\nwrites,", "\n\n\nthere are plainly locations in the phase space of the world from which\n… the world’s radius will inexorably head up and the\nworld’s entropy will inexorably head down. (2000: 90)\n", "\nSince that is the case, it doesn’t follow from law that the\nthermodynamic arrow will flip during re-contraction; therefore,\nwithout changing the fundamental laws, the Gold mechanism cannot\nexplain the thermodynamic arrow in the sense we want.", "\nFrom these considerations we can understand the basic dilemma\nthat runs throughout Price (1995, 1996): either we explain the earlier\nlow-entropy condition Gold-style or it is inexplicable by\ntime-symmetric physics. Because there is no net asymmetry in a Gold\nuniverse, we might paraphrase Price’s conclusion in a more\ndisturbing manner as the claim that the (local) thermodynamic arrow is\nexplicable just in case (globally) there isn’t one. However,\nnotice that this remark leaves open the idea that the laws governing\nexpansion or inflation are not time reversal invariant. (For more on\nPrice’s basic dilemma, see Callender 1998 and Price 1995.)", "\nFinally, it’s important to remember that this dilemma and the\nneed for a Past Hypothesis are dependent upon a particular physical\nset-up. Can we explain the thermodynamic arrow without invoking a Past\nHypothesis? Inspired by the idea of eternal spontaneous inflation,\nCarroll and Chen (2004, Other Internet Resources) describe a model in\nwhich new baby universes (or “pocket universes”) are\nrepeatedly born from existing universes. Each birth increases the\noverall entropy of the multiverse although within each baby universe\nwe have our familiar thermodynamic asymmetry. The crucial assumption\nin this model – one also found in the gravitational theory of\nBarbour, Koslowski, and Mercati (2014) – is that entropy is\nunbound. It can be arbitrarily high. With this assumption and in these\nmodels, one can do without a past Hypothesis. For discussion, see\nGoldstein, Tumulka, & Zanghi 2016 and Lazarovici and Reichert\n2020." ], "subsection_title": "2.3 Cosmology" }, { "content": [ "\nQuantum cosmology, it is often said, is the theory of the\nuniverse’s initial conditions. Presumably this entails that its\nposits are to be regarded as lawlike. Because theories are typically\nunderstood as containing a set of laws, quantum cosmologists\napparently assume that the distinction between laws and initial\nconditions is fluid. Particular initial conditions will be said to\nobtain as a matter of law. Hawking writes, for example,", "\n\n\nwe shall not have a complete model of the universe until we can say\nmore about the boundary conditions than that they must be whatever\nwould produce what we observe, (1987: 163).\n", "\nCombining such aspirations with the observation that thermodynamics\nrequires special boundary conditions leads quite naturally to the\nthought that “the second law becomes a selection principle for\nthe boundary conditions of the universe [for quantum cosmology]”\n(Laflamme 1994: 358). In other words, if one is to have a theory of\ninitial conditions, it would certainly be desirable to deduce initial\nconditions that will lead to the thermodynamic arrow. This is\nprecisely what many quantum cosmologists have sought. (This should be\ncontrasted with the arrows of time discussed in semiclassical quantum\ngravity, for example, the idea that quantum scattering processes in\nsystems with black holes violate the CPT theorem.) Since quantum\ncosmology is currently very speculative, it might be premature to\nstart worrying about what it says about time’s arrow.\nNevertheless, there has been a substantial amount of debate on this\nissue (see Haliwell et al. 1994)." ], "subsection_title": "2.4 Quantum Cosmology" }, { "content": [ "\nPenrose and Percival (1962) propose a general causal principle to\nhandle our problem. The principle states that the effects of\ninteractions happen after those interactions but not\nbefore. Similar to Reichenbach’s principle of the\ncommon cause, they suggest what they dub the Law of Conditional\nIndependence, namely, that “If A and B are two disjoint\n4-regions, and C is any 4-region which divides the union of the pasts\nof A and B into two parts, one containing A and the other containing\nB, then A and B are conditionally independent given c. That is,\nPr(a&b/c) = Pr(a/c) × Pr(b/c), for all a,b.” (Penrose\nand Percival 1962, p. 611). Here c is an event that is a common cause\nthat screens off the correlation between events in A and B.", "\nIn terms of statistical mechanics, this law would have the effect of\nmaking the phase space density associated with a system at a time\ndetermined by earlier events but not later events. This would more or\nless directly preclude the temporal \"parity of reasoning\" motivated\ntransitions assumed in the problem of the direction of time,\ntransition of type (2). To achieve this, the Law of Conditional\nIndependence must be time asymmetric, which it is, and it must be a\nkind of fundamental principle that restricts the lawlike correlation\notherwise allowed. After all, if we assume that the laws of nature are\ntime reversal invariant, then there is no asymmetry between pre- and\npost-interaction correlations.", "\nPrice 1996 (chapter 5) and Sklar 1993 hold that this nomic restriction\nis unwarranted or unexplanatory. There is the sense that the causal\nasymmetry should come out of more basic physics, not be baked into\nthis physics. Horwich 1987 is an example of someone trying to derive\nwhat he calls the fork asymmetry, which is similar to the Law of\nConditional Independence, from more basic assumptions. ", "\nA recent contribution that has some affinities with the Penrose and\nPercival move can be found in Myrvold 2020. " ], "subsection_title": "2.5 Causation" }, { "content": [ "\nSome philosophers have sought an answer to the problem of time’s\narrow by claiming that time itself is directed. They do not\nmean time is asymmetric in the sense intended by advocates of the\ntensed theory of time. Their proposals are firmly rooted in the idea\nthat time and space are properly represented on a four-dimensional\nmanifold. The main idea is that the asymmetries in time indicate\nsomething about the nature of time itself. Christensen (1993) argues\nthat this is the most economical response to our problem since it\nposits nothing besides time as the common cause of the asymmetries,\nand we already believe in time. A proposal similar to\nChristensen’s is Weingard’s “time-ordering\nfield” (1977). Weingard’s speculative thesis is that\nspacetime is temporally oriented by a “time potential”, a\ntimelike vector field that at every spacetime point directs a vector\ninto its future light cone. In other words, supposing our spacetime is\ntemporally orientable, Weingard wants to actually orient it. The main\nvirtue of this is that it provides a time sense everywhere, even in\nspacetimes containing closed timelike curves (so long as they’re\ntemporally orientable). As he shows, any explication of the\n“earlier than” relation in terms of some other physical\nrelation will have trouble providing a consistent description of time\ndirection in such spacetimes. Another virtue of the idea is that it is\nin principle capable of explaining all the temporal\nasymmetries. If coupled to the various asymmetries in time, it would\nbe the “master arrow” responsible for the arrows of\ninterest. As Sklar (1985) notes, Weingard’s proposal makes the\npast-future asymmetry very much like the up-down asymmetry. As the\nup-down asymmetry was reduced to the existence of a gravitational\npotential—and not an asymmetry of space itself—so the\npast-future asymmetry would reduce to the time potential—and not\nan asymmetry of time itself. Of course, if one thinks of the\ngravitational metric field as part of spacetime, there is a sense in\nwhich the reduction of the up-down asymmetry really was a reduction to\na spacetime asymmetry. And if the metric field is conceived as part of\nspacetime—which is itself a huge source of contention in\nphilosophy of physics—it is natural to think of Weingard’s\ntime-ordering field as also part of spacetime. Thus his proposal\nshares a lot in common with Christensen’s suggestion.", "\nThis sort of proposal has been criticized by Sklar on methodological\ngrounds. Sklar claims that scientists would not accept such an\nexplanation (1985: 111–2). One might point out, however, that\nmany scientists did believe in analogues of the time-ordering field as\npossible causes of the CP\n violations.[4]\n The time-ordering field, if it exists, would be an unseen (except\nthrough its effects) common cause of strikingly ubiquitous phenomena.\nScientists routinely accept such explanations. To find a problem with\nthe time-ordering field we need not invoke methodological scruples;\ninstead we can simply ask whether it does the job asked of it. Is\nthere a mechanism that will couple the time-ordering field to\nthermodynamic phenomena? Weingard says the time potential field needs\nto be suitably coupled (1977: 130) to the non-accidental asymmetric\nprocesses, but neither he nor Christensen elaborate on how this is to\nbe accomplished. Until this is addressed satisfactorily, this\nspeculative idea must be considered interesting yet embryonic. For\nmore recent work in this vein, see Maudlin 2002." ], "subsection_title": "2.6 Time Itself" }, { "content": [ "\nWhen explaining time’s arrow many philosophers and physicists\nhave focused their attention upon the unimpeachable fact that real\nsystems are open systems that are subjected to interactions of various\nsorts. Thermodynamic systems cannot be truly isolated. To take the\nmost obvious example, we can not shield a system from the influence of\ngravity. At best, we can move systems to locations feeling less and\nless gravitational force, but we can never completely decouple a\nsystem from the gravitational field. Not only do we ignore the weak\ngravitational force when doing classical thermodynamics, but we also\nignore less exotic matters, such as the walls in the standard gas in a\nbox scenario. We can do this because the time it takes for a gas to\nreach equilibrium with itself is vastly shorter than the time it takes\nthe gas plus walls system to reach equilibrium. For this reason we\ntypically discount the effects of the box walls on the gas.", "\nIn this approximation many have thought there lies a possible solution\nto the problem of the direction of time. Indeed, many have thought\nherein lies a solution that does not change the laws of\nclassical mechanics and does not allow for the nomological\npossibility of anti-thermodynamic behavior. In other words, advocates\nof this view seem to believe it embodies a third way. Blatt 1959;\nReichenbach 1956; Redhead and Ridderbos 1998, and to some extent,\nHorwich 1987 are a few works charmed by this idea.", "\nThe idea is to take advantage of what a random perturbation of the\nrepresentative phase point would do to the evolution of a system.\nGiven our Boltzmannian setup, there is a tremendous asymmetry in phase\nspace between the volumes of points leading to equilibrium and of\npoints leading away from equilibrium. If the representative point of a\nsystem were knocked about randomly, then due to this asymmetry, it\nwould be very probable that the system at any given time be on a\ntrajectory leading toward equilibrium. Thus, if it could be argued\nthat the earlier treatment of the statistical mechanics of ideal\nsystems ignored a random perturber in the environment of the system,\nthen one would seem to have a solution to our problems. Even if the\nperturbation were weak it would still have the desired effect. The\nweak “random” previously ignored knocking of the\nenvironment is is claimed to be the cause of the approach to\nequilibrium. Prima facie, this answer to the problem escapes\nthe appeal to special initial conditions and the appeal to new\nlaws.", "\nBut only prima facie. A number of criticisms have been\nleveled against this maneuver. One that seems on the mark is the\nobservation that if classical mechanics is to be a universal theory,\nthen the environment must be governed by the laws of classical\nmechanics as well. The environment is not some mechanism outside the\ngovernance of physical law, after all, and when we treat it too, the\n“deus ex machina”—the random\nperturber—disappears. If we treat the gas-plus-the-container\nwalls as a classical system, it is still governed by time-reversible\nlaws that will cause the same problem as we met with the gas alone. At\nthis point one sometimes sees the response that this combined system\nof gas plus walls has a neglected environment too, and so on, and so\non, until we get to the entire universe. It is then questioned whether\nwe have a right to expect laws to apply universally (Reichenbach 1956:\n81ff). Or the point is made that we cannot write down the Hamiltonian\nfor all the interactions a real system suffers, and so there will\nalways be something “outside” what is governed by the\ntime-reversible Hamiltonian. Both of these points rely, one suspects,\non an underlying instrumentalism about the laws of nature. Our problem\nonly arises if we assume or pretend that the world literally is the\nway the theory says; dropping this assumption naturally\n“solves” the problem. Rather than further address these\nresponses, let us turn to the claim that this maneuver need not modify\nthe laws of classical mechanics.", "\nIf one does not make the radical proclamation that physical law does\nnot govern the environment, then it is easy to see that whatever law\ndescribes the perturber’s behavior, it cannot be the laws of\nclassical mechanics \\(if\\) the environment is to do the job required\nof it. A time-reversal noninvariant law, in contrast to the time\nsymmetric laws of classical mechanics, must govern the external\nperturber. Otherwise we can in principle subject the whole system,\nenvironment plus system of interest, to a Loschmidt reversal. The\nsystem’s velocities will reverse, as will the velocities of the\nmillions of tiny perturbers. “Miraculously”, as if there\nwere a conspiracy between the reversed system and the millions of\n“anti-perturbers”, the whole system will return to a time\nreverse of its original state. What is more, this reversal will be\njust as likely as the original process if the laws are time reversal\ninvariant. A minimal criterion of adequacy, therefore, is that the\nrandom perturbers be time reversal noninvariant. But the laws\nof classical mechanics are time reversal invariant. Consequently, if\nthis “solution” is to succeed, it must exercise new laws\nand modify or supplement classical mechanics. (Since the perturbations\nneed to be genuinely random and not merely unpredictable, and since\nclassical mechanics is deterministic, the same sort of argument could\nbe run with indeterminism instead of irreversibility. See Price 2002\nfor a diagnosis of why people have made this mistake, and also for an\nargument objecting to interventionism for offering a\n“redundant” physical mechanism responsible for entropy\n increase.)[5]" ], "subsection_title": "2.7 Interventionism" }, { "content": [ "\nTo the best of our knowledge our world is fundamentally quantum\nmechanical, not classical mechanical. Does this change the situation?\n“Maybe” is perhaps the best answer. Not surprisingly,\nanswers to the question are affected by one’s interpretation of\nquantum mechanics. Quantum mechanics suffers from the notorious\nmeasurement problem, a problem which demands one or another\ninterpretation of the quantum formalism. These interpretations fall\nbroadly into two types, depending on their view of the unitary\nevolution of the quantum state (e.g., evolution according to the\nSchroedinger equation): they either say that there is something more\nthan the quantum state, or that the unitary evolution is not entirely\ncorrect. The former are called “no-collapse”\ninterpretations while the latter are dubbed “collapse”\ninterpretations. This is not the place to go into the details of these\ninterpretations, but we can still sketch the outlines of the picture\npainted by quantum mechanics (for more see Albert 1992).", "\nModulo some philosophical concerns about the meaning of time reversal\n(Albert 2000; Earman 2002), the equation governing the unitary\nevolution of the quantum state is time reversal invariant. For\ninterpretations that add something to quantum mechanics, this\ntypically means that the resulting theory is time reversal invariant\ntoo (since it would be odd or even inconsistent to have one part of\nthe theory invariant and the other part not). Since the resulting\ntheory is time reversal invariant, it is possible to generate the\nproblem of the direction of time just as we did with classical\nmechanics. While many details are altered in the change from classical\nto no-collapse quantum mechanics, the logical geography seems to\nremain the same.", "\nCollapse interpretations are more interesting with respect to our\ntopic. Collapses interrupt or outright replace the unitary evolution\nof the quantum state. To date, they have always done so in a time\nreversal noninvariant manner. The resulting theory,\ntherefore, is not time reversal invariant. This fact offers a\npotential escape from our problem: the transitions of type\n (2)\n in our above statement of the problem may not be lawful. And this has\nled many thinkers throughout the century to believe that collapses\nsomehow explain the thermodynamic time asymmetry.", "\nMostly these postulated methods fail to provide what we want. We think\ngases relax to equilibrium even when they’re not measured by\nBohrian observers or Wignerian conscious beings. This complaint is,\nadmittedly, not independent of more general complaints about the\nadequacy of these interpretations. But perhaps because of these\ncontroversial features they have not been pushed very far in\nexplaining thermodynamics.", "\nMore satisfactory collapse theories exist, however. One, due to\nGhirardi, Rimini, and Weber, commonly known as GRW, can describe\ncollapses in a closed system—no dubious appeal to observers\noutside the quantum system is required. Albert (1992, 2000) has\nextensively investigated the impact GRW would have on statistical\nmechanics and thermodynamics. GRW would ground a temporally asymmetric\nprobabilistic tendency for systems to evolve toward equilibrium.\nAnti-thermodynamic behavior is not impossible according to this\ntheory. Instead it is tremendously unlikely. The innovation of the\ntheory lies in the fact that although entropy is overwhelmingly likely\nto increase toward the future, it is not also overwhelmingly likely to\nincrease toward the past (because there are no dynamic backwards\ntransition probabilities provided by the theory). So the theory does\nnot suffer from a problem of the direction of time as stated\nabove.", "\nThis does not mean, however, that it removes the need for something\nlike the Past Hypothesis. GRW is capable of explaining why, given a\npresent nonequilibrium state, later states should have higher entropy;\nand it can do this without also implying that earlier states have\nhigher entropy too. But it does not explain how the universe ever got\ninto a nonequilibrium state in the first place. As indicated before,\nsome are not sure what would explain this fact, if anything,\nor whether it’s something we should even aspire to explain. The\nprincipal virtue GRW would bring to the situation, Albert thinks, is\nthat it would solve or bypass various troubles involving the nature of\nprobabilities in statistical mechanics.", "\nThe same type of benefit, plus arguably others, come from a recent\nproposal by Chen (forthcoming). Chen suggests that we adopt a position\nknown as density matrix realism to help understand time’s arrow.\nInstead of regarding the wavefunction as the basic ontology of quantum\ntheory, we take the quantum state to be represented by an impure\ndensity matrix. When we express the Past Hypothesis in terms of a\ndensity matrix, a number of virtues appear, including greater harmony\nbetween the probabilities of statistical mechanics and quantum\nmechanics. It may be that interpretations of quantum mechanics that\nare not like GRW can possess some of the same benefits that GRW\nbrings.", "\nMore detailed discussion of the impact quantum mechanics has on our\nproblem can be found in Albert 2000, North 2002, Price 2002 and Chen\nforthcoming. But if our superficial review is correct, we can say that\nquantum mechanics will not obviate our need for a Past Hypothesis\nthough it may well solve at least one problem related to the direction\nof time." ], "subsection_title": "2.8 Quantum Mechanics" }, { "content": [ "\nFinally, let’s return to a point made in passing about the\nstatus of the Past Hypothesis. Without some new physics that\neliminates or explains the Past Hypothesis, or some satisfactory\n“third way”, it seems we are left with a bald posit of\nspecial initial conditions. One can question whether there really is\nanything unsatisfactory about this (Sklar 1993; Callender 2004b). But\nperhaps we were wrong in the first place to think of the Past\nHypothesis as a contingent boundary condition. The question “why\nthese special initial conditions?” would be answered with\n“it’s physically impossible for them to be\notherwise”, which is always a conversation stopper. Indeed,\nFeynman (1965: 116) speaks this way when explaining the statistical\nversion of the second law.", "\nAbsent a particular understanding of laws of nature, there is perhaps\nnot much to say about the issue. But given particular conceptions of\nlawhood, it is clear that various judgments about this issue follow\nnaturally—as we will see momentarily. However, let’s\nacknowledge that this may be to get matters backwards. It might be\nsaid that we first ought to find out whether the boundary\nconditions are lawlike, and then devise a theory of\nlaw appropriate to the answer. To decide whether or not the boundary\nconditions are lawlike based merely on current philosophical theories\nof law is to prejudge the issue. Perhaps this objection is really\nevidence of the feeling that settling the issue based on one’s\nconception of lawhood seems a bit unsatisfying. It is hard to deny\nthis. Even so, it is illuminating to have a brief look at the\nrelationships between some conceptions of lawhood and the topic of\nspecial initial conditions. For discussion and references on laws of\nnature, please refer to the entry on that topic.", "\nFor instance, if one agrees with John Stuart Mill that from the laws\none should be able to deduce everything and one considers the\nthermodynamic part of that “everything”, then the special\ninitial condition will be needed for such a deduction. The modern heir\nof this conception of lawhood, the one associated with Frank Ramsey\nand David Lewis (see Loewer 1996), sees laws as the axioms of the\nsimplest, most powerful, consistent deductive system possible. It is\nlikely that the specification of a special initial condition would\nemerge as an axiom in such a system, for such a constraint may well\nmake the laws much more powerful than they otherwise would be.", "\nWe should not expect the naïve regularity view of laws to follow\nsuit, however. On this sort of account, roughly, if \\(B\\)s always\nfollow \\(A\\)s, then it is a law of nature that \\(A\\) causes \\(B\\). To\navoid finding laws everywhere, however, this account needs to assume\nthat \\(A\\)s and \\(B\\)s are instantiated plenty of times. But the\ninitial conditions occur only once.", "\nFor more robust realist conceptions of law, it’s difficult to\npredict whether the special initial conditions will emerge as lawlike.\nNecessitarian accounts like Pargetter’s (1984) maintain that it\nis a law that \\(P\\) in our world iff \\(P\\) obtains at every possible\nworld joined to ours by a nomic accessibility relation. Without more\nspecific information about the nature of the accessibility relations\nand the worlds to which we’re related, one can only guess\nwhether all of the worlds relative to ours have the same special\ninitial conditions. Nevertheless some realist theories offer\napparently prohibitive criteria, so they are able to make negative\njudgments. For instance, “universalist” theories\nassociated with David Armstrong say that laws are relations between\nuniversals. Yet a constraint on initial conditions isn’t in any\nnatural way put in this form; hence it would seem the universalist\ntheory would not consider this constraint lawlike.", "\nPhilosophical opinion is certainly divided. The problem is that a\nlawlike boundary condition lacks many of the features we ordinarily\nattribute to laws, e.g., multiple instances, governing temporal\nevolution, etc., yet different accounts of laws focus on different\nsubsets of these features. When we turn to the issue at hand, what we\nfind is the disagreement we expect." ], "subsection_title": "2.9 Lawlike Initial Conditions?" } ] }, { "main_content": [ "\nLife is filled with temporal asymmetries. This directedness is one of\nthe most general features of the world we inhabit. We can break this\ngeneral tendency down into a few more specific temporal arrows.", "\nThe above list is not meant to be exhaustive or especially clean.\nTemporal asymmetries are everywhere. We age and die. Punchlines are at\nthe ends of jokes. Propensities and dispositions and reproductive\nfitness are all future-directed. We prefer rags-to-riches stories to\nriches-to-rags stories. Obviously there are connections amongst many\nof these arrows. Some authors have explicitly or implicitly proposed\nvarious “dependency charts” that are supposed to explain\nwhich of the above arrows depend on which for their existence. Horwich\n(1987) argues for an explanatory relationship wherein the\ncounterfactual arrow depends on the causal arrow, which depends on the\narrow of explanation, which depends on the epistemological arrow.\nLewis (1979), by contrast, thinks an alleged over-determination of\ntraces grounds the asymmetry of counterfactuals and that this in turn\ngrounds the rest. Suhler and Callender (2011) ground the psychological\narrow on the causal and knowledge asymmetries. The chart one judges\nmost appropriate will depend, to a large degree, upon one’s\ngeneral philosophical stance on many large topics.", "\nWhich dependency chart is the correct one is not our concern here.\nRather, the second “problem of the direction of time”\nasks: do any (all?) of these arrows ultimately hold in virtue of the\nthermodynamic arrow of time (or what grounds it)?", "\nSklar (1985) provides useful examples to have in mind. Consider the\nup-down asymmetry. It plausibly reduces to the local gravitational\ngradient. Astronauts on the moon think down is the direction toward\nthe center of the moon, not wherever it was when they left Earth. By\ncontrast, there is (probably) merely a correlation between the\nleft-right asymmetry (say, in snail shells) and parity violations in\nhigh-energy particle physics. The second problem asks whether any of\nthe above temporal asymmetries are to the thermodynamic arrow as the\nup-down asymmetry is to the local gravitational gradient. Of course,\nwe don’t expect anything quite so straightforward. Sklar\ndescribes an experiment where iron dust inserted in the ear sacs of\nfish cause the fish to swim upside down when a magnet is held over the\ntank, presumably altering their sense of up and down. But as Jos\nUffink remarked to me, going inside a refrigerator doesn’t cause\nus to remember the future. The connections, if any, are bound to be\nsubtle." ], "section_title": "3. The Problem of the Direction of Time II", "subsections": [ { "content": [ "\nInspired by Boltzmann’s attempts in this regard, many\nphilosophers have sought such reductions, either partial or total.\nGrünbaum (1973) and Smart (1967) develop entropic accounts of the\nknowledge asymmetry. Lewis (1979) suspects the asymmetry of traces is\nlinked to the thermodynamic arrow but provides no specifics. Dowe\n(1992), like a few others, ties the direction of causation to the\nentropy gradient. And some have also tied the psychological arrow to\nthis gradient (for a discussion see Kroes 1985). Perhaps the most\nambitious attempts at grounding many arrows all at once can be found\nin Reichenbach 1956, Horwich 1987, and Albert 2000, 2015. Each of\nthese books offers possible thermodynamic explanations for the causal\nand epistemic arrows, as well as many subsidiary arrows.", "\nA straightforward reduction of these arrows to entropy is probably not\nin the cards (Earman 1974; Horwich 1987). Consider the epistemic arrow\nof time. The traditional entropic account claimed that because we know\nthere are many more entropy-increasing rather than entropy-decreasing\nsystems in the world (or our part of it), we can infer when we see a\nlow-entropy system that it was preceded and caused by an interaction\nwith something outside the system. To take the canonical example,\nimagine you are walking on the beach and come across a footprint in\nthe sand. You can infer that earlier someone walked by (in contrast to\nit arising as a random fluctuation). In other words, you infer, due to\nits high order, that it was caused by something previously also of\nhigh (or higher) order, i.e, someone walking.", "\nHowever, the entropic account faces some very severe challenges.\nFirst, do footprints on beaches have well-defined thermodynamic\nentropies? To describe the example we switched from low-entropy to\nhigh order, but the association between entropy and our ordinary\nconcept of order is tenuous at best and usually completely misleading.\n(To appreciate this, just consider what happens to your salad dressing\nafter it is left undisturbed. Order increases when the oil and vinegar\nseparate, yet entropy has increased.) To describe the range of systems\nabout which we have knowledge, the account needs something broader\nthan the thermodynamic entropy. But what? Reichenbach is forced to\nmove to a notion of quasi-entropy, losing the reduction in the\nprocess. Second, the entropic account doesn’t license the\ninference to a human being walking on the beach. All it tells you is\nthat the grains of sand in the footprint interacted with its\nenvironment previously, which barely scratches the surface of our\nability to tell detailed stories about what happened in the past.\nThird, even if we entertain a broader understanding of entropy, it\nstill doesn’t always work. Consider Earman’s (1974)\nexample of a bomb destroying a city. From the destruction we may infer\nthat a bomb went off; yet the bombed city does not have lower entropy\nthan its surroundings or even any type of intuitively higher order\nthan its surroundings." ], "subsection_title": "3.1 The Thermodynamic Reduction" } ] } ]

[ "Albert, David Z., 1992, Quantum Mechanics and Experience,\nCambridge, MA: Harvard University Press.", "–––, 2000, Time and Chance, Cambridge,\nMA: Harvard University Press.", "–––, 2015, After Physics, Cambridge,\nMA: Harvard University Press.", "Allori, Valia, 2015, “Maxwell’s Paradox: Classical\nElectrodynamics and its Time Reversal Invariance”,\nAnalytica, 1: 1–19.", "–––, 2020, Statistical Mechanics and\nScientific Explanation: Determinism, Indeterminism and Laws of\nNature, Singapore: World Scientific. doi:10.1142/11591", "Arntzenius, Frank, 1994, “The Classical Failure to Account\nfor Electromagnetic Arrows of Time”, in Tamara Horowitz &\nAlan Ira Janis (eds.), Scientific Failure, Lanham: Rowman\n& Littlefield, pp. 29–48.", "Atkinson, David, 2006, “Does Quantum Electrodynamics Have an\nArrow of Time?”, Studies in the History and Philosophy of\nModern Physics, 37(3): 528–541.\ndoi:10.1016/j.shpsb.2005.03.003", "Barbour, J., Koslowski, T. and Mercati, F., 2014,\n“Identification of a Gravitational Arrow of Time”,\nPhysical Review Letters, 113: 181101.", "Blatt, J.M., 1959, “An Alternative Approach to the Ergodic\nProblem”, Progress in Theoretical Physics, 22(6): 745.\ndoi:10.1143/PTP.22.745", "Boltzmann, Ludwig, 1895, “On Certain Questions of the Theory\nof Gases”, Nature, 51: 413–15.", "Bricmont, Jean, 1995, “Science of Chaos or Chaos in\nScience?”, Physicalia Magazine, 17(3–4):\n159–208.", "Brown, Harvey R., Wayne Myrvold, and Jos Uffink, 2009,\n“Boltzmann’s \\(H\\)-Theorem, Its Discontents, and the Birth\nof Statistical Mechanics ”, Studies in the History and\nPhilosophy of Science, 40(2): 174–191.\ndoi:10.1016/j.shpsb.2009.03.003", "Brown, Harvey R. and Jos Uffink, 2001, “The Origins of\nTime-Asymmetry in Thermodynamics: The Minus First Law”,\nStudies in the History and Philosophy of Modern Physics,\n32(4): 525–538. doi:10.1016/S1355-2198(01)00021-1", "Brush, S.G., 1976, The Kind of Motion We Call Heat,\nAmsterdam: North Holland.", "Callender, Craig, 1997, “What is ‘The Problem of the\nDirection of Time’?”, Philosophy of Science\n(Supplement), 64: S223–34. doi:10.1086/392602", "–––, 1998, “The View From No-when”,\nBritish Journal for the Philosophy of Science, 49(135):\n135–159. doi:10.1093/bjps/49.1.135", "–––, 1999, “Reducing Thermodynamics to\nStatistical Mechanics: The Case of Entropy”, Journal of\nPhilosophy, 96(7): 348–373. doi:10.5840/jphil199996733", "–––, 2004a, “There is No Puzzle about the\nLow Entropy Past”, in Christopher Hitchcock (ed.),\nContemporary Debates in the Philosophy of Science, Oxford:\nBlackwell, 240–256.", "–––, 2004b, “Measures, Explanation and the\nPast: Should ‘Special’ Initial Conditions Be\nExplained?”, British Journal for the Philosophy of\nScience, 55(2): 195–217. doi:10.1093/bjps/55.2.195", "–––, 2010, “The Past Hypothesis Meets\nGravity”, in Gerhard Ernst and Andreas Hüttemann (eds),\nTime, Chance and Reduction, Cambridge: Cambridge University\nPress, pp. 34–58.", "–––, 2011a, “The Past Histories of\nMolecules”, in Claus Beisbart & Stephan Hartmann (eds.),\nProbabilities in Physics, Oxford: Oxford University Press,\npp. 83–113. doi:10.1093/acprof:oso/9780199577439.003.0004", "–––, 2011b, “Hot and Heavy Matters in the\nFoundations of Statistical Mechanics”, Foundations of\nPhysics, 41(6): 960–981. doi:10.1007/s10701-010-9518-z", "Callender, Craig (ed.), 2011c, The Oxford Handbook of\nPhilosophy of Time, Oxford: Oxford University Press.", "Carathéodory, Constantin, 1909, “Untersuchungen\nüber die Grundlagen der Thermodynamik”, Mathematische\nAnnalen, 67(3): 355–386 doi:10.1007/BF01450409", "Carnot, Sadi, 1824, Réflexions sur la puissance motrice\ndu feu et sur les machines propres à développer cette\npuissance, Paris: Chez Bachelier, Libraire; translated as\nReflections on the Motive Power of Heat, R.H. 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[ "\n\nTime travel has been a staple of science fiction. With the advent of\ngeneral relativity it has been entertained by serious physicists. But,\nespecially in the philosophy literature, there have been arguments that\ntime travel is inherently paradoxical. The most famous paradox is the\ngrandfather paradox: you travel back in time and kill your grandfather,\nthereby preventing your own existence. To avoid inconsistency some\ncircumstance will have to occur which makes you fail in this attempt to\nkill your grandfather. Doesn't this require some implausible constraint\non otherwise unrelated circumstances? We examine such worries in the\ncontext of modern physics. " ]

[ { "content_title": "1. A Botched Suicide", "sub_toc": [] }, { "content_title": "2. Why Do Time Travel Suicides Get Botched?", "sub_toc": [] }, { "content_title": "3. Topology and Constraints", "sub_toc": [] }, { "content_title": "4. The General Possibility of Time Travel in General Relativity", "sub_toc": [] }, { "content_title": "5. Two Toy Models", "sub_toc": [] }, { "content_title": "6. Remarks and Limitations on the Toy Models", "sub_toc": [] }, { "content_title": "7. Slightly More Realistic Models of Time Travel", "sub_toc": [] }, { "content_title": "8. Even If There are Constraints, So What?", "sub_toc": [] }, { "content_title": "9. Quantum Mechanics to the Rescue?", "sub_toc": [] }, { "content_title": "10. Conclusions", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nYou are very depressed. You are suicidally depressed. You have a\ngun. But you do not quite have the courage to point the gun at yourself\nand kill yourself in this way. If only someone else would kill you,\nthat would be a good thing. But you can't really ask someone to kill\nyou. That wouldn't be fair. You decide that if you remain this\ndepressed and you find a time machine, you will travel back in time to\njust about now, and kill your earlier self. That would be good. In that\nway you even would get rid of the depressing time you will spend\nbetween now and when you would get into that time machine. You start to\nmuse about the coherence of this idea, when something amazing happens.\nOut of nowhere you suddenly see someone coming towards you with a gun\npointed at you. In fact he looks very much like you, except that he is\nbleeding badly from his left eye, and can barely stand up straight. You\nare at peace. You look straight at him, calmly. He shoots. You feel a\nsearing pain in your left eye. Your mind is in chaos, you stagger\naround and accidentally enter a strange looking cubicle. You drift off\ninto unconsciousness. After a while, you can not tell how long, you\ndrift back into consciousness and stagger out of the cubicle. You see\nsomeone in the distance looking at you calmly and fixedly. You realize\nthat it is your younger self. He looks straight at you. You are in\nterrible pain. You have to end this, you have to kill him, really kill\nhim once and for all. You shoot him, but your eyesight is so bad that\nyour aim is off. You do not kill him, you merely damage his left eye.\nHe staggers off. You fall to the ground in agony, and decide to study\nthe paradoxes of time travel more seriously." ], "section_title": "1. A Botched Suicide", "subsections": [] }, { "main_content": [ "\n\nThe standard worry about time travel is that it allows one to go\nback and kill one's younger self and thereby create paradox. More\ngenerally it allows for people or objects to travel back in time and to\ncause events in the past that are inconsistent with what in fact\nhappened. (See e.g., Gödel 1949, Earman 1972, Malament\n1985a&b, Horwich 1987.) A stone-walling response to this worry is\nthat by logic indeed inconsistent events can not both happen. Thus in\nfact all such schemes to create paradox are logically bound to fail. So\nwhat's the worry?", "\n\nWell, one worry is the question as to why such schemes always fail.\nDoesn't the necessity of such failures put prima facie unusual\nand unexpected constraints on the actions of people, or objects, that\nhave traveled in time? Don't we have good reason to believe that there\nare no such constraints (in our world) and thus that there is no time\ntravel (in our world)? We will later return to the issue of the\npalatability of such constraints, but first we want to discuss an\nargument that no constraints are imposed by time travel." ], "section_title": "2. Why Do Time Travel Suicides Get Botched?", "subsections": [] }, { "main_content": [ "\n\nWheeler and Feynman (1949) were the first to claim that the fact\nthat nature is continuous could be used to argue that causal influences\nfrom later events to earlier events, as are made possible by time\ntravel, will not lead to paradox without the need for any constraints.\nMaudlin (1990) showed how to make their argument precise and more\ngeneral, and argued that nonetheless it was not completely general.", "\n\nImagine the following set-up. We start off having a camera with a\nblack and white film ready to take a picture of whatever comes out of\nthe time machine. An object, in fact a developed film, comes out of the\ntime machine. We photograph it, and develop the film. The developed\nfilm is subsequently put in the time machine, and set to come out of\nthe time machine at the time the picture is taken. This surely will\ncreate a paradox: the developed film will have the opposite\ndistribution of black, white, and shades of gray, from the object that\ncomes out of the time machine. For developed black and white films\n(i.e. negatives) have the opposite shades of gray from the objects they\nare pictures of. But since the object that comes out of the time\nmachine is the developed film itself it we surely have a paradox.", "\n\nHowever, it does not take much thought to realize that there is no\nparadox here. What will happen is that a uniformly gray picture will\nemerge, which produces a developed film that has exactly the same\nuniform shade of gray. No matter what the sensitivity of the film is,\nas long as the dependence of the brightness of the developed film\ndepends in a continuous manner on the brightness of the object being\nphotographed, there will be a shade of gray that, when photographed,\nwill produce exactly the same shade of gray on the developed film. This\nis the essence of Wheeler and Feynman's idea. Let us first be a bit\nmore precise and then a bit more general.", "\n\nFor simplicity let us suppose that the film is always a uniform\nshade of gray (i.e. at any time the shade of gray does not vary by\nlocation on the film). The possible shades of gray of the film can then\nbe represented by the (real) numbers from 0, representing pure black,\nto 1, representing pure white.", "\n\nLet us now distinguish various stages in the chronogical order of\nthe life of the film. In stage S1 the film is\nyoung; it has just been placed in the camera and is ready to be\nexposed. It is then exposed to the object that comes out of the time\nmachine. (That object in fact is a later stage of the film itself). By\nthe time we come to stage S2 of the life of the\nfilm, it has been developed and is about to enter the time machine.\nStage S3 occurs just after it exits the time\nmachine and just before it is photographed. Stage\nS4 occurs after it has been photographed and before\nit starts fading away. Let us assume that the film starts out in stage\nS1 in some uniform shade of gray, and that the only\nsignificant change in the shade of gray of the film occurs between\nstages S1 and S2. During that\nperiod it acquires a shade of gray that depends on the shade of gray of\nthe object that was photographed. I.e., the shade of gray that the film\nacquires at stage S2 depends on the shade of gray\nit has at stage S3. The influence of the shade of\ngray of the film at stage S3, on the shade of gray\nof the film at stage S2, can be represented as a\nmapping, or function, from the real numbers between 0 and 1\n(inclusive), to the real numbers between 0 and 1 (inclusive). Let us\nsuppose that the process of photography is such that if one imagines\nvarying the shade of gray of an object in a smooth, continuous manner\nthen the shade of gray of the developed picture of that object will\nalso vary in a smooth, continuous manner. This implies that the\nfunction in question will be a continuous function. Now any continuous\nfunction from the real numbers between 0 and 1 (inclusive) to the real\nnumbers between 0 and 1 (inclusive) must map at least one number to\nitself. One can quickly convince oneself of this by graphing such\nfunctions. For one will quickly see that any continuous function f from\n[0,1] to [0,1] must intersect the line x=y somewhere,\nand thus there must be at least one point x such that\nf(x)=x. Such points are called fixed points\nof the function. Now let us think about what such a fixed point\nrepresents. It represents a shade of gray such that, when photographed,\nit will produce a developed film with exactly that same shade of gray.\nThe existence of such a fixed point implies a solution to the apparent\nparadox.", "\n\nLet us now be more general and allow color photography. One can\nrepresent each possible color of an object (of uniform color) by the\nproportions of blue, green and red that make up that color. (This is\nwhy television screens can produce all possible colors.) Thus one can\nrepresent all possible colors of an object by three points on three\northogonal lines x, y and z, that is to say,\nby a point in a three-dimensional cube. This cube is also known as the\n‘Cartesian product’ of the three line segments. Now, one\ncan also show that any continuous map from such a cube to itself must\nhave at least one fixed point. So color photography can not be used to\ncreate time travel paradoxes either!", "\n\nEven more generally, consider some system P which, as in\nthe above example, has the following life. It starts in some state\nS1, it interacts with an object that comes out of a\ntime machine (which happens to be its older self), it travels back in\ntime, it interacts with some object (which happens to be its younger\nself), and finally it grows old and dies. Let us assume that the set of\npossible states of P can be represented by a Cartesian product\nof n closed intervals of the reals, i.e., let us assume that\nthe topology of the state-space of P is isomorphic to a finite\nCartesian product of closed intervals of the reals. Let us further\nassume that the development of P in time, and the dependence\nof that development on the state of objects that it interacts with, is\ncontinuous. Then, by a well-known fixed point theorem in topology (see\ne.g., Hocking and Young 1961, p 273), no matter what the nature of the\ninteraction is, and no matter what the initial state of the object is,\nthere will be at least one state S3 of the older\nsystem (as it emerges from the time travel machine) that will influence\nthe initial state S1 of the younger system (when it\nencounters the older system) so that, as the younger system becomes\nolder, it develops exactly into state S3. Thus\nwithout imposing any constraints on the initial state\nS1 of the system P, we have shown that\nthere will always be perfectly ordinary, non-paradoxical, solutions, in\nwhich everything that happens, happens according to the usual laws of\ndevelopment. Of course, there is looped causation, hence presumably\nalso looped explanation, but what do you expect if there is looped\ntime?", "\n\nUnfortunately, for the fan of time travel, a little reflection\nsuggests that there are systems for which the needed fixed point\ntheorem does not hold. Imagine, for instance, that we have a dial that\ncan only rotate in a plane. We are going to put the dial in the time\nmachine. Indeed we have decided that if we see the later stage of the\ndial come out of the time machine set at angle x, then we will\nset the dial to x+90, and throw it into the time machine. Now\nit seems we have a paradox, since the mapping that consists of a\nrotation of all points in a circular state-space by 90 degrees does not\nhave a fixed point. And why wouldn't some state-spaces have the\ntopology of a circle?", "\n\nHowever, we have so far not used another continuity assumption which\nis also a reasonable assumption. So far we have only made the following\ndemand: the state the dial is in at stage S2 must\nbe a continuous function of the state of the dial at stage\nS3. But, the state of the dial at stage\nS2 is arrived at by taking the state of the dial at\nstage S1, and rotating it over some angle. It is\nnot merely the case that the effect of the interaction, namely the\nstate of the dial at stage S2, should be a\ncontinuous function of the cause, namely the state of the dial at stage\nS3. It is additionally the case that path taken to\nget there, the way the dial is rotated between stages\nS1 and S2 must be a continuous\nfunction of the state at stage S3. And, rather\nsurprisingly, it turns out that this can not be done. Let us illustrate\nwhat the problem is before going to a more general demonstration that\nthere must be a fixed point solution in the dial case.", "\n\nForget time travel for the moment. Suppose that you and I each have\na watch with a single dial neither of which is running. My watch is set\nat 12. You are going to announce what your watch is set at. My task is\ngoing to be to adjust my watch to yours no matter what announcement you\nmake. And my actions should have a continuous (single valued)\ndependence on the time that you announce. Surprisingly, this is not\npossible! For instance, suppose that if you announce “12”,\nthen I achieve that setting on my watch by doing nothing. Now imagine\nslowly and continuously increasing the announced times, starting at 12.\nBy continuity, I must achieve each of those settings by rotating my\ndial to the right. If at some point I switch and achieve the announced\ngoal by a rotation of my dial to the left, I will have introduced a\ndiscontinuity in my actions, a discontinuity in the actions that I take\nas a function of the announced angle. So I will be forced, by\ncontinuity, to achieve every announcement by rotating the dial to the\nright. But, this rotation to the right will have to be abruptly\ndiscontinued as the announcements grow larger and I eventually approach\n12 again, since I achieved 12 by not rotating the dial at all. So,\nthere will be a discontinuity at 12 at the latest. In general,\ncontinuity of my actions as a function of announced times can not be\nmaintained throughout if I am to be able to replicate all possible\nsettings. Another way to see the problem is that one can similarly\nreason that, as one starts with 12, and imagines continuously making\nthe announced times earlier, one will be forced, by continuity, to\nachieve the announced times by rotating the dial to the left. But the\nconclusions drawn from the assumption of continuous increases and the\nassumption of continuous decreases are inconsistent. So we have an\ninconsistency following from the assumption of continuity and the\nassumption that I always manage to set my watch to your watch. So, a\ndial developing according to a continuous dynamics from a given initial\nstate, can not be set up so as to react to a second dial, with which it\ninteracts, in such a way that it is guaranteed to always end up set at\nthe same angle as the second dial. Similarly, it can not be set up so\nthat it is guaranteed to always end up set at 90 degrees to the setting\nof the second dial. All of this has nothing to do with time travel.\nHowever, the impossibility of such set ups is what prevents us from\nenacting the rotation by 90 degrees that would create paradox in the\ntime travel setting.", "\n\nLet us now give the positive result that with such dials there will\nalways be fixed point solutions, as long as the dynamics is continuous.\nLet us call the state of the dial before it interacts with its older\nself the initial state of the dial. And let us call the state of the\ndial after it emerges from the time machine the final state of the\ndial. We can represent the possible initial and final states of the\ndial by the angles x and y that the dial can point at\ninitially and finally. The set of possible initial plus final states\nthus forms a torus. (See figure 1.)", "\n\n Figure 1", "\n\nSuppose that the dial starts at angle I. The initial angle\nI that the dial is at before it encounters its older self, and\nthe set of all possible final angles that the dial can have when it\nemerges from the time machine is represented by the circle I\non the torus (see figure 1). Given any possible angle of the emerging\ndial the dial initially at angle I will develop to some other\nangle. One can picture this development by rotating each point on\nI in the horizontal direction by the relevant amount. Since\nthe rotation has to depend continuously on the angle of the emerging\ndial, ring I during this development will deform into some\nloop L on the torus. Loop L thus represents the angle\nx that the dial is at when it is thrown into the time machine,\ngiven that it started at angle I and then encountered a dial\n(its older self) which was at angle y when it emerged from the\ntime machine. We therefore have consistency if x=y\nfor some x and y on loop L. Now, let loop\nC be the loop which consists of all the points on the torus\nfor which x=y. Ring I intersects C\nat point <i,i>. Obviously any continuous\ndeformation of I must still intersect C somewhere. So\nL must intersect C somewhere, say at\n<j,j>. But that means that no matter how the\ndevelopment of the dial starting at I depends on the angle of\nthe emerging dial, there will be some angle for the emerging dial such\nthat the dial will develop exactly into that angle (by the time it\nenters the time machine) under the influence of that emerging dial.\nThis is so no matter what angle one starts with, and no matter how the\ndevelopment depends on the angle of the emerging dial. Thus even for a\ncircular state-space there are no constraints needed other than\ncontinuity.", "\n\nUnfortunately there are state-spaces that escape even this argument.\nConsider for instance a pointer that can be set to all values between 0\nand 1, where 0 and 1 are not possible values. That is, suppose that we\nhave a state-space that is isomorphic to an open set of real numbers.\nNow suppose that we have a machine that sets the pointer to half the\nvalue that the pointer is set at when it emerges from the time\nmachine.", "\n\n Figure 2", "\n\nSuppose the pointer starts at value I. As before we can\nrepresent the combination of this initial position and all possible\nfinal positions by the line I. Under the influence of the\npointer coming out of the time machine the pointer value will develop\nto a value that equals half the value of the final value that it\nencountered. We can represent this development as the continuous\ndeformation of line I into line L, which is indicated\nby the arrows in Figure 2. This development is fully continuous. Points\n<x,y> on line I represent the initial\nposition x=I of the (young) pointer, and the position\ny of the older pointer as it emerges from the time machine. Points\n<x,y> on line L represent the position\nx that the younger pointer should develop into, given that it\nencountered the older pointer emerging from the time machine set at\nposition y. Since the pointer is designed to develop to half\nthe value of the pointer that it encounters, the line L\ncorresponds to x=1/2y. We have\nconsistency if there is some point such that it develops into that\npoint, if it encounters that point. Thus, we have consistency if there\nis some point <x,y> on line L such\nthat x=y. However, there is no such point: lines\nL and C do not intersect. Thus there is no consistent\nsolution, despite the fact that the dynamics is fully continuous.", "\n\nOf course if 0 were a possible value L and C would\nintersect at 0. This is surprising and strange: adding one point to the\nset of possible values of a quantity here makes the difference between\nparadox and peace. One might be tempted to just add the extra point to\nthe state-space in order to avoid problems. After all, one might say,\nsurely no measurements could ever tell us whether the set of possible\nvalues includes that exact point or not. Unfortunately there can be\ngood theoretical reasons for supposing that some quantity has a\nstate-space that is open: the set of all possible speeds of massive\nobjects in special relativity surely is an open set, since it includes\nall speeds up to, but not including, the speed of light. Quantities\nthat have possible values that are not bounded also lead to counter\nexamples to the presented fixed point argument. And it is not obvious\nto us why one should exclude such possibilities. So the argument that\nno constraints are needed is not fully general.", "\n\nAn interesting question of course is: exactly for which state-spaces\nmust there be such fixed points. We do not know the general answer.\n(But see Kutach 2003 for more on this issue.)" ], "section_title": "3. Topology and Constraints", "subsections": [] }, { "main_content": [ "\n\nTime travel has recently been discussed quite extensively in the\ncontext of general relativity. Time travel can occur in general\nrelativistic models in which one has closed time-like curves (CTC's). A\ntime like curve is simply a space-time trajectory such that the speed\nof light is never equalled or exceeded along this trajectory. Time-like\ncurves thus represent the possible trajectories of ordinary objects. If\nthere were time-like curves which were closed (formed a loop), then\ntravelling along such a curve one would never exceed the speed of\nlight, and yet after a certain amount of (proper) time one would return\nto a point in space-time that one previously visited. Or, by staying\nclose to such a CTC, one could come arbitrarily close to a point in\nspace-time that one previously visited. General relativity, in a\nstraightforward sense, allows time travel: there appear to be many\nspace-times compatible with the fundamental equations of General\nRelativity in which there are CTC's. Space-time, for instance, could\nhave a Minkowski metric everywhere, and yet have CTC's everywhere by\nhaving the temporal dimension (topologically) rolled up as a circle.\nOr, one can have wormhole connections between different parts of\nspace-time which allow one to enter ‘mouth A’ of\nsuch a wormhole connection, travel through the wormhole, exit the\nwormhole at ‘mouth B’ and re-enter ‘mouth\nA’ again. Or, one can have space-times which\ntopologically are R4, and yet have CTC's due to the\n‘tilting’ of light cones (Gödel space-times, Taub-NUT\nspace-times, etc.)", "\n\nGeneral relativity thus appears to provide ample opportunity for\ntime travel. Note that just because there are CTC's in a space-time,\nthis does not mean that one can get from any point in the space-time to\nany other point by following some future directed timelike curve. In\nmany space-times in which there are CTC's such CTC's do not occur all\nover space-time. Some parts of space-time can have CTC's while other\nparts do not. Let us call the part of a space-time that has CTC's the\n“time travel region\" of that space-time, while calling the rest\nof that space-time the \"normal region\". More precisely, the “time\ntravel region\" consists of all the space-time points p such\nthat there exists a (non-zero length) timelike curve that starts at\np and returns to p. Now let us start examining\nspace-times with CTC's a bit more closely for potential problems." ], "section_title": "4. The General Possibility of Time Travel in General Relativity", "subsections": [] }, { "main_content": [ "\n\nIn order to get a feeling for the sorts of implications that closed\ntimelike curves can have, it may be useful to consider two simple\nmodels. In space-times with closed timelike curves the traditional\ninitial value problem cannot be framed in the usual way. For it\npresupposes the existence of Cauchy surfaces, and if there are CTCs\nthen no Cauchy surface exists. (A Cauchy surface is a spacelike surface\nsuch that every inextendible timelike curve crosses it exactly once.\nOne normally specifies initial conditions by giving the conditions on\nsuch a surface.) Nonetheless, if the topological complexities of the\nmanifold are appropriately localized, we can come quite close. Let us\ncall an edgeless spacelike surface S a quasi-Cauchy\nsurface if it divides the rest of the manifold into two parts such that\na) every point in the manifold can be connected by a timelike curve to\nS, and b) any timelike curve which connects a point in one\nregion to a point in the other region intersects S exactly\nonce. It is obvious that a quasi-Cauchy surface must entirely inhabit\nthe normal region of the space-time; if any point p of\nS is in the time travel region, then any timelike curve which\nintersects p can be extended to a timelike curve which\nintersects S near p again. In extreme cases of time\ntravel, a model may have no normal region at all (e.g., Minkowski\nspace-time rolled up like a cylinder in a time-like direction), in\nwhich case our usual notions of temporal precedence will not apply. But\ntemporal anomalies like wormholes (and time machines) can be\nsufficiently localized to permit the existence of quasi-Cauchy\nsurfaces.", "\n\nGiven a timelike orientation, a quasi-Cauchy surface\nunproblematically divides the manifold into its past (i.e.,\nall points that can be reached by past-directed timelike curves from\nS) and its future (ditto mutatis mutandis).\nIf the whole past of S is in the normal region of the\nmanifold, then S is a partial Cauchy surface: every\ninextendible timelike curve which exists to the past of S\nintersects S exactly once, but (if there is time travel in the\nfuture) not every inextendible timelike curve which exists to the\nfuture of S intersects S. Now we can ask a\nparticularly clear question: consider a manifold which contains a time\ntravel region, but also has a partial Cauchy surface S, such\nthat all of the temporal funny business is to the future of S.\nIf all you could see were S and its past, you would not know\nthat the space-time had any time travel at all. The question is: are\nthere any constraints on the sort of data which can be put on\nS and continued to a global solution of the dynamics which are\ndifferent from the constraints (if any) on the data which can be put on\na Cauchy surface in a simply connected manifold and continued to a\nglobal solution? If there is time travel to our future, might we we\nable to tell this now, because of some implied oddity in the\narrangement of present things?", "\n\nIt is not at all surprising that there might be constraints on the\ndata which can be put on a locally space-like surface which passes\nthrough the time travel region: after all, we never think we can freely\nspecify what happens on a space-like surface and on another such\nsurface to its future, but in this case the surface at issue lies to\nits own future. But if there were particular constraints for data on a\npartial Cauchy surface then we would apparently need to have to rule\nout some sorts of otherwise acceptable states on S if there is\nto be time travel to the future of S. We then might be able to\nestablish that there will be no time travel in the future by simple\ninspection of the present state of the universe. As we will see, there\nis reason to suspect that such constraints on the partial Cauchy\nsurface are non-generic. But we are getting ahead of ourselves: first\nlet's consider the effect of time travel on a very simple dynamics.", "\n\nThe simplest possible example is the Newtonian theory of perfectly\nelastic collisions among equally massive particles in one spatial\ndimension. The space-time is two-dimensional, so we can represent it\ninitially as the Euclidean plane, and the dynamics is completely\nspecified by two conditions. When particles are traveling freely, their\nworld lines are straight lines in the space-time, and when two\nparticles collide, they exchange momenta, so the collision looks like\nan ‘X’ in space-time, with each particle changing\nits momentum at the\n impact.[1]\n The dynamics is purely local, in that one\ncan check that a set of world-lines constitutes a model of the dynamics\nby checking that the dynamics is obeyed in every arbitrarily small\nregion. It is also trivial to generate solutions from arbitrary initial\ndata if there are no CTCs: given the initial positions and momenta of a\nset of particles, one simply draws a straight line from each particle\nin the appropriate direction and continues it indefinitely. Once all\nthe lines are drawn, the worldline of each particle can be traced from\ncollision to collision. The boundary value problem for this dynamics is\nobviously well-posed: any set of data at an instant yields a unique\nglobal solution, constructed by the method sketched above.", "\n\nWhat happens if we change the topology of the space-time by hand to\nproduce CTCs? The simplest way to do this is depicted in figure 3: we\ncut and paste the space-time so it is no longer simply connected by\nidentifying the line L− with the line L+.\nParticles “going in” to L+ from below\n“emerge” from L− , and particles\n“going in” to L− from below\n“emerge” from L+.", "\n\n Figure 3: Inserting CTCs by Cut and Paste", "\n\nHow is the boundary-value problem changed by this alteration in the\nspace-time? Before the cut and paste, we can put arbitrary data on the\nsimultaneity slice S and continue it to a unique solution.\nAfter the change in topology, S is no longer a Cauchy surface,\nsince a CTC will never intersect it, but it is a partial Cauchy\nsurface. So we can ask two questions. First, can arbitrary data on\nS always be continued to a global solution? Second, is that\nsolution unique? If the answer to the first question is no,\nthen we have a backward-temporal constraint: the existence of the\nregion with CTCs places constraints on what can happen on S\neven though that region lies completely to the future of S. If\nthe answer to the second question is no, then we have an odd\nsort of indeterminism: the complete physical state on S does\nnot determine the physical state in the future, even though the local\ndynamics is perfectly deterministic and even though there is no other\npast edge to the space-time region in S's future (i.e., there\nis nowhere else for boundary values to come from which could\ninfluence the state of the region).", "\n\nIn this case the answer to the first question is yes and to\nthe second is no: there are no constraints on the data which\ncan be put on S, but those data are always consistent with an\ninfinitude of different global solutions. The easy way to see that\nthere always is a solution is to construct the minimal solution in the\nfollowing way. Start drawing straight lines from S as required\nby the initial data. If a line hits L− from the bottom,\njust continue it coming out of the top of L+ in the\nappropriate place, and if a line hits L+ from the bottom,\ncontinue it emerging from L− at the appropriate place.\nFigure 4 represents the minimal solution for a single particle which\nenters the time-travel region from the left:", "\n\n Figure 4: The Minimal Solution", "\n\nThe particle ‘travels back in time’ three times. It is\nobvious that this minimal solution is a global solution, since the\nparticle always travels inertially.", "\n\nBut the same initial state on S is also consistent with\nother global solutions. The new requirement imposed by the topology is\njust that the data going into L+ from the bottom match the\ndata coming out of L− from the top, and the data going\ninto L- from the bottom match the data coming out of\nL+ from the top. So we can add any number of vertical lines\nconnecting L- and L+ to a solution and still have a\nsolution. For example, adding a few such lines to the minimal solution\nyields:", "\n\n Figure 5: A Non-Minimal Solution", "\n\nThe particle now collides with itself twice: first before it reaches\nL+ for the first time, and again shortly before it exits the\nCTC region. From the particle's point of view, it is traveling to the\nright at a constant speed until it hits an older version of itself and\ncomes to rest. It remains at rest until it is hit from the right by a\nyounger version of itself, and then continues moving off, and the same\nprocess repeats later. It is clear that this is a global model of the\ndynamics, and that any number of distinct models could be generating by\nvarying the number and placement of vertical lines.", "\n\nKnowing the data on S, then, gives us only incomplete\ninformation about how things will go for the particle. We know that the\nparticle will enter the CTC region, and will reach L+, we know\nthat it will be the only particle in the universe, we know exactly\nwhere and with what speed it will exit the CTC region. But we cannot\ndetermine how many collisions the particle will undergo (if any), nor\nhow long (in proper time) it will stay in the CTC region. If the\nparticle were a clock, we could not predict what time it would indicate\nwhen exiting the region. Furthermore, the dynamics gives us no handle\non what to think of the various possibilities: there are no\nprobabilities assigned to the various distinct possible outcomes.", "\n\nChanging the topology has changed the mathematics of the situation\nin two ways, which tend to pull in opposite directions. On the one\nhand, S is no longer a Cauchy surface, so it is perhaps not\nsurprising that data on S do not suffice to fix a unique\nglobal solution. But on the other hand, there is an added constraint:\ndata “coming out” of L− must exactly match\ndata “going in” to L+, even though what comes out\nof L− helps to determine what goes into L+.\nThis added consistency constraint tends to cut down on solutions,\nalthough in this case the additional constraint is more than outweighed\nby the freedom to consider various sorts of data on\nL+/L-.", "\n\nThe fact that the extra freedom outweighs the extra constraint also\npoints up one unexpected way that the supposed paradoxes of time travel\nmay be overcome. Let's try to set up a paradoxical situation using the\nlittle closed time loop above. If we send a single particle into the\nloop from the left and do nothing else, we know exactly where it will\nexit the right side of the time travel region. Now suppose we station\nsomeone at the other side of the region with the following charge: if\nthe particle should come out on the right side, the person is to do\nsomething to prevent the particle from going in on the left in\nthe first place. In fact, this is quite easy to do: if we send a\nparticle in from the right, it seems that it can exit on the left and\ndeflect the incoming left-hand particle.", "\n\nCarrying on our reflection in this way, we further realize that if\nthe particle comes out on the right, we might as well send it\nback in order to deflect itself from entering in the first place. So\nall we really need to do is the following: set up a perfectly\nreflecting particle mirror on the right-hand side of the time travel\nregion, and launch the particle from the left so that—if\nnothing interferes with it—it will just barely hit\nL+. Our paradox is now apparently complete. If, on the one\nhand, nothing interferes with the particle it will enter the\ntime-travel region on the left, exit on the right, be reflected from\nthe mirror, re-enter from the right, and come out on the left to\nprevent itself from ever entering. So if it enters, it gets deflected\nand never enters. On the other hand, if it never enters then nothing\ngoes in on the left, so nothing comes out on the right, so nothing is\nreflected back, and there is nothing to deflect it from entering. So if\nit doesn't enter, then there is nothing to deflect it and it enters. If\nit enters, then it is deflected and doesn't enter; if it doesn't enter\nthen there is nothing to deflect it and it enters: paradox\ncomplete.", "\n\nBut at least one solution to the supposed paradox is easy to\nconstruct: just follow the recipe for constructing the minimal\nsolution, continuing the initial trajectory of the particle (reflecting\nit the mirror in the obvious way) and then read of the number and\ntrajectories of the particles from the resulting diagram. We get the\nresult of figure 6:", "\n\n Figure 6: Resolving the “Paradox”", "\n\nAs we can see, the particle approaching from the left never reaches\nL+: it is deflected first by a particle which emerges from\nL-. But it is not deflected by itself, as the paradox\nsuggests, it is deflected by another particle. Indeed, there are now\nfour particles in the diagram: the original particle and three\nparticles which are confined to closed time-like curves. It is not the\nleftmost particle which is reflected by the mirror, nor even the\nparticle which deflects the leftmost particle; it is another particle\naltogether.", "\n\nThe paradox gets it traction from an incorrect presupposition: if\nthere is only one particle in the world at S then there is\nonly one particle which could participate in an interaction in the time\ntravel region: the single particle would have to interact with its\nearlier (or later) self. But there is no telling what might come out of\nL− : the only requirement is that whatever comes out\nmust match what goes in at L+. So if you go to the trouble of\nconstructing a working time machine, you should be prepared for a\ndifferent kind of disappointment when you attempt to go back and kill\nyourself: you may be prevented from entering the machine in the first\nplace by some completely unpredictable entity which emerges from it.\nAnd once again a peculiar sort of indeterminism appears: if there are\nmany self-consistent things which could prevent you from entering,\nthere is no telling which is even likely to materialize.", "\n\nSo when the freedom to put data on L− outweighs the\nconstraint that the same data go into L+, instead of paradox\nwe get an embarrassment of riches: many solution consistent with the\ndata on S. To see a case where the constraint\n“outweighs” the freedom, we need to construct a very\nparticular, and frankly artificial, dynamics and topology. Consider the\nspace of all linear dynamics for a scalar field on a lattice. (The\nlattice can be though of as a simple discrete space-time.) We will\ndepict the space-time lattice as a directed graph. There is to be a\nscalar field defined at every node of the graph, whose value at a given\nnode depends linearly on the values of the field at nodes which have\narrows which lead to it. Each edge of the graph can be assigned a\nweighting factor which determines how much the field at the input node\ncontributes to the field at the output node. If we name the nodes by\nthe letters a, b, c, etc., and the edges by\ntheir endpoints in the obvious way, then we can label the weighting\nfactors by the edges they are associated with in an equally obvious\nway.", "\n\nSuppose that the graph of the space-time lattice is\nacyclic, as in figure 7. (A graph is Acyclic if one\ncan not travel in the direction of the arrows and go in a loop.)", "\n\n Figure 7: An Acyclic Lattice", "\n\nIt is easy to regard a set of nodes as the analog of a Cauchy\nsurface, e.g., the set {a, b, c}, and it is\nobvious if arbitrary data are put on those nodes the data will generate\na unique solution in the\n future.[2]\n If the value of the\nfield at node a is 3 and at node b is 7, then its\nvalue at node d will be 3Wad and\nits value at node e will be 3Wae\n+ 7Wbe. By varying the weighting factors\nwe can adjust the dynamics, but in an acyclic graph the future\nevolution of the field will always be unique.", "\n\nLet us now again artificially alter the topology of the lattice to\nadmit CTCs, so that the graph now is cyclic. One of the simplest such\ngraphs is depicted in figure 8: there are now paths which lead from\nz back to itself, e.g., z to y to\nz.", "\n\n Figure 8: Time Travel on a Lattice", "\n\nCan we now put arbitrary data on v and w, and\ncontinue that data to a global solution? Will the solution be\nunique?", "\n\nIn the generic case, there will be a solution and the solution will\nbe unique. The equations for the value of the field at x,\ny, and z are:", "x = vWvx +\nzWzx\n\n y = wWwy +\nzWzy\n\n z = xWxz +\nyWyz.\n\n", "\n\nSolving these equations for z yields", "z = (vWvx +\nzWzx)Wxz\n+ (wWwy +\nzWzy)Wyz,\n\n or \n\n\n\nz =\n(vWvxWxz\n+\nwWwyWyz)/\n(1 − WzxWxz\n−\nWzyWyz),\n", "\n\nwhich gives a unique value for z in the generic case. But\nlooking at the space of all possible dynamics for this lattice (i.e.,\nthe space of all possible weighting factors), we find a singularity in\nthe case where\n1−WzxWxz −\nWzyWyz = 0.\nIf we choose weighting factors in just this way, then arbitrary data at\nv and w cannot be continued to a global solution.\nIndeed, if the scalar field is everywhere non-negative, then this\nparticular choice of dynamics puts ironclad constraints on the value of\nthe field at v and w: the field there must be zero\n(assuming Wvx and Wwy to be\nnon-zero), and similarly all nodes in their past must have field value\nzero. If the field can take negative values, then the values at\nv and w must be so chosen that\nvWvxWxz\n=\n−wWwyWyz.\nIn either case, the field values at v and w are\nseverely constrained by the existence of the CTC region even though\nthese nodes lie completely to the past of that region. It is this sort\nof constraint which we find to be unlike anything which appears in\nstandard physics.", "\n\nOur toy models suggest three things. The first is that it may be\nimpossible to prove in complete generality that arbitrary data on a\npartial Cauchy surface can always be continued to a global\nsolution: our artificial case provides an example where it cannot. The\nsecond is that such odd constraints are not likely to be generic: we\nhad to delicately fine-tune the dynamics to get a problem. The third is\nthat the opposite problem, namely data on a partial Cauchy surface\nbeing consistent with many different global solutions, is\nlikely to be generic: we did not have to do any fine-tuning to get this\nresult. And this leads to a peculiar sort of indeterminism: the entire\nstate on S does not determine what will happen in the future\neven though the local dynamics is deterministic and there are no other\n“edges” to space-time from which data could influence the\nresult. What happens in the time travel region is constrained but not\ndetermined by what happens on S, and the dynamics does not\neven supply any probabilities for the various possibilities.\nThe example of the photographic negative discussed in section 3, then,\nseems likely to be unusual, for in that case there is a unique\nfixed point for the dynamics, and the set-up plus the dynamical laws\ndetermine the outcome. In the generic case one would rather\nexpect multiple fixed points, with no room for anything to\ninfluence, even probabilistically, which would be\nrealized.", "\n\nIt is ironic that time travel should lead generically not to\ncontradictions or to constraints (in the normal region) but to\nunderdetermination of what happens in the time travel region\nby what happens everywhere else (an underdetermination tied neither to\na probabilistic dynamics or to a free edge to space-time). The\ntraditional objection to time travel is that it leads to\ncontradictions: there is no consistent way to complete an arbitrarily\nconstructed story about how the time traveler intends to act. Instead,\nthough, it appears that the problem is underdetermination: the story\ncan be consistently completed in many different ways." ], "section_title": "5. Two Toy Models", "subsections": [] }, { "main_content": [ "\n\nThe two toys models presented above have the virtue of being\nmathematically tractable, but they involve certain simplifications and\npotential problems that lead to trouble if one tries to make them more\ncomplicated. Working through these difficulties will help highlight the\nconditions we have made use of.", "\n\nConsider a slight modification of the first simple model proposed to\nus by Adam Elga. Let the particles have an electric charge,\nwhich produces forces according to Coulomb’s law. Then set up a\nsituation like that depicted in figure 9:", " \n\n\n\nFigure 9: Set-up for Elga's Paradox\n", "\n\nThe dotted line indicates the path the particle will follow if no\nforces act upon it. The point labeled P is the left edge of\nthe time-travel region; the two labels are a reminder that the point at\nthe bottom and the point at the top are one and the same.", "\n\nElga's paradox is as follows: if no force acts on the particle, then\nit will enter the time-travel region. But if it enters the time travel\nregion, and hence reappears along the bottom edge, then its later self\nwill interact electrically with its earlier self, and the earlier self\nwill be deflected away from the time-travel region. It is easy to set\nup the case so that the deflection will be enough to keep the particle\nfrom ever entering the time-travel region in the first place. (For\ninstance, let the momentum of the incoming particle towards the time\ntravel region be very small. The mere existence of an identically\ncharged particle inside the time travel region will then be sufficient\nto deflect the incoming particle so that it never reaches\nL+.) But, of course, if the particle never enters\nthe region at all, then it will not be there to deflect\nitself….", "\n\nOne might suspect that some complicated collection of charged\nparticles in the time-travel-region can save the day, as it did with\nour mirror-reflection problem above. But (unless there are infinitely\nmany such particles) this can't work, as conservation of particle\nnumber and linear momentum show. Suppose that some finite collection of\nparticles emerges from L- and supplies the\nrepulsive electric force needed to deflect the incoming particle. Then\nexactly the same collection of particles must be “absorbed”\nat L+. So at all times after\nL+, the only particle there is in the world is the\nincoming particle, which has now been deflected away from its original\ntrajectory.", "\n\nThe deflection, though, means that the linear momentum of the\nparticle has changed from what is was before L-.\nBut that is impossible, by conservation of linear momementum. No matter\nhow the incoming particle interacts with particles in the time-travel\nregion, or how those particle interact with each other, total linear\nmomentum is conserved by the interaction. And whatever net linear\nmomentum the time-travelling particles have when they emerge from\nL-, that much linear momentum most be absorbed at\nL+. So the momentum of the incoming particle can't\nbe changed by the interaction: the particle can't have been deflected.\n(One could imagine trying to create a sort of “S” curve in\nthe trajectory of the incoming particle, first bending to the left and\nthen to the right, which leaves its final momentum equal to its initial\nmomentum, but moving it over in space so it misses\nL+. However, if the force at issue is repulsive,\nthen the bending back to the right can't be done. In the mirror example\nabove, the path of the incoming particle can be changed without\nviolating the conservation of momentum because at the end of the\nprocess momentum has been transferred to the mirror.)", "\n\nHow does Elga's example escape our analysis? Why can't a contintuity\nprinciple guarantee the existence of a solution here?", "\n\nThe continuity assumption breaks down because of two features of the\nexample: the concentration of the electric charge on a point particle,\nand the way we have treated (or, more accurately, failed to treat) the\npoint P, the edge of L+ (and\nL-). We have assumed that a point particle either\nhits L+, and then emerges from\nL-, or else it misses L+ and\nsails on into the region of space-time above it. This means that the\ncharge on the incoming particle only has two possibilities: either it\nis transported whole back in time or it completely avoids time travel\naltogether. Let's see how it alters the situation to imagine the charge\nitself to be continuous divisible.", "\n\nSuppose that, instead of being concentrated at a point, the incoming\nobject is a little stick, with electric charge distributed even across\nit (figure 10).", " \n\n\n\nFigure 10: Elga's Paradox with a Charged Bar\n", "\n\nOnce again, we set things up so that if there are no forces on the\nbar, it will be completely absorbed at L+. But we\nnow postulate that if the bar should hit the point P,\nit will fracture: part of it (the part that hits L+) will be\nsent back in time and the rest will continue on above\nL+. So continuity of a sort is restored: now we\nhave not just the possibility of the whole charge being sent back or\nnothing, we have the continuum degrees of charge in between.", "\n\nIt is not hard to see that the restoration of continuity restores\nthe existence of a consistent solution. If no charge is sent back\nthrough time, then the bar is not deflected and all of it hits\nL+ (and hence is sent back through time). If all\nthe charge is sent back through time, then is incoming bar is deflected\nto an extent that it misses L+ completely, and so\nno charge is sent back. But if just the right amount of charge is sent\nback through time, then the bar will be only partially deflected,\ndeflected so that it hits the edge point P, and is split into\na bit that goes back and a bit that does not, with the bit that goes\nback being just the right amount of charge to produce just that\ndeflection (figure 11).", " \n\n\n\nFigure 11: Solution to Elga's Paradox with a Charged Bar\n", "\n\nOur problem about conservation of momentum is also solved: piece of\nthe bar that does not time travel has lower momentum to the right at\nthe end than it had initially, but the piece that does time travel has\na higher momentum (due to the Coulomb forces), and everything balances\nout.", "\n\nIs it cheating to model the charged particle as a bar that can\nfracture? What if we insist that the particle is truly a point\nparticle, and hence that its time travel is an all-or-nothing\naffair?", "\n\nIn that case, we now have to worry about a question we have not yet\nconfronted: what happens if our point particle hits exactly at the\npoint P on the diagram? Does it time-travel or not?\nConfronting this question requires us to face up to a feature of the\nrather cheap way we implemented time travel in our toy models by\ncut-and-paste. The way we rejiggered the space-time structure had a\nrather severe consequence: the resulting space-time is no longer a\nmanifold: the topological structure at the point P is\ndifferent from the topological structure elsewhere. Mathematical\nphysicists simply don't deal with such structures: the usual procedure\nis to eliminate the offending point from the space-time and thus\nrestore the manifold structure. In this case, that would leave a\nbare singularity at point P, an open edge to\nspace-time into which anything could disappear and out of which, for\nall the physics tells us, anything could emerge.", "\n\nIn particular, if we insist that our particle is a point particle,\nthen if its trajectory should happen to intersect P it will\nsimply disappear. What could cause the extremely fortuitous result that\nthe trajectory strikes precisely at P? The emergence of some\nother charged particle, with just the right charge and trajectory,\nfrom P (on L-). And we are no\nlonger bound by any conservation laws: the bare singularity can both\nswallow and produce whatever mass or change or momentum we like. So if\nwe insist on point particles, then we have to take account of the\nsingularity, and that again saves the day.", "\n\nConsideration of these (slightly more complicated) toy models does\nnot replace the proving of theorems, of course. But they do serve to\nillustrate the sorts of consideration that necessarily come into play\nwhen trying to spell out the physics of time travel in all detail. Let\nus now discuss some results regarding some slightly more realistic\nmodels that have been discussed in the physics literature." ], "section_title": "6. Remarks and Limitations on the Toy Models", "subsections": [] }, { "main_content": [ "\n\nEcheverria, Klinkhammer and Thorne (1991) considered the case of\n3-dimensional single hard spherical ball that can go through a single\ntime travel wormhole so as to collide with its younger self.", "\n\n Figure 12", "\n\nThe threat of paradox in this case arises in the following form.\nThere are initial trajectories (starting in the non-time travel region\nof space-time) for the ball such that if such a trajectory is continued\n(into the time travel region), assuming that the ball does not undergo\na collision prior to entering mouth 1 of the wormhole, it will exit\nmouth 2 so as to collide with its earlier self prior to its entry into\nmouth 1 in such a way as to prevent its earlier self from entering\nmouth 1. Thus it seems that the ball will enter mouth 1 if and only if\nit does not enter mouth 1. Of course, the Wheeler-Feynman strategy is\nto look for a ‘glancing blow’ solution: a collision which\nwill produce exactly the (small) deviation in trajectory of the earlier\nball that produces exactly that collision. Are there always such\n solutions?[3]", "\n\nEcheverria, Klinkhammer & Thorne found a large class of initial\ntrajectories that have consistent ‘glancing blow’\ncontinuations, and found none that do not (but their search was not\ncompletely general). They did not produce a rigorous proof that every\ninitial trajectory has a consistent continuation, but suggested that it\nis very plausible that every initial trajectory has a consistent\ncontinuation. That is to say, they have made it very plausible that, in\nthe billiard ball wormhole case, the time travel structure of such a\nwormhole space-time does not result in constraints on states on\nspacelike surfaces in the non-time travel region.", "\n\nIn fact, as one might expect from our discussion in the previous\nsection, they found the opposite problem from that of inconsistency:\nthey found underdetermination. For a large class of initial\ntrajectories there are multiple different consistent ‘glancing\nblow’ continuations of that trajectory (many of which involve\nmultiple wormhole traversals). For example, if one initially has a ball\nthat is traveling on a trajectory aimed straight between the two\nmouths, then one obvious solution is that the ball passes between the\ntwo mouths and never time travels. But another solution is that the\nyounger ball gets knocked into mouth 1 exactly so as to come out of\nmouth 2 and produce that collision. Echeverria et al. do not note the\npossibility (which we pointed out in the previous section) of the\nexistence of additional balls in the time travel region. We conjecture\n(but have no proof) that for every initial trajectory of A\nthere are some, and generically many, multiple ball continuations.", "\n\nFriedman et al. 1990 examined the case of source free\nnon-self-interacting scalar fields traveling through such a time\ntravel wormhole and found that no constraints on initial conditions in\nthe non-time travel region are imposed by the existence of such time\ntravel wormholes. In general there appear to be no known counter\nexamples to the claim that in ‘somewhat realistic’\ntime-travel space-times with a partial Cauchy surface there are no\nconstraints imposed on the state on such a partial Cauchy surface by\nthe existence of CTC's. (See e.g., Friedman and Morris 1991, Thorne\n1994, and Earman 1995; in the Other Internet Resources, see Earman,\nSmeenk, and Wüthrich 2003.)", "\n\nHow about the issue of constraints in the time travel region\nT? Prima facie, constraints in such a region would\nnot appear to be surprising. But one might still expect that there\nshould be no constraints on states on a spacelike surface, provided\none keeps the surface ‘small enough’. In the physics\nliterature the following question has been asked: for any point\np in T, and any space-like surface S that\nincludes p is there a neighborhood E of p\nin S such that any solution on E can be extended to\na solution on the whole space-time? With respect to this question,\nthere are some simple models in which one has this kind of\nextendibility of local solutions to global ones, and some simple\nmodels in which one does not have such extendibility, with no clear\ngeneral pattern. The technical mathematical problems are amplified by the more conceptual problem of what it might mean to say that one could create a situation which forces the creation of closed timelike curves. (See e.g. Yurtsever 1990, Friedman et al. 1990,\nNovikov 1992, Earman 1995 and Earman, Smeenk and Wüthrich 2009; in the Other Internet Resources, see\nEarman, Smeenk and Wüthrich 2003). What are we to think of all of\nthis?" ], "section_title": "7. Slightly More Realistic Models of Time Travel", "subsections": [] }, { "main_content": [ "\n\nSince it is not obvious that one can rid oneself of all constraints\nin realistic models, let us examine the argument that time travel is\nimplausible, and we should think it unlikely to exist in our world, in\nso far as it implies such constraints. The argument goes something like\nthe following. In order to satisfy such constraints one needs some\npre-established divine harmony between the global (time travel)\nstructure of space-time and the distribution of particles and fields on\nspace-like surfaces in it. But it is not plausible that the actual\nworld, or any world even remotely like ours, is constructed with divine\nharmony as part of the plan. In fact, one might argue, we have\nempirical evidence that conditions in any spatial region can vary quite\narbitrarily. So we have evidence that such constraints, whatever they\nare, do not in fact exist in our world. So we have evidence that there\nare no closed time-like lines in our world or one remotely like it. We\nwill now examine this argument in more detail by presenting four\npossible responses, with counterresponses, to this argument.", "\n\nResponse 1. There is nothing implausible or new about such\nconstraints. For instance, if the universe is spatially closed, there\nhas to be enough matter to produce the needed curvature, and this puts\nconstraints on the matter distribution on a space-like hypersurface.\nThus global space-time structure can quite unproblematically constrain\nmatter distributions on space-like hypersurfaces in it. Moreover we\nhave no realistic idea what these constraints look like, so we hardly\ncan be said to have evidence that they do not obtain.", "\n\nCounterresponse 1. Of course there are constraining relations\nbetween the global structure of space-time and the matter in it. The\nEinstein equations relate curvature of the manifold to the matter\ndistribution in it. But what is so strange and implausible about the\nconstraints imposed by the existence of closed time-like curves is that\nthese constraints in essence have nothing to do with the Einstein\nequations. When investigating such constraints one typically treats the\nparticles and/or field in question as test particles and/or fields in a\ngiven space-time, i.e., they are assumed not to affect the metric of\nspace-time in any way. In typical space-times without closed time-like\ncurves this means that one has, in essence, complete freedom of matter\ndistribution on a space-like hypersurface. (See response 2 for some\nmore discussion of this issue). The constraints imposed by the\npossibility of time travel have a quite different origin and are\nimplausible. In the ordinary case there is a causal interaction between\nmatter and space-time that results in relations between global\nstructure of space-time and the matter distribution in it. In the time\ntravel case there is no such causal story to be told: there simply has\nto be some pre-established harmony between the global space-time\nstructure and the matter distribution on some space-like surfaces. This\nis implausible.", "\n\nResponse 2. Constraints upon matter distributions are nothing new.\nFor instance, Maxwell's equations constrain electric fields\nE on an initial surface to be related to the\n(simultaneous) charge density distribution ρ by the equation ρ\n= div(E). (If we assume that the E\nfield is generated solely by the charge distribution, this conditions\namounts to requiring that the E field at any point in space\nsimply be the one generated by the charge distribution according to\nCoulomb's inverse square law of electrostatics.) This is not\nimplausible divine harmony. Such constraints can hold as a matter of\nphysical law. Moreover, if we had inferred from the apparent free\nvariation of conditions on spatial regions that there could be no such\nconstraints we would have mistakenly inferred that ρ =\ndiv(E) could not be a law of nature.", "\n\nCounterresponse 2. The constraints imposed by the existence of\nclosed time-like lines are of quite a different character from the\nconstraint imposed by ρ = div(E). The\nconstraints imposed by ρ = div(E) on the\nstate on a space-like hypersurface are: (i) local constraints (i.e., to\ncheck whether the constraint holds in a region you just need to see\nwhether it holds at each point in the region), (ii) quite independent\nof the global space-time structure, (iii) quite independent of how the\nspace-like surface in question is embedded in a given space-time, and\n(iv) very simply and generally stateable. On the other hand, the\nconsistency constraints imposed by the existence of closed time-like\ncurves (i) are not local, (ii) are dependent on the global structure of\nspace-time, (iii) depend on the location of the space-like surface in\nquestion in a given space-time, and (iv) appear not to be simply\nstateable other than as the demand that the state on that space-like\nsurface embedded in such and such a way in a given space-time, do not\nlead to inconsistency. On some views of laws (e.g., David Lewis' view)\nthis plausibly implies that such constraints, even if they hold, could\nnot possibly be laws. But even if one does not accept such a view of\nlaws, one could claim that the bizarre features of such constraints\nimply that it is implausible that such constraints hold in our world or\nin any world remotely like ours.", "\n\nResponse 3. It would be strange if there are constraints in the\nnon-time travel region. It is not strange if there are constraints in\nthe time travel region. They should be explained in terms of the\nstrange, self-interactive, character of time travel regions. In this\nregion there are time-like trajectories from points to themselves. Thus\nthe state at such a point, in such a region, will, in a sense, interact\nwith itself. It is a well-known fact that systems that interact with\nthemselves will develop into an equilibrium state, if there is such an\nequilibrium state, or else will develop towards some singularity.\nNormally, of course, self-interaction isn't true instantaneous\nself-interaction, but consists of a feed-back mechanism that takes\ntime. But in time travel regions something like true instantaneous\nself-interaction occurs. This explains why constraints on states occur\nin such time travel regions: the states ‘ab initio’ have to\nbe ‘equilibrium states’. Indeed in a way this also provides\nsome picture of why indeterminism occurs in time travel regions: at the\nonset of self-interaction states can fork into different equi-possible\nequilibrium states.", "\n\nCounterresponse 3. This is explanation by woolly analogy. It all\ngoes to show that time travel leads to such bizarre consequences that\nit is unlikely that it occurs in a world remotely like ours.", "\n\nResponse 4. All of the previous discussion completely misses the\npoint. So far we have been taking the space-time structure as given,\nand asked the question whether a given time travel space-time structure\nimposes constraints on states on (parts of) space-like surfaces.\nHowever, space-time and matter interact. Suppose that one is in a\nspace-time with closed time-like lines, such that certain\ncounterfactual distributions of matter on some neighborhood of a point\np are ruled out if one holds that space-time structure fixed.\nOne might then ask “Why does the actual state near p in\nfact satisfy these constraints? By what divine luck or plan is this\nlocal state compatible with the global space-time structure? What if\nconditions near p had been slightly different?” And one might\ntake it that the lack of normal answers to these questions indicates\nthat it is very implausible that our world, or any remotely like it, is\nsuch a time travel universe. However the proper response to these\nquestion is the following. There are no constraints in any significant\nsense. If they hold they hold as a matter of accidental fact, not of\nlaw. There is no more explanation of them possible than there is of any\ncontingent fact. Had conditions in a neighborhood of p been\notherwise, the global structure of space-time would have been\ndifferent. So what? The only question relevant to the issue of\nconstraints is whether an arbitrary state on an arbitrary spatial\nsurface S can always be embedded into a space-time such that\nthat state on S consistently extends to a solution on the\nentire space-time.", "\n\nBut we know the answer to that question. A well-known theorem in\ngeneral relativity says the following: any initial data set on a three\ndimensional manifold S with positive definite metric has a\nunique embedding into a maximal space-time in which S is a\nCauchy surface (see e.g., Geroch and Horowitz 1979, p. 284 for more\ndetail), i.e., there is a unique largest space-time which has\nS as a Cauchy surface and contains a consistent evolution of\nthe initial value data on S. Now since S is a Cauchy\nsurface this space-time does not have closed time like curves. But it\nmay have extensions (in which S is not a Cauchy surface)\nwhich include closed timelike curves, indeed it may be that any\nmaximal extension of it would include closed timelike curves. (This\nappears to be the case for extensions of states on certain surfaces of\nTaub-NUT space-times. See Earman, Smeenk, and Wüthrich 2003 in\nthe Other Internet Resources). But these extensions, of course, will\nbe consistent. So properly speaking, there are no constraints on\nstates on space-like surfaces. Nonetheless the space-time in which\nthese are embedded may or may not include closed time-like curves.", "\n\nCounterresponse 4. This, in essence, is the stonewalling answer\nwhich we indicated at the beginning of section 2. However, whether or\nnot you call the constraints imposed by a given space-time on\ndistributions of matter on certain space-like surfaces ‘genuine\nconstraints’, whether or not they can be considered lawlike, and\nwhether or not they need to be explained, the existence of such\nconstraints can still be used to argue that time travel worlds are so\nbizarre that it is implausible that our world or any world remotely\nlike ours is a time travel world.", "\n\nSuppose that one is in a time travel world. Suppose that given the\nglobal space-time structure of this world, there are constraints\nimposed upon, say, the state of motion of a ball on some space-like\nsurface when it is treated as a test particle, i.e., when it is assumed\nthat the ball does not affect the metric properties of the space-time\nit is in. (There is lots of other matter that, via the Einstein\nequation, corresponds exactly to the curvature that there is everywhere\nin this time travel worlds.) Now a real ball of course does have some\neffect on the metric of the space-time it is in. But let us consider a\nball that is so small that its effect on the metric is negligible.\nPresumably it will still be the case that certain states of this ball\non that space-like surface are not compatible with the global time\ntravel structure of this universe.", "\n\nThis means that the actual distribution of matter on such a\nspace-like surface can be extended into a space-time with closed\ntime-like lines, but that certain counterfactual distributions of\nmatter on this space-like surface can not be extended into the same\nspace-time. But note that the changes made in the matter\ndistribution (when going from the actual to the counterfactual\ndistribution) do not in any non-negligible way affect the metric\nproperties of the space-time. Thus the reason why the global time\ntravel properties of the counterfactual space-time have to be\nsignificantly different from the actual space-time is not that there\nare problems with metric singularities or alterations in the metric\nthat force significant global changes when we go to the counterfactual\nmatter distribution. The reason that the counterfactual space-time has\nto be different is that in the counterfactual world the ball's initial\nstate of motion starting on the space-like surface, could not\n‘meet up’ in a consistent way with its earlier self (could\nnot be consistently extended) if we were to let the global structure of\nthe counterfactual space-time be the same as that of the actual\nspace-time. Now, it is not bizarre or implausible that there is a\ncounterfactual dependence of manifold structure, even of its topology,\non matter distributions on spacelike surfaces. For instance, certain\nmatter distributions may lead to singularities, others may not. We may\nindeed in some sense have causal power over the topology of the\nspace-time we live in. But this power normally comes via the Einstein\nequations. But it is bizarre to think that there could be a\ncounterfactual dependence of global space-time structure on the\narrangement of certain tiny bits of matter on some space-like surface,\nwhere changes in that arrangement by assumption do not affect the\nmetric anywhere in space-time in any significant way. It is\nimplausible that we live in such a world, or that a world even remotely\nlike ours is like that.", "\n\nLet us illustrate this argument in a different way by assuming that\nwormhole time travel imposes constraints upon the states of people\nprior to such time travel, where the people have so little mass/energy\nthat they have negligible effect, via the Einstein equation, on the\nlocal metric properties of space-time. Do you think it more plausible\nthat we live in a world where wormhole time travel occurs but it only\noccurs when people's states are such that these local states happen to\ncombine with time travel in such a way that nobody ever succeeds in\nkilling their younger self, or do you think it more plausible that we\nare not in a wormhole time travel\n world?[4]" ], "section_title": "8. Even If There are Constraints, So What?", "subsections": [] }, { "main_content": [ "\n\nThere has been a particularly clear treatment of time travel in the\ncontext of quantum mechanics by David Deutsch (see Deutsch 1991, and\nDeutsch and Lockwood 1994) in which it is claimed that quantum\nmechanical considerations show that time travel never imposes any\nconstraints on the pre-time travel state of systems. The essence of\nthis account is as follows.", "\n\nA quantum system starts in state S1, interacts with its\nolder self, after the interaction is in state S2,\ntime travels while developing into state S3, then\ninteracts with its younger self, and ends in state\nS4 (see figure 13).", "\n\n Figure 13", "\n\nDeutsch assumes that the set of possible states of this system are\nthe mixed states, i.e., are represented by the density matrices over\nthe Hilbert space of that system. Deutsch then shows that for any\ninitial state S1, any unitary interaction between\nthe older and younger self, and any unitary development during time\ntravel, there is a consistent solution, i.e., there is at least one\npair of states S2 and S3 such\nthat when S1 interacts with S3\nit will change to state S2 and\nS2 will then develop into S3.\nThe states S2, S3 and\nS4 will typically be not be pure states, i.e., will\nbe non-trivial mixed states, even if S1 is pure. In\norder to understand how this leads to interpretational problems let us\ngive an example. Consider a system that has a two dimensional Hilbert\nspace with as a basis the states\n \n and\n .\n Let us suppose that when state\n \n of the young system\nencounters state\n \n of the older system, they interact and the young\nsystem develops into state\n \n and the old system remains in state\n .\n In obvious\nnotation:", "13 develops into\n 24.", "\n\nSimilarly, suppose that:", "13 develops into\n 24, \n\n\n\n 13 develops into\n 24,\nand\n\n\n\n 13 develops into\n 24.\n", "\n\nLet us furthermore assume that there is no development of the state\nof the system during time travel, i.e., that\n 2\ndevelops into\n 3, and that\n 2\ndevelops into\n 3.", "\n\nNow, if the only possible states of the system were\n \n and\n \n (i.e., if there\nwere no superpositions or mixtures of these states), then there is a\nconstraint on initial states: initial state\n 1 is\nimpossible. For if\n 1 interacts with\n 3 then it\nwill develop into\n 2, which, during time travel, will develop\ninto\n 3, which inconsistent with the assumed\nstate\n 3. Similarly if\n 1\ninteracts with\n 3 it will develop into\n 2, which\nwill then develop into\n 3 which is also inconsistent. Thus the\nsystem can not start in state\n 1.", "\n\nBut, says Deutsch, in quantum mechanics such a system can also be in\nany mixture of the states\n \n and\n .\n Suppose that the older system, prior to the\ninteraction, is in a state S3 which is an equal\nmixture of 50%\n 3 and 50%\n 3. Then\nthe younger system during the interaction will develop into a mixture\nof 50%\n 2 and 50%\n 2, which\nwill then develop into a mixture of 50%\n 3 and\n 50%\n 3,\nwhich is consistent! More generally Deutsch uses a fixed point theorem\nto show that no matter what the unitary development during interaction\nis, and no matter what the unitary development during time travel is,\nfor any state S1 there is always a state\nS3 (which typically is not a pure state) which\ncauses S1 to develop into a state\nS2 which develops into that state\nS3. Thus quantum mechanics comes to the rescue: it\nshows in all generality that no constraints on initial states are\nneeded!", "\n\nOne might wonder why Deutsch appeals to mixed states: will\nsuperpositions of states\n \n and\n \n not suffice? Unfortunately such an idea does not\nwork. Suppose again that the initial state is\n 1. One\nmight suggest that that if state S3 is\n 1/√2 3\n +\n 1/√2 3 one\nwill obtain a consistent development. For one might think that when\ninitial state\n 1 encounters the superposition\n 1/√2 3\n +\n 1/√2 3, it\nwill develop into superposition\n 1/√2 2\n +\n 1/√2 2, and\nthat this in turn will develop into\n 1/√2 3\n +\n 1/√2 3, as\ndesired. However this is not correct. For initial state\n 1 when it\nencounters\n 1/√2 3 +\n 1/√2 3, will\ndevelop into the entangled state\n 1/√2 24\n +\n 1/√2 24. In so\nfar as one can speak of the state of the young system after this\ninteraction, it is in the mixture of 50%\n 2 and\n 50%\n 2,\nnot in the superposition\n 1/√2 2 +\n 1/√2 2. So\nDeutsch does need his recourse to mixed states.", "\n\nThis clarification of why Deutsch needs his mixtures does however\nindicate a serious worry about the simplifications that are part of\nDeutsch's account. After the interaction the old and young system will\n(typically) be in an entangled state. Although for purposes of a\nmeasurement on one of the two systems one can say that this system is\nin a mixed state, one can not represent the full state of the two\nsystems by specifying the mixed state of each separate part, as there\nare correlations between observables of the two systems that are not\nrepresented by these two mixed states, but are represented in the\njoint entangled state. But if there really is an entangled state of\nthe old and young systems directly after the interaction, how is one\nto represent the subsequent development of this entangled state? Will\nthe state of the younger system remain entangled with the state of the\nolder system as the younger system time travels and the older system\nmoves on into the future? On what space-like surfaces are we to\nimagine this total entangled state to be? At this point it becomes\nclear that there is no obvious and simple way to extend elementary\nnon-relativistic quantum mechanics to space-times with closed\ntime-like curves. There have been more sophisticated approaches than\nDeutsch's to time travel, using technical machinery from quantum field\ntheory and differentiable manifolds (see e.g., Friedman et al 1991,\nEarman, Smeenk, and Wüthrich 2003 in the Other Internet Resources,\nand references therein). But out of such approaches no results\nanywhere near as clear and interesting as Deutsch's have been\nforthcoming.", "\n\nHow does Deutsch avoid these complications? Deutsch assumes a mixed\nstate S3 of the older system prior to the\ninteraction with the younger system. He lets it interact with an\narbitrary pure state S1 younger system. After this\ninteraction there is an entangled state S′ of the two\nsystems. Deutsch computes the mixed state S2 of the\nyounger system which is implied by this entangled state\nS′. His demand for consistency then is just that this\nmixed state S2 develops into the mixed state\nS3. Now it is not at all clear that this is a\nlegitimate way to simplify the problem of time travel in quantum\nmechanics. But even if we grant him this simplification there is a\nproblem: how are we to understand these mixtures?", "\n\nIf we take an ignorance interpretation of mixtures we run into\ntrouble. For suppose that we assume that in each individual case each\nolder system is either in state\n 3 or in state\n 3 prior\nto the interaction. Then we regain our paradox. Deutsch instead\nrecommends the following, many worlds, picture of mixtures. Suppose we\nstart with state\n 1 in all worlds. In some of the many worlds\nthe older system will be in the\n 3 state, let us call them\nA-worlds, and in some worlds, B-worlds, it will be in\nthe\n 3 state. Thus in A-worlds after\ninteraction we will have state\n 2 , and in B-worlds we will have\nstate\n 2. During time travel the\n 2 state\nwill remain the same, i.e., turn into state\n 3, but\nthe systems in question will travel from A-worlds to\nB-worlds. Similarly the\n 2 states will travel from the\nB-worlds to the A-worlds, thus preserving\nconsistency.", "\n\nNow whatever one thinks of the merits of many worlds\ninterpretations, and of this understanding of it applied to mixtures,\nin the end one does not obtain genuine time travel in Deutsch's\naccount. The systems in question travel from one time in one world to\nanother time in another world, but no system travels to an earlier time\nin the same world. (This is so at least in the normal sense of the word\n‘world,’ the sense that one means when, for instance, one\nsays “there was, and will be, only one Elvis Presley in this\nworld.”) Thus, even if it were a reasonable view, it is not quite as\ninteresting as it may have initially seemed." ], "section_title": "9. Quantum Mechanics to the Rescue?", "subsections": [] }, { "main_content": [ "\n\nWhat remains of the killing-your-earlier-self paradox in general\nrelativistic time travel worlds is the fact that in some cases the\nstates on edgeless spacelike surfaces are\n‘overconstrained’, so that one has less than the usual\nfreedom in specifying conditions on such a surface, given the\ntime-travel structure, and in some cases such states are\n‘underconstrained’, so that states on edgeless space-like\nsurfaces do not determine what happens elsewhere in the way that they\nusually do, given the time travel structure. There can also be mixtures\nof those two types of cases. The extent to which states are\noverconstrained and/or underconstrained in realistic models is as yet\nunclear, though it would be very surprising if neither obtained. The\nextant literature has primarily focused on the problem of\noverconstraint, since that, often, either is regarded as a metaphysical\nobstacle to the possibility time travel, or as an epistemological\nobstacle to the plausibility of time travel in our world. While it is\ntrue that our world would be quite different from the way we normally\nthink it is if states were overconstrained, underconstraint seems at\nleast as bizarre as overconstraint. Nonetheless, neither directly rules\nout the possibility of time travel.", "\n\nIf time travel entailed contradictions then the issue would be\nsettled. And indeed, most of the stories employing time travel in\npopular culture are logically incoherent: one cannot “change”\nthe past to be different from what it was, since the past (like the\npresent and the future) only occurs once. But if the only requirement\ndemanded is logical coherence, then it seems all too easy. A clever\nauthor can devise a coherent time-travel scenario in which everything\nhappens just once and in a consistent way. This is just too cheap:\nlogical coherence is a very weak condition, and many things we take to\nbe metaphysically impossible are logically coherent. For example, it\ninvolves no logical contradiction to suppose that water is not\nmolecular, but if both chemistry and Kripke are right it is a\nmetaphysical impossibility. We have been interested not in logical\npossibility but in physical possibility. But even so, our conditions\nhave been relatively weak: we have asked only whether time-travel is\nconsistent with the universal validity of certain fundamental physical\nlaws and with the notion that the physical state on a surface prior to\nthe time travel region be unconstrained. It is perfectly possible that\nthe physical laws obey this condition, but still that time travel is\nnot metaphysically possible because of the nature of time itself.\nConsider an analogy. Aristotle believed that water is homoiomerous and\ninfinitely divisible: any bit of water could be subdivided, in\nprinciple, into smaller bits of water. Aristotle's view contains no\nlogical contradiction. It was certainly consistent with Aristotle's\nconception of water that it be homoiomerous, so this was, for him, a\nconceptual possibility. But if chemistry is right, Aristotle was wrong\nboth about what water is like and what is possible for it. It can't be\ninfinitely divided, even though no logical or conceptual analysis would\nreveal that.", "\n\nSimilarly, even if all of our consistency conditions can be met, it\ndoes not follow that time travel is physically possible, only that some\nspecific physical considerations cannot rule it out. The only serious\nproof of the possibility of time travel would be a demonstration of its\nactuality. For if we agree that there is no actual time travel in our\nuniverse, the supposition that there might have been involves\npostulating a substantial difference from actuality, a difference\nunlike in kind from anything we could know if firsthand. It is unclear\nto us exactly what the content of possible would be if one were to\neither maintain or deny the possibility of time travel in these\ncircumstances, unless one merely meant that the possibility is not\nruled out by some delineated set of constraints. As the example of\nAristotle's theory of water shows, conceptual and logical\n“possibility” do not entail possibility in a full-blooded\nsense. What exactly such a full-blooded sense would be in case of time\ntravel, and whether one could have reason to believe it to obtain,\nremain to us obscure." ], "section_title": "10. Conclusions", "subsections": [] } ]

[ "Deutsch, D. 1991. “Quantum mechanics near closed timelike\ncurves,” Physical Review D, 44: 3197-3217.", "Deutsch, D. and Lockwood, M. 1994. “The quantum physics of\ntime travel,” Scientific American, 270 (3):\n68-74.", "Earman, J. 1972. “Implications of causal propagation outsider\nthe null cone,” in Foundations of Space-Time Theory,\nMinnesota Studies in the Philosophy of Science, Vol VII,\nEarman, J., Glymour, C., and Stachel, J. (eds), pp. 94-108.\nMinneapolis: University of Minnesota Press.", "Earman, J. 1995. Bangs, Crunches, Whimpers and Shrieks:\nSingularities and Acausalities in Relativistic Spacetimes, New\nYork: Oxford University Press.", " Earman, J., Smeenk, C., and Wüthrich, C. 2009.“Do the\nlaws of physics forbid the operation of a time\nmachine?,” Synthese, 169 (1): 91-124.", "Echeverria, F., Klinkhammer, G., and Thorne, K. 1991.\n“Billiard ball in wormhole spacetimes with closed timelike\ncurves: classical theory,” Physical Review D, 44 (4):\n1077-1099.", "Friedman, J. et al. 1990. “Cauchy problem in spacetimes with\nclosed timelike lines,” Physical Review D, 42:\n1915-1930.", "Friedman, J. and Morris, M. 1991. “The Cauchy problem for the\nscalar wave equation is well defined on a class of spacetimes with\nclosed timelike curves,” Physical Review letters, 66:\n401-404.", "Geroch, R. and Horowitz, G. 1979. “Global structures of\nspacetimes,” in General Relativity, an Einstein Centenary\nSurvey, S. Hawking and W. Israel (eds.), Cambridge: Cambridge\nUniversity Press.", "Gödel, K. 1949. “A remark about the relationship\nbetween relativity theory and idealistic philosophy,”\nin Albert Einstein: Philosopher-Scientist, P. Schilpp (ed.),\nLa Salle: Open Court, pp. 557-562.", "Hocking, J., and Young, G. 1961. Topology, New York: Dover\nPublications.", "Horwich, P. 1987. “Time travel,” in Asymmetries in\ntime, Cambridge, MA: MIT Press.", "Kutach, D. 2003. “Time travel and consistency\nconstraint”, Philosophy of Science, 70: 1098-1113.", "Malament, D. 1985a. “’Time travel’ in the\nGödel universe,” PSA 1984, 2: 91-100, P. Asquith\nand P. Kitcher (eds.), East Lansing, MI: Philosophy of Science\nAssociation.", "Malament, D. 1985b. “Minimal acceleration requirements for\n‘time travel’ in Gödel spacetime,” Journal\nof Mathematical Physics, 26: 774-777.", "Maudlin, T. 1990. “Time Travel and topology,”\nPSA 1990, 1: 303-315, East Lansing, MI: Philosophy of Science\nAssociation.", "Novikov, I. 1992. “Time machine and self-consistent evolution\nin problems with self-interaction,” Physical Review D,\n45: 1989-1994.", "Thorne, K. 1994. Black Holes and Time Warps, Einstein's\nOutrageous Legacy, London and New York: W.W. Norton.", "Wheeler, J. and Feynman, R. 1949. “Classical electrodynamics\nin terms of direct interparticle action,” Reviews of Modern\nPhysics, 21: 425-434.", "Yurtsever, U. 1990. “Test fields on compact\nspace-times,” Journal of Mathematical Physics, 31:\n3064-3078." ]

[ { "href": "../determinism-causal/", "text": "determinism: causal" }, { "href": "../time-machine/", "text": "time machines" }, { "href": "../time-travel/", "text": "time travel" } ]

[ "An axiomatic theory of truth is a deductive theory of truth as a\nprimitive undefined predicate. Because of the liar and other\nparadoxes, the axioms and rules have to be chosen carefully in order\nto avoid inconsistency. Many axiom systems for the truth predicate\nhave been discussed in the literature and their respective properties\nbeen analysed. Several philosophers, including many deflationists, have endorsed axiomatic theories of truth in their\naccounts of truth. The logical properties of the formal theories are\nrelevant to various philosophical questions, such as questions about\nthe ontological status of properties, Gödel’s theorems,\ntruth-theoretic deflationism, eliminability of semantic notions and\nthe theory of meaning." ]

[ { "content_title": "1. Motivations", "sub_toc": [ "1.1 Truth, properties and sets", "1.2 Truth and reflection", "1.3 Truth-theoretic deflationism" ] }, { "content_title": "2. The base theory", "sub_toc": [ "2.1 The choice of the base theory", "2.2 Notational conventions" ] }, { "content_title": "3. Typed theories of truth", "sub_toc": [ "3.1 Definable truth predicates", "3.2 The \\(T\\)-sentences", "3.3 Compositional truth", "3.4 Hierarchical theories" ] }, { "content_title": "4. Type-free truth", "sub_toc": [ "4.1 Type-free \\(T\\)-sentences", "4.2 Compositionality", "4.3 The Friedman–Sheard theory and revision semantics", "4.4 The Kripke–Feferman theory", "4.5 Capturing the minimal fixed point", "4.6 Axiomatisations of Kripke’s theory with supervaluations" ] }, { "content_title": "5. Non-classical approaches to self-reference", "sub_toc": [ "5.1 The truth predicate in intuitionistic logic", "5.2 Axiomatising Kripke’s theory", "5.3 Adding a conditional" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "There have been many attempts to define truth in terms of\n correspondence,\n coherence or other notions. \nHowever, it is far from clear that truth is a definable notion. In\nformal settings satisfying certain natural conditions, Tarski’s\ntheorem on the undefinability of the truth predicate shows that a\ndefinition of a truth predicate requires resources that go beyond\nthose of the formal language for which truth is going to be defined.\nIn these cases definitional approaches to truth have to fail. By contrast,\nthe axiomatic approach does not presuppose that truth can be\ndefined. Instead, a formal language is expanded by a new primitive\npredicate for truth or satisfaction, and axioms for that predicate are then laid\ndown. This approach by itself does not preclude the possibility that the truth predicate\nis definable, although in many cases it can be shown that the truth\npredicate is not definable.", "In semantic theories of truth (e.g., Tarski 1935, Kripke 1975), in\ncontrast, a truth predicate is defined for a language, the so-called\nobject language. This definition is carried out in a metalanguage or\nmetatheory, which is typically taken to include set theory or at least\nanother strong theory or expressively rich interpreted\nlanguage. Tarski’s theorem on the undefinability of the truth\npredicate shows that, given certain general assumptions, the resources\nof the metalanguage or metatheory must go beyond the resources of the\nobject-language. So semantic approaches usually necessitate the use of\na metalanguage that is more powerful than the object-language for\nwhich it provides a semantics.", "As with other formal deductive systems, axiomatic theories of truth can be\npresented within very weak logical frameworks. These frameworks require very\nfew resources, and in particular, avoid the need for a strong metalanguage and\nmetatheory. ", "Formal work on axiomatic theories of truth has helped to shed some light on\nsemantic theories of truth. For instance, it has yielded information on what is\nrequired of a metalanguage that is sufficient for defining a truth predicate.\nSemantic theories of truth, in turn, provide one with the theoretical tools\nneeded for investigating models of axiomatic theories of truth and with\nmotivations for certain axiomatic theories. Thus axiomatic and semantic\napproaches to truth are intertwined.", "This entry outlines the most popular axiomatic theories of truth and\nmentions some of the formal results that have been obtained concerning them. We\ngive only hints as to their philosophical applications." ], "section_title": "1. Motivations", "subsections": [ { "content": [ "Theories of truth and predication are closely related to theories of\n properties and\n property attribution. To say that an open formula \\(\\phi(x)\\)\nis true of an individual \\(a\\) seems equivalent (in some sense)\nto the claim that \\(a\\) has the property of\nbeing such that \\(\\phi\\) (this property is signified by the open formula).\nFor example, one might say that ‘\\(x\\) is a poor philosopher’ is true\nof Tom instead of saying that Tom has the property of being a poor philosopher.\nQuantification over definable properties can then be mimicked in a language\nwith a truth predicate by quantifying over formulas. Instead of saying, for\ninstance, that \\(a\\) and \\(b\\) have exactly the same properties, one\nsays that exactly the same formulas are true of \\(a\\) and \\(b\\). The\nreduction of properties to truth works also to some extent for sets of\nindividuals.", "There are also reductions in the other direction: Tarski (1935) has\nshown that certain second-order existence assumptions (e.g.,\ncomprehension axioms) may be utilized to define truth (see the entry\non Tarski’s definition of\ntruth). The mathematical analysis of axiomatic theories of truth\nand second-order systems has exhibited many equivalences between these\nsecond-order existence assumptions and truth-theoretic\nassumptions.", "These results show exactly what is required for defining a truth predicate\nthat satisfies certain axioms, thereby sharpening Tarski’s insights into\ndefinability of truth. In particular, proof-theoretic equivalences described in\nSection 3.3 below make explicit to what extent a\nmetalanguage (or rather metatheory) has to be richer than the object language\nin order to be able to define a truth predicate.", "The equivalence between second-order theories and truth theories also has\nbearing on traditional metaphysical topics. The reductions of second-order\ntheories (i.e., theories of properties or sets) to axiomatic theories of truth\nmay be conceived as forms of reductive nominalism, for they replace existence\nassumptions for sets or properties (e.g., comprehension axioms) by\nontologically innocuous assumptions, in the present case by assumptions on the\nbehaviour of the truth predicate." ], "subsection_title": "1.1 Truth, properties and sets" }, { "content": [ "According to Gödel’s incompleteness theorems,\n the statement that Peano Arithmetic (PA)\nis consistent, in its guise as a number-theoretic statement (given the\ntechnique of Gödel numbering), cannot be derived in PA\nitself. But PA can be strengthened by adding this consistency\nstatement or by stronger axioms. In particular, axioms partially\nexpressing the soundness of PA can be added. These are known as\nreflection principles. An example of a reflection principle for PA\nwould be the set of\nsentences \\(Bew_{PA}(\\ulcorner \\phi \\urcorner)\n\\rightarrow \\phi\\) where \\(\\phi\\) is a formula of the language of\narithmetic, \\(\\ulcorner \\phi \\urcorner\\) a name for \\(\\phi\\)\nand \\(Bew_{PA}(x)\\) is the standard provability\npredicate for PA (‘\\(Bew\\)’ was introduced by\nGödel and is short for the German word\n‘beweisbar’, that is,\n‘provable’). ", "The process of adding reflection principles can be iterated: one\ncan add, for example, a reflection principle R for PA to PA; this\nresults in a new theory PA+R. Then one adds the reflection principle\nfor the system PA+R to the theory PA+R. This process can be continued\ninto the transfinite (see Feferman 1962 and Franzén 2004).", "The reflection principles express—at least\npartially—the soundness of the system. The most natural and full\nexpression of the soundness of a system involves the truth predicate\nand is known as the Global Reflection Principle (see Kreisel and\nLévy 1968). The Global Reflection Principle for a formal system\nS states that all sentences provable in S are true:", "\\(Bew_{S} (x)\\) expresses here provability of\nsentences in the system S (we omit discussion here of the problems of\ndefining \\(Bew_{S} (x))\\). The truth predicate\nhas to satisfy certain principles; otherwise the global reflection\nprinciple would be vacuous. Thus not only the global reflection\nprinciple has to be added, but also axioms for truth. If a natural\ntheory of truth like T(PA) below is added, however, it is no longer\nnecessary to postulate the global reflection principle explicitly, as\ntheories like T(PA) prove already the global reflection principle for\nPA. One may therefore view truth theories as reflection principles as\nthey prove soundness statements and add the resources to express these\nstatements.", "Thus instead of iterating reflection principles that are formulated\nentirely in the language of arithmetic, one can add by iteration new\ntruth predicates and correspondingly new axioms for the new truth\npredicates. Thereby one might hope to make explicit all the\nassumptions that are implicit in the acceptance of a theory like\nPA. The resulting theory is called the reflective closure of the\ninitial theory. Feferman (1991) has proposed the use of a single truth\npredicate and a single theory (KF), rather than a hierarchy of\npredicates and theories, in order to explicate the reflective closure\nof PA and other theories. (KF is discussed further\nin Section 4.4 below.)", "The relation of truth theories and (iterated) reflection principles\nalso became prominent in the discussion of truth-theoretic\ndeflationism (see Tennant 2002 and the follow-up discussion)." ], "subsection_title": "1.2 Truth and reflection" }, { "content": [ "Many proponents of\n deflationist theories of truth\n have chosen to treat truth as a primitive notion\nand to axiomatize it, often using some version of\nthe \\(T\\)-sentences as axioms. \\(T\\)-sentences are\nequivalences of the form\n\\(T\\ulcorner \\phi \\urcorner \\leftrightarrow \\phi\\), where \\(T\\) is the truth predicate, \\(\\phi\\) is a sentence\nand \\(\\ulcorner \\phi \\urcorner\\) is a name for the\nsentence \\(\\phi\\). (More refined axioms have also been discussed by\ndeflationists.) At first glance at least, the axiomatic approach seems\nmuch less ‘deflationary’ than those more traditional\ntheories which rely on a definition of truth in terms of\ncorrespondence or the like. If truth can be explicitly defined, it can\nbe eliminated, whereas an axiomatized notion of truth may and often\ndoes come with commitments that go beyond that of the base\ntheory. ", "If truth does not have any explanatory force, as some deflationists\nclaim, the axioms for truth should not allow us to prove any new\ntheorems that do not involve the truth predicate. Accordingly, Horsten (1995), Shapiro (1998) and Ketland (1999) have suggested that\na deflationary axiomatization of truth should be at\nleast conservative. The new axioms for truth are conservative\nif they do not imply any additional sentences (free of occurrences of\nthe truth-predicate) that aren’t already provable without the\ntruth axioms. Thus a non-conservative theory of truth adds new\nnon-semantic content to a theory and has genuine explanatory power,\ncontrary to many deflationist views. Certain natural theories of\ntruth, however, fail to be conservative (see Section\n3.3 below, Field 1999 and Shapiro 2002 for further\ndiscussion).", "According to many deflationists, truth serves merely the purpose of\nexpressing infinite conjunctions. It is plain that not all\ninfinite conjunctions can be expressed because there are uncountably\nmany (non-equivalent) infinite conjunctions over a countable\nlanguage. Since the language with an added truth predicate has only\ncountably many formulas, not every infinite conjunction can be\nexpressed by a different finite formula. The formal work on axiomatic\ntheories of truth has helped to specify exactly which infinite\nconjunctions can be expressed with a truth predicate. Feferman (1991)\nprovides a proof-theoretic analysis of a fairly strong system. (Again,\nthis will be explained in the discussion about KF\nin Section 4.4 below.)" ], "subsection_title": "1.3 Truth-theoretic deflationism" } ] }, { "main_content": [], "section_title": "2. The base theory", "subsections": [ { "content": [ "In most axiomatic theories, truth is conceived as a predicate of\nobjects. There is an extensive philosophical discussion on the\ncategory of objects to which truth applies: propositions conceived as\nobjects that are independent of any language, types and tokens of\nsentences and utterances, thoughts, and many other objects have been\nproposed. Since the structure of sentences considered as types is\nrelatively clear, sentence types have often been used as the objects\nthat can be true. In many cases there is no need to make very specific\nmetaphysical commitments, because only certain modest assumptions on\nthe structure of these objects are required, independently from\nwhether they are finally taken to be syntactic objects, propositions\nor still something else. The theory that describes the properties of\nthe objects to which truth can be attributed is called the base\ntheory. The formulation of the base theory does not involve the\ntruth predicate or any specific truth-theoretic assumptions. The base\ntheory could describe the structure of sentences, propositions and the\nlike, so that notions like the negation of such an object can then be\nused in the formulation of the truth-theoretic axioms.", "In many axiomatic truth theories, truth is taken as a predicate\napplying to the Gödel numbers of sentences. Peano arithmetic has\nproved to be a versatile theory of objects to which truth is applied,\nmainly because adding truth-theoretic axioms to Peano arithmetic\nyields interesting systems and because Peano arithmetic is equivalent\nto many straightforward theories of syntax and even theories of\npropositions. However, other base theories have been considered as\nwell, including formal syntax theories and set theories.", "Of course, we can also investigate theories which result by adding\nthe truth-theoretic axioms to much stronger theories like set\ntheory. Usually there is no chance of proving the consistency of set\ntheory plus further truth-theoretic axioms because the consistency of\nset theory itself cannot be established without assumptions\ntranscending set theory. In many cases not even relative consistency\nproofs are feasible. However, if adding certain truth-theoretic axioms\nto PA yields a consistent theory, it seems at least plausible that\nadding analogous axioms to set theory will not lead to an\ninconsistency. Therefore, the hope is that research on theories of\ntruth over PA will give an some indication of what will happen when we\nextend stronger theories with axioms for the truth predicate. However, Fujimoto (2012)\n has shown that some axiomatic truth theories over set theory differ from their counterparts over Peano arithmetic in some aspects." ], "subsection_title": "2.1 The choice of the base theory" }, { "content": [ "For the sake of definiteness we assume that the language of\narithmetic has exactly \\(\\neg , \\wedge\\) and \\(\\vee\\) as connectives and\n\\(\\forall\\) and \\(\\exists\\) as quantifiers. It has as individual constants\nonly the symbol 0 for zero; its only function symbol is the unary\nsuccessor symbol \\(S\\); addition and multiplication are expressed\nby predicate symbols. Therefore the only closed terms of the language\nof arithmetic are the numerals\n\\(0, S\\)(0), \\(S(S\\)(0)), \\(S(S(S\\)(0))),\n….", "\nThe language of arithmetic does not contain the unary predicate\nsymbol \\(T\\), so\nlet \\(\\mathcal{L}_T\\) be the\nlanguage of arithmetic augmented by the new unary predicate\nsymbol \\(T\\) for truth. If \\(\\phi\\) is a sentence\nof \\(\\mathcal{L}_T,\n\\ulcorner \\phi \\urcorner\\) is a name for \\(\\phi\\) in the\nlanguage \\(\\mathcal{L}_T\\);\nformally speaking, it is the numeral of\nthe Gödel number of\n\\(\\phi\\). In general, Greek letters like \\(\\phi\\) and \\(\\psi\\) are variables of\nthe metalanguage, that is, the language used for talking about\ntheories of truth and the language in which this entry is written\n(i.e., English enriched by some symbols). \\(\\phi\\) and \\(\\psi\\) range over\nformulas of the formal\nlanguage \\(\\mathcal{L}_T\\).", "In what follows, we use small, upper case italic letters\nlike \\({\\scriptsize A}, {\\scriptsize B},\\ldots\\) as\nvariables in \\(\\mathcal{L}_T\\)\nranging over sentences (or their Gödel numbers, to be\nprecise). Thus\n\\(\\forall{\\scriptsize A}(\\ldots{\\scriptsize A}\\ldots)\\)\nstands for\n\\(\\forall x(Sent_T (x)\n\\rightarrow \\ldots x\\ldots)\\),\nwhere \\(Sent_T (x)\\) expresses in the\nlanguage of arithmetic that \\(x\\) is a sentence of the language\nof arithmetic extended by the predicate symbol \\(T\\). The\nsyntactical operations of forming a conjunction of two sentences and\nsimilar operations can be expressed in the language of\narithmetic. Since the language of arithmetic does not contain any\nfunction symbol apart from the symbol for successor, these operations\nmust be expressed by sutiable predicate expressions. Thus one can say\nin the language \\(\\mathcal{L}_T\\)\nthat a negation of a sentence\nof \\(\\mathcal{L}_T\\) is true if and\nonly if the sentence itself is not true. We would write this as ", "The square brackets indicate that the operation of forming the negation of\n\\({\\scriptsize A}\\) is expressed in the language of arithmetic. Since the\nlanguage of arithmetic does not contain a function symbol representing the\nfunction that sends sentences to their negations, appropriate paraphrases\ninvolving predicates must be given. ", "Thus, for instance, the expression", "is a single sentence of the language \\(\\mathcal{L}_T\\) saying that a conjunction of\nsentences of \\(\\mathcal{L}_T\\) is true if\nand only if both sentences are true. In contrast, ", "is only a schema. That is, it stands for the set of all sentences\nthat are obtained from the above expression by substituting sentences\nof \\(\\mathcal{L}_T\\) for the Greek\nletters \\(\\phi\\) and \\(\\psi\\). The single sentence\n\\(\\forall{\\scriptsize A}\\forall{\\scriptsize B}(T[{\\scriptsize A} \\wedge{\\scriptsize B}] \\leftrightarrow \n(T{\\scriptsize A} \\wedge T{\\scriptsize B}))\\) implies all sentences\nwhich are instances of the schema, but the instances of the schema do\nnot imply the single universally quantified sentence. In general, the\nquantified versions are stronger than the corresponding schemata. " ], "subsection_title": "2.2 Notational conventions" } ] }, { "main_content": [ "In typed theories of truth, only the truth of sentences not\ncontaining the same truth predicate is provable, thus avoiding the\nparadoxes by observing Tarski’s distinction between object and\nmetalanguage." ], "section_title": "3. Typed theories of truth", "subsections": [ { "content": [ "Certain truth predicates can be defined within the language of\narithmetic. Predicates suitable as truth predicates for sublanguages\nof the language of arithmetic can be defined within the language of\narithmetic, as long as the quantificational complexity of the formulas\nin the sublanguage is restricted. In particular, there is a\nformula \\(Tr_0 (x)\\) that expresses\nthat \\(x\\) is a true atomic sentence of the language of\narithmetic, that is, a sentence of the form \\(n=k\\),\nwhere \\(k\\) and \\(n\\) are identical numerals. For further\ninformation on partial truth predicates see, for instance,\nHájek and Pudlak (1993), Kaye (1991) and Takeuti (1987).", "The definable truth predicates are truly redundant, because they\nare expressible in PA; therefore there is no need to introduce them\naxiomatically. All truth predicates in the following are not definable\nin the language of arithmetic, and therefore not redundant at least in\nthe sense that they are not definable. " ], "subsection_title": "3.1 Definable truth predicates" }, { "content": [ "The typed \\(T\\)-sentences are all equivalences of the\nform \\(T\\ulcorner \\phi \\urcorner \\leftrightarrow \\phi\\), where \\(\\phi\\) is a sentence not containing the truth\npredicate. Tarski (1935) called any theory proving these equivalences\n‘materially adequate’. Tarski (1935) criticised an\naxiomatization of truth relying only on the \\(T\\)-sentences, not\nbecause he aimed at a definition rather than an axiomatization of\ntruth, but because such a theory seemed too weak. Thus although the\ntheory is materially adequate, Tarski thought that\nthe \\(T\\)-sentences are deductively too weak. He observed, in\nparticular, that the \\(T\\)-sentences do not prove the principle\nof completeness, that is, the sentence\n\\(\\forall{\\scriptsize A}(T{\\scriptsize A}\\vee T[\\neg{\\scriptsize A}\\)])\nwhere the quantifier \\(\\forall{\\scriptsize A}\\) is restricted\nto sentences not containing T.", "Theories of truth based on the \\(T\\)-sentences, and their\nformal properties, have also recently been a focus of interest in the\ncontext of so-called deflationary theories of\ntruth. The \\(T\\)-sentences \\(T\\ulcorner \\phi \\urcorner \\leftrightarrow \\phi\\) (where \\(\\phi\\) does not contain \\(T)\\) are not\nconservative over first-order logic with identity, that is, they prove\na sentence not containing \\(T\\) that is not logically valid. For\nthe \\(T\\)-sentences prove that the sentences \\(0=0\\) and \\(\\neg 0=0\\) are\ndifferent and that therefore at least two objects exist. In other\nwords, the \\(T\\)-sentences are not conservative over the empty\nbase theory. If the \\(T\\)-sentences are added to PA, the\nresulting theory is conservative over PA. This means that the theory\ndoes not prove \\(T\\)-free sentences that are not already provable\nin PA. This result even holds if in addition to\nthe \\(T\\)-sentences also all induction axioms containing the\ntruth predicate are added. This may be shown by appealing to the\nCompactness Theorem.", "In the form outlined above, T-sentences express the equivalence between \\(T\\ulcorner \\phi \\urcorner\\) and \\(\\phi\\) only when \\(\\phi\\) is a sentence.\nIn order to capture the equivalence for properties \\((x\\) has property P iff ‘P’ is true of \\(x)\\) one must generalise the T-sentences. The result are usually referred to as the uniform T-senences and are formalised by the equivalences \n\\(\\forall x(T\\ulcorner \\phi(\\underline{x})\\urcorner \\leftrightarrow \\phi(x))\\) for each open formula \\(\\phi(v)\\) with at most \\(v\\) free in \\(\\phi\\).\nUnderlining the variable indicates it is bound from the outside.\nMore precisely, \\(\\ulcorner \\phi(\\underline{x})\\urcorner\\) stands for the result of replacing the variable \\(v\\)\nin \\(\\ulcorner \\phi(v)\\urcorner\\) by the numeral\nof \\(x\\)." ], "subsection_title": "3.2 The \\(T\\)-sentences" }, { "content": [ "As was observed already by Tarski (1935), certain desirable\ngeneralizations don’t follow from the T-sentences. For instance,\ntogether with reasonable base theories they don’t imply that a\nconjunction is true if both conjuncts are true.", "In order to obtain systems that also prove universally quantified\ntruth-theoretic principles, one can turn the inductive clauses of\nTarski’s definition of truth into axioms. In the following\naxioms, \\(AtomSent_{PA}(\\ulcorner{\\scriptsize A}\\urcorner)\\)\nexpresses that \\({\\scriptsize A}\\) is an atomic sentence of the\nlanguage of\narithmetic, \\(Sent_{PA}(\\ulcorner{\\scriptsize A}\\urcorner)\\)\nexpresses that \\({\\scriptsize A}\\) is a sentence of the language\nof arithmetic.", "Axiom 1 says that an atomic sentence of the language of Peano\narithmetic is true if and only if it is true according to the\narithmetical truth predicate for this language\n\\((Tr_0\\) was defined in Section\n3.1). Axioms 2–6 claim that truth commutes with all\nconnectives and quantifiers. Axiom 5 says that a universally\nquantified sentence of the language of arithmetic is true if and only\nif all its numerical instances are true.\n\n\\(Sent_{PA}(\\forall v{\\scriptsize A})\\)\nsays that \\({\\scriptsize A}(v)\\) is a formula with at\nmost \\(v\\) free (because\n\\(\\forall v{\\scriptsize A}(v)\\) is a\nsentence).", "If these axioms are to be formulated for a language like set theory\nthat lacks names for all objects, then axioms 5 and 6 require the use\nof a satisfaction relation rather than a unary truth predicate.", "Axioms in the style of 1–6 above played a central role\nin Donald Davidson‘s theory of meaning and\nin several deflationist approaches to truth. ", "The theory given by all axioms of PA and Axioms 1–6 but with\ninduction only for \\(T\\)-free formulae is conservative over PA,\nthat is, it doesn’t prove any new \\(T\\)-free theorems that\nnot already provable in PA. However, not all models of PA can be\nexpanded to models of PA + axioms 1–6. This follows from a\nresult due to Lachlan (1981). Kotlarski, Krajewski, and Lachlan (1981)\nproved the conservativeness very similar to PA + axioms 1–6 by\nmodel-theoretic means. Although several authors claimed that this result is also finitarily provable, no such\nproof was available until Enayat & Visser (2015) and Leigh\n(2015). Moreover, the theory given by PA + axioms 1–6 is relatively interpretable in PA. However, this result is sensitive to the choice of the base theory: it fails for finitely axiomatized theories (Heck 2015, Nicolai 2016). These proof-theoretic results have been used extensively in the discussion of truth-theoretic deflationism (see Cieśliński 2017).", "\nOf course PA + axioms 1–6 is restrictive insofar as it does not\ncontain the induction axioms in the language with the truth\npredicate.\n There are various labels for the system that is obtained by\nadding all induction axioms involving the truth predicate to the\nsystem PA + axioms 1–6: T(PA), CT, PA(S) or PA + ‘there is a\nfull inductive satisfaction class’. This theory is no longer\nconservative over its base theory PA. For instance one can formalise\nthe soundness theorem or global reflection principle for PA, that is,\nthe claim that all sentences provable in PA are true. The global\nreflection principle for PA in turn implies the consistency of PA,\nwhich is not provable in pure PA by\nGödel’s\n Second Incompleteness Theorem.\n Thus T(PA) is not conservative over PA. T(PA) is much\nstronger than the mere consistency statement for PA: T(PA) is\nequivalent to the second-order system ACA of arithmetical\ncomprehension (see Takeuti 1987 and Feferman 1991). More precisely,\nT(PA) and ACA are intertranslatable in a way that preserves all\narithmetical sentences. ACA is given by the axioms of PA with full\ninduction in the second-order language and the following comprehension\nprinciple:", "\nwhere \\(\\phi(x)\\) is any formula (in which \\(x\\) may or may\nnot be free) that does not contain any second-order quantifiers, but\npossibly free second-order variables. In T(PA), quantification\nover sets can be defined as quantification over formulas with\none free variable and membership as the truth of the formula as\napplied to a number. ", "\nAs the global reflection principle entails formal consistency, the conservativeness result for PA + axioms 1–6 implies that the global reflection principle for Peano arithmetic is not derivable in the typed compositional theory without expanding the induction axioms.\nIn fact, this theory proves neither the statement that all logical validities are true (global reflection for pure first-order logic) nor that all the Peano axioms of arithmetic are true.\nPerhaps surprisingly, of these two unprovable statements it is the former that is the stronger.\nThe latter can be added as an axiom and the theory remains conservative over PA (Enayat and Visser 2015, Leigh 2015).\nIn contrast, over PA + axioms 1–6, the global reflection principle for first-order logic is equivalent to global reflection for Peano arithmetic (Cieśliński 2010), and these two theories have the same arithmetic consequences as adding the axiom of induction for bounded \\((\\Delta_0)\\) formulas containing the truth predicate (Wcisło and Łełyk 2017).\n", "The transition from PA to T(PA) can be imagined as an act of reflection on the truth of \\(\\mathcal{L}\\)-sentences in PA. Similarly, the step from the typed \\(T\\)-sentences to the compositional axioms is also tied to a reflection principle, specifically the uniform reflection principle over the typed uniform \\(T\\)-sentences.\nThis is the collection of sentences \n\\(\\forall x\\, Bew_{S} (\\ulcorner \\phi(\\underline{x})\\urcorner) \\rightarrow \\phi(x) \\) where \\(\\phi\\) ranges over formulas in \\(\\mathcal{L}_T\\) with one free variable and S is the theory of the uniform typed T-sentences.\nUniform reflection exactly captures the difference between the two theories: the reflection principle is both derivable in T(PA) and suffices to derive the six compositional axioms (Halbach 2001).\nMoreover, the equivalence extends to iterations of uniform reflection, in that for any ordinal \\(\\alpha , 1 + \\alpha\\) iterations of uniform reflection over the typed \\(T\\)-sentences coincides with T(PA) extended by transfinite induction up to the ordinal \\(\\varepsilon_{\\alpha}\\), namely the \\(\\alpha\\)-th ordinal \\(\\kappa\\) with the property that \\(\\omega^{\\kappa} = \\kappa \\) (Leigh 2016).\n", "Much stronger fragments of second-order arithmetic can be\ninterpreted by type-free truth systems, that is, by theories of truth\nthat prove not only the truth of arithmetical sentences but also the\ntruth of sentences of the language \\(\\mathcal{L}_T\\) with the truth\npredicate; see Section 4 below." ], "subsection_title": "3.3 Compositional truth" }, { "content": [ "The above mentioned theories of truth can be iterated by\nintroducing indexed truth predicates. One adds to the language of PA\ntruth predicates indexed by ordinals (or ordinal notations) or one\nadds a binary truth predicate that applies to ordinal notations and\nsentences. In this respect the hierarchical approach does not fit the\nframework outlined in Section 2, because the language\ndoes not feature a single unary truth predicate applying to sentences\nbut rather many unary truth predicates or a single binary truth\npredicate (or even a single unary truth predicate applying to pairs of\nordinal notations and sentences).", "In such a language an axiomatization of Tarski’s hierarchy of truth\npredicates can be formulated. On the proof-theoretic side iterating\ntruth theories in the style of T(PA) corresponds to iterating\nelementary comprehension, that is, to iterating ACA. The system of\niterated truth theories corresponds to the system of ramified analysis\n(see Feferman 1991). ", "Visser (1989) has studied non-wellfounded\nhierarchies of languages and axiomatizations thereof. If one adds\nthe \\(T\\)-sentences \\(T_n\\ulcorner \\phi \\urcorner \\leftrightarrow \\phi\\) to the language of arithmetic where \\(\\phi\\) contains only\ntruth predicates \\(T_k\\)\nwith \\(k\\gt n\\) to PA, a theory is\nobtained that does not have a standard \\((\\omega\\)-)model." ], "subsection_title": "3.4 Hierarchical theories" } ] }, { "main_content": [ "The truth predicates in natural languages do not come with any\nouvert type restriction. Therefore typed theories of truth (axiomatic\nas well as semantic theories) have been thought to be inadequate for\nanalysing the truth predicate of natural language, although recently\nhierarchical theories have been advocated by Glanzberg (2015)\nand others. This is one motive for investigating type-free theories of\ntruth, that is, systems of truth that allow one to prove the truth of\nsentences involving the truth predicate. Some type-free theories of\ntruth have much higher expressive power than the typed theories that\nhave been surveyed in the previous section (at least as long as\nindexed truth predicates are avoided). Therefore type-free theories of\ntruth are much more powerful tools in the reduction of other theories\n(for instance, second-order ones). " ], "section_title": "4. Type-free truth", "subsections": [ { "content": [ "The set of\nall \\(T\\)-sentences \\(T\\ulcorner \\phi \\urcorner \\leftrightarrow \\phi\\), where \\(\\phi\\) is any sentence of the\nlanguage \\(\\mathcal{L}_T\\), that\nis, where \\(\\phi\\) may contain \\(T\\), is inconsistent with PA (or\nany theory that proves the diagonal lemma) because of\nthe Liar paradox. Therefore one might\ntry to drop from the set of all \\(T\\)-sentences only those that\nlead to an inconsistency. In other words, one may consider maximal\nconsistent sets of \\(T\\)-sentences. McGee (1992) showed that\nthere are uncountably many maximal sets of \\(T\\)-sentences that\nare consistent with PA. So the strategy does not lead to a single\ntheory. Even worse, given an arithmetical sentence (i.e., a sentence\nnot containing \\(T)\\) that can neither be proved nor disproved in\nPA, one can find a consistent \\(T\\)-sentence that decides this\nsentence (McGee 1992). This implies that many consistent sets\nof \\(T\\)-sentences prove false arithmetical statements. Thus the\nstrategy to drop just the \\(T\\)-sentences that yield an\ninconsistency is doomed. ", "A set of \\(T\\)-sentences that does not imply any false\narithmetical statement may be obtained by allowing only those \\(\\phi\\)\nin \\(T\\)-sentences \\(T\\ulcorner \\phi \\urcorner \\leftrightarrow \\phi\\) that contain \\(T\\) only positively, that is, in the\nscope of an even number of negation symbols. Like the typed theory\nin Section 3.2 this theory does not prove\ncertain generalizations but proves the same T-free sentences as the\nstrong type-free compositional Kripke-Feferman theory below (Halbach\n2009). Schindler (2015) obtained a deductively very strong truth theory based on stratified disquotational principles." ], "subsection_title": "4.1 Type-free \\(T\\)-sentences" }, { "content": [ "Besides the disquotational feature of truth, one would also like to\ncapture the compositional features of truth and generalize the axioms\nof typed compositional truth to the type-free case. To this end,\naxioms or rules concerning the truth of atomic sentences with the\ntruth predicate will have to be added and the restriction\nto \\(T\\)-free sentences in the compositional axioms will have to\nbe lifted. In order to treat truth like other predicates, one will add\nthe axiom\n\\(\\forall{\\scriptsize A}(T[T{\\scriptsize A}]\n\\leftrightarrow T{\\scriptsize A})\\) (where\n\\(\\forall{\\scriptsize A}\\) ranges over all sentences). If the\ntype restriction of the typed compositional axiom for\nnegation is removed, the axiom\n\\(\\forall{\\scriptsize A}(T[\\neg{\\scriptsize A}]\n\\leftrightarrow \\neg T{\\scriptsize A})\\) is obtained.", "However, the axioms\n\\(\\forall{\\scriptsize A}(T[T{\\scriptsize A}]\n\\leftrightarrow T{\\scriptsize A})\\) and\n\\(\\forall{\\scriptsize A}(T[\\neg{\\scriptsize A}]\n\\leftrightarrow \\neg T{\\scriptsize A})\\) are inconsistent over\nweak theories of syntax, so one of them has to be given up. If\n\\(\\forall{\\scriptsize A}(T[\\neg{\\scriptsize A}]\n\\leftrightarrow \\neg T{\\scriptsize A})\\) is retained, one will\nhave to find weaker axioms or rules for truth iteration, but truth\nremains a classical concept in the sense that\n\\(\\forall{\\scriptsize A}(T[\\neg{\\scriptsize A}]\n\\leftrightarrow \\neg T{\\scriptsize A})\\) implies the law of\nexcluded middle (for any sentence either the sentence itself or its\nnegation is true) and the law of noncontradiction (for no sentence the\nsentence itself and its negation are true). If, in contrast,\n\\(\\forall{\\scriptsize A}(T[\\neg{\\scriptsize A}]\n\\leftrightarrow \\neg T{\\scriptsize A})\\) is rejected and\n\\(\\forall{\\scriptsize A}(T[T{\\scriptsize A}]\n\\leftrightarrow T{\\scriptsize A})\\) retained, then it will\nbecome provable that either some sentences are true together with\ntheir negations or that for some sentences neither they nor their\nnegations are true, and thus systems of non-classical truth are\nobtained, although the systems themselves are still formulated in\nclassical logic. In the next two sections we overview the most\nprominent system of each kind." ], "subsection_title": "4.2 Compositionality" }, { "content": [ "The system FS, named after Friedman and Sheard (1987), retains the\nnegation axiom\n\\(\\forall{\\scriptsize A}(T[\\neg{\\scriptsize A}]\n\\leftrightarrow \\neg T{\\scriptsize A})\\). The further\ncompositional axioms are obtained by lifting the type restriction to\ntheir untyped counterparts:", "\n If \\(\\phi\\) is a theorem, one may infer\n \\(T\\ulcorner \\phi \\urcorner\\), and conversely, if\n \\(T\\ulcorner \\phi \\urcorner\\) is a theorem, one may\n infer \\(\\phi\\). ", "It follows from results due to McGee (1985) that FS is\n\\(\\omega\\)-inconsistent, that is, FS proves\n\\(\\exists x\\neg \\phi(x)\\), but proves also \\(\\phi\\)(0),\n\\(\\phi\\)(1), \\(\\phi\\)(2), … for some formula \\(\\phi(x)\\)\nof \\(\\mathcal{L}_T\\). The\narithmetical theorems of FS, however, are all correct.", "In FS one can define all finite levels of the classical Tarskian\nhierarchy, but FS isn’t strong enough to allow one to recover\nany of its transfinite levels. Indeed, Halbach (1994) determined its\nproof-theoretic strength to be precisely that of the theory of\nramified truth for all finite levels (i.e., finitely iterated T(PA);\nsee Section 3.4) or, equivalently, the theory of\nramified analysis for all finite levels. If either direction of the\nrule is dropped but the other kept, FS retains its proof-theoretic\nstrength (Sheard 2001).", "It is a virtue of FS that it is thoroughly classical: It is\nformulated in classical logic; if a sentence is provably true in FS,\nthen the sentence itself is provable in FS; and conversely if a\nsentence is provable, then it is also provably true. Its drawback is\nits \\(\\omega\\)-inconsistency. FS may be seen as an axiomatization of\nrule-of-revision semantics for all finite levels (see the entry on\nthe revision theory of truth)." ], "subsection_title": "4.3 The Friedman–Sheard theory and revision semantics" }, { "content": [ "The Kripke–Feferman theory retains the truth iteration axiom\n\\(\\forall{\\scriptsize A}(T[T{\\scriptsize A}]\n\\leftrightarrow T{\\scriptsize A})\\), but the notion of truth\naxiomatized is no longer classical because the negation axiom\n\\(\\forall{\\scriptsize A}(T[\\neg{\\scriptsize A}]\n\\leftrightarrow \\neg T{\\scriptsize A})\\) is dropped. ", "The semantical construction captured by this theory is a\ngeneralization of the Tarskian typed inductive definition of truth\ncaptured by T(PA). In the generalized definition one starts with the\ntrue atomic sentence of the arithmetical language and then one\ndeclares true the complex sentences depending on whether its\ncomponents are true or not. For instance, as in the typed case, if\n\\(\\phi\\) and \\(\\psi\\) are true, their conjunction \\(\\phi \\wedge \\psi\\) will be\ntrue as well. In the case of the quantified sentences their truth\nvalue is determined by the truth values of their instances (one could\nrender the quantifier clauses purely compositional by using a\nsatisfaction predicate); for instance, a universally quantified\nsentence will be declared true if and only if all its instances are\ntrue. One can now extend this inductive definition of truth to the\nlanguage \\(\\mathcal{L}_T\\) by\ndeclaring a sentence of the\nform \\(T\\ulcorner \\phi \\urcorner\\) true\nif \\(\\phi\\) is already true. Moreover one will declare\n\\(\\neg T\\ulcorner \\phi \\urcorner\\) true if\n\\(\\neg \\phi\\) is true. By making this idea precise, one obtains a variant\nof Kripke’s (1975) theory of truth with the so called Strong Kleene\nvaluation scheme (see the entry\non many-valued logic). If\naxiomatized it leads to the following system, which is known as KF\n(‘Kripke–Feferman’), of which several variants\nappear in the literature:", "\nApart from the truth-theoretic axioms, KF comprises all axioms of PA\nand all induction axioms involving the truth predicate. The system is\ncredited to Feferman on the basis of two lectures for the Association\nof Symbolic Logic, one in 1979 and the second in 1983, as well as in\nsubsequent manuscripts. Feferman published his version of the system\nunder the label Ref(PA) (‘weak reflective closure of PA’)\nonly in 1991, after several other versions of KF had already appeared\nin print (e.g., Reinhardt 1986, Cantini 1989, who both refer to this\nunpublished work by Feferman).", "KF itself is formulated in classical logic, but it describes a\nnon-classical notion of truth. For instance, one can\nprove \\(T\\ulcorner L\\urcorner \\leftrightarrow T\\ulcorner\\neg L\\urcorner\\)\nif \\(L\\) is the Liar sentence. Thus KF proves that either both\nthe liar sentence and its negation are true or that neither is\ntrue. So either is the notion of truth paraconsistent (a sentence is\ntrue together with its negation) or paracomplete (neither is\ntrue). Some authors have augmented KF with an axiom ruling out\ntruth-value gluts, which makes KF sound for Kripke’s model\nconstruction, because Kripke had ruled out truth-value gluts.", "Feferman (1991) showed that KF is proof-theoretically equivalent to\nthe theory of ramified analysis through all levels below\n\\(\\varepsilon_0\\), the limit of the sequence \\(\\omega ,\n\\omega^{\\omega},\n\\omega^{\\omega^{ \\omega} },\\ldots\\), or a theory of\nramified truth through the same ordinals. This result shows that in KF\nexactly \\(\\varepsilon_0\\) many levels of the classical Tarskian\nhierarchy in its axiomatized form can be recovered. Thus KF is far\nstronger than FS, let alone T(PA). Feferman (1991) devised also a\nstrengthening of KF that is as strong as full predicative analysis,\nthat is ramified analysis or truth up to the ordinal\n\\(\\Gamma_0\\).", "Just as with the typed truth predicate, the theory KF (more precisely, a common variant of it) can be obtained via an act of reflection on a system of untyped \\(T\\)-sentences. The system of \\(T\\)-sentences in question is the extension of the uniform positive untyped \\(T\\)-sentences by a primitive falsity predicate, that is, the theory features two unary predicates \\(T\\) and \\(F\\) and axioms", "\nfor every formula \\(\\phi(v)\\) positive in both \\(T\\) and \\(F\\), where \\(\\phi '\\) represents the De Morgan dual of \\(\\phi\\) (exchanging \\(T\\) for \\(F\\) and vice versa).\nFrom an application of uniform reflection over this disquotational theory, the truth axioms for the corresponding two predicate version of KF are derivable (Horsten and Leigh, 2016). The converse also holds, as does the generalisation to finite and transfinite iterations of reflection (Leigh, 2017).\n" ], "subsection_title": "4.4 The Kripke–Feferman theory" }, { "content": [ "As remarked above, if KF\nproves \\(T\\ulcorner \\phi \\urcorner\\) for some\nsentence \\(\\phi\\) then \\(\\phi\\) holds in all Kripke fixed point models. In\nparticular, there are \\(2^{\\aleph_0}\\) fixed\npoints that form a model of the internal theory of KF. Thus from the\nperspective of KF, the least fixed point (from which Kripke’s theory\nis defined) is not singled out. Burgess (2014) provides an\nexpansion of KF, named \\(\\mu\\)KF, that attempts to capture the minimal\nKripkean fixed point. KF is expanded by additional axioms that express\nthat the internal theory of KF is the smallest class closed under the\ndefining axioms for Kripkean truth. This can be formulated as a single\naxiom schema that states, for each open formula \\(\\phi\\), ", "\n If \\(\\phi\\) satisfies the same axioms of KF as the predicate \\(T\\)\n then \\(\\phi\\) holds of every true sentence.\n", "\nFrom a proof-theoretic perspective \\(\\mu\\)KF is significantly stronger\nthan KF. The single axiom schema expressing the minimality of the\ntruth predicate allows one to embed into \\(\\mu\\)KF the system\nID\\(_1\\) of one arithmetical inductive definition, an\nimpredicative theory. While intuitively plausible, \\(\\mu\\)KF suffers the\nsame expressive incompleteness as KF: Since the minimal Kripkean fixed\npoint forms a complete \\(\\Pi^{1}_1\\) set and the\ninternal theory of \\(\\mu\\)KF remains recursively enumerable, there are\nstandard models of the theory in which the interpretation of the truth\npredicate is not actually the minimal fixed point. At present there\nlacks a thorough analysis of the models of \\(\\mu\\)KF.\n" ], "subsection_title": "4.5 Capturing the minimal fixed point" }, { "content": [ "KF is intended to be an axiomatization of Kripke’s (1975)\nsemantical theory. This theory is based on partial logic with the\nStrong Kleene evaluation scheme. In Strong Kleene logic not every\nsentence \\(\\phi \\vee \\neg \\phi\\) is a theorem; in particular, this\ndisjunction is not true if \\(\\phi\\) lacks a truth\nvalue. Consequently \\(T\\ulcorner L\\vee \\neg L\\urcorner\\)\n(where \\(L\\) is the Liar sentence) is not a theorem of KF and its\nnegation is even provable. Cantini (1990) has proposed a system VF\nthat is inspired by the supervaluations scheme. In VF all classical\ntautologies are provably true\nand \\(T\\ulcorner L \\vee \\neg L\\urcorner\\), for instance, is a theorem of\nVF. VF can be formulated\nin \\(\\mathcal{L}_T\\) and uses\nclassical logic. It is no longer a compositional theory of\ntruth, for the following is not a theorem of VF:", "Not only is this principle inconsistent with the other axioms of\nVF, it does not fit the supervaluationist model for it\nimplies \\(T\\ulcorner L\\urcorner \\vee T\\ulcorner \\neg L\\urcorner\\),\nwhich of course is not correct because according to the intended\nsemantics neither the liar sentence nor its negation is true: both\nlack a truth value.", "Extending a result due to Friedman and Sheard (1987), Cantini\nshowed that VF is much stronger than KF: VF is proof-theoretically\nequivalent to the theory ID\\(_1\\) of non-iterated inductive\ndefinitions, which is not predicative. " ], "subsection_title": "4.6 Axiomatisations of Kripke’s theory with supervaluations" } ] }, { "main_content": [ "The theories of truth discussed thus far are all axiomatized in\nclassical logic. Some authors have also looked into axiomatic theories\nof truth based on non-classical logic (see, for example, Field 2008,\nHalbach and Horsten 2006, Leigh and Rathjen 2012). There are a number\nof reasons why a logic weaker than classical logic may be\npreferred. The most obvious is that by weakening the logic, some\ncollections of axioms of truth that were previously inconsistent\nbecome consistent. Another common reason is that the axiomatic theory\nin question intends to capture a particular non-classical semantics of\ntruth, for which a classical background theory may prove unsound." ], "section_title": "5. Non-classical approaches to self-reference", "subsections": [ { "content": [ "The inconsistency of the \\(T\\)-sentences does not rely on\nclassical reasoning. It is also inconsistent over much weaker logics\nsuch as minimal logic and partial logic. However, classical logic does\nplay a role in restricting the free use of principles of truth. For\ninstance, over a classical base theory, the compositional axiom for\nimplication \\((\\rightarrow)\\) is equivalent to the principle of completeness,\n\\(\\forall{\\scriptsize A}(T[{\\scriptsize A}] \\vee T[\\neg{\\scriptsize A}\\)]). If the logic under\nthe truth predicate is classical, completeness is equivalent to the compositional axiom for disjunction. Without the law of\nexcluded middle, FS can be formulated as a fully compositional theory\nwhile not proving the truth-completeness principle (Leigh & Rathjen\n2012). In addition, classical logic has an effect on attempts to\ncombine compositional and self-applicable axioms of truth. If, for\nexample, one drops the axiom of truth-consistency from FS (the\nleft-to-right direction of axiom 2 in Section 4.3)\nas well as the law of excluded middle for the truth predicate, it is\npossible to add consistently the truth-iteration axiom\n\\(\\forall{\\scriptsize A}(T[{\\scriptsize A}]\n\\rightarrow T[T{\\scriptsize A}])\\).\nThe resulting theory\nstill bears a strong resemblance to FS in that the constructive\nversion of the rule-of-revision semantics for all finite levels\nprovides a natural model of the theory, and the two theories share the same \\(\\Pi^{0}_2\\) consequences (Leigh & Rathjen 2012; Leigh, 2013). \nThis result should be contrasted with KF which, if formulated\nwithout the law of excluded middle, remains maximally consistent with\nrespect to its choice of truth axioms but is a conservative extension of\nHeyting arithmetic." ], "subsection_title": "5.1 The truth predicate in intuitionistic logic" }, { "content": [ "Kripke’s (1975) theory in its different guises is based on partial\nlogic. In order to obtain models for a theory in classical logic, the\nextension of the truth predicate in the partial model is used again as\nthe extension of truth in the classical model. In the classical model\nfalse sentences and those without a truth value in the partial model\nare declared not true. KF is sound with respect to these classical\nmodels and thus incorporates two distinct logics. The first is the\n‘internal’ logic of statements under the truth predicate\nand is formulated with the Strong Kleene valuation schema. The second\nis the ‘external’ logic which is full classical logic. An\neffect of formulating KF in classical logic is that the theory cannot\nbe consistently closed under the truth-introduction rule\n", "\n If \\(\\phi\\) is a theorem of KF, so is\n \\(T\\ulcorner \\phi \\urcorner\\).\n", "\nA second effect of classical logic is the statement of the excluded\nmiddle for the liar sentence. Neither the Liar sentence nor its\nnegation obtains a truth value in Kripke’s theory, so the disjunction\nof the two is not valid. The upshot is that KF, if viewed as an\naxiomatisation of Kripke’s theory, is not sound with respect to its\nintended semantics. For this reason Halbach and Horsten (2006) and\nHorsten (2011) explore an axiomatization of Kripke’s theory with\npartial logic as inner and outer logic. Their suggestion, a\ntheory labelled PKF (‘partial KF’), can be axiomatised as\na Gentzen-style two-sided sequent calculus based on Strong Kleene\nlogic (see the entry on many-valued\nlogic). PKF is formed by adding to this calculus the\nPeano–Dedekind axioms of arithmetic including full induction and\nthe compositional and truth-iteration rules for the truth predicate as\nproscribed by Kripke’s theory. The result is a theory of truth that is\nsound with respect to Kripke’s theory.\n", "Halbach and Horsten show that this axiomatization of Kripke’s\ntheory is significantly weaker than it’s classical cousin KF. The\nresult demonstrates that restricting logic only for sentences with the\ntruth predicate can hamper also the derivation of truth-free theorems.\n" ], "subsection_title": "5.2 Axiomatising Kripke’s theory" } ] } ]

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[ { "href": "../compositionality/", "text": "compositionality" }, { "href": "../goedel/", "text": "Gödel, Kurt" }, { "href": "../goedel-incompleteness/", "text": "Gödel, Kurt: incompleteness theorems" }, { "href": "../liar-paradox/", "text": "liar paradox" }, { "href": "../paradoxes-contemporary-logic/", "text": "paradoxes: and contemporary logic" }, { "href": "../properties/", "text": "properties" }, { "href": "../tarski-truth/", "text": "Tarski, Alfred: truth definitions" }, { "href": "../truth-deflationary/", "text": "truth: deflationation about" } ]

[ "\n\nA coherence theory of truth states that the truth of any (true)\nproposition consists in its coherence with some specified set of\npropositions. The coherence theory differs from its principal\ncompetitor, the correspondence theory of truth, in two essential\nrespects. The competing theories give conflicting accounts of the\nrelation that propositions bear to their truth conditions. (In this\narticle, ‘proposition’ is not used in any technical sense.\nIt simply refers to the bearers of truth values, whatever they may\nbe.) According to one, the relation is coherence, according to the\nother, it is correspondence. The two theories also give conflicting\naccounts of truth conditions. According to the coherence theory, the\ntruth conditions of propositions consist in other propositions. The\ncorrespondence theory, in contrast, states that the truth conditions\nof propositions are not (in general) propositions, but rather\nobjective features of the world. (Even the correspondence theorist\nholds that propositions about propositions have propositions as their\ntruth conditions.) Although the coherence and correspondence theories\nare fundamentally opposed in this way, they both present (in contrast\nto deflationary theories of truth) a substantive conception of\ntruth. That is, unlike deflationary theories, the coherence and\ncorrespondence theories both hold that truth is a property of\npropositions that can be analysed in terms of the sorts of\ntruth-conditions propositions have, and the relations propositions\nstand in to these conditions. " ]

[ { "content_title": "1. Versions of the Coherence Theory of Truth", "sub_toc": [] }, { "content_title": "2. Arguments for Coherence Theories of Truth", "sub_toc": [] }, { "content_title": "3. Criticisms of Coherence Theories of Truth", "sub_toc": [] }, { "content_title": "4. New Objections to Coherentism", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nThe coherence theory of truth has several versions. These versions\ndiffer on two major issues. Different versions of the theory give\ndifferent accounts of the coherence relation. Different varieties of\nthe theory also give various accounts of the set (or sets) of\npropositions with which true propositions cohere. (Such\na set will be called a specified set.) ", "\n\nAccording to some early versions of the coherence theory, the\ncoherence relation is simply consistency. On this view, to say that a\nproposition coheres with a specified set of propositions is to say that\nthe proposition is consistent with the set. This account of coherence\nis unsatisfactory for the following reason. Consider two propositions\nwhich do not belong to a specified set. These propositions could both\nbe consistent with a specified set and yet be inconsistent with each\nother. If coherence is consistency, the coherence theorist would have\nto claim that both propositions are true, but this is impossible.", "\n\nA more plausible version of the coherence theory states that the\ncoherence relation is some form of entailment. Entailment can be\nunderstood here as strict logical entailment, or entailment in some\nlooser sense. According to this version, a proposition coheres with a\nset of propositions if and only if it is entailed by members of the\nset. Another more plausible version of the theory, held for example in\nBradley (1914), is that coherence is mutual explanatory support\nbetween propositions.", "\n\nThe second point on which coherence theorists (coherentists, for\nshort) differ is the constitution of the specified set of propositions.\nCoherentists generally agree that the specified set consists of\npropositions believed or held to be true. They differ on the questions\nof who believes the propositions and when. At one extreme, coherence\ntheorists can hold that the specified set of propositions is the\nlargest consistent set of propositions currently believed by actual\npeople. For such a version of the theory, see Young (1995). According\nto a moderate position, the specified set consists of those\npropositions which will be believed when people like us (with finite\ncognitive capacities) have reached some limit of inquiry. For such a\ncoherence theory, see Putnam (1981). At the other extreme, coherence\ntheorists can maintain that the specified set contains the propositions\nwhich would be believed by an omniscient being. Some idealists seem to\naccept this account of the specified set.", "\n\nIf the specified set is a set actually believed, or even a set which\nwould be believed by people like us at some limit of inquiry,\ncoherentism involves the rejection of realism about truth. Realism\nabout truth involves acceptance of the principle of bivalence\n(according to which every proposition is either true or false) and the\nprinciple of transcendence (which says that a proposition may be true\neven though it cannot be known to be true). Coherentists who do not\nbelieve that the specified set is the set of propositions believed by\nan omniscient being are committed to rejection of the principle of\nbivalence since it is not the case that for every proposition either it\nor a contrary proposition coheres with the specified set. They reject\nthe principle of transcendence since, if a proposition coheres with a\nset of beliefs, it can be known to cohere with the set." ], "section_title": "1. Versions of the Coherence Theory of Truth", "subsections": [] }, { "main_content": [ "\n\nTwo principal lines of argument have led philosophers to adopt a\ncoherence theory of truth. Early advocates of coherence theories were\npersuaded by reflection on metaphysical questions. More recently,\nepistemological and semantic considerations have been the basis for\ncoherence theories. " ], "section_title": "2. Arguments for Coherence Theories of Truth", "subsections": [ { "content": [ "\n\nEarly versions of the coherence theory were associated with\nidealism. Walker (1989) attributes coherentism to Spinoza, Kant, Fichte\nand Hegel. Certainly a coherence theory was adopted by a number of\nBritish Idealists in the last years of the nineteenth century and the\nfirst decades of the twentieth. See, for example, Bradley\n(1914).", "\n\nIdealists are led to a coherence theory of truth by their\nmetaphysical position. Advocates of the correspondence theory believe\nthat a belief is (at least most of the time) ontologically distinct\nfrom the objective conditions which make the belief true. Idealists do\nnot believe that there is an ontological distinction between beliefs\nand what makes beliefs true. From the idealists’ perspective, reality\nis something like a collection of beliefs. Consequently, a belief\ncannot be true because it corresponds to something which is not a\nbelief. Instead, the truth of a belief can only consist in its\ncoherence with other beliefs. A coherence theory of truth which results\nfrom idealism usually leads to the view that truth comes in degrees. A\nbelief is true to the degree that it coheres with other beliefs.", "\n\nSince idealists do not recognize an ontological distinction between\nbeliefs and what makes them true, distinguishing between versions of\nthe coherence theory of truth adopted by idealists and an identity\ntheory of truth can be difficult. The article on Bradley in this\nEncyclopedia (Candlish 2006) argues that Bradley had an identity\ntheory, not a coherence theory.", "\n\nIn recent years metaphysical arguments for coherentism have found\nfew advocates. This is due to the fact that idealism is not widely\nheld." ], "subsection_title": "2.1 The Metaphysical Route to Coherentism" }, { "content": [ "\n\nBlanshard (1939, ch. XXVI) argues that a coherence theory of\njustification leads to a coherence theory of truth. His argument runs\nas follows. Someone might hold that coherence with a set of beliefs is\nthe test of truth but that truth consists in correspondence to\nobjective facts. If, however, truth consists in correspondence to\nobjective facts, coherence with a set of beliefs will not be a test of\ntruth. This is the case since there is no guarantee that a perfectly\ncoherent set of beliefs matches objective reality. Since coherence with\na set of beliefs is a test of truth, truth cannot consist in\ncorrespondence.", "\n\nBlanshard’s argument has been criticised by, for example, Rescher\n(1973). Blanshard’s argument depends on the claim that coherence with a\nset of beliefs is the test of truth. Understood in one sense, this\nclaim is plausible enough. Blanshard, however, has to understand this\nclaim in a very strong sense: coherence with a set of beliefs is an\ninfallible test of truth. If coherence with a set of beliefs is simply\na good but fallible test of truth, as Rescher suggests, the argument\nfails. The “falling apart” of truth and justification to which\nBlanshard refers is to be expected if truth is only a fallible test of\ntruth.", "\n\nAnother epistemological argument for coherentism is based on the\nview that we cannot “get outside” our set of beliefs and compare\npropositions to objective facts. A version of this argument was\nadvanced by some logical positivists including Hempel (1935) and\nNeurath (1983). This argument, like Blanshard’s, depends on a coherence\ntheory of justification. The argument infers from such a theory that we\ncan only know that a proposition coheres with a set of beliefs. We can\nnever know that a proposition corresponds to reality.", "\n\nThis argument is subject to at least two criticisms. For a start, it\ndepends on a coherence theory of justification, and is vulnerable to\nany objections to this theory. More importantly, a coherence theory of\ntruth does not follow from the premisses. We cannot infer from the fact\nthat a proposition cannot be known to correspond to reality that it\ndoes not correspond to reality. Even if correspondence theorists admit\nthat we can only know which propositions cohere with our beliefs, they\ncan still hold that truth consists in correspondence. If correspondence\ntheorists adopt this position, they accept that there may be truths\nwhich cannot be known. Alternatively, they can argue, as does Davidson\n(1986), that the coherence of a proposition with a set of beliefs is a\ngood indication that the proposition corresponds to objective facts and\nthat we can know that propositions correspond.", "\n\nCoherence theorists need to argue that propositions cannot\ncorrespond to objective facts, not merely that they cannot be known to\ncorrespond. In order to do this, the foregoing argument for coherentism\nmust be supplemented. One way to supplement the argument would be to\nargue as follows. As noted above, the correspondence and coherence\ntheories have differing views about the nature of truth conditions. One\nway to decide which account of truth conditions is correct is to pay\nattention to the process by which propositions are assigned truth\nconditions. Coherence theorists can argue that the truth conditions of\na proposition are the conditions under which speakers make a practice\nof asserting it. Coherentists can then maintain that speakers can only\nmake a practice of asserting a proposition under conditions the\nspeakers are able to recognise as justifying the proposition. Now the\n(supposed) inability of speakers to “get outside” of their beliefs is\nsignificant. Coherentists can argue that the only conditions speakers\ncan recognise as justifying a proposition are the conditions under\nwhich it coheres with their beliefs. When the speakers make a practice\nof asserting the proposition under these conditions, they become the\nproposition’s truth conditions. For an argument of this sort see Young\n(1995)." ], "subsection_title": "2.2 Epistemological Routes to Coherentism" } ] }, { "main_content": [ "\n\nAny coherence theory of truth faces two principal challenges. The first\nmay be called the specification objection. The second is the\ntranscendence objection. " ], "section_title": "3. Criticisms of Coherence Theories of Truth", "subsections": [ { "content": [ "\n\nAccording to the specification objection, coherence theorists have\nno way to identify the specified set of propositions without\ncontradicting their position. This objection originates in Russell\n(1907). Opponents of the coherence theory can argue as follows. The\nproposition (1) “Jane Austen was hanged for murder” coheres\nwith some set of propositions. (2) “Jane Austen died in her\nbed” coheres with another set of propositions. No one supposes\nthat the first of these propositions is true, in spite of the fact that\nit coheres with a set of propositions. The specification objection\ncharges that coherence theorists have no grounds for saying that (1) is\nfalse and (2) true.", "\n\nSome responses to the specification problem are unsuccessful. One\ncould say that we have grounds for saying that (1) is false and (2) is\ntrue because the latter coheres with propositions which correspond to\nthe facts. Coherentists cannot, however, adopt this response without\ncontradicting their position. Sometimes coherence theorists maintain\nthat the specified system is the most comprehensive system, but this\nis not the basis of a successful response to the specification\nproblem. Coherentists can only, unless they are to compromise their\nposition, define comprehensiveness in terms of the size of a\nsystem. Coherentists cannot, for example, talk about the most\ncomprehensive system composed of propositions which correspond to\nreality. There is no reason, however, why two or more systems cannot\nbe equally large. Other criteria of the specified system, to which\ncoherentists frequently appeal, are similarly unable to solve the\nspecification problem. These criteria include simplicity, empirical\nadequacy and others. Again, there seems to be no reason why two or\nmore systems cannot equally meet these criteria.", "\n\nAlthough some responses to the Russell’s version of the\nspecification objection are unsuccessful, it is unable to refute the\ncoherence theory. Coherentists do not believe that the truth of a\nproposition consists in coherence with any arbitrarily chosen set of\npropositions. Rather, they hold that truth consists in coherence with a\nset of beliefs, or with a set of propositions held to be true. No one\nactually believes the set of propositions with which (1) coheres.\nCoherence theorists conclude that they can hold that (1) is false\nwithout contradicting themselves.", "\n\nA more sophisticated version of the specification objection has been\nadvanced by Walker (1989); for a discussion, see Wright (1995). Walker\nargues as follows. In responding to Russell’s version of the\nspecification objection, coherentists claim that some set of\npropositions, call it S, is believed. They are committed to\nthe truth of (3) “S is believed.” The question of\nwhat it is for (3) to be true then arises. Coherence theorists might\nanswer this question by saying that “‘S is\nbelieved’ is believed” is true. If they give this answer,\nthey are apparently off on an infinite regress, and they will never\nsay what it is for a proposition to be true. Their plight is worsened\nby the fact that arbitrarily chosen sets of propositions can include\npropositions about what is believed. So, for example, there will be a\nset which contains “Jane Austen was hanged for murder,”\n“‘Jane Austen was hanged for murder’ is\nbelieved,” and so on. The only way to stop the regress seems to\nbe to say that the truth conditions of (3) consist in the objective\nfact S is believed. If, however, coherence theorists adopt\nthis position, they seem to contradict their own position by accepting\nthat the truth conditions of some proposition consist in facts, not in\npropositions in a set of beliefs.", "\n\nThere is some doubt about whether Walker’s version of the\nspecification objection succeeds. Coherence theorists can reply to\nWalker by saying that nothing in their position is inconsistent with\nthe view that there is a set of propositions which is\nbelieved. Even though this objective fact obtains, the truth conditions\nof propositions, including propositions about which sets of\npropositions are believed, are the conditions under which they cohere\nwith a set of propositions. For a defence of the coherence theory against\nWalker’s version of the specification objection, see Young (2001).", "\n\nA coherence theory of truth gives rise to a regress, but it is not a\nvicious regress and the correspondence theory faces a similar regress.\nIf we say that p is true if and only if it coheres with a\nspecified set of propositions, we may be asked about the truth\nconditions of “p coheres with a specified set.”\nPlainly, this is the start of a regress, but not one to worry\nabout. It is just what one would expect, given that the coherence\ntheory states that it gives an account of the truth conditions of all\npropositions. The correspondence theory faces a similar benign\nregress. The correspondence theory states that a proposition is true\nif and only if it corresponds to certain objective conditions. The\nproposition “p corresponds to certain objective\nconditions” is also true if and only if it corresponds to\ncertain objective conditions, and so on." ], "subsection_title": "3.1 The Specification Objection" }, { "content": [ "\n\nThe transcendence objection charges that a coherence theory of truth\nis unable to account for the fact that some propositions are true which\ncohere with no set of beliefs. According to this objection, truth\ntranscends any set of beliefs. Someone might argue, for example, that\nthe proposition “Jane Austen wrote ten sentences on November\n17th, 1807” is either true or false. If it is false, some other\nproposition about how many sentences Austen wrote that day is true. No\nproposition, however, about precisely how many sentences Austen wrote\ncoheres with any set of beliefs and we may safely assume that none will\never cohere with a set of beliefs. Opponents of the coherence theory\nwill conclude that there is at least one true proposition which does\nnot cohere with any set of beliefs.", "\n\nSome versions of the coherence theory are immune to the\ntranscendence objection. A version which holds that truth is coherence\nwith the beliefs of an omniscient being is proof against the objection.\nEvery truth coheres with the set of beliefs of an omniscient being. All\nother versions of the theory, however, have to cope with the objection,\nincluding the view that truth is coherence with a set of propositions\nbelieved at the limit of inquiry. Even at the limit of inquiry, finite\ncreatures will not be able to decide every question, and truth may\ntranscend what coheres with their beliefs.", "\n\nCoherence theorists can defend their position against the\ntranscendence objection by maintaining that the objection begs the\nquestion. Those who present the objection assume, generally without\nargument, that it is possible that some proposition be true even though\nit does not cohere with any set of beliefs. This is precisely what\ncoherence theorists deny. Coherence theorists have arguments for\nbelieving that truth cannot transcend what coheres with some set of\nbeliefs. Their opponents need to take issue with these arguments rather\nthan simply assert that truth can transcend what coheres with a\nspecified system." ], "subsection_title": "3.2 The Transcendence Objection" }, { "content": [ "\n\nRussell (1912) presented a third classic objection to the coherence\ntheory of truth. According to this objection, any talk about coherence\npresupposes the truth of the laws of logic. For example, Russell\nargues, to say that two propositions cohere with each other is to\npresuppose the truth of the law of non-contradiction. In this case,\ncoherentism has no account of the truth of law of\nnon-contradiction. If, however, the coherence theorist holds that the\ntruth of the law of non-contradiction depends on its coherence with a\nsystem of beliefs, and it were supposed to be false, then propositions\ncannot cohere or fail to cohere. In this case, the coherence theory of\ntruth completely breaks down since propositions cannot cohere with\neach other.", "\nCoherentists have a plausible response to this objection. They may\nhold that the law of non-contradiction, like any other truth, is true\nbecause it coheres with a system of beliefs. In particular, the law of\nnon-contradiction is supported by the belief that, for example,\ncommunication and reasoning would be impossible unless every system of\nbeliefs contains something like law of non-contradiction (and the\nbelief that communication and reasoning are possible). It is true\nthat, as Russell says, if the law is supposed not to cohere with a\nsystem of beliefs, then propositions can neither cohere nor fail to\ncohere. However, coherence theorists may hold, they do not suppose the\nlaw of non-contradiction to be false. On the contrary, they are likely\nto hold that any coherent set of beliefs must include the law of\nnon-contradiction or a similar law." ], "subsection_title": "3.3 The Logic Objection" } ] }, { "main_content": [ "\n Paul Thagard is the author of the first of two recent new arguments\n against the coherence theory. Thagard states his argument as\n follows:", "if there is a world independent of representations of it,\nas historical evidence suggests, then the aim of representation should\nbe to describe the world, not just to relate to other\nrepresentations. My argument does not refute the coherence theory, but\nshows that it implausibly gives minds too large a place in\nconstituting truth. (Thagard 2007: 29–30)", "\n\nThagard’s argument seems to be that if there is a mind-independent\nworld, then our representations are representations of the world. (He\nsays representations “should be” of the world, but the\nargument is invalid with the addition of the auxiliary verb.) The\nworld existed before humans and our representations, including our\npropositional representations. (So history and, Thagard would likely\nsay, our best science tells us.) Therefore, representations,\nincluding propositional representations, are representations of a\nmind-independent world. The second sentence of the passage just quoted\nsuggests that the only way that coherentists can reject this argument\nis to adopt some sort of idealism. That is, they can only reject the\nminor premiss of the argument as reconstructed. Otherwise they are\ncommitted to saying that propositions represent the world and, Thagard\nseems to suggest, this is to say that propositions have the sort of\ntruth-conditions posited by a correspondence theory. So the coherence\ntheory is false.", "\n\nIn reply to this argument, coherentists can deny that\npropositions are representations of a mind-independent world. To say\nthat a proposition is true is to say that it is supported by a\nspecified system of propositions. So, the coherentist can say,\npropositions are representations of systems of beliefs, not\nrepresentations of a mind-independent world. To assert a proposition\nis to assert that it is entailed by a system of beliefs. The\ncoherentist holds that even if there is a mind-independent world, it\ndoes not follow that the “the point” of representations is\nto represent this world. If coherentists have been led to their\nposition by an epistemological route, they believe that we cannot\n“get outside” our system of beliefs. If we cannot get\noutside of our system of beliefs, then it is hard to see how we can be\nsaid to represent a mind-independent reality.", "\n\nColin McGinn has proposed the other new objection to coherentism. He\nargues (McGinn 2002: 195) that coherence theorists are committed to\nidealism. Like Thagard, he takes idealism to be obviously false, so\nthe argument is a reductio. McGinn’s argument runs as\nfollows. Coherentists are committed to the view that, for example,\n‘Snow falls from the sky’ is true iff the belief that snow\nfalls from the sky coheres with other beliefs. Now it follows from\nthis and the redundancy biconditional (p is true\niff p) that snow falls from the sky iff the belief that snow\nfalls from the sky coheres with other beliefs. It appears then that\nthe coherence theorist is committed to the view that snow could not\nfall from the sky unless the belief that snow falls from the sky\ncoheres with other beliefs. From this it follows that how things are\ndepends on what is believed about them. This seems strange to McGinn\nsince he thinks, reasonably, that snow could fall from the sky even if\nthere were no beliefs about snow, or anything else. The linking of how\nthings are and how they are believed to be leads McGinn to say that\ncoherentists are committed to idealism, this being the view that how\nthings are is mind-dependent.", "\n\nCoherentists have a response to this objection. McGinn’s argument\nworks because he takes it that the redundancy biconditional means\nsomething like “p is true\nbecause p”. Only if redundancy biconditionals are\nunderstood in this way does McGinn’s argument go through. McGinn needs\nto be talking about what makes “Snow falls from the sky”\ntrue for his reductio to work. Otherwise, coherentists who reject his\nargument cannot be charged with idealism. He assumes, in a way that a\ncoherent theorist can regard as question-begging, that the truth-maker\nof the sentence in question is an objective way the world\nis. Coherentists deny that any sentences are made true by objective\nconditions. In particular, they hold that the falling of snow from the\nsky does not make “Snow falls from the sky”\ntrue. Coherentists hold that it, like any other sentence, is true\nbecause it coheres with a system of beliefs. So coherentists appear to\nhave a plausible defence against McGinn’s objection." ], "section_title": "4. New Objections to Coherentism", "subsections": [] } ]

[ "Blanshard, B., 1939, The Nature of Thought, London:\nGeorge Allen and Unwin.", "Bradley, F., 1914, Essays on Truth and Reality, Oxford:\nClarendon Press.", "Cavendish, S., 2006, “Francis H. Bradley”, in \nThe Stanford Encyclopedia of Philosophy, Fall 2006 \nEdition, Edward N. Zalta (ed.), URL =\nhttps://plato.stanford.edu/archives/fall2006/entries/bradley/.", "Davidson, D., 1986, “A Coherence Theory of Truth and\nKnowledge,” Truth And Interpretation, Perspectives on the\nPhilosophy of Donald Davidson, Ernest LePore (ed.), Oxford: Basil\nBlackwell, 307–19.", "Hempel, C., 1935, “On the Logical Positivists’ Theory of\nTruth,” Analysis, 2: 49–59.", "McGinn, Colin, 2002, “The Truth about Truth”, in\nWhat is Truth?, Richard Schantz (ed.), Berlin: Walter de\nGruyter, 194–204.", "Neurath, O., 1983, Philosophical Papers 1913–46,\nRobert S. Cohen and Marie Neurath (eds.), Dordrecht and\nBoston: D. Reidel.", "Putnam, H., 1981, Reason, Truth and History, Cambridge:\nCambridge University Press.", "Rescher, N., 1973, The Coherence Theory of Truth, Oxford:\nOxford University Press.", "Russell, B., 1907, “On the Nature of\nTruth”, Proceedings of the Aristotelian Society, 7:\n228–49.", "–––, 1912, The Problems of Philosophy,\nNew York: H. Holt.", "Thagard, P., 2007, “Coherence, Truth and the Development\nof Scientific Knowledge”, Philosophy of Science, 74:\n26–47.", "Walker, R.C.S., 1989, The Coherence Theory of Truth: Realism,\nanti-realism, idealism, London and New York: Routledge.", "Wright, C., 1995, “Critical Study: Ralph\nC.S. Walker, The Coherence Theory of Truth: Realism, anti-realism,\nidealism,” Synthese, 103: 279–302.", "Young, J.O., 1995, Global Anti-realism, Aldershot:\nAvebury.", "–––, 2001, “A Defence of the Coherence\nTheory of Truth”, The Journal of Philosophical\nResearch, 26: 89–101." ]

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[ "\n\nNarrowly speaking, the correspondence theory of truth is the view that\ntruth is correspondence to, or with, a fact—a view that was\nadvocated by Russell and Moore early in the 20th century. But the\nlabel is usually applied much more broadly to any view explicitly\nembracing the idea that truth consists in a relation to reality, i.e.,\nthat truth is a relational property involving a characteristic\nrelation (to be specified) to some portion of reality (to be\nspecified). This basic idea has been expressed in many ways, giving\nrise to an extended family of theories and, more often, theory\nsketches. Members of the family employ various concepts for the\nrelevant relation (correspondence, conformity, congruence, agreement,\naccordance, copying, picturing, signification, representation,\nreference, satisfaction) and/or various concepts for the relevant\nportion of reality (facts, states of affairs, conditions, situations,\nevents, objects, sequences of objects, sets, properties, tropes). The\nresulting multiplicity of versions and reformulations of the theory is\ndue to a blend of substantive and terminological differences.", "\n\nThe correspondence theory of truth is often associated with\nmetaphysical realism. Its traditional competitors, pragmatist, as well\nas coherentist, verificationist, and other epistemic theories of\ntruth, are often associated with idealism, anti-realism, or\nrelativism. In recent years, these traditional competitors have been\nvirtually replaced (at least in terms of publication space) by deflationary\ntheories of truth and, to a lesser extent, by the identity theory\n(note that these new competitors are typically not associated\nwith anti-realism). Still more recently, two further approaches have\nreceived considerable attention. One is truthmaker theory: it is\nsometimes viewed as a competitor to, sometimes as a more liberal\nversion of, the correspondence theory. The other is pluralism: it\nincorporates a correspondence account as one, but only one, ingredient\nof its overall account of truth." ]

[ { "content_title": "1. History of the Correspondence Theory", "sub_toc": [ "1.1 Metaphysical and Semantic Versions", "1.2 Object-Based and Fact-Based Versions" ] }, { "content_title": "2. Truthbearers, Truthmakers, Truth", "sub_toc": [ "2.1 Truthbearers", "2.2 Truthmakers", "2.3 Truth" ] }, { "content_title": "3. Simple Versions of the Correspondence Theory", "sub_toc": [] }, { "content_title": "4. Arguments for the Correspondence Theory", "sub_toc": [] }, { "content_title": "5. Objections to the Correspondence Theory", "sub_toc": [] }, { "content_title": "6. Correspondence as Isomorphism", "sub_toc": [] }, { "content_title": "7. Modified Versions of the Correspondence Theory", "sub_toc": [ "7.1 Logical Atomism", "7.2 Logical “Subatomism”", "7.3 Relocating Correspondence" ] }, { "content_title": "8. The Correspondence Theory and Its Competitors", "sub_toc": [ "8.1 Traditional Competitors", "8.2 Pluralism", "8.3 The Identity Theory of Truth", "8.4 Deflationism About Truth", "8.5 Truthmaker Theory" ] }, { "content_title": "9. More Objections to the Correspondence Theory", "sub_toc": [ "9.1 The Big Fact", "9.2 No Independent Access" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nThe correspondence theory is often traced back to Aristotle’s\nwell-known definition of truth (Metaphysics 1011b25):\n“To say of what is that it is not, or of what is not that it is,\nis false, while to say of what is that it is, and of what is not that\nit is not, is true”—but virtually identical formulations\ncan be found in Plato (Cratylus 385b2, Sophist\n263b). It is noteworthy that this definition does not highlight the\nbasic correspondence intuition. Although it does allude to a relation\n(saying something of something) to reality (what\nis), the relation is not made very explicit, and there is no\nspecification of what on the part of reality is responsible for the\ntruth of a saying. As such, the definition offers a muted, relatively\nminimal version of a correspondence theory. (For this reason it has\nalso been claimed as a precursor of deflationary theories of truth.)\nAristotle sounds much more like a genuine correspondence theorist in\nthe Categories (12b11, 14b14), where he talks of underlying\nthings that make statements true and implies that these things\n(pragmata) are logically structured situations or facts\n(viz., his sitting and his not sitting are said to\nunderlie the statements “He is sitting” and “He is\nnot sitting”, respectively). Most influential is\nAristotle’s claim in De Interpretatione (16a3) that\nthoughts are “likenesses” (homoiomata) of\nthings. Although he nowhere defines truth in terms of a\nthought’s likeness to a thing or fact, it is clear that such a\ndefinition would fit well into his overall philosophy of\nmind. (Cf. Crivelli 2004; Szaif 2006.)" ], "section_title": "1. History of the Correspondence Theory", "subsections": [ { "content": [ "\n\nIn medieval authors we find a division between\n“metaphysical” and “semantic” versions of the\ncorrespondence theory. The former are indebted to the\ntruth-as-likeness theme suggested by Aristotle’s overall views,\nthe latter are modeled on Aristotle’s more austere definition\nfrom Metaphysics 1011b25.", "\n\nThe metaphysical version presented by Thomas Aquinas is the\nbest known: “Veritas est adaequatio rei et\nintellectus” (Truth is the equation of thing and\nintellect), which he restates as: “A judgment is said to be true\nwhen it conforms to the external reality”. He tends to use\n“conformitas” and\n“adaequatio”, but also uses\n“correspondentia”, giving the latter a more\ngeneric sense (De Veritate, Q.1, A.1-3; cf. Summa\nTheologiae, Q.16). Aquinas credits the Neoplatonist Isaac Israeli\nwith this definition, but there is no such definition in\nIsaac. Correspondence formulations can be traced back to the Academic\nskeptic Carneades, 2nd century B.C., whom Sextus Empiricus\n(Adversos Mathematicos, vii, 168) reports as having taught\nthat a presentation “is true when it is in accord\n(symphonos) with the object presented, and false when it is\nin discord with it”. Similar accounts can be found in various\nearly commentators on Plato and Aristotle (cf. Künne 2003,\nchap. 3.1), including some Neoplatonists: Proklos (In Tim.,\nII 287, 1) speaks of truth as the agreement or adjustment\n(epharmoge) between knower and the known. Philoponus (In\nCat., 81, 25-34) emphasizes that truth is neither in the things\nor states of affairs (pragmata) themselves, nor in the\nstatement itself, but lies in the agreement between the two. He gives\nthe simile of the fitting shoe, the fit consisting in a relation\nbetween shoe and foot, not to be found in either one by itself. Note\nthat his emphasis on the relation as opposed to its relata is laudable\nbut potentially misleading, because x’s truth (its being\ntrue) is not to be identified with a relation, R, between x\nand y, but with a general relational property of x,\ntaking the form (∃y)(xRy &\nFy). Further early correspondence formulations can be found in\nAvicenna (Metaphysica, 1.8-9) and Averroes (Tahafut,\n103, 302). They were introduced to the scholastics by William of\nAuxerre, who may have been the intended recipient of Aquinas’\nmistaken attribution (cf. Boehner 1958; Wolenski 1994).", "\n\nAquinas’ balanced formula “equation of thing and\nintellect” is intended to leave room for the idea that\n“true” can be applied not only to thoughts and judgments\nbut also to things or persons (e.g. a true friend). Aquinas explains\nthat a thought is said to be true because it conforms to\nreality, whereas a thing or person is said to be true because\nit conforms to a thought (a friend is true insofar as, and because,\nshe conforms to our, or God’s, conception of what a friend ought\nto be). Medieval theologians regarded both, judgment-truth as well as\nthing/person-truth, as somehow flowing from, or grounded in, the\ndeepest truth which, according to the Bible, is God: “I am the\nway and the truth and the life” (John 14, 6). Their attempts to\nintegrate this Biblical passage with more ordinary thinking involving\ntruth gave rise to deep metaphysico-theological reflections. The\nnotion of thing/person-truth, which thus played a very important role\nin medieval thinking, is disregarded by modern and contemporary\nanalytic philosophers but survives to some extent in existentialist\nand continental philosophy.", "\n\nMedieval authors who prefer a semantic version of the\ncorrespondence theory often use a peculiarly truncated formula to\nrender Aristotle’s definition: A (mental) sentence is true if\nand only if, as it signifies, so it is (sicut significat, ita\nest). This emphasizes the semantic relation\nof signification while remaining maximally elusive about what\nthe “it” is that is signified by a true sentence and\nde-emphasizing the correspondence relation (putting it into the little\nwords “as” and “so”). Foreshadowing a favorite\napproach of the 20th century, medieval semanticists like Ockham\n(Summa Logicae, II) and Buridan (Sophismata, II)\ngive exhaustive lists of different truth-conditional clauses for\nsentences of different grammatical categories. They refrain from\nassociating true sentences in general with items from a single\nontological category. (Cf. Moody 1953; Adams McCord 1987; Perler\n2006.)", "\n\nAuthors of the modern period generally convey the impression that the\ncorrespondence theory of truth is far too obvious to merit much, or\nany, discussion. Brief statements of some version or other can be\nfound in almost all major writers; see e.g.: Descartes 1639, ATII 597;\nSpinoza, Ethics, axiom vi; Locke, Essay, 4.5.1;\nLeibniz, New Essays, 4.5.2; Hume, Treatise, 3.1.1;\nand Kant 1787, B82. Berkeley, who does not seem to offer any account\nof truth, is a potentially significant exception. Due to the influence\nof Thomism, metaphysical versions of the theory are much more popular\nwith the moderns than semantic versions. But since the moderns\ngenerally subscribe to a representational theory of the mind (the\ntheory of ideas), they would seem to be ultimately committed to\nspelling out relations like correspondence or conformity in terms of a\npsycho-semantic representation relation holding between ideas, or\nsentential sequences of ideas (Locke’s “mental\npropositions”), and appropriate portions of reality, thereby\neffecting a merger between metaphysical and semantic versions of the\ncorrespondence theory." ], "subsection_title": "1.1 Metaphysical and Semantic Versions" }, { "content": [ "\n\nIt is helpful to distinguish between “object-based” and\n“fact-based” versions of correspondence theories,\ndepending on whether the corresponding portion of reality is said to\nbe an object or a fact (cf. Künne 2003, chap. 3).", "\n\nTraditional versions of object-based theories assumed that\nthe truth-bearing items (usually taken to be judgments) have\nsubject-predicate structure. An object-based definition of truth might\nlook like this:", "A judgment is true if and only if its predicate\ncorresponds to its object (i.e., to the object referred to by the\nsubject term of the judgment).", "\n\nNote that this actually involves two relations to an object:\n(i) a reference relation, holding between the subject term of the\njudgment and the object the judgment is about (its object);\nand (ii) a correspondence relation, holding between the predicate term\nof the judgment and a property of the object. Owing to its reliance on\nthe subject-predicate structure of truth-bearing items, the account\nsuffers from an inherent limitation: it does not cover truthbearers\nthat lack subject-predicate structure (e.g. conditionals,\ndisjunctions), and it is not clear how the account might be extended\nto cover them. The problem is obvious and serious; it was nevertheless\nsimply ignored in most writings. Object-based correspondence was the\nnorm until relatively recently.", "\n\nObject-based correspondence became the norm through Plato’s\npivotal engagement with the problem of falsehood, which was\napparently notorious at its time. In a number of dialogues, Plato\ncomes up against an argument, advanced by various Sophists, to the\neffect that false judgment is impossible—roughly: To judge\nfalsely is to judge what is not. But one cannot judge what is\nnot, for it is not there to be judged. To judge something that is not\nis to judge nothing, hence, not to judge at all. Therefore, false\njudgment is impossible. (Cf. Euthydemus\n283e-288a; Cratylus 429c-e; Republic\n478a-c; Theaetetus 188d-190e.) Plato has no good answer to\nthis patent absurdity until the Sophist (236d-264b), where he\nfinally confronts the issue at length. The key step in his solution is\nthe analysis of truthbearers as structured complexes. A simple\nsentence, such as “Theaetetus sits.”, though simple as a\nsentence, is still a complex whole consisting of words of different\nkinds—a name (onoma) and a verb\n(rhema)—having different functions. By weaving together\nverbs with names the speaker does not just name a number of things,\nbut accomplishes something: meaningful speech (logos)\nexpressive of the interweaving of ideas (eidon\nsymploken). The simple sentence is true when Theaetetus, the\nperson named by the name, is in the state of sitting, ascribed to him\nthrough the verb, and false, when Theaetetus is not in that state but\nin another one (cf. 261c-263d; see Denyer 1991; Szaif\n1998). Only things that are show up in this account: in the\ncase of falsehood, the ascribed state still is, but it is a state\ndifferent from the one Theaetetus is in. The account is extended from\nspeech to thought and belief via Plato’s well known thesis that\n“thought is speech that occurs without voice, inside the soul in\nconversation with itself” (263e)—the historical origin of\nthe language-of-thought hypothesis. The account does not take into\nconsideration sentences that contain a name of something that is not\n(“Pegasus flies”), thus bequeathing to posterity a\nresidual problem that would become more notorious than the problem of\nfalsehood.", "\n\nAristotle, in De Interpretatione, adopts Plato’s\naccount without much ado—indeed, the beginning of De\nInterpretatione reads like a direct continuation of the passages\nfrom the Sophist mentioned above. He emphasizes that truth\nand falsehood have to do with combination and separation (cf. De\nInt. 16a10; in De Anima 430a25, he says: “where\nthe alternative of true and false applies, there we always find a sort\nof combining of objects of thought in a quasi-unity”). Unlike\nPlato, Aristotle feels the need to characterize simple affirmative and\nnegative statements (predications) separately—translating rather\nmore literally than is usual: “An affirmation is a predication\nof something toward something, a negation is a predication of\nsomething away from something” (De Int. 17a25). This\ncharacterization reappears early in the Prior Analytics\n(24a). It thus seems fair to say that the subject-predicate analysis\nof simple declarative sentences—the most basic feature of\nAristotelian term logic which was to reign supreme for many\ncenturies—had its origin in Plato’s response to a\nsophistical argument against the possibility of falsehood. One may\nnote that Aristotle’s famous definition of truth (see Section 1)\nactually begins with the definition of falsehood.", "\n\nFact-based correspondence theories became prominent only in\nthe 20th century, though one can find remarks in Aristotle that fit\nthis approach (see Section 1)—somewhat surprisingly in light of\nhis repeated emphasis on subject-predicate structure wherever truth\nand falsehood are concerned. Fact-based theories do not presuppose\nthat the truth-bearing items have subject-predicate structure; indeed,\nthey can be stated without any explicit reference to the structure of\ntruth-bearing items. The approach thus embodies an alternative\nresponse to the problem of falsehood, a response that may claim to\nextricate the theory of truth from the limitations imposed on it\nthrough the presupposition of subject-predicate structure inherited\nfrom the response to the problem of falsehood favored by Plato,\nAristotle, and the medieval and modern tradition.", "\n\nThe now classical formulation of a fact-based correspondence theory\nwas foreshadowed by Hume (Treatise, 3.1.1) and Mill\n(Logic, 1.5.1). It appears in its canonical form early in the\n20th century in Moore (1910-11, chap. 15) and Russell: “Thus a\nbelief is true when there is a corresponding fact, and is false when\nthere is no corresponding fact” (1912, p. 129; cf. also his\n1905, 1906, 1910, and 1913). The self-conscious emphasis\non facts as the corresponding portions of reality—and a\nmore serious concern with problems raised by\nfalsehood—distinguishes this version from its\nforeshadowings. Russell and Moore’s forceful advocacy of truth\nas correspondence to a fact was, at the time, an integral part of\ntheir defense of metaphysical realism. Somewhat ironically, their\nformulations are indebted to their idealist opponents, F. H. Bradley\n(1883, chaps. 1&2), and H. H. Joachim (1906), the latter was an\nearly advocate of the competing coherence theory, who had set up a\ncorrespondence-to-fact account of truth as the main target of his\nattack on realism. Later, Wittgenstein (1921) and Russell (1918)\ndeveloped “logical atomism”, which introduces an important\nmodification of the fact-based correspondence approach (see below,\nSection 7.1). Further modifications of the correspondence theory,\nbringing a return to more overtly semantic and broadly object-based\nversions, were influenced by Tarski’s (1935) technical work on\ntruth (cf. Field 1972, Popper 1972)." ], "subsection_title": "1.2 Object-Based and Fact-Based Versions" } ] }, { "main_content": [], "section_title": "2. Truthbearers, Truthmakers, Truth", "subsections": [ { "content": [ "\n\nCorrespondence theories of truth have been given for beliefs,\nthoughts, ideas, judgments, statements, assertions, utterances,\nsentences, and propositions. It has become customary to talk\nof truthbearers whenever one wants to stay neutral between\nthese choices. Five points should be kept in mind:" ], "subsection_title": "2.1 Truthbearers" }, { "content": [ "\n\nTalk of truthmakers serves a function similar, but\ncorrelative, to talk of truthbearers. A truthmaker is anything that\nmakes some truthbearer true. Different versions of the correspondence\ntheory will have different, and often competing, views about what sort\nof items true truthbearers correspond to (facts, states of affairs,\nevents, things, tropes, properties). It is convenient to talk of\ntruthmakers whenever one wants to stay neutral between these\nchoices. Four points should be kept in mind:" ], "subsection_title": "2.2 Truthmakers" }, { "content": [ "\n\nThe abstract noun “truth” has various uses. (a)\nIt can be used to refer to the general relational property\notherwise referred to as being true; though the latter label\nwould be more perspicuous, it is rarely used, even in philosophical\ndiscussions. (b) The noun “truth” can be used to\nrefer to the concept that “picks out” the\nproperty and is expressed in English by the adjective\n“true”. Some authors do not distinguish between concept\nand property; others do, or should: an account of the concept might\ndiffer significantly from an account of the property. To mention just\none example, one might maintain, with some plausibility, that an\naccount of the concept ought to succumb to the liar paradox\n(see the entry on the liar paradox),\notherwise it wouldn’t be an adequate account of our\nconcept of truth; this idea is considerably less plausible in the case\nof the property. Any proposed “definition of truth” might\nbe intend as a definition of the property or of the concept or both;\nits author may or may not be alive to the difference. (c) The\nnoun “truth” can be used, finally, to refer to some set of\ntrue truthbarers (possibly unknown), as in: “The truth is out\nthere”, and: “The truth about this matter will never be\nknown”." ], "subsection_title": "2.3 Truth" } ] }, { "main_content": [ "\n\nThe traditional centerpiece of any correspondence theory is a\ndefinition of truth. Nowadays, a correspondence definition is most\nlikely intended as a “real definition”, i.e., as a\ndefinition of the property, which does not commit its advocate to the\nclaim that the definition provides a synonym for the term\n“true”. Most correspondence theorists would consider it\nimplausible and unnecessarily bold to maintain that\n“true” means the same as “corresponds with\na fact”. Some simple forms of correspondence definitions of\ntruth should be distinguished (“iff” means “if and\nonly if”; the variable, “x”, ranges over\nwhatever truthbearers are taken as primary; the notion of\ncorrespondence might be replaced by various related notions):", "\n\n\n(1)\nx is true iff x corresponds to some fact;\n\nx is false iff x does not correspond to any fact.\n\n\n\n", "\n\n\n(2)\nx is true iff x corresponds to some state of\naffairs that obtains; \nx is false iff x corresponds to some state of\naffairs that does not obtain.\n\n\n", "\n\nBoth forms invoke portions of reality—facts/states of\naffairs—that are typically denoted by that-clauses or by\nsentential gerundives, viz. the fact/state of affairs that snow is\nwhite, or the fact/state of affairs of snow’s being\nwhite. (2)’s definition of falsehood is committed to there\nbeing (existing) entities of this sort that nevertheless fail to\nobtain, such as snow’s being green. (1)’s\ndefinition of falsehood is not so committed: to say that a fact does\nnot obtain means, at best, that there is no such fact, that no such\nfact exists. It should be noted that this terminology is not\nstandardized: some authors use “state of affairs” much\nlike “fact” is used here (e.g. Armstrong 1997). The\nquestion whether non-obtaining beings of the relevant sort are to be\naccepted is the substantive issue behind such terminological\nvariations. The difference between (2) and (1) is akin to the\ndifference between Platonism about properties (embraces uninstantiated\nproperties) and Aristotelianism about properties (rejects\nuninstantiated properties).", "\n\nAdvocates of (2) hold that facts are states of affairs that\nobtain, i.e., they hold that their account of truth is in effect an\nanalysis of (1)’s account of truth. So disagreement turns\nlargely on the treatment of falsehood, which (1) simply identifies\nwith the absence of truth.", "\n\nThe following points might be made for preferring (2) over (1):\n(a) Form (2) does not imply that things outside the category\nof truthbearers (tables, dogs) are false just because they don’t\ncorrespond to any facts. One might think this “flaw” of\n(1) is easily repaired: just put an explicit specification of the\ndesired category of truthbearers into both sides of (1). However, some\nworry that truthbearer categories, e.g. declarative sentences or\npropositions, cannot be defined without invoking truth and falsehood,\nwhich would make the resultant definition implicitly\ncircular. (b) Form (2) allows for items within the category\nof truthbearers that are neither true nor false, i.e., it allows for\nthe failure of bivalence. Some, though not all, will regard this as a\nsignificant advantage. (c) If the primary truthbearers are\nsentences or mental states, then states of affairs could be their\nmeanings or contents, and the correspondence relation in (2) could be\nunderstood accordingly, as the relation of representation,\nsignification, meaning, or having-as-content. Facts, on the other\nhand, cannot be identified with the meanings or contents of sentences\nor mental states, on pain of the absurd consequence that false\nsentences and beliefs have no meaning or content. (d) Take a\ntruth of the form ‘p or q’, where\n‘p’ is true and ‘q’\nfalse. What are the constituents of the corresponding fact? Since\n‘q’ is false, they cannot both be facts\n(cf. Russell 1906-07, p. 47f.). Form (2) allows that the fact\ncorresponding to ‘p or q’ is an\nobtaining disjunctive state of affairs composed of a state of affairs\nthat obtains and a state of affairs that does not obtain.", "\n\nThe main point in favor of (1) over (2) is that (1) is not committed\nto counting non-obtaining states of affairs, like the state of affairs\nthat snow is green, as constituents of reality.", "\n\n(One might observe that, strictly speaking, (1) and (2), being\nbiconditionals, are not ontologically committed to anything. Their\nrespective commitments to facts and states of affairs arise only when\nthey are combined with claims to the effect that there is something\nthat is true and something that is false. The discussion assumes some\nsuch claims as given.)", "\n\nBoth forms, (1) and (2), should be distinguished from:", "\n\n\n(3)\nx is true iff x corresponds to some fact that exists; \nx is false iff x corresponds to some fact that does not exist,\n\n\n\n", "\n\nwhich is a confused version of (1), or a confused version of (2), or,\nif unconfused, signals commitment to Meinongianism, i.e., the thesis\nthat there are things/facts that do not exist. The lure of (3) stems\nfrom the desire to offer more than a purely negative correspondence\naccount of falsehood while avoiding commitment to non-obtaining states\nof affairs. Moore at times succumbs to (3)’s temptations\n(1910-11, pp. 267 & 269, but see p. 277). It can also be found in\nthe 1961 translation of Wittgenstein (1921, 4.25), who uses\n“state of affairs” (Sachverhalt) to refer to\n(atomic) facts. The translation has Wittgenstein saying that an\nelementary proposition is false, when the corresponding state of\naffairs (atomic fact) does not exist—but the German original of\nthe same passage looks rather like a version of (2). Somewhat\nironically, a definition of form (3) reintroduces Plato’s\nproblem of falsehood into a fact-based correspondence theory, i.e.,\ninto a theory of the sort that was supposed to provide an alternative\nsolution to that very problem (see Section 1.2).", "\n\nA fourth simple form of correspondence definition was popular for a\ntime (cf. Russell 1918, secs. 1 & 3; Broad 1933, IV.2.23; Austin\n1950, fn. 23), but seems to have fallen out of favor:", "\n\n\n(4) x is true iff x\ncorresponds (agrees) with some fact; \n x is false iff x mis-corresponds (disagrees) with some fact.\n\n\n", "\n\nThis formulation attempts to avoid (2)’s commitment to\nnon-obtaining states of affairs and (3)’s commitment to\nnon-existent facts by invoking the relation of mis-correspondence, or\ndisagreement, to account for falsehood. It differs from (1) in that it\nattempts to keep items outside the intended category\nof x’s from being false: supposedly, tables and dogs\ncannot mis-correspond with a fact. Main worries about (4) are:\n(a) its invocation of an additional, potentially mysterious,\nrelation, which (b) seems difficult to tame: Which fact is\nthe one that mis-corresponds with a given falsehood? and: What keeps\na truth, which by definition corresponds with some fact, from also\nmis-corresponding with some other fact, i.e., from being a falsehood\nas well?", "\n\nIn the following, I will treat definitions (1) and (2) as\nparadigmatic; moreover, since advocates of (2) agree that obtaining\nstates of affairs are facts, it is often convenient to\ncondense the correspondence theory into the simpler formula provided\nby (1), “truth is correspondence to a fact”, at least as\nlong as one is not particularly concerned with issues raised by\nfalsehood." ], "section_title": "3. Simple Versions of the Correspondence Theory", "subsections": [] }, { "main_content": [ "\n\nThe main positive argument given by advocates of the correspondence\ntheory of truth is its obviousness. Descartes: “I have never had\nany doubts about truth, because it seems a notion so transcendentally\nclear that nobody can be ignorant of it...the word\n‘truth’, in the strict sense, denotes the conformity of\nthought with its object” (1639, AT II 597). Even philosophers\nwhose overall views may well lead one to expect otherwise tend to\nagree. Kant: “The nominal definition of truth, that it is the\nagreement of [a cognition] with its object, is assumed as\ngranted” (1787, B82). William James: “Truth, as any\ndictionary will tell you, is a property of certain of our ideas. It\nmeans their ‘agreement’, as falsity means their\ndisagreement, with ‘reality’” (1907,\np. 96). Indeed, The Oxford English Dictionary tells us:\n“Truth, n. Conformity with fact; agreement with\nreality”.", "\n\nIn view of its claimed obviousness, it would seem interesting to learn\nhow popular the correspondence theory actually is. There are some\nempirical data. The PhilPapers Survey (conducted in 2009;\ncf. Bourget and Chalmers 2014), more specifically, the part of the\nsurvey targeting all regular faculty members in 99 leading departments\nof philosophy, reports the following responses to the question:\n“Truth: correspondence, deflationary, or epistemic?”\nAccept or lean toward: correspondence 50.8%; deflationary 24.8%; other\n17.5%; epistemic 6.9%. The data suggest that correspondence-type\ntheories may enjoy a weak majority among professional philosophers and\nthat the opposition is divided. This fits with the observation that\ntypically, discussions of the nature of truth take some version of the\ncorrespondence theory as the default view, the view to be criticized\nor to be defended against criticism.", "\n\nHistorically, the correspondence theory, usually in an object-based\nversion, was taken for granted, so much so that it did not acquire\nthis name until comparatively recently, and explicit arguments for the\nview are very hard to find. Since the (comparatively recent) arrival\nof apparently competing approaches, correspondence theorists have\ndeveloped negative arguments, defending their view against objections\nand attacking (sometimes ridiculing) competing views." ], "section_title": "4. Arguments for the Correspondence Theory", "subsections": [] }, { "main_content": [ "\n\nObjection 1: Definitions like (1) or (2) are\ntoo narrow. Although they apply to truths from some domains of\ndiscourse, e.g., the domain of science, they fail for others, e.g.\nthe domain of morality: there are no moral facts.", "\n\nThe objection recognizes moral truths, but rejects the idea that\nreality contains moral facts for moral truths to correspond to. Logic\nprovides another example of a domain that has been\n“flagged” in this way. The logical positivists recognized\nlogical truths but rejected logical facts. Their intellectual\nancestor, Hume, had already given two definitions of\n“true”, one for logical truths, broadly conceived, the\nother for non-logical truths: “Truth or falsehood consists in an\nagreement or disagreement either to the real relations of\nideas, or to real existence and matter of fact”\n(Hume, Treatise, 3.1.1, cf. 2.3.10; see also\nLocke, Essay, 4.5.6, for a similarly two-pronged account but\nin terms of object-based correspondence).", "\n\nThere are four possible responses to objections of this sort:\n(a) Noncognitivism, which says that, despite appearances to\nthe contrary, claims from the flagged domain are not truth-evaluable\nto begin with, e.g., moral claims are commands or expressions of\nemotions disguised as truthbearers; (b) Error theory, which\nsays that all claims from the flagged domain are false; (c)\nReductionism, which says that truths from the flagged domain\ncorrespond to facts of a different domain regarded as unproblematic,\ne.g., moral truths correspond to social-behavioral facts, logical\ntruths correspond to facts about linguistic conventions; and\n(d) Standing firm, i.e., embracing facts of the flagged\ndomain.", "\n\nThe objection in effect maintains that there are different brands\nof truth (of the property being true, not just\ndifferent brands of truths) for different domains. On the face of it,\nthis conflicts with the observation that there are many obviously\nvalid arguments combining premises from flagged and unflagged\ndomains. The observation is widely regarded as refuting\nnon-cognitivism, once the most popular (concessive) response to the\nobjection.", "\n\nIn connection with this objection, one should take note of the\nrecently developed “multiple realizability” view of truth,\naccording to which truth is not to be identified\nwith correspondence to fact but can be realized by\ncorrespondence to fact for truthbearers of some domains of discourse\nand by other properties for truthbearers of other domains of\ndiscourse, including “flagged” domains. Though it retains\nimportant elements of the correspondence theory, this view does not,\nstrictly speaking, offer a response to the objection on behalf of the\ncorrespondence theory and should be regarded as one of its competitors\n(see below, Section 8.2).", "\n\nObjection 2: Correspondence theories are too\nobvious. They are trivial, vacuous, trading in mere platitudes.\nLocutions from the “corresponds to the facts”-family are\nused regularly in everyday language as idiomatic substitutes for\n“true”. Such common turns of phrase should not be taken to\nindicate commitment to a correspondence theory in any serious\nsense. Definitions like (1) or (2) merely condense some trivial idioms\ninto handy formulas; they don’t deserve the grand label\n“theory”: there is no theoretical weight behind them\n(cf. Woozley 1949, chap. 6; Davidson 1969; Blackburn 1984,\nchap. 7.1).", "\n\nIn response, one could point out: (a) Definitions like (1) or\n(2) are “mini-theories”—mini-theories are quite\ncommon in philosophy—and it is not at all obvious that they are\nvacuous merely because they are modeled on common usage. (b)\nThere are correspondence theories that go beyond these\ndefinitions. (c) The complaint implies that definitions like\n(1) and/or (2) are generally accepted and are, moreover, so shallow\nthat they are compatible with any deeper theory of truth. This makes\nit rather difficult to explain why some thinkers emphatically reject\nall correspondence formulations. (d) The objection implies\nthat the correspondence of S’s belief with a fact could\nbe said to consist in, e.g., the belief’s coherence\nwith S’s overall belief system. This is wildly\nimplausible, even on the most shallow understanding of\n“correspondence” and “fact”.", "\n\nObjection 3: Correspondence theories are\ntoo obscure.", "\n\nObjections of this sort, which are the most common, protest that the\ncentral notions of a correspondence theory carry unacceptable\ncommitments and/or cannot be accounted for in any respectable manner.\nThe objections can be divided into objections primarily aimed at the\ncorrespondence relation and its relatives (3.C1, 3.C2), and\nobjections primarily aimed at the notions of fact\nor state of affairs (3.F1, 3.F2):", "\n\n3.C1: The correspondence relation must be\nsome sort of resemblance relation. But truthbearers do not resemble\nanything in the world except other truthbearers—echoing\nBerkeley’s “an idea can be like nothing but an\nidea”.", "\n\n3.C2: The correspondence relation is very\nmysterious: it seems to reach into the most distant regions of space\n(faster than light?) and time (past and future). How could such a\nrelation possibly be accounted for within a naturalistic framework?\nWhat physical relation could it possibly be?", "\n\n3.F1: Given the great variety of complex\ntruthbearers, a correspondence theory will be committed to all sorts\nof complex “funny facts” that are ontologically\ndisreputable. Negative, disjunctive, conditional, universal,\nprobabilistic, subjunctive, and counterfactual facts have all given\ncause for complaint on this score.", "\n\n3.F2: All facts, even the most simple ones,\nare disreputable. Fact-talk, being wedded to that-clauses, is\nentirely parasitic on truth-talk. Facts are too much like\ntruthbearers. Facts are fictions, spurious sentence-like slices of\nreality, “projected from true sentences for the sake of\ncorrespondence” (Quine 1987, p. 213; cf. Strawson 1950)." ], "section_title": "5. Objections to the Correspondence Theory", "subsections": [] }, { "main_content": [ "\n\nSome correspondence theories of truth are two-liner mini-theories,\nconsisting of little more than a specific version of (1) or\n(2). Normally, one would expect a bit more, even from a philosophical\ntheory (though mini-theories are quite common in philosophy). One\nwould expect a correspondence theory to go beyond a mere definition\nlike (1) or (2) and discharge a triple task: it should tell us about\nthe workings of the correspondence relation, about the nature of\nfacts, and about the conditions that determine which truthbearers\ncorrespond to which facts.", "\n\nOne can approach this by considering some general principles a\ncorrespondence theory might want to add to its central principle to\nflesh out her theory. The first such principle says that the\ncorrespondence relation must not collapse into\nidentity—“It takes two to make a truth” (Austin\n1950, p. 118):", "\nNonidentity: No truth is identical with a fact\ncorrespondence to which is sufficient for its being a truth.\n", "\n\nIt would be much simpler to say that no truth is identical with a\nfact. However, some authors, e.g. Wittgenstein 1921, hold that a\nproposition (Satz, his truthbearer) is itself a fact, though\nnot the same fact as the one that makes the proposition true (see also\nKing 2007). Nonidentity is usually taken for granted by correspondence\ntheorists as constitutive of the very idea of a correspondence\ntheory—authors who advance contrary arguments to the effect that\ncorrespondence must collapse into identity regard their arguments as\nobjections to any form of correspondence theory (cf. Moore 1901/02,\nFrege 1918-19, p. 60).", "\n\nConcerning the correspondence relation, two aspects can be\ndistinguished: correspondence as correlation\nand correspondence as isomorphism (cf. Pitcher 1964; Kirkham\n1992, chap. 4). Pertaining to the first aspect, familiar from\nmathematical contexts, a correspondence theorist is likely to adopt\nclaim (a), and some may in addition adopt claim (b),\nof:", "\nCorrelation:\n(a) Every truth corresponds to exactly one fact;\n(b) Different truths correspond to different facts.\n", "\n\nTogether, (a) and (b) say that correspondence is a\none-one relation. This seems needlessly strong, and it is not easy to\nfind real-life correspondence theorists who explicitly embrace part\n(b): Why shouldn’t different truths correspond to the\nsame fact, as long as they are not too different? Explicit commitment\nto (a) is also quite rare. However, correspondence theorists\ntend to move comfortably from talk about a given truth to talk\nabout the fact it corresponds to—a move that signals\ncommitment to (a).", "\n\nCorrelation does not imply anything about the inner nature of the\ncorresponding items. Contrast this with correspondence\nas isomorphism, which requires the corresponding items to\nhave the same, or sufficiently similar, constituent structure. This\naspect of correspondence, which is more prominent (and more notorious)\nthan the previous one, is also much more difficult to make\nprecise. Let us say, roughly, that a correspondence theorist may want\nto add a claim to her theory committing her to something like the\nfollowing:", "\nStructure: If an item of kind K corresponds to a certain\nfact, then they have the same or sufficiently similar structure: the\noverall correspondence between a true K and a fact is a matter of\npart-wise correspondences, i.e. of their having corresponding\nconstituents in corresponding places in the same structure, or in\nsufficiently similar structures.\n", "\nThe basic idea is that truthbearers and facts are both complex\nstructured entities: truthbearers are composed of (other truthbearers\nand ultimately of) words, or concepts; facts are composed of (other\nfacts or states of affairs and ultimately of) things, properties, and\nrelations. The aim is to show how the correspondence relation is\ngenerated from underlying relations between the ultimate constituents\nof truthbearers, on the one hand, and the ultimate constituents of\ntheir corresponding facts, on the other. One part of the project will\nbe concerned with these correspondence-generating relations: it will\nlead into a theory that addresses the question how simple words, or\nconcepts, can be about things, properties, and relations;\ni.e., it will merge with semantics or psycho-semantics (depending on\nwhat the truthbearers are taken to be). The other part of the project,\nthe specifically ontological part, will have to provide identity\ncriteria for facts and explain how their simple constituents combine\ninto complex wholes. Putting all this together should yield an\naccount of the conditions determining which truthbearers correspond to\nwhich facts.", "\n\nCorrelation and Structure reflect distinct aspects of\ncorrespondence. One might want to endorse the former without the\nlatter, though it is hard to see how one could endorse the latter\nwithout embracing at least part (a) of the former.", "\n\nThe isomorphism approach offers an answer to objection 3.C1. Although\nthe truth that the cat is on the mat does not resemble the cat or the\nmat (the truth doesn’t meow or smell, etc.), it does resemble\nthe fact that the cat is on the mat. This is not a\nqualitative resemblance; it is a more abstract, structural\nresemblance.", "\n\nThe approach also puts objection 3.C2 in some perspective. The\ncorrespondence relation is supposed to reduce to underlying relations\nbetween words, or concepts, and reality. Consequently, a\ncorrespondence theory is little more than a spin-off from semantics\nand/or psycho-semantics, i.e. the theory of intentionality construed\nas incorporating a representational theory of the mind (cf. Fodor\n1989). This reminds us that, as a relation, correspondence is no\nmore—but also no less—mysterious than semantic relations\nin general. Such relations have some curious features, and they raise\na host of puzzles and difficult questions—most notoriously: Can\nthey be explained in terms of natural (causal) relations, or do they\nhave to be regarded as irreducibly non-natural aspects of reality?\nSome philosophers have claimed that semantic relations are too\nmysterious to be taken seriously, usually on the grounds that they are\nnot explainable in naturalistic terms. But one should bear in mind\nthat this is a very general and extremely radical attack on semantics\nas a whole, on the very idea that words and concepts can\nbe about things. The common practice to aim this attack\nspecifically at the correspondence theory seems misleading. As far as\nthe intelligibility of the correspondence relation is concerned, the\ncorrespondence theory will stand, or fall, with the general theory of\nreference and intentionality.", "\n\nIt should be noted, though, that these points concerning objections\n3.C1 and 3.C2 are not independent of one’s views about the\nnature of the primary truthbearers. If truthbearers are taken\nto be sentences of an ordinary language (or an idealized version\nthereof), or if they are taken to be mental representations (sentences\nof the language of thought), the above points hold without\nqualification: correspondence will be a semantic or psycho-semantic\nrelation. If, on the other hand, the primary truthbearers are taken to\nbe propositions, there is a complication:", "\n\nBut Russellians don’t usually renounce the correspondence theory\nentirely. Though they have no room for (1) from Section 3, when\napplied to propositions as truthbearers, correspondence will enter\ninto their account of truth for sentences, public or mental. The\naccount will take the form of Section 3’s (2), applied to\ncategories of truthbearers other than propositions, where Russellian\npropositions show up on the right-hand side in the guise of states of\naffairs that obtain or fail to obtain. Commitment to states of affairs\nin addition to propositions is sometimes regarded with scorn, as a\ngratuitous ontological duplication. But Russellians are not committed\nto states of affairs in addition to propositions, for\npropositions, on their view, must already be states of\naffairs. This conclusion is well nigh inevitable, once true\npropositions have been identified with facts. If a true proposition is\na fact, then a false proposition that might have been true would have\nbeen a fact, if it had been true. So, a (contingent) false proposition\nmust be the same kind of being as a fact, only not a fact—an\nunfact; but that just is a non-obtaining state of affairs under a\ndifferent name. Russellian propositions are states of affairs: the\nfalse ones are states of affairs that do not obtain, and the true ones\nare states of affairs that do obtain.", "\n\nThe Russellian view of propositions is popular nowadays. Somewhat\ncuriously, contemporary Russellians hardly ever refer to propositions\nas facts or states of affairs. This is because they are much concerned\nwith understanding belief, belief attributions, and the semantics of\nsentences. In such contexts, it is more natural to talk\nproposition-language than state-of-affairs-language. It feels odd\n(wrong) to say that someone believes a state of affairs, or that\nstates of affairs are true or false. For that matter, it also feels\nodd (wrong) to say that some propositions are facts, that facts are\ntrue, and that propositions obtain or fail to obtain. Nevertheless,\nall of this must be the literal truth, according to the\nRussellians. They have to claim that “proposition” and\n“state of affairs”, much like “evening star”\nand “morning star”, are different names for the same\nthings—they come with different associations and are at home in\nsomewhat different linguistic environments, which accounts for the\nfelt oddness when one name is transported to the other’s\nenvironment.", "\n\nReturning to the isomorphism approach in general, on a strict or\nnaïve implementation of this approach, correspondence will be a\none-one relation between truths and corresponding facts, which leaves\nthe approach vulnerable to objections against funny facts (3.F1): each\ntrue truthbearer, no matter how complex, will be assigned a matching\nfact. Moreover, since a strict implementation of isomorphism assigns\ncorresponding entities to all (relevant) constituents of truthbearers,\ncomplex facts will contain objects corresponding to the logical\nconstants (“not”, “or”, “if-then”,\netc.), and these “logical objects” will have to be\nregarded as constituents of the world. Many philosophers have found it\nhard to believe in the existence of all these funny facts and funny\nquasi-logical objects.", "\n\nThe isomorphism approach has never been advocated in a fully\nnaïve form, assigning corresponding objects to each and every\nwrinkle of our verbal or mental utterings. Instead, proponents try to\nisolate the “relevant” constituents of truthbearers\nthrough meaning analysis, aiming to uncover the logical form,\nor deep structure, behind ordinary language and thought. This deep\nstructure might then be expressed in an ideal-language\n(typically, the language of predicate logic), whose syntactic\nstructure is designed to mirror perfectly the ontological structure of\nreality. The resulting view—correspondence as isomorphism\nbetween properly analyzed truthbearers and facts—avoids\nassigning strange objects to such phrases as “the average\nhusband”, “the sake of”, and “the present king\nof France”; but the view remains committed to logically complex\nfacts and to logical objects corresponding to the logical\nconstants.", "\n\nAustin (1950) rejects the isomorphism approach on the grounds that it\nprojects the structure of our language onto the world. On his version\nof the correspondence theory (a more elaborated variant of (4) applied\nto statements), a statement as a whole is correlated to a state of\naffairs by arbitrary linguistic conventions without mirroring the\ninner structure of its correlate (cf. also Vision 2004). This approach\nappears vulnerable to the objection that it avoids funny facts at the\nprice of neglecting systematicity. Language does not provide separate\nlinguistic conventions for each statement: that would require too vast\na number of conventions. Rather, it seems that the truth-values of\nstatements are systematically determined, via a relatively small set\nof conventions, by the semantic values (relations to reality) of their\nsimpler constituents. Recognition of this systematicity is built right\ninto the isomorphism approach.", "\n\nCritics frequently echo Austin’s\n“projection”-complaint, 3.F2, that a traditional\ncorrespondence theory commits “the error of reading back into\nthe world the features of language” (Austin 1950, p. 155;\ncf. also, e.g., Rorty 1981). At bottom, this is a pessimistic stance:\nif there is a prima facie structural resemblance between a mode of\nspeech or thought and some ontological category, it is inferred,\npessimistically, that the ontological category is an illusion, a\nmatter of us projecting the structure of our language or thought into\nthe world. Advocates of traditional correspondence theories can be\nseen as taking the opposite stance: unless there are specific reasons\nto the contrary, they are prepared to assume, optimistically, that the\nstructure of our language and/or thought reflects genuine ontological\ncategories, that the structure of our language and/or thought is, at\nleast to a significant extent, the way it is because of the\nstructure of the world." ], "section_title": "6. Correspondence as Isomorphism", "subsections": [] }, { "main_content": [], "section_title": "7. Modified Versions of the Correspondence Theory", "subsections": [ { "content": [ "\n\nWittgenstein (1921) and Russell (1918) propose modified fact-based\ncorrespondence accounts of truth as part of their program of\nlogical atomism. Such accounts proceed in two stages. At the\nfirst stage, the basic truth-definition, say (1) from Section 3,\nis restricted to a special subclass of truthbearers, the\nso-called elementary or atomic truthbearers, whose\ntruth is said to consist in their correspondence to (atomic) facts:\nif x is elementary, then x is true iff x\ncorresponds to some (atomic) fact. This restricted definition serves\nas the base-clause for truth-conditional recursion-clauses given at\nthe second stage, at which the truth-values of non-elementary, or\nmolecular, truthbearers are explained recursively in terms of\ntheir logical structure and the truth-values of their simpler\nconstituents. For example: a sentence of the form\n‘not-p’ is true iff ‘p’ is\nfalse; a sentence of the form ‘p and q’\nis true iff ‘p’ is true and\n‘q’ is true; a sentence of the form\n‘p or q’ is true iff\n‘p’ is true or ‘q’ is true,\netc. These recursive clauses (called “truth conditions”)\ncan be reapplied until the truth of a non-elementary, molecular\nsentence of arbitrary complexity is reduced to the truth or falsehood\nof its elementary, atomic constituents.", "\n\nLogical atomism exploits the familiar rules, enshrined in the\ntruth-tables, for evaluating complex formulas on the basis of their\nsimpler constituents. These rules can be understood in two different\nways: (a) as tracing the ontological relations\nbetween complex facts and constituent simpler facts, or (b)\nas tracing logico-semantic relations, exhibiting how the\ntruth-values of complex sentences can be explained in terms of their\nlogical relations to simpler constituent sentences together with the\ncorrespondence and non-correspondence of simple, elementary sentences\nto atomic facts. Logical atomism takes option (b).", "\n\nLogical atomism is designed to go with the ontological view that the\nworld is the totality of atomic facts (cf. Wittgenstein 1921, 2.04);\nthus accommodating objection 3.F2 by doing without funny facts: atomic\nfacts are all the facts there are—although real-life atomists\ntend to allow conjunctive facts, regarding them as mere aggregates of\natomic facts. An elementary truth is true because it corresponds to an\natomic fact: correspondence is still isomorphism, but it holds\nexclusively between elementary truths and atomic facts. There is no\nmatch between truths and facts at the level of non-elementary,\nmolecular truths; e.g., ‘p’, ‘p\nor q’, and ‘p or r’ might\nall be true merely because ‘p’ corresponds to a\nfact). The trick for avoiding logically complex facts lies\nin not assigning any entities to the logical\nconstants. Logical complexity, so the idea goes, belongs to the\nstructure of language and/or thought; it is not a feature of the\nworld. This is expressed by Wittgenstein in an often quoted passage\n(1921, 4.0312): “My fundamental idea is that the ‘logical\nconstants’ are not representatives; that there can be no\nrepresentatives of the logic of facts”; and also by\nRussell (1918, p. 209f.): “You must not look about the real\nworld for an object which you can call ‘or’, and say\n‘Now look at this. This is ‘or’’”.", "\n\nThough accounts of this sort are naturally classified as versions of\nthe correspondence theory, it should be noted that they are strictly\nspeaking in conflict with the basic forms presented in Section\n3. According to logical atomism, it is not the case that for\nevery truth there is a corresponding fact. It is, however, still the\ncase that the being true of every truth is explained in terms\nof correspondence to a fact (or non-correspondence to any fact)\ntogether with (in the case of molecular truths) logical notions\ndetailing the logical structure of complex truthbearers. Logical\natomism attempts to avoid commitment to logically complex, funny facts\nvia structural analysis of truthbearers. It should not be\nconfused with a superficially similar account maintaining that\nmolecular facts are ultimately constituted by atomic facts. The latter\naccount would admit complex facts, offering an ontological analysis of\ntheir structure, and would thus be compatible with the basic forms\npresented in Section 3, because it would be compatible with the claim\nthat for every truth there is a corresponding fact. (For more on\nclassical logical atomism, see Wisdom 1931-1933, Urmson 1953, and the\nentries on\nRussell's logical atomism\nand \nWittgenstein's logical atomism \nin this encyclopedia.)", "\n\nWhile Wittgenstein and Russell seem to have held that the constituents\nof atomic facts are to be determined on the basis of a priori\nconsiderations, Armstrong (1997, 2004) advocates an a\nposteriori form of logical atomism. On his view, atomic facts are\ncomposed of particulars and simple universals (properties and\nrelations). The latter are objective features of the world that ground\nthe objective resemblances between particulars and explain their\ncausal powers. Accordingly, what particulars and universals there are\nwill have to be determined on the basis of total science.", "\n\nProblems: Logical atomism is not easy to sustain and\nhas rarely been held in a pure form. Among its difficulties are the\nfollowing: (a) What, exactly, are the elementary\ntruthbearers? How are they determined? (b) There are\nmolecular truthbearers, such as subjunctives and counterfactuals, that\ntend to provoke the funny-fact objection but cannot be handled by\nsimple truth-conditional clauses, because their truth-values do not\nseem to be determined by the truth-values of their elementary\nconstituents. (c) Are there universal facts corresponding to\ntrue universal generalizations? Wittgenstein (1921) disapproves of\nuniversal facts; apparently, he wants to re-analyze universal\ngeneralizations as infinite conjunctions of their instances. Russell\n(1918) and Armstrong (1997, 2004) reject this analysis; they admit\nuniversal facts. (d) Negative truths are the most notorious\nproblem case, because they clash with an appealing principle, the\n“truthmaker principle” (cf. Section 8.5), which says that\nfor every truth there must be something in the world that makes it\ntrue, i.e., every true truthbearer must have a truthmaker. Suppose\n‘p’ is elementary. On the account given above,\n‘not-p’ is true iff ‘p’ is\nfalse iff ‘p’ does not correspond to any fact;\nhence, ‘not-p’, if true, is not made true by any\nfact: it does not seem to have a truthmaker. Russell finds himself\ndriven to admit negative facts, regarded by many as paradigmatically\ndisreputable portions of reality. Wittgenstein sometimes talks of\natomic facts that do not exist and calls their very nonexistence a\nnegative fact (cf. 1921, 2.06)—but this is hardly an atomic fact\nitself. Armstrong (1997, chap. 8.7; 2004, chaps. 5-6) holds that\nnegative truths are made true by a second-order “totality\nfact” which says of all the (positive) first-order facts that\nthey are all the first-order facts.", "\n\nAtomism and the Russellian view of propositions (see\nSection 6). By the time Russell advocated logical atomism (around\n1918), he had given up on what is now referred to as the Russellian\nconception of propositions (which he and G. E. Moore held around\n1903). But Russellian propositons are popular nowadays. Note that\nlogical atomism is not for the friends of Russellian\npropositions. The argument is straightforward. We have logically\ncomplex beliefs some of which are true. According to the friends of\nRussellian propositions, the contents of our beliefs are Russellian\npropositions, and the contents of our true beliefs are true Russellian\npropositions. Since true Russellian propositions are facts, there must\nbe at least as many complex facts as there are true beliefs with\ncomplex contents (and at least as many complex states of affairs as\nthere are true or false beliefs with complex contents). Atomism may\nwork for sentences, public or mental, and for Fregean propositions;\nbut not for Russellian propositions.", "\n\nLogical atomism is designed to address objections to funny facts\n(3.F1). It is not designed to address objections to facts in general\n(3.F2). Here logical atomists will respond by defending (atomic)\nfacts. According to one defense, facts are needed because mere\nobjects are not sufficiently articulated to serve as\ntruthmakers. If a were the sole truthmaker of\n‘a is F’, then the latter should imply\n‘a is G’, for any\n‘G’. So the truthmaker for ‘a\nis F’ needs at least to involve a\nand Fness. But since Fness is a universal, it could\nbe instantiated in another object, b, hence the mere\nexistence of a and Fness is not sufficient for\nmaking true the claim ‘a\nis F’: a and Fness need to be tied\ntogether in the fact of a’s being F. Armstrong (1997)\nand Olson (1987) also maintain that facts are needed to make sense of\nthe tie that binds particular objects to universals.", "\n\nIn this context it is usually emphasized that facts do not\nsupervene on, hence, are not reducible to, their constituents.\nFacts are entities over and above the particulars and\nuniversals of which they are composed: a’s loving b\nand b’s loving a are not the same fact even though they\nhave the very same constituents.", "\n\nAnother defense of facts, surprisingly rare, would point out that many\nfacts are observable: one can see that the cat is on the mat;\nand this is different from seeing the cat, or the mat, or both. The\nobjection that many facts are not observable would invite the\nrejoinder that many objects are not observable either. (See Austin\n1961, Vendler 1967, chap. 5, and Vision 2004, chap. 3, for more\ndiscussion of anti-fact arguments; see also the\nentry facts in this encyclopedia.)", "\n\nSome atomists propose an atomistic version of definition (1), but\nwithout facts, because they regard facts as slices of reality too\nsuspiciously sentence-like to be taken with full ontological\nseriousness. Instead, they propose events and/or objects-plus-tropes\n(a.k.a. modes, particularized qualities, moments) as the corresponding\nportions of reality. It is claimed that these items are more\n“thingy” than facts but still sufficiently\narticulated—and sufficiently abundant—to serve as adequate\ntruthmakers (cf. Mulligan, Simons, and Smith 1984)." ], "subsection_title": "7.1 Logical Atomism" }, { "content": [ "\n\nLogical atomism aims at getting by without logically complex\ntruthmakers by restricting definitions like (1) or (2) from Section 3\nto elementary truthbearers and accounting for the truth-values of\nmolecular truthbearers recursively in terms of their logical structure\nand atomic truthmakers (atomic facts, events,\nobjects-plus-tropes). More radical modifications of the correspondence\ntheory push the recursive strategy even further, entirely discarding\ndefinitions like (1) or (2), and hence the need for atomic\ntruthmakers, by going, as it were,\n“subatomic”.", "\n\nSuch accounts analyze truthbearers, e.g., sentences, into their\nsubsentential constituents and dissolve the relation of correspondence\ninto appropriate semantic subrelations: names refer to, or\ndenote, objects; predicates (open sentences) apply to, or are\nsatisfied by objects. Satisfaction of complex predicates can\nbe handled recursively in terms of logical structure and satisfaction\nof simpler constituent predicates: an object o satisfies\n‘x is not F’ iff o does not\nsatisfy ‘x is F’; o satisfies\n‘x is F or x is G’\niff o satisfies ‘x is F’\nor o satisfies ‘x is G’; and so\non. These recursions are anchored in a base-clause addressing the\nsatisfaction of primitive predicates: an object o\nsatisfies ‘x is F’ iff o\ninstantiates the property expressed by ‘F’. Some\nwould prefer a more nominalistic base-clause for satisfaction, hoping\nto get by without seriously invoking properties. Truth for singular\nsentences, consisting of a name and an arbitrarily complex predicate,\nis defined thus: A singular sentence is true iff the object denoted by\nthe name satisfies the predicate. Logical machinery provided by Tarski\n(1935) can be used to turn this simplified sketch into a more general\ndefinition of truth—a definition that handles sentences\ncontaining relational predicates and quantifiers and covers molecular\nsentences as well. Whether Tarski’s own definition of truth can\nbe regarded as a correspondence definition, even in this modified\nsense, is under debate (cf. Popper 1972; Field 1972, 1986; Kirkham\n1992, chaps. 5-6; Soames 1999; Künne 2003, chap. 4; Patterson\n2008.)", "\n\nSubatomism constitutes a return to (broadly) object-based\ncorrespondence. Since it promises to avoid facts and all similarly\narticulated, sentence-like slices of reality, correspondence theorists\nwho take seriously objection 3.F2 favor this approach: not even\nelementary truthbearers are assigned any matching truthmakers. The\ncorrespondence relation itself has given way to two semantic relations\nbetween constituents of truthbearers and objects: reference (or\ndenotation) and satisfaction—relations central to any semantic\ntheory. Some advocates envision causal accounts of reference and\nsatisfaction (cf. Field 1972; Devitt 1982, 1984; Schmitt 1995;\nKirkham 1992, chaps. 5-6). It turns out that relational predicates\nrequire talk of satisfaction by ordered sequences of\nobjects. Davidson (1969, 1977) maintains that satisfaction by\nsequences is all that remains of the traditional idea of\ncorrespondence to facts; he regards reference and satisfaction as\n“theoretical constructs” not in need of causal, or any,\nexplanation.", "\n\nProblems: (a) The subatomistic approach\naccounts for the truth-values of molecular truthbearers in the same\nway as the atomistic approach; consequently, molecular truthbearers\nthat are not truth-functional still pose the same problems as in\natomism. (b) Belief attributions and modal claims pose\nspecial problems; e.g., it seems that “believes” is a\nrelational predicate, so that “John believes that snow is\nwhite” is true iff “believes” is satisfied by John\nand the object denoted by “that snow is white”; but the\nlatter appears to be a proposition or state of affairs, which\nthreatens to let in through the back-door the very sentence-like\nslices of reality the subatomic approach was supposed to avoid, thus\nundermining the motivation for going subatomic. (c) The\nphenomenon of referential indeterminacy threatens to undermine the\nidea that the truth-values of elementary truthbearers are always\ndetermined by the denotation and/or satisfaction of their\nconstituents; e.g., pre-relativistic uses of the term\n“mass” are plausibly taken to lack determinate reference\n(referring determinately neither to relativistic mass nor to rest\nmass); yet a claim like “The mass of the earth is greater than\nthe mass of the moon” seems to be determinately true even when\nmade by Newton (cf. Field 1973).", "\n\nProblems for both versions of modified correspondence\ntheories: (a) It is not known whether an entirely\ngeneral recursive definition of truth, one that covers all\ntruthbearers, can be made available. This depends on unresolved issues\nconcerning the extent to which truthbearers are amenable to the kind\nof structural analyses that are presupposed by the recursive\nclauses. The more an account of truth wants to exploit the internal\nstructure of truthbearers, the more it will be hostage to the\n(limited) availability of appropriate structural analyses of the\nrelevant truthbearers. (b) Any account of truth employing a\nrecursive framework may be virtually committed to taking sentences\n(maybe sentences of the language of thought) as primary\ntruthbearers. After all, the recursive clauses rely heavily on what\nappears to be the logico-syntactic structure of truthbearers, and it\nis unclear whether anything but sentences can plausibly be said to\npossess that kind of structure. But the thesis that sentences of any\nsort are to be regarded as the primary truthbearers is\ncontentious. Whether propositions can meaningfully be said to have an\nanalogous (albeit non-linguistic) structure is under debate\n(cf. Russell 1913, King 2007). (c) If clauses like\n“‘p or q’ is true iff\n‘p’ is true or ‘q’ is\ntrue” are to be used in a recursive account of our\nnotion of truth, as opposed to some other notion, it has to\nbe presupposed that ‘or’ expresses disjunction:\none cannot define “or” and “true” at the same\ntime. To avoid circularity, a modified correspondence theory (be it\natomic or subatomic) must hold that the logical connectives can be\nunderstood without reference to correspondence truth." ], "subsection_title": "7.2 Logical “Subatomism”" }, { "content": [ "\n\nDefinitions like (1) and (2) from Section 3 assume, naturally, that\ntruthbearers are true because they, the truthbearers themselves,\ncorrespond to facts. There are however views that reject this natural\nassumption. They propose to account for the truth of truthbearers of\ncertain kinds, propositions, not by way of their\ncorrespondence to facts, but by way of the correspondence to facts of\nother items, the ones that have propositions as their\ncontents. Consider the state of believing that p (or the\nactivity of judging that p). The state (the\nactivity) is not, strictly speaking, true or false; rather, what is\ntrue or false is its content, the proposition\nthat p. Nevertheless, on the present view, it is the state of\nbelieving that p that corresponds or fails to correspond to a\nfact. So truth/falsehood for propositions can be defined in the\nfollowing manner: x is a true/false proposition iff there is\na belief state B such that x is the content\nof B and B corresponds/fails to correspond to a\nfact.", "\n\nSuch a modification of fact-based correspondence can be found in Moore\n(1927, p. 83) and Armstrong (1973, 4.iv & 9). It can be adapted to\natomistic (Armstrong) and subatomistic views, and to views on which\nsentences (of the language of thought) are the primary bearers of\ntruth and falsehood. However, by taking the content-carrying states as\nthe primary corresponders, it entails that there are no\ntruths/falsehoods that are not believed by someone. Most advocates of\npropositions as primary bearers of truth and falsehood will regard\nthis as a serious weakness, holding that there are very many true and\nfalse propositions that are not believed, or even entertained, by\nanyone. Armstrong (1973) combines the view with an instrumentalist\nattitude towards propositions, on which propositions are mere\nabstractions from mental states and should not be taken seriously,\nontologically speaking." ], "subsection_title": "7.3 Relocating Correspondence" } ] }, { "main_content": [], "section_title": "8. The Correspondence Theory and Its Competitors", "subsections": [ { "content": [ "\n\nAgainst the traditional competitors—coherentist,\npragmatist, and verificationist and other epistemic theories of\ntruth—correspondence theorists raise two main sorts of\nobjections. First, such accounts tend to lead into\nrelativism. Take, e.g., a coherentist account of truth. Since it is\npossible that ‘p’ coheres with the belief system\nof S while ‘not-p’ coheres with the\nbelief system of S*, the coherentist account seems to imply,\nabsurdly, that contradictories, ‘p’ and\n‘not-p’, could both be true. To avoid embracing\ncontradictions, coherentists often commit themselves (if only\ncovertly) to the objectionable relativistic view that\n‘p’ is true-for-S and\n‘not-p’ is true-for-S*. Second,\nthe accounts tend to lead into some form of idealism or anti-realism,\ne.g., it is possible for the belief that p to cohere with\nsomeone’s belief system, even though it is not a fact that\np; also, it is possible for it to be a fact that p,\neven if no one believes that p at all or if the belief does\nnot cohere with anyone’s belief system. Cases of this sort are\nfrequently cited as counterexamples to coherentist accounts of\ntruth. Dedicated coherentists tend to reject such counterexamples,\ninsisting that they are not possible after all. Since it is hard to\nsee why they would not be possible, unless its being a fact that\np were determined by the belief’s coherence with other\nbeliefs, this reaction commits them to the anti-realist view that the\nfacts are (largely) determined by what we believe.", "\n\nThis offers a bare outline of the overall shape the debates tend to\ntake. For more on the correspondence theory vs. its traditional\ncompetitors see, e.g., Vision 1988; Kirkham 1992, chaps. 3, 7-8;\nSchmitt 1995; Künne 2003, chap. 7; and essays in Lynch\n2001. Walker 1989 is a book-lenght discussion of coherence theories of\ntruth. See also the entries on\n pragmatism,\n relativism,\n the coherence theory of truth, \nin this encyclopedia." ], "subsection_title": "8.1 Traditional Competitors" }, { "content": [ "\n\nThe correspondence theory is sometimes accused of overreaching itself:\nit does apply, so the objection goes, to truths from some domains of\ndiscourse, e.g., scientific discourse and/or discourse about everyday\nmidsized physical things, but not to truths from various other domains\nof discourse, e.g., ethical and/or aesthetic discourse (see the first\nobjection in Section 5 above). Alethic pluralism grows out of\nthis objection, maintaining that truth is constituted by\ndifferent properties for true propositions from different domains of\ndiscourse: by correspondence to fact for true propositions from the\ndomain of scientific or everyday discourse about physical things; by\nsome epistemic property, such as coherence or superassertibility, for\ntrue propositions from the domain of ethical and aesthetic discourse,\nand maybe by still other properties for other domains of\ndiscourse. This suggests a position on which the term\n“true” is multiply ambiguous, expressing different\nproperties when applied to propositions from different\ndomains. However, contemporary pluralists reject this problematic\nidea, maintaining instead that truth is “multiply\nrealizable”. That is, the term “true” is univocal,\nit expresses one concept or property, truth (being true), but one that\ncan be realized by or manifested in different\nproperties (correspondence to fact, coherence or superassertibility,\nand maybe others) for true propositions from different domains of\ndiscourse. Truth itself is not to be identified with any of its\nrealizing properties. Instead, it is characterized, quasi\naxiomatically, by a set of alleged “platitudes”,\nincluding, according to Crispin Wright’s (1999) version,\n“transparency” (to assert is to present as true),\n“contrast” (a proposition may be true without being\njustified, and v.v.), “timelesness” (if a proposition is\never true, then it always is), “absoluteness” (there is no\nsuch thing as a proposition being more or less true), and others.", "Though it contains the correspondence theory as one ingredient,\nalethic pluralism is nevertheless a genuine competitor, for it rejects\nthe thesis that truth is correspondence to reality. Moreover,\nit equally contains competitors of the correspondence theory as\nfurther ingredients.", "\n\nAlethic pluralism in its contemporary form is a relatively young\nposition. It was inaugurated by Crispin Wright (1992; see also 1999)\nand was later developed into a somewhat different form by Lynch\n(2009). Critical discussion is still at a relatively nascent stage\n(but see Vision 2004, chap. 4, for extended discussion of Wright). It\nwill likely focus on two main problem areas.", "\n\nFirst, it seems difficult to sort propositions into distinct\nkinds according to the subject matter they are about. Take, e.g., the\nproposition that killing is morally wrong, or the proposition that\nimmoral acts happen in space-time. What are they about? Intuitively,\ntheir subject matter is mixed, belonging to the physical domain, the\nbiological domain, and the domain of ethical discourse. It is hard to\nsee how pluralism can account for the truth of such mixed\npropositions, belonging to more than one domain of discourse: What\nwill be the realizing property?", "\n\nSecond, pluralists are expected to explain how the platitudes\ncan be “converted” into an account of truth itself. Lynch\n(2009) proposes to construe truth as a functional property,\ndefined in terms of a complex functional role which is given\nby the conjunction of the platitudes (somewhat analogous to the way in\nwhich functionalists in the philosophy of mind construe mental states\nas functional states, specified in terms of their functional\nroles—though in their case the relevant functional roles are\ncausal roles, which is not a feasible option when it comes to the\ntruth-role). Here the main issue will be to determine (a)\nwhether such an account really works, when the technical details are\nlaid out, and (b) whether it is plausible to claim that\nproperties as different as correspondence to a fact, on the one hand,\nand coherence or superassertibilty, on the other, can be said to play\none and the same role—a claim that seems required by the thesis\nthat these different properties all realize the same property, being\ntrue.", "\n\nFor more on pluralism, see e.g. the essays in Monnoyer (2007) and in\nPedersen & Wright (2013); and the entry on\n pluralist theories of truth \n in this encyclopedia." ], "subsection_title": "8.2 Pluralism" }, { "content": [ "\n\nAccording to the identity theory of truth, true propositions\ndo not correspond to facts, they are facts: the true\nproposition that snow is white = the fact that snow is white. This\nnon-traditional competitor of the correspondence theory threatens to\ncollapse the correspondence relation into identity. (See Moore\n1901-02; and Dodd 2000 for a book-length defense of this theory and\ndiscussion contrasting it with the correspondence theory; and see the\nentry\n the identity theory of truth: \n in this encyclopedia.)", "\n\nIn response, a correspondence theorist will point out: (a)\nThe identity theory is defensible only for propositions as\ntruthbearers, and only for propositions construed in a certain way,\nnamely as having objects and properties as constituents rather than\nideas or concepts of objects and properties; that is, for Russellian\npropositions. Hence, there will be ample room (and need) for\ncorrespondence accounts of truth for other types of truthbearers,\nincluding propositions, if they are construed as constituted, partly\nor wholly, of concepts of objects and\nproperties. (b) The identity theory is committed to the\nunacceptable consequence that facts are true. (c) The\nidentity theory rests on the assumption that that-clauses always\ndenote propositions, so that the that-clause in “the fact that\nsnow is white” denotes the proposition that snow is white. The\nassumption can be questioned. That-clauses can be understood as\nambiguous names, sometimes denoting propositions and sometimes\ndenoting facts. The descriptive phrases “the\nproposition…” and “the fact…” can be\nregarded as serving to disambiguate the succeeding ambiguous\nthat-clauses—much like the descriptive phrases in “the\nphilosopher Socrates” and “the soccer-player\nSocrates” serve to disambiguate the ambiguous name\n“Socrates” (cf. David 2002)." ], "subsection_title": "8.3 The Identity Theory of Truth" }, { "content": [ "\n\nAt present the most noticeable competitors to correspondence theories\nare deflationary accounts of truth (or\n‘true’). Deflationists maintain that correspondence\ntheories need to be deflated; that their central notions,\ncorrespondence and fact (and their relatives), play no legitimate role\nin an adequate account of truth and can be excised without loss. A\ncorrespondence-type formulation like", "(5) “Snow is white” is true iff it corresponds\nto the fact that snow is white,", "\n\nis to be deflated to", "(6) “Snow is white” is true iff snow is\nwhite,", "\n\nwhich, according to deflationists, says all there is to be said about\nthe truth of “Snow is white”, without superfluous\nembellishments (cf. Quine 1987, p. 213).", "\n\nCorrespondence theorists protest that (6) cannot lead to anything\ndeserving to be regarded as an account of truth. It is concerned with\nonly one particular sentence (“Snow is white”), and it\nresists generalization. (6) is a substitution instance of the\nschema", "(7) “p” is true iff\np,", "\n\nwhich does not actually say anything itself (it is not\ntruth-evaluable) and cannot be turned into a genuine generalization\nabout truth, because of its essential reliance on the schematic letter\n“p”, a mere placeholder. The attempt to turn (7) into a\ngeneralization produces nonsense along the lines of “For\nevery x, “x” is true\niff x”, or requires invocation of truth: “Every\nsubstitution instance of the schema ““p” is true iff\np” is true”. Moreover, no genuine generalizations\nabout truth can be accounted for on the basis of (7). Correspondence\ndefinitions, on the other hand, do yield genuine generalizations about\ntruth. Note that definitions like (1) and (2) in Section 3 employ\nordinary objectual variables (not mere schematic placeholders); the\ndefinitions are easily turned into genuine generalizations by\nprefixing the quantifier phrase “For every x”,\nwhich is customarily omitted in formulations intended as\ndefinitions.", "\n\nIt should be noted that the deflationist’s starting point, (5),\nwhich lends itself to deflating excisions, actually misrepresents the\ncorrespondence theory. According to (5), corresponding to the fact\nthat snow is white is sufficient and necessary for\n“Snow is white” to be true. Yet, according to (1) and (2),\nit is sufficient but not necessary: “Snow is white” will\nbe true as long as it corresponds to some fact or other. The genuine\narticle, (1) or (2), is not as easily deflated as the impostor\n(5).", "\n\nThe debate turns crucially on the question whether anything deserving\nto be called an “account” or “theory” of truth\nought to take the form of a genuine generalization (and ought to be\nable to account for genuine generalizations involving\ntruth). Correspondence theorists tend to regard this as a (minimal)\nrequirement. Deflationists argue that truth is a shallow (sometimes\n“logical”) notion—a notion that has no serious\nexplanatory role to play: as such it does not require a full-fledged\naccount, a real theory, that would have to take the form of a genuine\ngeneralization.", "\n\nThere is now a substantial body of literature on truth-deflationism in\ngeneral and its relation to the correspondence theory in particular;\nthe following is a small selection: Quine 1970, 1987; Devitt 1984;\nField 1986; Horwich 1990 & 19982; Kirkham 1992; Gupta\n1993; David 1994, 2008; Schmitt 1995; Künne 2003, chap. 4; Rami\n2009. Relevant essays are contained in Blackburn and Simmons 1999;\nSchantz 2002; Armour-Garb and Beall 2005; and Wright and Pedersen\n2010. See also the entry\n the deflationary theory of truth \nin this encyclopedia." ], "subsection_title": "8.4 Deflationism About Truth" }, { "content": [ "\n\nThis approach centers on the truthmaker\nor truthmaking principle: Every truth has a\ntruthmaker; or alternatively: For every truth there is something that\nmakes it true. The principle is usually understood as an expression of\na realist attitude, emphasizing the crucial contribution the world\nmakes to the truth of a proposition. Advocates tend to treat\ntruthmaker theory primarily as a guide to ontology, asking: To\nentities of what ontological categories are we committed as\ntruthmakers of the propositions we accept as true? Most advocates\nmaintain that propositions of different logical types can be made true\nby items from different ontological categories: e.g., propositions of\nsome types are made true by facts, others just by individual things,\nothers by events, others by tropes (cf., e.g. Armstrong 1997). This is\nclaimed as a significant improvement over traditional correspondence\ntheories which are understood—correctly in most but by no means\nall cases—to be committed to all truthmakers belonging to a\nsingle ontological category (albeit disagreeing about which category\nthat is). All advocates of truthmaker theory maintain that the\ntruthmaking relation is not one-one but many-many: some truths are\nmade true by more than one truthmaker; some truthmakers make true more\nthan one truth. This is also claimed as a significant improvement over\ntraditional correspondence theories which are often portrayed as\ncommitted to correspondence being a one-one relation. This portrayal\nis only partly justified. While it is fairly easy to find real-life\ncorrespondence theorists committing themselves to the view that each\ntruth corresponds to exactly one fact (at least by implication,\ntalking about the corresponding fact), it is difficult to\nfind real-life correspondence theorists committing themselves to the\nview that only one truth can correspond to a given fact (but see Moore\n1910-11, p. 256).", "\n\nA truthmaker theory may be presented as a competitor to the\ncorrespondence theory or as a version of the correspondence\ntheory. This depends considerably on how narrowly or broadly one\nconstrues “correspondence theory”, i.e. on terminological\nissues. Some advocates would agree with Dummett (1959, p. 14) who said\nthat, although “we have nowadays abandoned the correspondence\ntheory of truth”, it nevertheless “expresses one important\nfeature of the concept of truth…: that a statement is true only\nif there is something in the world in virtue of which it is\ntrue”. Other advocates would follow Armstrong who tends to\npresent his truthmaker theory as a liberal form of correspondence\ntheory; indeed, he seems committed to the view that the truth of a\n(contingent) elementary proposition consists in its\ncorrespondence with some (atomic) fact (cf. Armstrong 1997; 2004,\npp. 22-3, 48-50).", "\n\nIt is not easy to find a substantive difference between truthmaker\ntheory and various brands of the sort of modified correspondence\ntheory treated above under the heading “Logical Atomism”\n(see Section 7.1). Logical atomists, such as Russell (1918) and\nWittgenstein (1921), will hold that the truth or falsehood of every\ntruth-value bearer can be explained in terms of (can be derived from)\nlogical relations between truth-value bearers, by way of the recursive\nclauses, together with the base clauses, i.e., the correspondence and\nnon-correspondence of elementary truth-value bearers with facts. This\nrecursive strategy could be pursued with the aim to reject the\ntruthmaker principle: not all truths have truthmakers, only\nelementary truths have truthmakers (here understood as corresponding\natomic facts). But it could also be pursued—and this seems to\nhave been Russell’s intention at the time—with the aim\nto secure the truthmaker principle, even though the simple\ncorrespondence definition has been abandoned: not every truth\ncorresponds to a fact, only elementary truths do, but every\ntruth has a truthmaker; where the recursive clauses are\nsupposed to show how truthmaking without correspondence, but grounded\nin correspondence, comes about.", "\n\nThere is one straightforward difference between truthmaker theory and\nmost correspondence theories. The latter are designed to answer the\nquestion “What is truth?”. Simple (unmodified)\ncorrespondence theories center on a biconditional, such as\n“x is true iff x corresponds to a fact”,\nintended to convey a definition of truth (at least a\n“real definition” which does not commit them to the claim\nthat the term “true” is synonymous with “corresponds\nto a fact”—especially nowadays most correspondence\ntheorists would consider such a claim to be implausibly and\nunnecessarily bold). Modified correspondence theories also aim at\nproviding a definition of truth, though in their case the definition\nwill be considerably more complex, owing to the recursive character of\nthe account. Truthmaker theory, on the other hand, centers on\nthe truthmaker principle: For every truth there is something\nthat makes it true. Though this principle will deliver the\nbiconditional “x is true iff something makes x\ntrue” (since “something makes x true”\ntrivially implies “x is true”), this does not\nyield a promising candidate for a definition of truth: defining truth\nin terms of truthmaking would appear to be circular. Unlike most\ncorrespondence theories, truthmaker theory is not equipped, and\nusually not designed, to answer the question “What is\ntruth?”—at least not if one expects the answer to take the\nform of a feasible candidate for a definition of truth.", "\n\nThere is a growing body of literature on truthmaker theory; see for\nexample: Russell 1918; Mullligan, Simons, and Smith 1984; Fox 1987;\nArmstrong 1997, 2004; Merricks 2007; and the essays in Beebe and Dodd\n2005; Monnoyer 2007; and in Lowe and Rami 2009. See also the entry\non truthmakers in this encyclopedia." ], "subsection_title": "8.5 Truthmaker Theory" } ] }, { "main_content": [ "\n\nTwo final objections to the correspondence theory deserve separate\nmention." ], "section_title": "9. More Objections to the Correspondence Theory", "subsections": [ { "content": [ "\n\nInspired by an allegedly similar argument of Frege’s, Davidson\n(1969) argues that the correspondence theory is bankrupt because it\ncannot avoid the consequence that all true sentences correspond to the\nsame fact: the Big Fact. The argument is based on two crucial\nassumptions: (i) Logically equivalent sentences can be\nsubstituted salva veritate in the context ‘the fact\nthat...’; and (ii) If two singular terms denoting the same thing\ncan be substituted for each other in a given sentence salva\nveritate, they can still be so substituted if that sentence is\nembedded within the context ‘the fact that...’. In the\nversion below, the relevant singular terms will be the following:\n‘(the x such that x = Diogenes\n& p)’ and ‘(the x such\nthat x = Diogenes & q)’. Now, assume that\na given sentence, s, corresponds to the fact that p;\nand assume that ‘p’ and ‘q’\nare sentences with the same truth-value. We have:", "\n which, by (i), implies", " which, by (ii), implies", "\n which, by (i), implies", "\n\nSince the only restriction on ‘q’ was that it\nhave the same truth-value as ‘p’, it would follow\nthat any sentence s that corresponds to any fact corresponds\nto every fact; so that all true sentences correspond to the same\nfacts, thereby proving the emptiness of the correspondence\ntheory—the conclusion of the argument is taken as tantamount to\nthe conclusion that every true sentence corresponds to the totality of\nall the facts, i.e, the Big Fact, i.e., the world as a whole.", "\n\nThis argument belongs to a type now called “slingshot\narguments” (because a giant opponent is brought down by a single\nsmall weapon, allegedly). The first versions of this type of argument\nwere given by Church (1943) and Gödel (1944); it was later\nadapted by Quine (1953, 1960) in his crusade against quantified modal\nlogic. Davidson is offering yet another adaption, this time involving\nthe expression “corresponds to the fact that”. The\nargument has been criticized repeatedly. Critics point to the two\nquestionable assumptions on which it relies, (i) and (ii). It is far\nfrom obvious why a correspondence theorist should be tempted by either\none of them. Opposition to assumption (i) rests on the view that\nexpressibility by logically equivalent sentences may be a necessary,\nbut is not a sufficient condition for fact identity. Opposition to\nassumption (ii) rests on the observation that the (alleged) singular\nterms used in the argument are definite descriptions: their\nstatus as genuine singular terms is in doubt, and it is well-known\nthat they behave rather differently than proper names for which\nassumption (ii) is probably valid (cf. Follesdal 1966/2004; Olson\n1987; Künne 2003; and especially the extended discussion and\ncriticism in Neale 2001.)" ], "subsection_title": "9.1 The Big Fact" } ] } ]

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[ "\nDeflationism about truth, what is often simply called\n“deflationism”, is really not so much a theory of\ntruth in the traditional sense, as it is a different, newer sort\nof approach to the topic. Traditional theories of truth are part of a\nphilosophical debate about the nature of a supposed property of truth.\nPhilosophers offering such theories often make suggestions like the\nfollowing: truth consists in correspondence to the facts; truth\nconsists in coherence with a set of beliefs or propositions; truth is\nwhat is acceptable in the ideal limit of inquiry. According to\ndeflationists, such suggestions are mistaken, and, moreover, they all\nshare a common mistake. The common mistake is to assume that truth\nhas a nature of the kind that philosophers might find out\nabout and develop theories of. The main idea of the deflationary\napproach is (a) that all that can be significantly said about truth is\nexhausted by an account of the role of the expression\n‘true’ or of the concept of truth in our talk and thought,\nand (b) that, by contrast with what traditional views assume, this\nrole is neither metaphysically substantive nor explanatory. For\nexample, according to deflationary accounts, to say that ‘snow\nis white’ is true, or that it is true that snow is white, is in\nsome sense strongly equivalent to saying simply that snow is white,\nand this, according to the deflationary approach, is all that can be\nsaid significantly about the truth of ‘snow is white’.\nPhilosophers looking for some underlying nature of some truth property\nthat is attributed with the use of the expression ‘true’\nare bound to be frustrated, the deflationist says, because they are\nlooking for something that isn’t there.", "\nDeflationism comprises a variety of different versions, each of which\nhave gone by different names, including at least the following:\ndisquotationalism, minimalism, prosententialism, the redundancy\ntheory, the disappearance theory, the no-truth theory. There has not\nalways been terminological consensus in the literature about how to\nuse these labels: sometimes they have been used interchangeably;\nsometimes they have been used to mark distinctions between different\ndevelopments of the same general approach. The actual variety of\ndeflationary views has not always been clear in discussions of this\napproach, especially in the earlier literature, where important\ndifferences are occasionally missed. To help clear this up, we will\nuse ‘deflationism’ to denote the general approach we want\nto discuss and reserve other names for specific versions of that\napproach." ]

[ { "content_title": "1. Central Themes in Deflationism", "sub_toc": [ "1.1 The Equivalence Schema", "1.2 The Property of Truth", "1.3 The Utility of the Concept of Truth" ] }, { "content_title": "2. History of Deflationism", "sub_toc": [] }, { "content_title": "3. The Varieties of Contemporary Deflationism", "sub_toc": [ "3.1 Minimalism", "3.2 Disquotationalism", "3.3 Prosententialism" ] }, { "content_title": "4. Objections to Deflationism", "sub_toc": [ "4.1 The Explanatory Role of Truth", "4.2 Propositions Versus Sentences", "4.3 Correspondence", "4.4 Truth-Value Gaps", "4.5 The Generalization Problem", "4.6 Conservativeness", "4.7 Normativity", "4.8 Inflationist Deflationism?", "4.9 Truth and Meaning" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Central Themes in Deflationism", "subsections": [ { "content": [ "\nWhile deflationism can be developed in different ways, it is possible\nto isolate some central themes emphasized by most philosophers who\nthink of themselves as deflationists. These shared themes pertain to\nendorsing a kind of metaphysical parsimony and positing a\n“deflated” role for what we can call the alethic\nlocutions (most centrally, the expressions ‘true’ and\n‘false’) in the instances of what is often called\ntruth-talk. In this section, we will isolate three of these\nthemes. The first, and perhaps most overarching, one has already been\nmentioned: According to deflationists, there is some strong\nequivalence between a statement like ‘snow is white’ and a\nstatement like “‘snow is white’ is true,” and\nthis is all that can significantly be said about that application of\nthe notion of truth.", "\nWe may capture this idea more generally with the help of a schema,\nwhat is sometimes called the equivalence schema:", "\nIn this schema, the angle brackets indicate an appropriate\nname-forming or nominalizing device, e.g., quotation marks or\n‘the proposition that …’, and the occurrences of\n‘\\(p\\)’ are replaced with matching declarative sentences\nto yield instances of the schema.", "\nThe equivalence schema is often associated with the formal work of\n Alfred Tarski\n (1935 [1956], 1944), which introduced the schema,", "\nIn the instances of schema (T) (sometimes called “Convention\n(T)”), the ‘\\(X\\)’ gets filled in with a name of the\nsentence that goes in for the ‘\\(p\\)’, making (T) a\nversion of (ES). Tarski considered (T) to provide a criterion of\nadequacy for any theory of truth, thereby allowing that there could be\nmore to say about truth than what the instances of the schema cover.\nGiven that, together with the fact that he took the instances of (T)\nto be contingent, his theory does not qualify as deflationary.", "\nBy contrast with the Tarskian perspective on (T)/(ES), we can\nformulate the central theme of deflationism under consideration as the\nview, roughly, that the instances of (some version of) this schema do\ncapture everything significant that can be said about applications of\nthe notion of truth; in a slogan, the instances of the schema\nexhaust the notion of truth. Approaches which depart from\ndeflationism don’t disagree that (ES) tells us something about\ntruth; what they (with Tarski) deny is that it is exhaustive, that it\ntells us the whole truth about truth. Since such approaches add\nsubstantive explanations of why the instances of the equivalence\nschema hold, they are now often called inflationary\napproaches to truth. Inflationism is the general approach shared by\nsuch traditional views as the\n correspondence theory of truth,\n coherence theory of truth,\n pragmatic theory of truth,\n identity theory of truth, and primitivist theory of truth, These theories all share\na collection of connected assumptions about the alethic locutions, the\nconcept of truth, and the property of truth. Inflationary theories all\nassume that the expression ‘is true’ is a descriptive\npredicate, expressing an explanatory concept of truth, which\ndetermines a substantive property of truth. From that shared set of\npresuppositions, the various traditional inflationary theories then\ndiverge from one another by providing different accounts of the\nassumed truth property. On inflationary views, the nature of the truth\nproperty explains why the instances of (ES) hold. Deflationary views,\nby contrast, reject some if not all of the standard assumptions that\nlead to inflationary theories, resisting at least their move to\npositing any substantive truth property. Instead, deflationists offer\na different understanding of both the concept of truth and the\nfunctioning of the alethic locutions. A deflationist will take the\ninstances of (ES) to be “conceptually basic and explanatorily\nfundamental” (Horwich 1998a, 21, n. 4; 50), or to be direct\nconsequences of how the expression ‘true’ operates (cf.\nQuine 1970 [1986], Brandom 1988, and Field 1994a).", "\nIt is important to notice that even among deflationists the\nequivalence schema may be interpreted in different ways, and this is\none way to distinguish different versions of deflationism from one\nanother. One question about (ES) concerns the issue of what instances\nof the schema are assumed to be about (equivalently: to what the names\nin instances of (ES) are assumed to refer). According to one view, the\ninstances of this schema are about sentences, where a name for a\nsentence can be formulated simply by putting quotation marks around\nit. In other words, for those who hold what might be called a\nsententialist version of deflationism, the equivalence schema\nhas instances like (1):", "\nTo make this explicit, we might say that, according to sententialist\ndeflationism, the equivalence schema is:", "\nNotice that in this schema, the angle-brackets of (ES) have been\nreplaced by quotation marks.", "\nAccording to those who hold what might be called a\npropositionalist version of deflationism, by contrast,\ninstances of the equivalence schema are about propositions, where\nnames of propositions are, or can be taken to be, expressions of the\nform ‘the proposition that \\(p\\)’, where\n‘\\(p\\)’ is filled in with a declarative sentence. For the\npropositionalist, in other words, instances of the equivalence schema\nare properly interpreted not as being about sentences but instead as\nbeing about propositions, i.e., as biconditionals like (2) rather than\n(1):", "\nTo make this explicit, we might say that, according to\npropositionalist deflationism, the equivalence schema is:", "\nInterpreting the equivalence schema as (ES-sent) rather than as\n(ES-prop), or vice versa, thus yields different versions of\ndeflationism, sententialist and propositionalist versions,\nrespectively.", "\nAnother aspect that different readings of (ES) can vary across\nconcerns the nature of the equivalence that its instances assert. On\none view, the right-hand side and the left-hand side of such instances\nare synonymous or analytically equivalent. Thus, for sententialists\nwho endorse this level of equivalence, (1) asserts that,\n“‘Brutus killed Caesar’ is true” means just\nwhat ‘Brutus killed Caesar’ means; while for\npropositionalists who endorse analytic equivalence, (2) asserts that\n‘the proposition that Brutus killed Caesar is true’ means\nthe same as ‘Brutus killed Caesar’. A second view is that\nthe right-hand and left-hand sides of claims such as (1) and (2) are\nnot synonymous but are nonetheless necessarily equivalent; this view\nmaintains that the two sides of each equivalence stand or fall\ntogether in every possible world, despite having different meanings.\nAnd a third possible view is that claims such as (1) and (2) assert\nonly a material equivalence; this view interprets the ‘if and\nonly if’ in both (1) and (2) as simply the biconditional of\nclassical logic.", "\nThis tripartite distinction between analytic, necessary, and material\nequivalence, when combined with the distinction between sententialism\nand propositionalism, yields six different possible (although not\nexhaustive) readings of the instances of (ES):", "\nWhile different versions of deflationism can be correlated to some\nextent with different positions in this chart, some chart positions\nhave also been occupied by more than one version of deflationism. The\nlabels ‘redundancy theory’, ‘disappearance\ntheory’ and ‘no-truth theory’ have been used to\napply to analytic versions of deflationism: positions \\(\\mathbf{A}\\)\nor \\(\\mathbf{B}\\). But there is a sense in which position\n\\(\\mathbf{A}\\) is also occupied by versions of what is called\n“disquotationalism” (although the most prominent\ndisquotationalists tend to be leary of the notions of analyticity or\nsynonymy), and what is called “prosententialism” also\nposits an equivalence of what is said with the left- and right-hand\nsides of the instances of (ES). The latter version of deflationism,\nhowever, does this without making the left-hand sides about sentences\nnamed via quotation or about propositions understood as abstract\nentities. No deflationist has offered an account occupying position\n\\(\\mathbf{C}\\), \\(\\mathbf{E}\\), or \\(\\mathbf{F}\\) (although the\nexplicit inspiration some disquotationalists have found in\nTarski’s work and his deployment of material equivalence might\nmisleadingly suggest position \\(\\mathbf{E})\\). Paul Horwich (1998a)\nuses the label ‘minimalism’ for a version of\npropositionalist deflationism that takes the instances of (ES-prop) to\ninvolve a necessary equivalence, thereby occupying position\n\\(\\mathbf{D}\\). To a large extent, philosophers prefer one or another\n(or none) of the positions in the chart on the basis of their views\nfrom other parts of philosophy, typically their views about the\nphilosophy of language and metaphysics." ], "subsection_title": "1.1 The Equivalence Schema" }, { "content": [ "\nThe second theme we will discuss focuses on the fact that when we say,\nfor example, that the proposition that Brutus killed Caesar is true,\nwe seem to be attributing a property to that proposition, namely, the\nproperty of being true. Deflationists are typically wary of that\nclaim, insisting either that there is no property of being true at\nall, or, if there is one, it is of a certain kind, often called\n“thin” or “insubstantial”.", "\nThe suggestion that there is no truth property at all is advanced by\nsome philosophers in the deflationary camp; we will look at some\nexamples below. What makes this position difficult to sustain is that\n‘is true’ is grammatically speaking a predicate much like\n‘is metal’. If one assumes that grammatical predicates\nsuch as ‘is metal’ express properties, then, prima\nfacie, the same would seem to go for ‘is true.’ This\npoint is not decisive, however. For one thing, it might be possible to\ndistinguish the grammatical form of claims containing ‘is\ntrue’ from their logical form; at the level of logical form, it\nmight be, as prosententialists maintain, that ‘is true’ is\nnot a predicate. For another, nominalists about properties\nhave developed ways of thinking about grammatical predicates according\nto which these expressions don’t express properties at all. A\ndeflationist might appeal, perhaps selectively, to such proposals, in\norder to say that ‘is true’, while a predicate, does not\nexpress a property.", "\nWhatever the ultimate fate of these attempts to say that there is no\nproperty of truth may be, a suggestion among certain deflationists has\nbeen to concede that there is a truth property but to deny it is a\nproperty of a certain kind; in particular to deny that it is (as we\nwill say) a substantive property.", "\nTo illustrate the general idea, consider (3) and (4):", "\nDo the propositions that these sentences express share a property of\nbeing true? Well, in one intuitive sense they do: Since they both are\ntrue, we might infer that they both have the property of being true.\nFrom this point of view, there is a truth property: It is simply the\nproperty that all true propositions have.", "\nOn the other hand, when we say that two things share a property of\nFness, we often mean more than simply that they are both\n\\(F\\). We often mean that two things that are \\(F\\) have some\nunderlying nature in common, for example, that there is a common\nexplanation as to why they are both \\(F\\). It is in this second claim\nthat deflationists have in mind when they say that truth is not a\nsubstantive property. Thus, in the case of our example, what, if\nanything, explains the truth of (3) is that Caracas is the capital of\nVenezuela, and what explains this is the political history of\nVenezuela. On the other hand, what, if anything, explains the truth of\n(4) is that the earth revolves around the sun, and what explains this\nis the physical nature of the solar system. The physical nature of the\nsolar system, however, has nothing to do with the political history of\nVenezuela (or if it does, the connections are completely accidental!)\nand to that extent there is no shared explanation as to why (3) and\n(4) are both true. Therefore, in this substantive sense, they have no\nproperty in common.", "\nIt will help to bring out the contrast being invoked here if we\nconsider two properties distinct from a supposed property of being\ntrue: the property of being a game and the property of being a mammal.\nConsider the games of chess and catch. Do both of these have the\nproperty of being a game? Well, in one sense, they do: they are both\ngames that people can play. On the other hand, however, there is no\ncommon explanation as to why each counts as a game (cf. Wittgenstein\n1953, §66). We might then say that being a game is not a\nsubstantive property and mean just this. But now compare the property\nof being a mammal. If two things are mammals, they have the property\nof being a mammal, but in addition there is some common explanation as\nto why they are both mammals – both are descended from the same\nfamily of creatures, say. According to one development of\ndeflationism, the property of being true is more like the property of\nbeing a game than it is like the property of being a mammal.", "\nThe comparisons between being true, being a game, and being a mammal\nare suggestive, but they still do not nail down exactly what it means\nto say that truth is not a substantive property. The contemporary\nliterature on deflationism contains several different approaches to\nthe idea. One such approach, which we will consider in detail in\nSection 4.1, involves denying that truth plays an explanatory role.\nAnother approach, pursuing an analogy between being true and existing,\ndescribes truth as a “logical property” (for example,\nField 1992, 322; Horwich 1998a, 37; Künne 2003, 91). A further\napproach appeals to\n David Lewis’s\n (1983, 1986) view that, while every set of entities underwrites a\nproperty, there is a distinction between sparse, or\nnatural, properties and more motley or disjointed\nabundant properties. On this approach, a deflationist might\nsay that there is an abundant property of being true rather than a\nsparse one (cf. Edwards 2013, Asay 2014, Kukla and Winsberg 2015, and\nArmour-Garb forthcoming). A different metaphysical idea may be to\nappeal to the contemporary discussion of grounding and the distinction\nbetween groundable and ungroundable properties. In this context, a\ngroundable property is one that is capable of being grounded in some\nother property, whether or not it is in fact grounded; an ungroundable\nproperty is a property that is not groundable (see Dasgupta 2015, 2016\nand Rabin 2020). From this point of view, a deflationist might say\nthat being true is an ungroundable property. Hence it is unlike\nordinary, sparse/natural properties, such as being iron, which are\nboth capable of being grounded and are grounded, and it is also unlike\nfundamental physical properties, such as being a lepton, which are\ncapable of being grounded (in some other possible world) but are not\n(actually) grounded. We will not try to decide here which of these\ndifferent views of properties is correct but simply note that\ndeflationists who want to claim that there is a truth property, just\nnot a substantive one, have options for explaining what this\nmeans." ], "subsection_title": "1.2 The Property of Truth" }, { "content": [ "\nIn light of the two central ideas discussed so far – the idea\nthat the equivalence schema is exhaustive of the notion of truth and\nthe idea that there is no substantive truth property – you might\nwonder why we have a concept of truth in the first place. After all,\ncontrast this question with the explanation of why we have the concept\nof mammals. A natural suggestion is that it allows us to think and\ntalk about mammals and to develop theories of them. For deflationism,\nhowever, as we have just seen, being true is completely different from\nbeing a mammal; why then do we have a concept of truth? (An analogous\nquestion might be asked about the word ‘true’, i.e., why\nwe have the word ‘true’ and related words in our language\nat all. In the following discussion we will not discriminate between\nquestions about the concept of truth and questions about the word\n‘true’ and will move back and forth between them.)", "\nThe question of why we have the concept of truth allows us to\nintroduce a third central theme in deflationism, which is an emphasis\nnot merely on the property of truth but on the concept of truth, or,\nequivalently for present purposes, on the word ‘true’ (cf.\nLeeds 1978). Far from supposing that there is no point having the\nconcept of truth, deflationists are usually at pains to point out that\nanyone who has the concept of truth is in possession of a very useful\nconcept indeed; in particular, anyone who has this concept is in a\nposition to express generalizations that would otherwise require\nnon-standard logical devices, such as sentential variables and\nquantifiers for them.", "\nSuppose, for example, that Jones for whatever reason decides that\nSmith is an infallible guide to the nature of reality. We might then\nsay that Jones believes everything that Smith says. To say this much,\nhowever, is not to capture the content of Jones’s belief. In\norder to do that we need some way of generalizing on the embedded\nsentence positions in a claim like:", "\nTo generalize on the relationship indicated in (5), beyond just what\nSmith says about birds to anything she might say, what we want to do\nis generalize on the embedded occurrences of ‘birds are\ndinosaurs’. So, we need a (declarative) sentential variable,\n‘\\(p\\)’, and a universal quantifier governing it. What we\nwant is a way of capturing something along the lines of", "\nThe problem is that we cannot formulate this in English with our most\nfamiliar way of generalizing because the ‘\\(p\\)’ in the\nconsequent is in a sentence-in-use position, rather than mentioned or\nnominalized context (as it is in the antecedent), meaning that this\nformal variable cannot be replaced with a familiar English\nobject-variable expression, e.g., ‘it’.", "\nThis is where the concept of truth comes in. What we do in order to\ngeneralize in the way under consideration is employ the truth\npredicate with an object variable to produce the sentence,", "\nRe-rendering the quasi-formal (7) into natural language yields,", "\nOr, to put the same thing more colloquially:", "\nThe equivalence schema (ES-prop) allows us to use (7) (and therefore\n(9)) to express what it would otherwise require the unstatable (6) to\nexpress. For, on the basis of the schema, there is always an\nequivalence between whatever goes in for a sentence-in-use occurrence\nof the variable ‘\\(p\\)’ and a context in which that\nfilling of the sentential variable is nominalized. This reveals how\nthe truth predicate can be used to provide a surrogate for sentential\nvariables, simulating this non-standard logical device while still\ndeploying the standard object variables already available in ordinary\nlanguage (‘it’) and the usual object quantifiers\n(‘everything’) that govern them.", "\nThis is how the use of the truth predicate in (9) gives us the content\nof Jones’s belief. And the important point for deflationists is\nthat we could not have stated the content of this belief unless we had\nthe concept of truth (the expression ‘true’). In fact, for\nmost deflationists, it is this feature of the concept of truth –\nits role in the formation of these sorts of generalizations –\nthat explains why we have a concept of truth at all. This is, as it is\noften put, the raison d’être of the concept of\ntruth (cf. Field 1994a and Horwich 1998a)." ], "subsection_title": "1.3 The Utility of the Concept of Truth" } ] }, { "main_content": [ "\nAccording to Michael Dummett (1959 [1978]), deflationism originates\nwith\n Gottlob Frege,\n as expressed in this famous quote by the latter:", "\nIt is … worthy of notice that the sentence ‘I smell the\nscent of violets’ has just the same content as the sentence\n‘It is true that I smell the scent of violets’. So it\nseems, then, that nothing is added to the thought by my ascribing to\nit the property of truth. (Frege 1918, 6)\n", "\nThis passage suggests that Frege embraces a deflationary view in\nposition \\(\\mathbf{B}\\) (in the chart above), namely, an analytic\npropositionalist version of deflationism. But this interpretation of\nhis view is not so clear. As Scott Soames (1999, 21ff) points out,\nFrege (ibid.) distinguishes what we will call “opaque”\ntruth ascriptions, like ‘My conjecture is true’, from\ntransparent truth-ascriptions, like the one mentioned in the quote\nfrom Frege. Unlike with transparent cases, in opaque instances, one\ncannot simply strip ‘is true’ away and obtain an\nequivalent sentence, since the result is not even a sentence at\nall.", "\n\n Frank Ramsey\n is the first philosopher to have suggested a position like\n\\(\\mathbf{B}\\) (although he does not really accept propositions as\nabstract entities (see Ramsey 1927 (34–5) and 1929 (7)), despite\nsometimes talking in terms of propositions):", "\nTruth and falsity are ascribed primarily to propositions. The\nproposition to which they are ascribed may be either explicitly given\nor described. Suppose first that it is explicitly given; then it is\nevident that ‘It is true that Caesar was murdered’ means\nno more than that Caesar was murdered, and ‘It is false that\nCaesar was murdered’ means no more than Caesar was not murdered.\n…. In the second case in which the proposition is described and\nnot given explicitly we have perhaps more of a problem, for we get\nstatements from which we cannot in ordinary language eliminate the\nwords ‘true’ or ‘false’. Thus if I say\n‘He is always right’, I mean that the propositions he\nasserts are always true, and there does not seem to be any way of\nexpressing this without using the word ‘true’. But suppose\nwe put it thus ‘For all \\(p\\), if he asserts \\(p\\), \\(p\\) is\ntrue’, then we see that the propositional function \\(p\\) is true\nis simply the same as \\(p\\), as e.g. its value ‘Caesar was\nmurdered is true’ is the same as ‘Caesar was\nmurdered’. (Ramsey 1927, 38–9)\n", "\nOn Ramsey’s redundancy theory (as it is often called), the truth\noperator, ‘it is true that’ adds no content when prefixed\nto a sentence, meaning that in the instances of what we can think of\nas the truth-operator version of (ES),", "\nthe left- and right-hand sides are meaning-equivalent. But Ramsey\nextends his redundancy theory beyond just the transparent instances of\ntruth-talk, maintaining that the truth predicate is, in principle,\neliminable even in opaque ascriptions of the form ‘\\(B\\) is\ntrue’ (which he (1929, 15, n. 7) explains in terms of sentential\nvariables via a formula along the lines of ‘\\(\\exists\np\\) (\\(p \\amp B\\) is a belief that \\(p\\))’) and in explicitly\nquantificational instances, like ‘Everything Einstein said is\ntrue’ (explained as above). As the above quote illustrates,\nRamsey recognizes that in truth ascriptions like these the truth\npredicate fills a grammatical need, which keeps us from eliminating it\naltogether, but he held that even in these cases it contributes no\ncontent to anything said using it.", "\n\n A.J. Ayer\n endorses a view similar to Ramsey’s. The following quote shows\nthat he embraces a meaning equivalence between the two sides of the\ninstances of both the sentential (position \\(\\mathbf{A})\\) and\nsomething like (since, despite his use of the expression\n‘proposition’ to mean sentence, he also considers\ninstances of truth-talk involving the prefix ‘it is true\nthat’, which could be read as employing\n‘that’-clauses) the propositional (position\n\\(\\mathbf{B})\\) version of (ES).", "\n[I]t is evident that a sentence of the form “\\(p\\) is\ntrue” or “it is true that \\(p\\)” the reference to\ntruth never adds anything to the sense. If I say that it is true that\nShakespeare wrote Hamlet, or that the proposition\n“Shakespeare wrote Hamlet” is true, I am saying\nno more than that Shakespeare wrote Hamlet. Similarly, if I\nsay that it is false that Shakespeare wrote the Iliad, I am\nsaying no more than that Shakespeare did not write the Iliad.\nAnd this shows that the words ‘true’ and\n‘false’ are not used to stand for anything, but function\nin the sentence merely as assertion and negation signs. That is to\nsay, truth and falsehood are not genuine concepts. Consequently, there\ncan be no logical problem concerning the nature of truth. (Ayer 1935,\n28. Cf. Ayer 1936 [1952, 89])\n", "\n\n Ludwig Wittgenstein,\n under Ramsey’s influence, makes claims with strong affinities\nto deflationism in his later work. We can see a suggestion of an\nendorsement of deflationary positions \\(\\mathbf{A}\\) or \\(\\mathbf{B}\\)\nin his (1953, §136) statement that “\\(p\\) is true \\(=\np\\)” and “\\(p\\) is false = not-\\(p\\)”, indicating\nthat ascribing truth (or falsity) to a statement just amounts to\nasserting that very proposition (or its negation). Wittgenstein also\nexpresses this kind of view in manuscripts from the 1930s, where he\nclaims, “What he says is true = Things are as he says” and\n“[t]he word ‘true’ is used in contexts such as\n‘What he says is true’, but that says the same thing as\n‘He says \\(\\ldquo p\\rdquo,\\) and \\(p\\) is the\ncase’”. (Wittgenstein 1934 [1974, 123]) and 1937 [2005,\n61]), respectively)", "\n\n Peter Strawson’s\n views on truth emerge most fully in his 1950 debate with\n J.L. Austin.\n In keeping with deflationary position \\(\\mathbf{B}\\), Strawson (1950,\n145–7) maintains that an utterance of ‘It is true that\n\\(p\\)’ just makes the same statement as an utterance of\n‘\\(p\\)’. However, in Strawson 1949 and 1950, he further\nendorses a performative view, according to which an utterance\nof a sentence like ‘That is true’ mainly functions to do\nsomething beyond mere re-assertion. This represents a shift\nto an account of what the expression ‘true’ does,\nfrom traditional accounts of what truth is, or even accounts of what\n‘true’ means.", "\nAnother figure briefly mentioned above who looms large in the\ndevelopment of deflationism is\n Alfred Tarski,\n with his (1935 [1956] and 1944) identification of a precise criterion\nof adequacy for any formal definition of truth: its implying all of\nthe instances of what is sometimes called “Convention (T)”\nor “the (T)-schema”,", "\nTo explain this schema a bit more precisely, in its instances the\n‘\\(X\\)’ gets replaced by a name of a sentence from the\nobject-language for which the truth predicate is being\ndefined, and the ‘\\(p\\)’ gets replaced by a sentence that\nis a translation of that sentence into the meta-language in which the\ntruth predicate is being defined. For Tarski, the ‘if and only\nif’ deployed in any instance of (T) expresses just a material\nequivalence, putting his view at position \\(\\mathbf{E}\\) in the chart\nfrom Section 1.1. Although this means that Tarski is not a\ndeflationist himself (cf. Field 1994a, Ketland 1999, and Patterson\n2012), there is no denying the influence that his work and its\npromotion of the (T)-schema have had on deflationism. Indeed, some\nearly deflationists, such as\n W.V.O. Quine\n and Stephen Leeds, are quite explicit about taking inspiration from\nTarski’s work in developing their “disquotational”\nviews, as is Horwich in his initial discussion of deflationism. Even\ncritics of deflationism have linked it with Tarski: Hilary Putnam\n(1983b, 1985) identifies deflationists as theorists who “refer\nto the work of Alfred Tarski and to the semantical conception of\ntruth” and who take Tarski’s work “as a solution to\nthe philosophical problem of truth”.", "\nThe first fully developed deflationary view is the one that Quine\n(1970 [1986, 10–2]) presents. Given his skepticism about the\nexistence of propositions, Quine takes sentences to be the primary\nentities to which ‘is true’ may be applied, making the\ninstances of (ES-sent) the equivalences that he accepts. He defines a\ncategory of sentence that he dubs “eternal”, viz.,\nsentence types that have all their indexical/contextual factors\nspecified, the tokens of which always have the same truth-values. It\nis for these sentences that Quine offers his disquotational view. As\nhe (ibid., 12) puts it,", "\n\n\nThis cancellatory force of the truth predicate is explicit in\nTarski’s paradigm:\n\n\n‘Snow is white’ is true if and only if snow is white.\n\n\n\nQuotation marks make all the difference between talking about words\nand talking about snow. The quotation is a name of a sentence that\ncontains the name, namely ‘snow’, of snow. By calling the\nsentence true, we call snow white. The truth predicate is a device of\ndisquotation.\n", "\nAs this quote suggests, Quine sees Tarski’s formal work on\ndefining truth predicates for formalized languages and his criterion\nof adequacy for doing so as underwriting a disquotational analysis of\nthe truth predicate. This makes Quine’s view a different kind of\nposition-\\(\\mathbf{A}\\) account, since he takes the left-hand side of\neach instance of (ES-sent) to be, as we will put it (since Quine\nrejects the whole idea of meaning and meaning equivalence), something\nlike a mere syntactic variant of the right-hand side. This also means\nthat Quine’s version of deflationism departs from inflationism\nby rejecting the latter’s presupposition that truth predicates\nfunction to describe the entities they get applied to, the\nway that other predicates, such as ‘is metal’, do.", "\nQuine also emphasizes the importance of the truth predicate’s\nrole as a means for expressing the kinds of otherwise inexpressible\ngeneralizations discussed in Section 1.3. As he (1992, 80–1)\nexplains it,", "\nThe truth predicate proves invaluable when we want to generalize along\na dimension that cannot be swept out by a general term … The\nharder sort of generalization is illustrated by generalization on the\nclause ‘time flies’ in ‘If time flies then time\nflies’…. We could not generalize as in ‘All men are\nmortal’ because ‘time flies’ is not, like\n‘Socrates’, a name of one of a range of objects (men) over\nwhich to generalize. We cleared this obstacle by semantic\nascent: by ascending to a level where there were indeed objects\nover which to generalize, namely linguistic objects, sentences.\n", "\nSo, if we want to generalize on embedded sentence-positions within\nsome sentences, “we ascend to talk of truth and sentences”\n(Quine 1970 [1986, 11]). This maneuver allows us to “affirm some\ninfinite lot of sentences that we can demarcate only by talking about\nthe sentences” (ibid., 12).", "\nLeeds (1978) (following Quine) makes it clear how the truth predicate\nis crucial for extending the expressive power of a language, despite\nthe triviality that disquotationalism suggests for the transparent\ninstances of truth-talk. He (ibid., 121) emphasizes the logical role\nof the truth predicate in the expression of certain kinds of\ngeneralizations that would otherwise be inexpressible in natural\nlanguage. Leeds, like Quine, notes that a central utility of the truth\npredicate, in virtue of its yielding every instance of (ES-sent), is\nthe simulation of quantification into sentence-positions. But, unlike\nQuine, Leeds glosses this logical role in terms of expressing\npotentially infinite conjunctions (for universal generalization) or\npotentially infinite disjunctions (for existential generalization).\nThe truth predicate allows us to use the ordinary devices of\nfirst-order logic in ways that provide surrogates for the non-standard\nlogical devices this would otherwise require. Leeds is also clear\nabout accepting the consequences of deflationism, that is, of taking\nthe logically expressive role of the truth predicate to exhaust its\nfunction. In particular, he points out that there is no need to think\nthat truth plays any sort of explanatory role. We will return\nto this point in Section 4.1.", "\nDorothy Grover, Joseph Camp, and Nuel Belnap (1975) develop a\ndifferent variety of deflationism that they call a\n“prosentential theory”. This theory descends principally\nfrom Ramsey’s views. In fact, Ramsey (1929, 10) made what is\nprobably the earliest use of the term ‘pro-sentence’ in\nhis account of the purpose of truth-talk. Prosentences are explained\nas the sentence-level analog of pronouns. As in the case of pronouns,\nprosentences inherit their content anaphorically from other linguistic\nitems, in this case from some sentence typically called the\nprosentence’s “anaphoric antecedent” (although it\nneed not actually occur before the prosentence). As Grover, et\nal. develop this idea, this content inheritance can happen in two\nways. The most basic one is called “lazy” anaphora. Here\nthe prosentence could simply be replaced with a repetition of its\nantecedent, as in the sort of case that Strawson emphasized, where one\nsays “That is true” after someone else has made an\nassertion. According to Grover, et al., this instance of\ntruth-talk is a prosentence that inherits its content anaphorically\nfrom the other speaker’s utterance, so that the two speakers\nassert the same thing. As a result, Grover, et al. would take\nthe instances of (ES) to express meaning equivalences, but since they\n(ibid., 113–5) do not take the instances of truth-talk on the\nleft-hand sides of these equivalences to say anything about\nany named entities, they would not read (ES) as either (ES-sent) or\n(ES-prop) on their standard interpretations. So, while their\nprosententialism is similar to views in position \\(\\mathbf{A}\\) or in\nposition \\(\\mathbf{B}\\) in the chart above, it is also somewhat\ndifferent from both.", "\nGrover, et al.’s project is to develop the theory\n“that ‘true’ can be thought of always as part of a\nprosentence” (ibid., 83). They explain that ‘it is\ntrue’ and ‘that is true’ are generally available\nprosentences that can go into any sentence-position. They consider\nthese expressions to be “atomic” in the sense of not being\nsusceptible to a subject-predicate analysis giving the\n‘that’ or ‘it’ separate references (ibid.,\n91). Both of these prosentences can function in the “lazy”\nway, and Grover, et al. claim (ibid., 91–2, 114) that\n‘it is true’ can also operate as a quantificational\nprosentence (i.e., a sentential variable), for example, in a\nre-rendering of a sentence like,", "\nin terms of a “long-form” equivalent claim, such as", "\nOne immediate concern that this version of prosententialism faces\npertains to what one might call the “paraphrastic\ngymnastics” that it requires. For example, a sentence like\n‘It is true that humans are causing climate change’ is\nsaid to have for its underlying logical form the same form as\n‘Humans are causing climate change. That is true’ (ibid.,\n94). As a result, when one utters an instance of truth-talk of the\nform ‘It is true that \\(p\\)’, one states the content of\nthe sentence that goes in for ‘\\(p\\)’ twice. In\ncases of quotation, like “‘Birds are dinosaurs’ is\ntrue”, Grover, et al. offer the following rendering,\n‘Consider: Birds are dinosaurs. That is true’ (ibid.,\n103). But taking this as the underlying form of quotational instance\nof truth-talk requires rejecting the standard view that putting\nquotation marks around linguistic items forms names of those items.\nThese issues raise concerns regarding the adequacy of this version of\nprosententialism." ], "section_title": "2. History of Deflationism", "subsections": [] }, { "main_content": [ "\nIn this section, we explain the details of three prominent,\ncontemporary accounts and indicate some concerns peculiar to each." ], "section_title": "3. The Varieties of Contemporary Deflationism", "subsections": [ { "content": [ "\nMinimalism is the version of deflationism that diverges the least from\ninflationism because it accepts many of the standard inflationary\npresuppositions, including that ‘is true’ is a predicate\nused to describe entities as having (or lacking) a truth property.\nWhat makes minimalism a version of deflationism is its denial of\ninflationism’s final assumption, namely, that the property\nexpressed by the truth predicate has a substantive nature. Drawing\ninspiration from Leeds (1978), Horwich (1982, 182) actually coins the\nterm ‘deflationism’ while describing “the\ndeflationary redundancy theory which denies the existence of surplus\nmeaning and contends that Tarski’s schema [“\\(p\\)”\nis true iff \\(p\\)] is quite sufficient to capture the concept.”\nMinimalism, Horwich’s mature deflationary position (1998a [First\nEdition, 1990]), adds to this earlier view. In particular, Horwich\n(ibid., 37, 125, 142) comes to embrace the idea that ‘is\ntrue’ does express a property, but it is merely a “logical\nproperty” (cf. Field 1992), rather than any substantive or\nnaturalistic property of truth with an analyzable underlying nature\n(Horwich 1998a, 2, 38, 120–1).", "\nOn the basis of natural language considerations, Horwich (ibid.,\n2–3, 39–40) holds that propositions are what the alethic\nlocutions describe directly. Any other entities that we can properly\ncall true are so only derivatively, on the basis of having some\nrelation to true propositions (ibid., 100–1 and Horwich 1998b,\n82–5). This seems to position Horwich well with respect to\nexplaining the instances of truth-talk that cause problems for Quine\nand Leeds, e.g., those about beliefs and theories. Regarding truth\napplied directly to propositions, however, Horwich (1998a, 2–3)\nstill explicitly endorses the thesis that Leeds emphasizes about the\nutility of the truth predicate (and, Horwich adds, the concept it\nexpresses), namely, that it “exists solely for the sake of a\ncertain logical need”. While Horwich (ibid., 138–9) goes\nso far as to claim that the concept of truth has a\n“non-descriptive” function, he does not follow Quine and\nLeeds all the way to their rejection of the assumption that the\nalethic predicates function to describe truth-bearers. Rather, his\n(ibid., 31–3, 37) point of agreement with them is that the\nmain function of the truth predicate is its role in providing\na means for generalizing on embedded sentence positions, rather than\nsome role in the indication of specifically truth-involving states of\naffairs. Even so, Horwich (ibid., 38–40) still contends that the\ninstances of truth-talk do describe propositions, in the sense that\nthey make statements about them, and they do so by\nattributing a property to those propositions.", "\nThe version of (ES) that Horwich (1998a, 6) makes the basis of his\ntheory is what he also calls “the equivalence schema”,", "\nSince he takes truth-talk to involve describing propositions with a\npredicate, Horwich considers ‘it is true that \\(p\\)’ to be\njust a trivial variant of ‘The proposition that \\(p\\) is\ntrue’, meaning that his (E) is a version of (ES-prop) rather\nthan of Ramsey’s (ES-op). He also employs the notation\n‘\\(\\langle p\\rangle\\)’ as shorthand specifically for\n‘the proposition that \\(p\\)’, generating a further\nrendering of his equivalence schema (ibid., 10) that we can clearly\nrecognize as a version of (ES-prop), namely", "\nHorwich considers the instances of (E) to constitute the axioms of\nboth an account of the property of truth and an account of the concept\nof truth, i.e., what is meant by the word ‘true’ (ibid.,\n136). According to minimalism, the instances of (E) are explanatorily\nfundamental, which Horwich suggests is a reason for taking them to be\nnecessary (ibid., 21, n. 4). This, combined with his view that the\nequivalence schema applies to propositions, places his minimalism in\nposition \\(\\mathbf{D}\\) in the chart given in Section 1.1. The\ninstances of (ES-prop) are thus explanatory of the functioning of the\ntruth predicate (of its role as a de-nominalizer of\n‘that’-clauses (ibid., 5)), rather than being explained by\nthat functioning (as the analogous equivalences are for both\ndisquotationalism and prosententialism). Moreover, Horwich (ibid., 50,\n138) claims that they are also conceptually basic and a\npriori. He (ibid., 27–30, 33, 112) denies that truth admits\nof any sort of explicit definition or reductive analysis in terms of\nother concepts, such as reference or predicate-satisfaction. In fact,\nHorwich (ibid., 10–1, 111–2, 115–6) holds that these\nother semantic notions should both be given their own, infinitely\naxiomatized, minimalist accounts, which would then clarify the\nnon-reductive nature of the intuitive connections between them and the\nnotion of truth.", "\nHorwich (ibid., 27–30) maintains that the infinite axiomatic\nnature of minimalism is unavoidable. He (ibid., 25) rejects the\npossibility of a finite formulation of minimalism via the use\nof\n substitutional quantification.\n On the usual understanding of this non-standard type of\nquantification, the quantifiers govern variables that serve to mark\nplaces in linguistic strings, indicating that either all or some of\nthe elements of an associated substitution class of linguistic items\nof a particular category can be substituted in for the variables.\nSince it is possible for the variables so governed to take sentences\nas their substitution items, this allows for a type of quantification\ngoverning sentence positions in complex sentences. Using this sort of\nsentential substitutional quantification, the thought is, one can\nformulate a finite general principle that expresses Horwich’s\naccount of truth as follows:", "\nwhere ‘\\(\\Sigma\\)’ is the existential substitutional\nquantifier. (GT) is formally equivalent to the formulation that Marian\nDavid (1994, 100) presents as disquotationalism’s definition of\n‘true sentence’, here formulated for propositions instead.\nHorwich’s main reason for rejecting the proposed finite\nformulation of minimalism, (GT), is that an account of substitutional\nquantifiers seems (contra David 1994, 98–9) to require an appeal\nto truth (since the quantifiers are explained as expressing that at\nleast one or that every item in the associated substitution class\nyields a true sentence when substituted in for the governed\nvariables), generating circularity concerns (Horwich 1998a,\n25–6).", "\nMoreover, on Horwich’s (ibid., 4, n. 1; Cf. 25, 32–3)\nunderstanding, the point of the truth predicate is to provide a\nsurrogate for substitutional quantification and sentence-variables in\nnatural language, so as “to achieve the effect of generalizing\nsubstitutionally over sentences … but by means of ordinary\n[quantifiers and] variables (i.e., pronouns), which range over\nobjects” (italics original). Horwich maintains that the\ninfinite “list-like” nature of minimalism poses no problem\nfor the view’s adequacy with respect to explaining all of our\nuses of the truth predicate, and the bulk of Horwich 1998a attempts to\nestablish just that. However, Anil Gupta (1993a, 365) has pointed out\nthat minimalism’s infinite axiomatization in terms of the\ninstances of (E) for every (non-paradox-inducing) proposition makes it\nmaximally ideologically complex, in virtue of involving every other\nconcept. (Moreover, the overtly “fragmented” nature of the\ntheory also makes it particularly vulnerable to the Generalization\nProblem that Gupta has raised, which we discuss in Section 4.5,\nbelow.)", "\nChristopher Hill (2002) attempts to deal with some of the problems\nthat Horwich’s view faces, by presenting a view that he takes to\nbe a newer version of minimalism, replacing Horwich’s\nequivalence schema with a universally quantified formula, employing a\nkind of substitutional quantification to provide a finite definition\nof ‘true thought (proposition)’. Hill’s (ibid., 22)\nformulation of his account,", "\nis formally similar to the formulation of minimalism in terms of (GT)\nthat Horwich rejects, but to avoid the circularity concerns driving\nthat rejection, Hill’s (ibid., 18–22) idea is to offer\nintroduction and elimination rules in the style of Gerhard Gentzen\n(1935 [1969]) as a means for defining the substitutional quantifiers.\nHorwich (1998a, 26) rejects even this inference-rule sort of approach,\nbut he directs his critique against defining linguistic\nsubstitutional quantification this way. Hill takes his substitutional\nquantifiers to apply to thoughts (propositions) instead of sentences.\nBut serious concerns have been raised regarding the coherence of this\nnon-linguistic notion of substitutional quantification (cf. David\n2006, Gupta 2006b, Simmons 2006). As a result, it is unclear that\nHill’s account is an improvement on Horwich’s version of\nminimalism." ], "subsection_title": "3.1 Minimalism" }, { "content": [ "\nLike minimalism, disquotationalism agrees with inflationary accounts\nof truth that the alethic locutions function as predicates, at least\nlogically speaking. However, as we explained in discussing\nQuine’s view in Section 2, disquotationalism diverges from\ninflationary views (and minimalism) at their shared assumption that\nthese (alethic) predicates serve to describe the entities\npicked out by the expressions with which they are combined,\nspecifically as having or lacking a certain property.", "\nAlthough Quine’s disquotationalism is inspired by Tarski’s\nrecursive method for defining a truth predicate, that method is not\nwhat Quine’s view emphasizes. Field’s contemporary\ndisquotationism further departs from that aspect of Tarski’s\nwork by looking directly to the instances of the (T)-schema that the\nrecursive method must generate in order to satisfy Tarski’s\ncriterion of material adequacy. Tarski himself (1944, 344–5)\nsuggests at one point that each instance of (T) could be considered a\n“partial definition” of truth and considers (but\nultimately rejects; see Section 4.5) the thesis that a logical\nconjunction of all of these partial definitions amounts to a general\ndefinition of truth (for the language that the sentences belonged to).\nGeneralizing slightly from Tarski, we can call this alternative\napproach “(T)-schema disquotationalism”, in contrast with\nthe Tarski-inspired approach that David (1994, 110–1) calls\n“recursive disquotationalism”. Field (1987, 1994a)\ndevelops a version of (T)-schema disquotationalism that he calls\n“pure disquotational truth”, focusing specifically on the\ninstances of his preferred version of (ES), the “disquotational\nschema” (Field 1994a, 258),", "\nSimilar to the “single principle” formulation, (GT),\nrejected by Horwich (but endorsed by Hill), Field (ibid., 267) allows\nthat one could take a “generalized” version of\n(T/ES-sent), prefixed with a universal substitutional quantifier,\n‘\\(\\Pi\\)’, as having axiomatic status, or one could\nincorporate schematic sentence variables directly into one’s\ntheorizing language and reason directly with (T/ES-sent) as a schema\n(cf. ibid., 259). Either way, in setting out his version of\ndeflationism, Field (ibid., 250), in contrast with Horwich, does not\ntake the instances of his version of (ES) as fundamental but instead\nas following from the functioning of the truth predicate. On\nField’s reading of (T/ES-sent), the use of the truth predicate\non the left-hand side of an instance does not add any cognitive\ncontent beyond that which the mentioned utterance has (for the\nspeaker) on its own when used (as on the right-hand-side of\n(T/ES-sent)). As a result, each instance of (T/ES-sent) “holds\nof conceptual necessity, that is, by virtue of the cognitive\nequivalence of the left and right hand sides” (ibid., 258). This\nplaces Field’s deflationism also in position \\(\\mathbf{A}\\) in\nthe chart from Section 1.1.", "\nFollowing Leeds and Quine, Field (1999, 533–4) sees the central\nutility of a purely disquotational truth predicate to be providing for\nthe expression of certain “fertile generalizations” that\ncannot be made without using the truth predicate but which do not\nreally involve the notion of truth. Field (1994a, 264) notes that the\ntruth predicate plays “an important logical role: it allows us\nto formulate certain infinite conjunctions and disjunctions that\ncan’t be formulated otherwise [n. 17: at least in a language\nthat does not contain substitutional quantifiers]”.", "\nField’s disquotationalism addresses some of the worries that\narose for earlier versions of this variety of deflationism, due to\ntheir connections with Tarski’s method of defining truth\npredicates. It also explains how to apply a disquotational truth\npredicate to ambiguous and indexical utterances, thereby going beyond\nQuine’s (1970 [1986]) insistence on taking eternal sentences as\nthe subjects of the instances of (ES-sent) (cf. Field 1994a,\n278–81). So, Field’s view addresses some of the concerns\nthat David (1994, 130–66) raises for disquotationalism. However,\nan abiding concern about this variety of deflationism is that it is an\naccount of truth as applied specifically to sentences. This opens the\ndoor to a version of the complaint that Strawson (1950) makes against\nAustin’s account of truth, that it is not one’s act of\nstating [here: the sentence one utters] but what thereby gets stated\nthat is the target of a truth ascription. William Alston (1996, 14)\nmakes a similar point. While disquotationalists do not worry much\nabout this, this scope restriction might strike others as problematic\nbecause it raises questions about how we are to understand truth\napplied to beliefs or judgments, something that Hill (2002) worries\nabout. Field (1978) treats beliefs as mental states relating thinkers\nto sentences (of a language of thought). But David (1994, 172–7)\nraises worries for applying disquotationalism to beliefs, even in the\ncontext of an account like Field’s. The view that we believe\nsentences remains highly controversial, but it is one that, it seems,\na Field-style disquotationalist must endorse. Similarly, such\ndisquotationalists must take scientific theories to consist of sets of\nsentences, in order for truth to be applicable to them. This too runs\nup against Strawson’s complaint because it suggests that one\ncould not state the same theory in a different language. These sorts\nof concerns continue to press for disquotationalists." ], "subsection_title": "3.2 Disquotationalism" }, { "content": [ "\nAs emerges from the discussion of Grover, et al. (1975) in\nSection 2, prosententialism is the form of deflationism that contrasts\nthe most with inflationism, rejecting even the latter’s initial\nassumption that the alethic locutions function as predicates. Partly\nin response to the difficulties confronting Grover, et\nal.’s prosentential account, Robert Brandom (1988 and 1994)\nhas developed a variation on their view with an important\nmodification. In place of taking the underlying logic of\n‘true’ as having this expression occur only as a\nnon-separable component of the semantically atomic prosentential\nexpressions, ‘that is true’ and ‘it is true’,\nBrandom treats ‘is true’ as a separable\nprosentence-forming operator. “It applies to a\nterm that is a sentence nominalization or that refers to or picks out\na sentence tokening. It yields a prosentence that has that tokening as\nits anaphoric antecedent” (Brandom 1994, 305). In this way,\nBrandom’s account avoids most of the paraphrase concerns that\nGrover, et al.’s prosententialism faces, while still\nmaintaining prosententialism’s rejection of the contention that\nthe alethic locutions function predicatively. As a consequence of his\noperator approach, Brandom gives quantificational uses of prosentences\na slightly different analysis. He (re)expands instances of truth-talk\nlike the following,", "\n“back” into longer forms, such as", "\nand explains only the second ‘it’ as involved in a\nprosentence. The first ‘it’ in (8*) and (11) still\nfunctions as a pronoun, anaphorically linked to a set of noun\nphrases (sentence nominalizations) supplying objects (sentence\ntokenings) as a domain being quantified over with standard (as opposed\nto sentential or “propositional”) quantifiers (ibid.,\n302).", "\nBrandom presents a highly flexible view that takes ‘is\ntrue’ as a general “denominalizing” device that\napplies to singular terms formed from the nominalization of sentences\nbroadly, not just to pronouns that indicate them. A sentence like\n‘It is true that humans are causing climate change’,\nconsidered via a re-rendering as ‘That humans are\ncausing climate change is true’, is already a\nprosentence on his view, as is a quote-name case like\n“‘Birds are dinosaurs’ is true”, and an opaque\ninstance of truth-talk like ‘Goldbach’s Conjecture is\ntrue’. In this way, Brandom offers a univocal and broader\nprosentential account, according to which, “[i]n each use, a\nprosentence will have an anaphoric antecedent that determines a class\nof admissible substituends for the prosentence (in the lazy case, a\nsingleton). This class of substituends determines the significance of\nthe prosentence associated with it” (ibid.). As a result,\nBrandom can accept both (ES-sent) and (ES-prop) – the latter\nunderstood as involving no commitment to propositions as entities\n– on readings closer to their standard interpretations, taking\nthe instances of both to express meaning equivalences. Brandom’s\naccount thus seems to be located in both position \\(\\mathbf{A}\\) and\nposition \\(\\mathbf{B}\\) in the chart from Section 1.1, although, as\nwith any prosententialist view, it still denies that the instances of\n(ES) say anything about either sentences or propositions.", "\nDespite its greater flexibility, however, Brandom’s account\nstill faces the central worry confronting prosentential views, namely\nthat truth-talk really does seem predicative, and not just in its\nsurface grammatical form but in our inferential practices with it as\nwell. In arguing for the superiority of his view over that of Grover,\net al., Brandom states that “[t]he account of truth\ntalk should bear the weight of … divergence of logical from\ngrammatical form only if no similarly adequate account can be\nconstructed that lacks this feature” (ibid., 304). One might\nfind it plausible to extend this principle beyond grammatical form, to\nbehavior in inferences as well. This is an abiding concern for\nattempts to resist inflationism by rejecting its initial assumption,\nnamely, that the alethic locutions function as predicates." ], "subsection_title": "3.3 Prosententialism" } ] }, { "main_content": [ "\nIn the remainder of this article, we consider a number of objections\nto deflationism. These are by no means the only objections that have\nbeen advanced against the approach, but they seem to be particularly\nobvious and important ones." ], "section_title": "4. Objections to Deflationism", "subsections": [ { "content": [ "\nThe first objection starts from the observation that (a) in certain\ncontexts an appeal to the notion of truth appears to have an\nexplanatory role and (b) deflationism seems to be inconsistent with\nthat appearance. Some of the contexts in which truth seems to have an\nexplanatory role involve philosophical projects, such as the\n theory of meaning\n (which we will consider below) or explaining the nature of\n knowledge.\n In these cases, the notion of explanation at issue is not so much\ncausal as it is conceptual (see Armour-Garb and Woodbridge\nforthcoming, for more on this). But the notion of truth seems also\nsometimes to play a causal explanatory role, especially with\nregard to explaining various kinds of success – mainly the\nsuccess of scientific theories/method (cf. Putnam 1978 and Boyd 1983)\nand of people’s behavior (cf. Putnam 1978 and Field 1987), but\nalso the kind of success involved in learning from others (Field\n1972). The causal-explanatory role that the notion of truth appears to\nplay in accounts of these various kinds of success has seemed to many\nphilosophers to constitute a major problem for deflationism. For\nexample, Putnam (1978, 20–1, 38) claims, “the notions of\n‘truth’ and ‘reference’ have a\ncausal-explanatory role in … an explanation of the\nbehavior of scientists and the success of science”, and\n“the notion of truth can be used in causal explanations –\nthe success of a man’s behavior may, after all, depend on the\nfact that certain of his beliefs are true – and the\nformal logic of ‘true’ [the feature emphasized by\ndeflationism] is not all there is to the notion of\ntruth”.", "\nWhile a few early arguments against deflationism focus on the role of\ntruth in explanations of the success of science (see Williams 1986 and\nFine 1984a, 1984b for deflationary responses to Putnam and Boyd on\nthis), according to Field (1994a, 271), “the most serious worry\nabout deflationism is that it can’t make sense of the\nexplanatory role of truth conditions: e.g., their role in explaining\nbehavior, or their role in explaining the extent to which behavior is\nsuccessful”. While few theorists endorse the thesis that\nexplanations of behavior in general need to appeal to the notion of\ntruth (even a pre-deflationary Field (1987, 84–5) rejects this,\nbut see Devitt 1997, 325–330, for an opposing position),\nexplanations of the latter, i.e., of behavioral success,\nstill typically proceed in terms of an appeal to truth. This poses a\nprima facie challenge to deflationary views. To illustrate\nthe problem, consider the role of the truth-value of an\nindividual’s belief in whether that person succeeds in\nsatisfying her desires. Let us suppose that Mary wants to get to a\nparty, and she believes that it is being held at 1001 Northside\nAvenue. If her belief is true, then, other things being equal, she is\nlikely to get to the party and get what she wants. But suppose that\nher belief is false, and the party is in fact being held at 1001\nSouthside Avenue. Then it would be more likely, other things being\nequal, that she won’t get what she wants. In an example of this\nsort, the truth of her belief seems to be playing a particular role in\nexplaining why she gets what she wants.", "\nAssuming that Mary’s belief is true, and she gets to the party,\nit might seem natural to say that the latter success occurs\nbecause her belief is true, which might seem to pose a\nproblem for deflationists. However, truth-involving explanations of\nparticular instances of success like this don’t really pose a\ngenuine problem. This is because if we are told the specific content\nof the relevant belief, it is possible to replace the apparently\nexplanatory claim that the belief is true with an equivalent claim\nthat does not appeal to truth. In Mary’s particular case, we\ncould replace i) the claim that she believes that the party is being\nheld at 1001 Northside Avenue, and her belief is true, with ii) the\nclaim that she believes that the party is being held at 1001 Northside\nAvenue, and the party \\(is\\) being held at 1001 Northside Avenue. A\ndeflationist can claim that the appeal to truth in the explanation of\nMary’s success just provides an expressive convenience\n(including, perhaps, the convenience of expressing what would\notherwise require an infinite disjunction (of conjunctions like ii)),\nby saying just that what Mary believed was true, if one did not know\nexactly which belief Mary acted on) (cf. Horwich 1998a, 22–3,\n44–6).", "\nWhile deflationists seem to be able to account for appeals to truth in\nexplanations of particular instances of success, the explanatory-role\nchallenge to deflationism also cites the explanatory role that an\nappeal to truth appears to play in explaining the phenomenon of\nbehavioral success more generally. An explanation of this sort might\ntake the following form:", "\n\n\n[1]\nPeople act (in general) in such a way that their goals will be\nobtained (as well as possible in the given situation), or in such a\nway that their expectations will not be frustrated, …\nif their beliefs are true.\n[2]\nMany beliefs [people have about how to attain their goals]\nare true.\n[3]\nSo, as a consequence of [1] and [2], people have a tendency to\nattain certain kinds of goals. (Putnam 1978, 101)\n\n", "\nThe generality of [1] in this explanation seems to cover more cases\nthan any definite list of actual beliefs that someone has could\ninclude. Moreover, the fact that [1] supports counterfactuals by\napplying to whatever one might possibly believe (about attaining\ngoals) suggests that it is a law-like generalization. If the truth\npredicate played a fundamental role in the expression of an\nexplanatory law, then deflationism would seem to be\nunsustainable.", "\nA standard deflationary response to this line of reasoning involves\nrejecting the thesis that [1] is a law, seeing it (and truth-involving\nclaims like it) instead as functioning similarly to how the claim\n‘What Mary believes is true’ functions in an explanation\nof her particular instance of behavioral success, just expressing an\neven more indefinite, and thus potentially infinite claim. The latter\nis what makes a claim like [1] seem like an explanatory law, but even\nconsidering this indefiniteness, the standard deflationary account of\n[1] claims that the function of the appeal to the notion of truth\nthere is still just to express a kind of generalization. One way to\nbring out this response is to note that, similar to the deflationary\n“infinite disjunction” account of the claim ‘What\nMary believes is true’, generalizations of the kind offered in\n[1] entail infinite conjunctions of their instances, which\nare claims that can be formulated without appeal to truth. For\nexample, in the case of explaining someone, \\(A\\), accomplishing their\ngoal of getting to a party, deflationsts typically claim that the role\nof citing possession of a true belief is really just to express an\ninfinite conjunction with something like the following form:", "\nIf \\(A\\) believes that the party is 1001 Northside Avenue, and the\nparty is at 1001 Northside Avenue, then \\(A\\) will get what they want;\nand if \\(A\\) believes that the party is at 1001 Southside Avenue, and\nthe party is at 1001 Southside Ave, then \\(A\\) will get what they\nwant; and if \\(A\\) believes that party is at 17 Elm St, and the party\nis at 17 Elm St, then \\(A\\) will get what they want; … and so\non.\n", "\nThe equivalence schema (ES) allows one to capture this infinite\nconjunction (of conditionals) in a finite way. For, on the basis of\nthe schema, one can reformulate the infinite conjunction as:", "\nIf \\(A\\) believes that the party is 1001 Northside Avenue, and that\nthe party is 1001 Northside Avenue is true, then \\(A\\) will get what\nthey want; and if \\(A\\) believes that the party is at 1001 Southside\nAvenue, and that the party is at 1001 Southside Avenue is true, then\n\\(A\\) will get what they want, and if \\(A\\) believes that the party is\nat 17 Elm Street, and that the party is at 17 Elm Street is true, then\n\\(A\\) will get what they want; … and so on.\n", "\nIn turn, this (ES)-reformulated infinite conjunction can be expressed\nas a finite statement with a universal quantifier ranging over\npropositions:", "\nFor every proposition \\(x\\), if what \\(A\\) believes \\(= x\\), and \\(x\\)\nis true, then \\(A\\) will get what they want, other things being equal.\n", "\nThe important point for a deflationist is that one could not express\nthe infinite conjunction regarding the agent’s beliefs and\nbehavioral success unless one had the concept of truth. But\ndeflationists also claim that this is all that the notion of truth is\ndoing here and in similar explanations (cf. Leeds 1978, 1995; Williams\n1986, Horwich 1998a).", "\nHow successful is this standard deflationary response? There are\nseveral critiques in the literature. Some (e.g., Damnjanovic 2005)\nargue that there is no distinction in the first place between\nappearing in a causal-explanatory generalization and being a\ncausal-explanatory property. After all, suppose it is a true\ngeneralization that metal objects conduct electricity. That would\nnormally be taken as sufficient to show that being metal is a\ncausal-explanatory property that one can cite in explaining why\nsomething conducts electricity. But isn’t this a counter, then,\nto deflationism’s thesis that, assuming there is a property of\ntruth at all, it is at most an insubstantial one? If a property is a\ncausal or explanatory property, after all, it is hard to view it as\ninsubstantial.", "\nThe reasoning at issue here may be presented conveniently by expanding\non the general argument considered above and proceeding from an\napparently true causal generalization to the falsity of deflationism\n(ibid.):", "\n\n\nP1.\nIf a person \\(A\\) has true beliefs, they will get what they want,\nother things being equal.\nC1.\nTherefore, if \\(A\\) has beliefs with the property of being true,\n\\(A\\) will get what they want other things being equal.\nC2.\nTherefore, the property of being true appears in a\ncausal-explanatory generalization.\nC3.\nTherefore, the property of being true is a causal-explanatory\nproperty.\nC4.\nTherefore, deflationism is false.\n\n", "\nCan a deflationist apply the standard deflationary response to this\nargument? Doing so would seem to involve rejecting the inference from\nC2 to C3. After all, the standard reply would say that the role that\nthe appeal to truth plays in P1, the apparent causal generalization,\nis simply its generalizing role of expressing a potentially infinite,\ndisjointed conjunction of unrelated causal connections (cf. Leeds\n1995). So, applying this deflationary response basically hinges on the\nplausibility of rejecting the initial assumption that there is no\ndistinction between appearing in a causal-explanatory generalization\nand being a causal-explanatory property.", "\nIt is worth noting two other responses beyond the standard one that a\ndeflationist might make to the reasoning just set out. The first\noption is to deny the step from P1 to C1. This inference involves the\nexplicit introduction of the property of being true, and, as we have\nseen, some deflationists deny that there is a truth property at all\n(cf. Quine 1970 [1986], Grover, et al. 1975, Leeds 1978,\nBrandom 1994). But, as we noted above, the idea that there is no truth\nproperty may be difficult to sustain given the apparent fact that\n‘is true’ functions grammatically as a predicate.", "\nThe second option is to deny the final step from C3 to C4 and concede\nthat there is a sense in which truth is a causal-explanatory property\nand yet say that it is still not a substantive property (cf.\nDamnjanovic 2005). For example, some philosophers (e.g., Friedman\n1974, van Fraassen 1980, Kitcher 1989, Jackson and Pettit 1990) have\noffered different understandings of\n scientific explanation\n and causal explanation, according to which being a causal and\nexplanatory property might not conflict with being insubstantial\n(perhaps by being an abundant or ungroundable property). This might be\nenough to sustain a deflationary position.", "\nThe standard deflationary response to the explanatory-role challenge\nhas also met with criticisms focused on providing explanations of\ncertain “higher-level” phenomena. Philip Kitcher (2002,\n355–60) concludes that Horwich’s (1998a, 22–3)\napplication of the standard response, in his account of how the notion\nof truth functions in explanations of behavioral success, misses the\nmore systematic role that truth plays in explaining patterns\nof successful behavior, such as when mean-ends beliefs flow from a\nrepresentational device, like a map. Chase Wrenn (2011) agrees with\nKitcher that deflationists need to explain systematic as opposed to\njust singular success, but against Kitcher he argues that\ndeflationists are actually better off than inflationists on this\nfront. Will Gamester (2018, 1252–5) raises a different\n“higher-level factor” challenge, one based on the putative\ninability of the standard deflationary account of the role of truth in\nexplanations of behavioral success to distinguish between coincidental\nand non-coincidental success. Gamester (ibid., 1256–7) claims\nthat an inflationist could mark and account for the difference between\nthe two kinds of success with an explanation that appeals to the\nnotion of truth. But it is not clear that a deflationist cannot also\navail herself of a version of this truth-involving explanation, taking\nit just as the way of expressing in natural language what one might\nformally express with sentential variables and quantifiers (cf. Ramsey\n1927, 1929; Prior 1971, Wrenn 2021, and Armour-Garb and Woodbridge\nforthcoming)." ], "subsection_title": "4.1 The Explanatory Role of Truth" }, { "content": [ "\nWe noted earlier that deflationism can be presented in either a\nsententialist version or a propositionalist version. Some philosophers\nhave suggested, however, that the choice between these two versions\nconstitutes a dilemma for deflationism (Jackson, Oppy, and Smith\n1994). The objection is that if deflationism is construed in\naccordance with propositionalism, then it is trivial, but if it is\nconstrued in accordance with sententialism, it is false. To illustrate\nthe dilemma, consider the following claim:", "\nNow, does ‘snow is white’ in (12) refer to a\nsentence or a proposition? If, on the one hand, we take (12) to be\nabout a sentence, then, assuming (12) can be interpreted as making a\nnecessary claim, it is false. On the face of it, after all, it takes a\nlot more than snow’s being white for it to be the case that\n‘snow is white’ is true. In order for ‘snow is\nwhite’ to be true, it must be the case not only that snow is\nwhite, it must, in addition, be the case that ‘snow is\nwhite’ means that snow is white. But this is a fact\nabout language that (12) ignores. On the other hand, suppose we take\n‘snow is white’ in (12) to denote the proposition\nthat snow is white. Then the approach looks to be trivial, since the\nproposition that snow is white is defined as being the one that is\ntrue just in case snow is white. Thus, deflationism faces the dilemma\nof being false or trivial.", "\nOne response for the deflationist is to remain with the\npropositionalist version of their doctrine and accept its triviality.\nA trivial doctrine, after all, at least has the advantage of being\ntrue.", "\nA second response is to resist the suggestion that propositionist\ndeflationism is trivial. For one thing, the triviality here does not\nhave its source in the concept of truth, but rather in the concept of\na proposition. Moreover, even if we agree that the proposition that\nsnow is white is defined as the one that is true if and only if snow\nis white, this still leaves open whether truth is a substantive\nproperty of that proposition; as such it leaves open whether\ndeflationism or inflationism is correct.", "\nA third response to this dilemma is to accept that deflationism\napplies inter alia to sentences, but to argue (following\nField 1994a) that the sentences to which it applies must be\ninterpreted sentences, i.e., sentences which already have\nmeaning attached to them. While it takes more than snow being white to\nmake the sentence ‘snow is white’ true, when we think of\nit as divorced from its meaning, that is not so clear when we treat it\nas having the meaning it in fact has." ], "subsection_title": "4.2 Propositions Versus Sentences" }, { "content": [ "\nIt is often said to be a platitude that true statements correspond to\nthe facts. The so-called “correspondence theory of truth”\nis built around this intuition and tries to explain the notion of\ntruth by appealing to the notions of correspondence and fact. But even\nif one does not build one’s approach to truth around\nthis intuition, many philosophers regard it as a condition of adequacy\non any approach that it accommodate this correspondence intuition.", "\nIt is often claimed, however, that deflationism has trouble meeting\nthis adequacy condition. One way to bring out the problem here is by\nfocusing on a particular articulation of the correspondence intuition,\none favored by deflationists themselves (e.g., Horwich 1998a).\nAccording to this way of spelling it out, the intuition that a certain\nsentence or proposition “corresponds to the facts” is the\nintuition that the sentence or proposition is true because of\nhow the world is; that is, the truth of the proposition is\nexplained by some fact, which is usually external to the\nproposition itself. We might express this by saying that someone who\nendorses the correspondence intuition so understood would endorse:", "\nThe problem with (6) is that, when we combine it with deflationism\n– or at least with a necessary version of that approach –\nwe can derive something that is plainly false. Anyone who assumes that\nthe instances of the equivalence schema are necessary would clearly be\ncommitted to the necessary truth of:", "\nAnd, since (7) is a necessary truth, under that assumption, it is very\nplausible to suppose that (6) and (7) together entail:", "\nBut (8) is clearly false. The reason is that the ‘because’\nin (6) and (8) is a causal or explanatory relation, and plausibly such\nrelations must obtain between distinct relata. But the relata in (8)\nare (obviously) not distinct. Hence, (8) is false, and this means that\nthe conjunction of (6) and (7) must be false, and that deflationism is\ninconsistent with the correspondence intuition. To borrow a phrase of\nMark Johnston’s (1989) – who mounts a similar argument in\na different context – we might say that if deflationism is true,\nthen what seems to be a perfectly good explanation in (6) goes\nmissing; if deflationism is true, after all, then (6) is\nequivalent to (8), and (8) is not an explanation of anything.", "\nOne way a deflationist might attempt to respond to this objection is\nby providing a different articulation of the correspondence intuition.\nFor example, one might point out that the connection between the\nproposition that snow is white being true and snow’s being white\nis not a contingent connection and suggest that this rules out (6) as\na successful articulation of the correspondence intuition. That\nintuition (one might continue) is more plausibly given voice by", "\nHowever, when (6*) is conjoined with (7), one cannot derive the\nproblematic (8), and thus, one might think, the objection from\ncorrespondence might be avoided. Now, certainly this is a possible\nsuggestion; the problem with it, however, is that a deflationist who\nthinks that (6*) is true is most plausibly construed as holding a\nsententialist, rather than a propositionalist, version of\ndeflationism. A sententialist version of deflationism will supply a\nversion of (7), viz.:", "\nwhich, at least if it is interpreted as a necessary (or analytic)\ntruth, will conspire with (6*) to yield (8). And we are back where we\nstarted.", "\nAnother response would be to object that ‘because’ creates\nan opaque context – that is, the kind of context within\nwhich one cannot substitute co-referring expressions and preserve\ntruth. However, for this to work, ‘because’ must create an\nopaque context of the right kind. In general, we can distinguish two\nkinds of opaque context: intensional contexts, which allow\nthe substitution of necessarily co-referring expressions but not\ncontingently co-referring expressions; and\n hyperintensional\n contexts, which do not even allow the substitution of necessarily\nco-referring expressions. If the inference from (6) and (7) to (8) is\nto be successfully blocked, it is necessary that ‘because’\ncreates a hyperintensional context. A proponent of the correspondence\nobjection might try to argue that while ‘because’ creates\nan intensional context, it does not create a hyperintensional context.\nBut since a hyperintensional reading of ‘because’ has\nbecome standard fare, this approach remains open to a deflationist and\nis not an ad hoc fix.", "\nA final, and most radical, response would be to reject the\ncorrespondence intuition outright. This response is not as drastic as\nit sounds. In particular, deflationists do not have to say that\nsomeone who says ‘the proposition that snow is white corresponds\nto the facts’ is speaking falsely. Deflationists might do better\nby saying that such a person is simply using a picturesque or ornate\nway of saying that the proposition is true, where truth is understood\nin accordance with deflationism. Indeed, a deflationist can even agree\nthat, for certain rhetorical or conversational purposes, it might be\nmore effective to use talk of “correspondence to the\nfacts”. Nevertheless, it is important to see that this response\ndoes involve a burden, since it involves rejecting a condition of\nadequacy that many regard as binding." ], "subsection_title": "4.3 Correspondence" }, { "content": [ "\nAccording to some metaethicists\n (moral non-cognitivists\n or expressivists), moral claims – such as the injunction that\none ought to return people’s phone calls – are neither\ntrue nor false. The same situation holds, according to some\nphilosophers of language, for claims that presuppose the existence of\nsomething which does not in fact exist, such as the claim that the\npresent King of France is bald; for sentences that are vague, such as\n‘These grains of sand constitute a heap’; and for\nsentences that are paradoxical, such as those that arise in connection\nwith the\n Liar Paradox.\n Let us call this thesis the gap, since it finds a gap in the\nclass of sentences between those that are true and those that are\nfalse.", "\nThe deflationary approach to truth has seemed to be inconsistent with\nthe gap, and this has been thought by some (e.g., Dummett 1959 [1978,\n4] and Holton 2000) to be an objection. The reason for the apparent\ninconsistency flows from a natural way to extend the deflationary\napproach from truth to falsity. The most natural thing for a\ndeflationist to do is to introduce a falsity schema like:", "\nFollowing Holton (1993, 2000), we consider (F-sent) to be the relevant\nschema for falsity, rather than some propositional schema, since the\nstandard understanding of a gappy sentence is as one that does not\nexpress a proposition (cf. Jackson, et al. 1994).", "\nWith a schema like (F-sent) in hand, deflationists could say things\nabout falsity similar to what they say about truth: (F-sent) exhausts\nthe notion of falsity, there is no substantive property of falsity,\nthe utility of the concept of falsity is just a matter of facilitating\nthe expression of certain generalizations, etc.", "\nHowever, there is a seeming incompatibility between (F-sent) and the\ngap. Suppose, for reductio, that ‘S’ is a\nsentence that is neither true nor false. In that case, it is not the\ncase that ‘S’ is true, and it is not the case that\n‘S’ is false. But then, by (ES-sent) and (F-sent), we can\ninfer that it is not the case that S, and it is not the case that\nnot-S; in short: \\({\\sim}\\)S and \\({\\sim}{\\sim}\\)S, which is a\nclassical contradiction. Clearly, then, we must give up one of these\nthings. But which one can we give up consistently with\ndeflationism?", "\nIn the context of ethical non-cognitivism, one possible response to\nthe apparent dilemma is to distinguish between a deflationary account\nof truth and a deflationary account of truth-aptitude (cf.\nJackson, et al. 1994). By accepting an inflationary account\nof the latter, one can claim that ethical statements fail the robust\ncriteria of “truth-aptitude” (reidentified in terms of\nexpression of belief), even if a deflationary view of truth still\nallows the application of the truth predicate to them, via\ninstances of (ES). In the case of\n vagueness,\n one might adopt epistemicism about it and claim that vague sentences\nactually have truth-values, we just can’t know them (cf.\nWilliamson 1994. For an alternative, see Field 1994b).", "\nWith respect to the Liar Paradox, the apparent conflict between\ndeflationism and the gap has led some (e.g., Simmons 1999) to conclude\nthat deflationism is hobbled with respect to dealing with the problem,\nsince most prominent approaches to doing so, stemming from the work of\nSaul Kripke (1975), involve an appeal to truth-value gaps. One\nalternative strategy a deflationist might pursue in attempting to\nresolve the Liar is to offer a non-classical logic. Field 2008 adopts\nthis approach and restricts the law of the excluded middle. JC Beall\n(2002) combines truth-value gaps with Kleene logic (see the entry on\n many-valued Logic)\n and makes use of both weak and strong\n negation.\n Armour-Garb and Beall (2001, 2003) argue that deflationists can and\nshould be\n dialetheists\n and accept that some truthbearers are both true and not true (see\nalso, Woodbridge 2005, 152–3, on adopting a\n paraconsistent logic\n that remains “quasi-classical”). By contrast, Armour-Garb\nand Woodbridge (2013, 2015) develop a version of the\n“meaningless strategy” with respect to the Liar (based on\nGrover 1977), which they claim a deflationist can use to dissolve that\nparadox and semantic pathology more generally, without accepting\ngenuine truth-value gaps or giving up classical logic." ], "subsection_title": "4.4 Truth-Value Gaps" }, { "content": [ "\nSince deflationists place such heavy emphasis on the role of the\nconcept of truth in expressing generalizations, it seems somewhat\nironic that certain versions of deflationism have been criticized for\nbeing incapable of accounting for generalizations involving\ntruth (Gupta 1993a, 1993b; Field 1994a, 2008; Horwich 1998a\n(137–8), 2001; Halbach 1999 and 2011 (57–9); Soames 1999,\nArmour-Garb 2004, 2010, 2011). The “Generalization\nProblem” (henceforth, \\(GP)\\) captures the worry that a\ndeflationary account of truth is inadequate for explaining our\ncommitments to general facts we express with certain uses of\n‘true’. This raises the question of whether and, if so,\nhow, deflationary accounts earn the right to endorse such\ngeneralizations.", "\nAlthough Tarski (1935 [1956]) places great importance on the instances\nof his (T)-schema, he comes to recognize that those instances do not\nprovide a fully adequate way of characterizing truth. Moreover, even\nwhen the instances of (T) are taken as theorems, Tarski (ibid.) points\nout that taken all together they are insufficient for proving a\n‘true’-involving generalization like", "\nsince the collection of the instances of (T) is \\(\\omega\\)-incomplete\n(where a theory, \\(\\theta\\), is \\(\\omega\\)-incomplete if\n\\(\\theta\\) can prove every instance of an open formula\n‘\\(Fx\\)’ but cannot prove the universal generalization,\n‘\\(\\forall xFx\\)’).", "\nWe arrive at a related problem when we combine a reliance on the\ninstances of some version of (ES) with Quine’s view about the\nfunctioning and utility of the truth predicate. He (1992, 81)\nconsiders the purpose of (A) to be to express a generalization over\nsentences like the following:", "\nQuine points out that we want to be able to generalize on the embedded\nsentences in those conditionals, by semantically ascending,\nabstracting logical form, and deriving (A). But, as Tarski (ibid.)\nnotes, this feat cannot be achieved, given only a commitment to (the\ninstances of) (T). From (T) and (A), we can prove (B) and (C) but,\ngiven the finitude of deduction, when equipped only with the instances\nof (T), we cannot prove (A). As a consequence of the Compactness\nTheorem of first-order logic, anything provable from the totality of\nthe instances of (T) is provable from just finitely many of them, so\nany theory that takes the totality of the instances of (T) to\ncharacterize truth will be unable to prove any generalization like\n(A).", "\nTo address the question of why we need to be able to prove these\ntruth-involving generalizations, suppose that we accept a proposition\nlike \\(\\langle\\)Every proposition of the form \\(\\langle\\)if \\(p\\),\nthen \\(p\\rangle\\) is true\\(\\rangle\\). Call this proposition\n“\\(\\beta\\)”. Now take ‘\\(\\Gamma\\)’ to stand\nfor the collection of propositions that are the instances of\n\\(\\beta\\). Horwich (2001) maintains that an account of the meaning of\n‘true’ will be adequate only if it aids in explaining why\nwe accept the members of \\(\\Gamma\\), where such explanations amount to\nproofs of those propositions by, among other things, employing an\nexplanatory premise that does not explicitly concern the truth\npredicate. So, one reason it is important to be able to prove a\n‘true’-involving generalization is because this is a\ncondition of adequacy for an account of the meaning of that term. One\nmight argue that anyone who grasps the concept of truth, and that of\nthe relevant conditional, should be said to know \\(\\beta\\). But if a\ngiven account of truth, together with an account of the conditional\n(along, perhaps, with an account of other logical notions), does not\nentail \\(\\beta\\), then it does not provide an acceptable account of\ntruth.", "\nHere is another reason for thinking that generalizations like\n\\(\\beta\\) must be proved. A theory of the meaning of\n‘true’ should explain our acceptance of propositions like\n\\(\\beta\\), which, as Gupta (1993a) and Hill (2002) emphasize, should\nbe knowable a priori by anyone who possesses the concept of\ntruth (and who grasps the relevant logical concepts). But if such a\nproposition can be known a priori on the basis of a grasp of\nthe concept of truth (and of the relevant logical concepts), then a\ntheory that purports to specify the meaning of ‘true’\nshould be able to explain our acceptance of that proposition. But if\nan account of the meaning of ‘true’ is going to do this,\nit must be possible to derive the proposition from one or more of the\nclauses that constitute our grasp of the concept of truth.", "\nThis creates a problem for a Horwichian minimalist. Let us suppose\nthat \\(\\beta\\) is one of the general propositions that must be\nprovable. Restricted to the resources available through\nHorwich’s minimalism, we can show that \\(\\beta\\) cannot be\nderived.", "\nIf a Horwichian minimalist could derive \\(\\beta\\), it would have to be\nderived from the instances of", "\nBut there cannot be a valid derivation of a universal generalization\nfrom a set of particular propositions unless that set is inconsistent.\nSince, according to Horwich (1998a), every instance of (E) that is\npart of his theory of truth is consistent, it follows that there\ncannot be a derivation of \\(\\beta\\) from the instances of (E). This is\na purely logical point. As such, considerations of pure logic dictate\nthat our acceptance of \\(\\beta\\) cannot be explained by\nHorwich’s account of truth. Since Horwich takes all instances of\nthe propositional version of (T) (i.e., (ES-prop)) as axioms, he can\nprove each of those instances. But, as we have seen, restricted to the\ninstances of the equivalence schema, he cannot prove the\ngeneralization, \\(\\beta\\), i.e., \\(\\langle\\)Every proposition of the\nform \\(\\langle\\)if \\(p\\) then \\(p\\rangle\\) is true\\(\\rangle\\).", "\nSome deflationists respond to the GP by using a version of (GT) to\nformulate their approach:", "\nIn this context, there are two things to notice about (GT). First, it\nis not a schema but a universally quantified formula. For this reason,\nit is possible to derive a generalization like \\(\\beta\\) from it.\nSecond, the existential quantifier, ‘\\(\\Sigma\\)’, in (GT)\nmust be a higher-order quantifier (see the entry on\n second-order and higher-order logic)\n that quantifies into sentential positions. We mentioned above an\napproach that takes this quantifier as a substitutional one, where the\nsubstitution class consists of sentences. We also mentioned\nHill’s (2002) alternative version that takes the substitution\nclass to be the set of all propositions. Künne (2003) suggests a\ndifferent approach that takes ‘\\(\\Sigma\\)’ to be an\nobjectual (domain and values) quantifier ranging over propositions.\nHowever, parallel to Horwich’s rejection of (GT) discussed in\nSection 3.1, all of these approaches have drawn criticism on the\ngrounds that the use of higher-order quantifiers to define truth is\ncircular (cf. Platts 1980, McGrath 2000), and may get the extension of\nthe concept of truth wrong (cf. Sosa 1993).", "\nAn alternative deflationist approach to the GP attempts to show that,\ndespite appearances, certain deflationary theories do have the\nresources to derive the relevant generalizations. Field (1994a,\n2001a), for example, suggests that we allow reasoning with schemas\ndirectly and proposes rules that would allow the derivation of\ngeneralizations. Horwich (1998a, 2001) suggests a more informal\napproach according to which we are justified in deriving \\(\\beta\\)\nsince an informal inspection of a derivation of some instance of\n\\(\\beta\\) shows us that we could derive any instance of it. For\nreplies to Horwich, see Armour-Garb 2004, 2010, 2011; Gupta 1993a,\n1993b; and Soames 1999. For responses to Armour-Garb’s attack on\nHorwich 2001, see Oms 2019 and Cieśliński 2018." ], "subsection_title": "4.5 The Generalization Problem" }, { "content": [ "\nAn ideal theory of truth will be both consistent (e.g., avoid the Liar\nParadox) and adequate (e.g., allow us to derive all the essential laws\nof truth, such as those at issue in the Generalization Problem). Yet\nit has recently been argued that even if deflationists can provide a\nconsistent theory of truth and avoid the GP, they still cannot provide\nan adequate theory.", "\nThis argument turns on the notion of a conservative extension of a\ntheory. Informally, a conservative extension of a theory is one that\ndoes not allow us to prove anything that could not be proved from the\noriginal, unextended theory. More formally, and applied to theories of\ntruth, a truth theory, \\(Tr\\) is conservative over some theory \\(T\\)\nformulated in language \\(L\\) if and only if for every sentence\n\\(\\phi\\) of \\(L\\) in which the truth predicate does not occur, if \\(Tr\n\\cup L \\vdash \\phi\\), then \\(L \\vdash \\phi\\) (where\n‘\\(\\vdash\\)’ represents provability). Certain\ntruth theories are conservative over arithmetic – e.g., theories\nthat implicitly define truth using only the instances of some version\nof (ES) – and certain truth theories are not – e.g.,\nTarski’s (1935 [1956], 1944) compositional theory. Specifically,\nthe addition of certain truth theories allows us to prove that\narithmetic is consistent, something that we cannot do if we are\nconfined to arithmetic itself.", "\nIt has been argued (a) that conservative truth theories are inadequate\nand (b) that deflationists are committed to conservative truth\ntheories. (See Shapiro 1998 and Ketland 1999; Horsten 1995 provides an\nearlier version of this argument.) We will explain the arguments for\n(a) below but to get a flavor of the arguments for (b), consider\nShapiro’s rhetorical question: “How thin can the notion of\narithmetic truth be, if by invoking it we can learn more about the\nnatural numbers?” Shapiro is surely right to press deflationists\non their frequent claims that truth is “thin” or\n“insubstantial”. It might also be a worry for\ndeflationists if any adequate truth theory allowed us to derive\nnon-logical truths, if they endorse the thesis that truth is merely a\n“logical property”. On the other hand, deflationists\nthemselves insist that truth is an expressively useful device, and so\nthey cannot be faulted for promoting a theory of truth that allows us\nto say more about matters not involving truth.", "\nTo see an argument for (a), consider a Gödel sentence, \\(G\\),\nformulated within the language of Peano Arithmetic (henceforth,\n\\(PA)\\). \\(G\\) is not a theorem of PA if PA is consistent (cf. the\nentry on\n Gödel’s incompleteness theorems).\n But \\(G\\) becomes a theorem when PA is expanded by adding certain\nplausible principles that appear to govern a truth predicate. Thus,\nthe resultant theory of arithmetical truth is strong enough to prove G\nand appears therefore to be non-conservative over arithmetic. If, as\nhas been argued by a number of theorists, any adequate account of\ntruth will be non-conservative over a base theory, then deflationists\nappear to be in trouble.", "\nUnderstood in this way, the “Conservativeness Argument”\n(henceforth, \\(CA)\\) is a variant of the objection considered in\nSection 4.1, claiming that truth plays an explanatory role that\ndeflationism cannot accommodate. There are several deflationary\nresponses to the CA. Field (1999) argues that the worries that arise\nfrom the claim that deflationists are in violation of explanatory\nconservativeness is unfounded. He (ibid., 537) appeals to the\nexpressive role of the truth predicate and maintains that\ndeflationists are committed to a form of “explanatory\nconservativeness” only insofar as there are no explanations in\nwhich the truth predicate is not playing its generalizing role. As a\nresult, he (ibid.) notes that “any use of ‘true’ in\nexplanations which derives solely from its role as a device of\ngeneralization should be perfectly acceptable”. For responses to\nField, see Horsten 2011 (61) and Halbach 2011 (315–6).", "\nResponding to the CA, Daniel Waxman (2017) identifies two readings of\n‘conservativeness’, one semantic and the other syntactic,\nwhich correspond to two conceptions of arithmetic. On the first\nconception, arithmetic is understood categorically as given\nby the standard model. On the second conception, arithmetic is\nunderstood axiomatically and is captured by the acceptance of\nsome first-order theory, such as PA. Waxman argues that deflationism\ncan be conservative given either conception, so that the CA does not\ngo through.", "\nJulien Murzi and Lorenzo Rossi (2018) argue that Waxman’s\nattempt at marrying deflationism with conservativeness – his\n“conservative deflationism” – is unsuccessful. They\n(ibid.) reject the adoption of this view on the assumption that\none’s conception of arithmetic is axiomatic, claiming, in\neffect, that a deflationist’s commitment to a conservative\nconception of truth is misguided (cf. Halbach 2011, Horsten 2011,\nCieśliński 2015, and Galinon 2015).", "\nJody Azzouni (1999) defends the “first-order\ndeflationist”, viz., a deflationist who endorses what Waxman\n(ibid.) calls “the axiomatic conception of arithmetic” and\nwhose subsequent understanding cannot rule out the eligibility of\nnon-standard models. Azzouni accepts the need to prove certain\n‘true’-involving generalizations, but he maintains that\nthere are some generalizations that are about truths that a\nfirst-order deflationist need not prove. He further contends that if\none does extend her theory of truth in a way that allows her to\nestablish these generalizations, she should not expect her theory to\nbe conservative, nor should she continue describing it as a\ndeflationary view of truth. For a response to Azzouni\n(ibid.), see Waxman (2017, 453).", "\nIn line with Field’s response to the CA, Lavinia Picollo and\nThomas Schindler (2020) argue that the conservativeness constraint\nimposed by Horsten 1995, Shapiro 1998, Ketland 1999, and others is not\na reasonable requirement to impose on deflationary accounts. They\ncontend that the insistence on conservativeness arises from making too\nmuch of the metaphor of “insubstantiality” and that it\nfails to see what the function of the truth predicate really amounts\nto. Their leading idea is that, from a deflationist’s\nperspective, the logico-linguistic function of the truth predicate is\nto simulate sentential and predicate quantification in a first-order\nsetting (cf. Horwich 1998a, 4, n. 1). They maintain that, for a\ndeflationist, in conjunction with first-order quantifiers, the truth\npredicate has the same function as sentential and predicate\nquantifiers. So, we should not expect the deflationist’s truth\ntheory to conservatively extend its base theory." ], "subsection_title": "4.6 Conservativeness" }, { "content": [ "\nIt is commonly said that our beliefs and assertions aim at truth, or\npresent things as being true, and that truth is therefore a\nnorm of assertion and belief. This putative fact about truth\nand assertion in particular has been seen to suggest that deflationism\nmust be false (cf. Wright 1992 and Bar-On and Simmons 2007). However,\nthe felt incompatibility between normativity and deflationism is\ndifficult to make precise.", "\nThe first thing to note is that there is certainly a sense in which\ndeflationism is consistent with the idea that truth is a norm of\nassertion. To illustrate this, notice (as we saw in examining\ntruth’s putative explanatory role) that we can obtain an\nintuitive understanding of this idea without mentioning truth at all,\nso long as we focus on a particular case. Suppose that for whatever\nreason Mary sincerely believes that snow is green, has good evidence\nfor this belief, and on the basis of this belief and evidence asserts\nthat snow is green. We might say that there is a norm of assertion\nthat implies that Mary is still open to criticism in this case. After\nall, since snow is not green, there must be something\nincorrect or defective about Mary’s assertion\n(and similarly for her belief). It is this incorrectness or\ndefectiveness that the idea that truth is a norm of assertion (and\nbelief) is trying to capture.", "\nTo arrive at a general statement of the norm that lies behind this\nparticular case, consider that here, what we recognize is", "\nTo generalize on this, what we want to do is generalize on the\npositions occupied by ‘snow is green’ and express\nsomething along the lines of", "\nThe problem of providing a general statement like (14) is the same\nissue first raised in Section 1.3, and the solution by now should be\nfamiliar. To state the norm in general we would need to be able to do\nsomething we seem unable to do in ordinary language, namely, employ\nsentential variables and quantifiers for them. But this is where the\nnotion of truth comes in. Because (ES) gives us its\ncontraposition,", "\nReading ‘\\(\\langle p\\rangle\\)’ as ‘that\n\\(p\\)’, we can reformulate (14) as", "\nBut since the variable ‘\\(p\\)’ occurs only in nominalized\ncontexts in (15), we can replace it with an object variable,\n‘\\(x\\)’, and bind this with an ordinary objectual\nquantifier, to get", "\nOr, to put it as some philosophers might:", "\nIn short, then, deflationists need not deny that we appeal to the\nnotion of truth to express a norm of assertion; on the\ncontrary, the concept of truth seems required to state that very\ngeneralization.", "\nIf deflationists can account for the fact that we must apply the\nnotion of truth to express a norm of assertion, then does normativity\npose any problem for deflationism? Crispin Wright (1992, 15–23)\nargues that it does, claiming that deflationism is inherently unstable\nbecause there is a distinctive norm for assertoric practice that goes\nbeyond the norms for warranted assertibility – that the norms of\ntruth and warranted assertibility are potentially extensionally\ndivergent. This separate norm of truth, he claims, is already implicit\njust in acceptance of the instances of (ES). He points out that not\nhaving warrant to assert some sentence does not yield having warrant\nto assert its negation. However, because (ES) gives us (ES-con), we\nhave, in each instance, an inference (going from right to left) from\nthe sentence mentioned not being true to the negation of the sentence.\nBut the instance of (ES) for the negation of any sentence,", "\ntakes us (again, going from right to left) from the negated sentence\nto an ascription of truth to that negated sentence. Thus, some\nsentence not being true does yield that the negation of the\nsentence is true, in contrast with warranted assertibility. This\ndifference, Wright (ibid., 18) claims, reveals that, by\ndeflationism’s own lights, the truth predicate expresses a\ndistinct norm governing assertion, which is incompatible with the\ndeflationary contention “that ‘true’ is only\ngrammatically a predicate whose role is not to attribute a substantial\ncharacteristic”.", "\nRejecting Wright’s argument for the instability of deflationism,\nIan Rumfitt (1995, 103) notes that if we add the ideas of denying\nsomething and of having warrant for doing so\n(“anti-warrant”) to Wright’s characterization of\ndeflationism, this would make ‘is not true’ simply a\ndevice of rejection governed by the norm that “[t]he predicate\n‘is not true’ may be applied to any sentence for which one\nhas an anti-warrant”. But then truth-talk’s behavior with\nnegation would not have to be seen as indicating that it marks a\ndistinct norm beyond justified assertibility and justifiable\ndeniability, which would be perfectly compatible with\ndeflationism.", "\nField (1994a, 264–5) offers a deflationary response to\nWright’s challenge (as well as to a similar objection regarding\nnormativity from Putnam (1983a, 279–80)), pointing again to the\ngeneralizing role of the truth predicate in such normative desires as\none to utter only true sentences or one to have only true beliefs.\nField agrees with Wright that truth-talk expresses a norm beyond\nwarranted assertibility, but he (1994a, 265) also maintains that\n“there is no difficulty in desiring that all one’s beliefs\nbe disquotationally true; and not only can each of us desire such\nthings, there can be a general practice of badgering other to into\nhaving such desires”. Horwich (1996, 879–80) argues that\nWright’s rejection of deflationism does not follow from showing\nthat one can use the truth predicate to express a norm beyond\nwarranted assertibility. Like Field, Horwich claims that Wright missed\nthe point that, in the expression of such a norm, the truth predicate\nis just playing its generalizing role. For other objections to\ndeflationism based on truth’s normative role, see Price 1998,\n2003 and McGrath 2003." ], "subsection_title": "4.7 Normativity" }, { "content": [ "\nAnother objection to deflationism begins by drawing attention to a\nlittle-known doctrine about truth that G.E. Moore held at the\nbeginning of the 20th Century. Richard Cartwright (1987, 73) describes\nthe view as follows: “a true proposition is one that has a\ncertain simple unanalyzable property, and a false proposition is one\nthat lacks the property”. This doctrine about truth is to be\nunderstood as the analogue for the doctrine that Moore held about\ngoodness, namely that goodness is a simple, unanalyzable quality.", "\nThe potential problem that this Moorean view about truth presents for\ndeflationism might best be expressed in the form of a question: What\nis the difference between the Moorean view and deflationism? One might\nreply that, according to deflationary theories, the concept of truth\nhas an important logical role, i.e., expressing certain\ngeneralizations, whereas the concept of goodness does not. However,\nthis doesn’t really answer our question. For one thing, it\nisn’t clear that Moore’s notion of truth does not also\ncapture generalizations, since it too will yield all of the instances\nof (ES). For another, the idea that the concept of truth plays an\nimportant logical role doesn’t distinguish the metaphysics of\ndeflationary conceptions from the metaphysics of the Moorean view, and\nit is the metaphysics of the matter that the present objection really\nbrings into focus. Alternatively, one might suggest that the\ndistinction between truth according to Moore’s view and\ndeflationary conceptions of truth is the distinction between having a\nsimple unanalyzable nature, and not having any underlying nature at\nall. But what is that distinction? It is certainly not obvious that\nthere is any distinction between having a nature about which nothing\ncan be said and having no nature at all.", "\nHow might a deflationist respond to this alleged problem? The key move\nwill be to focus on the property of being true. For the Moorean, this\nproperty is a simple unanalyzable one. But deflationists need not be\ncommitted to this. As we have seen, some deflationists think that\nthere is no truth property at all. And even among deflationists who\naccept that there is some insubstantial truth property, it is not\nclear that this is the sort of property that the Moorean has in mind.\nTo say that a property is unanalyzable suggests that the property is a\nfundamental property. One might understand this in something like the\nsense that Lewis proposes, i.e., as a property that is sparse and\nperfectly natural. Or one might understand a fundamental property as\none that is groundable but not grounded in anything. But deflationists\nneed not understand a purported property of being true in either of\nthese ways. As noted in Section 1.2, they may think of it as an\nabundant property rather than a sparse one, or as one that is\nungroundable. In this way, there are options available for\ndeflationists who want to distinguish themselves from the Moorean view\nof truth." ], "subsection_title": "4.8 Inflationist Deflationism?" } ] } ]

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(Page\nreference is to the reprint.)", "–––, 1983b, “On Truth,” in Leigh\nCauman, et al. (eds.), How Many Questions? Essays in\nHonor of Sidney Morgenbesser, Indianapolis: Hackett Publishing,\npp. 35–56; reprinted in Putnam 1994, pp. 315–29. (Page\nreference is to the reprint.)", "–––, 1985, “A Comparison of Something with\nSomething Else,” New Literary History, 17: 61–79;\nreprinted in Putnam 1994, pp. 330–50. (Page reference is to the\nreprint.)", "–––, 1991, “Does the Disquotational Theory\nReally Solve All Philosophical Problems?”\nMetaphilosophy, 22(1-2): 1–13; reprinted in Putnam\n1994, pp. 264–78. (Page references is to the reprint.)", "–––, 1994, Words and Life, James Conant\n(ed.), Cambridge, MA: Harvard University Press.", "Quine, W.v.O., 1960, Word and Object, Cambridge, MA: MIT\nPress.", "–––, 1970 [1986], Philosophy of Logic,\nCambridge, MA: Harvard University Press. (Page reference is to the 2nd\nedition, 1986.)", "–––, 1981, Theories and Things,\nCambridge, MA: Harvard University Press.", "–––, 1992, Pursuit of Truth, Revised\nEdition, Cambridge, MA: Harvard University Press.", "Ramsey, Frank, 1927, “Facts and Propositions,”\nProceedings of the Aristotelian Society, 7 (Supplementary):\n153–70; reprinted in David Mellor (ed.), Philosophical\nPapers, Cambridge: Cambridge University Press, 1990, pp.\n34–51. (Page references is to the reprint.)", "–––, 1929, On Truth: Original Manuscript\nMaterials (1927–1929), Episteme, 16, Nicholas\nRescher and Ulrich Majer (eds.), Dordrecht: Kluwer Academic\nPublishers, 1991.", "Rabin, Gabriel, 2020, “Fundamentality Physicalism,”\nInquiry, published online January 2, 2020.\ndoi:10.1080/0020174X.2019.1688177", "Rescher, Nicholas, 1969, Many-Valued Logic, New York:\nMcGraw-Hill.", "Restall, Greg, 2006, “Minimalists Can (and Should) Be\nEpistemicists, and it Helps if They Are Revision Theorists Too,”\nin Beall and Armour-Garb 2006, pp. 97–106.", "Rumfitt, Ian, 1995, “Truth Wronged: Crispin Wright’s\nTruth and Objectivity,” Ratio (New Series),\nVIII(1): 100–7.", "Schantz, Richard, 1998, “Was Tarski a Deflationist?”\nLogic and Logical Philosophy, 6: 157–72.", "Sellars, Wilfrid, 1974, “Meaning as Functional\nClassification,” Synthese, 27(3): 417–37.", "–––, 1979, Naturalism and Ontology,\nAtascadero: Ridgeview Publishing Company.", "Simmons, Keith, 1999, “Deflationary Truth and the\nLiar,” Journal of Philosophical Logic, 28:\n455–88.", "–––, 2006, “Deflationism and the Autonomy\nof Truth,” Philosophy and Phenomenological Research,\n72(1): 196–204.", "Shapiro, Stewart, 1998, “Proof and Truth: Through Thick and\nThin,” Journal of Philosophy, XCV(10):\n493–521.", "–––, 2005, “Gurus, Logical Consequence,\nand Truth Bearers: What Is It That Is True,” in Armour-Garb and\nBeall 2005, pp. 153–70.", "Soames, Scott, 1999, Understanding Truth, Oxford: Oxford\nUniversity Press.", "Sosa, Ernest, 1993, “Epistemology, Realism, and Truth: The\nFirst Philosophical Perspectives Lecture,” Language and\nLogic: Philosophical Perspectives, 7: 1–16.", "Stalnaker, Robert, 1970, “Pragmatics,”\nSynthese, 22(1-2): 272–89.", "–––,1973, “Pragmatic\nPresuppositions,” reprinted in Context and Content,\nOxford: Oxford University Press, 1999, pp. 47–62. (Page\nreference is to the reprint.)", "Strawson, Peter, 1949, “Truth,” Analysis,\n9(6): 83–97.", "–––, 1950, “Truth,” Proceeding\nof the Aristotelian Society (Supplementary Volume), 24:\n129–56.", "Tarski, Alfred, 1935 [1956], “Der Wahrheitsbegriff in den\nformalisierten Sprachen,” Studio Philosophica, 1:\n261–405. Translated in 1956 by J.H. Woodger as “The\nConcept of Truth in Formalized Languages,” reprinted in John\nCorcoran (ed.), Logic, Semantics, Mathematics, Second\nEdition, Indianapolis: Hackett Publishing, 1983, pp. 152–278.\n(Page reference is to the reprint.)", "–––, 1944, “The Semantic Conception of\nTruth,” Philosophy and Phenomenological Research, 4(4):\n341–75.", "Van Fraassen, Bas, 1980, The Scientific Image, Oxford:\nClarendon Press.", "Williams, Michael, 1986, “Do We (Epistemologists) Need a\nTheory of Truth?”Philosophical Topics, 14(1):\n223–42.", "–––, 1999, “Meaning and Deflationary\nTruth,” Journal of Philosophy, XCVI(11):\n545–64.", "Waxman, Daniel, 2017, “Deflationism, Arithmetic, and the\nArgument from Conservativeness,” Mind, 126(502):\n429–63.", "Williamson, Timothy, 1994, Vagueness, London: Routledge\nPress.", "Wittgenstein, Ludwig, 1934 [1974], Philosophical Grammar,\nR. Rhees (ed.) and A. Kenny (trans.), Oxford: Blackwell\nPublishing.", "–––, 1937 [2005], The Big Typescript: TS\n213, C. Grant, Louis Luckhardt and Maximilian Aue (eds. and\ntranslators), Oxford: Blackwell Publishing.", "–––, 1953 [2009], Philosophical\nInvestigations, G.E.M. Anscombe, P.M.S. Hacker, and Joachim\nSchulte (eds.), Oxford: Blackwell Publishing, revised 4th\nedition.", "Woodbridge, James, 2005, “Truth as a Pretense,” in\nMark Kalderon (ed.), Fictionalism in Metaphysics, Oxford:\nOxford University Press, pp. 134–77.", "Wrenn, Chase, 2011, “Practical Success and the Nature of\nTruth,” Synthese, 181(3): 451–70.", "–––, 2021, “Deflating the Success-Truth\nConnection,” Australasian Journal of Philosophy,\npublished online October 24, 2021.\ndoi:10.1080/00048402.2021.1966483", "Wright, Crispin, 1992, Truth and Objectivity, Cambridge,\nMA: Harvard University Press.", "Yablo, Stephen,1985, “Truth and Reflection,”\nJournal of Philosophical Logic, 14(3): 297–349.", "–––, 1993, “Paradox Without\nSelf-Reference,” Analysis, 53(4): 251–2." ]

[ { "href": "../propositions/", "text": "propositions" }, { "href": "../tarski-truth/", "text": "Tarski, Alfred: truth definitions" }, { "href": "../truth/", "text": "truth" }, { "href": "../truth-axiomatic/", "text": "truth: axiomatic theories of" }, { "href": "../truth-correspondence/", "text": "truth: correspondence theory of" } ]

[ "\nThe identity theory of truth was influential in the formative years of\nmodern analytic philosophy, and has come to prominence again recently.\nBroadly speaking, it sees itself as a reaction against correspondence\ntheories of truth, which maintain that truth-bearers are made\ntrue by facts. The identity theory maintains, against this, that\nat least some truth-bearers are not made true by, but are\nidentical with, facts. The theory is normally applied not at\nthe level of declarative sentences, but to what such sentences\nexpress. It is these items—or, again, some of them—that\nare held to be identical with facts. Identity theorists diverge over\nthe details of this general picture, depending on what exactly they\ntake declarative sentences to express, whether Fregean thoughts (at\nthe level of sense), Russellian propositions (at the level of\nreference), or both, and depending also on how exactly facts are\nconstrued. But, to give a precise illustration, an identity theorist\nwho thinks that declarative sentences express Russellian propositions\nwill typically hold that true such propositions are identical with\nfacts. The significance of the identity theory, for its supporters, is\nthat it appears to make available the closing of a certain gap that\nmight otherwise be thought to open up between language and world\nand/or between mind and world. If its supporters are right about this,\nthe identity theory of truth potentially has profound consequences\nboth in metaphysics and in the philosophies of mind and language." ]

[ { "content_title": "1. Definition and Preliminary Exposition", "sub_toc": [] }, { "content_title": "2. Historical Background", "sub_toc": [] }, { "content_title": "3. Motivation", "sub_toc": [] }, { "content_title": "4. Identity, Sense, and Reference", "sub_toc": [] }, { "content_title": "5. Difficulties with the Theory and Possible Solutions", "sub_toc": [ "5.1 The modal problem", "5.2 The “right fact” problem", "5.3 The “slingshot” problem", "5.4 The congruence problem", "5.5 The individuation problem", "5.6 Truth and Intrinsicism" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nDeclarative sentences seem to take truth-values, for we say things\nlike", "\nBut sentences are apparently not the only bearers of truth-values: for\nwe also seem to allow that what such sentences express, or mean, may\nbe true or false, saying such things as", "\nand", "\nor", "\nIf, provisionally, we call the things that declarative sentences\nexpress, or mean, their contents—again provisionally,\nthese will be such things as that Socrates is wise—then\nthe identity theory of truth, in its most general form, states that\n(cf. Baldwin 1991: 35):", "\nA fact is here to be thought of as, very generally, a way things\nare, or a way the world is. On this approach, the\nidentity theory secures an intimate connection between language (what\nlanguage expresses) and world. Of course there would in principle be\ntheoretical room for a view that identified not the content of, say,\nthe true declarative sentence “Socrates is wise”—let\nus assume from now on that this sentence is true—with the fact\nthat Socrates is wise, but rather that sentence itself. But\nthis is not a version of the theory that anyone has ever advanced, nor\ndoes it appear that it would be plausible to do so (see Candlish\n1999b: 200–2; Künne 2003: 6). The early Wittgenstein does\nregard sentences as being themselves facts, but they are not identical\nwith the facts that make them true.", "\nAlternatively, and using a different locution, one might say that, to\ncontinue with the same example,", "\nThe idea here is that (6) makes a connection between language and\nreality: on the left-hand side we have something expressed by a piece\nof language, and on the right-hand side we allude to a bit of reality.\nNow (6) might look truistic, and that status has indeed been claimed\nfor the identity theory, at least in one of its manifestations. John\nMcDowell has argued that what he calls true “thinkables”\nare identical with facts (1996: 27–8, 179–80). Thinkables\nare things like that Socrates is wise regarded as possible\nobjects of thought. For we can think that Socrates is wise;\nand it can also be the case that Socrates is wise. So the\nidea is that what we can think can also be (identical with) what is\nthe case. That identity, McDowell claims, is truistic. On this\napproach, one might prefer one’s identity theory to take the\nform (cf. Hornsby 1997: 2):", "\nOn this approach the identity theory explicitly aims to secure an\nintimate connection between mind (what we think) and world.", "\nA point which has perhaps been obscured in the literature on this\ntopic, but which should be noticed, is that (7) asserts a relation of\nsubordination: it says that true thinkables are a (proper or improper)\nsubset of facts; it implicitly allows that there might be facts that\nare not identical with true thinkables. So (7) is not to be confounded\nwith its converse,", "\nwhich asserts the opposite subordination, and says that facts are a\n(proper or improper) subset of true thinkables, implicitly allowing,\nthis time, that there might be true thinkables that are not identical\nwith facts. (8) is therefore distinct from (7), and if (7) is\ncontroversial, (8) is equally or more so, but for reasons that are at\nleast in part different. (8) denies the existence of facts that cannot\nbe grasped in thought. But many philosophers hold it to be evident\nthat there are, or at least could be, such facts—perhaps certain\nfacts involving indefinable real numbers, for example, or in some\nother way going beyond the powers of human thought. So (8) could be\nfalse; its status remains to be established; it can hardly be regarded\nas truistic. Accordingly, one might expect that an identity theorist\nwho wished to affirm (7), and certainly anyone who wanted to say that\n(7) (or (6)) was truistic, would—at least qua identity\ntheorist—steer clear of (8), and leave its status sub\njudice. In fact, however, a good number of identity theorists,\nboth historical and contemporary, incorporate (8) as well as—or\neven instead of—(7) into their statement of the theory. Richard\nCartwright, who published the first modern discussion of the theory in\n1987, wrote that if one were formulating the theory, it would say\n“that every true proposition is a fact and every fact a true\nproposition” (1987: 74). McDowell states that", "\n\n\ntrue thinkables already belong just as much to the world as to minds\n[i.e., (7)], and things that are the case already belong just as much\nto minds as to the world [i.e., (8)]. It should not even seem that we\nneed to choose a direction in which to read the claim of identity.\n(2005: 84)\n", "\nJennifer Hornsby takes the theory to state that true thinkables and\nfacts coincide (1997: 2, 9, 17, 20)—they are the same\nset—so that she in effect identifies that theory with the\nconjunction of (7) and (8), as also, in effect, does Julian Dodd\n(2008a: passim). Now, (8) is certainly an interesting thesis\nthat merits much more consideration than it has hitherto received (at\nleast in the recent philosophical literature), and, as indicated, some\nexpositions of the identity theory have as much invested in (8) as in\n(5) or (7): on this point see further\n §2\n below. Nevertheless, it will make for clarity of discussion if we\nassociate the identity theory of truth, more narrowly, with something\nalong the lines of (5) or (7), and omit (8) from this particular\n discussion.[2]\n That will be the policy here.", "\nWhether or not (6) is truistic, both (5) and (7) involve technical or\nsemi-technical vocabulary; moreover, they have been advanced as moves\nin a technical debate, namely one concerning the viability of the\ncorrespondence theory of truth. For these reasons it seems difficult\nto regard them as truisms (see Dodd 2008a: 179). What (5) and (7)\nmean, and which of them one will prefer as one’s statement of\nthe identity theory of truth, if one is favorably disposed to that\ntheory—one may of course be happy with both—will depend,\namong other things, on what exactly one thinks about the nature of\nsuch entities as that Socrates is wise. In order to get clear\non this point, discussion of the identity theory has naturally been\nconducted in the context of the Fregean semantical hierarchy, which\ndistinguishes between levels of language, sense, and reference. Frege\nrecognized what he called “thoughts” (Gedanken)\nat the level of sense corresponding to (presented by) declarative\nsentences at the level of language. McDowell’s thinkables are\nmeant to be Fregean thoughts: the change of terminology is intended to\nstress the fact that these entities are not thoughts in the sense of\ndated and perhaps spatially located individual occurrences (thinking\nevents), but are abstract contents that are at least in principle\navailable to be grasped by different thinkers at different times and\nplaces. So a Fregean identity theory of truth would regard both such\nentities as that Socrates is wise and, correlatively, facts\nas sense-level entities: this kind of identity theory will then state\nthat true such entities are identical with facts. This approach will\nnaturally favor (7) as its expression of the identity theory.", "\nBy contrast with Frege, Russell abjured the level of sense and (at\nleast around 1903–4) recognized what, following Moore, he called\n“propositions” as worldly entities composed of objects and\nproperties. A modern Russellian approach might adopt these\npropositions—or something like them: the details of\nRussell’s own conception are quite vague—as the referents\nof declarative sentences, and identity theorists who followed this\nline might prefer to take a particular reading of (5) as their slogan.\nSo these Russellians would affirm something along the lines of:", "\nby contrast with the Fregean", "\nThis way of formulating the relevant identity claims has the advantage\nof suggesting that it would, at least in principle, be open to a\ntheorist to combine (9) and (10) in a hybrid position that (i)\ndeparted from Russell and followed Frege by admitting both a\nlevel of Fregean sense and one of reference, and also, having\nadmitted both levels to the semantic hierarchy, (ii) both\nlocated Fregean thoughts at the level of sense and located\nRussellian propositions at the level of reference. Sense being mode of\npresentation of reference, the idea would be that declarative\nsentences refer, via Fregean thoughts, to Russellian\npropositions (for this disposition, see Gaskin 2006: 203–20;\n2008: 56–127). So someone adopting this hybrid approach would\naffirm both (9) and (10). Of course, the facts mentioned in (9) would\nbe categorially different from the facts mentioned in (10),\nand one might choose to avoid confusion by distinguishing them\nterminologically, and perhaps also by privileging one set of facts,\nontologically, over the other. If one wanted to follow this\nprivileging strategy, one might say, for instance, that only\nreference-level facts were genuine facts, the relata\nof the identity relation at the level of sense being merely\nfact-like entities, not bona fide facts. That would\nbe to give the combination of (9) and (10) a Russellian spin.\nAlternatively, someone who took the hybrid line might prefer to give\nit a Fregean spin, saying that the entities with which true Fregean\nthoughts were identical were the genuine facts, and that the\ncorresponding entities at the level of reference that true Russellian\npropositions were identical with were not facts as such, but fact-like\ncorrelates of the genuine facts. Without more detail, of course, these\nprivileging strategies leave the status of the entities they are\ntreating as merely fact-like unclear; and, as far as the\nFregean version of the identity theory goes, commentators who identify\nfacts with sense-level Fregean thoughts usually, as we shall see,\nrepudiate reference-level Russellian propositions altogether, rather\nthan merely downgrading their ontological status, and so affirm (10)\nbut reject (9). We shall return to these issues in\n §4\n below." ], "section_title": "1. Definition and Preliminary Exposition", "subsections": [] }, { "main_content": [ "\nThe expression “the identity theory of truth” was first\nused—or, at any rate, first used in the relevant sense—by\nStewart Candlish in an article on F. H. Bradley published in 1989. But\nthe general idea of the theory had been in the air during the 1980s:\nfor example, in a discussion first published in 1985, concerning John\nMackie’s theory of truth, McDowell criticized that theory for\nmaking ", "\n\ntruth consist in a relation of correspondence (rather than identity)\nbetween how things are and how things are represented as being. (1985\n[1998: 137 n. 21]) \n", "\nThe implication is that identity would be the right way to conceive\nthe given relation. And versions of the identity theory go back at\nleast to Bradley (see, e.g., Bradley 1914: 112–13; for further\ndiscussion and references, see Candlish 1989; 1995; 1999b:\n209–12; T. Baldwin 1991: 36–40), and to the founding\nfathers of the analytic tradition (Sullivan 2005: 56–7 n. 4).\nThe theory can be found in G. E. Moore’s “The Nature of\nJudgment” (1899), and in the entry he wrote on\n“Truth” for J. Baldwin’s Dictionary of\nPhilosophy and Psychology (1902–3; reprinted Moore 1993:\n4–8, 20–1; see T. Baldwin 1991: 40–3). Russell\nembraced the identity theory at least during the period of his 1904\ndiscussions of Meinong (see, e.g., 1973: 75), possibly also in his\nThe Principles of Mathematics of 1903, and for a few years\nafter these publications as well (see T. Baldwin 1991: 44–8;\nCandlish 1999a: 234; 1999b: 206–9). Frege has a statement of the\ntheory in his 1919 essay “The Thought”, and may have held\nit earlier (Frege 1918–19: 74 [1977: 25]; see Hornsby 1997:\n4–6; Milne 2010: 467–8).", "\nWittgenstein’s Tractatus (1922) is usually held to\npropound a correspondence rather than an identity theory of truth;\nhowever this is questionable. In the Tractatus, declarative\nsentences (Sätze) are said to be facts (arrangements of\nnames), and states of affairs (Sachlagen,\nSachverhalte, Tatsachen) are also said to be facts\n(arrangements of objects). If the Tractatus is taken to put\nforward a correspondence theory of truth, then presumably the idea is\nthat a sentence will be true just if there is an appropriate relation\nof correspondence (an isomorphism) between sentence and state of\naffairs. However, the problem with this interpretation is that, in the\nTractatus, a relation of isomorphism between a sentence and\nreality is generally conceived as a condition of the\nmeaningfulness of that sentence, not specifically of its\ntruth. False sentences, as well as true, are isomorphic with\nstates of affairs—only, in their case the states of affairs do\nnot obtain. For Wittgenstein, states of affairs may either obtain or\nfail to obtain—both possibilities are, in general, available to\n them.[3]\n Correlatively, it has been suggested that the Tractatus\ncontains two different conceptions of fact, a factive and a\nnon-factive one. According to the former conception, facts necessarily\nobtain or are the case; according to the latter, facts may fail to\nobtain or not be the case. This non-factive conception has been\ndiscerned at Tractatus 1.2–1.21, and at 2.1 (see\nJohnston 2013: 382). Given that, in the Tractatus, states of\naffairs (and perhaps facts) have two poles—obtaining or being\nthe case, and non-obtaining or not being the case—it seems to\nfollow that, while Wittgenstein is committed to a correspondence\ntheory of meaning, his theory of truth must be (some\nversion of) an identity theory, along the lines of ", "\n\n\nA declarative sentence is true just if what it is semantically\ncorrelated with is identical with an obtaining state of affairs (a\nfactive fact). \n", "\n(Identity theorists normally presuppose the factive conception of\nfacts, so that “factive” is redundant in the phrase\n“factive facts”, and that is the policy which will be\nfollowed here.) Though a bipolar conception of facts (if indeed\nWittgenstein has it) may seem odd, the bipolar conception of states of\naffairs (which, it is generally agreed, he does have) seems quite\nnatural: here the identity theorist says that a true proposition is\nidentical with an obtaining state of affairs (see Candlish &\nDamnjanovic 2018: 271–2).", "\nPeter Sullivan has suggested a different way of imputing an identity\ntheory to the Tractarian Wittgenstein (2005: 58–9). His idea is\nthat Wittgenstein’s simple objects are to be identified with\nFregean senses, and that in effect the Tractatus contains an\nidentity theory along the lines of (7) or (10). Sullivan’s\nground for treating Tractarian objects as senses is that, like\nbona fide Fregean senses, they are transparent: they\ncannot be grasped in different ways. An apparent difficulty with this\nview is that there is plausibly more to Fregean sense than just the\nproperty of transparency: after all, Russell also attached the\nproperty of transparency to his basic objects, but it has not been\nsuggested that Russellian basic objects are really senses, and the\nsuggestion would seem to have little going for it (partly, though not\nonly, because Russell himself disavowed the whole idea of Fregean\nsense).The orthodox position, which will be presupposed here, is that\nthe Tractarian Wittgenstein like Russell, finds no use for a level of\nFregean sense, so that his semantical hierarchy consists exclusively\nof levels of language and reference, with nothing of a mediatory or\nsimilar nature located between these levels. (Wittgenstein does appeal\nto the concepts of sense and reference in the\nTractatus, but it is generally agreed that they do not figure\nin a Fregean way, according to which both names and sentences, for\nexample, have both sense and reference; for Wittgenstein, by contrast,\nsentences have sense but not reference, whereas names have reference\nbut not sense.)" ], "section_title": "2. Historical Background", "subsections": [] }, { "main_content": [ "\nWhat motivates the identity theory of truth? It can be viewed as a\nresponse to difficulties that seem to accrue to at least some versions\nof the correspondence theory (cf. Dodd 2008a: 120, 124). The\ncorrespondence theory of truth holds that truth consists in a relation\nof correspondence between something linguistic or quasi-linguistic, on\nthe one hand, and something worldly on the other. Generally, the items\non the worldly end of the relation are taken to be facts or\n(obtaining) states of affairs. For many purposes these two latter\nkinds of entity (facts, obtaining states of affairs) are assimilated\nto one another, and that strategy will be followed here. The exact\nnature of the correspondence theory will then depend on what the other\nrelatum is taken to be. The items mentioned so far make\navailable three distinct versions of the correspondence theory,\ndepending on whether this relatum is taken to consist of\ndeclarative sentences, Fregean thoughts, or Russellian propositions.\nModern correspondence theorists make a distinction between\ntruth-bearers, which would typically fall under one of these\nthree classifications, and\n truth-makers,[4]\n the worldly entities making truth-bearers true, when they are true.\nIf these latter entities are facts, then true declarative sentences,\nFregean thoughts, or Russellian propositions—whichever of these\none selects as the relata of the correspondence relation on the\nlanguage side of the language–world divide—correspond to\nfacts in the sense that facts are what make those sentences, thoughts,\nor propositions true, when they are true. (Henceforth we shall\nnormally speak simply of thoughts and propositions, understanding\nthese to be Fregean thoughts and Russellian propositions respectively,\nunless otherwise specified.)", "\nThat, according to the correspondence theorist (and the identity\ntheorist can agree so far), immediately gives us a constraint on the\nshape of worldly facts. Take our sample sentence “Socrates is\nwise”, and recall that this sentence is here assumed to be true.\nAt the level of reference we encounter the object Socrates and\n(assuming realism about\n properties)[5]\n the property of wisdom. Both of these may be taken to be entities in\nthe world, but it is plausible that neither amounts to a fact: neither\namounts to a plausible truth-maker for the sentence “Socrates is\nwise”, or for its expressed thought, or for its expressed\nproposition. That is because the man Socrates, just as such, and the\nproperty of wisdom, just as such, are not, so the argument goes,\npropositionally structured, either jointly or severally, and so do not\namount to enough to make it true that Socrates is wise (cf. D.\nArmstrong 1997: 115–16; Dodd 2008a: 7; Hofweber 2016: 288). Even\nif we add in further universals, such as the relation of\ninstantiation, and indeed the instantiation of instantiation to any\ndegree, the basic point seems to be unaffected. In fact it can\nplausibly be maintained (although some commentators disagree; Merricks\n2007: ch. 1, passim, and pp. 82, 117, 168; Asay 2013:\n63–4; Jago 2018: passim, e.g., pp. 73, 84, 185, 218,\n250, though cf. p. 161) that the man Socrates, just as such, is not\neven competent to make it true that Socrates exists; for that we need\nthe existence of the man Socrates. Hence, it would appear\nthat, if there are to be truth-makers in the world, they will have to\nbe structured, syntactically or quasi-syntactically, in the same\ngeneral way as declarative sentences, thoughts, and propositions. For\nconvenience we can refer to structure in this general sense as\n“propositional structure”: the point then is that neither\nSocrates, nor the property of wisdom, nor (if we want to adduce it)\nthe relation of instantiation is, just as such, propositionally\nstructured. Following this line of argument through, we reach the\nconclusion that nothing short of full-blown, propositionally\nstructured entities like the fact that Socrates is wise will\nbe competent to make the sentence “Socrates is wise”, or\nthe thought or proposition expressed by that sentence, true. (A\nquestion that arises here is whether tropes might be able to provide a\n“thinner” alternative to such ontologically\n“rich” entities as the fact that Socrates is\nwise. One problem that seems to confront any such strategy is\nthat of making the proposed alternative a genuine one, that is, of\nconstruing the relevant tropes in such a way that they do not simply\ncollapse into, or ontologically depend on, entities of the relatively\nrich form that Socrates is wise. For discussion see Dodd\n2008a: 7–9.)", "\nThe question facing the correspondence theorist is now: if such\npropositionally structured entities are truth-makers, are they\ntruth-makers for sentences, thoughts, or propositions? It is at this\npoint that the identity theorist finds the correspondence theory\nunsatisfactory. Consider first the suggestion that the worldly fact\nthat Socrates is wise is the truth-maker for the\nreference-level proposition that Socrates is wise (see, e.g.,\nJago 2018: 72–3, and passim). There surely are such\nfacts as the fact that Socrates is wise: we talk about such\nthings all the time. The problem would seem to be not with the\nexistence of such facts, but rather with the relation of\ncorrespondence which is said by the version of the correspondence\ntheory that we are currently considering to obtain between the fact\nthat Socrates is wise and the proposition that Socrates\nis wise. As emerges from this way of expressing the difficulty,\nthere seems to be no linguistic difference between the way we talk\nabout propositions and the way we talk about facts, when these\nentities are specified by “that” clauses. That suggests\nthat facts just are true propositions. If that is right, then\nthe relation between facts and true propositions is not one of\ncorrespondence—which, as Frege famously observed (Frege\n1918–19: 60 [1977: 3]; cf. Künne 2003: 8; Milne 2010:\n467–8), implies the distinctness of the\nrelata—but identity.", "\nThis line of argument can be strengthened by noting the following\npoint about explanation. Correspondence theorists have typically\nwanted the relation of correspondence to explain truth: they\nhave usually wanted to say that it is because the proposition\nthat Socrates is wise corresponds to a fact that it is true,\nand because the proposition that Socrates is\nfoolish—or rather: It is not the case that Socrates is\nwise (after all, his merely being foolish is not enough to\nguarantee that he is not wise, for he might, like James I and VI, be\nboth wise and foolish)—does not correspond to a fact that it is\nfalse. But the distance between the true proposition that Socrates\nis wise and the fact that Socrates is wise seems to be\ntoo small to provide for explanatory leverage. Indeed the identity\ntheorist’s claim is that there is no distance at all. Suppose we\nask: Why is the proposition that Socrates is wise true? If we\nreply by saying that it is true because it is a fact that Socrates\nis wise, we seem to have explained nothing, but merely repeated\nourselves (cf. Strawson 1971: 197; Anscombe 2000: 8; Rasmussen 2014:\n39–43). So correspondence apparently gives way to identity as\nthe relation which must hold or fail to hold between a proposition and\na state of affairs if the proposition is to be true or false: the\nproposition is true just if it is identical with an obtaining state of\naffairs and false if it is not (cf. Horwich 1998: 106). And it would\nseem that, if the identity theorist is right about this disposition,\nexplanatory pretensions will have to be abandoned: for while it will\nbe correct to say that a proposition is true just if it is identical\nwith a fact, false otherwise, it is hard to see that much of substance\nhas thereby been said about truth (cf. Hornsby 1997; 2; Dodd 2008a;\n135).", "\nIt might be replied here that there are circumstances in which we\ntolerate statements of the form “A because\nB” when an appropriate identity—perhaps even\nidentity of sense, or reference, or both—obtains between\n“A” and “B”. For example, we say\nthings like “He is your first cousin because he is a child of a\nsibling of one of your parents” (Künne 2003: 155). But here\nit is plausible that there is a definitional connection between\nleft-hand side and right-hand side, which seems not to hold of ", "\n\n\nThe proposition that Socrates is wise is true because it is a\nfact that Socrates is wise. \n", "\nIn the latter case there is surely no question of definition; rather,\nwe are supposed, according to the correspondence theorist, to have an\nexample of metaphysical explanation, and that is just what, according\nto the identity theorist, we do not have. After all, the identity\ntheorist will insist, it seems obvious that the relation, whatever it\nis, between the proposition that Socrates is wise and the\nfact that Socrates is wise must, given that the proposition\nis true, be an extremely close one: what could this relation be? If\nthe identity theorist is right that the relation cannot be one of\nmetaphysical explanation (in either direction), then it looks as\nthough it will be hard to resist the insinuation of the linguistic\ndata that the relation is one of identity.", "\nIt is for this reason that identity theorists sometimes insist that\ntheir position should not be defined in terms of an identity between\ntruth-bearer and truth-maker: that way of expressing the theory looks\ntoo much in thrall to correspondence theorists’ talk (cf.\nCandlish 1999b: 200–1, 213). For the identity theorist, to speak\nof both truth-makers and truth-bearers would imply that the things\nallegedly doing the truth-making were distinct from the things that\nwere made true. But, since in the identity theorist’s view there\nare no truth-makers distinct from truth-bearers, if the latter are\nconceived as propositions, and since nothing can make itself true, it\nfollows that there are no truth-makers simpliciter, only\ntruth-bearers. It seems to follow, too, that it would be ill-advised\nto attack the identity theory by pointing out that some (or all)\ntruths lack truth-makers (so Merricks 2007: 181): so long as truths\nare taken to be propositions, that is exactly what identity theorists\nthemselves say. From the identity theorist’s point of view,\ntruth-maker theory looks very much like an exercise in splitting the\nlevel of reference in half and then finding a bogus match between the\ntwo halves (see McDowell 1998: 137 n. 21; Gaskin 2006: 203; 2008:\n119–27). For example, when David Armstrong remarks that ", "\n\n\nWhat is needed is something in the world which ensures that a\nis F, some truth-maker or ontological ground for\na’s being F. What can this be except the state of\naffairs of a’s being F? (1991: 190) \n", "\nthe identity theorist is likely to retort that a’s being\nF, which according to Armstrong “ensures” that\na is F,just is the entity (whatever it is)\nthat a is F. The identity theorist maps conceptual\nconnections that we draw between the notions of proposition, truth,\nfalsity, state of affairs, and fact. These connections look trivial,\nwhen spelt out—of course, an identity theorist will counter that\nto go further would be to fall into error—so that to speak of an\nidentity theory can readily appear too grand (McDowell 2005:\n83; 2007: 352. But cf. David 2002: 126). So much for the thesis that\nfacts are truth-makers and propositions truth-bearers; an\nexactly parallel argument applies to the version of the correspondence\ntheory that treats facts as truth-makers and thoughts as\ntruth-bearers.", "\nConsider now the suggestion that obtaining states of affairs, as the\ncorrespondence theorist conceives them, make declarative\nsentences (as opposed to propositions) true (cf. Horwich 1998:\n106–7). In this case there appears to be no threat of triviality\nof the sort that apparently plagued the previous version of the\ncorrespondence theory, because states of affairs like that\nSocrates is wise are genuinely distinct from linguistic items\nsuch as the sentence “Socrates is wise”. To that extent\nfriends of the identity theory need not jib at the suggestion that\nsuch sentences have worldly truth-makers, if that is how the relation\nof correspondence is being glossed. But they might question the\nappropriateness of the gloss. For, they might point out, it does not\nseem possible, without falsification, to draw detailed links between\nsentences and bits of the world. After all, different sentences in the\nsame or different languages can “correspond” to the same\nbit of the world, and these different sentences might have very\ndifferent (numbers of) components. The English sentence “There\nare cows” contains three words: are there then three bits in the\nworld corresponding to this sentence, and making it true? (cf. Neale\n2001: 177). The sentence “Cows\nexist” contains only two words, but would not the correspondence\ntheorist want to say that it was made true by the same chunk of\nreality? And when we take other languages into account, there seems in\nprinciple to be no reason to privilege any particular number and say\nthat a sentence corresponding to the relevant segment of reality must\ncontain that number of words: why might there not, in\nprinciple, be sentences of actual or possible languages such that, for\nany n ≥ 1, there existed a sentence comprising n\nwords and meaning the same as the English “There are\ncows”? (In fact, is English not already such a language? Just\nprefix and then iterate ad lib. a vacuous operator like\n“Really”.)", "\nIn a nutshell, then, the identity theorist’s case against the\ncorrespondence theory is that, when the truth-making relation is\nconceived as originating in a worldly fact (or similar) and having as\nits other relatum a true sentence, the claim that this\nrelation is one of correspondence cannot be made out; if, on the other\nhand, the relevant relation targets a proposition (or\nthought), then that relation must be held to be one of identity, not\ncorrespondence." ], "section_title": "3. Motivation", "subsections": [] }, { "main_content": [ "\nIdentity theorists are agreed that, in the case of any particular\nrelevant identity, a fact will constitute the worldly relatum\nof the relation, but there is significant disagreement among them on\nthe question what the item on the other end of the relation\nis—whether a thought or a proposition (or both). As we have\nseen, there are three possible positions here: (i) one which places\nthe identity relation exclusively between true thoughts and facts,\n(ii) one which places it exclusively between true propositions and\nfacts, and (iii) a hybrid position which allows identities of both\nsorts (identities obtaining at the level of sense will of course be\nquite distinct from identities obtaining at the level of reference).\nWhich of these positions an identity theorist adopts will depend on\nwider metaphysical and linguistic considerations that are strictly\nextraneous to the identity theory as such.", "\nIdentity theorists who favor (i) generally do so because they want to\nhave nothing to do with propositions as such. That is to say,\nsuch theorists eschew propositions as reference-level\nentities: of course the word “proposition”\nmay be, and sometimes is, applied to Fregean thoughts at the level of\nsense, rather than to Russellian propositions at the level of\nreference. For example, Hornsby (1997: 2–3) uses\n“proposition” and “thinkable” interchangeably.\nSo far, this terminological policy might be considered neutral with\nrespect to the location of propositions and thinkables in the Fregean\nsemantic hierarchy: that is to say, if one encounters a theorist who\ntalks about “thinkables” and “propositions”,\neven identifying them, one does not, just so far, know where in the\nsemantic hierarchy this theorist places these entities. In particular,\nwe cannot assume, unless we are specifically told so, that our\ntheorist locates either propositions or thinkables at the level of\nsense. After all, someone who houses propositions at the\nlevel of reference holds that these reference-level entities are\nthinkable, in the sense that they are graspable in\nthought (perhaps via thoughts at the level of sense). But they\nare not thinkables if this latter word is taken, as it is by\nMcDowell and Hornsby, to be a technical term referring to entities at\nthe level of sense. For clarity the policy here will be to continue to\napply the word “proposition” exclusively to Russellian\npropositions at the level of reference. Such propositions, it is\nplausible to suppose, can be grasped in thought, but by definition\nthey are not thoughts or thinkables, where these two latter terms\nhave, respectively, their Fregean and McDowellian meanings. It is\nworth noting that this point, though superficially a merely\nterminological one, engages significantly with the interface between\nthe philosophies of language and mind that was touched on in the\nopening paragraph. Anyone who holds that reference-level propositions\ncan, in the ordinary sense, be thought—are thinkable—is\nlikely to be unsatisfied with any terminology that seems to limit the\ndomain of the thinkable and of what is thought to the level of sense\n(On this point see further below in this section, and Gaskin 2020:\n101–2).", "\nUsually, as has been noted, identity theorists who favor (i) above\nhave this preference because they repudiate propositions as that term\nis being employed here: that is, they repudiate propositionally\nstructured reference-level entities. There are several reasons why\nsuch identity theorists feel uncomfortable with propositions when\nthese are understood to be reference-level entities. There is a fear\nthat such propositions, if they existed, would have to be construed as\ntruth-makers; and identity theorists, as we have seen, want to have\nnothing to do with truth-makers (Dodd 2008a: 112). That fear could\nperhaps be defused if facts were also located at the level of\nreference for true propositions to be identical with. This move would\ntake us to an identity theory in the style of (ii) or (iii) above.\nAnother reason for suspicion of reference-level propositions is that\ncommentators often follow Russell in his post-1904 aversion\nspecifically to false objectives, that is, to false\npropositions in re (Russell 1966: 152; Cartwright 1987:\n79–84). Such entities are often regarded as too absurd to take\nseriously as components of reality (so T. Baldwin 1991: 46; Dodd 1995:\n163; 1996; 2008a: 66–70, 113–14, 162–6). More\nespecially, it has been argued that false propositions in re\ncould not be unities, that the price of unifying a proposition at the\nlevel of reference would be to make it true: if this point were\ncorrect it would arguably constitute a reductio ad absurdum\nof the whole idea of reference-level propositions, since it is\nplausible to suppose that if there cannot be false reference-level\npropositions, there cannot be true ones either (see Dodd 2008a: 165).\nIf, on the other hand, one is happy with the existence of propositions\nin re or reference-level propositions, both true and\n false,[6]\n one is likely to favor an identity theory in the style of (ii) or\n(iii). And, once one has got as far as jettisoning (i) and deciding\nbetween (ii) and (iii), there must surely be a good case for adopting\n(iii): for if one has admitted propositionally structured entities\nboth at the level of sense (as senses of declarative sentences) and at\nthe level of reference (propositions), there seems no good reason not\nto be maximally liberal in allowing identities between entities of\nthese two types and, respectively, sense- and reference-level kinds of\nfact (or fact-like entities).", "\nAgainst what was suggested above about Frege\n (§2),\n it has been objected that Frege could not have held an identity\ntheory of truth (Baldwin 1991: 43); the idea here is that, even if he\nhad acknowledged states of affairs as bona fide elements of\nreality, Frege could not have identified true thoughts with them on\npain of confusing the levels of sense and reference. As far as the\nexegetical issue is concerned, the objection might be said to overlook\nthe possibility that Frege identified true thoughts with facts\nconstrued as sense-level entities, rather than with states of\naffairs taken as reference-level entities; and, as we have\nnoted, Frege does indeed appear to have done just this (see Dodd &\nHornsby 1992). Still, the objection raises an important theoretical\nissue. It would surely be a serious confusion to try to construct an\nidentity across the categorial division separating sense and\nreference, in particular to attempt to identify true Fregean thoughts\nwith reference-level facts or states of\n affairs.[7]\n It has been suggested that McDowell and Hornsby are guilty of this\n confusion;[8]\n they have each rejected the\n charge,[9]\n insisting that, for them, facts are not reference-level entities, but\nare, like Fregean thoughts, sense-level\n entities.[10]", "\nBut, if one adheres to the Fregean version of the identity theory ((i)\nabove), which identifies true thoughts with facts located at the level\nof sense, and admits no correlative identity, in addition, connecting\ntrue propositions located at the level of reference with facts or\nfact-like entities also located at that level, it looks as though one\nfaces a difficult dilemma. At what level in the semantical hierarchy\nis the world to be placed? Suppose first one puts it at the level of\nreference (this appears to be Dodd’s favored view: see 2008a:\n180–1, and passim). In that case the world will contain\nno facts or propositions, but just objects and properties hanging\nloose in splendid isolation from one another, a dispensation which\nlooks like a version of Kantian transcendental idealism. (Simply\ninsisting that the properties include not merely monadic but also\npolyadic ones, such as the relation of instantiation, will not in\nitself solve the problem: we will still just have a bunch of separate\nobjects, properties, and relations.) If there are no true\npropositions—no facts—or even false propositions to be\nfound at the level of reference, but if also, notwithstanding that\nabsence, the world is located there, the objects it contains will, it\nseems, have to be conceived as bare objects, not as things of certain\nsorts. Some philosophers of a nominalistic bias might be happy with\nthis upshot; but the problem is how to make sense of the idea of a\nbare object—that is, an object not characterized by any\nproperties. (Properties not instantiated by any objects, by contrast,\nwill not be problematic, at least not for a realist.)", "\nSo suppose, on the other hand, that one places the world at the level\nof sense, on the grounds that the world is composed of facts, and that\nthat is where facts are located. This ontological dispensation is\nexplicitly embraced by McDowell (1996: 179). The problem with this way\nout of the dilemma would seem to be that, since Fregean senses are\nconstitutively modes of presentation of referents, the strategy under\ncurrent consideration would take the world to be made up of modes of\npresentation—but of what? Of objects and properties? These are\ncertainly reference-level entities, but if they are presented by items\nin the realm of sense, which is being identified on this approach with\nthe world, then again, as on the first horn of the dilemma, they would\nappear to be condemned to an existence at the level of reference in\nsplendid isolation from one another, rather than in propositionally\nstructured combinations, so that once more we would seem to be\ncommitted to a form of Kantian transcendental idealism (see Suhm,\nWagemann, & Wessels 2000: 32; Sullivan 2005: 59–61; Gaskin\n2006:199–203). Both ways out of the dilemma appear to have this\nunattractive consequence. The only difference between those ways\nconcerns where exactly in the semantic hierarchy we locate the world;\nbut it is plausible that that issue, in itself, is or ought to be of\nless concern to metaphysicians than the requirement to avoid divorcing\nobjects from the properties that make those objects things of certain\nsorts; and both ways out of the dilemma appear to flout this\nrequirement.", "\nTo respect the requirement, we need to nest reference-level objects\nand properties in propositions, or proposition-like structures, also\nlocated at the level of reference. And then some of these structured\nreference-level entities—the true or obtaining ones—will,\nit seems, be facts, or at least fact-like. Furthermore, once one\nacknowledges the existence of facts, or fact-like entities, existing\nat the level of sense, it seems in any case impossible to\nprevent the automatic generation of facts, or fact-like entities,\nresiding at the level of reference. For sense is mode of\npresentation of reference. So we need reference-level facts or\nfact-like entities to be what sense-level facts or fact-like entities\npresent. One has to decide how to treat these variously\nhoused fact-like entities theoretically. If one were to insist that\nthe sense-level fact-like entities were the genuine and only\nfacts, the corresponding reference-level entities would be no\nbetter than fact-like, and contrariwise. But, regardless\nwhether the propositionally structured entities automatically\ngenerated in this way by sense-level propositionally structured\nentities are to be thought of as proper facts or merely as fact-like\nentities, it would seem perverse not to identify the world with these\n entities.[11]\n For to insist on continuing to identify the world with sense-level\nrather than reference-level propositionally structured entities would\nseem to fly in the face of a requirement to regard the world as\nmaximally objective and maximally non-perspectival. McDowell himself\nhopes to avert any charge of embracing an unacceptable idealism\nconsequent on his location of the world at the level of sense by\nrelying on the point that senses present their references directly,\nnot descriptively, so that reference is, as it were, contained in\nsense (1996: 179–80). To this it might be objected that the\nrequirement of maximal objectivity forces an identification of the\nworld with the contained, not the containing, entities in this\nscenario, which in turn seems to force the upshot—if the threat\nof Kantian transcendental idealism is really to be obviated—that\nthe contained entities be propositionally structured as such, that is,\nas contained entities, and not simply in virtue of being\ncontained in propositionally structured containing entities. (For a\ndifferent objection to McDowell, see Sullivan 2005: 60 n. 6.)" ], "section_title": "4. Identity, Sense, and Reference", "subsections": [] }, { "main_content": [], "section_title": "5. Difficulties with the Theory and Possible Solutions", "subsections": [ { "content": [ "\nG. E. Moore drew attention to a point that might look (and has been\nheld to be) problematic for the identity theory (Moore 1953: 308; Fine\n1982: 46–7; Künne 2003: 9–10). The proposition\nthat Socrates is wise exists in all possible worlds where\nSocrates and the property of wisdom exist, but in some of those worlds\nthis proposition is true and in others it is false. The fact that\nSocrates is wise, by contrast, only exists in those worlds where\nthe proposition both exists and is true. So it would seem that the\nproposition that Socrates is wise cannot be identical with\nthe fact that Socrates is wise. They have different modal\nproperties, and so by the principle of the indiscernibility of\nidenticals they cannot be identical.", "\nNote, first, that this problem, if it is a problem, has nothing\nespecially to do with the identity theory of truth or with facts. It\nseems to arise already for true propositions and propositions taken\nsimpliciter before ever we get to the topic of facts. That\nis, one might think that the proposition that Socrates is\nwise is identical with the true proposition that Socrates is\nwise (assuming, as we are doing, that this proposition\nis true); but we then face the objection that the proposition\ntaken simpliciter and the true proposition differ in their\nmodal properties, since (as one might suppose) the true proposition\nthat Socrates is wise does not exist at worlds where the\nproposition that Socrates is wise is false, but the\nproposition taken simpliciter does. Indeed the problem, if it\nis a problem, is still more general, and purported solutions to it go\nback at least to the Middle Ages (when it was discussed in connection\nwith Duns Scotus’ formal distinction; see Gaskin 2002 [with\nreferences to further relevant literature]). Suppose that Socrates is\na cantankerous old curmudgeon. Now grumpy Socrates, one would think,\nis identical with Socrates. But in some other possible worlds Socrates\nis of a sunny and genial disposition. So it would seem that Socrates\ncannot be identical with grumpy Socrates after all, because in these\nother possible worlds, while Socrates goes on existing, grumpy\nSocrates does not exist—or so one might argue.", "\nCan the identity theorist deal with this problem, and if so how? Here\nis one suggestion. Suppose we hold, staying with grumpy Socrates for a\nmoment, that, against the assumption made at the end of the last\nparagraph, grumpy Socrates does in fact exist in worlds where\nSocrates has a sunny disposition. The basis for this move would be the\nthought that, after all, grumpy Socrates is identical with\nSocrates, and Socrates exists in these other worlds. So\ngrumpy Socrates exists in those worlds too; it is just that he is not\ngrumpy in those worlds. (Suppose Socrates is very grumpy;\nsuppose in fact that grumpiness is so deeply ingrained in his\ncharacter that worlds in which he is genial are quite far away.\nSomeone surveying the array of possible worlds, starting from the\nactual world and moving out in circles, and stumbling at long last\nupon a world with a pleasant Socrates in it, might register the\ndiscovery by exclaiming, with relief, “Oh look! Grumpy Socrates\nis not grumpy over here!”.) Similarly, one might contend, the\ntrue proposition, and fact, that Socrates is wise goes on\nexisting in the worlds where Socrates is not wise, because the true\nproposition, and fact, that Socrates is wise just is\nthe proposition that Socrates is wise, and that proposition\ngoes on existing in these other worlds, but in those worlds that true\nproposition, and fact, is not a true proposition, or a fact. (In\nScotist terms one might say that the proposition that Socrates is\nwise and the fact that Socrates is wise are really\nidentical but formally distinct.)", "\nThis solution was, in outline, proposed by Richard Cartwright in his\n1987 discussion of the identity theory (Cartwright 1987: 76–8;\ncf. David 2002: 128–9; Dodd 2008a: 86–8; Candlish &\nDamnjanovic 2018: 265–6). According to Cartwright, the true\nproposition, and fact, that there are subways in Boston\nexists in other possible worlds where Boston does not have subways,\neven though in those worlds that fact would be not be a fact.\n(Compare: grumpy Socrates exists in worlds where Socrates is genial\nand sunny, but he is not grumpy there.) So even in worlds where it is\nnot a fact that Boston has subways, that\nfact, namely the fact that Boston has subways, continues to\nexist. Cartwright embellishes his solution with two controversial\npoints. First, he draws on Kripke’s distinction between rigid\nand non-rigid designation, suggesting that his solution can be\ndescribed by saying that the expression “The fact that\nBoston has subways” is a non-rigid designator. But it is\nplausible that that expression goes on referring to, or being\nsatisfied by (depending on how exactly one wants to set up the\nsemantics of definite descriptions: see Gaskin 2008: 56–81), the\nfact that Boston has subways in possible worlds where Boston\ndoes not have subways; it is just that, though that fact exists in\nthose worlds, it is not a fact there. But that upshot does not appear\nto derogate from the rigidity of the expression in\nquestion. Secondly, Cartwright allows for a true\nreading of “The fact that there are subways in Boston\nmight not have been the fact that there are subways in\nBoston”. But it is arguable that we should say that this\nsentence is just false (David 2002: 129). The fact that there are\nsubways in Boston would still have gone on being the same\nfact in worlds where Boston has no subways, namely the fact\nthat there are subways in Boston; it is just that in those\nworlds this fact would not have been a fact. You\nmight say: in that world the fact that there are subways\nin Boston would not be correctly described as a fact, but in\ntalking about that world we are talking about it from the point of\nview of our world, and in our world it is a fact. (Similarly with\ngrumpy Socrates.)", "\nNow, an objector may want to press the following point against the\nabove purported solution to the difficulty. Consider again the fact\nthat Socrates is wise. Surely, it might be said, it is more\nnatural to maintain that that fact does not exist in a\npossible world where Socrates is not wise, rather than that it exists\nthere all right, but is not a fact. After all, imagine a conversation\nabout a world in which Socrates is not wise and suppose that Speaker\nA claims that Socrates is indeed wise in that world. Speaker\nB might counter with ", "\n\n\nNo, sorry, you’re wrong: there is no such fact in that world;\nthe purported fact that Socrates is wise simply does not\nexist in that world. \n", "\nIt might seem odd to insist that B is not allowed to say this\nand must say instead ", "\n\n\nYes, you’re right that there is such a fact in that world,\nnamely the fact that Socrates is wise, but in that world\nthat fact is not a fact;. \n", "\nHow might the identity theorist respond to this objection? One\npossible strategy would be to make a distinction between fact\nand factuality, as follows. Factuality, one might\nsay, is a reification of facts. Once you have a fact, you also get, as\nan ontological spin-off, the factuality of that fact. The\nfact, being a proposition, exists at all possible worlds where the\nproposition exists, though in some of these worlds it may not be a\nfact: it will not be a fact in worlds where the proposition is false.\nThe factuality of that fact, by contrast, only exists at those worlds\nwhere the fact is a fact—where the proposition is true.\nSo factuality is a bit like a trope. Compare grumpy Socrates again.\nGrumpy Socrates, the identity theorist might contend, exists at all\nworlds where Socrates exists, though at some of those worlds he is not\ngrumpy. But Socrates’ grumpiness—that particular\ntrope—exists only at worlds where Socrates is grumpy. That seems\nto obviate the problem, because the suggestion being canvassed here is\nthat grumpy Socrates is identical not with Socrates’\ngrumpiness—so that the fact that these two entities have\ndifferent modal properties need embarrass no one—but rather with\nSocrates. Similarly, the suggestion is that the proposition\nthat Socrates is wise is identical not with the\nfactuality of the fact that Socrates is wise, but\njust with that fact. So the identity theorist would\naccommodate the objector’s point by insisting that\nfacts exist at possible worlds where their\nfactualities do not exist.", "\nThe reader may be wondering why this problem was ever raised against\nthe identity theory of truth in the first place. After all, the\nidentity theorist does not say that propositions simpliciter\nare identical with facts, but that true propositions are\nidentical with facts, and now true propositions and facts surely have\nexactly the same modal properties: for regardless how things\nare with the sheer proposition that Socrates is wise, at any\nrate the true proposition that Socrates is wise must\nsurely be thought to exist at the same worlds as the fact that\nSocrates is wise, whatever those worlds are. However, as against\nthis quick way with the purported problem, there stands the intuition,\nmentioned and exploited above, that the true proposition that\nSocrates is wise is identical with the proposition that\nSocrates is wise. So long as that intuition is in play, the\nproblem does indeed seem to arise—for true propositions, in the\nfirst instance, and then for facts by transitivity of identity. But\nthe identity theorist will maintain that, as explained, the problem\nhas a satisfactory solution." ], "subsection_title": "5.1 The modal problem" }, { "content": [ "\nCandlish, following Cartwright, has urged that the identity theory of\ntruth is faced with the difficulty of getting hold of the “right\nfact” (Cartwright 1987: 74–5; Candlish 1999a: 238–9;\n1999b: 202–4). Consider a version of the identity theory that\nstates:", "\nCandlish’s objection is now that (11)", "\n\n\ndoes not specify which fact has to be identical with the\nproposition for the proposition to be true. But what the identity\ntheory requires is not that a true proposition be identical with\nsome fact or other, it is that it be identical with the\nright fact. (1999b: 203)\n", "\nIn another paper Candlish puts the matter like this:", "\n\n\nBut after all, any proposition might be identical with some\nfact or other (and there are reasons identified in the\nTractatus for supposing that all propositions are themselves\nfacts), and so all might be true. What the identity theory needs to\ncapture is the idea that it is by virtue of being identical\nwith the appropriate fact that a proposition is true. (1999a:\n239)\n", "\nThe reference to the Tractatus is suggestive. Of course, it\nmight be objected that the Tractatus does not have\npropositions in the sense of that word figuring here: that is, it does\nnot recognize Russellian propositions (propositions at the level of\nreference). Nor indeed does it appear to recognize Fregean thoughts.\nIn the Tractatus, as we have noted\n (§2),\n declarative sentences (Sätze) are facts (arrangements\nof names), and states of affairs (Sachlagen,\nSachverhalte, Tatsachen) are also facts\n(arrangements of objects). Even so, Candlish’s allusion to the\nTractatus reminds us that propositions (in our sense)\nare Tractarian inasmuch as they are structured\narrangements of entities, namely objects and properties.\n(Correlatively, thoughts are structured arrangements of senses.) False\npropositions (and false thoughts) will equally be arrangements of\nobjects and properties (respectively, senses). So the difficulty that\nCartwright and Candlish have identified can be put like this.\nPlausibly any proposition, whether or not it is true, is\nidentical with some fact or other given that a proposition is\nan arrangement of entities of the appropriate sort. But if\npropositions just are facts, then every proposition\nis identical with some fact—at the very least, with\nitself—whether it is true or false. So the right-to-left\ndirection of (11) looks incorrect.", "\nJ. C. Beall (2000) attempts to dissolve this problem on the identity\ntheorist’s behalf by invoking the principle of the\nindiscernibility of identicals. His proposal works as follows. If we\nask, in respect of (11), what the “right” fact is, it\nseems that we can answer that the “right” fact must at\nleast have the property of being identical with the proposition\nthat p, and the indiscernibility principle then guarantees\nthat there is only one such fact. This proposal is open to an obvious\nretort. Suppose that the proposition that p is false.\nThat proposition will still be identical with itself, and if we are\nsaying (in Wittgensteinian spirit) that propositions are facts, then\nthat proposition will be identical with at least one fact, namely\nitself. So it will satisfy the right-hand side of (11), its falsity\nnotwithstanding. But reflection on this retort suggests a patch-up to\nBeall’s proposal: why not say that the right fact is\nthe fact that p? We would then be able to gloss (11)\nwith", "\nFalsity, it seems, now no longer presents a difficulty, because if it\nis false that p then it is not a fact that\np, so that (a) fails, and there is no appropriate\ncandidate for the proposition that p to be identical\n with.[13]\n Notice that, in view of the considerations already aired in\nconnection with the modal problem ((i) of this section), caution is\nhere required. Suppose that it is true that p in the\nactual world, but false in some other possible world. According to the\nstrategy that we have been considering on the identity\ntheorist’s behalf, it would be wrong to say that, in the\npossible world where it is false that p, there is no\nsuch fact as the fact that p. The strategy has it that\nthere is indeed such a fact, because it is (in the actual world) a\nfact that p, and that fact, and the true proposition,\nthat p, go on existing in the possible world where it\nis false that p; it is just that that fact is\nnot a fact in that possible world. But (12), the identity\ntheorist will maintain, deals with this subtlety. In the possible\nworld we are considering, where it is false that p,\nthough the fact that p exists, it is not a fact\nthat p, so (a) fails, and there is accordingly no risk\nof our getting hold of the “wrong” fact. Note also that if\na Wittgensteinian line is adopted, while the (false) proposition that\np will admittedly be identical with a fact—at\nthe very least with itself—it will be possible, given the\nfailure of (a), for the identity theorist to contend with a clear\nconscience that that fact is the wrong fact, which does not\nsuffice to render the proposition true." ], "subsection_title": "5.2 The “right fact” problem" }, { "content": [ "\nIf the notorious “slingshot” argument worked, it would\npose a problem for the identity theory of truth. The argument exists\nin a number of different, though related, forms, and this is not the\nplace to explore all of these in\n detail.[14]\n Here we shall look briefly at what is one of the simplest and most\nfamiliar versions of the argument, namely Davidson’s. This\nversion of the argument aims to show that if true declarative\nsentences refer to anything (for example to propositions or facts),\nthen they all refer to the same thing (to the “Great\nProposition”, or to the “Great Fact”). This upshot\nwould be unacceptable to an identity theorist of a Russellian cast,\nwho thinks that declarative sentences refer to propositions, and that\ntrue such propositions are identical with facts: any such theorist is\nnaturally going to want to insist that the propositions referred to by\ndifferent declarative sentences are, at least in general, distinct\nfrom one another, and likewise that the facts with which distinct true\npropositions are identical are also distinct from one another.\nDavidson expresses the problem that the slingshot argument purportedly\nthrows up as follows:", "\n\n\nThe difficulty follows upon making two reasonable assumptions: that\nlogically equivalent singular terms have the same reference; and that\na singular term does not change its reference if a contained singular\nterm is replaced by another with the same reference. But now suppose\nthat “R” and “S” abbreviate any\ntwo sentences alike in truth value. (1984: 19)\n", "\nHe then argues that the following four sentences have the same\nreference:", "\n(The hat over a variable symbolizes the description operator: so\n“\\(\\hat{z}\\)” means the \\(z\\) such that …)\nThis is because (13) and (14) are logically equivalent, as are (15)\nand (16), while the only difference between (14) and (15) is that (14)\ncontains the expression (Davidson calls it a “singular\nterm”) “\\(\\hat{z} (z\\! =\\! z \\amp R)\\)” whereas (15)\ncontains “\\(\\hat{z} (z\\! =\\! z \\amp S)\\)”,", "\n\n\nand these refer to the same thing if S and R are alike\nin truth value. Hence any two sentences have the same reference if\nthey have the same truth value. (1984: 19)\n", "\nThe difficulty with this argument, as a number of writers have pointed\nout (see, e.g., Yourgrau 1987; Gaskin 1997: 153 n. 17; Künne\n2003: 133–41), and the place where the identity theorist is\nlikely to raise a cavil, lies in the first assumption on which it\ndepends. Davidson calls this assumption “reasonable”, but\nit has been widely questioned. It states “that logically\nequivalent singular terms have the same reference”. But\nintuitively, the ideas of logical equivalence and reference seem to be\nquite distinct, indeed to have, as such, little to do with one\nanother, so that it would be odd if there were some a priori\nreason why the assumption had to hold. And it is not difficult to\nthink of apparent counterexamples: the sentence “It is\nraining” is logically equivalent to the sentence “It is\nraining and (either Pluto is larger than Mercury or it is not the case\nthat Pluto is larger than Mercury)”, but the latter sentence\nseems to carry a referential payload that the former does not. Of\ncourse, if declarative sentences refer to truth-values, as Frege\nthought, then the two sentences will indeed be co-referential, but to\nassume that sentences refer to truth-values would be question-begging\nin the context of an argument designed to establish that all true\nsentences refer to the same thing." ], "subsection_title": "5.3 The “slingshot” problem" }, { "content": [ "\nA further objection to the identity theory, going back to an\nobservation of Strawson’s, takes its cue from the point that\ncanonical names of propositions and of facts are often not\nstraightforwardly congruent with one another: they are often not\nintersubstitutable salva congruitate (or, if they are, they\nmay not be intersubstitutable salva veritate) (Strawson 1971:\n196; cf. Künne 2003: 10–12). For example, we say that\npropositions are true, not that they obtain, whereas we say that facts\nobtain, not that they are true. How serious is this point? The\nobjection in effect presupposes that for two expressions to be\nco-referential, or satisfied by one and the same thing, they must be\nsyntactically congruent, have the same truth-value potential, and\nmatch in terms of general contextual suitability. The assumption of\nthe syntactic congruence of co-referential expressions is\ncontroversial, and it may be possible for the identity theorist simply\nto deny it (see Gaskin 2008: 106–10, for argument on the point,\nwith references to further literature; cf. Dodd 2008a: 83–6.).\nWhether co-referential expressions must be syntactically congruent\ndepends on one’s conception of reference, a matter that cannot\nbe further pursued here (for discussion see Gaskin 2008: ch. 2; 2020:\nchs. 3–5).", "\nThere has been a good deal of discussion in the literature concerning\nthe question whether an identification of facts with true propositions\nis undermined not specifically by phenomena of syntactic\nincongruence but rather by failure of relevant intersubstitutions to\npreserve truth-values (see, e.g., King 2007: ch. 5; King in\nKing, Soames, & Speaks 2014: 64–70, 201–8; Hofweber\n2016: 215–23; Candlish & Damnjanovic 2018: 264). The\ndiscussion has focused on examples like the following:", "\nThe problem here is said to be that the substitution of “true\nproposition” for “fact” or vice versa generates\ndifferent readings (in particular, readings with different\ntruth-values). Suppose Daniel has to memorize a list of true\npropositions, of which one is the proposition that this is a leap\nyear. Then it is contended that we can easily imagine a scenario in\nwhich (17) and (18) differ in truth-value. Another way of putting the\nsame point might be to say that (17) is equivalent to", "\nbut that (18) is not equivalent to (21), because—so the argument\ngoes—(18) but not (21) would be true if Daniel had memorized his\nlist of true propositions without realizing that they were\ntrue. Similar differences can be argued to apply, mutatis\nmutandis, to (19) and (20). Can the identity theorist deal with\nthis difficulty?", "\nIn the first place one might suggest that the alleged mismatch between\n(17) and (18) is less clear than the objector claims. (17) surely does\nhave a reading like the one that is said to be appropriate for (18).\nSuppose Daniel has to memorize a list of facts. (17) could then\ndiverge in truth-value from", "\nFor there is a reading of (17) on which, notwithstanding (17)’s\ntruth, (22) is false: this is the reading on which Daniel has indeed\nmemorized a list of facts, but without necessarily realizing that the\nthings he is memorizing are facts. He has memorized the\nrelevant fact (that this is a leap year), we might say, but not\nas a fact. That is parallel to the reading of (18) according\nto which Daniel has memorized the true proposition that this is a leap\nyear, but not as a true proposition. The identity theorist\nmight then aver that, perhaps surprisingly, the same point actually\napplies to the simple (21), on the grounds that this sentence can mean\nthat Daniel remembers the propositional object that this is a leap\nyear (from a list of such objects, say, that he has been asked to\nmemorize), with no implication that he remembers it either as a\nproposition or as a fact. So, according to this\nresponse, the transparent reading of (18)—which has Daniel\nremember the propositional object, namely that this is a leap\nyear, but not necessarily remember it as a fact, or even\nas the propositional object that this is a leap year (he\nremembers it under some other mode of presentation)—is also\navailable for (17) and for (21).", "\nWhat about the opaque reading of either (17) or (21), which implies\nthat Daniel knows for a fact that this is a leap\nyear—is that reading available for (18) too? The identity\ntheorist might maintain that this reading is indeed available, and\nthen explain why we tend not to use sentences like (18) in the\nrelevant sense, preferring sentences of the form of (17) or (21), on\nthe basis of the relative technicality of the vocabulary of (18). The\nidea would be that it is just an accident of language that we prefer\neither (17) or (21) to (18) where what is in question is the sense\nthat implies that Daniel has propositional knowledge that this is a\nleap year (is acquainted with that fact as a fact), as opposed to\nhaving mere acquaintance, under some mode of presentation or other,\nwith the propositional object which happens to be (the fact) that\nthis is a leap year. And if we ask why we prefer (17) or (21)\nto", "\nthen the answer will be the Gricean one that (23) conveys less\ninformation than (17) or (21), under the reading of these two\nsentences that we are usually interested in, according to which Daniel\nremembers the relevant fact as a fact, for (23) is compatible with the\nfalsity of “This is a leap year”. Hence to use (23) in a\nsituation where one was in a position to use (17) or (21) would carry\na misleading conversational implicature. That, at any rate, is one\npossible line for the identity theorist to take. (It is worth noting\nhere that, if the identity theorist is right about this, it will\nfollow that the “know that” construction will be subject\nto a similar ambiguity as the “remember that”\nconstruction, given that remembering is a special case of knowing.\nThat is: “A knows that p” will mean\neither “A is acquainted with the fact that\np, and is acquainted with it as a fact” or\nmerely “A is acquainted with the fact that\np, but not necessarily with it as\nsuch—either as a fact or even as a propositional\nobject”.)" ], "subsection_title": "5.4 The congruence problem" }, { "content": [ "\nIt might appear that we individuate propositions more finely than\nfacts: for example, one might argue that the fact that Hesperus is\nbright is the same fact as the fact that Phosphorus is\nbright, but that the propositions in question are different (see\non this point Künne 2003: 10–12; Candlish & Damnjanovic\n2018: 266–7). The identity theorist has a number of strategies\nin response to this objection. One would be simply to deny it, and\nmaintain that facts are individuated as finely as propositions: if one\nis a supporter of the Fregean version of the identity theory, this is\nlikely to be one’s response (see, e.g., Dodd 2008a: 90–3).\nAlternatively, one might respond by saying that, if there is a good\npoint hereabouts, at best it tells only against the Fregean and\nRussellian versions of the identity theory, not against the hybrid\nversion. The identity theory in the hybrid version can agree that we\nsometimes think of facts as extensional, reference-level entities and\nsometimes also individuate propositions or proposition-like entities\nintensionally. Arguably, these twin points do indeed tell against\neither a strict Fregean or a strict Russellian version of the identity\ntheory: they tell against the strict Fregean position because, as well\nas individuating facts intensionally, we also, sometimes, individuate\nfacts extensionally; and they tell against the strict Russellian\nposition because, as well as individuating facts extensionally, we\nalso, sometimes, individuate facts intensionally. But it is plausible\nthat the hybrid version of the identity theory is not touched by the\nobjection, because that version of the theory accommodates\npropositionally structured and factual entities at both levels of\nsense and reference, though different sorts of these entities at these\ndifferent levels—either propositions at the level of sense and\ncorrelative proposition-like entities at the level of reference or\nvice versa, and similarly, mutatis mutandis, for\nfacts and fact-like entities. It will follow, then, for this version\nof the identity theory, that Fregean thoughts and Russellian\npropositions are available, if true, to be identical with the factual\nentities of the appropriate level (sense and reference, respectively),\nand the individuation problem will not then, it seems, arise.\nPropositions or propositionally structured entities will be\nindividuated just as finely as we want them to be individuated, and at\neach level of resolution there will be facts or fact-like entities,\nindividuated to the same resolution, for them to be identical with, if\n true.[15]" ], "subsection_title": "5.5 The individuation problem" } ] } ]

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Moore: Selected\nWritings, Thomas Baldwin (ed.), London: Routledge.", "Neale, Stephen., 2001, “Meaning, Truth and Ontology”,\nin Interpreting Davidson, Petr Kotatko, Peter Pagin, and\nGabriel Segal (eds), Stanford, CA: CSLI Publications,\n155–197.", "Rasmussen, Joshua, 2014, Defending the Correspondence Theory\nof Truth, Cambridge: Cambridge University Press.\ndoi:10.1017/CBO9781107415102", "Russell, Bertrand, 1903, The Principles of Mathematics,\nCambridge: Cambridge University Press.", "–––, 1966, Philosophical Essays,\nLondon: Routledge.", "–––, 1973, Essays in Analysis, Douglas\nLackey (ed.), London: Allen and Unwin.", "Stenius, Erik, 1960, Wittgenstein’s Tractatus: a\nCritical Exposition of the Main Lines of Thought, Oxford:\nBlackwell.", "Strawson, P. F., 1971, Logico-Linguistic Papers, London:\nMethuen.", "Suhm, Christian, Philip Wagemann, and Florian Wessels, 2000,\n“Ontological Troubles with Facts and Objects in McDowell’s\nMind and World”, in Willaschek 2000: 27–33.", "Sullivan, Peter M., 2005, “Identity Theories of Truth and\nthe Tractatus”, Philosophical Investigations,\n28(1): 43–62. doi:10.1111/j.1467-9205.2005.00240.x", "Willaschek, Marcus (ed.), 2000, John McDowell: Reason and\nNature, Münster: Münsteraner Vorlesungen zur\nPhilosophie 3.\n [Willaschek 2000 available online]", "Wittgenstein, Ludwig, 1922, Tractatus\nLogico-Philosophicus, London: Routledge.", "Wright, Crispin, 1999, “Truth: a Traditional Debate\nReviewed”, in Truth, Simon Blackburn and Keith Simmons\n(eds.), Oxford: Oxford University Press, pp. 203–238.", "Yourgrau, Palle, 1987, “Frege on Truth and\nReference.”, Notre Dame Journal of Formal Logic, 28(1):\n132–138. doi:10.1305/ndjfl/1093636851" ]

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[ "\n\nThe plausibility of theories of truth has often been observed to\nvary, sometimes extensively, across different domains or regions of\ndiscourse. Because of this variance, the problems internal to each such\ntheory become salient as they overgeneralize. A natural suggestion is\ntherefore that not all (declarative) sentences in all domains are true\nin exactly the same way. Sentences in mathematics, morals, comedy,\nchemistry, politics, and gastronomy may be true in different ways, if\nand when they are ever true. ‘Pluralism about truth’ names\nthe thesis that there is more than one way of being true." ]

[ { "content_title": "1. Alethic pluralism about truth: a plurality of properties", "sub_toc": [ "1.1 Strength", "1.2 Related kinds of pluralism and neighboring views", "1.3 Alethic pluralism, inflationism, and deflationism" ] }, { "content_title": "2. Motivating pluralism: the scope problem", "sub_toc": [] }, { "content_title": "3. Prominent versions of pluralism", "sub_toc": [ "3.1 Platitude-based strategies", "3.2 Correspondence pluralism" ] }, { "content_title": "4. Objections to pluralism and responses", "sub_toc": [ "4.1 Ambiguity", "4.2 The scope problem as a pseudo-problem", "4.3 The criteria problem", "4.4 The instability challenge", "4.5 Problems regarding mixed discourse", "4.5 The problem of generalization", "4.6 The problem of normativity" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Alethic pluralism about truth: a plurality of properties", "subsections": [ { "content": [ "\n\nThe pluralist’s thesis that there are many ways of being true\nis typically construed as being tantamount to the claim that the number\nof truth properties is greater than one. However, this basic\ninterpretation,", "\n\nis compatible with both moderate as well as more radical\nprecisifications. According to moderate pluralism, at least one way of\nbeing true among the multitude of others is universally shared:", "\n\nAccording to strong pluralism, however, there is no such universal\nor common way of being true:", "\n\nPrecisifying pluralism about truth in these two ways brings several\nconsequences to the fore. Firstly, both versions of pluralism conflict\nwith strong monism about truth:", "\n\nSecondly, moderate—but not strong—pluralism is\ncompatible with a moderate version of monism about truth:", "\n\n(2) and (5) are compatible because (5) does not rule out the\npossibility that the truth property had by all true sentences might be\none among the multitude of truth properties endorsed by the moderate\npluralist (i.e., by someone who endorses (2)). Only strong pluralism in\n(3) entails the denial of the claim that all true sentences are true in\nthe same way. Thus, moderate pluralists and moderate monists\ncan in principle find common ground." ], "subsection_title": "1.1 Strength" }, { "content": [ "\n\nNot infrequently, pluralism about truth fails to be distinguished\nfrom various other theses about associated conceptual, pragmatic,\nlinguistic, semantic, and normative phenomena. Each of these other theses involves\nattributing plurality to a different aspect of the analysandum\n(explanandum, definiendum, etc.). For instance, linguistically, one may\nmaintain that there is a plurality of truth predicates (Wright 1992;\nTappolet 1997; Lynch 2000; Pedersen 2006, 2010). Semantically, one may\nmaintain that alethic terms like ‘true’ have multiple\nmeanings (Pratt 1908; Tarski 1944; Kölbel 2008, 2013; Wright 2010).\nCognitively or conceptually, one may maintain that there is a\nmultiplicity of truth concepts or regimented ways of conceptualizing\ntruth (Künne 2003; cf. Lynch 2006). Normatively, one might think\nthat truth has a plurality of profiles (Ferrari 2016, 2018).", "\n\nThese parameters or dimensions suggest that pluralism is itself not\njust a single, monolithic theory (see also Sher 1998; Wright\n2013). Any fully developed version of pluralism about truth is likely\nto make definitive commitments about at least some of these other\nphenomena. (However, it hardly entails them; one can consistently be\nan alethic pluralist about truth, for instance, without necessarily\nhaving commitments to linguistic pluralism about truth predicates, or\nabout concepts like fact or actuality.) Nonetheless, theses about\nthese other phenomena should be distinguished from pluralism about\ntruth, as understood here.", "\n\nLikewise, pluralism about truth must be distinguished from several\nneighbouring views, such as subjectivism, contextualism, relativism, or\neven nihilism about truth. For example, one can maintain some form of\nsubjectivism about truth while remaining agnostic about how many ways\nof being true there are. Or again, one can consistently maintain that\nthere is exactly one way of being true, which is always and everywhere\ndependent on context. Nor is it inconsistent to be both a pluralist and\nan absolutist or other anti-relativist about truth. For example, one\nmight argue that each of the different ways of being true holds\nabsolutely if it holds at all (Wright 1992). Alternatively, one might\nexplicate a compatibilist view, in which there are at least two kinds\nof truth, absolute and relative truth (Joachim 1905), or deflationist\nand substantivist (Kölbel 2013). Such views would be, necessarily,\npluralistic. Occasionally, pluralists have also been lumped together\nwith various groups of so-called ‘nihilists’,\n‘deniers’, and ‘cynics’, and even associated\nwith an ‘anything goes’ approach to truth (Williams 2002).\nHowever, any version of pluralism is prima facie inconsistent with any\nview that denies truth properties, such as nihilism and certain forms\nof nominalism." ], "subsection_title": "1.2 Related kinds of pluralism and neighboring views" }, { "content": [ "\n\nThe foregoing varieties of pluralism are consistent with various\nfurther analyses of pluralists’ ideas about truth. For instance,\npluralists may—but need not—hold that truth properties are\nsimply one-place properties, since commitments to truth’s being\nmonadic are orthogonal to commitments to its being monistic. However,\nmost pluralists converge on the idea that truth is a substantive\nproperty and take this idea as the point of departure for articulating\ntheir view.", "\n\nA property is substantive just in case there is more to its nature\nthan what is given in our concept of the property. A paradigmatic\nexample of a substantive property is the property of being water. There\nis more to the nature of water—being composed of H\\(_2\\)O,\ne.g.—than what is revealed in our concept of water (the\ncolourless, odourless liquid that comes out of taps, fills lakes,\netc.)", "\n\nThe issue of substantiveness connects with one of the major issues\nin the truth debate: the rift between deflationary theories of truth\nand their inflationary counterparts (Horwich 1990; Edwards 2013b;\nKünne 2003; Sher 2016b; Wyatt 2016; Wyatt & Lynch 2016). A common way to understand the divide between\ndeflationists and inflationists is in terms of the question whether or\nnot truth is a substantive property. Inflationists endorse this idea,\nwhile deflationists reject it. More specifically, deflationists and\ninflationists can be seen as disagreeing over the following claim:", "\n\nThe inflationist accepts (6). According to her, it is not\ntransparent in the concept of truth that being true is a matter of\npossessing some further property (cohering, corresponding, etc.). This\nmakes truth a substantive property. The deflationist, on the other\nhand, rejects (6) because she is committed to the idea that everything\nthere is to know about truth is transparent in the concept—which,\non the deflationist’s view, is exhausted by the disquotational\nschema (‘\\(p\\)’ is true if, and only if, \\(p)\\), or some principle\nlike it.", "\n\nDeflationists also tend to reject a further claim about\ntruth’s explanatory role:", "\n\nInflationists, on the other hand, typically accept both (6) and\n(7).", "\n\nStrong and moderate versions of pluralism are perhaps best\nunderstood as versions of a non-traditional inflationary theory (for an exception, see Beall 2013; for refinements, see Edwards 2012b and Ferrari & Moruzzi forthcoming).\nPluralists side with inflationists on (6) and (7), and so, their views\ncount as inflationary. Yet, traditional inflationary theories are also\npredominantly monistic. They differ about which property\n\\(F\\)—coherence, identity, superwarrant, correspondence,\netc.—truth consists in, but concur that there is precisely one\nsuch property:", "\n\nThe monistic supposition in (8) is tantamount to the claim that\nthere is but one way of being true. In opposing that claim, pluralism\ncounts as non-traditional." ], "subsection_title": "1.3 Alethic pluralism, inflationism, and deflationism" } ] }, { "main_content": [ "\n\nPluralists’ rejection of (8) typically begins by rendering it as a\nclaim about the invariant nature of truth across all regions of\ndiscourse (Acton 1935; Wright 1992, 1996; Lynch 2000, 2001; for more\non domains see Edwards 2018b; Kim & Pedersen 2018, Wyatt 2013; Yu\n2017). Thus rendered, the claim appears to be at odds with the\nfollowing observation:", "\n\nFor example, some theories—such as correspondence\ntheories—seem intuitively plausible when applied to truths about\nladders, ladles, and other ordinary objects. However, those theories\nseem much less convincing when applied to truths about comedy, fashion,\nethical mores, numbers, jurisprudential dictates, etc. Conversely,\ntheories that seem intuitively plausible when applied to legal, comic,\nor mathematical truths—such as those suggesting that the nature\nof truth is coherence—seem less convincing when applied to truths\nabout the empirical world.", "\n\nPluralists typically take traditional inflationary theories of truth\nto be correct in analyzing truth in terms of some substantive property\n\\(F\\). Yet, the problem with their monistic suppositions lies with\ngeneralization: a given property \\(F\\) might be necessary and\nsufficient for explaining why sentences about a certain subject matter\nare true, but no single property is necessary and sufficient for\nexplaining why \\(p\\) is true for all sentences \\(p\\), whatever its subject\nmatter. Subsequently, those theories’ inability to generalize\ntheir explanatory scope beyond the select few regions of discourse for\nwhich they are intuitively plausible casts aspersion on their candidate\nfor \\(F\\). This problem has gone by various names, but has come to\nbe known as ‘the scope problem’ (Lynch 2004b, 2009; cf. Sher\n1998).", "\n\nPluralists respond to the scope problem by first rejecting (8) and\nreplacing it with:", "\n\nWith (10), pluralists contend that the nature of truth is not a\nsingle property \\(F\\) that is invariant across all regions of\ndiscourse; rather the true sentences in different regions of discourse\nmay consist in different properties among the plurality\n\\(F_1 , \\ldots ,F_n\\) that\nconstitute truth’s nature.", "\n\nThe idea that truth is grounded in various properties\n\\(F_1 , \\ldots ,F_n\\) might be\nfurther introduced by way of analogy. Consider water. We ordinarily\nthink and talk about something’s being water as if it were just\none thing—able to exist in different states, but nevertheless\nconsisting in just one property (H\\(_2\\)O). But it would be a\nmistake to legislate in advance that we should be monists about water,\nsince the nature of water is now known to vary more than our intuitions\nwould initially have it. The isotopic distribution of water allows for\ndifferent molecular structures, to include hydroxonium\n(H\\(_3\\)O), deuterium oxide (D\\(_2\\)O), and so-called\n‘semi-heavy water’ (HDO). Or again, consider sugar, the\nnature of which includes glucose, fructose, lactose, cellulose, and\nsimilar other such carbohydrates. For the pluralist, so too might truth\nbe grounded as a plurality of more basic properties.", "\n\nOne reason to take pluralism about truth seriously, then, is that it\nprovides a solution to the scope problem. In rejecting the\n‘one-size-fits-all’ approach to truth, pluralists formulate\na theory whose generality is guaranteed by accommodating the various\nproperties \\(F_1 , \\ldots ,F_n\\) by\nwhich true sentences come to be true in different regions of discourse.\nA second and related reason is that the view promises to be\nexplanatory. Variance in the nature of truth in turn explains why\ntheories of truth perform unequally across various regions of\ndiscourse—i.e., why they are descriptively adequate and\nappropriate in certain regions of discourse, but not others. For\npluralists, the existence of different kinds of truths is symptomatic\nof the non-uniform nature of truth itself. Subsequently, taxonomical\ndifferences among truths might be better understood by formulating\ndescriptive models about how the nature of truth might vary between\nthose taxa." ], "section_title": "2. Motivating pluralism: the scope problem", "subsections": [] }, { "main_content": [], "section_title": "3. Prominent versions of pluralism", "subsections": [ { "content": [ "\n\nMany pluralists have followed Wright (1992) in supposing that\ncompliance with platitudes is what regiments and characterizes the\nbehavior and content of truth-predicates. Given a corollary account of\nhow differences in truth predicates relate to differences among truth\nproperties, this supposition suggests a platitude-based strategy for\npositing many ways of being true. Generally, a strategy will be\nplatitude-based if it is intended to show that a certain collection of\nplatitudes \\(p_1 , \\ldots ,p_n\\) suffices for\nunderstanding the analysandum or explanandum. By\n‘platitude’, philosophers generally mean certain\nuncontroversial expressions about a given topic or domain. Beyond that,\nconceptions about what more something must be or have to count as\nplatitudinous vary widely.", "\n\nA well-known version of platitude-based pluralism is discourse\npluralism. The simplest versions of this view make the following four\nclaims. Firstly, discourse exhibits natural divisions, and so can be\nstably divided into different regions \\(D_1 , \\ldots ,D_n\\). Secondly, the platitudes subserving some\n\\(D_i\\) may be different than those subserving\n\\(D_j\\). Thirdly, for any pair \\((D_i,\nD_j)\\), compliance with different platitudes\nsubserving each region of discourse can, in principle, result in\nnumerically distinct truth predicates \\((t_i,\nt_j)\\). Finally, numerically distinct truth predicates\ndesignate different ways of being true.", "\n\nDiscourse pluralism is frequently associated with Crispin Wright\n(1992, 1996, 2001), although others have held similar views (see, e.g.,\nPutnam 1994: 515). Wright has argued that discourse pluralism is\nsupported by what he calls ‘minimalism’. According to\nminimalism, compliance with both the disquotational schema and the\noperator schema,", "\n\nas well as other ‘parent’ platitudes, is both necessary\nand sufficient for some term \\(t_i\\) to qualify as\nexpressing a concept worth regarding as TRUTH (1992: 34–5).\nWright proposed that the parent platitudes, which basically serve as\nvery superficial formal or syntactic constraints, fall into two\nsubclasses: those connecting truth with assertion\n(‘transparency’),", "\n\nand those connecting truth with logical operations\n(‘embedding’),", "\n\nAny such term complying with these parent platitudes, regardless of\nregion of discourse, counts as what Wright called a\n‘lightweight’ or ‘minimal’ truth predicate.\nYet, the establishment of some \\(t\\) as a minimal truth predicate\nis compatible, argued Wright, with the nature of truth consisting in\ndifferent things in different domains (2001: 752).", "\n\nWright (2001) has also suggested that lightweight truth predicates\ntend to comply with five additional subclasses of platitudes, including\nthose connecting truth with reality (‘correspondence’) and\neternity (‘stability’),", "\n\nand those disconnecting truth from epistemic state\n(‘opacity’), justification (‘contrast’), and\nscalar degree (‘absoluteness’),", "\n\nThe idea is that \\(t\\) may satisfy additional platitudes beyond\nthese, and in doing so may increase its ‘weight’. For\nexample, some \\(t_i\\) may be a more heavyweight truth\npredicate than \\(t_j\\) in virtue of satisfying\nplatitudes which entail that truth be evidence-transcendent or that\nthere be mind-independent truth-makers. Finally, differences in what\nconstitutes truth in \\(D_1 , \\ldots ,D_n\\) are tracked by differences in the weight of\nthese predicates. In this way, Wright is able to accommodate the\nintuition that sentences about, e.g., macromolecules in biochemistry\nare amenable to realist truth in a way that sentences about\ndistributive welfare in ethics may not be.", "\n\nDistinctions among truth predicates, according to the discourse\npluralist, are due to more and less subtle differences among platitudes\nand principles with which they must comply. For example, assuming that\naccuracy of reflection is a matter of degree, predicates for truth and\ntruthlikeness diverge because a candidate predicate may comply with\neither (18) or else either of (26) or (27); to accommodate both, two\ncorollary platitudes must be included to make explicit that accurate\nreflection in the case of truth is necessarily maximal and that degrees\nof accuracy are not equivalent to degrees of truth. Indeed, it is not\nunusual for platitudes to presuppose certain attendant semantic or\nmetaphysical views. For example,", "\n\nrequires anti-nominalist commitments, an ontological commitment to\npropositions, and commitments to the expression relation (translation\nrelations, an account of synonymy, etc.). Discourse pluralists\nrequiring predicates to comply with (28) in order to count as\ntruth-predicates must therefore be prepared to accommodate other claims\nthat go along with (28) as a package-deal.", "\n‘Functionalism about truth’ names the thesis that truth\nis a functional kind. The most comprehensive and systematic development\nof a platitude-based version of functionalism comes from Michael Lynch,\nwho has been at the forefront of ushering in pluralist themes and\ntheses (see Lynch 1998, 2000, 2001, 2004c, 2005a, 2005b, 2006, 2009, 2012, 2013; Devlin\n2003). Lynch has urged that we need to think about truth in terms of\nthe ‘job’ or role, \\(F\\), that true sentences stake\nout in our discursive practices (2005a: 29).", "\n\nInitially, Lynch’s brand of functionalism attempted to\nimplicitly define the denotation of ‘truth’ using the\nquasi-formal technique of Ramsification. The technique commences by\ntreating ‘true’ as the theoretical term \\(\\tau\\)\nissued by the theory \\(T\\) and targeted for implicit definition.\nFirstly, the platitudes and principles of the theory are amassed\n\\((T: p_1 , \\ldots ,p_n)\\) so that\nthe \\(F\\)-role can be specified holistically. Secondly, a certain\nsubset \\(A\\) of essential platitudes \\((p_i ,\n\\ldots ,p_k)\\) must be extracted from \\(T\\),\nand are then conjoined. Thirdly, following David Lewis, \\(T\\) is\nrewritten as", "\n\nso as to isolate the \\(\\tau\\)-terms from the non-theoretical\n(‘old, original, other’) \\(o\\)-terms. Fourthly, all\ninstances of ‘true’ and other cognate or closely related\n\\(\\tau\\)-terms are then replaced by subscripted variables\n\\(x_1 , \\ldots ,x_n\\). The resulting\nopen sentence is prefixed with existential quantifiers to bind them.\nNext, the Ramsey sentence is embedded in a material biconditional; this\nallows functionalists to then specify the conditions by which a given\ntruth-apt sentence \\(p\\) has a property that plays the \\(F\\)-role:", "\n\nwhere, say, the variable \\(x_1\\) is the one that\nreplaced ‘true’. Having specified the conditions under\nwhich \\(p\\) has some property realizing \\(F\\), functionalists can then\nderive another material biconditional stating that \\(p\\) is true iff \\(p\\) has\nsome property realizing the \\(F\\)-role.", "\n\nHowever, as Lynch (2004: 394) cautioned, biconditionals that specify\nnecessary and sufficient conditions for \\(p\\) to be true still leave open\nquestions about the ‘deep’ metaphysical nature of truth.\nThus, given the choice, Lynch—following up on a suggestion from\nPettit (1996: 886)—urged functionalists to identify truth, not\nwith the properties realizing the \\(F\\)-role in a given region of\ndiscourse, but with the \\(F\\)-role itself. Doing so is one way to\ntry to secure the ‘unity’ of truth (on the presumption that\nthere is just one \\(F\\)-role). Hence, to say that truth is a\nfunctional kind \\(F\\) is to say that the \\(\\tau\\)-term\n‘truth’ denotes the property of having a property that\nplays the \\(F\\)-role, where the \\(F\\)-role is tantamount to\nthe single unique second-order property of being \\(F\\).\nAccordingly, this theory proposes that something is true just in case\nit is \\(F\\).", "\n\nTwo consequences are apparent. Firstly, the functionalist’s\ncommitment to alethic properties realizing the \\(F\\)-role seems to\nbe a commitment to a grounding thesis. This explains why Lynch’s\nversion of alethic functionalism fits the pattern typical of\ninflationary theories of truth, which are committed to (6) and\n(7) above. Secondly, however, like most traditional inflationary\ntheories, Lynch’s functionalism about truth appears to be\nmonistic. Indeed, the functionalist commitment to identifying truth\nwith and only with the unique property of being \\(F\\) seems to\nentail a commitment to strong alethic monism in (5) rather than\npluralism (Wright 2005). Nonetheless, it is clear that Lynch’s\nversion does emphasize that sentences can have the property of being\n\\(F\\) in different ways. The theory thus does a great deal to\naccommodate the intuitions that initially motivate the pluralist thesis\nthat there is more than one way of being true, and to finesse a fine\nline between monism and pluralism.", "\n\nFor pluralists, this compromise may not be good enough, and critics\nof functionalism about truth have raised several concerns. One\nstumbling block for functionalist theories is a worry about epistemic\ncircularity. As Wright (2010) observes, any technique for implicit\ndefinition, such as Ramsification, proceeds on the basis of explicit\ndecisions that the platitudes and principles constitutive of the\nmodified Ramsey sentence are themselves true, and making explicit\ndecisions that they are true requires already knowing in advance what\ntruth is. Lynch (2013a) notes that the problem is not peculiar to\nfunctionalism about truth, generalizing to virtually all approaches\nthat attempt to fix the denotation of ‘true’ by appeal to\nimplicit definition. Some might want to claim that it generalizes even\nfurther, namely to any theory of truth whatsoever. Another issue is\nthat the \\(F\\)-role becomes disunified to the extent that\n\\(T\\) can accommodate substantially different platitudes and\nprinciples. Recall that the individuation and identity conditions of\nthe \\(F\\)-role—with which truth is identified—are\ndetermined holistically by the platitudes and principles constituting\n\\(T\\). So where \\(T\\) is constituted by expressions of the\nbeliefs and commitments of ordinary folk, pluralists could try to show\nthat these beliefs and commitments significantly differ across\nepistemic communities (see, e.g., Næss 1938a, b; Maffie 2002;\nUlatowski 2017, Wyatt 2018). In that case, Ramsification over\nsignificantly different principles may yield implicit definitions of\nnumerically distinct role properties\n\\(F_1, F_2 , \\ldots ,F_n\\), each of which is a warranted claimant to being\ntruth." ], "subsection_title": "3.1 Platitude-based strategies" }, { "content": [ "\n\nThe correspondence theory is often invoked as exemplary of\ntraditional monistic theories of truth, and thus as a salient rival to\npluralism about truth. Prima facie, however, the two are consistent.\nThe most fundamental principle of any version of the correspondence\ntheory,", "\n\nspecifies what truth consists in. Since it involves no covert\ncommitment about how many ways of being true there are, it does not\nrequire denying that there is more than one (Wright & Pedersen\n2010). In principle, there may be different ways of consisting in\ncorrespondence that yield different ways of being true. Subsequently,\nwhether the two theories turn out to be genuine rivals depends on\nwhether further commitments are made to explicitly rule out\npluralism.", "\n\nCorrespondence theorists have occasionally made proposals that combine\ntheir view with a version of pluralism. An early—although not\nfully developed—proposal of this kind was made by Henry Acton\n(1935: 191). Two recent proposals are noteworthy and have been\ndeveloped in detail. Gila Sher (1998, 2004, 2005, 2013, 2015, 2016a) has\npicked up the project of expounding on the claim that sentence in\ndomains like logic correspond to facts in a different way than do\nsentences in other domains, while Terence Horgan and colleagues\n(Horgan 2001; Horgan & Potrč 2000, 2006; Horgan & Timmons\n2002; Horgan & Barnard 2006; Barnard & Horgan 2013)\nhave elaborated a view that involves a defense of the claim that not\nall truths correspond to facts in the same way.", "\n\nFor Sher, truth does not consist in different properties in\ndifferent regions of discourse (e.g., superwarrant in macroeconomics,\nhomomorphism in immunology, coherence in film studies, etc.). Rather,\nit always and everywhere consists in correspondence. Taking\n‘correspondence’ to generally refer to an \\(n\\)-place\nrelation \\(R\\), Sher advances a version of correspondence\npluralism by countenancing different ‘forms’, or ways of\ncorresponding. For example, whereas the physical form of correspondence\ninvolves a systematic relation between the content of physical\nsentences and the physical structure of the world, the logical form of\ncorrespondence involves a systematic relation between the logical\nstructure of sentences and the formal structure of the world, while the\nmoral form of correspondence involves a relation between the moral\ncontent of sentences and (arguably) the psychological or sociological\nstructure of the world.", "\n\nSher’s view can be regarded as a moderate form of pluralism.\nIt combines the idea that truth is many with the idea that truth is\none. Truth is many on Sher’s view because there are different\nforms of correspondence. These are different ways of being true. At the\nsame time, truth is one because these different ways of being true are\nall forms of correspondence.", "\n\nFor Sher, a specific matrix of ‘factors’ determines the\nunique form of correspondence as well as the correspondence principles\nthat govern our theorizing about them. Which factors are in play\ndepends primarily on the satisfaction conditions of predicates. For\nexample, the form of correspondence for logical truths of the form", "\n\nis determined solely by the logical factor, which is reflected by\nthe universality of the union of the set of self-identical things and\nits complement. Or again, consider the categorical sentences", "\n\nand", "\n\nBoth (33) and (34) involve a logical factor, which is reflected in\ntheir standard form as I-statements (i.e., some \\(S\\) are \\(P)\\), as well as\nthe satisfaction conditions of the existential quantifier and copula; a\nbiological factor, which is reflected in the satisfaction conditions\nfor the predicate ‘is human’; and a normative factor, which\nis reflected in the satisfaction conditions for the predicates\n‘is disadvantaged’ and ‘is vain’. But whereas\n(34) involves a psychological factor, which is reflected in the\nsatisfaction conditions for ‘is vain’, (33) does not. Also,\n(33) may involve a socioeconomic factor, which is reflected in the\nsatisfaction conditions for ‘is disadvantaged’, whereas\n(34) does not.", "\n\nBy focusing on subsentential factors instead of supersentential\nregions of discourse, Sher offers a more fine-grained way to\nindividuate ways in which true sentences correspond. (Sher supposes\nthat we cannot name the correspondent of a given true sentence since\nthere is no single discrete hypostatized entity beyond the\n\\(n\\)-tuples of objects, properties and relations, functions,\nstructures (complexes, configurations), etc. that already populate\nreality.) The upshot is a putative solution to problems of mixed\ndiscourse (see §4 below): the truth of sentences like", "\n\nis determined by all of the above factors, and which\nis—despite the large overlap—a different kind of truth than\neither of the atomic sentences (33) and (34), according to Sher.", "\n\nFor their part, Horgan and colleagues propose a twist on the\ncorrespondence theorist’s claim that truth consists in a\ncorrespondence relation \\(R\\) obtaining between a given\ntruth-bearer and a fact. They propose that there are exactly two\nspecies of the relation \\(R\\): ‘direct’\n(\\(R_{dir}\\)) and ‘indirect correspondence’\n(\\(R_{ind}\\)), and thus exactly two ways of being true.\nFor Horgan and colleagues, which species of \\(R\\)—and thus\nwhich way of being true—obtains will depend on the austerity of\nontological commitments involved in assessing sentences; in turn, which\ncommitments are involved depends on discursive context and operative\nsemantic standards. For example, an austere ontology commits to only a\nsingle extant object: namely, the world (affectionally termed the\n‘blobject’). Truths about the blobject, such as", "\n\nif it is one, correspond to it directly. Truths about things other\nthan the blobject correspond to them indirectly. For example, sentences\nsuch as", "\n\nmay be true even if the extension of the predicate\n‘university’ is—strictly speaking—empty or what\nis referred to by ‘online universities’ is not in the\nnon-empty extension of ‘university’. In short, \\(p\\) is\ntrue\\(_1\\) iff \\(p\\) is \\(R_{dir}\\)-related to the\nblobject given contextually operative standards \\(c_i,\nc_j , \\ldots ,c_m\\).\nAlternatively, \\(p\\) is true\\(_2\\) iff \\(p\\) is\n\\(R_{ind}\\)-related to non-blobject entities given\ncontextually operative standards \\(c_j,\nc_k , \\ldots ,c_n\\). So, truth\nalways consists in correspondence. But the two types of correspondence\nimply that there is more than one way of being true." ], "subsection_title": "3.2 Correspondence pluralism" } ] }, { "main_content": [], "section_title": "4. Objections to pluralism and responses", "subsections": [ { "content": [ "\n\nSome take pluralists to be committed to the thesis that\n‘true’ is ambiguous: since the pluralist thinks that there\nis a range of alethically potent properties (correspondence, coherence,\netc.), ‘true’ must be ambiguous between these different\nproperties. This is thought to raise problems for pluralists. According\nto one objection, the pluralist appears caught in a grave dilemma.\n‘True’ is either ambiguous or unambiguous. If it is, then\nthere is a spate of further problems awaiting (see\n§4.4–§4.6 below). If it is not, then there is only one\nmeaning of ‘true’ and thus only one property designated by\nit; so pluralism is false.", "\n\nFriends of pluralism have tended to self-consciously distance\nthemselves from the claim that ‘true’ is ambiguous (e.g.,\nWright 1996: 924, 2001; Lynch 2001, 2004b, 2005c). Generally, however,\nthe issue of ambiguity for pluralism has not been well-analyzed. Yet,\none response has been investigated in some detail. According to this\nresponse, the ambiguity of ‘true’ is simply to be taken as\na datum. ‘True’ is de facto ambiguous (see, e.g., Schiller\n1906; Pratt 1908; Kaufmann 1948; Lucas 1969; Kölbel 2002, 2008;\nSher 2005; Wright 2010). Alfred Tarski, for instance, wrote:", "\n\n\nThe word ‘true’, like other words from our everyday\nlanguage, is certainly not unambiguous. […] We should reconcile\nourselves with the fact that we are confronted, not with one concept,\nbut with several different concepts which are denoted by one word; we\nshould try to make these concepts as clear as possible (by means of\ndefinition, or of an axiomatic procedure, or in some other way); to\navoid further confusion we should agree to use different terms for\ndifferent concepts […]. (1944: 342, 355)\n", "\n\nIf ‘true’ is ambiguous de facto, as some authors have\nsuggested, then the ambiguity objection may turn out to\nbe—again—not so much an objection or disconfirmation of the\ntheory, but rather just a datum about ‘truth’-talk in\nnatural language that should be explained or explained away by theories\nof truth. In that case, pluralists seem no worse off—and possibly\nbetter—than any number of other truth theorists.", "\n\nA second possible line of response from pluralists is that their\nview is not necessarily inconsistent with a monistic account of either\nthe meaning of ‘true’ or the concept TRUTH. After all,\n‘true’ is ambiguous only if it can be assigned more than\none meaning or semantic structure; and it has more than one meaning\nonly if there is more than one stable conceptualization or concept\nTRUTH supporting each numerically distinct meaning. Yet, nothing about\nthe claim that there is more than one way of being true entails, by\nitself, that there is more than one concept TRUTH. In principle, the\nnature of properties like being true—whether homomorphism,\nsuperassertibility, coherence, etc.—may outstrip the concept\nthereof, just as the nature of properties like being water—such\nas H\\(_2\\)O, H\\(_3\\)O, XYZ, etc.—may outstrip the\nconcept WATER (see, e.g., Wright 1996, 2001; Alston 2002; Lynch 2001,\n2005c, 2006). Nor is monism about truth necessarily inconsistent with\nsemantic or conceptual pluralism. The supposition that TRUTH is both\nmany and one (i.e., ‘moderate monism’) neither rules out\nthe construction of multiple concepts or meanings thereof, nor rules\nout the proliferation of uses to express those concepts or meanings.\nFor example, suppose that the only way of being true turns out to be a\nstructural relation \\(R\\) between reality and certain\nrepresentations thereof. Such a case is consistent with the existence\nof competing conceptions of what \\(R\\) consists in: weak\nhomomorphism, isomorphism, ‘seriously dyadic’\ncorrespondence, a causal \\(n\\)-place correspondence relation, etc.\nA more sensitive conclusion, then, is just that the objection from\nambiguity is an objection to conceptual or semantic pluralism, not to\nany alethic theory—pluralism or otherwise." ], "subsection_title": "4.1 Ambiguity" }, { "content": [ "\n\nAccording to the so-called ‘Quine-Sainsbury objection’,\npluralists’ postulation of ambiguity in metalinguistic alethic\nterms is not actually necessary, and thus not well-motivated. This is\nbecause taxonomical differences among kinds of truths in different\ndomains can be accounted for simply by doing basic ontology in\nobject-level languages.", "\n\n\n[E]ven if it is one thing for ‘this tree is an oak’ to\nbe true, another thing for ‘burning live cats is cruel’ to\nbe true, and yet another for ‘Buster Keaton is funnier than\nCharlie Chaplin’ to be true, this should not lead us to suppose\nthat ‘true’ is ambiguous; for we get a better explanation\nof the differences by alluding to the differences between trees,\ncruelty, and humor. (Sainsbury 1996: 900; see also Quine 1960: 131)\n", "\n\nGenerally, pluralists have not yet developed a response to the\nQuine-Sainsbury objection. And for some, this is because the real force\nof the Quine-Sainsbury objection lies in its exposure of the scope\nproblem as a pseudo-problem (Dodd 2013; see also Asay 2018). Again, the idea is that\ntraditional inflationary theories postulate some candidate for\n\\(F\\) but the applicability and plausibility of \\(F\\) differs\nacross regions of discourse. No such theory handles the truths of\nmoral, mathematical, comic, legal, etc. discourse equally well; and\nthis suggests that these theories, by their monism, face limitations on\ntheir explanatory scope. Pluralism offers a non-deflationary solution.\nYet, why think that these differences among domains mark an alethic\ndifference in truth per se, rather than semantic or discursive\ndifferences among the sentences comprising those domains? There is more\nthan one way to score a goal in soccer, for example (via corner kick,\nricochet off the foot of an opposing player or the head of a teammate,\nobstruct the goalkeeper, etc.), but it is far from clear that this\nentails pluralism about the property of scoring a goal in soccer.\n(Analogy belongs to an anonymous referee.) Pluralists have yet to\nadequately address this criticism (although see Blackburn 2013; Lynch 2013b, 2018; Wright 1998 for further discussion)." ], "subsection_title": "4.2 The scope problem as a pseudo-problem" }, { "content": [ "\n\nPluralists who invoke platitude-based strategies bear the burden of\narticulating inclusion and exclusion criteria for determining which\nexpressions do, or do not, count as members of the essential subset of\nplatitudes upon which this strategy is based (Wright, 2005). Candidates\ninclude: ordinariness, intuitiveness, uninformativeness, wide use or\ncitation, uncontroversiality, a prioricity, analyticity,\nindefeasibility, incontrovertibility, and sundry others. But none has\nproven to be uniquely adequate, and there is nothing close to a\nconsensus about which criteria to rely on.", "\n\nFor instance, consider the following two conceptions. One conception\ntakes platitudes about \\(x\\) to be expressions that must be\nendorsed on pain of being linguistically incompetent with the\napplication of the terms \\(t_1 , \\ldots ,t_n\\) used to talk about \\(x\\) (Nolan 2009).\nHowever, this conception does not readily allow for disagreement: prima\nfacie, it is not incoherent to think that two individuals, each of whom\nis competent with the application of\n\\(t_1 (x), \\ldots ,t_n (x)\\), may differ as to whether some \\(p\\)\nmust be endorsed or whether some expression is genuinely platitudinous.\nFor instance, consider the platitude in (17), which connects being\ntrue with corresponding with reality. Being linguistically competent\nwith terms for structural relations like correspondence does not force\nendorsement of claims that connect truth with correspondence; no one\nnot already in the grip of the correspondence theory would suppose that\nthey must endorse (17), and those who oppose it would certainly suppose\notherwise. Further inadequacies beleaguer this conception. It makes no\nprovision for degrees of either endorsement or linguistic incompetence.\nIt makes no distinction between theoretical and non-theoretical terms,\nmuch less restrict \\(t_1 (x), \\ldots ,t_n (x)\\) to non-theoretical terms. Nor does\nit require that platitudes themselves be true. On one hand, this\nconsequently leaves open the possibility that universally-endorsed but\nfalse or otherwise alethically defective expressions are included in\nthe platitude-based analysis of ‘true’. An old platitude\nabout whales, for example—one which was universally endorsed on\npain of being linguistically incompetent—prior to whales being\nclassified as cetaceans—was that they are big fish. The worry,\nthen, is that the criteria may allow us to screen in certain\n‘fish stories’ about truth. This would be a major problem\nfor advocates of Ramsification and other forms of implicit definition,\nsince those techniques work only on the presupposition that all input\nbeing Ramsified over or implicitly defined is itself true (Wright\n2010). On the other hand, making explicit that platitudes must also be\ntrue seems to entail that they are genuine ‘truisms’\n(Lynch 2005c), though discovering which ones are truly indefeasible is\na further difficulty—one made more difficult by the possibility\nof error theories (e.g., Devlin 2003) suggesting that instances of the\n\\(T\\)-schema are universally false. Indeed, we are inclined to say\ninstances of disquotational, equivalence, and operator schemas are\nsurely candidates for being platitudinous if anything is; but to say\nthat they must be endorsed on pain of being linguistically incompetent\nis to rule out a priori error theories about instances of the\n\\(T\\)-schema.", "\n\nA second, closely related conception is that platitudes are\nexpressions, which—in virtue of being banal, vacuous, elementary,\nor otherwise trivial—are acceptable by anyone who understands\nthem (Horwich 1990). The interaction of banality or triviality with\nacceptance does rule out a wide variety of candidate expressions,\nhowever. For instance, claims that are acceptable by anyone who\nunderstands them may still be too substantive or informative to count\nas platitudinous, depending on what they countenance. Similarly, claims\nthat are too ‘thin’ or neutral to vindicate any particular\ntheory \\(T\\) may still be too substantive or informative to count\nas genuinely platitudinous on this conception (Wright 1999). This is\nparticularly so given that nothing about a conception of platitudes as\n‘pretheoretical claims’ strictly entails that they reduce\nto mere banalities (Vision 2004). Nevertheless, criteria like banality\nor triviality plus acceptance might also screen in too few expressions\n(perhaps as few as one, such as a particular instance of the\n\\(T\\)-schema). Indeed, it is an open question whether any of the\nprinciples in (11)–(28) would count as platitudes on this\nconception.", "\n\nAn alternative conception emphasizes that the criteria should\ninstead be the interaction of informality, truth, a prioricity, or\nperhaps even analyticity (Wright 2001: 759). In particular, platitudes\nneed not take the form of an identity claim, equational definition, or\na material biconditional. At the extreme, expressions can be as\ncolloquial as you please so long as they remain true a priori (or\nanalytically). These latter criteria are commonly appealed to, but are\nalso not with problems. Firstly, a common worry is whether there are\nany strictly analytic truths about truth, and, if there are, whether\nthey can perform any serious theoretical work. Secondly, these latter\ncriteria would exclude certain truths that are a posteriori but no less\nuseful to a platitude-based strategist." ], "subsection_title": "4.3 The criteria problem" }, { "content": [ "\n\nAnother objection to pluralism is that it is an inherently instable\nview: i.e., as soon as the view is formulated, simple reasoning renders\nit untenable (Pedersen 2006, 2010; see also Tappolet 1997, 2000; Wright\n2012). This so-called instability challenge can be presented\nas follows. According to the moderate pluralist, there is more than one\ntruth property \\(F_1 , \\ldots ,F_n\\). Yet, given \\(F_1 , \\ldots ,F_n\\), it seems we should recognize another truth\nproperty:", "\n\nObserve that \\(F_U\\) is not merely some property\npossessed by every \\(p\\) which happens to have one of\n\\(F_1 , \\ldots ,F_n\\). (The property\nof being a sentence is one such a property, but it poses no trouble to\nthe pluralist.) Rather, \\(F_U\\) must be an alethic\nproperty whose extension perfectly positively covaries with the\ncombined extension of the pluralist truth properties\n\\(F_1 , \\ldots ,F_n\\). And since\nnothing is required for the existence of this new property other than\nthe truth properties already granted by the pluralist, (38) gives a\nnecessary and sufficient condition for \\(F_U\\) to be had\nby some \\(p\\): a sentence \\(p\\) is \\(F_U\\) just in case \\(p\\) is\n\\(F_1 \\vee \\cdots \\vee F_n\\). Thus,\nany sentence that is any of \\(F_1 , \\ldots ,F_n\\) may be true in some more generic or universal\nway, \\(F_U\\). This suggests, at best, that strong\npluralism is false, and moderate monism is true; and at worst, there\nseems to be something instable, or self-refuting, about pluralism.", "\n\nPluralists can make concessive or non-concessive responses to the\ninstability challenge. A concessive response grants that such a truth\nproperty exists, but maintains that it poses no serious threat to\npluralism. A non-concessive response is one intended to rebut the\nchallenge, e.g., by rejecting the existence of a common or universal\ntruth property. One way of trying to motivate this rejection of\n\\(F_U\\) is by attending to the distinction between\nsparse and abundant properties, and then demonstrating that alethic\nproperties like truth must be sparse and additionally argue that the\nwould-be trouble-maker \\(F_U\\) is an abundant property.\nAccording to sparse property theorists, individuals must be unified by\nsome qualitative similarity in order to share a property. For example,\nall even numbers are qualitatively similar in that they share the\nproperty of being divisible by two without remainder. Now, consider a\nsubset of very diverse properties \\(G_1 , \\ldots ,G_n\\) possessed by an individual \\(a\\). Is there\nsome further, single property of being \\(G_1\\), or\n…, or \\(G_n\\) that \\(a\\) has? Such a further\nproperty, were it to exist, would be highly disjunctive; and it may\nseem unclear what, if anything, individuals that were\n\\(G_1\\), or …, or \\(G_n\\) would\nhave in common—other than being \\(G_1\\), or\n…, or \\(G_n\\). According to sparse property\ntheorists, the lack of qualitative similarity means that this putative\ndisjunctive property is not a property properly so-called. Abundant\nproperty theorists, on the other hand, deny that qualitative similarity\nis needed in order for a range of individuals to share a property.\nProperties can be as disjunctive as you like. Indeed, for any set\n\\(A\\) there is at least one property had by all members of\n\\(A\\)—namely, being a member of \\(A\\). And since there\nis a set of all things that have some disjunctive property, there is a\nproperty—abundantly construed—had by exactly those things.\nIt thus seems difficult to deny the existence of \\(F_U\\)\nif the abundant conception of properties is adopted. So pluralists who\nwant to give a non-concessive response to the metaphysical instability\nchallenge may want to endorse the sparse conception (Pedersen 2006).\nThis is because the lack of uniformity in the nature of truth across\ndomains is underwritten by a lack of qualitative similarity between the\ndifferent truth properties that apply to specific domains of discourse.\nThe truth property \\(F_U\\) does not exist, because truth\nproperties are to be thought of in accordance with the sparse\nconception.", "\n\nEven if the sparse conception fails to ground pluralists’\nrejection of the existence of the universal truth property\n\\(F_U\\), a concessive response to the instability\nchallenge is still available. Pluralists can make a strong case that\nthe truth properties \\(F_1 , \\ldots ,F_n\\) are more fundamental than the universal truth\nproperty \\(F_U\\) (Pedersen 2010). This is because\n\\(F_U\\) is metaphysically dependent on\n\\(F_1 , \\ldots ,F_n\\), in the sense\nthat \\(F_U\\) is introduced in virtue of its being one of\n\\(F_1 , \\ldots ,F_n\\), and not\nvice-versa. Hence, even if the pluralist commits to the existence of\n\\(F_U\\)—and hence, to moderate metaphysical\nmonism—there is still a clear sense in which her view is\ndistinctively more pluralist than monist." ], "subsection_title": "4.4 The instability challenge" }, { "content": [ "\n\nThe content of some atomic sentences seems to hark exclusively from\na particular region of discourse. For instance, ‘lactose is a\nsugar’ concerns chemical reality, while ‘\\(7 + 5 = 12\\)’\nis solely about the realm of numbers (and operations on these). Not all\ndiscourse is pure or exclusive, however; we often engage in so-called\n‘mixed discourse’, in which contents from different regions\nof discourse are combined. For example, consider:", "\n\nMixed atomic sentences such as (39) are thought to pose problems for\npluralists. It seems to implicate concepts from the physical domain\n(causation), the mental domain (pain), and the moral domain (badness)\n(Sher 2005: 321–22). Yet, if pluralism is correct, then in which\nway is (39) true? Is it true in the way appropriate to talk of the\nphysical, the mental, or the moral? Is it true in neither of these\nways, or in all of these three ways, or in some altogether different\nway?", "\n\nThe source of the problem may be the difficulty in classifying\ndiscursive content—a classificatory task that is an urgent one\nfor pluralists. For it is unclear how they can maintain that regions of\ndiscourse \\(D_1 , \\ldots ,D_n\\)\npartially determine the ways in which sentences can be true without a\nprocedure for determining which region of discourse\n\\(D_i\\) a given \\(p\\) belongs to.", "\n\nOne suggestion is that a mixed atomic sentence \\(p\\) belongs to\nno particular domain. Another is that it belongs to several (Wyatt 2013). Lynch (2005b:\n340–41) suggested paraphrasing mixed atomic sentences as\nsentences that are classifiable as belonging to particular domains. For\nexample, (39) might be paraphrased as:", "\n\nUnlike (39), the paraphrased (40) appears to be a pure atomic\nsentence belonging to the domain of morals. This proposal remains\nunderdeveloped, however. It is not at all clear that (40) counts as a\nfelicitous paraphrase of (39), and, more generally, unclear whether all\nmixed atomic sentences can be paraphrased such that they belong to just\none domain without thereby altering their meaning, truth-conditions, or\ntruth-values.", "\n\nAnother possible solution addresses the problem head-on by\nquestioning whether atomic sentences really are mixed, thereby denying\nthe need for any such paraphrases. Consider the following\nsentences:", "\n\nPrima facie, what determines the domain-membership of (41) and (42)\nis the aesthetic and legal predicates ‘is beautiful’ and\n‘is illegal’, respectively. It is an aesthetic matter\nwhether the Mona Lisa is beautiful; this is because (41) is true in\nsome way just in case the Mona Lisa falls in the extension of the\naesthetic predicate ‘is beautiful’ (and mutatis mutandis\nfor (42)). In the same way, we might take (39) to exclusively belong to\nthe moral domain given that the moral predicate ‘is\nbad’. (This solution was presented in the first 2012 version of this entry; see Edwards 2018a for later, more detailed treatment.)", "\n\nIt is crucial to the latter two proposals that any given mixed\natomic sentence \\(p\\) has its domain membership essentially, since such\nmembership is what determines the relevant kind of truth. Sher (2005,\n2011) deals with the problem of mixed atomic sentences differently. On\nher view, the truth of a mixed atomic sentence is not accounted for by\nmembership to some specific domain; rather the ‘factors’\ninvolved in the sentence determine a specific form of correspondence,\nand this specific form of correspondence is what accounts for the truth\nof \\(p\\). The details about which specific form of correspondence obtains\nis determined at the sub-sentential levels of reference, satisfaction,\nand fulfillment. For example, the form of correspondence that accounts\nfor the truth of (39) obtains as a combination of the physical\nfulfillment of ‘the causing of \\(x\\)’, the mental\nreference of ‘pain’, and the moral satisfaction of\n‘\\(x\\) is bad’ (2005: 328). No paraphrase is\nneeded.", "\n\nAnother related problem pertains to two or more sentences joined by\none or more logical connectives, as in", "\n\nUnlike atomic sentences, the mixing here takes place at the\nsentential rather than sub-sentential level: (43) is a conjunction,\nwhich mixes the pure sentence ‘\\(7 + 5 = 12\\)’ with the pure\nsentence ‘killing innocent people is wrong’. (There are, of\ncourse, also mixed compounds that involve mixed atomic sentences.) For\nmany theorists, each conjunct seems to be true in a different way, if\ntrue at all: the first conjunct in whatever way is appropriate to moral\ntheory, and the second conjunct in whatever way is appropriate to\narithmetic. But then, how is the pluralist going to account for the\ntruth of the conjunction (Tappolet 2000: 384)? Pluralists owe an answer\nto the question of which way, exactly, a conjunction is true when its\nconjuncts are true in different ways.", "\n\nAdditional complications arise for pluralists who commit to facts\nbeing what make sentences true (e.g., Lynch 2001: 730), or other such\ntruth-maker or -making theses. Prima facie, we would reasonably expect\nthere to be different kinds of facts that make the conjuncts of (43)\ntrue, and which subsequently account for the differences in their\ndifferent ways of being true. However, what fact or facts makes true\nthe mixed compound? Regarding (43), is it the mathematical fact, the\nmoral fact, or some further kind of fact? On one hand, the claims that\nmathematical or moral facts, respectively, make \\(p\\) true seem to betray\nthe thought that both facts contribute equally to the truth of the\nmixed compound. On the other hand, the claim that some third\n‘mixed’ kind of fact makes \\(p\\) true leaves the pluralist with\nthe uneasy task of telling a rather alchemist story about\nfact-mixtures.", "\n\nFunctionalists about truth (e.g., Lynch 2005b: 396–97) propose\nto deal with compounds by distinguishing between two kinds of realizers\nof the \\(F\\)-role. The first is an atomic realizer, such that an\natomic proposition \\(p\\) is true iff \\(p\\) has a property that realizes the\n\\(F\\)-role. The second is a compound realizer, such that a\ncompound \\(q * r\\) (where \\(q\\) and \\(r\\) may themselves be complex) is true\niff", "\n\nThe realizers for atomic sentences are properties like\ncorrespondence, coherence, and superwarrant. The realizer properties\nfor compounds are special, in the sense that realizer properties for a\ngiven kind of compound are only had by compounds of that kind. Witness\nthat each of these compound realizer properties requires any of its\nbearers to be an instance of a specific truth-function. Pure and mixed\ncompounds are treated equally on this proposal: when true, they are\ntrue because they instantiate the truth-function for conjunction,\nhaving two or more conjuncts that have a property that realizes the\n\\(F\\)-role (and mutatis mutandis for disjunctions and material\nconditionals).", "\n\nHowever, this functionalist solution to the problem of mixed\ncompounds relies heavily on that theory’s monism—i.e., its\ninsistence that the single role property \\(F\\) is a universal\ntruth property. This might leave one wondering whether a solution is\nreadily available to someone who rejects the existence of such a\nproperty. One strategy is simply to identify the truth of conjunctions, disjunctions, and conditionals with the kind of properties specified by (44), (45), and (46), respectively (as opposed to taking them to be realizers of a single truth property). Thus, e.g., the truth of any conjunction simply \\(is\\) to be an instance of the truth-function for conjunction with conjuncts that have the property that plays the \\(F\\)-role for them (Kim & Pedersen 2018, Pedersen & Lynch 2018 (Sect. 20.6.2.1). Another strategy is to try to use the resources of multi-valued logic. For example, one can posit an ordered set of designated\nvalues for each way of being true \\(F_1 , \\ldots ,F_n\\) (perhaps according to their status as\n‘heavyweight’ or ‘lightweight’), and then take\nconjunction to be a minimizing operation and disjunction a maximizing\none, i.e., \\(v(p \\wedge q) = \\min\\{v(p), v(q)\\}\\)\nand \\(v(p \\vee q) = \\max\\{v(p), v(q)\\}\\).\nResultingly, each conjunction and disjunction—whether pure or\nmixed—will be either true in some way or false in some way\nstraightforwardly determined by the values of the constituents. For\nexample, consider the sentences", "\n\nSuppose that (47) is true in virtue of corresponding to physical\nreality, while (48) true in virtue of cohering with a body of law; and\nsuppose further that correspondence \\((F_1)\\) is more\n‘heavyweight’ than coherence \\((F_2)\\).\nSince conjunction is a minimizing operation and \\(F_2 \\lt F_1\\), then ‘heat is mean molecular\nkinetic energy and manslaughter is a felony’ will be\n\\(F_2\\). Since disjunction is a maximizing operation,\nthen ‘heat is mean molecular kinetic energy or manslaughter is a\nfelony’ will be \\(F_1\\).", "\n\nThe many-valued solution to the problem of mixed compounds just\noutlined is formally adequate because it determines a way that each\ncompound is true. However, while interesting, the proposal needs to be\nsubstantially developed in several respects. For example, how is\nnegation treated—are there several negations, one for each way of\nbeing true, or is there a single negation? Also, taking ‘heat is\nmean molecular kinetic energy and manslaughter is a felony’ to be\ntrue in the way appropriate to law betrays a thought that seems at\nleast initially compelling, viz. that both conjuncts\ncontribute to the truth of the conjunction. Alternatively, one could\ntake mixed compounds to be true in some third way. However, this would\nleave the pluralist with the task of telling some story about how this\nthird way of being true relates to the other two. Again substantial\nwork needs to be done.", "\n\nEdwards (2008) proposed another solution to the problem of mixed\nconjunctions, the main idea of which is to appeal to the following\nbiconditional schema:", "\n\nEdwards suggests that pluralists can answer the challenge that mixed\nconjunctions pose by reading the stated biconditional as having an\norder of determination: \\(p \\wedge q\\) is true\\(_k\\) in\nvirtue of \\(p\\)’s being true\\(_i\\) and \\(q\\)’s being\ntrue\\(_j\\), but not vice-versa. This, he maintains,\nexplains what kind of truth a conjunction \\(p \\wedge q\\) has when its\nconjuncts are true in different ways; for the conjunction is\ntrue\\(_k\\) in virtue of having conjuncts that are both\ntrue, where it is inessential whether the conjuncts are true in the\nsame way. Truth\\(_k\\) is a further way of being true\nthat depends on the conjuncts being true in some way without reducing\nto either of them. The property true\\(_k\\) is thus not a\ngeneric or universal truth property that applies to the conjuncts as\nwell as the conjunction.", "\n\nAs Cotnoir (2009) emphasizes, Edwards’ proposal provides too\nlittle information about the nature of true\\(_k\\). What\nlittle is provided makes transparent the commitment to\ntrue\\(_k\\)’s being a truth property had only by\nconjunctions, in which case it is unclear whether Edwards’s\nsolution can generalize. In this regard, Edwards’ proposal is\nsimilar to Lynch’s functionalist proposal, which is committed to\nthere being a specific realizer property for each type of logical\ncompound.", "\n\nMixed inferences—inferences involving truth-apt sentences from\ndifferent domains—appear to be yet another problem for the\npluralist (Tappolet 1997, 2000; Pedersen 2006). One can illustrate the\nproblem by supposing, with the pluralist, that there are two ways of\nbeing true, one of which is predicated of the antecedent of a\nconditional and the other as its consequent. It can be left open in\nwhat way the conditional itself is true. Consider the following\ninference:", "\n\nThis inference would appear to be valid. However, it is not clear\nthat pluralists can account for its validity by relying on the standard\ncharacterization of validity as necessary truth preservation from\npremises to conclusion. Given that the truth properties applicable to\nrespectively (51) and (52) are different, what truth property is\npreserved in the inference? The pluralist owes an explanation of how\nthe thesis that there are many ways of being true can account for the\nvalidity of mixed inferences.", "\n\nBeall (2000) argued that the account of validity used in\nmulti-valued logics gives pluralists the resources to deal with the\nproblem of mixed inferences. For many-valued logics, validity is\naccounted for in terms of preservation of designated value, where\ndesignated values can be thought of as ways of being true, while\nnon-designated values can be thought of as ways of being false.\nAdopting a designated-value account of validity, pluralists can simply\ntake \\(F_1 , \\ldots ,F_n\\) to be the\nrelevant designated values and define an inference as valid just in\ncase the conclusion is designated if each premise is designated (i.e.,\none of \\(F_1 , \\ldots ,F_n)\\). On\nthis account, the validity of (mixed) arguments whose premises and\nconclusion concern different regions of discourse is evaluable in terms\nof more than one of \\(F_1 , \\ldots ,F_n\\); the validity of (pure) arguments whose premises\nand conclusion pertain to the same region of discourse is evaluable in\nterms of the same \\(F_i\\) (where \\(1 \\le i \\le n)\\). An immediate rejoinder is that the term\n‘true’ in ‘ways of being true’ refers to a\nuniversal way of being true—i.e., being designated simpliciter\n(Tappolet 2000: 384). If so, then the multi-valued solution comes at\nthe cost of inadvertently acknowledging a universal truth property. Of\ncourse, as noted, the existence of a universal truth property poses a\nthreat only to strong pluralism." ], "subsection_title": "4.5 Problems regarding mixed discourse" }, { "content": [ "\n\nAlethic terms are useful devices for generalizing. For instance,\nsuppose we wish to state the law of excluded middle. A tedious way\nwould be to produce a long—indeed,\ninfinite—conjunction:", "\n\nHowever, given the equivalence schema for propositions,", "\n\nthere is a much shorter formula, which captures what (54) is meant\nto express by using ‘true’, but without loss of explanatory\npower (Horwich 1990: 4):", "\n\nAlethic terms are also useful devices for generalizing over what\nspeakers say, as in", "\n\nThe utility of a generalization like (56) is not so much that it\neliminates the need to rely on an infinite conjunction, but that it is\n‘blind’ (i.e., made under partial ignorance of what was\nsaid).", "\n\nPluralists seem to have difficulty accounting for truth’s use\nas a device for generalization. One response is to simply treat uses of\n‘is true’ as elliptical for ‘is true in one way or\nanother’. In doing so, pluralists account for generalization\nwithout sacrificing their pluralism. A possible drawback, however, is\nthat it may commit pluralists to the claim that ‘true’\ndesignates the disjunctive property of being \\(F_1\n\\vee \\cdots \\vee F_n\\). Granting the existence of\nsuch a property gives pluralists a story to tell about generalizations\nlike (55) and (56), but the response is a concessive one available only\nto moderate pluralists. However, as noted in §4.2.3, the existence\nof such a property is not a devastating blow to all pluralists, since\nthe domain-specific truth properties \\(F_1 , \\ldots ,F_n\\) remain explanatorily basic in relation to the\nproperty of being \\(F_1 \\vee \\cdots \\vee F_n\\)." ], "subsection_title": "4.5 The problem of generalization" } ] } ]

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[ "\nPragmatic theories of truth are usually associated either with C.S.\nPeirce’s proposal that true beliefs will be accepted “at\nthe end of inquiry” or with William James’ proposal that\ntruth be defined in terms of utility. More broadly, however, pragmatic\ntheories of truth focus on the connection between truth and epistemic\npractices, notably practices of inquiry and assertion. Depending on\nthe particular pragmatic theory, true statements might be those that\nare useful to believe, that are the result of inquiry, that have\nwithstood ongoing examination, that meet a standard of warranted\nassertibility, or that represent norms of assertoric discourse. Like\nother theories of truth (e.g., coherence and deflationary theories)\npragmatic theories of truth are often put forward as an alternative to\ncorrespondence theories of truth. Unlike correspondence theories,\nwhich tend to see truth as a static relation between a truth-bearer\nand a truth-maker, pragmatic theories of truth tend to view truth as a\nfunction of the practices people engage in, and the commitments people\nmake, when they solve problems, make assertions, or conduct scientific\ninquiry. More broadly, pragmatic theories tend to emphasize the\nsignificant role the concept of truth plays across a range of\ndisciplines and discourses: not just scientific and fact-stating\ndiscourse but also ethical, legal, and political discourse as\nwell.", "\nPragmatic theories of truth have the effect of shifting attention away\nfrom what makes a statement true and toward what people mean or do in\ndescribing a statement as true. While sharing many of the impulses\nbehind deflationary theories of truth (in particular, the idea that\ntruth is not a substantial property), pragmatic theories also tend to\nview truth as more than just a useful tool for making generalizations.\nPragmatic theories of truth thus emphasize the broader practical and\nperformative dimensions of truth-talk, stressing the role truth plays\nin shaping certain kinds of discourse. These practical dimensions,\naccording to pragmatic theories, are essential to understanding the\nconcept of truth.", "\nAs these references to pragmatic theories (in the plural) would\nsuggest, over the years a number of different approaches have been\nclassified as “pragmatic”. This points to a degree of\nambiguity that has been present since the earliest formulations of the\npragmatic theory of truth: for example, the difference between\nPeirce’s (1878 [1986: 273]) claim that truth is “the\nopinion which is fated to be ultimately agreed to by all who\ninvestigate” and James’ (1907 [1975: 106]) claim that truth “is\nonly the expedient in the way of our thinking”. Since then the\nsituation has arguably gotten worse, not better. The often-significant\ndifferences between various pragmatic theories of truth can make it\ndifficult to determine their shared commitments (if any), while also\nmaking it difficult to critique these theories overall. Issues with\none version may not apply to other versions, which means that\npragmatic theories of truth may well present more of a moving target\nthan do other theories of truth. While few today would equate truth\nwith expedience or utility (as James often seems to do) there remains\nthe question of what the pragmatic theory of truth stands for and how\nit is related to other theories. Still, pragmatic theories of truth\ncontinue to be put forward and defended, often as serious alternatives\nto more widely accepted theories of truth" ]

[ { "content_title": "1. History of the Pragmatic Theory of Truth", "sub_toc": [ "1.1 Peirce’s Pragmatic Theory of Truth", "1.2 James’ Pragmatic Theory of Truth", "1.3 Dewey’s Pragmatic Theory of Truth" ] }, { "content_title": "2. Neo-Pragmatic Theories of Truth", "sub_toc": [] }, { "content_title": "3. Truth as a Norm of Inquiry and Assertion", "sub_toc": [] }, { "content_title": "4. Common Features", "sub_toc": [] }, { "content_title": "5. Critical Assessments", "sub_toc": [ "5.1 Three Classic Objections and Responses", "5.2 The Fundamental Objection" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThe history of the pragmatic theory of truth is tied to the history of\nclassical American pragmatism. According to the standard account, C.S.\nPeirce gets credit for first proposing a pragmatic theory of truth,\nWilliam James is responsible for popularizing the pragmatic theory,\nand John Dewey subsequently reframed truth in terms of warranted\nassertibility (for this reading of Dewey see Burgess & Burgess\n2011: 4). More specifically, Peirce is associated with the idea that\ntrue beliefs are those that will withstand future scrutiny; James with\nthe idea that true beliefs are dependable and useful; Dewey with the\nidea that truth is a property of well-verified claims (or\n“judgments”)." ], "section_title": "1. History of the Pragmatic Theory of Truth", "subsections": [ { "content": [ "\nThe American philosopher, logician and scientist Charles Sanders\nPeirce (1839–1914) is generally recognized for first proposing a\n“pragmatic” theory of truth. Peirce’s pragmatic\ntheory of truth is a byproduct of his pragmatic theory of meaning. In\na frequently-quoted passage in “How to Make Our Ideas\nClear” (1878), Peirce writes that, in order to pin down the\nmeaning of a concept, we must:", "\n\n\nConsider what effects, which might conceivably have practical\nbearings, we conceive the object of our conception to have. Then, our\nconception of these effects is the whole of our conception of the\nobject. (1878 [1986: 266])\n", "\nThe meaning of the concept of “truth” then boils down to\nthe “practical bearings” of using this term: that is, of\ndescribing a belief as true. What, then, is the practical difference\nof describing a belief as “true” as opposed to any number\nof other positive attributes such as “creative”,\n“clever”, or “well-justified”? Peirce’s\nanswer to this question is that true beliefs eventually gain general\nacceptance by withstanding future inquiry. (Inquiry, for Peirce, is\nthe process that takes us from a state of doubt to a state of stable\nbelief.) This gives us the pragmatic meaning of truth and leads Peirce\nto conclude, in another frequently-quoted passage, that:", "\n\n\nAll the followers of science are fully persuaded that the processes of\ninvestigation, if only pushed far enough, will give one certain\nsolution to every question to which they can be applied.…The\nopinion which is fated to be ultimately agreed to by all who\ninvestigate, is what we mean by the truth. (1878 [1986: 273])\n", "\nPeirce realized that his reference to “fate” could be\neasily misinterpreted. In a less-frequently quoted footnote to this\npassage he writes that “fate” is not meant in a\n“superstitious” sense but rather as “that which is\nsure to come true, and can nohow be avoided” (1878 [1986: 273]).\nOver time Peirce moderated his position, referring less to fate and\nunanimous agreement and more to scientific investigation and general\nconsensus (Misak 2004). The result is an account that views truth as\nwhat would be the result of scientific inquiry, if scientific inquiry\nwere allowed to go on indefinitely. In 1901 Peirce writes that:", "\n\n\nTruth is that concordance of an abstract statement with the ideal\nlimit towards which endless investigation would tend to bring\nscientific belief. (1901a [1935: 5.565])\n", "\nConsequently, truth does not depend on actual unanimity or an actual\nend to inquiry:", "\n\n\nIf Truth consists in satisfaction, it cannot be any actual\nsatisfaction, but must be the satisfaction which would\nultimately be found if the inquiry were pushed to its ultimate and\nindefeasible issue. (1908 [1935: 6.485], emphasis in original)\n", "\nAs these references to inquiry and investigation make clear,\nPeirce’s concern is with how we come to have and hold the\nopinions we do. Some beliefs may in fact be very durable but would not\nstand up to inquiry and investigation (this is true of many cognitive\nbiases, such as the Dunning-Kruger effect where people remain\nblissfully unaware of their own incompetence). For Peirce, a true\nbelief is not simply one we will hold onto obstinately. Rather, a true\nbelief is one that has and will continue to hold up to sustained\ninquiry. In the practical terms Peirce prefers, this means that to\nhave a true belief is to have a belief that is dependable in the face\nof all future challenges. Moreover, to describe a belief as true is to\npoint to this dependability, to signal the belief’s scientific\nbona fides, and to endorse it as a basis for action.", "\nBy focusing on the practical dimension of having true beliefs, Peirce\nplays down the significance of more theoretical questions about the\nnature of truth. In particular, Peirce is skeptical that the\ncorrespondence theory of truth—roughly, the idea that true\nbeliefs correspond to reality—has much useful to say about the\nconcept of truth. The problem with the correspondence theory of truth,\nhe argues, is that it is only “nominally” correct and\nhence “useless” (1906 [1998: 379, 380]) as far as describing\ntruth’s practical value. In particular, the correspondence\ntheory of truth sheds no light on what makes true beliefs valuable,\nthe role of truth in the process of inquiry, or how best to go about\ndiscovering and defending true beliefs. For Peirce, the importance of\ntruth rests not on a “transcendental” (1901a [1935: 5.572])\nconnection between beliefs on the one hand and reality on the other,\nbut rather on the practical connection between doubt and belief, and\nthe processes of inquiry that take us from the former to the\nlatter:", "\n\n\nIf by truth and falsity you mean something not definable in terms of\ndoubt and belief in any way, then you are talking of entities of whose\nexistence you can know nothing, and which Ockham’s razor would\nclean shave off. Your problems would be greatly simplified, if,\ninstead of saying that you want to know the “Truth”, you\nwere simply to say that you want to attain a state of belief\nunassailable by doubt. (1905 [1998: 336])\n", "\nFor Peirce, a true belief is one that is indefeasible and\nunassailable—and indefeasible and unassailable for all the right\nreasons: namely, because it will stand up to all further inquiry and\ninvestigation. In other words, ", "\n\n\nif we were to reach a stage where we could no longer improve upon a\nbelief, there is no point in withholding the title “true”\nfrom it. (Misak 2000: 101)\n" ], "subsection_title": "1.1 Peirce’s Pragmatic Theory of Truth" }, { "content": [ "\nPeirce’s contemporary, the psychologist and philosopher William\nJames (1842–1910), gets credit for popularizing the pragmatic\ntheory of truth. In a series of popular lectures and articles, James\noffers an account of truth that, like Peirce’s, is grounded in\nthe practical role played by the concept of truth. James, too,\nstresses that truth represents a kind of satisfaction: true beliefs\nare satisfying beliefs, in some sense. Unlike Peirce, however, James\nsuggests that true beliefs can be satisfying short of being\nindefeasible and unassailable: short, that is, of how they would stand\nup to ongoing inquiry and investigation. In the lectures published as\nPragmatism: A New Name for Some Old Ways of Thinking (1907)\nJames writes that:", "\n\n\nIdeas…become true just in so far as they help us get into\nsatisfactory relation with other parts of our experience, to summarize\nthem and get about among them by conceptual short-cuts instead of\nfollowing the interminable succession of particular phenomena. (1907\n[1975: 34])\n", "\nTrue ideas, James suggests, are like tools: they make us more\nefficient by helping us do what needs to be done. James adds to the\nprevious quote by making the connection between truth and utility\nexplicit:", "\n\n\nAny idea upon which we can ride, so to speak; any idea that will carry\nus prosperously from any one part of our experience to any other part,\nlinking things satisfactorily, working securely, simplifying, saving\nlabor; is true for just so much, true in so far forth, true\ninstrumentally. This is the ‘instrumental’ view\nof truth. (1907 [1975: 34])\n", "\nWhile James, here, credits this view to John Dewey and F.C.S.\nSchiller, it is clearly a view he endorses as well. To understand\ntruth, he argues, we must consider the pragmatic\n“cash-value” (1907 [1975: 97]) of having true beliefs and\nthe practical difference of having true ideas. True beliefs, he\nsuggests, are useful and dependable in ways that false beliefs are\nnot: ", "\n\n\nyou can say of it then either that “it is useful because it is\ntrue” or that “it is true because it is useful”.\nBoth these phrases mean exactly the same thing. (1907 [1975: 98]) \n", "\nPassages such as this have cemented James’ reputation for\nequating truth with mere utility (something along the lines of:\n“< p > is true just in case it is useful to believe\nthat p” [see Schmitt 1995: 78]). (James does offer the\nqualification “in the long run and on the whole of course”\n(1907 [1975: 106]) to indicate that truth is different from instant\ngratification, though he does not say how long the long run should\nbe.) Such an account might be viewed as a watered-down version of\nPeirce’s account that substitutes “cash-value” or\nsubjective satisfaction for indefeasibility and unassailability in the\nface of ongoing inquiry and investigation. Such an account might also\nbe viewed as obviously wrong, given the undeniable existence of\nuseless truths and useful falsehoods.", "\nIn the early twentieth century Peirce’s writings were not yet\nwidely available. As a result, the pragmatic theory of truth was\nfrequently identified with James’ account—and, as we will\nsee, many philosophers did view it as obviously wrong. James, in turn,\naccused his critics of willful misunderstanding: that because he wrote\nin an accessible, engaging style his critics “have boggled at\nevery word they could boggle at, and refused to take the spirit rather\nthan the letter of our discourse” (1909 [1975: 99]). However, it\nis also the case that James tends to overlook or intentionally\nblur—it is hard to say which—the distinction between (a)\ngiving an account of true ideas and (b) giving an account of the\nconcept of truth. This means that, while James’ theory might\ngive a psychologically realistic account of why we care about the\ntruth (true ideas help us get things done) his theory fails to shed\nmuch light on what the concept of truth exactly is or on what makes an\nidea true. And, in fact, James often seems to encourage this reading.\nIn the preface to The Meaning of Truth he doubles down by\nquoting many of his earlier claims and noting that “when the\npragmatists speak of truth, they mean exclusively something about the\nideas, namely their workableness” (1909 [1975: 6],\nemphasis added). James’ point seems to be this: from a practical\nstandpoint, we use the concept of truth to signal our confidence in a\nparticular idea or belief; a true belief is one that can be acted\nupon, that is dependable and that leads to predictable outcomes; any\nfurther speculation is a pointless distraction.", "\nWhat then about the concept of truth? It often seems that James\nunderstands the concept of truth in terms of verification: thus,\n“true is the name for whatever idea starts the\nverification-process, useful is the name for its completed function in\nexperience” (1907 [1975: 98]). And, more generally:", "\n\n\nTruth for us is simply a collective name for verification-processes,\njust as health, wealth, strength, etc., are names for other processes\nconnected with life, and also pursued because it pays to pursue them.\n(1907 [1975: 104])\n", "\nJames seems to claim that being verified is what makes an idea true,\njust as having a lot of money is what makes a person wealthy. To be\ntrue is to be verified:", "\n\n\nTruth happens to an idea. It becomes true, is\nmade true by events. Its verity is in fact an event,\na process: the process namely of its verifying itself, its\nveri-fication. Its validity is the process of its\nvalid-ation. (1907 [1975: 97], emphasis in original)\n", "\nLike Peirce, James argues that a pragmatic account of truth is\nsuperior to a correspondence theory because it specifies, in concrete\nterms, what it means for an idea to correspond or “agree”\nwith reality. For pragmatists, this agreement consists in being led\n“towards that reality and no other” in a way that yields\n“satisfaction as a result” (1909 [1975: 104]). By\nsometimes defining truth in terms of verification, and by unpacking\nthe agreement of ideas and reality in pragmatic terms, James’\naccount attempts to both criticize and co-opt the correspondence\ntheory of truth. It appears James wants to have his cake and eat it\ntoo." ], "subsection_title": "1.2 James’ Pragmatic Theory of Truth" }, { "content": [ "\nJohn Dewey (1859–1952), the third figure from the golden era of\nclassical American pragmatism, had surprisingly little to say about\nthe concept of truth especially given his voluminous writings on other\ntopics. On an anecdotal level, as many have observed, the index to his\n527 page Logic: The Theory of Inquiry (1938 [2008]) has only\none reference to “truth”, and that to a footnote\nmentioning Peirce. Otherwise the reader is advised to “See\nalso assertibility”.", "\nAt first glance, Dewey’s account of truth looks like a\ncombination of Peirce and James. Like Peirce, Dewey emphasizes the\nconnection between truth and rigorous scientific inquiry; like James,\nDewey views truth as the verified result of past inquiry rather than\nas the anticipated result of inquiry proceeding into an indefinite\nfuture. For example, in 1911 he writes that:", "\n\n\nFrom the standpoint of scientific inquiry, truth indicates not just\naccepted beliefs, but beliefs accepted in virtue of a certain\nmethod.…To science, truth denotes verified beliefs,\npropositions that have emerged from a certain procedure of inquiry and\ntesting. By that I mean that if a scientific man were asked to point\nto samples of what he meant by truth, he would pick…beliefs\nwhich were the outcome of the best technique of inquiry available in\nsome particular field; and he would do this no matter what his\nconception of the Nature of Truth. (1911 [2008: 28])\n", "\nFurthermore, like both Peirce and James, Dewey charges correspondence\ntheories of truth with being unnecessarily obscure because these\ntheories depend on an abstract (and unverifiable) relationship between\na proposition and how things “really are” (1911 [2008:\n34]). Finally, Dewey also offers a pragmatic reinterpretation of the\ncorrespondence theory that operationalizes the idea of correspondence:\n", "\n\n\nOur definition of truth…uses correspondence as a mark of a\nmeaning or proposition in exactly the same sense in which it is used\neverywhere else…as the parts of a machine correspond. (1911\n[2008: 45])\n", "\nDewey has an expansive understanding of “science”. For\nDewey, science emerges from and is continuous with everyday processes\nof trial and error—cooking and small-engine repair count as\n“scientific” on his account—which means he should\nnot be taken too strictly when he equates truth with scientific\nverification. (Peirce and James also had expansive understandings of\nscience.) Rather, Dewey’s point is that true propositions, when\nacted on, lead to the sort of predictable and dependable outcomes that\nare hallmarks of scientific verification, broadly construed. From a\npragmatic standpoint, scientific verification boils down to the\nprocess of matching up expectations with outcomes, a process that\ngives us all the “correspondence” we could ask for.", "\nDewey eventually came to believe that conventional philosophical terms\nsuch as “truth” and “knowledge” were burdened\nwith so much baggage, and had become so fossilized, that it was\ndifficult to grasp the practical role these terms had originally\nserved. As a result, in his later writings Dewey largely avoids\nspeaking of “truth” or “knowledge” while\nfocusing instead on the functions played by these concepts. By his\n1938 Logic: The Theory of Inquiry Dewey was speaking of\n“warranted assertibility” as the goal of inquiry, using\nthis term in place of both “truth” and\n“knowledge” (1938 [2008: 15–16]). In 1941, in a\nresponse to Russell entitled “Propositions, Warranted\nAssertibility, and Truth”, he wrote that “warranted\nassertibility” is a “definition of the nature of knowledge\nin the honorific sense according to which only true beliefs are\nknowledge” (1941: 169). Here Dewey suggests that\n“warranted assertibility” is a better way of capturing the\nfunction of both knowledge and truth insofar as both are goals of\ninquiry. His point is that it makes little difference, pragmatically,\nwhether we describe the goal of inquiry as “acquiring more\nknowledge”, “acquiring more truth”, or better yet,\n“making more warrantably assertible judgments”.", "\nBecause it focuses on truth’s function as a goal of inquiry,\nDewey’s pragmatic account of truth has some unconventional\nfeatures. To begin with, Dewey reserves the term “true”\nonly for claims that are the product of controlled inquiry. This means\nthat claims are not true before they are verified but that, rather, it\nis the process of verification that makes them true: ", "\n\n\ntruth and falsity are properties only of that subject-matter which is\nthe end, the close, of the inquiry by means of which it is\nreached. (1941: 176) \n", "\nSecond, Dewey insists that only “judgments”—not\n“propositions”—are properly viewed as truth-bearers.\nFor Dewey, “propositions” are the proposals and working\nhypotheses that are used, via a process of inquiry, to generate\nconclusions and verified judgments. As such, propositions may be more\nor less relevant to the inquiry at hand but they are not, strictly\nspeaking true or false (1941: 176). Rather, truth and falsity are\nreserved for “judgments” or “the settled outcome of\ninquiry” (1941: 175; 1938 [2008: 124]; Burke 1994): for claims,\nin other words, that are warrantedly assertible. Third, Dewey\ncontinues to argue that this pragmatic approach to truth is “the\nonly one entitled to be called a correspondence theory of truth”\n(1941: 179) using terms nearly identical to those he used in 1911:", "\n\n\nMy own view takes correspondence in the operational sense…of\nanswering, as a key answers to conditions imposed by a lock,\nor as two correspondents “answer” each other; or, in\ngeneral, as a reply is an adequate answer to a question or\ncriticism—; as, in short, a solution answers the\nrequirements of a problem. (1941: 178)\n", "\nThanks to Russell (e.g., 1941: Ch. XXIII) and others, by 1941 Dewey\nwas aware of the problems facing pragmatic accounts of truth. In\nresponse, we see him turning to the language of “warranted\nassertibility”, drawing a distinction between\n“propositions” and “judgments”, and grounding\nthe concept of truth (or warranted assertibility) in scientific\ninquiry (Thayer 1947; Burke 1994). These adjustments were designed to\nextend, clarify, and improve on Peirce’s and James’\naccounts. Whether they did so is an open question. Certainly many,\nsuch as Quine, concluded that Dewey was only sidestepping important\nquestions about truth: that Dewey’s strategy was “simply\nto avoid the truth predicate and limp along with warranted\nbelief” (Quine 2008: 165).", "\nPeirce, James, and Dewey were not the only ones to propose or defend a\npragmatic theory of truth in the nineteenth and early twentieth\ncenturies. Others, such as F.C.S. Schiller (1864–1937), also put\nforward pragmatic theories (though Schiller’s view, which he\ncalled “humanism”, also attracted more than its share of\ncritics, arguably for very good reasons). Pragmatic theories of truth\nalso received the attention of prominent critics, including Russell\n(1909, 1910 [1994]), Moore (1908), Lovejoy (1908a,b) among others.\nSeveral of these criticisms will be considered later; suffice it to\nsay that pragmatic theories of truth soon came under pressure that led\nto revisions and several successor approaches over the next\nhundred-plus years. ", "\nHistorically Peirce, James, and Dewey had the greatest influence in\nsetting the parameters for what makes a theory of truth\npragmatic—this despite the sometimes significant differences\nbetween their respective accounts, and that over time they modified\nand clarified their positions in response to both criticism and\nover-enthusiastic praise. While this can make it difficult to pin down\na single definition of what, historically, counted as a pragmatic\ntheory of truth, there are some common themes that cut across each of\ntheir accounts. First, each account begins from a pragmatic analysis\nof the meaning of the truth predicate. On the assumption that\ndescribing a belief, claim, or judgment as “true” must\nmake some kind of practical difference, each of these accounts\nattempts to describe what this difference is. Second, each account\nthen connects truth specifically to processes of inquiry: to describe\na claim as true is to say that it either has or will stand up to\nscrutiny. Third, each account rejects correspondence theories of truth\nas overly abstract, “transcendental”, or metaphysical. Or,\nmore accurately, each attempts to redefine correspondence in pragmatic\nterms, as the agreement between a claim and a predicted outcome. While\nthe exact accounts offered by Peirce, James, and Dewey found few\ndefenders—by the mid-twentieth century pragmatic theories of\ntruth were largely dormant—these themes did set a trajectory for\nfuture versions of the pragmatic theory of truth." ], "subsection_title": "1.3 Dewey’s Pragmatic Theory of Truth" } ] }, { "main_content": [ "\nPragmatic theories of truth enjoyed a resurgence in the last decades\nof the twentieth century. This resurgence was especially visible in\ndebates between Hilary Putnam (1926–2016) and Richard Rorty\n(1931–2007) though broadly pragmatic ideas were defended by\nother philosophers as well (Bacon 2012: Ch. 4). (One example is\nCrispin Wright’s superassertibility theory (1992, 2001) which he\nclaims is “as well equipped to express the aspiration for a\ndeveloped pragmatist conception of truth as any other candidate”\n(2001: 781) though he does not accept the pragmatist label.) While\nthese “neo-pragmatic” theories of truth sometimes\nresembled the classical pragmatic accounts of Peirce, James, or Dewey,\nthey also differed significantly, often by framing the concept of\ntruth in explicitly epistemic terms such as assertibility or by\ndrawing on intervening developments in the field.", "\nAt the outset, neo-pragmatism was motivated by a renewed\ndissatisfaction with correspondence theories of truth and the\nmetaphysical frameworks supporting them. Some neo-pragmatic theories\nof truth grew out of a rejection of metaphysical realism (e.g., Putnam\n1981; for background see Khlentzos 2016). If metaphysical realism\ncannot be supported then this undermines a necessary condition for the\ncorrespondence theory of truth: namely, that there be a\nmind-independent reality to which propositions correspond. Other\nneo-pragmatic approaches emerged from a rejection of\nrepresentationalism: if knowledge is not the mind representing\nobjective reality—if we cannot make clear sense of how the mind\ncould be a “mirror of nature” to use Rorty’s (1979)\nterm—then we are also well-advised to give up thinking of truth\nin realist, correspondence terms. Despite these similar starting\npoints, neo-pragmatic theories took several different and evolving\nforms over the final decades of the twentieth century.", "\nAt one extreme some neo-pragmatic theories of truth seemed to endorse\nrelativism about truth (whether and in what sense they did remains a\npoint of contention). This view was closely associated with\ninfluential work by Richard Rorty (1982, 1991a,b). The rejection of\nrepresentationalism and the correspondence theory of truth led to the\nconclusion that inquiry is best viewed as aiming at agreement or\n“solidarity”, not knowledge or truth as these terms are\ntraditionally understood. This had the radical consequence of\nsuggesting that truth is no more than “what our peers will,\nceteris paribus, let us get away with saying” (Rorty\n1979: 176; Rorty [2010a: 45] admits this phrase is provocative) or\njust “an expression of commendation” (Rorty 1991a: 23).\nNot surprisingly, many found this position deeply problematic since it\nappears to relativize truth to whatever one’s audience will\naccept (Baghramian 2004: 147). A related concern is that this position\nalso seems to conflate truth with justification, suggesting that if a\nclaim meets contextual standards of acceptability then it also counts\nas true (Gutting 2003). Rorty for one often admitted as much, noting\nthat he tended to “swing back and forth between trying to reduce\ntruth to justification and propounding some form of minimalism about\ntruth” (1998: 21).", "\nA possible response to the accusation of relativism is to claim that\nthis neo-pragmatic approach does not aim to be a full-fledged theory\nof truth. Perhaps truth is actually a rather light-weight concept and\ndoes not need the heavy metaphysical lifting implied by putting\nforward a “theory”. If the goal is not to describe what\ntruth is but rather to describe how “truth” is used, then\nthese uses are fairly straightforward: among other things, to make\ngeneralizations (“everything you said is true”), to\ncommend (“so true!”), and to caution (“what you said\nis justified, but it might not be true”) (Rorty 1998: 22; 2000:\n4). None of these uses requires that we embark on a possibly fruitless\nhunt for the conditions that make a proposition true, or for a proper\ndefinition or theory of truth. If truth is “indefinable”\n(Rorty 2010b: 391) then this account cannot be definition or theory of\ntruth, relativist or otherwise.", "\nThis approach differs in some noteworthy ways from earlier pragmatic\naccounts of truth. For one thing it is able to draw on, and draw\nparallels with, a range of well-developed non-correspondence theories\nof truth that begin (and sometimes end) by stressing the fundamental\nequivalence of “S is p” and\n“‘S is p’ is true”. These\ntheories, including disquotationalism, deflationism, and minimalism,\nsimply were not available to earlier pragmatists (though Peirce does\nat times discuss the underlying notions). Furthermore, while Peirce\nand Dewey, for example, were proponents of scientific inquiry and\nscientific processes of verification, on this neo-pragmatic approach\nscience is no more objective or rational than other disciplines: as\nRorty put it, “the only sense in which science is exemplary is\nthat it is a model of human solidarity” (1991b: 39). Finally, on\nthis approach Peirce, James, and Dewey simply did not go far enough:\nthey failed to recognize the radical implications of their accounts of\ntruth, or else failed to convey these implications adequately. In turn\nmuch of the critical response to this kind of neo-pragmatism is that\nit goes too far by treating truth merely as a sign of commendation\n(plus a few other functions). In other words, this type of\nneo-pragmatism goes to unpragmatic extremes (e.g., Haack 1998; also\nthe exchange in Rorty & Price 2010).", "\nA less extreme version of neo-pragmatism attempts to preserve\ntruth’s objectivity and independence while still rejecting\nmetaphysical realism. This version was most closely associated with\nHilary Putnam, though Putnam’s views changed over time (see\nHildebrand 2003 for an overview of Putnam’s evolution). While\nthis approach frames truth in epistemic terms—primarily in terms\nof justification and verification—it amplifies these terms to\nensure that truth is more than mere consensus. For example, this\napproach might identify “being true with being warrantedly\nassertible under ideal conditions” (Putnam 2012b: 220). More\nspecifically, it might demand “that truth is independent of\njustification here and now, but not independent of all\njustification” (Putnam 1981: 56).", "\nRather than play up assertibility before one’s peers or\ncontemporaries, this neo-pragmatic approach frames truth in terms of\nideal warranted assertibility: namely, warranted assertibility in the\nlong run and before all audiences, or at least before all\nwell-informed audiences. Not only does this sound much less relativist\nbut it also bears a strong resemblance to Peirce’s and\nDewey’s accounts (though Putnam, for one, resisted the\ncomparison: “my admiration for the classical pragmatists does\nnot extend to any of the different theories of truth that Peirce,\nJames, and Dewey advanced” [2012c: 70]).", "\nTo repeat, this neo-pragmatic approach is designed to avoid the\nproblems facing correspondence theories of truth while still\npreserving truth’s objectivity. In the 1980s this view was\nassociated with Putnam’s broader program of “internal\nrealism”: the idea that “what objects does the world\nconsist of? is a question that it only makes sense to ask\nwithin a theory or description” (Putnam 1981: 49,\nemphasis in original). Internal realism was designed as an alternative\nto metaphysical realism that dispensed with achieving an external\n“God’s Eye Point of View” while still preserving\ntruth’s objectivity, albeit internal to a given theory. (For\nadditional criticisms of metaphysical realism see Khlentzos 2016.) In\nthe mid-1990s Putnam’s views shifted toward what he called\n“natural realism” (1999; for a critical discussion of\nPutnam’s changing views see Wright 2000). This shift came about\nin part because of problems with defining truth in epistemic terms\nsuch as ideal warranted assertibility. One problem is that it is\ndifficult to see how one can verify either what these ideal conditions\nare or whether they have been met: one might attempt to do so by\ntaking an external “god’s eye view”, which would be\ninconsistent with internal realism, or one might come to this\ndetermination from within one’s current theory, which would be\ncircular and relativistic. (As Putnam put it, “to talk of\nepistemically ‘ideal’ connections must either be\nunderstood outside the framework of internal realism or it too must be\nunderstood in a solipsistic manner ” (2012d: 79–80).)\nSince neither option seems promising this does not bode well for\ninternal realism or for any account of truth closely associated with\nit.", "\nIf internal realism cannot be sustained then a possible fallback\nposition is “natural realism”—the view “that\nthe objects of (normal ‘veridical’) perception are\n‘external’ things, and, more generally, aspects of\n‘external’ reality” (Putnam 1999: 10)—which\nleads to a reconciliation of sorts with the correspondence theory of\ntruth. A natural realism suggests “that true empirical\nstatements correspond to states of affairs that actually obtain”\n(Putnam 2012a: 97), though this does not commit one to a\ncorrespondence theory of truth across the board. Natural realism\nleaves open the possibility that not all true statements\n“correspond” to a state of affairs, and even those that do\n(such as empirical statements) do not always correspond in the same\nway (Putnam 2012c: 68–69; 2012a: 98). While not a ringing\nendorsement of the correspondence theory of truth, at least as\ntraditionally understood, this neo-pragmatic approach is not a\nflat-out rejection either.", "\nViewing truth in terms of ideal warranted assertibility has obvious\npragmatic overtones of Peirce and Dewey. Viewing truth in terms of a\ncommitment to natural realism is not so clearly pragmatic though some\nparallels still exist. Because natural realism allows for different\ntypes of truth-conditions—some but not all statements are true\nin virtue of correspondence—it is compatible with the\ntruth-aptness of normative discourse: just because ethical statements,\nfor example, do not correspond in an obvious way to ethical state of\naffairs is no reason to deny that they can be true (Putnam 2002). In\naddition, like earlier pragmatic theories of truth, this neo-pragmatic\napproach redefines correspondence: in this case, by taking a pluralist\napproach to the correspondence relation itself (Goodman 2013).", "\nThese two approaches—one tending toward relativism, the other\ntending toward realism—represented the two main currents in late\ntwentieth century neo-pragmatism. Both approaches, at least initially,\nframed truth in terms of justification, verification, or\nassertibility, reflecting a debt to the earlier accounts of Peirce,\nJames, and Dewey. Subsequently they evolved in opposite directions.\nThe first approach, often associated with Rorty, flirts with\nrelativism and implies that truth is not the important philosophical\nconcept it has long been taken to be. Here, to take a neo-pragmatic\nstance toward truth is to recognize the relatively mundane functions\nthis concept plays: to generalize, to commend, to caution and not much\nelse. To ask for more, to ask for something “beyond the here and\nnow”, only commits us to “the banal thought that we might\nbe wrong” (Rorty 2010a: 45). The second neo-pragmatic approach,\ngenerally associated with Putnam, attempts to preserve truth’s\nobjectivity and the important role it plays across scientific,\nmathematical, ethical, and political discourse. This could mean simply\n“that truth is independent of justification here and now”\nor “that to call a statement of any kind…true is to say\nthat it has the sort of correctness appropriate to the kind of\nstatement it is” (2012a: 97–98). On this account truth\npoints to standards of correctness more rigorous than simply what our\npeers will let us get away with saying." ], "section_title": "2. Neo-Pragmatic Theories of Truth", "subsections": [] }, { "main_content": [ "\nMore recently—since roughly the turn of the twenty-first\ncentury—pragmatic theories of truth have focused on\ntruth’s role as a norm of assertion or inquiry. These theories\nare sometimes referred to as “new pragmatic” theories to\ndistinguish them from both classical and neo-pragmatic accounts (Misak\n2007b; Hookway 2016). Like neo-pragmatic accounts, these theories\noften build on, or react to, positions besides the correspondence\ntheory: for example, deflationary, minimal, and pluralistic theories\nof truth. Unlike some of the neo-pragmatic accounts discussed above,\nthese theories give relativism a wide berth, avoid defining truth in\nterms of concepts such as warranted assertibility, and treat\ncorrespondence theories of truth with deep suspicion.", "\nOn these accounts truth plays a unique and necessary role in\nassertoric discourse (Price 1998, 2003, 2011; Misak 2000, 2007a,\n2015): without the concept of truth there would be no difference\nbetween making assertions and, to use Frank Ramsey’s nice\nphrase, “comparing notes” (1925 [1990: \n247]). Instead, \ntruth provides the “convenient friction” that “makes\nour individual opinions engage with one another” (Price 2003:\n169) and “is internally related to inquiry, reasons, and\nevidence” (Misak 2000: 73).", "\nLike all pragmatic theories of truth, these “new”\npragmatic accounts focus on the use and function of truth. However,\nwhile classical pragmatists were responding primarily to the\ncorrespondence theory of truth, new pragmatic theories also respond to\ncontemporary disquotational, deflationary, and minimal theories of\ntruth (Misak 1998, 2007a). As a result, new pragmatic accounts aim to\nshow that there is more to truth than its disquotational and\ngeneralizing function (for a dissenting view see Freedman 2006).\nSpecifically, this “more” is that the concept of truth\nalso functions as a norm that places clear expectations on speakers\nand their assertions. In asserting something to be true, speakers take\non an obligation to specify the consequences of their assertion, to\nconsider how their assertions can be verified, and to offer reasons in\nsupport of their claims: ", "\n\n\nonce we see that truth and assertion are intimately\nconnected—once we see that to assert that p is true is to\nassert p—we can and must look to our practices of\nassertion and to the commitments incurred in them so as to say\nsomething more substantial about truth. (Misak 2007a: 70) \n", "\nTruth is not just a goal of inquiry, as Dewey claimed, but actually a\nnorm of inquiry that sets expectations for how inquirers conduct\nthemselves.", "\nMore specifically, without the norm of truth assertoric discourse\nwould be degraded almost beyond recognition. Without the norm of\ntruth, speakers could be held accountable only for either insincerely\nasserting things they don’t themselves believe (thus violating\nthe norm of “subjective assertibility”) or for asserting\nthings they don’t have enough evidence for (thus violating the\nnorm of “personal warranted assertibility”) (Price 2003:\n173–174). The norm of truth is a condition for genuine\ndisagreement between people who speak sincerely and with, from their\nown perspective, good enough reasons. It provides the\n“friction” we need to treat disagreements as genuinely\nneeding resolution: otherwise, “differences of opinion would\nsimply slide past one another” (Price 2003: 180–181). In\nsum, the concept of truth plays an essential role in making assertoric\ndiscourse possible, ensuring that assertions come with obligations and\nthat conflicting assertions get attention. Without truth, it is no\nlonger clear to what degree assertions would still be assertions, as\nopposed to impromptu speculations or musings. (Correspondence theories\nshould find little reason to object: they too can recognize that truth\nfunctions as a norm. Of course, correspondence theorists will want to\nadd that truth also requires correspondence to reality, a step\n“new” pragmatists will resisting taking.)", "\nIt is important that this account of truth is not a definition or\ntheory of truth, at least in the narrow sense of specifying necessary\nand sufficient conditions for a proposition being true. (That is,\nthere is no proposal along the lines of “S is true\niff…”; though see Brown (2015: 69) for a Deweyan\ndefinition of truth and Heney (2015) for a Peircean response.) As\nopposed to some versions of neo-pragmatism, which viewed truth as\n“indefinable” in part because of its supposed simplicity\nand transparency, this approach avoids definitions because the concept\nof truth is implicated in a complex range of assertoric practices.\nInstead, this approach offers something closer to a “pragmatic\nelucidation” of truth that gives “an account of the role\nthe concept plays in practical endeavors” (Misak 2007a: 68; see\nalso Wiggins 2002: 317).", "\nThe proposal to treat truth as a norm of inquiry and assertion can be\ntraced back to both classical and neo-pragmatist accounts. In one\nrespect, this account can be viewed as adding on to neo-pragmatic\ntheories that reduce truth to justification or “personal\nwarranted assertibility”. In this respect, these newer pragmatic\naccounts are a response to the problems facing neo-pragmatism. In\nanother respect, new pragmatic accounts can be seen as a return to the\ninsights of classical pragmatists updated for a contemporary audience.\nFor example, while Peirce wrote of beliefs being “fated”\nto be agreed upon at the “ideal limit” of\ninquiry—conditions that to critics sounded metaphysical and\nunverifiable—a better approach is to treat true beliefs as those\n“that would withstand doubt, were we to inquire as far as we\nfruitfully could on the matter” (Misak 2000: 49). On this\naccount, to say that a belief is true is shorthand for saying that it\n“gets thing right” and “stands up and would continue\nto stand up to reasons and evidence” (Misak 2015: 263, 265).\nThis pragmatic elucidation of the concept of truth attempts to capture\nboth what speakers say and what they do when they describe a claim as\ntrue. In a narrow sense the meaning of truth—what speakers are\nsaying when they use this word—is that true beliefs are\nindefeasible. However, in a broader sense the meaning of truth is also\nwhat speakers are doing when they use this word, with the proposal\nhere that truth functions as a norm that is constitutive of assertoric\ndiscourse.", "\nAs we have seen, pragmatic accounts of truth focus on the function the\nconcept plays: specifically, the practical difference made by having\nand using the concept of truth. Early pragmatic accounts tended to\nanalyze this function in terms of the practical implications of\nlabeling a belief as true: depending on the version, to say that a\nbelief is true is to signal one’s confidence, or that the belief\nis widely accepted, or that it has been scientifically verified, or\nthat it would be assertible under ideal circumstances, among other\npossible implications. These earlier accounts focus on the function of\ntruth in conversational contexts or in the context of ongoing\ninquiries. The newer pragmatic theories discussed in this section take\na broader approach to truth’s function, addressing its role not\njust in conversations and inquiries but in making certain kinds of\nconversations and inquiries possible in the first place. By viewing\ntruth as a norm of assertion and inquiry, these more recent pragmatic\ntheories make the function of truth independent of what individual\nspeakers might imply in specific contexts. Truth is not just what is\nassertible or verifiable (under either ideal or non-ideal\ncircumstances), but sets objective expectations for making assertions\nand engaging in inquiry. Unlike neo-pragmatists such as Rorty and\nPutnam, new pragmatists such as Misak and Price argue that truth plays\na role entirely distinct from justification or warranted\nassertibility. This means that, without the concept of truth and the\nnorm it represents, assertoric discourse (and inquiry in general)\nwould dwindle into mere “comparing notes”." ], "section_title": "3. Truth as a Norm of Inquiry and Assertion", "subsections": [] }, { "main_content": [ "\nPragmatic theories of truth have evolved to where a variety of\ndifferent approaches are described as “pragmatic”. These\ntheories often disagree significantly with each other, making it\ndifficult either to define pragmatic theories of truth in a simple and\nstraightforward manner or to specify the necessary conditions that a\npragmatic theory of truth must meet. As a result, one way to clarify\nwhat makes a theory of truth pragmatic is to say something about what\npragmatic theories of truth are not. Given that pragmatic theories of\ntruth have often been put forward in contrast to prevailing\ncorrespondence and other “substantive” theories of truth\n(Wyatt & Lynch, 2016), this suggests a common commitment shared by\nthe pragmatic theories described above.", "\nOne way to differentiate pragmatic accounts from other theories of\ntruth is to distinguish the several questions that have historically\nguided discussions of truth. While some have used decision trees to\ncategorize different theories of truth (Lynch 2001a; Künne 2003),\nor have proposed family trees showing relations of influence and\naffinity (Haack 1978), another approach is to distinguish separate\n“projects” that examine different dimensions of the\nconcept of truth (Kirkham 1992). (These projects also break into\ndistinct subprojects; for a similar approach see Frapolli 1996.) On\nthis last approach the first, “metaphysical”, project aims\nto identify the necessary and sufficient conditions for “what it\nis for a statement…to be true” (Kirkham 1992: 20; Wyatt\n& Lynch call this the “essence project” [2016: 324]).\nThis project often takes the form of identifying what makes a\nstatement true: e.g., correspondence to reality, or coherence with\nother beliefs, or the existence of a particular state of affairs. A\nsecond, “justification”, project attempts to specify\n“some characteristic, possessed by most true\nstatements…by reference to which the probable truth or falsity\nof the statement can be judged” (Kirkham 1992: 20). This often\ntakes the form of giving a criterion of truth that can be used to\ndetermine whether a given statement is true. Finally, the\n“speech-act” project addresses the question of “what\nare we doing when we make utterances” that\n“ascribe truth to some statement?” (Kirkham 1992: 28).\nUnfortunately, truth-theorists have not always been clear on which\nproject they are pursuing, which can lead to confusion about what\ncounts as a successful or complete theory of truth. It can also lead\nto truth-theorists talking past each other when they are pursuing\ndistinct projects with different standards and criteria of\nsuccess.", "\nIn these terms, pragmatic theories of truth are best viewed as\npursuing the speech-act and justification projects. As noted above,\npragmatic accounts of truth have often focused on how the concept of\ntruth is used and what speakers are doing when describing statements\nas true: depending on the version, speakers may be commending a\nstatement, signaling its scientific reliability, or committing\nthemselves to giving reasons in its support. Likewise, pragmatic\ntheories often focus on the criteria by which truth can be judged:\nagain, depending on the version, this may involve linking truth to\nverifiability, assertibility, usefulness, or long-term durability.\nWith regard to the speech-act and justification projects pragmatic\ntheories of truth seem to be on solid ground, offering plausible\nproposals for addressing these projects. They are on much less solid\nground when viewed as addressing the metaphysical project. As we will\nsee, it is difficult to defend the idea, for example, that either\nutility, verifiability, or widespread acceptance are necessary and\nsufficient conditions for truth or are what make a statement true.", "\nThis would suggest that the opposition between pragmatic and\ncorrespondence theories of truth is partly a result of their pursuing\ndifferent projects. From a pragmatic perspective, the problem with the\ncorrespondence theory is its pursuit of the metaphysical project that,\nas its name suggests, invites metaphysical speculation about the\nconditions which make sentences true—speculation that can\ndistract from more central questions of how the truth predicate is\nused and how true beliefs are best recognized and acquired. (Pragmatic\ntheories of truth are not alone in raising these concerns (David\n2016).) From the standpoint of correspondence theories and other\naccounts that pursue the metaphysical project, pragmatic theories will\nlikely seem incomplete, sidestepping the most important questions\n(Howat 2014). But from the standpoint of pragmatic theories, projects\nthat pursue or prioritize the metaphysical project are deeply\nmisguided and misleading.", "\nThis supports the following truism: a common feature of pragmatic\ntheories of truth is that they focus on the practical function that\nthe concept of truth plays. Thus, whether truth is a norm of inquiry\n(Misak), a way of signaling widespread acceptance (Rorty), stands for\nfuture dependability (Peirce), or designates the product of a process\nof inquiry (Dewey), among other things, pragmatic theories shed light\non the concept of truth by examining the practices through which\nsolutions to problems are framed, tested, asserted, and\ndefended—and, ultimately, come to be called true. Pragmatic\ntheories of truth can thus be viewed as making contributions to the\nspeech-act and justification projects by focusing especially on the\npractices people engage in when they solve problems, make assertions,\nand conduct scientific inquiry. Of course, even though pragmatic\ntheories of truth largely agree on which questions to address and in\nwhat order, this does not mean that they agree on the answers to these\nquestions, or on how to best formulate the meaning and function of\ntruth.", "\nAnother common commitment of pragmatic theories of truth—besides\nprioritizing the speech-act and justification projects—is that\nthey do not restrict truth to certain topics or types of inquiry. That\nis, regardless of whether the topic is descriptive or normative,\nscientific or ethical, pragmatists tend to view it as an opportunity\nfor genuine inquiry that incorporates truth-apt assertions. The\ntruth-aptness of ethical and normative statements is a notable feature\nacross a range of pragmatic approaches, including Peirce’s (at\nleast in some of his moods, e.g., 1901b [1958: 8.158]), Dewey’s\ntheory of valuation (1939), Putnam’s questioning of the\nfact-value dichotomy (2002), and Misak’s claim that “moral\nbeliefs must be in principle responsive to evidence and\nargument” (2000: 94; for a dissenting view see Frega 2013). This\nbroadly cognitivist attitude—that normative statements are\ntruth-apt—is related to how pragmatic theories of truth\nde-emphasize the metaphysical project. As a result, from a pragmatic\nstandpoint one of the problems with the correspondence theory of truth\nis that it can undermine the truth-aptness of normative claims. If, as\nthe correspondence theory proposes, a necessary condition for the\ntruth of a normative claim is the existence of a normative fact to\nwhich it corresponds, and if the existence of normative facts is\ndifficult to account for (normative facts seem ontologically distinct\nfrom garden-variety physical facts), then this does not bode well for\nthe truth-aptness of normative claims or the point of posing, and\ninquiring into, normative questions (Lynch 2009). If the\ncorrespondence theory of truth leads to skepticism about normative\ninquiry, then this is all the more reason, according to pragmatists,\nto sidestep the metaphysical project in favor of the speech-act and\njustification projects.", "\nAs we have seen, pragmatic theories of truth take a variety of\ndifferent forms. Despite these differences, and despite often being\naverse to being called a “theory”, pragmatic theories of\ntruth do share some common features. To begin with, and unlike many\ntheories of truth, these theories focus on the pragmatics of\ntruth-talk: that is, they focus on how truth is used as an essential\nstep toward an adequate understanding of the concept of truth (indeed,\nthis come close to being an oxymoron). More specifically, pragmatic\ntheories look to how truth is used in epistemic contexts where people\nmake assertions, conduct inquiries, solve problems, and act on their\nbeliefs. By prioritizing the speech-act and justification projects,\npragmatic theories of truth attempt to ground the concept of truth in\nepistemic practices as opposed to the abstract relations between\ntruth-bearers (such as propositions or statements) and truth-makers\n(such as states of affairs) appealed to by correspondence theories\n(MacBride 2018). Pragmatic theories also recognize that truth can play\na fundamental role in shaping inquiry and assertoric\ndiscourse—for example, by functioning as a norm of these\npractices—even when it is not explicitly mentioned. In this\nrespect pragmatic theories are less austere than deflationary theories\nwhich limit the use of truth to its generalizing and disquotational\nroles. And, finally, pragmatic theories of truth draw no limits, at\nleast at the outset, to the types of statements, topics, and inquiries\nwhere truth may play a practical role. If it turns out that a given\ntopic is not truth-apt, this is something that should be discovered as\na characteristic of that subject matter, not something determined by\nhaving chosen one theory of truth or another (Capps 2017)." ], "section_title": "4. Common Features", "subsections": [] }, { "main_content": [ "\nPragmatic theories of truth have faced several objections since first\nbeing proposed. Some of these objections can be rather narrow,\nchallenging a specific pragmatic account but not pragmatic theories in\ngeneral (this is the case with objections raised by other pragmatic\naccounts). This section will look at more general objections: either\nobjections that are especially common and persistent, or objections\nthat pose a challenge to the basic assumptions underlying pragmatic\ntheories more broadly." ], "section_title": "5. Critical Assessments", "subsections": [ { "content": [ "\nSome objections are as old as the pragmatic theory of truth itself.\nThe following objections were raised in response to James’\naccount in particular. While James offered his own responses to many\nof these criticisms (see especially his 1909 [1975]), versions of\nthese objections often apply to other and more recent pragmatic\ntheories of truth (for further discussion see Haack 1976; Tiercelin\n2014).", "\nOne classic and influential line of criticism is that, if the\npragmatic theory of truth equates truth with utility, this definition\nis (obviously!) refuted by the existence of useful but false beliefs,\non the one hand, and by the existence of true but useless beliefs on\nthe other (Russell 1910 [1994] and Lovejoy 1908a,b). In short, there\nseems to be a clear and obvious difference between describing a belief\nas true and describing it as useful: ", "\n\n\nwhen we say that a belief is true, the thought we wish to convey is\nnot the same thought as when we say that the belief furthers our\npurposes; thus “true” does not mean “furthering our\npurposes”. (Russell 1910 [1994: 98]) \n", "\nWhile this criticism is often aimed especially at James’ account\nof truth, it plausibly carries over to any pragmatic theory. So\nwhether truth is defined in terms of utility, long-term durability or\nassertibility (etc.), it is still an open question whether a useful or\ndurable or assertible belief is, in fact, really true. In other words,\nwhatever concept a pragmatic theory uses to define truth, there is\nlikely to be a difference between that concept and the concept of\ntruth (e.g., Bacon 2014 questions the connection between truth and\nindefeasibility).", "\nA second and related criticism builds on the first. Perhaps utility,\nlong-term durability, and assertibility (etc.) should be viewed not as\ndefinitions but rather as criteria of truth, as yardsticks for\ndistinguishing true beliefs from false ones. This seems initially\nplausible and might even serve as a reasonable response to the first\nobjection above. Falling back on an earlier distinction, this would\nmean that appeals to utility, long-term durability, and assertibility\n(etc.) are best seen as answers to the justification and not the\nmetaphysical project. However, without some account of what truth is,\nor what the necessary and sufficient conditions for truth are, any\nattempt to offer criteria of truth is arguably incomplete: we cannot\nhave criteria of truth without first knowing what truth is. If so,\nthen the justification project relies on and presupposes a successful\nresolution to the metaphysical project, the latter cannot be\nsidestepped or bracketed, and any theory which attempts to do so will\ngive at best a partial account of truth (Creighton 1908; Stebbing\n1914).", "\nAnd a third objection builds on the second. Putting aside the question\nof whether pragmatic theories of truth adequately address the\nmetaphysical project (or address it at all), there is also a problem\nwith the criteria of truth they propose for addressing the\njustification project. Pragmatic theories of truth seem committed, in\npart, to bringing the concept of truth down to earth, to explaining\ntruth in concrete, easily confirmable, terms rather than the abstract,\nmetaphysical correspondence of propositions to truth-makers, for\nexample. The problem is that assessing the usefulness (etc.) of a\nbelief is no more clear-cut than assessing its truth: beliefs may be\nmore or less useful, useful in different ways and for different\npurposes, or useful in the short- or long-run. Determining whether a\nbelief is really useful is no easier, apparently, than determining\nwhether it is really true: “it is so often harder to determine\nwhether a belief is useful than whether it is true” (Russell\n1910 [1994: 121]; also 1946: 817). Far from making the concept of\ntruth more concrete, and the assessment of beliefs more\nstraightforward, pragmatic theories of truth thus seem to leave the\nconcept as opaque as ever.", "\nThese three objections have been around long enough that pragmatists\nhave, at various times, proposed a variety of responses. One response\nto the first objection, that there is a clear difference between\nutility (etc.) and truth, is to deny that pragmatic approaches are\naiming to define the concept of truth in the first place. It has been\nargued that pragmatic theories are not about finding a word or concept\nthat can substitute for truth but that they are, rather, focused on\ntracing the implications of using this concept in practical contexts.\nThis is what Misak (2000, 2007a) calls a “pragmatic\nelucidation”. Noting that it is “pointless” to offer\na definition of truth, she concludes that “we ought to attempt\nto get leverage on the concept, or a fix on it, by exploring its\nconnections with practice” (2007a: 69; see also Wiggins 2002).\nIt is even possible that James—the main target of Russell and\nothers—would agree with this response. As with Peirce, it often\nseems that James’ complaint is not with the correspondence\ntheory of truth, per se, as with the assumption that the\ncorrespondence theory, by itself, says much interesting or important\nabout the concept of truth. (For charitable interpretations of what\nJames was attempting to say see Ayer 1968, Chisholm 1992, Bybee 1984,\nCormier 2001, 2011, and Perkins 1952; for a reading that emphasizes\nPeirce’s commitment to correspondence idioms see Atkins\n2010.)", "\nThis still leaves the second objection: that the metaphysical project\nof defining truth cannot be avoided by focusing instead on finding the\ncriteria for truth (the “justification project”). To be\nsure, pragmatic theories of truth have often been framed as providing\ncriteria for distinguishing true from false beliefs. The distinction\nbetween offering a definition as opposed to offering criteria would\nsuggest that criteria are separate from, and largely inferior to, a\ndefinition of truth. However, one might question the underlying\ndistinction: as Haack (1976) argues, ", "\n\n\nthe pragmatists’ view of meaning is such that a dichotomy\nbetween definitions and criteria would have been entirely unacceptable\nto them. (1976: 236) \n", "\nIf meaning is related to use (as pragmatists generally claim) then\nexplaining how a concept is used, and specifying criteria for\nrecognizing that concept, may provide all one can reasonably expect\nfrom a theory of truth. Deflationists have often made a similar point\nthough, as noted above, pragmatists tend to find deflationary accounts\nexcessively austere.", "\nEven so, there is still the issue that pragmatic criteria of truth\n(whatever they are) do not provide useful insight into the concept of\ntruth. If this concern is valid, then pragmatic criteria, ironically,\nfail the pragmatic test of making a difference to our understanding of\ntruth. This objection has some merit: for example, if a pragmatic\ncriterion of truth is that true beliefs will stand up to indefinite\ninquiry then, while it is possible to have true beliefs, “we are\nnever in a position to judge whether a belief is true or not”\n(Misak 2000: 57). In that case it is not clear what good it serves to\nhave a pragmatic criterion of truth. Pragmatic theories of truth might\ntry to sidestep this objection by stressing their commitment to both\nthe justification and the speech-act project. While pragmatic\napproaches to the justification project spell out what truth means in\nconversational contexts—to call a statement true is to cite its\nusefulness, durability, etc.—pragmatic approaches to the\nspeech-act project point to what speakers do in using the concept of\ntruth. This has the benefit of showing how the concept of\ntruth—operating as a norm of assertion, say—makes a real\ndifference to our understanding of the conditions on assertoric\ndiscourse. Pragmatic theories of truth are, as a result, wise to\npursue both the justification and the speech-act projects. By itself,\npragmatic approaches to the justification project are likely to\ndisappoint.", "\nThese classic objections to the pragmatic theory of truth raise\nseveral important points. For one thing, they make it clear that\npragmatic theories of truth, or at least some historically prominent\nversions of it, do a poor job if viewed as providing a strict\ndefinition of truth. As Russell and others noted, defining truth in\nterms of utility or similar terms is open to obvious counter-examples.\nThis does not bode well for pragmatic attempts to address the\nmetaphysical project. As a result, pragmatic theories of truth have\nevolved often by focusing on the justification and speech-act projects\ninstead. This is not to say that each of the above objections have\nbeen met. It is still an open question whether the metaphysical\nproject can be avoided as many pragmatic theories attempt to do (e.g.,\nFox 2008 argues that epistemic accounts such as Putnam’s fail to\nexplain the value of truth as well as more traditional approaches do).\nIt is also an open question whether, as they evolve in response to\nthese objections, pragmatic theories of truth invite new lines of\ncriticism." ], "subsection_title": "5.1 Three Classic Objections and Responses" } ] } ]

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New York: Henry Holt and Company: 154–168 (chapter\n6); reprinted in John Dewey: The Middle Works (Volume 6), J.\nBoydston, (ed.), Carbondale, IL: Southern Illinois University Press,\n2008, pp. 3–11.", "–––, 1911 [2008], “The Problem of\nTruth”, Old Penn, Weekly Review of the University of\nPennsylvania, 9: 522–528, 556–563, 620–625;\nreprinted in John Dewey: The Middle Works (Volume 6), J.\nBoydston, (ed.), Carbondale, IL: Southern Illinois University Press,\n2008, pp. 12–68.", "–––, 1938 [2008], Logic: The Theory of\nInquiry, New York: Henry Holt and Company; reprinted in John\nDewey: The Later Works (Volume 12), J. Boydston, (ed.),\nCarbondale, IL: Southern Illinois University Press.", "–––, 1939, Theory of Valuation,\nChicago: University of Chicago Press.", "–––, 1941, “Propositions, Warranted\nAssertibility, and Truth”, The Journal of Philosophy,\n38(7): 169–186. doi:10.2307/2017978", "Dummett, Michael, 1959, “Truth”, Proceedings of\nthe Aristotelian Society, 59(1): 141–162.\ndoi:10.1093/aristotelian/59.1.141", "Fine, Arthur, 2007, “Relativism, Pragmatism, and the\nPractice of Science”, in Misak 2007b: 50–67.", "Fox, John, 2008, “What Is at Issue between Epistemic and\nTraditional Accounts of Truth?”, Australasian Journal of\nPhilosophy, 86(3): 407–420. doi:10.1080/00048400802001939", "Frapolli, Maria J., 1996, “The Logical Enquiry into\nTruth”, History and Philosophy of Logic, 17(1–2):\n179–197. doi:10.1080/01445349608837263", "Freedman, Karyn L., 2006, “Disquotationalism, Truth and\nJustification: The Pragmatist’s Wrong Turn”, Canadian\nJournal of Philosophy, 36(3): 371–386.\ndoi:10.1353/cjp.2006.0016", "Frega, Roberto, 2013, “Rehabilitating Warranted\nAssertibility: Moral Inquiry and the Pragmatic Basis of\nObjectivity”, The Southern Journal of Philosophy,\n51(1): 1–23. doi:10.1111/sjp.12006", "Goodman, Russell, 2013, “Some Sources of Putnam’s\nPluralism”, in Baghramian 2013: 205–218.", "Gross, Steven, Nicholas Tebben, and Michael Williams (eds.), 2015,\nMeaning Without Representation: Essays on Truth, Expression,\nNormativity, and Naturalism, New York: Oxford University Press.\ndoi:10.1093/acprof:oso/9780198722199.001.0001", "Gutting, Gary, 2003, “Rorty’s Critique of\nEpistemology”, in Richard Rorty, Charles Guignon and\nDavid R. 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Zalta (ed.), forthcoming URL =\n <https://plato.stanford.edu/archives/win2018/entries/truthmakers/>.", "Misak, Cheryl, 1998, “Deflating Truth: Pragmatism vs.\nMinimalism”, Monist, 81(3): 407–425.\ndoi:10.5840/monist199881322", "–––, 2000, Truth, Politics, Morality,\nNew York: Routledge.", "–––, 2004, Truth and the End of Inquiry: A\nPeircean Account of Truth (expanded edition), New York: Oxford\nUniversity Press. doi:10.1093/0199270597.001.0001", "–––, 2007a, “Pragmatism and\nDeflationism”, in Misak 2007b: 68–90.", "–––, (ed.), 2007b, New Pragmatists, New\nYork: Oxford University Press.", "–––, 2015, “Pragmatism and the Function of\nTruth”, in Gross, Tebben, and Williams 2015: 262–278.\ndoi:10.1093/acprof:oso/9780198722199.003.0013", "Moore, G. 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Baldwin (ed.): 718–720; reprinted in Collected Papers\nof Charles Sanders Peirce (Volumes V and VI), Charles Hartshorne,\nand Paul Weiss (eds.), Cambridge, MA: Harvard University Press, 1935,\npp. 394–398.", "–––, 1901b [1958], “Review of Sidney\nEdward Mezes's Ethics”, The Nation, 73: 325–326;\nreprinted in Collected Papers of Charles Sanders Peirce\n(Volume VIII), A. Burks (ed.), Cambridge, MA: Harvard University\nPress, 1958, pp. 122–123.", "–––, 1906 [1998], “The Basis of\nPragmaticism in the Normative Sciences”, unpublished manuscript;\nreprinted in The Essential Peirce (Volume 2), The Peirce\nEdition Project (eds.), Bloomington, IN: Indiana University Press,\n1998, pp. 371–397. doi:10.5840/monist190515230", "–––, 1908 [1935], “A Neglected Argument\nfor the Existence of God”, Hibbert Journal, 7:\n90–112; reprinted in Collected Papers of Charles Sanders\nPeirce (Volumes V and VI), Charles Hartshorne and Paul Weiss\n(eds.), Cambridge, MA: Harvard University Press, 1935,\npp. 311–339.", "–––, 1898 [1992], Reasoning and the Logic of\nThings: The Cambridge Conferences Lectures of 1898, K.L. 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Cited\npages from the 1994 Routledge, New York, edition, pp.\n112–130.", "–––, 1941, An Inquiry Into Meaning and\nTruth, London: Allen and Unwin.", "–––, 1946, History of Western\nPhilosophy, New York: Routledge.", "Schmitt, Frederick, 1995, Truth: A Primer, Boulder, CO:\nWestview.", "Stebbing, L. Susan, 1914, Pragmatism and French\nVoluntarism, Cambridge: Cambridge University Press.\n [Stebbing 1914 available online]", "Talisse, Robert B. and Scott Akin, 2008, Pragmatism: A Guide\nfor the Perplexed, New York: Continuum.", "Thayer, H. S., 1947, “Two Theories of Truth: The Relation\nbetween the Theories of John Dewey and Bertrand Russell”,\nThe Journal of Philosophy, 44(19): 516.\ndoi:10.2307/2019905", "Tiercelin, Claudine, 2014, “Pragmatist Truth: Cash Value or\nIdeal Value? The Main Objections”, in The Pragmatists and\nthe Human Logic of Truth, Paris: Collège de France,\nchapter 2. doi:10.4000/books.cdf.3655", "Wiggins, David, 2002, “An Indefinabilist cum Normative View\nand Marks of Truth”, in R. Shantz (ed.), What Is\nTruth?, Berlin: De Gruyter, pp. 316–332.", "Wright, Crispin, 1992, Truth and Objectivity, Cambridge\nMA: Harvard University Press.", "–––, 2000, “Truth as Sort of Epistemic:\nPutnam’s Peregrinations”, Journal of Philosophy,\n97(6): 335–364. doi:10.5840/jphil200097617", "–––, 2001, “Minimalism, Deflationism,\nPragmatism, Pluralism”, in Lynch 2001b: 751–787.", "Wyatt, Jeremy and Michael Lynch, 2016, “From One to Many:\nRecent Work on Truth”, American Philosophical\nQuarterly, 53(4): 323–340." ]

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[ "\n\nConsider the following sentence:", "\n\nIt has long been known that the sentence, (1), produces a paradox, the\nso-called liar's paradox: it seems impossible consistently to\nmaintain that (1) is true, and impossible consistently to maintain\nthat (1) is not true: if (1) is true, then (1) says, truly, that (1)\nis not true so that (1) is not true; on the other hand, if (1) is not\ntrue, then what (1) says is the case, i.e., (1) is true. (For details,\nsee Section 1, below.) Given such a paradox, one might be sceptical of\nthe notion of truth, or at least of the prospects of giving a\nscientifically respectable account of truth. ", "\nAlfred Tarski's great accomplishment was to show how to give —\ncontra this scepticism — a formal definition of truth for a wide\nclass of formalized languages. Tarski did not, however, show\nhow to give a definition of truth for languages (such as\nEnglish) that contain their own truth predicates. He thought\nthat this could not be done, precisely because of the liar's\nparadox. More generally, Tarski reckoned that any language\nwith its own truth predicate would be inconsistent, as long as it\nobeyed the rules of standard classical logic, and had the ability to\nrefer to its own sentences. As we will see in our remarks on Theorem\n2.1 in Section 2.3, Tarski was not quite right: there are consistent\nclassical interpreted languages that refer to their own sentences and\nhave their own truth predicates. (This point originates in Gupta 1982\nand is strengthened in Gupta and Belnap 1993.)", "\n Given the close connection between meaning and\ntruth, it is widely held that any semantics for a language\nL, i.e., any theory of meaning for L, will be\nclosely related to a theory of truth for L: indeed, it is\ncommonly held that something like a Tarskian theory of truth for\nL will be a central part of a semantics for L. Thus,\nthe impossibility of giving a Tarskian theory of truth for languages\nwith their own truth predicates threatens the project of giving a\nsemantics for languages with their own truth predicates.", "\n\nWe had to wait until the work of Kripke 1975 and of Martin &\nWoodruff 1975 for a systematic formal proposal of a semantics for\nlanguages with their own truth predicates. The basic thought is\nsimple: take the offending sentences, such as (1), to be neither\ntrue nor false. Kripke, in particular, shows how to implement\nthis thought for a wide variety of languages, in effect employing a\nsemantics with three values, true, false and\n neither.[1]\n It is safe to\nsay that Kripkean approaches have replaced Tarskian pessimism as the\nnew orthodoxy concerning languages with their own truth\npredicates.", "\n \nOne of the main rivals to the three-valued semantics is the Revision\nTheory of Truth, or RTT, independently conceived by Hans Herzberger\nand Anil Gupta, and first presented in publication in Herzberger 1982a\nand 1982b, Gupta 1982 and Belnap 1982 — the first monographs on\nthe topic are Yaqūb 1993 and the locus classicus, Gupta\n& Belnap 1993. The RTT is designed to model the kind of reasoning\nthat the liar sentence leads to, within a two-valued\ncontext. (See Section 5.2 on the question of whether the RTT is\ngenuinely two-valued.) The central idea is the idea of a revision\nprocess: a process by which we revise hypotheses about\nthe truth-value of one or more sentences. The present article's\npurpose is to outline the Revision Theory of Truth. We proceed as\nfollows:" ]

[ { "content_title": "1. Semiformal introduction", "sub_toc": [] }, { "content_title": "2. Framing the problem", "sub_toc": [ "2.1 Truth languages", "2.2 Ground models ", "2.3 Three ground models" ] }, { "content_title": "3. Basic notions of the RTT", "sub_toc": [ "3.1 Revision rules", "3.2 Revision sequences" ] }, { "content_title": "4. Interpreting the formalism", "sub_toc": [ "4.1 The signification of T", "4.2 The ‘iff’ in the T-biconditionals ", "4.3 The paradoxical reasoning ", "4.4 The signification thesis ", "4.5 The supervenience of semantics ", "4.6 A nonsupervenient interpretation of the formalism" ] }, { "content_title": "5. Further issues", "sub_toc": [ "5.1 Three-valued semantics", "5.2 Two values?", "5.3 Amendments to the RTT", "5.4 Revision theory for circularly defined concepts ", "5.5 Axiomatic Theories of Truth and the Revision Theory", "5.6 Applications", "5.7 An open question " ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nLet's take a closer look at the sentence (1), given above:", "\n\n\n(1) is not true.\n(1)\n\n\n", "\n\nIt will be useful to make the paradoxical reasoning explicit. First,\nsuppose that ", "\n\n\n(1) is not true.\n(2)\n\n\n", "\n\nIt seems an intuitive principle concerning truth that, for any\nsentence p, we have the so-called T-biconditional", "\n\n\n‘p’ is true iff\n p.\n(3)\n\n\n", "\n\n(Here we are using ‘iff’ as an abbreviation for ‘if\nand only if’.) In particular, we should have ", "\n\n\n‘(1) is not true’ is true iff\n (1) is not true.\n(4)\n\n\n", "\n\nThus, from (2) and (4), we get ", "\n\n\n‘(1) is not true’ is true.\n(5)\n\n\n", "\n\nThen we can apply the identity,\n", "\n\n\n(1) = ‘(1) is not true.’\n(6)\n\n\n", "\n\nto conclude that (1) is true. This all shows that if (1) is not true,\nthen (1) is true. Similarly, we can also argue that if (1) is true\nthen (1) is not true. So (1) seems to be both true and not true: hence\nthe paradox. As stated above, the three-valued approach to the paradox\ntakes the liar sentence, (1), to be neither true nor false. Exactly\nhow, or even whether, this move blocks the above reasoning is a matter\nfor debate. ", "\nThe RTT is not designed to block reasoning of the above\nkind, but to model it-or most of\n it.[2]\n As stated above,\nthe central idea is the idea of a revision process: a process\nby which we revise hypotheses about the truth-value of one or\nmore sentences.", "\n Consider the reasoning regarding the liar sentence, (1)\nabove. Suppose that we hypothesize that (1) is not true. Then,\nwith an application of the relevant T-biconditional, we might revise\nour hypothesis as follows:", "\n\n\nHypothesis:\n(1) is not true.\n\n\n\nT-biconditional:\n‘(1) is not true’ is true iff (1) is not true.\n\n\n\nTherefore:\n‘(1) is not true’ is true.\n\n\n\nKnown identity:\n(1) = ‘(1) is not true’.\n\n\n\nConclusion:\n(1) is true.\n\n\n\nNew revised hypothesis:\n(1) is true.\n\n\n", "\nWe could continue the revision process, by revising our hypothesis once\nagain, as follows:\n", "\n\n\nNew hypothesis:\n(1) is true.\n\n\n\nT-biconditional:\n‘(1) is not true’ is true iff (1) is not true.\n\n\n\nTherefore:\n‘(1) is not true’ is not true.\n\n\n\nKnown identity:\n(1) = ‘(1) is not true’.\n\n\n\nConclusion:\n(1) is not true.\n\n\n\nNew new revised\nhypothesis: \n(1) is not true.\n\n\n", "\n\nAs the revision process continues, we flip back and forth between\ntaking the liar sentence to be true and not true.", "\nExample 1.1 It is worth seeing how this kind of\nrevision reasoning works in a case with several interconnected sentences. Let's apply\nthe revision idea to the following three sentences:\n\n\n\n\n(8) is true or (9) is true.\n(7)\n\n\n\n(7) is true.\n(8)\n\n\n\n(7) is not true.\n(9)\n\n\n\n\n\n\nInformally, we might reason as follows. Either (7) is true or (7) is\nnot true. Thus, either (8) is true or (9) is true. Thus, (7) is true.\nThus (8) is true and (9) is not true, and (7) is still true. Iterating\nthe process once again, we get (8) is true, (9) is not\ntrue, and (7) is true. More formally, consider any initial hypothesis,\nh0, about the truth values of (7), (8) and\n(9). Either h0 says that (7) is true or\nh0 says that (7) is not true. In either case, we\ncan use the T-biconditional to generate our revised hypothesis\nh1: if h0 says that (7) is\ntrue, then h1 says that ‘(7) is true’\nis true, i.e. that (8) is true; and if h0 says\nthat (7) is not true, then h1 says that ‘(7) is\nnot true’ is true, i.e. that (9) is true. So\nh1 says that either (8) is true or (9) is true. So\nh2 says that ‘(8) is true or (9) is\ntrue’ is true. In other words, h2 says that\n(7) is true. So no matter what hypothesis h0 we\nstart with, two iterations of the revision process lead to a\nhypothesis that (7) is true. Similarly, three or more\niterations of the revision process, lead to the hypothesis that (7) is\ntrue, (8) is true and (9) is not true — regardless of our initial\nhypothesis. In Section 3, we will reconsider this example in a more\nformal context. \n\n", "\n\n One thing to note is that, in Example 1.1, the revision process\nyields stable truth values for all three sentences. The\nnotion of a sentence stably true in all revision sequences\nwill be a central notion for the RTT. The revision-theoretic treatment\ncontrasts, in this case, with the three-valued approach: on most ways\nof implementing the three-valued idea, all three sentences, (7), (8)\nand (9), turn out to be neither true nor\n false.[3]\n In this case, the\nRTT arguably better captures the correct informal reasoning than does\nthe three-valued approach: the RTT assigns to the sentences (7), (8)\nand (9) the truth-values that were assigned to them by the informal\nreasoning given at the beginning of the example. " ], "section_title": "1. Semiformal introduction", "subsections": [] }, { "main_content": [], "section_title": "2. Framing the problem", "subsections": [ { "content": [ "\n\nThe goal of the RTT is not to give a paradox-free account of\ntruth. Rather, the goal of the RTT is to give an account of our often\nunstable and often paradoxical reasoning about truth. RTT seeks, more\nspecifically, to give a a two-valued account that assigns stable\nclassical truth values to sentences when intuitive reasoning would\nassign stable classical truth values. We will present a formal\nsemantics for a formal language: we want that language to have both a\ntruth predicate and the resources to refer to its own sentences. ", "\n\nLet us consider a first-order language L, with connective\n&, ∨, and ¬, quantifiers ∀ and ∃, the equals sign =,\nvariables, and some stock of names, function symbols and relation\nsymbols. We will say that L is a truth language, if\nit has a distinguished predicate T and\nquotation marks ‘ and ’, which will be used to form\nquote names: if A is a sentence of L, then\n‘A’ is a name. Let SentL\n= {A : A is a sentence of L}.", "\n\nIt will be useful to identify the T-free fragment of a truth language L: the first-order language L− that has the same names, function symbols and relation symbols as L, except the unary predicate T. Since L− has the same names as L, including the same quote names, L− will have a quote name ‘A’ for every sentence A of\nL. Thus ∀xTx is not a sentence of L−, but ‘∀xTx’ is a name of L− and ∀x(x = ‘∀xTx’) is a sentence of L−.\n" ], "subsection_title": "2.1 Truth languages" }, { "content": [ "\n\nOther than the truth predicate, we will assume that our language is interpreted classically. More precisely, let a ground model for L be a\nclassical model M = <D, I > for L−, the T-free fragment of L, satisfying\nthe following:", " \n\nClauses (1) and (2) simply specify what it is for M to be a\nclassical model of the T-free fragment of\nL. Clauses (3) and (4) ensure that L, when\ninterpreted, can talk about its own sentences. Given a ground model, we will consider the prospects of providing a satisfying interpretation of T. The most obvious desideratum is that the ground model, expanded to include an interpretation of T, satisfy Tarski's T-biconditionals, i.e., the biconditionals of the form", "\nT ‘A’ iff A\n ", "\n\nfor each A ∈ SentL.", "\n\nSome useful terminology: Given a ground model M\nfor L and a name, function symbol or relation\nsymbol X, we can think of I(X) as the\ninterpretation or, to borrow a term from Gupta and Belnap,\nthe signification of X. Gupta and Belnap\ncharacterize an expression's or concept's signification in a\nworld w as “an abstract something that carries all the\ninformation about all the expression's [or concept's] extensional\nrelations in w.” If we want to\ninterpret Tx as ‘x\nis true’, then, given a ground model M, we would like\nto find an appropriate signification, or an appropriate range of\nsignifications, for T. " ], "subsection_title": "2.2 Ground models" }, { "content": [ "\n\nWe might try to assign to T\na classical signification, by expanding M to a\nclassical model M′ =\n<D′, I′ > for all of\nL, including T. Also recall that we want\nM′ to satisfy the T-biconditionals: for our immediate\npurposes, let us interpret these classically. Let us say that an\nexpansion M′ of a ground model M\nis Tarskian iff M′ is a classical model and\nall of the T-biconditionals, interpreted classically, are true\nin M′. We would like to expand ground models to\nTarskian models. We consider three ground models in order to assess\nour prospects for doing this.", " Ground\nmodel M1 Our first ground model is\na formalization of Example 1.1, above. Suppose that\nL1 contains three non-quote names, α,\nβ, and γ, and no predicates other\nthan T. Let M1 =\n<D1, I1 >\nbe as follows:\n \n\n\n\nD1\n=\nSentL1\n\n\n\nI1(α)\n=\nTβ \n ∨\n Tγ\n\n\n\nI1(β)\n=\nTα\n\n\n\nI1(γ)\n=\n¬Tα\n\n\n\n\nGround model M2 Suppose that\nL2 contains one non-quote names, τ, and no predicates other than T.\nLet M2 =\n<D2, I2 > be as follows:\n \n\n\n\nD2\n=\nSentL2\n\n\n\nI2(τ)\n=\nTτ\n\n\n\n\n\nGround model M3 Suppose that\nL3 contains one non-quote names, λ, and no predicates other than T.\nLet M3 =\n<D3, I3 > be as follows:\n \n\n\n\nD3\n=\nSentL3\n\n\n\nI3(λ)\n=\n¬Tλ\n\n\n\n", "\n\nTheorem 2.1 \n(1) M1 can be expanded to exactly one Tarskian model: in this model, the sentences (Tβ \n ∨\n Tγ) and Tα are true, while the sentence ¬Tα is false.\n(2) M2 can be expanded to exactly two Tarskian models, in one of which the sentence Tτ is true and in the other of which the sentence Tτ is false.\n(3) M3 cannot be expanded to a Tarskian model.\n", "\nThe proofs of (1) and (2) are beyond the scope of this article, but some remarks are in order.", "\n Re (1): The fact that M1 can be expanded to a Tarskian model is not surprising, given the reasoning in Example 1.1, above: any initial hypothesis about the truth values of the three sentences in question leads, after three iterations of the revision process, to a stable hypothesis that (Tβ \n ∨\n Tγ) and Tα are true, while ¬Tα is false.\nThe fact that M1 can be expanded to exactly one Tarskian model needs the so-called Transfer Theorem, Gupta and Belnap 1993, Theorem 2D.4. ", "\nRemark: In the introductory remarks, above, we claim that there are consistent classical interpreted languages that refer to their own sentences and have their own truth predicates. Clauses (1) of Theorem 2.1 delivers an example. Let M1′ be the unique Tarskian expansion of M1. Then the language L1, interpreted by M1′ is an interpreted language that has its own truth predicate satisfying the T-biconditionals classically understood, obeys the rules of standard classical logic, and has the ability to refer to each of its own sentences. Thus Tarski was not quite right in his view that any language with its own truth predicate would be inconsistent, as long as it obeyed the rules of standard classical logic, and had the ability to refer to its own sentences.", " \n\nRe (2): The only potential problematic self-reference is in the sentence Tτ, the so-called truth teller, which says of itself that it is true. Informal reasoning suggests that the truth teller can consistently be assigned either classical truth value: if you assign it the value t then no paradox is produced, since the sentence now truly says of itself that it is true; and if you assign it the value f then no paradox is produced, since the sentence now falsely says of itself that it is true. Theorem 2.1 (2) formalizes this point, i.e., M2 can be expanded to one Tarskian model in which Tτ is true and one in which Tτ is false. The fact that M2 can be expanded to exactly two Tarskian models needs the Transfer Theorem, alluded to above. Note that the language L2, interpreted by either of these expansions, provides another example of an interpreted language that has its own truth predicate satisfying the T-biconditionals classically understood, obeys the rules of standard classical logic, and has the ability to refer to each of its own sentences. ", "\n\nProof of (3). Suppose that M3′ = <D3, I3′ > is a classical expansion of M3 to all of L3. Since M3′ is an expansion of M3, I3 and I3′ agree on all the names of L3. So", "\n I3 ′(λ) = I3(λ) =\n ¬Tλ =\n I3(‘¬Tλ’) =\n I3 ′(‘¬Tλ’).\n", "\n\nSo the sentences Tλ and\nT ‘¬Tλ’\nhave the same truth value in M3′. So the\nT-biconditional", " \n\nT ‘¬Tλ’ \n ≡ ¬Tλ \n", "\n\nis false in M3′.", "\nRemark: The language L3 interpreted by the ground model M3 formalizes the liar's paradox, with the sentence ¬Tλ as the offending liar's sentence. Thus, despite Theorem 2.1, Clauses (1) and (2), Clause (3) strongly suggests that in a semantics for languages capable of expressing their own truth concepts, T cannot, in general, have a classical signification; and the ‘iff’ in the T-biconditionals will not be read as the classical biconditional. We take these suggestions up in Section 4, below." ], "subsection_title": "2.3 Three ground models" } ] }, { "main_content": [], "section_title": "3. Basic notions of the RTT", "subsections": [ { "content": [ "\n\n In Section 1, we informally sketched the central thought of the\nRTT, namely, that we can use the T-biconditionals to generate a\nrevision rule — a rule for revising a hypothesis about the\nextension of the truth predicate. Here we will formalize this notion,\nand work through an example from Section 1. ", "\n \nIn general, let L be a truth language and M be a ground model\nfor L. An hypothesis is a function\nh : D → {t,\nf}. A hypothesis will in effect be a hypothesized\nclassical interpretation for T. Let's work\nwith an example that combines Examples 2.1 and 2.3. We will state the\nexample formally, but reason in a semiformal way, to transition from\none hypothesized extension of\nT to another. ", " Example 3.1 Suppose that\nL contains four non-quote names, α, β, γ and\nλ and no predicates other than T.\nAlso suppose that M =\n<D, I > is as follows:\n \n\n\n\nD\n=\nSentL\n\n\n\nI(α)\n=\nTβ \n ∨\n Tγ\n\n\n\nI(β)\n=\nTα\n\n\n\nI(γ)\n=\n¬Tα\n\n\n\nI(λ)\n=\n¬Tλ\n\n\n\n\n\nIt will be convenient to let\n\n \n\n\n\nA\nbe the sentence\nTβ\n ∨\n Tγ\n\n\n\nB\nbe the sentence\nTα\n\n\n\nC\nbe the sentence\n¬Tα\n\n\n\nX\nbe the sentence\n¬Tλ\n\n\n\n\n\nThus:\n\n \n\n\n\nD\n=\nSentL \n\n\n\nI(α)\n=\nA\n\n\n\nI(β)\n=\nB\n\n\n\nI(γ)\n=\nC\n\n\n\nI(λ)\n=\nX\n\n\n\n\n \n\nSuppose that the hypothesis h0 hypothesizes that\nA is false, B is true, C is false and\nX is true. Thus\n\n\n\n\nh0(A)\n=\nf\n\n\n\nh0(B)\n=\nt\n\n\n\nh0(C)\n=\nf\n\n\n\nh0(X)\n=\nf \n\n\n\n\n\n\nNow we will engage in some semiformal reasoning, on the basis of\nhypothesis h0. Among the four sentences,\nA, B, C and X,\nh0 puts only B in the extension of\nT. Thus, reasoning from\nh0, we conclude that\n \n\n\n\n¬Tα\nsince the referent of α is not in the extension of\nT\n\n\n\nTβ\nsince the referent of β is in the extension of\nT\n\n\n\n¬Tγ\nsince the referent of γ is not in the extension of\nT\n\n\n\n¬Tλ\nsince the referent of λ is not in the extension of\nT.\n\n\n\n\n\n\nThe T-biconditional for the four sentence A, B,\nC and X are as follows: \n \n\n\n\n(TA)\nA is true iff Tβ\n ∨\n Tγ\n\n\n\n(TB)\nB is true iff Tα\n\n\n\n(TC)\nC is true iff ¬Tα\n\n\n\n(TX)\nX is true iff ¬Tλ\n\n\n\n\n\n\nThus, reasoning from h0, we conclude that\n\n \n\n\n\nA is true\n\n\n\nB is not true\n\n\n\nC is true\n\n\n\nX is true\n\n\n\n\n\n\nThis produces our new hypothesis h1:\n\n\n \n\n\nh1(A)\n=\nt\n\n\n\n h1(B)\n=\nf\n\n\n\n h1(C)\n=\nt\n\n\n\n h1(X)\n=\nt \n\n\n\n\n \n\nLet's revise our hypothesis once again. So now we will engage in some\nsemiformal reasoning, on the basis of hypothesis\nh1. Hypothesis h1 puts\nA, C and X, but not B, in the\nextension of the T. Thus, reasoning from\nh1, we conclude that \n \n\n\n\nTα\nsince the referent of a is in the extension of\nT\n\n\n\n¬Tβ\nsince the referent of β is in the extension of\nT\n\n\n\nTγ\nsince the referent of γ is not in the extension of\nT\n\n\n\nTλ\nsince the referent of λ is not in the extension of\nT\n\n\n\n\n\n\nRecall the T-biconditional for the four sentence A,\nB, C and X, given above. Reasoning from\nh1 and these T-biconditionals, we conclude\nthat\n \n\n\n\nA is true\n\n\n\nB is true\n\n\n\nC is not true\n\n\n\nX is not true\n\n\n\n\n\n\nThis produces our new new hypothesis h2:\n\n\n\n\n\nh2(A)\n=\nt\n\n\n\nh2(B)\n=\nt\n\n\n\nh2(C)\n=\nf\n\n\n\nh2(X)\n=\nf \n\n\n\n\n\n□\n", "\n\nLet's formalize the semiformal reasoning carried out in Example\n3.1. First we hypothesized that certain sentences were, or were not,\nin the extension of T. Consider ordinary\nclassical model theory. Suppose that our language has a predicate\nG and a name a, and that we have a model M\n= <D, I > which places the\nreferent of a inside the extension of G:", "\n I(G)(I(α)) = t\n", "\n\nThen we conclude, classically, that the sentence Ga is true\nin M. It will be useful to have some notation for the\nclassical truth value of a sentence S in a classical model\nM. We will write\nValM(S). In this case,\nValM(Ga) =\nt. In Example 3.1, we did not start with a classical\nmodel of the whole language L, but only a classical model of\nthe T-free fragment of L. But then\nwe added a hypothesis, in order to get a classical model of all of\nL. Let's use the notation M + h for the\nclassical model of all of L that you get when you extend\nM by assigning T an extension via\nthe hypothesis h. Once you have assigned an extension to the\npredicate T, you can calculate the truth\nvalues of the various sentences of L. That is, for each\nsentence S of L, we can calculate", "\nValM + h(S)\n", "\n\nIn Example 3.1, we started with hypothesis h0 as follows:\n", "\n\n\nh0(A)\n=\nf\n\n\n\nh0(B)\n=\nt\n\n\n\nh0(C)\n=\nf\n\n\n\nh0(X)\n=\nf\n\n\n", "\nThen we calculated as follows:\n", "\n\n\nValM+h0(Tα)\n=\nf\n\n\n\nValM+h0(Tβ)\n=\nt\n\n\n\nValM+h0(Tγ)\n=\nf\n\n\n\nValM+h0(Tλ)\n=\nf\n\n\n", "\nAnd then we concluded as follows:\n", "\n\n\nValM+h0(A)\n=\nValM+h0(Tβ\n ∨\n Tγ) = t\n\n\n\nValM+h0(B)\n=\nValM+h0(¬Tα) = f\n\n\n\nValM+h0(C)\n=\nValM+h0(Tα) = t\n\n\n\nValM+h0(X)\n=\nValM+h0(¬Tλ) = t\n\n\n", "\nThese conclusions generated our new hypothesis, h1:\n", "\n\n\nh1(A)\n=\nt\n\n\n\nh1(B)\n=\nf\n\n\n\nh1(C)\n=\nt\n\n\n\nh1(X)\n=\nt\n\n\n", "\nNote that, in general,\n", "\n h1(S) =\n ValM+h0(S).\n", "\n\nWe are now prepared to define the revision rule given by a\nground model M = <D, I >. In general,\ngiven an hypothesis h, let M + h =\n<D, I′ > be the model of L which\nagrees with M on the T-free\nfragment of L, and which is such that\nI′(T) = h. So\nM + h is just a classical model for all of\nL. For any model M + h of all of L\nand any sentence A if L, let\nValM+h(A) be the ordinary\nclassical truth value of A in M + h. ", "\nDefinition 3.2\n Suppose that L is a truth language and\nthat M = <D, I > is a ground model \nfor L. The\nrevision rule, τM, is the function mapping\nhypotheses to hypotheses, as follows:\n \n\n\nτM(h)(d)\n=\n{\nt, if d ∈ D\n is a sentence of L and\n ValM+h(d) = t\n \n f, otherwise\n\n\n\n", " \n\nThe ‘otherwise’ clause tells us that if d is not\na sentence of L, then, after one application of revision, we\nstick with the hypothesis that d is not\n true.[5]\n Note that, in Example 3.1, h1 =\nτM(h0) and\nh2 =\nτM(h1). We will often drop\nthe subscripted ‘M’ when the context make it\nclear which ground model is at issue." ], "subsection_title": "3.1 Revision rules" }, { "content": [ "\n\nLet's pick up Example 3.1 and see what happens when we iterate the\napplication of the revision rule. ", " Example 3.3 (Example 3.2 continued)\n \n Recall that L contains four non-quote names, α,\nβ, γ and λ and no predicates other than\nT. Also recall that M = \n<D, I > is as follows:\n\n \n\n\nD\n=\nSentL\n\n\n\n\n\nI(α)\n=\nA\n=\nTβ\n ∨\n Tγ\n\n\n\nI(β)\n=\nB\n=\nTα\n\n\n\nI(γ)\n=\nC\n=\n¬Tα\n\n\n\nI(λ)\n=\nX\n=\n¬Tλ\n\n\n\n", "\n\nThe following table indicates what happens with repeated applications\nof the revision rule τM to the hypothesis\nh0 from Example 3.1. In this table, we will write\nτ instead of τM:", " \n\n\nS\nh0(S)\nτ(h0)(S) \nτ2(h0)(S)\nτ3(h0)(S)\nτ4(h0)(S)\n…\n\n\n\nA\nf\nt\nt\nt\nt\n…\n\n\n\nB\nt\nf\nt\nt\nt\n…\n\n\n\nC\nf\nt\nf\nf\nf\n…\n\n\n\nX\nf\nt\nf\nt\nf\n…\n\n\n", "\n\nSo h0 generates a revision sequence (see\nDefinition 3.7, below). And A and B are stably\ntrue in that revision sequence (see Definition 3.6, below), while\nC is stably false. The liar sentence X is,\nunsurprisingly, neither stably true nor stably false: the liar\nsentence is unstable. A similar calculation would show that\nA is stably true, regardless of the initial hypothesis: thus\nA is categorically true (see Definition 3.8).", "\n\nBefore giving a precise definition of a revision sequence, we\ngive an example where we would want to carry the revision process\nbeyond the finite stages, h, τ1(h),\nτ2(h), τ3(h), and so\non.", "\nExample 3.4 Suppose that L contains\n nonquote names α0, α1,\n α2, α3, …, and unary\n predicates G and T. Now we will\n specify a ground model M =\n <D, I > where the name\n α0 refers to some tautology, and where \n\n\n the name\n α1 refers to the sentence\n Tα0 \n the name\n α2 refers to the sentence\n Tα1 \n the name\n a3 refers to the sentence\n Ta2 \n …\n\n\n More formally, let A0 be the sentence\n Tα0\n ∨\n ¬Tα0,\n and for each n ≥ 0, let An+1\n be the sentence\n Tαn. Thus\n A1 is the sentence\n Tα0, and\n A2 is the sentence\n Tα1, and\n A3 is the sentence\n Tα2, and so on. Our\n ground model M =\n <D, I > is as follows:\n\n\n \n\nD\n=\nSentL\n\n\n\nI(αn)\n=\nAn\n\n\n\nI(G)(A) = t \niff\nA = An for some n\n\n\n\n\n\nThus, the extension of G is the following set of sentences:\n{A0, A1,\nA2, A3, … } =\n{(Tα0\n ∨\n ¬Tα0),\n Tα0, \n Ta1,\n Ta2,\n Ta3,\n… }. Finally let B be the sentence\n ∀x(Gx ⊃\nTx). Let h be any\n hypothesis for which we have, for\n each natural number n,\n\n\n h(An) = h(B) =\n f. \n\n\n\n The following table indicates what happens with repeated applications\nof the revision rule τM to the hypothesis\nh. In this table, we will write τ instead of\nτM:\n \n\n\n\nS\nh(S)\nt(h)(S)\nτ2(h)(S)\nτ3(h)(S)\nτ4(h)(S)\n…\n\n\n\nA0 \nf\nt\nt\nt\nt\n…\n\n\n\nA1 \nf\nf\nt\nt\nt\n…\n\n\n\nA2 \nf\nf\nf\nt\nt\n…\n\n\n\nA3 \nf\nf\nf\nf\nt\n…\n\n\n\nA4 \nf\nf\nf\nf\nf\n…\n\n\n\n\n\n\n\n\n\n\n\n\n\nB\nf\nf\nf\nf\nf\n…\n\n\n\n\n\n \nAt the 0th stage, each An is\noutside the hypothesized extension of T. But\nfrom the nth stage onwards,\nAn is in the hypothesized\nextension of T. So, for each n, the\nsentence An is eventually stably\nhypothesized to be true. Despite this, there is no finite\nstage at which all the An's are\nhypothesized to be true: as a result the sentence B = \n ∀x(Gx ⊃\n Tx)\n remains false at each finite stage. This\nsuggests extending the process as follows: \n \n\n\n\nS\nh(S)\nτ(h)(S)\nτ2(h)(S)\nτ3(h)(S)\n…\nω\nω+1\nω+2\n…\n\n\n\nA0 \nf\nt\nt\nt\n…\nt\nt\nt\n…\n\n\n\nA1 \nf\nf\nt\nt\n…\nt\nt\nt\n…\n\n\n\nA2 \nf\nf\nf\nt\n…\nt\nt\nt\n…\n\n\n\nA3 \nf\nf\nf\nf\n…\nt\nt\nt\n…\n\n\n\nA4 \nf\nf\nf\nf\n…\nt\nt\nt\n…\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nB\nf\nf\nf\nf\n…\nf\nt\nt\n…\n\n\n\n\n\n\nThus, if we allow the revision process to proceed beyond the finite\nstages, then the sentence B = \n ∀x(Gx ⊃\n Tx) is stably true from the \nω+1st stage onwards. □\n", "\n In Example 3.4, the intuitive verdict is that not only should each\nAn receive a stable truth value of\nt, but so should the sentence B =\n∀x(Gx ⊃\nTx). The only way to ensure this is\nto carry the revision process beyond the finite stages. So we will\nconsider revision sequences that are very long: not only will a\nrevision sequence have a nth stage for each finite\nnumber n, but a ηth stage for every\nordinal number η. (The next paragraph is to help the\nreader unfamiliar with ordinal numbers.)", "\n\n One way to think of the ordinal\nnumbers is as follows. Start with the finite natural numbers:", "\n 0, 1, 2, 3,… \n", "\n\n Add a number, ω, greater than all of these but not the\n immediate successor of any of them: ", "\n 0, 1, 2, 3, …, ω\n", "\n And then take the successor of ω, its successor,\nand so on:", "\n 0, 1, 2, 3, …, ω, ω+1, ω+2, ω+3\n… ", "\n Then add a number ω+ω, or ω×2, greater than\nall of these (and again, not the immediate successor of any), and\nstart over, reiterating this process over and over:", "\n 0, 1, 2, 3, …, \nω, ω+1, ω+2, ω+3, …,\n ω×2, (ω×2)+1, (ω×2)+2,\n (ω×2)+3, …, \nω×3,\n (ω×3)+1, (ω×3)+2, (ω×3)+3, \n … \n   \n", "\nAt the end of this, we add an ordinal number ω×ω or\nω2:", "\n 0, 1, 2, …, ω, ω+1, ω+2,\n…, ω×2, (ω×2)+1, …, \n ω×3, …, ω×4, …, \nω×5, …, ω2,\n ω2+1, … ", "\n The ordinal numbers have the following structure: every ordinal\nnumber has an immediate successor known as a successor\nordinal; and for any infinitely ascending sequence of ordinal\nnumbers, there is a limit ordinal which is greater than all\nthe members of the sequence and which is not the immediate successor\nof any member of the sequence. Thus the following are successor\nordinals: 5, 178, ω+12, (ω×5)+56,\nω2+8; and the following are limit ordinals: ω,\nω×2, ω2, (ω2+ω),\netc. Given a limit ordinal η, a sequence S of objects is\nan η-long sequence if there is an object\nSδ for every ordinal δ < η. We\nwill denote the class of ordinals as\n On.\n Any sequence S of objects is an\n On-long\n sequence if there is an object Sδ for every\nordinal δ.", " \n\nWhen assessing whether a sentence receives a\nstable truth value, the RTT considers sequences of hypotheses of\nlength\n On.\n So suppose that S is an \n On-long\n sequence of hypotheses, and let ζ and η range over\nordinals. Clearly, in order for S to represent the revision\nprocess, we need the ζ+1st hypothesis to be generated\nfrom the ζth hypothesis by the revision rule. So we\ninsist that Sζ+1 =\nτM(Sζ). But what\nshould we do at a limit stage? That is, how should we set\nSη(δ) when η is a limit ordinal?\nClearly any object that is stably true [false] up to that\nstage should be true [false] at that stage. Thus consider\nExample 3.2. The sentence A2, for example, is true\nup to the ωth stage; so we set A2\nto be true at the ωth stage. For objects\nthat do not stabilize up to that stage, Gupta and Belnap 1993 adopt a\nliberal policy: when constructing a revision sequence S, if\nthe value of the object d ∈ D has not\nstabilized by the time you get to the limit stage η, then you can\nset Sη(δ) to be whichever of\nt or f you like. Before we give the\nprecise definition of a revision sequence, we continue with\nExample 3.3 to see an application of this idea. ", "\nExample 3.5 (Example 3.3 continued) \n Recall that L contains four non-quote names, α,\nβ, γ and λ and no predicates other than\nT. Also recall that M = \n<D, I > is as follows:\n \n\n\n\nD\n=\nSentL\n\n\n\n\n\nI(α)\n=\nA\n=\nTβ\n ∨\n Tγ\n\n\n\nI(β)\n=\nB\n=\nTα\n\n\n\nI(γ)\n=\nC\n=\n¬Tα\n\n\n\nI(λ)\n=\nX\n=\n¬Tλ\n\n\n\n\n\n\nThe following table indicates what happens with repeated applications\nof the revision rule τM to the hypothesis\nh0 from Example 3.1. For each ordinal η, we\nwill indicate the ηth hypothesis by\nSη (suppressing the index M on\nτ). Thus S0 = h0,\nS1 = τ(h0),\nS2 = τ2(h0),\nS3 = τ3(h0),\nand Sω, the ωth hypothesis,\nis determined in some way from the hypotheses leading up to it. So,\nstarting with h0 from Example 3.3, our revision\nsequence begins as follows: \n \n\n\n\nS\nS0(S)\nS1(S)\nS2(S)\nS3(S)\nS4(S)\n…\n\n\n\nA\nf\nt\nt\nt\nt\n…\n\n\n\nB\nt\nf\nt\nt\nt\n…\n\n\n\nC\nf\nt\nf\nf\nf\n…\n\n\n\nX\nf\nt\nf\nt\nf\n…\n\n\n\n\n\n What happens at the ωth stage? A and\nB are stably true up to the ωth\nstage, and C is stably false up to the\nωth stage. So at the ωth\nstage, we must have the following:\n \n\n\n\nS\nS0(S)\nS1(S)\nS2(S)\nS3(S)\nS4(S)\n…\nSω(S)\n\n\n\nA\nf\nt\nt\nt\nt\n…\nt\n\n\n\nB\nt\nf\nt\nt\nt\n…\nt\n\n\n\nC\nf\nt\nf\nf\nf\n…\nf\n\n\n\nX\nf\nt\nf\nt\nf\n…\n? \n\n\n\n\n\n\nBut the entry for Sω(X) can be\neither t or f. In other words, the\ninitial hypothesis h0 generates at least two\nrevision sequences. Every revision sequence S that has\nh0 as its initial hypothesis must have\nSω(A) = t,\nSω(B) = t, and\nSω(C) = f. But there is\nsome revision sequence S, with h0 as its\ninitial hypothesis, and with Sω(X)\n= t; and there is some revision sequence\nS′, with h0 as its initial\nhypothesis, and with Sω′(X) =\nf. □\n\n", "\n We are now ready to define the notion of a revision\nsequence: ", "\n Definition 3.6 \n Suppose\nthat L is a truth language, and that M = \n <D, I >\nis a ground model. Suppose that S is an \n On-long\n sequence of hypotheses. Then we say that d ∈ D\nis stably t [f] in\nS iff for some ordinal θ we\nhave\n\n \n Sζ(d) = t\n[f], for every ordinal ζ ≥ θ.\n \n\n\n Suppose that S is a η-long sequence of hypothesis for\nsome limit ordinal η. Then we say that d ∈\nD is stably t [f]\nin S iff for some ordinal θ < η we have\n\n\n Sζ(d) =\n t [f], for every ordinal ζ\nsuch that ζ ≥ θ and ζ < η.\n \n\n\n\nIf S is an \n On-long\n sequence of hypotheses and η is a limit ordinal, then\nS|η is the initial segment of S up to\nbut not including η. Note that S|η is a\nη-long sequence of hypotheses. \n ", "\n\nDefinition 3.7 \n Suppose that L is a truth language, and that M =\n<D, I > is a ground\nmodel. Suppose that S is an \n On-long\n sequence of hypotheses. S is a revision sequence\nfor M iff\n\n\n\nSζ+1 =\n τM(Sζ),\nfor each ζ ∈ \n On, and\n\nfor each limit ordinal η and each d ∈\nD, if d is stably t\n[f] in S|η, then\nSη(d) = t\n[f]. \n\n\n\n\n\nDefinition 3.8 \n Suppose that L is a truth language, and that M =\n<D, I > is a ground model. We\nsay that the sentence A is categorically true\n[false] in M iff A is stably\nt [f] in every revision sequence for\nM. We say that A is categorical in\nM iff A is either categorically true or\ncategorically false in M.\n\n", "\n\nWe now illustrate these concepts with an example. The example will also\nillustrate a new concept to be defined afterwards. ", " Example 3.9 \n Suppose that L is\na truth language containing nonquote names β,\nα0, α1, α2,\nα3, …, and unary predicates G and\nT. Let B be the sentence\n\n\n Tβ \n ∨\n ∀x∀y(Gx\n & ¬Tx & Gy\n & ¬Ty ⊃ x=y). \n\n\n\n\nLet A0 be the sentence ∃x(Gx\n & ¬Tx). And for each\nn ≥ 0, let An+1 be the\nsentence Tαn.\nConsider the following ground model M =\n<D, I > \n\n \n\n\nD\n=\nSentL\n\n\n\nI(β)\n=\nB\n\n\n\nI(αn)\n=\nAn\n\n\n\nI(G)(A) = t \niff\nA = An for some n\n\n\n\n\n\n\nThus, the extension of G is the following set of sentences:\n {A0, A1,\nA2, A3, … } =\n{Tα0,\nTα1,\nT α2,\nTα3, … }. Let\nh be any hypothesis for which we have, h(B)\n= f and for each natural number n,\n\n\n\n h(An) = f.\n\n\n\n And let S be a revision sequence whose initial hypothesis is\nh, i.e., S0 = h. The following\ntable indicates some of the values of\nSγ(C), for sentences C\n∈ {B, A0, A1,\nA2, A3, … }. In the top\nrow, we indicate only the ordinal number representing the stage in the\nrevision process. \n \n\n\n\n0\n1\n2\n3\n…\nω\nω+1\nω+2\nω+3\n…\nω×2\n(ω×2)+1\n(ω×2)+2\n…\n\n\n\nB\nf\nf\nf\nf\n…\nf\nt\nt\nt\n…\nt\nt\nt\n…\n\n\n\nA0 \nf\nt\nt\nt\n…\nt\nf\nt\nt\n…\nt\nf\nt\n…\n\n\n\nA1 \nf\nf\nt\nt\n…\nt\nt\nf\nt\n…\nt\nt\nf\n…\n\n\n\nA2 \nf\nf\nf\nt\n…\nt\nt\nt\nf\n…\nt\nt\nt\n…\n\n\n\nA3 \nf\nf\nf\nf\n…\nt\nt\nt\nt\n…\nt\nt\nt\n…\n\n\n\nA4 \nf\nf\nf\nf\n…\nt\nt\nt\nt\n…\nt\nt\nt\n…\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nIt is worth contrasting the behaviour of the sentence B and the\nsentence A0. From the ω+1st stage\non, B is stabilizes as true. In fact, B is stably\ntrue in every revision sequence for M. Thus, B is\ncategorically true in M. The sentence A0,\nhowever, never quite stabilizes: it is usually true, but within a few\nfinite stages of a limit ordinal, the sentence A0\ncan be false. In these circumstances, we say that\nA0 is nearly stably true (See Definition\n3.10, below.) In fact, A0 is nearly stably true in\nevery revision sequence for M. □ \n\n", "\n\nExample 3.9 illustrates not only the notion of stability in a revision\nsequence, but also of near stability, which we define now: ", "\n\nDefinition 3.10. Suppose that L is a\ntruth language, and that M =\n<D, I > is a ground\nmodel. Suppose that S is an \n On-long sequence of hypotheses. Then we say\nthat d ∈ D is nearly stably\nt [f] in S iff for\nsome ordinal θ we have\n\n\n for every ζ ≥ θ, there is a natural number n\nsuch that, for every m ≥ n,\nSζ+m(d) =\nt [f]. \n \n\n", "\n\nGupta and Belnap 1993 characterize the difference between stability\nand near stability as follows: “Stability simpliciter\nrequires an element [in our case a sentence] to settle down to a value\nx [in our case a truth value] after some initial\nfluctuations say up to [an ordinal η]… In contrast, near\nstability allows fluctuations after η also, but these fluctuations\nmust be confined to finite regions just after limit\nordinals” (p. 169). Gupta and Belnap 1993 introduce two theories of\ntruth, T* and\nT#, based on stability and near\nstability. Theorems 3.12 and 3.13, below, illustrate an advantage of\nthe system T#, i.e., the system\nbased on near stability. ", "\nDefinition 3.11 \n Suppose that L is a truth language, and that M =\n<D, I > is a ground model. We\nsay that a sentence A is valid in M\nby T* iff A is\nstably true in every revision sequence. And we say that a sentence\nA is valid in M by\nT# iff A is nearly\nstably true in every revision sequence.\n\n\n\nTheorem 3.12 \n Suppose that L is a truth language, and that M =\n<D, I > is a ground model. Then,\nfor every sentence A of L, the following is valid in\nM by T#:\n\n\n T‘¬A’ ≡\n¬T‘A’.\n\n\n\n\nTheorem 3.13 \n There is a truth language L and a ground model M =\n<D, I > and a sentence\nA of L such that the following is not valid\nin M by T*:\n\n\n T ‘¬A’ ≡\n¬T ‘A’.\n\n\n", "\n\nGupta and Belnap 1993, Section 6C, note similar advantages of\nT# over\nT*. For example,\nT# does, but\nT* does not, validate the\nfollowing semantic principles: ", "\n T ‘A & B’\n ≡\nT ‘A’ &\n T ‘B’ \n\n\n T ‘A \n ∨\n B’ ≡\nT ‘A’ \n ∨\n T ‘B’ \n\n", "\n Gupta and Belnap remain noncommittal about which of\nT# and\nT* (and a further alternative\nthat they define, Tc) is\npreferable." ], "subsection_title": "3.2 Revision sequences" } ] }, { "main_content": [ "\n\n The main formal notions of the RTT are the notion of a revision\nrule (Definition 3.2), i.e., a rule for revising hypotheses; and a\nrevision sequence (Definition 3.7), a sequence of hypotheses\ngenerated in accordance with the appropriate revision rule. Using\nthese notions, we can, given a ground model, specify when a sentence\nis stably, or nearly stably, true or false in a particular\nrevision sequence. Thus we could define two theories of truth,\nT* and\nT#, based on stability and near\nstability. The final idea is that each of these theories delivers a\nverdict on which sentences of the language are categorically\nassertible, given a ground model. ", "\n\nNote that we could use revision-theoretic notions to make rather\nfine-grained distinctions among sentences: Some sentences are unstable\nin every revision sequence; others are stable in every revision\nsequence, though stably true in some and stably false in others; and\nso on. Thus, we can use revision-theoretic ideas to give a\nfine-grained analysis of the status of various sentences, and of the\nrelationships of various sentences to one another.", "\n\n Recall the suggestion made at the end of Section 2:", "\n In a semantics for languages capable of expressing their own truth\nconcepts, T will not, in general, have a\nclassical signification; and the ‘iff’ in the\nT-biconditionals will not be read as the classical biconditional.\n ", "\n\nGupta and Belnap fill out these suggestions in the following way. " ], "section_title": "4. Interpreting the formalism", "subsections": [ { "content": [ "\n\n First, they suggest that the signification of\nT, given a ground model M, is the\nrevision rule τM itself. As noted in the\npreceding paragraph, we can give a fine-grained analysis of sentences'\nstatuses and interrelations on the basis of notions generated directly\nand naturally from the revision rule τM. Thus,\nτM is a good candidate for the signification\nof T, since it does seem to be “an abstract\nsomething that carries all the information about all [of\nT's] extensional relations” in\nM. (See Gupta and Belnap's characterization of an\nexpression's signification, given in Section 2, above.) " ], "subsection_title": "4.1 The signification of T" }, { "content": [ "\n\nGupta and Belnap's related suggestion concerning the ‘iff’\nin the T-biconditionals is that, rather than being the classical\nbiconditional, this ‘iff’ is the distinctive biconditional\nused to define a previously undefined concept. In 1993, Gupta\nand Belnap present the revision theory of truth as a special case of a\nrevision theory of circularly defined concepts. Suppose that\nL is a language with a unary predicate F and a\nbinary predicate R. Consider a new concept expressed by a\npredicate G, introduced through a definition like this:", "\n Gx =df\n ∀y(Ryx ⊃ Fx) \n ∨\n ∃y(Ryx & Gx). \n ", "\n\nSuppose that we start with a domain of discourse, D, and an\ninterpretation of the predicate F and the relation symbol\nR. Gupta and Belnap's revision-theoretic treatment of\nconcepts thus circularly introduced allows one to give categorical\nverdicts, for certain d ∈ D about whether or\nnot d satisfies G. Other objects will be unstable\nrelative to G: we will be able categorically to assert\nneither that d satisfies G nor that d does not\nsatisfy G. In the case of truth, Gupta and Belnap take the\nset of T-biconditionals of the form", "\n\n\nT ‘A’\n =df A\n(10)\n\n\n", "\n\ntogether to give the definition of the concept of truth. It is their\ntreatment of ‘=df’ (the\n‘iff’ of definitional concept introduction), together with\nthe T-biconditionals of the form (10), that determine the revision\nrule τM. " ], "subsection_title": "4.2 The ‘iff’ in the T-biconditionals" }, { "content": [ "\n\nRecall the liar sentence, (1), from the beginning of this article:", "\n\n\n(1) is not true\n(1)\n\n\n", "\n In Section 1, we claimed that the RTT is designed to model, rather\nthan block, the kind of paradoxical reasoning regarding (1). But we\nnoted in footnote 2 that the RTT does avoid contradictions in these\nsituations. There are two ways to see this. First, while the RTT does\nendorse the biconditional", "\n (1) is true iff (1) is not true,\n", "\n the relevant ‘iff’ is not the material biconditional, as\nexplained above. Thus, it does not follow that both (1) is true and\n(1) is not true. Second, note that on no hypothesis can we conclude\nthat both (1) is true and (1) is not true. If we keep it firmly in\nmind that revision-theoretical reasoning is hypothetical rather than\ncategorical, then we will not infer any contradictions from the\nexistence of a sentence such as (1), above." ], "subsection_title": "4.3 The paradoxical reasoning" }, { "content": [ "\n\nGupta and Belnap's suggestions, concerning the signification of\nT and the interpretation of the\n‘iff’ in the T-biconditionals, dovetail nicely with two\nclosely related intuitions articulated in Gupta & Belnap 1993. The\nfirst intuition, loosely expressed, is “that the T-biconditionals are\nanalytic and fix the meaning of ‘true’” (p. 6).\nMore tightly expressed, it becomes the “Signification Thesis” (p. 31):\n“The T-biconditionals fix the signification of truth in every world\n[where a world is represented by a ground\n model].”[6]\n Given the revision-theoretic treatment of the definition\n‘iff’, and given a ground model M, the T-biconditionals\n(10) do, as noted, fix the suggested signification of\nT, i.e., the revision rule\nτM." ], "subsection_title": "4.4 The signification thesis" }, { "content": [ "\n\nThe second intuition is the supervenience of the signification of\ntruth. This is a descendant of M. Kremer's 1988 proposed\nsupervenience of semantics. The idea is simple: which\nsentences fall under the concept truth should be fixed by (1)\nthe interpretation of the nonsemantic vocabulary, and (2) the\nempirical facts. In non-circular cases, this intuition is particularly\nstrong: the standard interpretation of “snow” and “white” and the\nempirical fact that snow is white, are enough to determine that the\nsentence “snow is white” falls under the concept truth. The\nsupervenience of the signification of truth is the thesis that the\nsignification of truth, whatever it is, is fixed by the ground model\nM. Clearly, the RTT satisfies this principle. ", "\n\nIt is worth seeing how a theory of truth might violate this\nprinciple. Consider the truth-teller sentence, i.e., the sentence that\nsays of itself that it is true:", "\n\n\n(11) is true\n(11)\n\n\n", "\n\nAs noted above, Kripke's three-valued semantics allows three truth\nvalues, true (t), false (f), and\nneither (n). Given a ground model M = \n <D, I > for a truth\nlanguage L, the candidate interpretations of\nT are three-valued interpretations, i.e.,\nfunctions h : D →\n{ t, f,\nn }. Given a three-valued interpretation of\nT, and a scheme for evaluating the truth\nvalue of composite sentences in terms of their parts, we can specify a\ntruth value ValM+h(A) =\nt, f or n, for\nevery sentence A of L. The central theorem of the\nthree-valued semantics is that, given any ground model M,\nthere is a three-valued interpretation h of\nT so that, for every sentence A, we\nhave\nValM+h(T ‘A’)\n =\n ValM+h(A).[7]\n We will call such an interpretation of T an\nacceptable interpretation. Our point here is this: if there's\na truth-teller, as in (11), then there is not only one acceptable\ninterpretation of T; there are three: one\naccording to which (11) is true, one according to which (11) is false,\nand one according to which (11) is neither. Thus, there is no single\n“correct” interpretation of T given a ground\nmodel M. Thus the three-valued semantics seems to violate the\nsupervenience of\n semantics.[8]\n", "\n\n The RTT does not assign a truth value to the truth-teller,\n(11). Rather, it gives an analysis of the kind of reasoning that one\nmight engage in with respect to the truth-teller: If we start with a\nhypothesis h according to which (11) is true, then upon\nrevision (11) remains true. And if we start with a hypothesis\nh according to which (11) is not true, then upon revision\n(11) remains not true. And that is all that the concept of truth\nleaves us with. Given this behaviour of (11), the RTT tells us that\n(11) is neither categorically true nor categorically false, but this\nis quite different from a verdict that (11) is neither true nor\nfalse. " ], "subsection_title": "4.5 The supervenience of semantics" }, { "content": [ "\n\nWe note an alternative interpretation of the revision-theoretic\nformalism. Yaqūb 1993 agrees with Gupta and Belnap that the\nT-biconditionals are definitional rather than material biconditionals,\nand that the concept of truth is therefore circular. But Yaqūb\ninterprets this circularity in a distinctive way. He argues that,", "\n since the truth conditions of some sentences involve reference to\ntruth in an essential, irreducible manner, these conditions can only\nobtain or fail in a world that already includes an extension of the\ntruth predicate. Hence, in order for the revision process to determine\nan extension of the truth predicate, an initial extension of\nthe predicate must be posited. This much follows from circularity and\nbivalence. (1993, 40)\n", "\n Like Gupta and Belnap, Yaqūb posits no privileged extension for\nT. And like Gupta and Belnap, he sees the\nrevision sequences of extensions of T, each\nsequence generated by an initial hypothesized extension, as “capable\nof accommodating (and diagnosing) the various kinds of problematic and\nunproblematic sentences of the languages under consideration” (1993,\n41). But, unlike Gupta and Belnap, he concludes from these\nconsiderations that “truth in a bivalent language is not\nsupervenient” (1993, 39). He explains in a footnote: for truth to\nbe supervenient, the truth status of each sentence must be “fully\ndetermined by nonsemantical facts”. Yaqūb does not explicitly\nuse the notion of a concept's signification. But Yaqūb\nseems committed to the claim that the signification of\nT — i.e., that which determines the\ntruth status of each sentence — is given by a particular\nrevision sequence itself. And no revision sequence is determined by\nthe nonsemantical facts, i.e., by the ground model, alone: a revision\nsequence is determined, at best, by a ground model and an initial\n hypothesis.[9]\n " ], "subsection_title": "4.6 A nonsupervenient interpretation of the formalism" } ] }, { "main_content": [], "section_title": "5. Further issues", "subsections": [ { "content": [ "\n\nWe have given only the barest exposition of the three-valued\nsemantics, in our discussion of the supervenience of the signification\nof truth, above. Given a truth language L and a ground model\nM, we defined an acceptable three-valued\ninterpretation of T as an interpretation \n h : D →\n{ t, f,\nn } such that\nValM+h(T‘A’)\n= ValM+h(A) for each\nsentence A of L. In general, given a ground model\nM, there are many acceptable interpretations of\nT. Suppose that each of these is indeed a\ntruly acceptable interpretation. Then the three-valued semantics\nviolates the supervenience of the signification of\nT. ", "\n\n Suppose, on the other hand, that, for each ground model M,\nwe can isolate a privileged acceptable interpretation as the\ncorrect interpretation of T. Gupta and\nBelnap present a number of considerations against the three-valued\nsemantics, so conceived. (See Gupta & Belnap 1993, Chapter 3.) One\nprincipal argument is that the central theorem, i.e., that for each\nground model there is an acceptable interpretation, only holds when\nthe underlying language is expressively impoverished in certain ways:\nfor example, the three-valued approach fails if the language has a\nconnective ~ with the following truth table: ", "\n\n\nA\n~A\n\n\n\nt \nf \n\n\n\nf \nt \n\n\n\nn \nt \n\n\n", "\nThe only negation operator that the three-valued approach can handle\nhas the following truth table:", "\n\n\nA\n¬A\n\n\n\nt \nf \n\n\n\nf \nt \n\n\n\nn \nn \n\n\n", "\n\nBut consider the liar that says of itself that it is ‘not’\ntrue, in this latter sense of ‘not’. Gupta and Belnap urge\nthe claim that this sentence “ceases to be intuitively paradoxical”\n(1993, 100). The claimed advantage of the RTT is its ability to describe\nthe behaviour of genuinely paradoxical sentences: the genuine liar is\nunstable under semantic evaluation: “No matter what we hypothesize its\nvalue to be, semantic evaluation refutes our hypothesis.” The\nthree-valued semantics can only handle the “weak liar”, i.e., a\nsentence that only weakly negates itself, but that is not guaranteed\nto be paradoxical: “There are appearances of the liar here, but they\ndeceive.” \n", "\n\nWe've thus far reviewed two of Gupta and Belnap's complaints against\nthree-valued approaches, and now we raise a third: in the\nthree-valued theories, truth typically behaves like a nonclassical\nconcept even when there’s no vicious reference in the\nlanguage. Without defining terms here, we note that one popular\nprecisification of the three-valued approach, is to take the correct\ninterpretation of T to be that given by the ‘least fixed\npoint’ of the ‘strong Kleene scheme’: putting aside\ndetails, this interpretation always assigns the truth value n to the\nsentence ∀x(Tx ∨\n¬Tx), even when the ground model allows\nno circular, let alone vicious, reference. Gupta and Belnap claim an\nadvantage for the RTT: according to revision-theoretic approach, they\nclaim, truth always behaves like a classical concept when there is no\nvicious reference.", "\n\nKremer 2010 challenges this claim by precisifying it as a formal claim\nagainst which particular revision theories\n(e.g. T*\nor T#, see Definition 3.11,\nabove) and particular three-valued theories can be tested. As it turns\nout, on many three-valued theories, truth does in fact behave like a\nclassical concept when there's no vicious reference: for\nexample, the least fixed point of a natural variant of the\nsupervaluation scheme always assigns T a\nclassical interpretation in the absence of vicious reference. Granted,\ntruth behaves like a classical concept when there’s no vicious\nreference on Gupta and Belnap's\ntheory T*, but, so Kremer argues,\ndoes not on Gupta and Belnap's\ntheory T#. This discussion is\nfurther taken up by Wintein 2014." ], "subsection_title": "5.1 Three-valued semantics" }, { "content": [ "\nA contrast presupposed by this entry is between allegedly two-valued\ntheories, like the RTT, and allegedly three-valued or other\nmany-valued rivals. One might think of the RTT itself as providing\ninfinitely many semantic values, for example one value for every\npossible revision sequence. Or one could extract three semantic values\nfor sentences: categorical truth, categorical falsehood, and\nuncategoricalness.", "\nIn reply, it must be granted that the RTT generates\nmany statuses available to sentences. Similarly, three-valued\napproaches also typically generate many statuses available to\nsentences. The claim of two-valuedness is not a claim about statuses\navailable to sentences, but rather a claim about the truth\nvalues presupposed in the whole enterprise." ], "subsection_title": "5.2 Two values?" }, { "content": [ "\n\nWe note three ways to amend the RTT. First, we might put constraints\non which hypotheses are acceptable. For example, Gupta and Belnap 1993\nintroduce a theory, Tc, of truth\nbased on consistent hypotheses: an hypothesis h is\nconsistent iff the set\n{A : h(A) =\nt} is a complete consistent set of sentences. The\nrelative merits of T*,\nT# and\nTc are discussed in Gupta &\nBelnap 1993, Chapter 6.", "\n Second, we might adopt a more restrictive limit policy than\nGupta and Belnap adopt. Recall the question asked in Section 3: How\nshould we set Sη(d) when η is a\nlimit ordinal? We gave a partial answer: any object that is stably\ntrue [false] up to that stage should be true [false]\nat that stage. We also noted that for an object d\n∈ D that does not stabilize up to the stage η, Gupta\nand Belnap 1993 allow us to set Sη(d)\nas either t or f. In a similar\ncontext, Herzberger 1982a and 1982b assigns the value\nf to the unstable objects. And Gupta originally\nsuggested, in Gupta 1982, that unstable elements receive whatever\nvalue they received at the initial hypothesis\nS0.", "\n\n These first two ways of amending the RTT both, in effect, restrict\nthe notion of a revision sequence, by putting constraints on which of\nour revision sequences really count as acceptable revision\nsequences. The constraints are, in some sense local: the first\nconstraint is achieved by putting restrictions on which hypotheses can\nbe used, and the second constraint is achieved by putting restrictions\non what happens at limit ordinals. A third option would be to put more\nglobal constraints on which putative revision sequences count as\nacceptable. Yaqūb 1993 suggests, in effect, a limit rule whereby\nacceptable verdicts on unstable sentences at some limit stage η\ndepend on verdicts rendered at other limit stages.\nYaqūb argues that these constraints allow us to avoid certain\n“artifacts”. For example, suppose that a ground model M =\n<D, I > has two independent\nliars, by having two names α and β, where\nI(α) = ¬Tα and\nI(β) =\n¬Tβ. Yaqūb argues that it is\na mere “artifact” of the revision semantics, naively presented, that\nthere are revision sequences in which the sentence\n¬Tα ≡\n¬Tβ is stably true, since the two\nliars are independent. His global constraints are developed to rule\nout such sequences. (See Chapuis 1996 for further discussion.) " ], "subsection_title": "5.3 Amendments to the RTT" }, { "content": [ "\n\nAs indicated in our discussion, in Section 4, of the ‘iff’\nin the T-biconditionals, Gupta and Belnap present the RTT as a special\ncase of a revision theory of circularly defined concepts. To\nreconsider the example from Section 4. Suppose that L is a\nlanguage with a unary predicate F and a binary predicate R. Consider a\nnew concept expressed by a predicate G, introduced through a\ndefinition, D, like this: ", "\n Gx = df A(x,G)\n", "\n where A(x,G) is the formula", "\n ∀y(Ryx ⊃ Fx) \n ∨\n ∃y(Ryx & Gx).\n", "\n In this context, a ground model is a classical model\nM = <D, I > of the language\nL: we start with a domain of discourse, D, and an\ninterpretation of the predicate F and the relation symbol\nR. We would like to extend M to an interpretation of\nthe language L + G. So, in this context, an\nhypothesis will be thought of as an hypothesized extension for the\nnewly introduced concept G. Formally, a hypothesis is simply\na function h : D →\n{t, f}. Given a hypothesis\nh, we take M+h to be the classical model\nM+h =\n<D, I′ >, where\nI′ interprets F and R in the same way\nas I, and where I′(G) = h.\nGiven a hypothesized interpretation h of G, we\ngenerate a new interpretation of G as follows: and object\nd ∈ D is in the new extension of G\njust in case the defining formula A(x,G) is\ntrue of d in the model M+h. Formally, we\nuse the ground model M and the definition D to\ndefine a revision rule,\nδD,M, mapping hypotheses to\nhypotheses, i.e., hypothetical interpretations of G to\nhypothetical interpretations of G. In particular, for any\nformula B with one free variable x, and d\n∈ D, we can define the truth value\nValM+h,d(B) in\nthe standard way. Then,", "\n δD,M(h)(d) =\n ValM+h,d(A)\n", "\n\n Given a revision rule δD,M, we\ncan generalize the notion of a revision sequence, which is\nnow a sequence of hypothetical extensions of G rather than\nT. We can generalize the notion of a\nsentence B being stably true, nearly stably\ntrue, etc., relative to a revision sequence. Gupta and Belnap\nintroduce the systems S* and\nS#, analogous to\nT* and\nT#,\nas\n follows:[10]\n", "\nDefinition 5.1.\n\n A sentence B is valid on the definition\nD in the ground model M in the\nsystem S* (notation \n M ⊨*,D B)\n iff B is stably true relative to each revision sequence for\nthe revision rule δD,M.\n\nA sentence B is valid on the definition\nD in the ground model M in the\nsystem S# (notation \n M ⊨#,D B)\n iff B is nearly stably true relative\nto each revision sequence for the revision rule\nδD,M.\n\nA sentence B is valid on the definition\nD in the system S*\n(notation \n ⊨*,D B)\n iff for all\nclassical ground models M, we have \n M ⊨*,D B.\n\nA sentence B is valid on the definition\nD in the system S#\n(notation\n ⊨#,D B)\n iff\nfor all classical ground models M, we have \n M ⊨#,D B.\n\n", "\n\nOne of Gupta and Belnap's principle open questions is whether there is\na complete calculus for these systems: that is, whether, for each\ndefinition D, either of the following two sets of sentences is\nrecursively axiomatizable:\n {B : ⊨*,D B}\nand \n {B : ⊨#,D B}.\n Kremer 1993 proves that the answer is no: he shows that there is a\ndefinition D such that each of these sets of sentences is of\ncomplexity at least Π12, thereby putting a\nlower limit on the complexity of S* and\nS#. (Antonelli 1994a and 2002 shows that\nthis is also an upper limit.) ", "\n Kremer's proof exploits an intimate relationship between circular\ndefinitions understood revision-theoretically and circular\ndefinitions understood as inductive definitions: the theory\nof inductive definitions has been quite well understood for some\ntime. In particular, Kremer proves that every inductively defined\nconcept can be revision-theoretically defined. The expressive power\nand other aspects of the revision-theoretic treatment of circular\ndefinitions is the topic of much interesting work: see Welch 2001,\nLöwe 2001, Löwe and Welch 2001, and Kühnberger et\nal. 2005." ], "subsection_title": "5.4 Revision theory for circularly defined concepts" }, { "content": [ "\n\nThe RTT is a clear example of a semantically motivated theory of\ntruth. Quite a different tradition seeks to give a satisfying\naxiomatic theory of truth. Granted we cannot retain all of classical\nlogic and all of our intuitive principles regarding truth, especially\nif we allow vicious self-reference. But maybe we can arrive at\nsatisfying axiom systems for truth, that, for example, maintain\nconsistency and classical logic, but give up only a little bit when it\ncomes to our intuitive principles concerning truth, such as the\nT-biconditionals (interpreted classically); or maintain consistency\nand all of the T-biconditionals, but give up only a little bit of\nclassical logic. Halbach 2011 comprehensively studies such axiomatic\ntheories (mainly those that retain classical logic), and Horsten 2011\nis in the same tradition. Both Chapter 14 of Halbach 2011 and Chapter\n8 of Horsten 2011 study the relationship between the Friedman-Sheard\ntheory FS and the revision semantics, with some interesting\nresults. For more work on axiomatic systems and the RTT, see Horsten\net al 2012.", "\n\nField 2008 makes an interesting contribution to axiomatic theorizing\nabout truth, even though most of the positive work in the book\nconsists of model building and is therefore semantics. In particular,\nField is interested in producing a theory as close to classical logic\nas possible, which at the same time retains all T-biconditionals (the\nconditional itself will be nonclassical) and which at the same time\ncan express, in some sense, the claim that such and such a sentence is\ndefective. Field uses tools from multivalued logic, fixed-point\nsemantics, and revision theory to build models showing, in effect,\nthat a very attractive axiomatic system is consistent. Field’s\nconstruction is an intricate interplay between using fixed-point\nconstructions for successively interpreting T, and revision sequences\nfor successively interpreting the nonclassical conditional — the\nfinal interpretation being determined by a sort of\nsuper-revision-theoretic process." ], "subsection_title": "5.5 Axiomatic Theories of Truth and the Revision Theory" }, { "content": [ "\n\nGiven Gupta and Belnap's general revision-theoretic treatment of\ncircular definitions-of which their treatment of truth is a\nspecial case-one would expect revision-theoretic ideas to be applied\nto other concepts. Antonelli 1994b applies these ideas to\nnon-well-founded sets: a non-well-founded set X can be\nthought of as circular, since, for some X0,\n…, Xn we have X ∈\nX0 ∈ … ∈\nXn ∈ X. Chapuis 2003\napplies revision-theoretic ideas to rational decision making. Also,\nsee Wang 2011 for a discussion of revision theory and abstract\nobjects, and Asmus 2013 for a discussion of revision theory and\nvagueness.", "\n\nIn the last decade, there has been increasing interest in bridging the\ngap between classic debates on the nature of truth —\ndeflationism, the correspondence theory, minimalism, pragmatism, and\nso on — and formal work on truth, motivated by the liar's\nparadox. The RTT is tied to pro-sententialism by Belnap 2006;\ndeflationism, by Yaqūb 2008; and minimalism, by Restall 2005.", "We must also mention Gupta 2006. In this work, Gupta argues that an\nexperience provides the experiencer, not with a straightforward\nentitlement to a proposition, but rather with a hypothetical\nentitlement: as explicated in Berker 2011, if subject S has\nexperience e and is entitled to hold view v (where\nS’s view is the totality of S’s concepts,\nconceptions, and beliefs), then S is entitled to believe a certain\nclass of perceptual judgements, Γ(v). (Berker uses\n“propositions” instead of “perceptual judgements” in his formulation.)\nBut this generates a problem: how is S entitled to hold a view? There\nseems to be a circular interdependence between entitlements to views\nand entitlements to perceptual judgements. Here, Gupta appeals to a\ngeneral form of revision theory — generalizing beyond both the\nrevision theory of truth and the revision theory of circularly defined\nconcepts (Section 5.4, above) — to given an account of how\n“hypothetical perceptual entitlements could yield categorical\nentitlements” (Berker 2011)." ], "subsection_title": "5.6 Applications" } ] } ]

[ "Antonelli, G.A., 1994a, “The complexity of\nrevision”, Notre Dame Journal of Formal Logic, 35:\n204–218. ", "–––, 1994b, “Non-well-founded sets via revision\nrules”,\nJournal of Philosophical Logic, 23: 633–679. ", "–––, 2002, “The complexity of revision,\nrevised”, Notre Dame Journal of Formal Logic, 43:\n75–78. ", "Asmus C.M., 2013, “Vagueness and revision\nsequences”, Synthese, 190: 953–974.", "Belnap, N., 1982, “Gupta's rule of revision theory of truth”,\nJournal of Philosophical Logic, 11: 103–116. ", "–––, 2006, “Prosentence, Revision, Truth, and\nParadox”, Philosophy and Phenomenological Research, 73:\n705–712.", "Berker S., 2011, “Gupta’s\ngambit”, Philosophical Studies, 152: 17–39.", "Chapuis, A., 1996, “Alternate revision theories of truth”,\nJournal of Philosophical Logic, 25: 399–423. ", "–––, 2003, “An application of circular definitions:\nrational decision”, in Löwe, Malzkorn, and Räsch (eds.),\nFoundations of the Formal Sciences II: Applications of\nMathematical Logic in Philosophy and Linguistics, Dordrecht:\nKluwer, 47–54. ", "Field H., 2008, Saving Truth from Paradox, Oxford: Oxford\nUniversity Press.", "Gupta, A., 1982, “Truth and paradox”, Journal of\nPhilosophical Logic, 11: 1–60. ", "–––, 2006, Empiricism and Experience, Oxford: Oxford\nUniversity Press.", "Gupta, A., and Belnap, N., 1993, The Revision Theory of\nTruth, Cambridge, MA: MIT Press. ", "Halbach, V., 2011, Axiomatic Theories of Truth,\nCambridge: Cambridge University Press.", "Hammer, E., 2003, “The Revision Theory of Truth”, \nThe Stanford Encyclopedia of Philosophy (Spring 2003 Edition),\n Edward N. Zalta (ed.), URL =\n <https://plato.stanford.edu/archives/spr2003/entries/truth-revision/>.", "Herzberger, H.G., 1982, “Notes on naive\nsemantics”, Journal of Philosophical Logic, 11:\n61–102. ", "–––, 1982, “Naive semantics and the liar\nparadox”,\nJournal of Philosophy, 79: 479–497. ", "Horsten, L., 2011, The Tarskian Turn: Deflationism and\nAxiomatic Truth, Cambridge, MA: MIT Press.", "Horsten, L., Leigh, G.E., Leitgeb, H., and Welch, P., 2012,\n“Revision Revisited”, The Review of Symbolic\nLogic, 5: 642–665.", "Kremer, M., 1988, “Kripke and the logic of\ntruth”, Journal of Philosophical Logic, 17:\n225–78. ", "Kremer, P., 1993, “The Gupta-Belnap systems\nS# and S* are\nnot axiomatisable”, Notre Dame Journal of Formal Logic, 34:\n583–596. ", "–––, 2010, “How Truth Behaves When There’s No\nVicious Reference”, Journal of Philosophical Logic, 39:\n345–367.", "Kripke, S., 1975, “Outline of a theory of\ntruth”, Journal of Philosophy, 72: 690–716. ", "Kühnberger, K., Löwe, B., Möllerfeld, M., and\nWelch, P., 2005, “Comparing inductive and circular definitions:\nparameters, complexity and games”, Studia Logica, 81:\n79–98.", "Löwe, B., 2001 “Revision sequences and computers with an infinite\namount of time”, Journal of Logic and Computation, 11: 25–40. ", "Löwe, B., and Welch, P., 2001, “Set-theoretic absoluteness\nand the revision theory of truth”, Studia Logica, 68(1):\n21–41.", "Martin, R., and Woodruff, P., 1975, “On representing\n‘True-in-L’ in L”, Philosophia, 5:\n217–221.", "Restall, G., 2005, “Minimalists about Truth Can (and Should)\nBe Epistemicists, and it Helps if They Are Revision Theorists\ntoo”, in Deflation and Paradox, JC Beall and\n B. Armour-Garb (eds.), Oxford: Oxford University Press,\n97–106.", "Wang, W., 2011, “Theories of abstract objects without ad hoc\nrestriction”, Erkenntnis 74: 1–15.", "Welch, P., 2001, “On Gupta-Belnap revision theories of truth,\nKripkean fixed points, and the Next stable set”, Bulletin for\nSymbolic Logic, 7: 345–360.", "Wintein, S., 2014, “Alternative Ways for Truth to Behave\nWhen There's no Vicious Reference”, Journal of\nPhilosophical Logic 43: 665–690.", "Yaqūb, A., 1993, The Liar Speaks the Truth : A Defense\nof the Revision Theory of Truth, Oxford: Oxford University\nPress.", "–––, 2008, “Two types of\ndeflationist”, Synthese, 165: 77–106." ]

[ { "href": "../curry-paradox/", "text": "Curry’s paradox" }, { "href": "../definitions/", "text": "definitions" }, { "href": "../liar-paradox/", "text": "liar paradox" }, { "href": "../tarski-truth/", "text": "Tarski, Alfred: truth definitions" }, { "href": "../truth/", "text": "truth" }, { "href": "../truth-axiomatic/", "text": "truth: axiomatic theories of" } ]

[ "\nChurch’s type theory, aka simple type theory, is a formal\nlogical language which includes classical first-order and\npropositional logic, but is more expressive in a practical sense. It\nis used, with some modifications and enhancements, in most modern\napplications of type theory. It is particularly well suited to the\nformalization of mathematics and other disciplines and to specifying\nand verifying hardware and software. It also plays an important role\nin the study of the formal semantics of natural language. When\nutilizing it as a meta-logic to semantically embed expressive\n(quantified) non-classical logics further topical applications are\nenabled in artificial intelligence and philosophy.", "\nA great wealth of technical knowledge can be expressed very naturally\nin it. With possible enhancements, Church’s type theory\nconstitutes an excellent formal language for representing the\nknowledge in automated information systems, sophisticated automated\nreasoning systems, systems for verifying the correctness of\nmathematical proofs, and a range of projects involving logic and\nartificial intelligence. Some examples and further references are\ngiven in Sections\n 1.2.2\n and\n 5\n below. ", "\nType theories are also called higher-order logics, since they allow\nquantification not only over individual variables (as in first-order\nlogic), but also over function, predicate, and even higher order\nvariables. Type theories characteristically assign types to entities,\ndistinguishing, for example, between numbers, sets of numbers,\nfunctions from numbers to sets of numbers, and sets of such functions.\nAs illustrated in\n Section 1.2.2\n below, these distinctions allow one to discuss the conceptually rich\nworld of sets and functions without encountering the paradoxes of\nnaive set theory.", "\nChurch’s type theory is a formulation of type theory that was\nintroduced by Alonzo Church in Church 1940. In certain respects, it is\nsimpler and more general than the type theory introduced by Bertrand\nRussell in Russell 1908 and Whitehead & Russell 1927a. Since\nproperties and relations can be regarded as functions from entities to\ntruth values, the concept of a function is taken as primitive in\nChurch’s type theory, and the λ-notation which Church\nintroduced in Church 1932 and Church 1941 is incorporated into the\nformal language. Moreover, quantifiers and description operators are\nintroduced in a way so that additional binding mechanisms can be\navoided, λ-notation is reused instead. λ-notation is\nthus the only binding mechanism employed in Church’s type\ntheory." ]

[ { "content_title": "1. Syntax", "sub_toc": [ "1.1 Fundamental Ideas", "1.2 Formulas", "1.3 Axioms and Rules of Inference", "1.4 A Formulation Based on Equality" ] }, { "content_title": "2. Semantics", "sub_toc": [] }, { "content_title": "3. Metatheory", "sub_toc": [ "3.1 Lambda-Conversion", "3.2 Higher-Order Unification", "3.3 A Unifying Principle", "3.4 Cut-Elimination and Cut-Simulation", "3.5 Expansion Proofs", "3.6 The Decision Problem" ] }, { "content_title": "4. Automation", "sub_toc": [ "4.1 Machine-Oriented Proof Calculi", "4.2 Early Proof Assistants", "4.3 Automated Theorem Provers", "4.4 (Counter-)Model Finding" ] }, { "content_title": "5. Applications", "sub_toc": [ "5.1 Semantics of Natural Language", "5.2 Mathematics and Computer Science", "5.3 Computational Metaphysics and Artificial Intelligence" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Syntax", "subsections": [ { "content": [ "\nWe start with an informal description of the fundamental ideas\nunderlying the syntax of Church’s formulation of type\ntheory.", "\nAll entities have types, and if α and β are types, the type\nof functions from elements of type β to elements of type α\nis written as \\((\\alpha \\beta)\\). (This notation was introduced by\nChurch, but some authors write \\((\\beta \\rightarrow \\alpha)\\) instead\nof \\((\\alpha \\beta)\\). See, for example, Section 2 of the entry on\n type theory.)", "\nAs noted by Schönfinkel (1924), functions of more than one\nargument can be represented in terms of functions of one argument when\nthe values of these functions can themselves be functions. For\nexample, if f is a function of two arguments, for each element\nx of the left domain of f there is a function g\n(depending on x) such that \\(gy = fxy\\) for each element\ny of the right domain of f. We may now write \\(g = fx\\),\nand regard f as a function of a single argument, whose value\nfor any argument x in its domain is a function \\(fx\\), whose\nvalue for any argument y in its domain is fxy.", "\nFor a more explicit example, consider the function + which carries any\npair of natural numbers to their sum. We may denote this function by\n\\(+_{((\\sigma \\sigma)\\sigma)}\\), where \\(\\sigma\\) is the type of\nnatural numbers. Given any number x, \\([+_{((\\sigma\n\\sigma)\\sigma)}x]\\) is the function which, when applied to any number\ny, gives the value \\([[+_{((\\sigma \\sigma)\\sigma)}x]y]\\), which\nis ordinarily abbreviated as \\(x + y\\). Thus \\([+_{((\\sigma\n\\sigma)\\sigma)}x]\\) is the function of one argument which adds\nx to any number. When we think of \\(+_{((\\sigma\n\\sigma)\\sigma)}\\) as a function of one argument, we see that it maps\nany number x to the function \\([+_{((\\sigma\n\\sigma)\\sigma)}x]\\).", "\nMore generally, if f is a function which maps n-tuples\n\\(\\langle w_{\\beta},x_{\\gamma},\\ldots ,y_{\\delta},z_{\\tau}\\rangle\\) of\nelements of types \\(\\beta\\), \\(\\gamma\\),…, \\(\\delta\\)\n,\\(\\tau\\), respectively, to elements of type α, we may assign to\nf the type \\(((\\ldots((\\alpha \\tau)\\delta)\\ldots\n\\gamma)\\beta)\\). It is customary to use the convention of association\nto the left to omit parentheses, and write this type symbol simply as\n\\((\\alpha \\tau \\delta \\ldots \\gamma \\beta)\\).", "\nA set or property can be represented by a function (often called\ncharacteristic function) which maps elements to truth values,\nso that an element is in the set, or has the property, in question iff\nthe function representing the set or property maps that element to\ntruth. When a statement is asserted, the speaker means that it is\ntrue, so that \\(s x\\) means that \\(s x\\) is true, which also expresses\nthe assertions that s maps x to truth and that \\(x \\in\ns\\). In other words, \\(x \\in s\\) iff \\(s x\\). We take \\({o}\\) as the\ntype symbol denoting the type of truth values, so we may speak of any\nfunction of type \\(({o}\\alpha)\\) as a set of elements of type\nα. A function of type \\((({o}\\alpha)\\beta)\\) is a binary\nrelation between elements of type β and elements of type α.\nFor example, if \\(\\sigma\\) is the type of the natural numbers, and\n\\(<\\) is the order relation between natural numbers, \\(<\\) has\ntype \\(({o}\\sigma \\sigma)\\), and for all natural numbers x and\n\\(y, {<}x y\\) (which we ordinarily write as \\(x < y)\\) has the\nvalue truth iff x is less than y. Of course, \\(<\\)\ncan also be regarded as the function which maps each natural number\nx to the set \\(<x\\) of all natural numbers y such\nthat x is less than y. Thus sets, properties, and\nrelations may be regarded as particular kinds of functions.\nChurch’s type type theory is thus a logic of functions, and, in\nthis sense, it is in the tradition of the work of Frege’s\nBegriffsschrift. The opposite approach would be to reduce\nfunctions to relations, which was the approach taken by Whitehead and\nRussell (1927a) in the Principia Mathematica.", "\nExpressions which denote elements of type α are called wffs\nof type α. Thus, statements of type theory are wffs of type\n\\({o}\\).", "\nIf \\(\\bA_{\\alpha}\\) is a wff of type α in which \\(\\bu_{\\alpha\n\\beta}\\) is not free, the function (associated with) \\(\\bu_{\\alpha\n\\beta}\\) such that \\(\\forall \\bv_{\\beta}[\\bu_{\\alpha \\beta}\\bv_{\\beta}\n= \\bA_{\\alpha}]\\) is denoted by \\([\\lambda \\bv_{\\beta}\\bA_{\\alpha}]\\).\nThus \\(\\lambda \\bv_{\\beta}\\) is a variable-binder, like \\(\\forall\n\\bv_{\\beta}\\) or \\(\\exists \\bv_{\\beta}\\) (but with a quite different\nmeaning, of course); λ is known as an abstraction\noperator. \\([\\lambda \\bv_{\\beta}\\bA_{\\alpha}]\\) denotes the\nfunction whose value on any argument \\(\\bv_{\\beta}\\) is\n\\(\\bA_{\\alpha}\\), where \\(\\bv_{\\beta}\\) may occur free in\n\\(\\bA_{\\alpha}\\). For example, \\([\\lambda n_{\\sigma}[4\\cdot\nn_{\\sigma}+3]]\\) denotes the function whose value on any natural\nnumber n is \\(4\\cdot n+3\\). Hence, when we apply this function\nto the number 5 we obtain \\([\\lambda n_{\\sigma}[4\\cdot n_{\\sigma}+3]]5\n= 4\\cdot 5+3 = 23\\).", "\nWe use \\(\\textsf{Sub}(\\bB,\\bv,\\bA)\\) as a notation for the result of\nsubstituting \\(\\bB\\) for \\(\\bv\\) in \\(\\bA\\), and\n\\(\\textsf{SubFree}(\\bB,\\bv,\\bA)\\) as a notation for the result of\nsubstituting \\(\\bB\\) for all free occurrences of \\(\\bv\\) in \\(\\bA\\).\nThe process of replacing \\([\\lambda\n\\bv_{\\beta}\\bA_{\\alpha}]\\bB_{\\beta}\\) by\n\\(\\textsf{SubFree}(\\bB_{\\beta},\\bv_{\\beta},\\bA_{\\alpha})\\) (or\nvice-versa) is known as β-conversion, which is one form\nof λ-conversion. Of course, when \\(\\bA_{{o}}\\) is a\nwff of type \\({o}\\), \\([\\lambda \\bv_{\\beta}\\bA_{{o}}]\\) denotes the\nset of all elements \\(\\bv_{\\beta}\\) (of type \\(\\beta)\\) of which\n\\(\\bA_{{o}}\\) is true; this set may also be denoted by\n\\(\\{\\bv_{\\beta}|\\bA_{{o}}\\}\\). For example, \\([\\lambda x\\ x<y]\\)\ndenotes the set of x such that x is less than y\n(as well as that property which a number x has if it is less\nthan y). In familiar set-theoretic notation, ", "\nwould be written", "\n(By the Axiom of Extensionality for truth values, when \\(\\bC_{{o}}\\)\nand \\(\\bD_{{o}}\\) are of type \\({o}, \\bC_{{o}} \\equiv \\bD_{{o}}\\) is\nequivalent to \\(\\bC_{{o}} = \\bD_{{o}}\\).)", "\nPropositional connectives and quantifiers can be assigned types and\ncan be denoted by constants of these types. The negation function maps\ntruth values to truth values, so it has type \\(({o}{o})\\). Similarly,\ndisjunction and conjunction (etc.) are binary functions from truth\nvalues to truth values, so they have type \\(({o}{o}{o})\\).", "\nThe statement \\(\\forall \\bx_{\\alpha}\\bA_{{o}}\\) is true iff the set\n\\([\\lambda \\bx_{\\alpha}\\bA_{{o}}]\\) contains all elements of type\nα. A constant \\(\\Pi_{{o}({o}\\alpha)}\\) can be introduced (for\neach type symbol \\(\\alpha)\\) to denote a property of sets: a set\n\\(s_{{o}\\alpha}\\) has the property \\(\\Pi_{{o}({o}\\alpha)}\\) iff\n\\(s_{{o}\\alpha}\\) contains all elements of type α. With this\ninterpretation ", "\nshould be true, as well as ", "\nfor any wff \\(\\bA_{{o}}\\) and variable \\(\\bx_{\\alpha}\\). Since by\nλ-conversion we have ", "\nequation can be written more simply as ", "\nThus, \\(\\forall \\bx_{\\alpha}\\) can be defined in terms of\n\\(\\Pi_{{o}({o}\\alpha)}\\), and λ is the only variable-binder\nthat is needed." ], "subsection_title": "1.1 Fundamental Ideas" }, { "content": [ "\nBefore we state the definition of a “formula”, a word of\ncaution is in order. The reader may be accustomed to thinking of a\nformula as an expression which plays the role of an assertion in a\nformal language, and of a term as an expression which designates an\nobject. Church’s terminology is somewhat different, and provides\na uniform way of discussing expressions of many different types. What\nwe call well-formed formula of type α\n(\\(\\textrm{wff}_{\\alpha}\\)) below would in more standard terminology\nbe called term of type α, and then only certain terms,\nnamely those with type \\({o}\\), would be called formulas. Anyhow, in\nthis entry we have decided to stay with Church’s original\nterminology. Another remark concerns the use of some specific\nmathematical notation. In what follows, the entry distinguishes\nbetween the symbols \\(\\imath\\), \\(\\iota_{(\\alpha({o}\\alpha))}\\), and \\(\\atoi\\). The first is\nthe symbol used for the type of individuals; the second is the symbol\nused for a logical constant (see\n Section 1.2.1\n below); the third is the symbol used as a variable-binding operator\nthat represents the definite description “the” (see\n Section 1.3.4).\n The reader should not confuse them and check to see that the browser\nis displaying these symbols correctly.", "\nType symbols are defined inductively as follows:", "\nThe primitive symbols are the following:", "\nA formula is a finite sequence of primitive symbols. Certain\nformulas are called well-formed formulas (wffs). We\nwrite \\(\\textrm{wff}_{\\alpha}\\) as an abbreviation for wff of\ntype α, and define this concept inductively as follows:", "\nNote, for example, that by (a) \\(\\nsim_{({o}{o})}\\) is a\nwff\\(_{({o}{o})}\\), so by (b) if \\(\\bA_{{o}}\\) is a wff\\(_{{o}}\\),\nthen \\([\\nsim_{({o}{o})}\\bA_{{o}}]\\) is a wff\\(_{{o}}\\). Usually, the\nlatter wff will simply be written as \\(\\nsim \\bA\\). It is often\nconvenient to avoid parentheses, brackets and type symbols, and use\nconventions for omitting them. For formulas we use the convention of\nassociation to the right, and we may write \\(\\lor_{((oo)o)}\\bA_{{o}}\n\\bB_{{o}}\\) instead of \\([[\\lor_{((oo)o)}\\bA_{{o}}] \\bB_{{o}}]\\). For\ntypes the corresponding convention is association to the left, and we\nmay write \\(ooo\\) instead of \\(((oo)o)\\).", "\nThe last definition is known as the Leibnizian definition of equality.\nIt asserts that x and y are the same if y has\nevery property that x has. Actually, Leibniz called his\ndefinition “the identity of indiscernibles” and gave it in\nthe form of a biconditional: x and y are the same if\nx and y have exactly the same properties. It is not\ndifficult to show that these two forms of the definition are logically\nequivalent.", "\nWe now provide a few examples to illustrate how various assertions and\nconcepts can be expressed in Church’s type theory.", "\n Example 1 To express the assertion that\n“Napoleon is charismatic” we introduce constants\n\\(\\const{Charismatic}_{{o}\\imath}\\) and \\(\\const{Napoleon}_{\\imath}\\),\nwith the types indicated by their subscripts and the obvious meanings,\nand assert the wff ", "\nIf we wish to express the assertion that\n“Napoleon has all the properties of a great\ngeneral”, we might consider interpreting this to mean that\n“Napoleon has all the properties of some great\ngeneral”, but it seems more appropriate to interpret this\nstatement as meaning that “Napoleon has all the properties\nwhich all great generals have”. If the constant\n\\(\\const{GreatGeneral}_{{o}\\imath}\\) is added to the formal language,\nthis can be expressed by the wff ", "\nAs an example of such a property, we note that the sentence\n“Napoleon’s soldiers admire him” can be\nexpressed in a similar way by the wff ", "\nBy λ-conversion, this is equivalent to ", "\nThis statement asserts that one of the properties which Napoleon has\nis that of being admired by his soldiers. The property itself is\nexpressed by the wff ", "\nExample 2 We illustrate some potential applications\nof type theory with the following fable.", "\n\n\nA rich and somewhat eccentric lady named Sheila has an ostrich and a\ncheetah as pets, and she wishes to take them from her hotel to her\nremote and almost inaccessible farm. Various portions of the trip may\ninvolve using elevators, boxcars, airplanes, trucks, very small boats,\ndonkey carts, suspension bridges, etc., and she and the pets will not\nalways be together. She knows that she must not permit the ostrich and\nthe cheetah to be together when she is not with them.\n", "\nWe consider how certain aspects of this problem can be formalized so\nthat Sheila can use an automated reasoning system to help analyze the\npossibilities.", "\nThere will be a set Moments of instants or intervals of time\nduring the trip. She will start the trip at the location\n\\(\\const{Hotel}\\) and moment \\(\\const{Start}\\), and end it at the\nlocation \\(\\const{Farm}\\) and moment \\(\\const{Finish}\\). Moments will\nhave type \\(\\tau\\), and locations will have type \\(\\varrho\\). A\nstate will have type \\(\\sigma\\) and will specify the location\nof Sheila, the ostrich, and the cheetah at a given moment. A\nplan will specify where the entities will be at each moment\naccording to this plan. It will be a function from moments to states,\nand will have type \\((\\sigma \\tau)\\). The exact representation of\nstates need not concern us, but there will be functions from states to\nlocations called \\(\\const{LocationOfSheila}\\),\n\\(\\const{LocationOfOstrich}\\), and \\(\\const{LocationOfCheetah}\\) which\nprovide the indicated information. Thus,\n\\(\\const{LocationOfSheila}_{\\varrho \\sigma}[p_{\\sigma \\tau}t_{\\tau}]\\)\nwill be the location of Sheila according to plan \\(p_{\\sigma \\tau}\\)\nat moment \\(t_{\\tau}\\). The set \\(\\const{Proposals}_{{o}(\\sigma\n\\tau)}\\) is the set of plans Sheila is considering.", "\nWe define a plan p to be acceptable if, according to that plan,\nthe group starts at the hotel, finishes at the farm, and whenever the\nostrich and the cheetah are together, Sheila is there too. Formally,\nwe define \\(\\const{Acceptable}_{{o}(\\sigma \\tau)}\\) as ", "\nWe can express the assertion that Sheila has a way to accomplish her\nobjective with the formula", "\nExample 3 We now provide a mathematical example.\nMathematical ideas can be expressed in type theory without introducing\nany new constants. An iterate of a function f from a\nset to itself is a function which applies f one or more times.\nFor example, if \\(g(x) = f(f(f(x)))\\), then g is an iterate of\nf.\n\\([\\text{ITERATE+}_{{o}(\\imath\\imath)(\\imath\\imath)}f_{\\imath\\imath}g_{\\imath\\imath}]\\)\nmeans that \\(g_{\\imath\\imath}\\) is an iterate of \\(f_{\\imath\\imath}\\).\n\\(\\text{ITERATE+}_{{o}(\\imath\\imath)(\\imath\\imath)}\\) is defined\n(inductively) as ", "\nThus, g is an iterate of f if g is in every set\np of functions which contains f and which contains the\nfunction \\(\\lambda\nx_{\\imath}f_{\\imath\\imath}[j_{\\imath\\imath}x_{\\imath}]\\) (i.e.,\nf composed with j) whenever it contains j.", "\nA fixed point of f is an element y such that\n\\(f(y) = y\\).", "\nIt can be proved that if some iterate of a function f has a\nunique fixed point, then f itself has a fixed point. This\ntheorem can be expressed by the wff ", "\nSee Andrews et al. 1996, for a discussion of how this theorem, which\nis called THM15B, can be proved automatically.", "\nExample 4 An example from philosophy is\nGödel’s variant of the ontological argument for the\nexistence of God. This example illustrates two interesting\naspects:", "\nExample 5 Suppose we omit the use of type symbols in\nthe definitions of wffs. Then we can write the formula \\(\\lambda\nx\\nsim[xx]\\), which we shall call \\(\\textrm{R}\\). It can be regarded as\ndenoting the set of all sets x such that x is not in\nx. We may then consider the formula \\([\\textrm{R R}]\\), which\nexpresses the assertion that \\(\\textrm{R}\\) is in itself. We can clearly\nprove \\([\\textrm{R R}] \\equiv [[\\lambda x\\nsim [xx]] \\textrm{R}]\\), so by\nλ-conversion we can derive \\([\\textrm{R R}] \\equiv\\,\n\\nsim[\\textrm{R R}]\\), which is a contradiction. This is\nRussell’s paradox. Russell’s discovery of this paradox\n(Russell 1903, 101-107) played a crucial role in the development of\ntype theory. Of course, when type symbols are present, \\(\\textrm{R}\\) is not\nwell-formed, and the contradiction cannot be derived." ], "subsection_title": "1.2 Formulas" }, { "content": [ "\nWe start by listing the axioms for what we shall call elementary\ntype theory. ", "\nThe theorems of elementary type theory are those theorems which can be\nderived, using the rules of inference, from Axioms\n(1)–\\((6^{\\alpha})\\) (for all type symbols \\(\\alpha)\\). We shall\nsometimes refer to elementary type theory as \\(\\cT\\). It embodies the\nlogic of propositional connectives, quantifiers, and\nλ-conversion in the context of type theory.", "\nTo illustrate the rules and axioms introduced above, we give a short\nand trivial proof in \\(\\cT\\). Following each wff of the proof, we\nindicate how it was inferred. (The proof is actually quite\ninefficient, since line 3 is not used later, and line 7 can be derived\ndirectly from line 5 without using line 6. The additional proof lines\nhave been inserted to illustrate some relevant aspects. For the sake\nof readability, many brackets have been deleted from the formulas in\nthis proof. The diligent reader should be able to restore them.) ", "\nNote that (3) can be written as ", "\nand (7) can be written as ", "\nWe have thus derived a well known law of quantification theory. We\nillustrate one possible interpretation of the wff \\((7')\\) (which\nis closely related to Axiom 6) by considering a situation in which a\nrancher puts some horses in a corral and leaves for the night. Later,\nhe cannot remember whether he closed the gate to the corral. While\nreflecting on the situation, he comes to a conclusion which can be\nexpressed by \\((7')\\) if we take the horses to be the elements of\ntype \\(\\imath\\), interpret \\(p_{{o}}\\) to mean “the gate was\nclosed”, and interpret \\(r_{{o}\\imath}\\) so that\n\\(r_{{o}\\imath}x_{\\imath}\\) asserts “\\(x_{\\imath}\\) left the\ncorral”. With this interpretation, \\((7')\\) says ", "\n\n\nIf it is true of every horse that the gate was closed or that the\nhorse left the corral, then the gate was closed or every horse left\nthe corral.\n", "\nTo the axioms listed above we add the axioms below to obtain\nChurch’s type theory.", "\nThe axioms of boolean and functional extensionality are the following:\n", "\nChurch did not include Axiom \\(7^{{o}}\\) in his list of axioms in\nChurch 1940, but he mentioned the possibility of including it. Henkin\ndid include it in Henkin 1950.", "\nThe expression ", "\nstands for ", "\nFor example, ", "\nstands for ", "\nBy λ-conversion, this is equivalent to ", "\nwhich reduces by λ-conversion to ", "\nThis asserts that there is a unique element which has the property\n\\(P_{{o}\\alpha}\\). From this example we can see that in general,\n\\(\\exists_1\\bx_{\\alpha}\\bA_{{o}}\\) expresses the assertion that\n“there is a unique \\(\\bx_{\\alpha}\\) such that\n\\(\\bA_{{o}}\\)”.", "\nWhen there is a unique such element \\(\\bx_{\\alpha}\\), it is convenient\nto have the notation \\(\\atoi\\bx_{\\alpha}\\bA_{{o}}\\) to represent the\nexpression “the \\(\\bx_{\\alpha}\\) such that \\(\\bA_{{o}}\\)”.\nRussell showed in Whitehead & Russell 1927b how to provide\ncontextual definitions for such notations in his formulation of type\ntheory. In Church’s type theory \\(\\atoi\\bx_{\\alpha}\\bA_{{o}}\\)\nis defined as \\(\\iota_{\\alpha({o}\\alpha)}[\\lambda\n\\bx_{\\alpha}\\bA_{{o}}]\\). Thus, \\(\\atoi\\) behaves like a\nvariable-binding operator, but it is defined in terms of λ with\nthe aid of the constant \\(\\iota_{\\alpha({o}\\alpha)}\\). Thus, λ\nis still the only variable-binding operator that is needed.", "\nSince \\(\\bA_{{o}}\\) describes \\(\\bx_{\\alpha},\n\\iota_{\\alpha({o}\\alpha)}\\) is called a description operator.\nAssociated with this notation is the following:", "\nThis says that when the set \\(p_{{o}\\alpha}\\) has a unique member,\nthen \\(\\iota_{\\alpha({o}\\alpha)}p_{{o}\\alpha}\\) is in\n\\(p_{{o}\\alpha}\\), and therefore is that unique member. Thus, this\naxiom asserts that \\(\\iota_{\\alpha({o}\\alpha)}\\) maps one-element sets\nto their unique members.", "\nIf from certain hypotheses one can prove ", "\nthen by using Axiom \\(8^{\\alpha}\\) one can derive ", "\nwhich can also be written as ", "\nWe illustrate the usefulness of the description operator with a small\nexample. Suppose we have formalized the theory of real numbers, and\nour theory has constants \\(1_{\\varrho}\\) and \\(\\times_{\\varrho \\varrho\n\\varrho}\\) to represent the number 1 and the multiplication function,\nrespectively. (Here \\(\\varrho\\) is the type of real numbers.) To\nrepresent the multiplicative inverse function, we can define the wff\n\\(\\textrm{INV}_{\\varrho \\varrho}\\) as ", "\nOf course, in traditional mathematical notation we would not write the\ntype symbols, and we would write \\(\\times_{\\varrho \\varrho\n\\varrho}z_{\\varrho}x_{\\varrho}\\) as \\(z \\times x\\) and write\n\\(\\textrm{INV}_{\\varrho \\varrho}z\\) as \\(z^{-1}\\). Thus \\(z^{-1}\\) is\ndefined to be that x such that \\(z \\times x = 1\\). When\nZ is provably not 0, we will be able to prove \\(\\exists_1\nx_{\\varrho}[\\times_{\\varrho \\varrho \\varrho} \\textrm{Z x}_{\\varrho} =\n1_{\\varrho}]\\) and \\(Z \\times Z^{-1} = 1\\), but if we cannot establish\nthat Z is not 0, nothing significant about \\(Z^{-1}\\) will be\nprovable.", "\nThe Axiom of Choice can be expressed as follows in Church’s type\ntheory: ", "\n\\((9^{\\alpha})\\) says that the choice function\n\\(\\iota_{\\alpha({o}\\alpha)}\\) chooses from every nonempty set\n\\(p_{{o}\\alpha}\\) an element, designated as\n\\(\\iota_{\\alpha({o}\\alpha)}p_{{o}\\alpha}\\), of that set. When this\nform of the Axiom of Choice is included in the list of axioms,\n\\(\\iota_{\\alpha({o}\\alpha)}\\) is called a selection operator instead\nof a description operator, and \\(\\atoi\\bx_{\\alpha} \\bA_{{o}}\\) means\n“an \\(\\bx_{\\alpha}\\) such that \\(\\bA_{{o}}\\)” when there\nis some such element \\(\\bx_{\\alpha}\\). These selection operators have\nthe same meaning as Hilbert’s \\(\\epsilon\\)-operator (Hilbert\n1928). However, we here provide one such operator for each type\nα.", "\nIt is natural to call \\(\\atoi\\) a definite description operator in\ncontexts where \\(\\atoi\\bx_{\\alpha}\\bA_{{o}}\\) means “the\n\\(\\bx_{\\alpha}\\) such that \\(\\bA_{{o}}\\)”, and to call it an\nindefinite description operator in contexts where\n\\(\\atoi\\bx_{\\alpha}\\bA_{{o}}\\) means “an \\(\\bx_{\\alpha}\\) such\nthat \\(\\bA_{{o}}\\)”.", "\nClearly the Axiom of Choice implies the Axiom of Descriptions, but\nsometimes formulations of type theory are used which include the Axiom\nof Descriptions, but not the Axiom of Choice.", "\nAnother formulation of the Axiom of Choice simply asserts the\nexistence of a choice function without explicitly naming it: ", "\nNormally when one assumes the Axiom of Choice in type theory, one\nassumes it as an axiom schema, and asserts AC\\(^{\\alpha}\\) for each\ntype symbol α. A similar remark applies to the axioms for\nextensionality and description. However, modern proof systems for\nChurch’s type theory, which are, e.g., based on resolution, do\nin fact avoid the addition of such axiom schemata for reasons as\nfurther explained in\n Sections 3.4\n and\n 4\n below. They work with more constrained, goal-directed proof rules\ninstead.", "\nBefore proceeding, we need to introduce some terminology. \\(\\cQ_0\\) is\nan alternative formulation of Church’s type theory which will be\ndescribed in\n Section 1.4\n and is equivalent to the system described above using Axioms\n(1)–(8). A type symbol is propositional if the only symbols\nwhich occur in it are \\({o}\\) and parentheses.", "\nYasuhara (1975) defined the relation “\\(\\ge\\)” between\ntypes as the reflexive transitive closure of the minimal relation such\nthat \\((\\alpha \\beta) \\ge \\alpha\\) and \\((\\alpha \\beta) \\ge \\beta\\).\nHe established that:", "\nThe existence of a choice functions for “higher” types\nthus entails the existence of choice functions for “lower”\ntypes, the opposite is generally not the case though.", "\nBüchi (1953) has shown that while the schemas expressing the\nAxiom of Choice and Zorn’s Lemma can be derived from each other,\nthe relationships between the particular types involved are\ncomplex.", "\nOne can define the natural numbers (and therefore other basic\nmathematical structures such as the real and complex numbers) in type\ntheory, but to prove that they have the required properties (such as\nPeano’s Postulates), one needs an Axiom of Infinity. There are\nmany viable possibilities for such an axiom, such as those discussed\nin Church 1940, section 57 of Church 1956, and section 60 of Andrews\n2002." ], "subsection_title": "1.3 Axioms and Rules of Inference" }, { "content": [ "\nIn\n Section 1.2.1,\n \\(\\nsim_{({o}{o})}, \\lor_{(({o}{o}){o})}\\), and the\n\\(\\Pi_{({o}({o}\\alpha))}\\)’s were taken as primitive\nconstants, and the wffs \\(\\sfQ_{{o}\\alpha \\alpha}\\) which denote\nequality relations at type α were defined in terms of these. We\nnow present an alternative formulation \\(\\cQ_0\\) of Church’s\ntype theory in which there are primitive constants \\(\\sfQ_{{o}\\alpha\n\\alpha}\\) denoting equality, and \\(\\nsim_{({o}{o})},\n\\lor_{(({o}{o}){o})}\\), and the \\(\\Pi_{({o}({o}\\alpha))}\\)’s\nare defined in terms of the \\(\\sfQ_{{o}\\alpha \\alpha}\\)’s.", "\nTarski (1923) noted that in the context of higher-order logic, one can\ndefine propositional connectives in terms of logical equivalence and\nquantifiers. Quine (1956) showed how both quantifiers and connectives\ncan be defined in terms of equality and the abstraction operator\nλ in the context of Church’s type theory. Henkin (1963)\nrediscovered these definitions, and developed a formulation of\nChurch’s type theory based on equality in which he restricted\nattention to propositional types. Andrews (1963) simplified the axioms\nfor this system.", "\n\\(\\cQ_0\\) is based on these ideas, and can be shown to be equivalent\nto a formulation of Church’s type theory using Axioms\n(1)–(8) of the preceding sections. This section thus provides an\nalternative to the material in the preceding Sections\n1.2.1–1.3.4. More details about \\(\\cQ_0\\) can be found in\nAndrews 2002.", "\n\\(T_{{o}}\\) denotes truth. The meaning of \\(\\Pi_{{o}({o}\\alpha)}\\)\nwas discussed in\n Section 1.1.\n To see that this definition of \\(\\Pi_{{o}({o}\\alpha)}\\) is\nappropriate, note that \\(\\lambda x_{\\alpha}T\\) denotes the set of all\nelements of type α, and that\n\\(\\Pi_{{o}({o}\\alpha)}s_{{o}\\alpha}\\) stands for\n\\(\\sfQ_{{o}({o}\\alpha)({o}\\alpha)}[\\lambda x_{\\alpha}T]\ns_{{o}\\alpha}\\), respectively for \\([\\lambda x_{\\alpha}T] =\ns_{{o}\\alpha}\\). Therefore \\(\\Pi_{{o}({o}\\alpha)}s_{{o}\\alpha}\\)\nasserts that \\(s_{{o}\\alpha}\\) is the set of all elements of type\nα, so \\(s_{{o}\\alpha}\\) contains all elements of type α.\nIt can be seen that \\(F_{{o}}\\) can also be written as \\(\\forall\nx_{{o}}x_{{o}}\\), which asserts that everything is true. This is\nfalse, so \\(F_{{o}}\\) denotes falsehood. The expression \\(\\lambda\ng_{{o}{o}{o}}[g_{{o}{o}{o}}x_{{o}}y_{{o}}]\\) can be used to represent\nthe ordered pair \\(\\langle x_{{o}},y_{{o}}\\rangle\\), and the\nconjunction \\(x_{{o}} \\land y_{{o}}\\) is true iff \\(x_{{o}}\\) and\n\\(y_{{o}}\\) are both true, i.e., iff \\(\\langle T_{{o}},T_{{o}}\\rangle\n= \\langle x_{{o}},y_{{o}}\\rangle\\). Hence \\(x_{{o}} \\land y_{{o}}\\)\ncan be expressed by the formula \\([\\lambda\ng_{{o}{o}{o}}[g_{{o}{o}{o}}T_{{o}}T_{{o}}]] = [\\lambda\ng_{{o}{o}{o}}[g_{{o}{o}{o}}x_{{o}}y_{{o}}]]\\).", "\nOther propositional connectives and the existential quantifier are\neasily defined. By using \\(\\iota_{(\\imath({o}\\imath))}\\), one can\ndefine description operators \\(\\iota_{\\alpha({o}\\alpha)}\\) for all\ntypes α.", "\n\\(\\cQ_0\\) has a single rule of inference.", "\nRule R: From \\(\\bC\\) and \\(\\bA_{\\alpha} =\n\\bB_{\\alpha}\\), to infer the result of replacing one occurrence of\n\\(\\bA_{\\alpha}\\) in \\(\\bC\\) by an occurrence of \\(\\bB_{\\alpha}\\),\nprovided that the occurrence of \\(\\bA_{\\alpha}\\) in \\(\\bC\\) is not (an\noccurrence of a variable) immediately preceded by λ.", "\nThe axioms for \\(\\cQ_0\\) are the following:" ], "subsection_title": "1.4 A Formulation Based on Equality" } ] }, { "main_content": [ "\nIt is natural to compare the semantics of type theory with the\nsemantics of first-order logic, where the theorems are precisely the\nwffs which are valid in all interpretations. From an intuitive point\nof view, the natural interpretations of type theory are standard\nmodels, which are defined below. However, it is a consequence of\nGödel’s Incompleteness Theorem (Gödel 1931) that\naxioms (1)–(9) do not suffice to derive all wffs which are valid in\nall standard models, and there is no consistent recursively\naxiomatized extension of these axioms which suffices for this purpose.\nNevertheless, experience shows that these axioms are sufficient for\nmost purposes, and Leon Henkin considered the problem of clarifying in\nwhat sense they are complete. The definitions and theorem below\nconstitute Henkin’s (1950) solution to this problem, which is\noften referred to as general semantics or Henkin\nsemantics.", "\nA frame is a collection \\(\\{\\cD_{\\alpha}\\}_{\\alpha}\\) of\nnonempty domains (sets) \\(\\cD_{\\alpha}\\), one for each type symbol\nα, such that \\(\\cD_{{o}} = \\{\\sfT,\\sfF\\}\\) (where \\(\\sfT\\)\nrepresents truth and \\(\\sfF\\) represents falsehood), and \\(\\cD_{\\alpha\n\\beta}\\) is some collection of functions mapping \\(\\cD_{\\beta}\\) into\n\\(\\cD_{\\alpha}\\). The members of \\(\\cD_{\\imath}\\) are called\nindividuals.", "\nAn interpretation \\(\\langle \\{\\cD_{\\alpha}\\}_{\\alpha},\n\\frI\\rangle\\) consists of a frame and a function \\(\\frI\\) which maps\neach constant C of type α to an appropriate element of\n\\(\\cD_{\\alpha}\\), which is called the denotation of C.\nThe logical constants are given their standard denotations.", "\nAn assignment of values in the frame\n\\(\\{\\cD_{\\alpha}\\}_{\\alpha}\\) to variables is a function \\(\\phi\\) such\nthat \\(\\phi \\bx_{\\alpha} \\in \\cD_{\\alpha}\\) for each variable\n\\(\\bx_{\\alpha}\\). (Notation: The assignment \\(\\phi[a/x]\\) maps\nvariable x to value a and it is identical with \\(\\phi\\)\nfor all other variable symbols different from x.)", "\nAn interpretation \\(\\cM = \\langle \\{\\cD_{\\alpha}\\}_{\\alpha},\n\\frI\\rangle\\) is a general model (aka Henkin model)\niff there is a binary function \\(\\cV\\) such that\n\\(\\cV_{\\phi}\\bA_{\\alpha} \\in \\cD_{\\alpha}\\) for each assignment\n\\(\\phi\\) and wff \\(\\bA_{\\alpha}\\), and the following conditions are\nsatisfied for all assignments and all wffs:", "\nIf an interpretation \\(\\cM\\) is a general model, the function \\(\\cV\\)\nis uniquely determined. \\(\\cV_{\\phi}\\bA_{\\alpha}\\) is called the\nvalue of \\(\\bA_{\\alpha}\\) in \\(\\cM\\) with respect to\n\\(\\phi\\).", "\nOne can easily show that the following statements hold in all general\nmodels \\(\\cM\\) for all assignments \\(\\phi\\) and all wffs \\(\\bA\\) and\n\\(\\bB\\):", "\nThe semantics of general models is thus as expected. However, there is\na subtlety to note regarding the following condition for arbitrary\ntypes α:", "\nWhen the definitions of\n Section 1.2.1\n are employed, where equality has been defined in terms of\nLeibniz’ principle, then this statement is not implied for all\ntypes α. It only holds if we additionally require that the\ndomains \\(\\cD_{{o}\\alpha}\\) contain all the unit sets of objects of\ntype α, or, alternatively, that the domains\n\\(\\cD_{{o}\\alpha\\alpha}\\) contain the respective identity relations on\nobjects of type α (which entails the former). The need for this\nadditional requirement, which is not included in the original work of\nHenkin (1950), has been demonstrated in Andrews 1972a.", "\nWhen instead the alternative definitions of\n Section 1.4\n are employed, then this requirement is obviously met due to the\npresence of the logical constants \\(\\sfQ_{{o}\\alpha \\alpha}\\) in the\nsignature, which by definition denote the respective identity\nrelations on the objects of type α and therefore trivially\nensure their existence in each general model \\(\\cM\\). It is therefore\na natural option to always assume primitive equality constants (for\neach type α) in a concrete choice of base system for\nChurch’s type theory, just as realized in Andrews’ system\n\\(\\cQ_0\\).", "\nAn interpretation \\(\\langle \\{\\cD_{\\alpha}\\}_{\\alpha}, \\frI\\rangle\\)\nis a standard model iff for all α and \\(\\beta ,\n\\cD_{\\alpha \\beta}\\) is the set of all functions from \\(\\cD_{\\beta}\\)\ninto \\(\\cD_{\\alpha}\\). Clearly a standard model is a general\nmodel.", "\nWe say that a wff \\(\\bA\\) is valid in a model \\(\\cM\\) iff\n\\(\\cV_{\\phi}\\bA = \\sfT\\) for every assignment \\(\\phi\\) into \\(\\cM\\). A\nmodel for a set \\(\\cH\\) of wffs is a model in which each wff of\n\\(\\cH\\) is valid.", "\nA wff \\(\\bA\\) is valid in the general [standard]\nsense iff \\(\\bA\\) is valid in every general [standard] model.\nClearly a wff which is valid in the general sense is valid in the\nstandard sense, but the converse of this statement is false.", "\nCompleteness and Soundness Theorem (Henkin 1950):\nA wff is a theorem if and only if it is valid in the general\nsense.", "\nNot all frames belong to interpretations, and not all interpretations\nare general models. In order to be a general model, an interpretation\nmust have a frame satisfying certain closure conditions which are\ndiscussed further in Andrews 1972b. Basically, in a general model\nevery wff must have a value with respect to each assignment.", "\nA model is said to be finite iff its domain of individuals is\nfinite. Every finite model for \\(\\cQ_0\\) is standard (Andrews 2002,\nTheorem 5404), but every set of sentences of \\(\\cQ_0\\) which has\ninfinite models also has nonstandard models (Andrews2002, Theorem\n5506).", "\nAn understanding of the distinction between standard and nonstandard\nmodels can clarify many phenomena. For example, it can be shown that\nthere is a model \\(\\cM = \\langle \\{\\cD_{\\alpha}\\}_{\\alpha},\n\\frI\\rangle\\) in which \\(\\cD_{\\imath}\\) is infinite, and all the\ndomains \\(\\cD_{\\alpha}\\) are countable. Thus \\(\\cD_{\\imath}\\) and\n\\(\\cD_{{o}\\imath}\\) are both countably infinite, so there must be a\nbijection h between them. However, Cantor’s Theorem\n(which is provable in type theory and therefore valid in all models)\nsays that \\(\\cD_{\\imath}\\) has more subsets than members. This\nseemingly paradoxical situation is called Skolem’s Paradox. It\ncan be resolved by looking carefully at Cantor’s Theorem, i.e.,\n\\(\\nsim \\exists g_{{o}\\imath\\imath}\\forall f_{{o}\\imath}\\exists\nj_{\\imath}[g_{{o}\\imath\\imath}j_{\\imath} = f_{{o}\\imath}]\\), and\nconsidering what it means in a model. The theorem says that there is\nno function \\(g \\in \\cD_{{o}\\imath\\imath}\\) from \\(\\cD_{\\imath}\\) into\n\\(\\cD_{{o}\\imath}\\) which has every set \\(f_{{o}\\imath} \\in\n\\cD_{{o}\\imath}\\) in its range. The usual interpretation of the\nstatement is that \\(\\cD_{{o}\\imath}\\) is bigger (in cardinality) than\n\\(\\cD_{\\imath}\\). However, what it actually means in this model is\nthat h cannot be in \\(\\cD_{{o}\\imath\\imath}\\). Of course,\n\\(\\cM\\) must be nonstandard.", "\nWhile the Axiom of Choice is presumably true in all standard models,\nthere is a nonstandard model for \\(\\cQ_0\\) in which AC\\(^{\\imath}\\) is\nfalse (Andrews 1972b). Thus, AC\\(^{\\imath}\\) is not provable in\n\\(\\cQ_0\\).", "\nThus far, investigations of model theory for Church’s type\ntheory have been far less extensive than for first-order logic.\nNevertheless, there has been some work on methods of constructing\nnonstandard models of type theory and models in which various forms of\nextensionality fail, models for theories with arbitrary (possibly\nincomplete) sets of logical constants, and on developing general\nmethods of establishing completeness of various systems of axioms with\nrespect to various classes of models. Relevant papers include Andrews\n1971, 1972a,b, and Henkin 1975. Further related work can be found in\nBenzmüller et al. 2004, Brown 2004, 2007, and Muskens 2007." ], "section_title": "2. Semantics", "subsections": [] }, { "main_content": [], "section_title": "3. Metatheory", "subsections": [ { "content": [ "\nThe first three rules of inference in\n Section 1.3.1\n are called rules of λ-conversion. If \\(\\bD\\) and\n\\(\\bE\\) are wffs, we write \\(\\bD \\conv \\bE\\) to indicate that \\(\\bD\\)\ncan be converted to \\(\\bE\\) by applications of these rules. This is an\nequivalence relation between wffs. A wff \\(\\bD\\) is in\nβ-normal form iff it has no well-formed parts of the\nform \\([[\\lambda \\bx_{\\alpha}\\bB_{\\beta}]\\bA_{\\alpha}]\\). Every wff is\nconvertible to one in β-normal form. Indeed, every sequence of\ncontractions (applications of rule 2, combined as necessary with\nalphabetic changes of bound variables) of a wff is finite; obviously,\nif such a sequence cannot be extended, it terminates with a wff in\nβ-normal form. (This is called the strong normalization theorem.)\nBy the Church-Rosser Theorem, this wff in β-normal form is unique\nmodulo alphabetic changes of bound variables. For each wff \\(\\bA\\) we\ndenote by \\({\\downarrow}\\bA\\) the first wff (in some enumeration) in\nβ-normal form such that \\(\\bA \\conv {\\downarrow} \\bA\\). Then \\(\\bD\n\\conv \\bE\\) if and only if \\({\\downarrow} \\bD = {\\downarrow} \\bE\\).", "\nBy using the Axiom of Extensionality one can obtain the following\nderived rule of inference:", "\n\n\n\\(\\eta\\)-Contraction. Replace a well-formed part \\([\\lambda\n\\by_{\\beta}[\\bB_{\\alpha \\beta}\\by_{\\beta}]]\\) of a wff by\n\\(\\bB_{\\alpha \\beta}\\), provided \\(\\by_{\\beta}\\) does not occur free\nin \\(\\bB_{\\alpha \\beta}\\).\n", "\nThis rule and its inverse (which is called\n\\(\\eta\\)-Expansion) are sometimes used as additional rules of\nλ-conversion. See Church 1941, Stenlund 1972, Barendregt 1984,\nand Barendregt et al. 2013 for more information about\nλ-conversion.", "\nIt is worth mentioning (again) that λ-abstraction replaces the\nneed for comprehension axioms in Church’s type theory." ], "subsection_title": "3.1 Lambda-Conversion" }, { "content": [ "\nThe challenges in higher-order unification are outlined very briefly.\nMore details on the topic are given in Dowek 2001; its utilization in\nhigher-order theorem provers is also discussed in Benzmüller\n& Miller 2014.", "\nDefinition. A higher-order unifier for a\npair \\(\\langle \\bA,\\bB\\rangle\\) of wffs is a substitution \\(\\theta\\)\nfor free occurrences of variables such that \\(\\theta \\bA\\) and\n\\(\\theta \\bB\\) have the same β-normal form. A higher-order\nunifier for a set of pairs of wffs is a unifier for each of the pairs\nin the set.", "\nHigher-order unification differs from first-order unification (Baader\n& Snyder 2001) in a number of important respects. In\nparticular:", "\nHowever, an algorithm has been devised (Huet 1975, Jensen &\nPietrzykowski 1976), called pre-unification, which will find\na unifier for a set of pairs of wffs if one exists. The pre-unifiers\ncomputed by Huet’s procedure are substitutions that can reduce\nthe original unification problem to one involving only so called\nflex-flex unification pairs. Flex-flex pairs have variable\nhead symbols in both terms to be unified and they are known to always\nhave a solution. The concrete computation of these solutions can thus\nbe postponed or omitted. Pre-unification is utilized in all the\nresolution based theorem provers mentioned in\n Section 4.\n ", "\nPattern unification refers a small subset of unification\nproblems, first studied by Miller 1991, whose identification has been\nimportant for the construction of practical systems. In a pattern\nunification problem every occurrence of an existentially quantified\nvariable is applied to a list of arguments that are all distinct\nvariables bound by either a λ-binder or a universal quantifier\nin the scope of the existential quantifier. Thus, existentially\nquantified variables cannot be applied to general terms but a very\nrestricted set of bound variables. Pattern unification, like\nfirst-order unification, is decidable and most general unifiers exist\nfor solvable problems. This is why pattern unification is preferably\nemployed (when applicable) in some state-of-the-art theorem provers\nfor Church’s type theory. " ], "subsection_title": "3.2 Higher-Order Unification" }, { "content": [ "\nThe Unifying Principle was introduced in Smullyan 1963 (see\nalso Smullyan 1995) as a tool for deriving a number of basic\nmetatheorems about first-order logic in a uniform way. The principle\nwas extended to elementary type theory by Andrews (1971) and to\nextensional type theory, that is, Henkin’s general semantics\nwithout description or choice, by Benzmüller, Brown and Kohlhase\n(2004). We outline these extensions in some more detail below.", "\nThe Unifying Principle was extended to elementary type theory (the\nsystem \\(\\cT\\) of\n Section 1.3.2)\n in Andrews 1971 by applying ideas in Takahashi 1967. This Unifying\nPrinciple for \\(\\cT\\) has been used to establish cut-elimination for\n\\(\\cT\\) in Andrews 1971 and completeness proofs for various systems of\ntype theory in Huet 1973a, Kohlhase 1995, and Miller 1983. We first\ngive a definition and then state the principle.", "\nDefinition. A property \\(\\Gamma\\) of finite sets of\nwffs\\(_{{o}}\\) is an abstract consistency property iff for\nall finite sets \\(\\cS\\) of wffs\\(_{{o}}\\), the following properties\nhold (for all wffs A, B):", "\nNote that consistency is an abstract consistency\nproperty.", "\nUnifying Principle for \\(\\cT\\). If \\(\\Gamma\\) is an\nabstract consistency property and \\(\\Gamma(\\cS)\\), then \\(\\cS\\) is\nconsistent in \\(\\cT\\).", "\nHere is a typical application of the Unifying Principle. Suppose there\nis a procedure \\(\\cM\\) which can be used to refute sets of sentences,\nand we wish to show it is complete for \\(\\cT\\). For any set of\nsentences, let \\(\\Gamma(\\cS)\\) mean that \\(\\cS\\) is not refutable by\n\\(\\cM\\), and show that \\(\\Gamma\\) is an abstract consistency property.\nNow suppose that \\(\\bA\\) is a theorem of \\(\\cT\\). Then \\(\\{\\nsim\n\\bA\\}\\) is inconsistent in \\(\\cT\\), so by the Unifying Principle not\n\\(\\Gamma(\\{\\nsim \\bA\\})\\), so \\(\\{\\nsim \\bA\\}\\) is refutable by\n\\(\\cM\\).", "\nExtensions of the above Unifying principle towards Church’s type\ntheory with general semantics were studied since the mid nineties. A\nprimary motivation was to support (refutational) completeness\ninvestigations for the proof calculi underlying the emerging\nhigher-order automated theorem provers (see\n Section 4\n below). The initial interest was on a fragment of Church’s type\ntheory, called extensional type theory, that includes the\nextensionality axioms, but excludes \\(\\iota_{(\\alpha({o}\\alpha))}\\)\nand the axioms for it (description and choice were largely neglected\nin the automated theorem provers at the time). Analogous to before, a\ndistinction has been made between extensional type theory with\ndefined equality (as in\n Section 1.2.1,\n where equality is defined via Leibniz’ principle) and\nextensional type theory with primitive equality (e.g., system\n\\(\\cQ_0\\) as in\n Section 1.4,\n or, alternatively, a system based on logical constants\n\\(\\nsim_{({o}{o})}, \\lor_{(({o}{o}){o})}\\), and the\n\\(\\Pi_{({o}({o}\\alpha))}\\)’s as in\n Section 1.2.1,\n but with additional primitive logical constants\n\\(=_{{o}\\alpha\\alpha}\\) added).", "\nA first attempt towards a Unifying Principle for extensional type\ntheory with primitive equality is presented in Kohlhase 1993. The\nconditions given there, which are still\n incomplete[1],\n were subsequently modified and complemented as follows:" ], "subsection_title": "3.3 A Unifying Principle" }, { "content": [ "\nCut-elimination proofs (see also the SEP entry on\n proof theory)\n for Church’s type theory, which are often closely related to\nsuch proofs (Takahashi 1967, 1970; Prawitz 1968; Mints 1999) for other\nformulations of type theory, may be found in Andrews 1971, Dowek &\nWerner 2003, and Brown 2004. In Benzmüller et al. 2009 it is\nshown how certain wffs\\(_{{o}}\\), such as axioms of extensionality,\ndescriptions, choice (see\n Sections 1.3.3\n to\n 1.3.5),\n and induction, can be used to justify cuts in cut-free sequent\ncalculi for elementary type theory. Moreover, the notions of\ncut-simulation and cut-strong axioms are introduced\nin this work, and the need for omitting defined equality and for\neliminating cut-strong axioms such as extensionality,\ndescription, choice and induction in machine-oriented calculi (e.g.,\nby replacing them with more constrained, goal-directed rules) in order\nto reduce cut-simulation effects are discussed as a major\nchallenge for higher-order automated theorem proving. In other words,\nincluding cut-strong axioms in a machine-oriented proof calculus for\nChurch’s type theory is essentially as bad as including a cut\nrule, since the cut rule can be mimicked by them." ], "subsection_title": "3.4 Cut-Elimination and Cut-Simulation" }, { "content": [ "\nAn expansion proof is a generalization of the notion of a\nHerbrand expansion of a theorem of first-order logic; it provides a\nvery elegant, concise, and nonredundant representation of the\nrelationship between the theorem and a tautology which can be obtained\nfrom it by appropriate instantiations of quantifiers and which\nunderlies various proofs of the theorem. Miller (1987) proved that a\nwff \\(\\bA\\) is a theorem of elementary type theory if and only if\n\\(\\bA\\) has an expansion proof.", "\nIn Brown 2004 and 2007, this concept is generalized to that of an\nextensional expansion proof to obtain an analogous theorem\ninvolving type theory with extensionality." ], "subsection_title": "3.5 Expansion Proofs" }, { "content": [ "\nSince type theory includes first-order logic, it is no surprise that\nmost systems of type theory are undecidable. However, one may look for\nsolvable special cases of the decision problem. For example, the\nsystem \\(\\cQ_{0}^1\\) obtained by adding to \\(\\cQ_0\\) the additional\naxiom \\(\\forall x_{\\imath}\\forall y_{\\imath}[x_{\\imath}=y_{\\imath}]\\)\nis decidable.", "\nAlthough the system \\(\\cT\\) of elementary type theory is analogous to\nfirst-order logic in certain respects, it is a considerably more\ncomplex language, and special cases of the decision problem for\nprovability in \\(\\cT\\) seem rather intractable for the most part.\nInformation about some very special cases of this decision problem may\nbe found in Andrews 1974, and we now summarize this.", "\nA wff of the form \\(\\exists \\bx^1 \\ldots \\exists \\bx^n [\\bA=\\bB]\\) is\na theorem of \\(\\cT\\) iff there is a substitution \\(\\theta\\) such that\n\\(\\theta \\bA \\conv \\theta \\bB\\). In particular, \\(\\vdash \\bA=\\bB\\) iff\n\\(\\bA \\conv \\bB\\), which solves the decision problem for wffs of the\nform \\([\\bA=\\bB]\\). Naturally, the circumstance that only trivial\nequality formulas are provable in \\(\\cT\\) changes drastically when\naxioms of extensionality are added to \\(\\cT\\). \\(\\vdash \\exists\n\\bx_{\\beta}[\\bA=\\bB]\\) iff there is a wff \\(\\bE_{\\beta}\\) such that\n\\(\\vdash[\\lambda \\bx_{\\beta}[\\bA=\\bB]]\\bE_{\\beta}\\), but the decision\nproblem for the class of wffs of the form \\(\\exists\n\\bx_{\\beta}[\\bA=\\bB]\\) is unsolvable.", "\nA wff of the form \\(\\forall \\bx^1 \\ldots \\forall \\bx^n\\bC\\), where\n\\(\\bC\\) is quantifier-free, is provable in \\(\\cT\\) iff \\({\\downarrow}\n\\bC\\) is tautologous. On the other hand, the decision problem for wffs\nof the form \\(\\exists \\bz\\bC\\), where \\(\\bC\\) is quantifier-free, is\nunsolvable. (By contrast, the corresponding decision problem in\nfirst-order logic with function symbols is known to be solvable\n(Maslov 1967).) Since irrelevant or vacuous quantifiers can always be\nintroduced, this shows that the only solvable classes of wffs of\n\\(\\cT\\) in prenex normal form defined solely by the structure of the\nprefix are those in which no existential quantifiers occur." ], "subsection_title": "3.6 The Decision Problem" } ] }, { "main_content": [], "section_title": "4. Automation", "subsections": [ { "content": [ "\nThe development, respectively improvement, of machine-oriented proof\ncalculi for Church’s type theory is still a challenge research\ntopic. Compared, e.g., to the theoretical and practical maturity\nachieved in first-order automated theorem proving, the area is still\nin its infancy. Obviously, the challenges are also much bigger than in\nfirst-order logic. The practically way more expressive nature of the\nterm-language of Church’s type theory causes a larger, bushier\nand more difficult to traverse proof search space than in first-order\nlogic. Moreover, remember that unification, which constitutes a very\nimportant control and filter mechanism in first-order theorem proving,\nis undecidable (in general) in type theory; see\n Section 3.2.\n On the positive side, however, there is a chance to find\nsignificantly shorter proofs than in first-order logic. This is well\nillustrated with a small, concrete example in Boolos 1987. Clearly,\nmuch further progress is needed to further leverage the practical\nrelevance of existing calculi for Church’s type theory and their\nimplementations (see\n Section 4.3).\n The challenges include", "\nIt is planned that future editions of this article further elaborate\non machine-oriented proof calculi for Church’s type theory. For\nthe time being, however, we provide only a selection of historical and\nmore recent references for the interested reader (see also\n Section 5 below):" ], "subsection_title": "4.1 Machine-Oriented Proof Calculi" }, { "content": [ "\nEarly computer systems for proving theorems of Church’s type\ntheory (or extensions of it) include HOL (Gordon 1988; Gordon &\nMelham 1993), TPS (Andrews et al. 1996; Andrews & Brown 2006),\nIsabelle (Paulson 1988, 1990), PVS (Owre et al. 1996; Shankar 2001),\nIMPS (Farmer et al. 1993), HOL\nLight (Harrison 1996), OMEGA (Siekmann et al. 2006), and λClam\n(Richardson et al. 1998). See\n Other Internet References\n section below for links to further info on these and other provers\nmentioned later. ", "\nThe majority of the above systems focused (at least initially) on\ninteractive proof and provided rather limited support for additional\nproof automation. Full proof automation was pioneered, in particular,\nby the TPS project. Progress was made in the nineties, when other\nprojects started similar activities, respectively, enforced theirs.\nHowever, the resource investments and achievements were lacking much\nbehind those seen in first-order theorem proving. Significant progress\nwas fostered only later, in particular, through the development of a\ncommonly supported syntax for Church’s type theory, called TPTP\nTHF (Sutcliffe & Benzmüller 2010), and the inclusion, from\n2009 onwards, of a TPTP THF division in the yearly CASC competitions\n(kind of world championships for automated theorem proving; see\nSutcliffe 2016 for further details)." ], "subsection_title": "4.2 Early Proof Assistants" }, { "content": [ "\nAn selection of theorem provers for Church’s type theory is\npresented. The focus is on systems that have successfully participated\nin TPTP THF CASC competitions in the past. The latest editions of most\nmentioned systems can be accessed online via the SystemOnTPTP\ninfrastructure (Sutcliffe 2017). Nearly all mentioned systems produce\nverifiable proof certificates in the TPTP TSTP syntax. Further details\non the automation of Church’s type theory are given in\nBenzmüller & Miller 2014.", "\nThe TPS prover (Andrews et al. 1996, Andrews & Brown 2006) can be\nused to prove theorems of elementary type theory or extensional type\ntheory automatically, interactively, or semi-automatically. When\nsearching for a proof automatically, TPS first searches for an\nexpansion proof (Miller 1987) or an extensional expansion proof (Brown\n2004, 2007) of the theorem. Part of this process involves searching\nfor acceptable matings (Andrews 1981, Bishop 1999). The behavior of\nTPS is controlled by sets of flags, also called modes. A simple\nscheduling mechanism is employed in the latest versions of TPS to\nsequentially run a about fifty modes for a limited amount of time. TPS\nwas the winner of the first THF CASC competition in 2009.", "\nThe LEO-II prover (Benzmüller et al. 2015) is the successor of\nLEO (Benzmüller & Kohlhase 1998b, which was hardwired with\nthe OMEGA proof assistant (LEO stands for Logical Engine of OMEGA).\nThe provers are based on the RUE-resolution calculi developed in\nBenzmüller 1999a,b. LEO\nwas the first prover to implement calculus rules for extensionality to\navoid cut-simulation effects. LEO-II inherits and adapts them, and\nprovides additional calculus rules for description and choice. The\nprover, which internally collaborates with first-order provers\n(preferably E) and SAT solvers, has pioneered cooperative\nhigher-order/first-order proof automation. Since the prover is often\ntoo weak to find a refutation among the steadily growing set of\nclauses on its own, some of the clauses in LEO-II’s search space\nattain a special status: they are first-order clauses modulo the\napplication of an appropriate transformation function. Therefore,\nLEO-II progressively launches time limited calls with these clauses to\na first-order theorem prover, and when the first-order prover reports\na refutation, LEO-II also terminates. Parts of these ideas were\nalready implemented in the predecessor LEO. Communication between\nLEO-II and the cooperating first-order theorem provers uses the TPTP\nlanguage and standards. LEO-II was the winner of the second THF CASC\ncompetition in 2010.", "\nThe Satallax prover (Brown 2012) is based on a complete ground tableau\ncalculus for Church’s type theory with choice (Backes &\nBrown 2011). An initial tableau branch is formed from the assumptions\nof a conjecture and negation of its conclusion. From that point on,\nSatallax tries to determine unsatisfiability or satisfiability of this\nbranch. Satallax progressively generates higher-order formulas and\ncorresponding propositional clauses. Satallax uses the SAT solver\nMiniSat as an engine to test the current set of propositional clauses\nfor unsatisfiability. If the clauses are unsatisfiable, the original\nbranch is unsatisfiable. Satallax provides calculus rules for\nextensionality, description and choice. If there are no quantifiers at\nfunction types, the generation of higher-order formulas and\ncorresponding clauses may terminate. In that case, if MiniSat reports\nthe final set of clauses as satisfiable, then the original set of\nhigher-order formulas is satisfiable (by a standard model in which all\ntypes are interpreted as finite sets). Satallax was the winner of the\nTHF CASC competition in 2011 and since 2013. ", "\nThe Isabelle/HOL system (Nipkow, Wenzel, & Paulson 2002) has\noriginally been designed as an interactive prover. However, in order\nto ease user interaction several automatic proof tactics have been\nadded over the years. By appropriately scheduling a subset of these\nproof tactics, some of which are quite powerful, Isabelle/HOL has\nsince about 2011 been turned also into an automatic theorem prover for\nTPTP THF (and other TPTP syntax formats), that can be run from a\ncommand shell like other provers. The most powerful proof tactics that\nare scheduled by Isabelle/HOL include the Sledgehammer tool\n(Blanchette et al. 2013),\nwhich invokes a sequence of external first-order and higher-order\ntheorem provers, the model finder Nitpick (Blanchette &\nNipkow 2010), the equational reasoner simp, the untyped\ntableau prover blast, the simplifier and classical reasoners\nauto, force, and fast, and the best-first\nsearch procedure best. In contrast to all other automated\ntheorem provers mentioned above, the TPTP incarnation of Isabelle/HOL\ndoes not yet output proof certificates. Isabelle/HOL was the winner of\nthe THF CASC competition in 2012. ", "\nThe agsyHOL prover is based on a generic lazy narrowing proof search\nalgorithm. Backtracking is employed and a comparably small search\nstate is maintained. The prover outputs proof terms in sequent style\nwhich can be verified in the Agda system. ", "\ncoqATP implements (the non-inductive) part of the calculus of\nconstructions (Bertot & Castéran 2004). The system outputs\nproof terms which are accepted as proofs (after the addition of a few\ndefinitions) by the Coq proof assistant. The prover employs axioms for\nfunctional extensionality, choice, and excluded middle. Boolean\nextensionality is not supported. In addition to axioms, a small\nlibrary of basic lemmas is employed. ", "\nThe Leo-III prover implements a paramodulation calculus for\nChurch’s type theory (Steen 2018). The system, which is a\ndescendant of LEO and LEO-II, provides calculus rules for\nextensionality, description and choice. The system has put an emphasis\non the implementation of an efficient set of underlying data\nstructures, on simplification routines and on heuristic rewriting. In\nthe tradition of its predecessors, Leo-III cooperates with first-order\nreasoning tools using translations to many-sorted first-order logic.\nThe prover accepts every common TPTP syntax dialect and is thus very\nwidely applicable. Recently, the prover has also been extended to\nnatively supports almost every normal higher-order modal logic.", "\nZipperposition (Bentkamp et al. 2018) is new and inspiring\nhigher-order theorem prover which, at the current state of\ndevelopment, is still working for a comparably weak fragment of\nChurch’s type theory, called lambda-free higher-order\nlogic (a comprehension-free higher-order logic,\nwhich is nevertheless supporting λ-notation). The system, which\nis based on superposition calculi, is developed bottom up, and it is\nprogressively extended towards stronger fragments of Church’s\ntype theory and to support other relevant extensions such datatypes,\nrecursive functions and arithmetic. ", "\nVarious so called proof hammers, in the spirit of\nIsabelle’s Sledgehammer tool, have recently been developed and\nintegrated with modern proof assistants. Prominent examples include\nHOL(y)Hammer (Kaliszyk & Urban 2015) for HOL Light and a similar\nhammer (Czaika & Kaliszyk 2018) for the proof assistant Coq. " ], "subsection_title": "4.3 Automated Theorem Provers" }, { "content": [ "\nSupport for finding finite models or countermodels for formulas of\nChurch’s type theory was implemented already in the\ntableau-based prover HOT (Konrad 1998). Restricted (counter-)model\nfinding capabilities are also implemented in the provers Satallax,\nLEO-II and LEO-III. The most advanced (finite) model finding support\nis currently realized in the systems Nitpick, Nunchaku and Refute. These tools\nhave been integrated with the Isabelle proof assistant. Nitpick is\nalso available as a standalone tool that accepts TPTP THF syntax. The\nsystems are particularly valuable for exposing errors and\nmisconceptions in problem encodings, and for revealing bugs in the THF\ntheorem provers." ], "subsection_title": "4.4 (Counter-)Model Finding" } ] }, { "main_content": [], "section_title": "5. Applications", "subsections": [ { "content": [ "\nChurch’s type theory plays an important role in the study of the\nformal semantics of natural language. Pioneering work on this was done\nby Richard Montague. See his papers “English as a formal\nlanguage”, “Universal grammar”, and “The\nproper treatment of quantification in ordinary English”, which\nare reprinted in Montague 1974. A crucial component of\nMontague’s analysis of natural language is the definition of a\ntensed intensional logic (Montague 1974: 256), which is an enhancement\nof Church’s type theory. Montague Grammar had a huge impact, and\nhas since been developed in many further directions, not least in\nTypelogical/Categorical Grammar. Further related work on intensional\nand higher-order modal logic is presented in Gallin 1975 and Muskens\n2006." ], "subsection_title": "5.1 Semantics of Natural Language" }, { "content": [ "\nProof assistants based on Church’s Type Theory, including\nIsabelle/HOL, HOL Light, HOL4, and PVS, have been successfully\nutilized in a broad range of application in computer science and\nmathematics.", "\nApplications in computer science include the verification of hardware,\nsoftware and security protocols. A prominent example is the\nL4.verified project in which Isabelle/HOL was used to formally prove\nthat the seL4 operating system kernel implements an abstract,\nmathematical model specifying of what the kernel is supposed to do\n(Klein et al. 2018). ", "\nIn mathematics proof assistants have been applied for the development\nof libraries mathematical theories and the verification of challenge\ntheorems. An early example is the mathematical library that was\ndeveloped since the eighties in the TPS project. A exemplary list of\ntheorems that were proved automatically with TPS is given in Andrews\net al. 1996. A very prominent recent example is Hales Flyspeck in\nwhich HOL Light was employed to develop a formal proof for\nKepler’s conjecture (Hales et al. 2017). An example that\nstrongly exploits automation support in Isabelle/HOL with Sledgehammer\nand Nitpick is presented in Benzmüller & Scott forthcoming.\nIn this work different axiom systems for category theory were explored\nand compared. ", "\nA solid overview on past and ongoing formalization projects can be\nobtained by consulting respective sources such as Isabelle’s\nArchive of Formal Proofs, the Journal of Formalized Reasoning, or the\nTHF entries in Sutcliffe’s TPTP problem library. ", "\nFurther improving proof automation within these proof\nassistants—based on proof hammering tools or on other forms of\nprover integration—is relevant for minimizing interaction effort\nin future applications. " ], "subsection_title": "5.2 Mathematics and Computer Science" } ] } ]

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Selected Papers Of\nRichard Montague, edited and with an introduction by Richmond H.\nThomason, New Haven: Yale University Press.", "Muskens, Reinhard, 2006, “Higher Order Modal Logic”,\nin Handbook of Modal Logic, Patrick Blackburn, Johan Van\nBenthem, and Frank Wolter (eds.), Amsterdam: Elsevier,\n621–653.", "–––, 2007, “Intensional Models for the\nTheory of Types”, The Journal of Symbolic Logic, 72(1):\n98–118. doi:10.2178/jsl/1174668386", "Nipkow, Tobias, Markus Wenzel, and Lawrence C. Paulson (eds.),\n2002, Isabelle/HOL: A Proof Assistant for Higher-Order Logic,\n(Lecture Notes in Computer Science 2283), Berlin, Heidelberg: Springer\nBerlin Heidelberg. doi:10.1007/3-540-45949-9", "Owre, S., S. Rajan, J. M. Rushby, N. Shankar, and M. Srivas, 1996,\n“PVS: Combining Specification, Proof Checking, and Model\nChecking”, in Computer Aided Verification, Rajeev Alur\nand Thomas A. Henzinger (eds.), (Lecture Notes in Computer Science\n1102), Berlin, Heidelberg: Springer Berlin Heidelberg, 411–414.\ndoi:10.1007/3-540-61474-5_91", "Paulson, Lawrence C, 1988, “Isabelle: The next Seven Hundred\nTheorem Provers”, in 9th International Conference on\nAutomated Deduction, Ewing Lusk and Ross Overbeek (eds.),\n(Lecture Notes in Computer Science 310), Berlin/Heidelberg:\nSpringer-Verlag, 772–773. doi:10.1007/BFb0012891", "–––, 1990, “A Formulation of the Simple\nTheory of Types (for Isabelle)”, in COLOG-88, Per\nMartin-Löf and Grigori Mints (eds.), (Lecture Notes in Computer\nScience 417), Berlin, Heidelberg: Springer Berlin Heidelberg,\n246–274. doi:10.1007/3-540-52335-9_58", "Prawitz, Dag, 1968, “Hauptsatz for Higher Order\nLogic”, The Journal of Symbolic Logic, 33(3):\n452–457. doi:10.2307/2270331", "Quine, W. V., 1956, “Unification of Universes in Set\nTheory”, The Journal of Symbolic Logic, 21(3):\n267–279. doi:10.2307/2269102", "Richardson, Julian, Alan Smaill, and Ian Green, 1998,\n“System Description: Proof Planning in Higher-Order Logic with\nΛClam”, in Kirchner and Kirchner 1998: 129–133.\ndoi:10.1007/BFb0054254", "Robinson, Alan and Andrei Voronkov (eds.), 2001, Handbook of\nAutomated Reasoning, Volumes 1 and 2, Amsterdam: Elsevier\nScience.", "Russell, Bertrand, 1903, The Principles of Mathematics,\nCambridge: Cambridge University Press.", "–––, 1908, “Mathematical Logic as Based on\nthe Theory of Types”, American Journal of Mathematics,\n30(3): 222–262. Reprinted in van Heijenoort 1967: 150–182.\ndoi:10.2307/2369948", "Schönfinkel, M., 1924, “Über die Bausteine der\nmathematischen Logik”, Mathematische Annalen,\n92(3–4): 305–316. Translated in van Heijenoort 1967: 355–366.\ndoi:10.1007/BF01448013", "Schütte, Kurt, 1960, “Syntactical and Semantical\nProperties of Simple Type Theory”, The Journal of Symbolic\nLogic, 25(4): 305–326. doi:10.2307/2963525", "Shankar, Natarajan, 2001, “Using Decision Procedures with a\nHigher-Order Logic”, in Theorem Proving in Higher Order\nLogics, Richard J. Boulton and Paul B. Jackson (eds.), (Lecture\nNotes in Computer Science 2152), Berlin, Heidelberg: Springer Berlin\nHeidelberg, 5–26. doi:10.1007/3-540-44755-5_3", "Siekmann, Jörg H. and Graham Wrightson (eds.), 1983,\nAutomation of Reasoning, (Classical Papers on Computational\nLogic 1967–1970: Vol. 2), Berlin, Heidelberg: Springer Berlin\nHeidelberg. doi:10.1007/978-3-642-81955-1", "Siekmann, Jörg, Christoph Benzmüller, and Serge\nAutexier, 2006, “Computer Supported Mathematics with\nΩMEGA”, Journal of Applied Logic, 4(4):\n533–559. doi:10.1016/j.jal.2005.10.008", "Smullyan, Raymond M., 1963, “A Unifying Principal in\nQuantification Theory”, Proceedings of the National Academy\nof Sciences, 49(6): 828–832. doi:10.1073/pnas.49.6.828", "–––, 1995, First-Order Logic, New York:\nDover, second corrected edition.", "Steen, Alexander, 2018, Extensional Paramodulation for\nHigher-Order Logic and its Effective Implementation Leo-III,\nPh.D. dissertation, Series: Dissertations in Artificial Intelligence\n(DISKI), Volume 345, Berlin: AKA-Verlag (IOS Press).", "Steen, Alexander and Christoph Benzmüller, 2018, “The\nHigher-Order Prover Leo-III”, in Galmiche et al. 2018:\n108–116. doi:10.1007/978-3-319-94205-6_8", "Stenlund, Sören, 1972, Combinators, λ-Terms and\nProof Theory, (Synthese Library 42), Dordrecht: Springer\nNetherlands. doi:10.1007/978-94-010-2913-1", "Sutcliffe, Geoff, 2016, “The CADE ATP System\nCompetition—CASC”, AI Magazine, 37(2): 99–101.\ndoi:10.1609/aimag.v37i2.2620", "–––, 2017, “The TPTP Problem Library and\nAssociated Infrastructure: From CNF to TH0, TPTP v6.4.0”,\nJournal of Automated Reasoning, 59(4): 483–502.\ndoi:10.1007/s10817-017-9407-7", "Sutcliffe, Geoff and Christoph Benzmüller, 2010,\n“Automated Reasoning in Higher-Order Logic Using the TPTP THF\nInfrastructure”, Journal of Formalized Reasoning, 3(1):\n1–27. doi:10.6092/issn.1972-5787/1710", "Takahashi, Moto-o, 1967, “A Proof of Cut-Elimination Theorem\nin Simple Type-Theory”, Journal of the Mathematical Society\nof Japan, 19(4): 399–410. doi:10.2969/jmsj/01940399", "–––, 1970, “A System of Simple Type Theory\nof Gentzen Style with Inference on Extensionality, and the Cut\nElimination in It”, Commentarii Mathematici Universitatis\nSancti Pauli, 18(2):129–147.", "Takeuti, Gaisi, 1987, Proof Theory, second edition,\nAmsterdam: North-Holland.", "Tarski, Alfred [Tajtelbaum, Alfred], 1923, “Sur Le Terme\nPrimitif de La Logistique”, Fundamenta Mathematicae, 4:\n196–200. Translated in Tarski 1956, 1–23.\ndoi:10.4064/fm-4-1-196-200", "–––, 1956, Logic, Semantics,\nMetamathematics: Papers from 1923 to 1938, Oxford: Oxford\nUniversity Press.", "van Heijenoort, Jean, 1967, From Frege to Gödel. A Source\nBook in Mathematical Logic 1879–1931, Cambridge, MA:\nHarvard University Press.", "Whitehead, Alfred N. and Bertrand Russell, 1927a, Principia\nMathematica, Volume 1, Cambridge: Cambridge University Press,\nsecond edition.", "–––, 1927b, “Incomplete Symbols”, in\nWhitehead & Russell 1927a: 66–84; reprinted in van\nHeijenoort 1967: 216–223.", "Yasuhara, Mitsuru, 1975, “The Axiom of Choice in\nChurch’s Type Theory” (abstract), Notices of the\nAmerican Mathematical Society, 22(January): A34.\n [Yashuhara 1975 available online]" ]

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[ "\n“The problem of universals” in general is a historically\nvariable bundle of several closely related, yet in different\nconceptual frameworks rather differently articulated metaphysical,\nlogical, and epistemological questions, ultimately all connected to\nthe issue of how universal cognition of singular things is possible.\nHow do we know, for example, that the Pythagorean theorem holds\nuniversally, for all possible right triangles?\nIndeed, how can we have any awareness of a potential infinity of all\npossible right triangles, given that we could only see a finite number\nof actual ones? How can we universally indicate all possible right\ntriangles with the phrase ‘right triangle’? Is there\nsomething common to them all signified by this phrase? If so, what is\nit, and how is it related to the particular right triangles? The\nmedieval problem of universals is a logical, and historical,\ncontinuation of the ancient problem generated by\nPlato’s (428–348 B.C.E.) theory answering such a bundle of\nquestions, namely, his theory of Ideas or Forms." ]

[ { "content_title": "1. Introduction", "sub_toc": [] }, { "content_title": "2. The Emergence of the Problem", "sub_toc": [] }, { "content_title": "3. The Origin of the Specifically Medieval Problem of Universals", "sub_toc": [] }, { "content_title": "4. Boethius’ Aristotelian Solution", "sub_toc": [] }, { "content_title": "5. Platonic Forms as Divine Ideas", "sub_toc": [ "Divine Ideas and Divine Simplicity", "Illuminationism vs. Abstractionism" ] }, { "content_title": "6. Universals According to Abelard’s Aristotelian Conception", "sub_toc": [] }, { "content_title": "7. Universal Natures in Singular Beings and in Singular Minds", "sub_toc": [] }, { "content_title": "8. Universals in the ", "sub_toc": [] }, { "content_title": "9. Universals in the ", "sub_toc": [] }, { "content_title": "10. The Separation of the ", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Primary Literature", "Secondary Literature" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThe inherent problems with Plato’s original theory were\nrecognized already by Plato himself. In his Parmenides Plato\nfamously raised several difficulties, for which he apparently did not\nprovide satisfactory answers. Aristotle (384–322 B.C.E.), with all\ndue reverence to his teacher, consistently rejected Plato’s\ntheory, and heavily criticized it throughout his own work. (Hence the\nfamous saying, amicus Plato sed magis amica\n veritas).[1]\n Nevertheless, despite this explicit doctrinal conflict, Neo-Platonic\nphilosophers, pagans (such as Plotinus ca. 204–270, and\nPorphyry, ca. 234–305) and Christians (such as Augustine,\n354–430, and Boethius, ca. 480–524) alike, observed a\nbasic concordance between Plato’s and Aristotle’s\napproach, crediting Aristotle with an explanation of how the human\nmind acquires its universal concepts of particular things from\nexperience, and Plato with providing an explanation of how the\nuniversal features of particular things are established by being\nmodeled after their universal\n archetypes.[2]\n In any case, it was this general attitude toward the problem in late\nantiquity that set the stage for the ever more sophisticated medieval\n discussions.[3]\n In these discussions, the concepts of the human mind, therefore, were\nregarded as posterior to the particular things represented by these\nconcepts, and hence they were referred to as universalia post\nrem (‘universals after the thing’). The universal\nfeatures of singular things, inherent in these things themselves, were\nreferred to as universalia in re (‘universals in the\nthing’), answering the universal exemplars in the divine mind,\nthe universalia ante rem (‘universals before the\n thing’).[4]\n All these, universal concepts, universal features of singular things,\nand their exemplars, are expressed and signified by means of some\nobviously universal signs, the universal (or common) terms of human\nlanguages. For example, the term ‘man’, in English is a\nuniversal term, because it is truly predicable of all men in one and\nthe same sense, as opposed to the singular term\n‘Socrates’, which in the same sense, i.e., when not used\nequivocally, is only predicable of one man (hence the need to add an\nordinal number to the names of kings and popes of the same name).", "\nDepending on which of these items (universal features of singular\nthings, their universal concepts, or their universal names) they\nregarded as the primary, really existing universals, it is customary\nto classify medieval authors as being realists,\nconceptualists, or nominalists, respectively. The\nrealists are supposed to be those who assert the existence of\nreal universals in and/or before particular things,\nthe conceptualists those who allow universals only, or\nprimarily, as concepts of the mind, whereas nominalists would\nbe those who would acknowledge only, or primarily, universal words.\nBut this rather crude classification does not adequately reflect the\ngenuine, much more subtle differences of opinion between medieval\nthinkers. (No wonder one often finds in the secondary literature\ndistinctions between, “moderate” and “extreme”\nversions of these crudely defined positions.) In the first place,\nnearly all medieval thinkers agreed on the existence of\nuniversals before things in the form of divine ideas existing\nin the divine\n mind,[5]\n but all of them denied their existence in the form of\nmind-independent, real, eternal entities originally posited by Plato.\nFurthermore, medieval thinkers also agreed that particular things have\ncertain features which the human mind is able to comprehend in a\nuniversal fashion, and signify by means of universal terms. As we\nshall see, their disagreements rather concerned the types of the\nrelationships that hold between the particular things, their\nindividual, yet universally comprehensible features, the universal\nconcepts of the mind, and the universal terms of our languages, as\nwell as the ontological status of, and distinctions between, the\nindividualized features of the things and the universal concepts of\nthe mind. Nevertheless, the distinction between “realism”\nand “nominalism”, especially, when it is used to refer to\nthe distinction between the radically different ways of doing\nphilosophy and theology in late-medieval times, is quite justifiable,\nprovided we clarify what really separated these ways, as I\nhope to do in the later sections of this article.", "\nIn this brief summary account, I will survey the problem both from a\nsystematic and from a historical point of view. In the next section I\nwill first motivate the problem by showing how naturally the questions\nconcerning universals emerge if we consider how we come to know a\nuniversal claim, i.e., one that concerns a potentially infinite number\nof particulars of a given kind, in a simple geometrical demonstration.\nI will also briefly indicate why a naïve Platonic answer to these\nquestions in terms of the theory of perfect Forms, however plausible\nit may seem at first, is inadequate. In the third section, I will\nbriefly discuss how the specific medieval questions concerning\nuniversals emerged, especially in the context of answering\nPorphyry’s famous questions in his introduction to\nAristotle’s Categories, which will naturally lead us to\na discussion of Boethius’ Aristotelian answers to these\nquestions in his second commentary on Porphyry in the fourth section.\nHowever, Boethius’ Aristotelian answers anticipated only one\nside of the medieval discussions: the mundane, philosophical theory of\nuniversals, in terms of Aristotelian abstractionism. But the other\nimportant, Neo-Platonic, theological side of the issue provided by\nBoethius, and, most importantly, by St. Augustine, was for medieval\nthinkers the theory of ontologically primary universals as the\ncreative archetypes of the divine mind, the Divine Ideas. Therefore,\nthe fifth section is going to deal with the main ontological and\nepistemological problems generated by this theory, namely, the\napparent conflict between divine simplicity and the multiplicity of\ndivine ideas, on the one hand, and the tension between the Augustinian\ntheory of divine illumination and Aristotelian abstractionism, on the\nother. Some details of the early medieval Boethian-Aristotelian\napproach to the problem and its combination with the Neo-Platonic\nAugustinian tradition before the influx of the newly\nrecovered logical, metaphysical, and physical writings of Aristotle\nand their Arabic commentaries in the second half of the\n12th century will be taken up in the sixth section, in\nconnection with Abelard’s (1079–1142) discussion of\nPorphyry’s questions. The seventh section will discuss some\ndetails of the characteristic metaphysical approach to the problem in\nthe 13th century, especially as it was shaped by the\ninfluence of Avicenna’s (980–1037) doctrine of common\nnature. The eighth section outlines the most general features of the\nlogical conceptual framework that served as the common background for\nthe metaphysical disagreements among the authors of this period. I\nwill argue that it is precisely this common logical-semantical\nframework that allows the grouping together of authors who endorse\nsometimes radically different metaphysics and epistemologies (not only\nin this period, but also much later, well into the early modern\nperiod) as belonging to what in later medieval philosophy came to be\nknown as the “realist” via antiqua, the\n“old way” of doing philosophy and theology. By contrast,\nit was precisely the radically different logical-semantical approach\ninitiated by William Ockham (ca. 1280–1350), and articulated and\nsystematized most powerfully by Jean Buridan (ca. 1300–1358),\nthat distinguished the “nominalist” via moderna,\nthe “modern way” of doing philosophy and theology from the\nsecond half of the 14th century. The general, distinctive\ncharacteristics of this “modern way” will be the discussed\nin the ninth section. Finally, the concluding tenth section will\nbriefly indicate how the separation of the two viae, in\naddition to a number of extrinsic social factors, contributed to the\ndisintegration of scholastic discourse, and thereby to the\ndisappearance of the characteristically medieval problem of\nuniversals, as well as to the re-mergence of recognizably the same\nproblem in different guises in early modern philosophy." ], "section_title": "1. Introduction", "subsections": [] }, { "main_content": [ "\nIt is easy to see how the problem of universals emerges, if we\nconsider a geometrical demonstration, for example, the demonstration\nof Thales’ theorem. According to the theorem, any triangle\ninscribed in a semicircle is a right triangle, as is shown in the\nfollowing diagram:", "\nLooking at this diagram, we can see that all we need to prove is that\nthe angle at vertex D of triangle ABD is a right angle. The proof is\neasy once we realize that since lines AC, DC, and BC are the radii of\na circle, the triangles ACD and DCB are isosceles triangles, whence\ntheir base angles are equal. For then, if we denote the angles of ABD\nby the names of their vertices, this fact entails that D=A + B; and\nso, since A + B + D=180o, it follows that 2A +\n2B=180o; therefore, A + B=90o, that is,\nD=90o, q. e. d.", "\nOf course, from our point of view, the important thing about this\ndemonstration is not so much the truth of its conclusion as\nthe way it proves this conclusion. For the conclusion is a\nuniversal theorem, which has to concern all possible triangles\ninscribed in any possible semicircle whatsoever, not just the one\ninscribed in the semicircle in the figure above. Yet, apparently, in\nthe demonstration above we were talking only about that triangle. So,\nhow can we claim that whatever we managed to prove concerning that\nparticular triangle will hold for all possible triangles?", "\nIf we take a closer look at the diagram, we can easily see the appeal\nof the Platonic answer to this question. For upon a closer look, it is\nclear that, despite appearances to the contrary, this demonstration\ncannot be about the triangle in this diagram. Indeed, in the\ndemonstration we assumed that the lines AC, DC, and BC were all\nperfectly equal, straight lines. However, if we zoom in on the figure,\nwe can clearly see that these lines are far from being equal; in fact,\nthey are not even straight lines:", "\nThe demonstration was certainly not about the collection of jagged\nblack surfaces that we can see here. Rather, the demonstration\nconcerned something we did not see with our bodily eyes, but what we\nhad in mind all along, understanding it to be a triangle, with\nperfectly straight edges, touching a perfect circle in three\nunextended points, which are all perfectly equidistant from the center\nof the circle. The figure we could see was only a convenient\n“reminder” of what we are supposed to have in mind when we\nwant to prove that a certain property, namely, that it is a right\ntriangle, has to belong to the object in our mind in virtue of what it\nis, namely, a triangle inscribed in a semicircle. Obviously, the\nconclusion applies perfectly only to the perfect triangle we had in\nmind, whereas it holds for the visible figure only insofar as, and to\nthe extent that, this figure resembles the object we had in mind. But\nthis figure fails to have this property precisely insofar as, and to\nthe extent that, it falls short of the object in our mind.", "\nHowever, on the basis of this point it should also be clear that the\nconclusion does apply to this figure, and every other visible\ntriangle inscribed in a semicircle as well, insofar as, and to the\nextent that, it manages to imitate the properties of the perfect\nobject in our mind. Therefore, the Platonic answer to the question of\nwhat this demonstration was about, namely, that it was about a\nperfect, ideal triangle, which is invisible to the eyes, but is\ngraspable by our understanding, at once provides us with an\nexplanation of the possibility of universal, necessary knowledge. By\nknowing the properties of the Form or Idea, we know all its\nparticulars, i.e., all the things that imitate it, insofar as they\nimitate or participate in it. So, the Form itself is a universal\nentity, a universal model of all its particulars; and since it is the\nknowledge of this universal entity that can enable us to know at once\nall its particulars, it is absolutely vital for us to know\nwhat it is, what it is like, and exactly\nhow it is related to its particulars. However,\nobviously, all these questions presuppose that it is\nat all, namely, that such a universal entity exists.", "\nBut the existence of such an entity seems to be rather precarious.\nConsider, for instance, the perfect triangle we were supposed to have\nin mind during the demonstration of Thales’ theorem. If it is a\nperfect triangle, it obviously has to have three sides, since a\nperfect triangle has to be a triangle, and nothing can be a triangle\nunless it has three sides. But of those three sides either at least\ntwo are equal or none, that is to say, the triangle in question has to\nbe either isosceles or scalene (taking ‘isosceles’\nbroadly, including even equilateral triangles, for the sake of\nsimplicity). However, since it is supposed to be the universal model\nof all triangles, and not only of isosceles triangles, this\nperfect triangle cannot be an isosceles, and for the same reason it\ncannot be a scalene triangle either. Therefore, such a universal\ntriangle would have to have inconsistent properties, namely,\nboth that it is either isosceles or scalene and that\nit is neither isosceles nor scalene. However, obviously nothing can\nhave these properties at the same time, so nothing can be a universal\ntriangle any more than a round square. So, apparently, no universal\ntriangle can exist. But then, what was our demonstration about? Just a\nlittle while ago, we concluded that it could not be directly about any\nparticular triangle (for it was not about the triangle in the figure,\nand it was even less about any other particular triangle not in the\nfigure), and now we had to conclude that it could not be about a\nuniversal triangle either. But are there any further alternatives? It\nseems obvious that through this demonstration we do gain universal\nknowledge concerning all particulars. Yet it is also clear that we do\nnot, indeed, we cannot gain this knowledge by examining all\nparticulars, both because they are potentially infinite and because\nnone of them perfectly satisfies the conditions stated in the\ndemonstration. So, there must have been something wrong in our\ncharacterization of the universal, which compelled us to conclude\nthat, in accordance with that characterization, universals could not\nexist. Therefore, we are left with a whole bundle of questions\nconcerning the nature and characteristics of universals, questions\nthat cannot be left unanswered if we want to know how universal,\nnecessary knowledge is possible, if at all." ], "section_title": "2. The Emergence of the Problem", "subsections": [] }, { "main_content": [ "\nWhat we may justifiably call the first formulation of “the\nmedieval problem of universals” (distinguishing it from\nthe both logically and historically related ancient problems of\nPlato’s Theory of Forms) was precisely such a bundle of\nquestions famously raised by Porphyry in his Isagoge, that\nis, his Introduction to Aristotle’s Categories. As he\nwrote:", "\n(1) Since, Chrysaorius, to teach about Aristotle’s\nCategories it is necessary to know what genus and difference\nare, as well as species, property, and accident, and since reflection\non these things is useful for giving definitions, and in general for\nmatters pertaining to division and demonstration, therefore I shall\ngive you a brief account and shall try in a few words, as in the\nmanner of an introduction, to go over what our elders said about these\nthings. I shall abstain from deeper enquiries and aim, as appropriate,\nat the simpler ones.\n\n\n(2) For example, I shall beg off saying anything about (a) whether\ngenera and species are real or are situated in bare thoughts alone,\n(b) whether as real they are bodies or incorporeals, and (c) whether\nthey are separated or in sensibles and have their reality in\nconnection with them. Such business is profound, and requires another,\ngreater investigation. Instead I shall now try to show how the\nancients, the Peripatetics among them most of all, interpreted genus\nand species and the other matters before us in a more logical fashion.\n[Porphyry, Isagoge, in Spade 1994 (henceforth, Five\nTexts), p. 1.]\n", "\nEven though in this way, by relegating them to a “greater\ninvestigation”, Porphyry left these questions unanswered, they\ncertainly proved to be irresistible for his medieval Latin\ncommentators, beginning with Boethius, who produced not just one, but\ntwo commentaries on Porphyry’s text; the first based on Marius\nVictorinus’s (fl. 4th c.) translation, and\nthe second on his\n own.[6]", "\nIn the course of his argument, Boethius makes it quite clear what sort\nof entity a universal would have to be.", "\nA universal must be common to several particulars\n\n\n\nin its entirety, and not only in part\n\nsimultaneously, and not in a temporal succession, and\n\nit should constitute the substance of its\n particulars.[7]\n \n", "\nHowever, as Boethius argues, nothing in real existence can satisfy\nthese conditions. The main points of his argument can be reconstructed\nas follows.", "\nAnything that is common to many things in the required manner has to\nbe simultaneously, and as a whole, in the substance of these many\nthings. But these many things are several beings precisely because\nthey are distinct from one another in their being, that is to say, the\nact of being of one is distinct from the act of being of the other.\nHowever, if the universal constitutes the substance of a particular,\nthen it has to have the same act of being as the particular, because\nconstituting the substance of something means precisely this, namely,\nsharing the act of being of the thing in question, as the\nthing’s substantial part. But the universal is supposed to\nconstitute the substance of all of its distinct particulars, as a\nwhole, at the same time. Therefore, the one act of being of the\nuniversal entity would have to be identical with all the distinct acts\nof being of its several particulars at the same time, which is\n impossible.[8]", "\nThis argument, therefore, establishes that no one thing can be a\nuniversal in its being, that is to say, nothing can be both one being\nand common to many beings in such a manner that it shares its act of\nbeing with those many beings, constituting their substance.", "\nThis can easily be visualized in the following diagram, where the tiny\nlightning bolts indicate the acts of being of the entities involved,\nnamely, a woman, a man, and their universal humanity (the larger\ndotted figure).", "\nBut then, Boethius goes on, we should perhaps say that the universal\nis not one being, but rather many beings, that is, [the collection\n of][9]\n those constituents of the individual essences of its particulars on\naccount of which they all fall under the same universal predicable.\nFor example, on this conception, the genus ‘animal’ would\nnot be some one entity, a universal animality over and above the\nindividual animals, yet somehow sharing its being with them all\n(since, as we have just seen, that is impossible), but rather [the\ncollection of] the individual animalities of all animals.", "\nBoethius rejects this suggestion on the ground that whenever there are\nseveral generically similar entities, they have to have a genus;\ntherefore, just as the individual animals had to have a genus, so too,\ntheir individual animalities would have to have another one. However,\nsince the genus of animalities cannot be one entity, some\n‘super-animality’ (for the same reason that the genus of\nanimals could not be one entity, on the basis of the previous\nargument), it seems that the genus of animalities would have to be a\nnumber of further ‘super-animalities’. But then again, the\nsame line of reasoning should apply to these\n‘super-animalities’, giving rise to a number of\n‘super-super-animalities’, and so on to infinity, which is\nabsurd. Therefore, we cannot regard the genus as some real being even\nin the form of [a collection of] several distinct entities. Since\nsimilar reasonings would apply to the other Porphyrian predicables as\nwell, no universal can exist in this way.", "\nNow, a universal either exists in reality independently of a mind\nconceiving of it, or it only exists in the mind. If it exists in\nreality, then it either has to be one being or several beings. But\nsince it cannot exist in reality in either of these two ways, Boethius\nconcludes that it can only exist in the\n mind.[10]", "\nHowever, to complicate matters, it appears that a universal cannot\nexist in the mind either. For, as Boethius says, the universal\nexisting in the mind is some universal understanding of some thing\noutside the mind. But then this universal understanding is either\ndisposed in the same way as the thing is, or differently. If it is\ndisposed in the same way, then the thing also must be universal, and\nthen we end up with the previous problem of a really existing\nuniversal. On the other hand, if it is disposed differently, then it\nis false, for “what is understood otherwise than the thing is is\nfalse” (Five Texts, Spade 1994, p. 23 (21)). But then,\nall universals in the understanding would have to be false\nrepresentations of their objects; therefore, no universal knowledge\nwould be possible, whereas our considerations started out precisely\nfrom the existence of such knowledge, as seems to be clear, e.g., in\nthe case of geometrical knowledge." ], "section_title": "3. The Origin of the Specifically Medieval Problem of Universals", "subsections": [] }, { "main_content": [ "\nBoethius’ solution of the problem stated in this form consists\nin the rejection of this last argument, by pointing out the ambiguity\nof the principle that “what is understood otherwise than the\nthing is is false”. For in one sense this principle states the\nobvious, namely, that an act of understanding that represents a thing\nto be otherwise than the thing is is false. This is\nprecisely the reading of this principle that renders it plausible.\nHowever, in another sense this principle would state that an act of\nunderstanding which represents the thing in a manner which is\ndifferent from the manner in which the thing exists is false. In this\nsense, then, the principle would state that if the mode of\nrepresentation of the act of understanding is different from the mode\nof being of the thing, then the act of understanding is false. But\nthis is far from plausible. In general, it is simply not true that a\nrepresentation can be true or faithful only if the mode of\nrepresentation matches the mode of being of the thing represented. For\nexample, a written sentence is a true and faithful representation of a\nspoken sentence, although the written sentence is a visible, spatial\nsequence of characters, whereas the spoken sentence is an audible,\ntemporal pattern of articulated sounds. So, what exists as an audible\npattern of sounds is represented visually, that is, the mode of\nexistence of the thing represented is radically different from the\nmode of its representation. In the same way, when particular things\nare represented by a universal act of thought, the things exist in a\nparticular manner, while they are represented in a universal manner,\nstill, this need not imply that the representation is false. But this\nis precisely the sense of the principle that the objection exploited.\nTherefore, since in this sense the principle can be rejected, the\nobjection is not\n conclusive.[11]", "\nHowever, it still needs to be shown that in the particular case of\nuniversal representation the mismatch between the mode of its\nrepresentation and the mode of being of the thing represented does in\nfact not entail the falsity of the representation. This can easily be\nseen if we consider the fact that the falsity of an act of\nunderstanding consists in representing something to be in a\nway it is not. That is to say, properly speaking, it is only an act of\njudgment that can be false, by which we think something\nto be somehow. But a simple act of understanding, by\nwhich we simply understand something without thinking it to\nbe somehow, that is, without attributing anything to it, cannot\nbe false. For example, I can be mistaken if I form in my mind the\njudgment that a man is running, whereby I conceive a man\nto be somehow, but if I simply think of a man without\nattributing either running or not running to him, I certainly cannot\nmake a mistake as to how he\n is.[12]\n In the same way, I would be mistaken if I were to think that a\ntriangle is neither isosceles nor scalene, but I am certainly not in\nerror if I simply think of a triangle without thinking either that it\nis isosceles or that it is scalene. Indeed, it is precisely this\npossibility that allows me to form the universal mental\nrepresentation, that is, the universal concept of all particular\ntriangles, regardless of whether they are isosceles or scalene. For\nwhen I think of a triangle in general, then I certainly do not think\nof something that is a triangle and is neither isosceles nor scalene,\nfor that is impossible, but I simply think of a triangle, not thinking\nthat it is an isosceles and not thinking that it is a scalene\ntriangle. This is how the mind is able to separate in thought what are\ninseparable in real existence. Being either isosceles or scalene is\ninseparable from a triangle in real existence. For it is impossible\nfor something to be a triangle, and yet not to be an\nisosceles and not to be a scalene triangle either.\nStill, it is not impossible for something to be thought to be\na triangle and not to be thought to be an isosceles\nand not to be thought to be a scalene triangle\neither (although of course, it still has to be thought to be\neither-isosceles-or-scalene). This separation in thought of those\nthings that cannot be separated in reality is the process of\n abstraction.[13]\n In general, by means of the process of abstraction, our mind (in\nparticular, the faculty of our mind Aristotle calls active\nintellect (nous poietikos, in Greek, intellectus\nagens, in Latin) is able to form universal representations of\nparticular objects by disregarding what distinguishes them, and\nconceiving of them only in terms of those of their features in respect\nof which they do not differ from one another.", "\nIn this way, therefore, if universals are regarded as universal mental\nrepresentations existing in the mind, then the contradictions emerging\nfrom the Platonic conception no longer pose a threat. On this\nAristotelian conception, universals need not be thought of as somehow\nsharing their being with all their distinct particulars, for their\nbeing simply consists in their being thought of, or rather, the\nparticulars’ being thought of in a universal manner. This is\nwhat Boethius expresses by saying in his final replies to\nPorphyry’s questions the following:", "\n\n\n… genera and species subsist in one way, but are understood in\nan another. They are incorporeal, but subsist in sensibles, joined to\nsensibles. They are understood, however, as subsisting by themselves,\nand as not having their being in others. [Five Texts, Spade\n1994, p. 25]\n", "\nBut then, if in this way, by positing universals in the mind, the most\nobvious inconsistencies of Plato’s doctrine can be avoided, no\nwonder that Plato’s “original” universals, the\nuniversal models which particulars try to imitate by their features,\nfound their place, in accordance with the long-standing Neo-Platonic\ntradition, in the divine\n mind.[14]\n It is this tradition that explains Boethius’ cautious\nformulation of his conclusion concerning Aristotelianism pure and\nsimple, as not providing us with the whole story. As he writes:", "\n\n\n… Plato thinks that genera and species and the rest are not\nonly understood as universals, but also exist and subsist apart from\nbodies. Aristotle, however, thinks that they are understood as\nincorporeal and universal, but subsist in sensibles.\n\n\nI did not regard it as appropriate to decide between their views. For\nthat belongs to a higher philosophy. But we have carefully followed\nout Aristotle’s view here, not because we would recommend it the\nmost, but because this book, [the Isagoge], is written about\nthe Categories, of which Aristotle is the author. [Five\nTexts, Spade 1994, p. 25]\n" ], "section_title": "4. Boethius’ Aristotelian Solution", "subsections": [] }, { "main_content": [ "\nBesides Boethius, the most important mediator between the Neo-Platonic\nphilosophical tradition and the Christianity of the Medieval Latin\nWest, pointing out also its theological implications, was St.\nAugustine. In a passage often quoted by medieval authors in their\ndiscussions of divine ideas, he writes as follows:", "\n\n\n… in Latin we can call the Ideas “forms” or\n“species”, in order to appear to translate word for word.\nBut if we call them “reasons”, we depart to be sure from a\nproper translation — for reasons are called “logoi”\nin Greek, not Ideas — but nevertheless, whoever wants to use\nthis word will not be in conflict with the fact. For Ideas are certain\nprincipal, stable and immutable forms or reasons of things. They are\nnot themselves formed, and hence they are eternal and always stand in\nthe same relations, and they are contained in the divine\nunderstanding. [Spade 1985, Other Internet Resources, p.\n 383][15]\n ", "\nAs we could see from Boethius’ solution, in this way, if\nPlatonic Forms are not universal beings existing in a universal\nmanner, but their universality is due to a universal manner of\nunderstanding, we can avoid the contradictions arising from the\n“naïve” Platonic conception. Nevertheless, placing\nuniversal ideas in the divine mind as the archetypes of creation, this\nconception can still do justice to the Platonic intuition that what\naccounts for the necessary, universal features of the ephemeral\nparticulars of the visible world is the presence of some universal\nexemplars in the source of their being. It is precisely in virtue of\nhaving some insight into these exemplars themselves that we can have\nthe basis of universal knowledge Plato was looking for. As St.\nAugustine continues:", "\n\n\nAnd although they neither arise nor perish, nevertheless everything\nthat is able to arise and perish, and everything that does arise and\nperish, is said to be formed in accordance with them. Now it is denied\nthat the soul can look upon them, unless it is a rational one, [and\neven then it can do so] only by that part of itself by which it\nsurpasses [other things] — that is, by its mind and reason, as\nif by a certain “face”, or by an inner and intelligible\n“eye”. To be sure, not each and every rational soul in\nitself, but [only] the one that is holy and pure, that [is the one\nthat] is claimed to be fit for such a vision, that is, the one that\nkeeps that very eye, by which these things are seen, healthy and pure\nand fair and like the things it means to see. What devout man imbued\nwith true religion, even though he is not yet able to see these\nthings, nevertheless dares to deny, or for that matter fails to\nprofess, that all things that exist, that is, whatever things are\ncontained in their own genus with a certain nature of their own, so\nthat that they might exist, are begotten by God their author, and that\nby that same author everything that lives is alive, and that the\nentire safe preservation and the very order of things, by which\nchanging things repeat their temporal courses according to a fixed\nregimen, are held together and governed by the laws of a supreme God?\nIf this is established and granted, who dares to say that God has set\nup all things in an irrational manner? Now if it is not correct to say\nor believe this, it remains that all things are set up by reason, and\na man not by the same reason as a horse — for that is absurd to\nsuppose. Therefore, single things are created with their own reasons.\nBut where are we to think these reasons exist, if not in the mind of\nthe creator? For he did not look outside himself, to anything placed\n[there], in order to set up what he set up. To think that is\nsacrilege. But if these reasons of all things to be created and\n[already] created are contained in the divine mind, and [if] there\ncannot be anything in the divine mind that is not eternal and\nunchangeable, and [if] Plato calls these principal reasons of things\n“Ideas”, [then] not only are there Ideas but they are\ntrue, because they are eternal and [always] stay the same way, and\n[are] unchangeable. And whatever exists comes to exist, however it\nexists, by participation in them. But among the things set up by God,\nthe rational soul surpasses all [others], and is closest to God when\nit is pure. And to the extent that it clings to God in charity, to\nthat extent, drenched in a certain way and lit up by that intelligible\nlight, it discerns these reasons, not by bodily eyes but by that\nprincipal [part] of it by which it surpasses [everything else], that\nis, by its intelligence. By this vision it becomes most blessed. These\nreasons, as was said, whether it is right to call them Ideas or forms\nor species or reasons, many are permitted to call [them] whatever they\nwant, but [only] to a very few [is it permitted] to see what is true.\n[Spade 1985, Other Internet Resources, pp. 383–384]\n", "\nAugustine’s conception, then, saves Plato’s original\nintuitions, yet without their inconsistencies, while it also combines\nhis philosophical insights with Christianity. But, as a rule, a really\nintriguing solution of a philosophical problem usually gives rise to a\nnumber of further problems. This solution of the original problem with\nPlato’s Forms is no exception." ], "section_title": "5. Platonic Forms as Divine Ideas", "subsections": [ { "content": [ "\nFirst of all, it generates a particular ontological/theological\nproblem concerning the relationship between God and His Ideas. For\naccording to the traditional philosophical conception of divine\nperfection, God’s perfection demands that He is absolutely\nsimple, without any composition of any sort of\n parts.[16]\n So, God and the divine mind are not related to one another as a man\nand his mind, namely as a substance to one of its several powers, but\nwhatever powers God has He is. Furthermore, the\nDivine Ideas themselves cannot be regarded as being somehow the\neternal products of the divine mind distinct from the divine mind, and\nthus from God Himself, for the only eternal being is God, and\neverything else is His creature. Now, since the Ideas are not\ncreatures, but the archetypes of creatures in God’s mind, they\ncannot be distinct from God. However, as is clear from the passage\nabove, there are several Ideas, and there is only one God. So how can\nthese several Ideas possibly be one and the same God?", "\nAugustine never explicitly raised the problem, but for example\nAquinas, who (among others) did, provided the following rather\nintuitive solution for it (ST1, q. 15, a. 2). The Divine Ideas are in\nthe Divine Mind as its objects, i.e., as the things understood. But\nthe diversity of the objects of an act of understanding need not\ndiversify the act itself (as when understanding the Pythagorean\ntheorem, we understand both squares and triangles). Therefore, it is\npossible for the self-thinking divine essence to understand itself in\na single act of understanding so perfectly that this act of\nunderstanding not only understands the divine essence as it is in\nitself, but also in respect of all possible ways in which it can be\nimperfectly participated by any finite creature. The cognition of the\ndiversity of these diverse ways of participation accounts for the\nplurality of divine ideas. But since all these diverse ways are\nunderstood in a single eternal act of understanding, which is nothing\nbut the act of divine being, and which in turn is again the divine\nessence itself, the multiplicity of ideas does not entail any\ncorresponding multiplicity of the divine essence. To be sure, this\nsolution may still give rise to the further questions as to what these\ndiverse ways are, exactly how they are related to the divine essence,\nand how their diversity is compatible with the unity and simplicity of\nthe ultimate object of divine thought, namely, divine essence itself.\nIn fact, these are questions that were raised and discussed in detail\nby authors such as Henry of Ghent (c. 1217–1293), Thomas of\nSutton (ca. 1250–1315), Duns Scotus (c. 1266–1308) and\n others.[17]" ], "subsection_title": "5.1 Divine Ideas and Divine Simplicity" }, { "content": [ "\nAnother major issue connected to the doctrine of divine ideas, as\nshould also be clear from the previously quoted passage, was the\nbundle of epistemological questions involved in Augustine’s\ndoctrine of divine illumination. The doctrine — according to\nwhich the human soul, especially “one that is holy and\npure”, obtains a specific supernatural aid in its acts of\nunderstanding, by gaining a direct insight into the Divine Ideas\nthemselves — received philosophical support in terms of a\ntypically Platonic argument in Augustine’s De Libero\n Arbitrio.[18]\n The argument can be reconstructed as follows.", "\nThe Augustinian Argument for Illumination.\n\n\n\nI can come to know from experience only something that can be\nfound in experience [self-evident]\n\nAbsolute unity cannot be found in experience [assumed]\n\nTherefore, I cannot come to know absolute unity from experience.\n[1,2]\n\nWhatever I know, but I cannot come to know from experience, I came\nto know from a source that is not in this world of experiences.\n[self-evident]\n\nI know absolute unity. [assumed]\n\nTherefore, I came to know absolute unity from a source that is not\nin this world of experiences. [3,4,5]\n\n\n\nProof of 2. Whatever can be found in experience is some\nmaterial being, extended in space, and so it has to have a multitude\nof spatially distinct parts. Therefore, it is many in respect of those\nparts. But what is many in some respect is not one in that respect,\nand what is not one in some respect is not absolutely one. Therefore,\nnothing can be found in experience that is absolutely one, that is,\nnothing in experience is an absolute unity.\n\n\nProof of 5. I know that whatever is given in experience has\nmany parts (even if I may not be able to discern those parts by my\nsenses), and so I know that it is not an absolute unity. But I can\nhave this knowledge only if I know absolute unity, namely, something\nthat is not many in any respect, not even in respect of its parts,\nfor, in general, I can know that something is F in a certain respect,\nand not an F in some other respect, only if I know what it is for\nsomething to be an F without any qualification. (For example, I know\nthat the two halves of a body, taken together, are not absolutely two,\nfor taken one by one, they are not absolutely one, since they are also\ndivisible into two halves, etc. But I can know this only because I\nknow that for obtaining absolutely two things [and not just two\nmultitudes of further things], I would have to have two things that in\nthemselves are absolutely one.) Therefore, I know absolute unity.\n", "\nIt is important to notice here that this argument (crucially) assumes\nthat the intellect is passive in acquiring its concepts. According to\nthis assumption, the intellect merely receives the cognition of its\nobjects as it finds them. By contrast, on the Aristotelian conception,\nthe human mind actively processes the information it receives from\nexperience through the senses. So by means of its faculty\nappropriately called the active or agent intellect, it is able to\nproduce from a limited number of experiences a universal concept\nequally representing all possible particulars falling under that\nconcept. In his commentary on Aristotle’s De Anima\nAquinas insightfully remarks:", "\n\n\nThe reason why Aristotle came to postulate an active intellect was his\nrejection of Plato’s theory that the essences of sensible things\nexisted apart from matter, in a state of actual intelligibility. For\nPlato there was clearly no need to posit an active intellect. But\nAristotle, who regarded the essences of sensible things as existing in\nmatter with only a potential intelligibility, had to invoke some\nabstractive principle in the mind itself to render these essences\nactually intelligible. [In De Anima, bk. 3, lc. 10]\n", "\nOn the basis of these and similar considerations, therefore, one may\nconstruct a rather plausible Aristotelian counterargument, which is\ndesigned to show that we need not necessarily gain our concept of\nabsolute unity from a supernatural source, for it is possible for us\nto obtain it from experience by means of the active intellect. Of\ncourse, similar considerations should apply to other concepts as\nwell.", "\nAn Aristotelian-Thomistic counterargument from\nabstraction.\n\n\n\nI know from experience everything whose concept my active\nintellect is able to abstract from experience. [self-evident]\n\nBut my active intellect is able to abstract from experience the\nconcept of unity, since we all experience each singular thing as being\none, distinct from another. [self-evident, common\n experience][19]\n \nTherefore, I know unity from experience by abstraction. [1,2]\n\nWhenever I know something from experience by abstraction, I know\nboth the thing whose concept is abstracted and its limiting conditions\nfrom which its concept is abstracted. [self-evident]\n\nTherefore, I know both unity and its limiting conditions from\nwhich its concept is abstracted. [3,4]\n\nBut whenever I know something and its limiting conditions, and I\ncan conceive of it without its limiting conditions (and this is\nprecisely what happens in abstraction), I can conceive of its\nabsolute, unlimited realization. [self-evident]\n\nTherefore, I can conceive of the absolute, unlimited realization\nof unity, based on the concept of unity I acquired from experience by\nabstraction. [5,6]\n\nTherefore, it is not necessary for me to have a preliminary\nknowledge of absolute unity before all experience, from a source other\nthan this world of experiences. [7]\n\n", "\nTo be sure, we should notice here that this argument does\nnot falsify the doctrine of illumination.\nProvided it works, it only invalidates the\nAugustinian-Platonic argument for illumination. Furthermore,\nthis is obviously not a sweeping, knock-down refutation of the idea\nthat at least some of our concepts perhaps could not so simply be\nderived from experience by abstraction; in fact, in the particular\ncase of unity, and in general, in connection with our transcendental\nnotions (i.e., notions that apply in each Aristotelian category, so\nthey transcend the limits of each one of them, such as the\nnotions of being, unity, goodness,\ntruth, etc.), even the otherwise consistently Aristotelian\nAquinas would have a more complicated story to tell (see Klima 2000b).\nNevertheless, although Aquinas would still leave some room for\nillumination in his epistemology, he would provide for illumination an\nentirely naturalistic interpretation, as far as the acquisition of our\nintellectual concepts of material things is concerned, by simply\nidentifying it with the “intellectual light in us”, that\nis, the active intellect, which enables us to acquire these concepts\nfrom experience by\n abstraction.[20]\n Duns Scotus, who opposed Aquinas on so many other points, takes\nbasically the same stance on this issue. Other medieval theologians,\nespecially such prominent “Augustinians” as Bonaventure,\nMatthew of Aquasparta, or Henry of Ghent, would provide greater room\nfor illumination in the form of a direct, specific, supernatural\ninfluence needed for human intellectual cognition in this life besides\nthe general divine cooperation needed for the workings of our natural\npowers, in particular, the abstractive function of the active\n intellect.[21]\n But they would not regard illumination as supplanting, but rather as\nsupplementing intellectual abstraction.", "\nAs we could see, Augustine makes recognition of truth dependent on\ndivine illumination, a sort of irradiation of the intelligible light\nof divine ideas, which is accessible only to the few who are\n“holy and pure”.", "\nBut this seems to go against at least", "\n\n\n1. the experience that there are knowledgeable non-believers or\npagans\n\n\n2. the Aristotelian insight that we can have infallible comprehension\nof the first principles of scientific demonstrations for which we only\nneed the intellectual concepts that we can acquire naturally, from\nexperience by\n abstraction,[22]\n ", "\nand", "\n\n\n3. the philosophical-theological consideration that if human reason,\nman’s natural faculty for acquiring truth were not sufficient\nfor performing its natural function, then human nature would be\nnaturally defective in its noblest part, precisely in which it was\ncreated after the image of God.\n", "\nIn fact, these are only some of the problems explicitly raised and\nconsidered by medieval Augustinians, which prompted their ever more\nrefined accounts of the role of illumination in human cognition.", "\nFor example, Matthew of Aquasparta, recapitulating St. Bonaventure,\nwrites as follows:", "\n\n\nPlato and his followers stated that the entire essence of cognition\ncomes forth from the archetypal or intelligible world, and from the\nideal reasons; and they stated that the eternal light contributes to\ncertain cognition in its evidentness as the entire and sole reason for\ncognition, as Augustine in many places recites, in particular in bk.\nviii. c. 7 of The City of God: ‘The light of minds for\nthe cognition of everything is God himself, who created\neverything’.\n\n\nBut this position is entirely mistaken. For although it appears to\nsecure the way of wisdom, it destroys the way of knowledge.\nFurthermore, if that light were the entire and sole reason for\ncognition, then the cognition of things in the Word would not differ\nfrom their cognition in their proper kind, neither would the cognition\nof reason differ from the cognition of revelation, nor philosophical\ncognition from prophetic cognition, nor cognition by nature from\ncognition by grace.\n\n\nThe other position was apparently that of Aristotle, who claimed that\nthe entire essence of cognition is caused and comes from below,\nthrough the senses, memory, and experience, [working together] with\nthe natural light of our active intellect, which abstracts the species\nfrom phantasms and makes them actually understood. And for this reason\nhe did not claim that the eternal is light necessary for cognition,\nindeed, he never spoke about it. And this opinion of his is obvious in\nbk. 2 of the Posterior Analytics. […]\n\n\nBut this position seems to be very deficient. For although it builds\nthe way of knowledge, it totally destroys the way of wisdom.\n[…]\n\n\nTherefore, I take it that one should maintain an intermediate position\nwithout prejudice, by stating that our cognition is caused both from\nbelow and from above, from external things as well as the ideal\nreasons.\n\n\n[…] God has provided our mind with some intellectual light, by\nmeans of which it would abstract the species of objects from the\nsensibles, by purifying them and extracting their quiddities, which\nare the per se objects of the intellect. […] But this light is\nnot sufficient, for it is defective, and is mixed with obscurity,\nunless it is joined and connected to the eternal light, which is the\nperfect and sufficient reason for cognition, and the intellect attains\nand somehow touches it by its upper part.\n\n\nHowever the intellect attains that light or those eternal reasons as\nthe reason for cognition not as sole reason, for then, as has been\nsaid, cognition in the Word would not differ from cognition in proper\nkind, nor the cognition of wisdom would differ from the cognition of\nknowledge. Nor does it attain them as the entire reason, for then it\nwould not need the species and similitudes of things; but this is\nfalse, for the Philosopher says, and experience teaches, that if\nsomeone loses a sense, then he loses that knowledge of things which\ncomes from that sense. [DHCR, pp. 94–96]\n", "\nIn this way, taking the intermediate position between Platonism and\nAristotelianism pure and simple, Matthew interprets Augustine’s\nPlatonism as being compatible with the Aristotelian view, crediting\nthe Aristotelian position with accounting for the specific empirical\ncontent of our intellectual concepts, while crediting the Platonic\nview with accounting for their certainty in grasping the natures of\nthings. Still, it may not appear quite clear exactly what the\ncontribution of the eternal light is, indeed, whether it is necessary\nat all. After all, if by abstraction we manage to gain those\nintellectual concepts that represent the natures of things, what else\nis needed to have a grasp of those natures?", "\nHenry of Ghent, in his detailed account of the issue, provides an\ninteresting answer to this question. Henry first distinguishes\ncognition of a true thing from the cognition of the truth of the\nthing. Since any really existing thing is truly what it is (even if it\nmay on occasion appear something else), any cognition of any really\nexisting thing is the cognition of a true thing. But cognition of a\ntrue thing may occur without the cognition of its truth, since the\nlatter is the cognition that the thing adequately corresponds to its\nexemplar in the human or divine mind. For example, if I draw a circle,\nwhen a cat sees it, then it sees the real true thing as it is\npresented to it. Yet the cat is simply unable to judge whether it is a\ntrue circle in the sense that it really is what it is supposed to be,\nnamely, a locus of points equidistant from a given point. By contrast,\na human being is able to judge the truth of this thing, insofar as he\nor she would be able to tell that my drawing is not really and truly a\ncircle, but is at best a good approximation of what a true circle\nwould be.", "\nNow, in intellectual cognition, just as in the sensory cognition of\nthings, when the intellect simply apprehends a true thing, then it\nstill does not have to judge the truth of the thing, even though it\nmay have a true apprehension, adequately representing the thing. But\nthe cognition of the truth of the thing only occurs in a judgment,\nwhen the intellect judges the adequacy of the thing to its\nexemplar.", "\nBut since a thing can be compared to two sorts of exemplar, namely, to\nthe exemplar in the human mind, and to the exemplar in the divine\nmind, the cognition of the truth of a thing is twofold, relative to\nthese two exemplars. The exemplar of the human mind, according to\nHenry, is nothing but the Aristotelian abstract concept of the thing,\nwhereby the thing is simply apprehended in a universal manner, and\nhence its truth is judged relative to this concept, when the intellect\njudges that the thing in question falls under this concept or not. As\nHenry writes:", "\n\n\n[…] attending to the exemplar gained from the thing as the\nreason for its cognition in the cognizer, the truth of the thing can\nindeed be recognized, by forming a concept of the thing that conforms\nto that exemplar; and it is in this way that Aristotle asserted that\nman gains knowledge and cognition of the truth from purely natural\nsources about changeable natural things, and that this exemplar is\nacquired from things by means of the senses, as from the first\nprinciple of art and science. […] So, by means of the universal\nnotion in us that we have acquired from the several species of animals\nwe are able to realize concerning any thing that comes our way whether\nit is an animal or not, and by means of the specific notion of donkey\nwe realize concerning any thing that comes our way whether it is a\ndonkey or not. [HQO, a. 1, q. 2, fol. 5 E-F]\n", "\nBut this sort of cognition of the truth of a thing, although it is\nintellectual, universal cognition, is far from being the infallible\nknowledge we are seeking. As Henry argues further:", "\n\n\nBut by this sort of acquired exemplar in us we do not have the\nentirely certain and infallible cognition of truth. Indeed, this is\nentirely impossible for three reasons, the first of which is taken\nfrom the thing from which this exemplar is abstracted, the second from\nthe soul, in which this exemplar is received, and the third from the\nexemplar itself that is received in the soul about the thing.\n\n\nThe first reason is that this exemplar, since it is abstracted from\nchangeable things, has to share in the nature of changeability.\nTherefore, since physical things are more changeable than mathematical\nobjects, this is why the Philosopher claimed that we have a greater\ncertainty of knowledge about mathematical objects than about physical\nthings by means of their universal species. And this is why Augustine,\ndiscussing this cause of the uncertainty of the knowledge of natural\nthings in q. 9 of his Eighty-Three Different Questions, says\nthat from the bodily senses one should not expect the pure truth\n[syncera veritas]\n\n\n… The second reason is that the human soul, since it is\nchangeable and susceptible to error, cannot be rectified to save it\nfrom swerving into error by anything that is just as changeable as\nitself, or even more; therefore, any exemplar that it receives from\nnatural things is necessarily just as changeable as itself, or even\nmore, since it is of an inferior nature, whence it cannot rectify the\nsoul so that it would persist in the infallible truth.\n\n\n… The third reason is that this sort of exemplar, since it is\nthe intention and species of the sensible thing abstracted from the\nphantasm, is similar to the false as well as to the true [thing], so\nthat on its account these cannot be distinguished. For it is by means\nof the same images of sensible things that in dreams and madness we\njudge these images to be the things, and in sane awareness we judge\nthe things themselves. But the pure truth can only be perceived by\ndiscerning it from falsehood. Therefore, by means of such an exemplar\nit is impossible to have certain knowledge, and certain cognition of\nthe truth. And so if we are to have certain knowledge of the truth,\nthen we have to turn our mind away from the senses and sensible\nthings, and from every intention, no matter how universal and\nabstracted from sensible things, to the unchangeable truth existing\nabove the mind […]. [ibid., fol. 5. F]\n", "\nSo, Henry first distinguished between the cognition of a true thing\nand the intellectual cognition of the truth of a thing, and then,\nconcerning the cognition of the truth of the thing, he distinguished\nbetween the cognition of truth by means of a concept abstracted from\nthe thing and “the pure truth” [veritas syncera vel\nliquida], which he says cannot be obtained by means of such\nabstracted concepts.", "\nBut then the question naturally arises: what is this “pure\ntruth”, and how can it be obtained, if at all? Since cognition\nof the pure truth involves comparison of objects not to their acquired\nexemplar in the human mind, but to their eternal exemplar in the\ndivine mind, in the ideal case it would consist in some sort of direct\ninsight into the divine ideas, enabling the person who has this access\nto see everything in its true form, as “God meant it to\nbe”, and also see how it fails to live up to its idea due to its\ndefects. So, it would be like the direct intuition of two objects, one\nsensible, another intelligible, on the basis of which one could also\nimmediately judge how closely the former approaches the latter. But\nthis sort of direct intuition of the divine ideas is only the share of\nangels and the souls of the blessed in beatific vision; it is\ngenerally not granted in this life, except in rare, miraculous cases,\nin rapture, or prophetic vision.", "\nTherefore, if there is to be any non-miraculous recognition of this\npure truth in this life, then it has to occur differently. Henry\nargues that even if we do not have a direct intuition of divine ideas\nas the objects cognized (whereby their particulars are recognized as\nmore or less approximating them), we do have the cognition of the\nquiddities of things as the objects cognized by reason of some\nindirect cognition of their ideas. The reason for this, Henry says, is\nthe following:", "\n\n\n…for our concept to be true by the pure truth, the soul,\ninsofar as it is informed by it, has to be similar to the truth of the\nthing outside, since truth is a certain adequacy of the thing and the\nintellect. And so, as Augustine says in bk. 2 of On Free Choice of\nthe Will, since the soul by itself is liable to slip from truth\ninto falsity, whence by itself it is not informed by the truth of any\nthing, although it can be informed by it, but nothing can inform\nitself, for nothing can give what it does not have; therefore, it is\nnecessary that it be informed of the pure truth of a thing by\nsomething else. But this cannot be done by the exemplar received from\nthe thing itself, as has been shown earlier [in the previously quoted\npassage — GK]. It is necessary, therefore, that it be informed\nby the exemplar of the unchangeable truth, as Augustine intends in the\nsame place. And this is why he says in On True Religion that\njust as by its truth are true those that are true, so too by its\nsimilitude are similar those that are similar. It is necessary,\ntherefore, that the unchangeable truth impress itself into our\nconcept, and that it transform our concept to its own character, and\nthat in this way it inform our mind with the expressed truth of the\nthing by the same similitude that the thing itself has in the first\ntruth. [HQO a. 1, q. 2, fol. 7, I]\n", "\nSo, when we have the cognition of the pure truth of a thing, then we\ncannot have it in terms of the concept acquired from the thing, yet,\nsince we cannot have it from a direct intuition of the divine exemplar\neither, the way we can have it is that the acquired concept primarily\nimpressed on our mind will be further clarified, but no longer by a\nsimilarity of the thing, but by the similarity of the divine exemplar\nitself. Henry’s point seems to be that given that the external\nthing itself is already just a (more or less defective) copy of the\nexemplar, the (more or less defective) copy of this copy can only be\nimproved by means of the original exemplar, just as a copy of a poor\nrepro of some original picture can only be improved by retouching the\ncopy not on the basis of the poor repro, but on the basis of the\noriginal. But since the external thing is fashioned after its divine\nidea, the “retouching” of the concept in terms of the\noriginal idea does yield a better representation of the thing; indeed,\nso much better that on the basis of this “retouched”\nconcept we are even able to judge just how well the thing realizes its\nkind.", "\nFor example, when I simply have the initial simple concept of circle\nabstracted from circular objects I have seen, that concept is good\nenough for me to tell circular objects apart from non-circular ones.\nBut with this simple, unanalyzed concept in mind, I may still not be\nable to say what a true circle is supposed to be, and accordingly,\nexactly how and to what extent the more or less circular objects I see\nfail or meet this standard. However, when I come to understand that a\ncircle is a locus of points equidistant from a given point, I will\nrealize by means of a clear and distinct concept what it was that I\noriginally conceived in a vague and confused manner in my original\nconcept of\n circle.[23]", "\nTo be sure, I do not come to this definition of circle by looking up\nto the heaven of Ideas; in fact, I may just be instructed about it by\nmy geometry teacher. But what is not given to me by my geometry\nteacher is the understanding of the fact that what is expressed by the\ndefinition is indeed what I originally rather vaguely conceived by my\nconcept abstracted from visible circles. This “flash” of\nunderstanding, when I realize that it is necessary for anything that\ntruly matches the concept of a circle to be such as described in the\ndefinition, would be an instance of receiving illumination without any\nparticular, miraculous\n revelation.[24]", "\nHowever, even if in this light Henry’s distinctions between the\ntwo kinds of truths and the corresponding differences of concepts make\ngood sense, and even if we accept that the concepts primarily accepted\nfrom sensible objects need to be further worked on in order to provide\nus with true, clear understanding of the natures of things, it is not\nclear that this further work cannot be done by the natural faculties\nof our mind, assuming only the general influence of God in sustaining\nits natural operations, but without performing any direct and specific\n“retouching” of our concepts “from above”.\nUsing our previous analogy of the acquired concept as the copy of a\npoor repro of an original, we may say that if we have a number of\ndifferent poor, fuzzy repros that are defective in a number of\ndifferent ways, then in a long and complex process of collating them,\nwe might still be able discern the underlying pattern of the original,\nand thus produce a copy that is actually closer to the original than\nany of the direct repros, without ever being allowed a glimpse of the\noriginal.", "\nIn fact, this was precisely the way Aristotelian theologians, such as\nAquinas, interpreted Augustine’ conception of illumination,\nreducing God’s role to providing us with the intelligible light\nnot by directly operating on any of our concepts in particular, but\nproviding the mind with “a certain likeness of the uncreated\nlight, obtained through participation” (ST1, q. 84, a. 5c),\nnamely, the agent intellect.", "\nMatthew of Aquasparta quite faithfully describes this view,\nassociating it with the Aristotelian position he rejects:", "\n\n\nSome people engaged in “philosophizing” [quidam\nphilosophantes] follow this position, although not entirely, when\nthey assert that that light is the general cause of certain cognition,\nbut is not attained, and its special influence is not necessary in\nnatural cognition; but the light of the agent intellect is sufficient\ntogether with the species and similitudes of things abstracted and\nreceived from the things; for otherwise the operation of [our] nature\nwould be rendered vacuous, our intellect would understand only by\ncoincidence, and our cognition would not be natural, but supernatural.\nAnd what Augustine says, namely, that everything is seen in and\nthrough that light, is not to be understood as if the intellect would\nsomehow attain that light, nor as if that light would have some\nspecific influence on it, but in such a way that the eternal God\nnaturally endowed us with intellectual light, in which we naturally\ncognize and see all cognizable things that are within the scope of\nreason. [DHCR, p. 95]\n", "\nAlthough Matthew vehemently rejects this position as going against\nAugustine’s original intention (“which is unacceptable,\nsince he is a prominent teacher, whom catholic teachers and especially\ntheologians ought to follow” — as Matthew says), this\nview, in ever more refined versions, gained more and more ground\ntoward the end of the 13th century, adopted not only by Aquinas and\nhis followers, but also by his major opponents, namely, Scotus and his\n followers.[25]", "\nStill, illuminationism and abstractionism were never treated by\nmedieval thinkers as mutually exclusive alternatives. They rather\nserved as the two poles of a balancing act in judging the respective\nroles of nature and direct divine intervention in human intellectual\n cognition.[26]", "\nAlthough Platonism definitely survived throughout the Middle Ages (and\nbeyond), in the guise of the interconnected doctrines of divine ideas,\nparticipation, and illumination, there was a quite general\nAristotelian\n consensus,[27]\n especially after Abelard’s time, that the mundane universals of\nthe species and genera of material beings exist as such in the\nhuman mind, as a result of the mind’s abstracting from\ntheir individuating conditions. But consensus concerning this much by\nno means entailed a unanimous agreement on exactly what the universals\nthus abstracted are, what it is for them to exist in the mind, how\nthey are related to their particulars, what their real foundation in\nthose particulars is, what their role is in the constitution of our\nuniversal knowledge, and how they contribute to the encoding and\ncommunication of this knowledge in the various human languages. For\nalthough the general Aristotelian stance towards universals\nsuccessfully handles the inconsistencies quite obviously generated by\na naïve Platonist ontology, it gives rise precisely to these\nfurther problems of its own." ], "subsection_title": "5.2 Illuminationism vs. Abstractionism" } ] }, { "main_content": [ "\nIt was Abelard who first dealt with the problem of universals\nexplicitly in this form. Having relatively easily disposed of putative\nuniversal forms as real entities corresponding to Boethius’\ndefinition, in his Logica Ingredientibus he concludes that\ngiven Aristotle’s definition of universals in his On\nInterpretation as those things that can be predicated of several\nthings, it is only universal words that can be regarded as\nreally existing universals. However, since according to\nAristotle’s account in the same work, words are meaningful in\nvirtue of signifying concepts in the mind, Abelard soon arrives at the\nfollowing questions:", "\nThese questions open up a new chapter in the history of the problem of\nuniversals. For these questions add a new aspect to the bundle of the\noriginally primarily ontological, epistemological, and theological\nquestions constituting the problem, namely, they add a\nsemantic aspect. On the Aristotelian conception of universals\nas universal predicables, there obviously are\nuniversals, namely, our universal words. But the universality of our\nwords is clearly not dependent on the physical qualities of our\narticulate sounds, or of the various written marks indicating them,\nbut on their representative function. So, to give an account of the\nuniversality of our universal words, we have to be able to tell in\nvirtue of what they have this universal representative function, that\nis to say, we have to be able to assign a common cause by the\nrecognition of which in terms of a common concept we can give\na common name to a potential infinity of individuals\nbelonging to the same kind.", "\nBut this common cause certainly cannot be a common thing in\nthe way Boethius described universal things, for, as we have seen, the\nassumption of the existence of such a common thing leads to\ncontradictions. To be sure, Abelard also provides a number of further\narguments, dealing with several refinements of Boethius’\ncharacterization of universals proposed by his contemporaries, such as\nWilliam of Champeaux, Bernard of Chartres, Clarembald of Arras,\nJocelin of Soissons, and Walter of Mortagne – but I cannot go\ninto those details\n here.[28]\n The point is that he refutes and rejects all these suggestions to\nsave real universals either as common things, having their own real\nunity, or as collections of several things, having a merely collective\nunity. The gist of his arguments against the former view is that the\nuniversal thing on that view would have to have its own numerical\nunity, and therefore, since it constitutes the substance of all its\nsingulars, all these singulars would have to be substantially one and\nthe same thing which would have to have all their contrary properties\nat the same time, which is impossible. The main thrust of his\narguments against the collection-theory is that collections are\narbitrary integral wholes of the individuals that make them up, so\nthey simply do not fill the bill of the Porphyrian characterizations\nof the essential predicables such as genera and\n species.[29]", "\nSo, the common cause of the imposition of universal words cannot be\nany one thing, or a multitude of things; yet, being a common\ncause, it cannot be nothing. Therefore, this common cause,\nwhich Abelard calls the\n status[30]\n of those things to which it is common, is a cause, but it is a cause\nwhich is a non-thing. However strange this may sound, Abelard observes\nthat sometimes we do assign causes which are not\nthings. For example, when we say “The ship was wrecked\nbecause the pilot was absent”, the cause that we assign, namely,\nthat the pilot was absent is not some thing, it is rather\nhow things were, i.e., the way things were, which in\nthis case we signify by the whole proposition “The pilot was\n absent”.[31]\n From the point of view of understanding what Abelard’s\nstatus are, it is significant that he assimilates the causal\nrole of status as the common cause of imposition to causes\nthat are signified by whole propositions. These significata\nof whole propositions, which in English we may refer to by using the\ncorresponding “that-clauses” (as I did above, referring to\nthe cause of the ship’s wreck by the phrase “that the\npilot was absent”), and in Latin by an\naccusative-with-infinitive construction, are what Abelard calls the\ndicta of propositions. These dicta, not being\nidentifiable with any single thing, yet, not being nothing, constitute\nan ontological realm that is completely different from that of\nordinary things. But it is also in this realm that Abelard’s\ncommon causes of imposition may find their place.", "\nAbelard says that the common cause of imposition of a universal name\nhas to be something in which things falling under that name agree. For\nexample, the name ‘man’ (in the sense of ‘human\nbeing’, and not in the sense of ‘male human being’)\nis imposed on all humans on account of something in which all humans,\nas such, agree. But that in which all humans as such agree is that\neach one of them is a man, that is, each one agrees with all others in\ntheir being a man. So, it is their being human [esse\nhominem] that is the common cause Abelard was looking for, and\nthis is what he calls the status of man. The status\nof man is not a thing; it is not any singular man, for obviously no\nsingular man is common to all men, and it is not a universal man, for\nthere is no such a thing. But being a man is common in the\nrequired manner (i.e., it is something in which all humans agree), yet\nit is clearly not a thing. For let us consider the singular\npropositions ‘Socrates is a man’ [Socrates est\nhomo], ‘Plato is a man’ [Plato est homo],\netc. These signify their dicta, namely, Socrates’s\nbeing a man [Socratem esse hominem], and Plato’s being\na man [Platonem esse hominem], etc. But then it is clear that\nif we abstract from the singular subjects and retain what is common to\nthem all, we can get precisely the status in which all these\nsubjects agree, namely, being a man [esse hominem]. So, the\nstatus, just like the dicta from which they can be\nobtained, constitute an ontological realm that is entirely different\nfrom that of ordinary things.", "\nStill, despite the fact that it clearly has to do something with\nabstraction, an activity of the mind, Abelard insists that a\nstatus is not a concept of our mind. The reason for his\ninsistence is that the status, being the common\ncause of imposition of a common name, must be something real, the\nexistence of which is not dependent on the activity of our minds. A\nstatus is there in the nature of things, regardless of\nwhether we form a mental act whereby we recognize it or not. In fact,\nfor Abelard, a status is an object of the divine mind,\nwhereby God preconceives the state of his creation from\n eternity.[32]\n A concept, or mental image of our mind, however, exists as\nthe object of our mind only insofar as our mind performs the mental\nact whereby it forms this object. But this object, again, is not a\nthing, indeed, not any more than any other fictitious object of our\nminds. However, what distinguishes the universal concept from\na merely fictitious object of our mind is that the former\ncorresponds to a status of really existing singular things,\nwhereas the latter does not have anything corresponding to it.", "\nTo be sure, there are a number of points left in obscurity by\nAbelard’s discussion concerning the relationships of the items\ndistinguished here. For example, Abelard says that we cannot conceive\nof the status. However, it seems that we can only signify by\nour words whatever we can conceive. Yet, Abelard insists that besides\nour concepts, our words must signify the status\n themselves.[33]\n A solution to the problem is only hinted at in Abelard’s remark\nthat the names can signify status, because “their\ninventor meant to impose them in accordance with certain\nnatures or characteristics of things, even if he did not know how to\nthink out the nature or characteristic of the thing” (Five\nTexts, Spade 1994, p. 46 (116)). So, we may assume that although\nthe inventor of the name does not know the status, his vague,\n“senses-bound” conception, from which he takes\nhis word’s signification, is directed at the status, as\nto that which he intends to\n signify.[34]\n However, Abelard does not work out this suggestion in any further\ndetail. Again, it is unclear how the status is related to the\nindividualized natures of the things that agree in the\nstatus. If the status is what the divine mind\nconceives of the singulars in abstraction from them, why\ncouldn’t the nature itself be conceived in the same way? –\nafter all, the abstract nature would not have to be a thing any more\nthan a status is, for its existence would not be\nreal being, but merely its being conceived.\nFurthermore, it seems quite plausible that Abelard’s\nstatus could be derived by abstraction from singular\ndicta with the same predicate, as suggested above. But\ndicta are the quite ordinary significata of\nour propositions, which Abelard never treats as\nepistemologically problematic, so why would the status, which\nwe could apparently abstract from them, be accessible only to the\ndivine mind?", "\nI’m not suggesting that Abelard could not provide acceptable and\ncoherent answers to these and similar questions and\n problems.[35]\n But perhaps these problems also contributed to the fact that by the\n13th century his doctrine of status was no longer\nin currency. Another historical factor that may have contributed to\nthe waning of Abelard’s theory was probably the influence of the\nnewly translated Aristotelian writings along with the Arabic\ncommentaries that flooded the Latin West in the second half of the\n12th century." ], "section_title": "6. Universals According to Abelard’s Aristotelian Conception", "subsections": [] }, { "main_content": [ "\nThe most important influence in this period from our point of view\ncame from Avicenna’s doctrine distinguishing the absolute\nconsideration of a universal nature from what applies to the same\nnature in the subject in which it exists. The distinction is neatly\nsummarized in the following passage.", "\nHorsehood, to be sure, has a definition that does not demand\nuniversality. Rather it is that to which universality happens. Hence\nhorsehood itself is nothing but horsehood only. For in itself it is\nneither many nor one, neither is it existent in these sensibles nor in\nthe soul, neither is it any of these things potentially or actually in\nsuch a way that this is contained under the definition of horsehood.\nRather [in itself it consists] of what is horsehood\n only.[36]\n ", "\nIn his little treatise On Being and Essence, Aquinas explains\nthe distinction in greater detail in the following words:", "\n\n\nA nature, however, or essence …can be considered in two ways.\nFirst, we can consider it according to its proper notion, and this is\nits absolute consideration; and in this way nothing is true of it\nexcept what pertains to it as such; whence if anything else is\nattributed to it, that will yield a false attribution. …In the\nother way [an essence] is considered as it exists in this or that\n[individual]; and in this way something is predicated of it per\naccidens [non-essentially or coincidentally], on account of that\nin which it exists, as when we say that a man is white because\nSocrates is white, although this does not pertain to man as such.\n\n\nA nature considered in this way, however, has two sorts of existence.\nIt exists in singulars on the one hand, and in the soul on the other,\nand from each of these [sorts of existence] it acquires accidents. In\nthe singulars, furthermore, the essence has several [acts of]\nexistence according to the multiplicity of singulars. Nevertheless, if\nwe consider the essence in the first, or absolute, sense, none of\nthese pertain to it. For it is false to say that the essence of man,\nconsidered absolutely, has existence in this singular, because if\nexistence in this singular pertained to man insofar as he is man, man\nwould never exist, except as this singular. Similarly, if it pertained\nto man insofar as he is man not to exist in this singular, then the\nessence would never exist in the singular. But it is true to say that\nman, but not insofar as he is man, may be in this singular or in that\none, or else in the soul. Therefore, the nature of man considered\nabsolutely abstracts from every existence, though it does not exclude\nany. And the nature thus considered is what is predicated of each\n individual.[37]\n ", "\nSo, a common nature or essence according to its absolute consideration\nabstracts from all existence, both in the singulars and in the mind.\nYet, and this is the important point, it is the same nature\nthat informs both the singulars that have this nature and the minds\nconceiving of them in terms of this nature. To be sure, this sameness\nis not numerical sameness, and thus it does not yield numerically one\nnature. On the contrary, it is the sameness of several, numerically\ndistinct realizations of the same information-content, just like the\nsameness of a book in its several copies. Just as there is no such a\nthing as a universal book over and above the singular copies of the\nsame book, so there is no such a thing as a universal nature existing\nover and above the singular things of the same nature; still, just as\nit is true to say that the singular copies are the copies of the\nsame book, so it is true to say that these singulars are of\nthe same nature.", "\nIndeed, this analogy also shows why this conception should be so\nappealing from the point of view of the original epistemological\nproblem of the possibility of universal knowledge, without entailing\nthe ontological problems of naïve Platonism. For just as we do\nnot need to read all copies of the same book in order to know what we\ncan find on the same page in the next copy (provided it is not a\ncorrupt\n copy),[38]\n so we can know what may apply to all singulars of the same nature\nwithout having to experience them all. Still, we need not assume that\nwe can have this knowledge only if we can get somehow in a mysterious\ncontact with the universal nature over and above the singulars; all we\nneed is to learn how “to read” the singulars in our\nexperience to discern the “common message”, the universal\nnature, informing them all, uniformly, yet in their distinct\nsingularity. (Note that “reading the singulars” is not a\nmere metaphor: this is precisely what geneticists are quite literally\ndoing in the process of gene sequencing, for instance, in the human\ngenome project.) Therefore, the same nature is not the\nsame in the same way as the same individual having this\nnature is the same as long as it exists. For that same\nnature, insofar as it is regarded as the same, does not\neven exist at all; it is said to be the same only insofar as it is\nrecognizable as the same, if we disregard everything\nthat distinguishes its instances in several singulars. (Note here that\nwhoever would want to deny such a recognizable sameness in\nand across several singulars would have to deny that he is able to\nrecognize the same words or the same letters in various sentences; so\nsuch a person would not be able to read, write, or even to speak, or\nunderstand human speech. But then we shouldn’t really worry\nabout such a person in a philosophical debate.)", "\nHowever, at this point some further questions emerge. If this common\nnature is recognizably the same on account of disregarding\nits individuating conditions in the singulars, then isn’t it the\nresult of abstraction; and if so, isn’t it in the abstractive\nmind as its object? But if it is, then how can Aquinas say that it\nabstracts both from being in the singulars and from\nbeing in the mind?", "\nHere we should carefully distinguish between what we can say about\nthe same nature as such, and what we can say about\nthe same nature on account of its conditions as it\nexists in this or that subject. Again, using our analogy, we can\ncertainly consistently say that the same book in its first edition was\n200 pages, whereas in the second only 100, because it was printed on\nlarger pages, but the book itself, as such, is neither 200 nor 100\npages, although it can be either. In the same way, we can consistently\nsay that the same nature as such is neither in the singulars\nnor in the mind, but of course it is only insofar as it is in the mind\nthat it can be recognizably the same, on account of the\nmind’s abstraction. Therefore, that it is abstract and is\nactually recognized as the same in its many instances is something\nthat belongs to the same nature only on account of being conceived by\nthe abstractive mind. This is the reason why the nature is called a\nuniversal concept, insofar as it is in the mind. Indeed, it\nis only under this aspect that it is properly called a universal. So,\nalthough that which is predicable of several\nsingulars is nothing but the common nature as such, considered\nabsolutely, still, that it is predicable pertains to the same\nnature only on account of being conceived by the abstractive\nintellect, insofar as it is a concept of the mind.", "\nAt any rate, this is how Aquinas solves the paralogism that seems to\narise from this account, according to which the true claims that\nSocrates is a man and man is a species would seem to entail the\nfalsity that Socrates is a species. For if we say that in the\nproposition ‘Socrates is a man’ the predicate signifies\nhuman nature absolutely, but the same nature, on account of its\nabstract character, is a species, the false conclusion seems\ninevitable (Klima 1993a).", "\nHowever, since the common nature is not a species in its absolute\nconsideration, but only insofar as it is in the mind, the conclusion\ndoes not follow. Indeed, this reasoning would be just as invalid as\nthe one trying to prove that this book, pointing to the second edition\nwhich is actually 100 pages, is 200 pages, because the same book was\n200 hundred pages in its first edition. For just as its being 200\npages belongs to the same book only in its first edition, so its being\na species belongs to human nature only as it exists in the mind.", "\nSo, to sum up, we have to distinguish here between the nature existing\nin this singular (such as the individualized human nature of Socrates,\nwhich is numerically one item, mind-independently existing in\nSocrates), the universal (such as the species of human nature existing\nonly in the mind as its object considered in abstraction from the\nindividuating conditions it has in the singular humans), and the\nnature according to its absolute consideration (such as human nature\nconsidered in abstraction both from its existence in the singulars as\nits subjects and in the mind as its object). What establishes the\ndistinction of these items is the difference of what can be truly said\nof them on account of the different conditions they have in this or\nthat. What establishes the unity of these items, however, is that they\nare somehow the same nature existing and considered under different\nconditions. For the human nature in Socrates is numerically one, it is\nnumerically distinct from the human nature in Plato, and it has real,\nmind-independent existence, which is in fact nothing but the existence\nof Socrates, i.e., Socrates’ life. However, although the human\nnature in Socrates is a numerically distinct item from the human\nnature in Plato, insofar as it is human nature, it is formally, in\nfact, specifically the same nature, for it is human nature, and not\nanother, specifically different, say, feline or canine nature. It is\nprecisely this formal, specific, mind-independent sameness of these\nitems (for, of course, say, this cat and that cat do not differ\ninsofar as they are feline, regardless of whether there is anyone to\nrecognize this) that allows the abstractive human mind to recognize\nthis sameness by abstracting from those individuating conditions on\naccount of which this individualized nature in this individual\nnumerically differs from that individualized nature in that\nindividual. Thus, insofar as the formally same nature is actually\nconsidered by a human mind in abstraction from these individualizing\nconditions, it is a universal, a species, an abstract object of a\nmental act whereby a human mind conceives of any individualized human\nnature without its individuating conditions. But, as we could see\nearlier, nothing can be a human nature existing without its\nindividuating conditions, although any individualized human nature can\nbe thought of without thinking of its necessarily conjoined\nindividuating conditions (just as triangular shape can be thought of\nwithout thinking its necessarily conjoined conditions of being\nisosceles or being scalene). So for this universal concept to be is\nnothing but to be thought of, to be an object of the abstractive human\nmind. Finally, human nature in its absolute consideration is the same\nnature abstracted even from this being, i.e., even from being an\nobject of the mind. Thus, as opposed to both in its existence in\nindividuals and in the mind, neither existence, nor non-existence, nor\nunity, nor disunity or multiplicity belongs to it, as it is considered\nwithout any of these; indeed, it is considered without considering its\nbeing considered, for it is considered only in terms of what belongs\nto it on account of itself, not considering anything that has to\nbelong to it on account of something else in which it can only be\n(i.e., whether in the mind or in reality). So, the nature according to\nits absolute consideration does not have numerical unity or\nmultiplicity, which it has as it exists in individuals, nor does it\nhave the formal unity that it has in the consideration of the mind\n(insofar as it is one species among many), but it has that formal\nunity which precedes even the recognition of this unity by the\nabstractive\n mind.[39]", "\nNevertheless, even if with these distinctions Aquinas’ solution\nof the paralogism works and what he says about the existence and unity\nvs. multiplicity of a common nature can be given a consistent\ninterpretation, the emergence of the paralogism itself and the\ncomplexities involved in explaining it away, as well as the problems\ninvolved in providing this consistent interpretation show the inherent\ndifficulties of this account. The main difficulty is the trouble of\nkeeping track of what we are talking about when it becomes crucial to\nknow what pertains to what on account of what; in general, when the\nconditions of identity and distinction of the items we are talking\nabout become variable and occasionally rather unclear.", "\nIndeed, we can appreciate just how acute these difficulties may become\nif we survey the items that needed to be distinguished in what may be\ndescribed as the common conceptual framework of the\n“realist” via antiqua, the “old way”\nof doing philosophy and theology, before the emergence of the\n“modern way”, the “nominalist” via\nmoderna challenging some fundamental principles of the older\nframework, resulting mostly from the semantic innovations introduced\nby William Ockham. The survey of these items and the problems they\ngenerate will then allow us to see in greater detail the main\nmotivation for Ockham’s innovations." ], "section_title": "7. Universal Natures in Singular Beings and in Singular Minds", "subsections": [] }, { "main_content": [ "\nIn this framework, we have first of all the universal or common terms\nof spoken and written languages, which are common on account of being\nimposed upon universal concepts of the human mind. The concepts\nthemselves are universal on account of being obtained by the activity\nof the abstractive human mind from experiences of singulars. But the\nprocess of concept formation also involves various stages.", "\nIn the first place, the sensory information collected by the single\nsenses is distinguished, synthesized, and collated by the higher\nsensory faculties of the common sense [sensus communis] and\nthe so-called cogitative power [vis cogitativa], to be stored\nin sensory memory as phantasms, the sensory representations\nof singulars in their singularity. The active intellect\n[intellectus agens] uses this sensory information to extract\nits intelligible content and produce the intelligible species\n[species intelligibiles], the universal representations of\nseveral individuals in their various degrees of formal unity,\ndisregarding their distinctive features and individuating conditions\nin the process of abstraction.", "\nThe intelligible species are stored in the intellectual memory of the\npotential intellect [intellectus possibilis], which can then\nuse them to form the corresponding concept in an act of thought, for\nexample, in forming a judgment. The intelligible species and the\nconcepts themselves, being formed by individual human minds, are\nindividual in their being, insofar as they pertain to this or that\nhuman mind. However, since they are the result of abstraction, in\ntheir information content they are universal.", "\nNow insofar as this universal information content is common to all\nminds that form these concepts at all, and therefore it is a common\nintelligible content gained by these minds from their objects insofar\nas they are conceived by these minds in a universal manner, later\nscholastic thinkers refer to it as the objective concept\n[conceptus obiectivus], distinguishing it from the formal or\nsubjective concepts [conceptus formales seu subiectivi],\nwhich are the individual acts of individual minds carrying this\ninformation (just as the individual copies of a book carry the\ninformation content of the\n book).[40]\n It is this objective concept that is identified as the universal of\nthe human mind (distinguished from the universals of the divine mind),\nnamely, a species, a genus, a difference, a property, or an accident.\n(Note that these are only the simple concepts. Complex concepts, such\nas those corresponding to complex terms and propositions are the\nproducts of the potential intellect using these concepts in its\nfurther operations.)", "\nThese universals, then, as the objective concepts of the mind, would\nbe classified as beings of reason [entia rationis], the being\nof which consists in their being conceived (cf. Klima 1993b and\nSchmidt 1966). To be sure, they are not merely fictitious objects, for\nthey are grounded in the nature of things insofar as they carry the\nuniversal information content abstracted from the singulars. But then\nagain, the universal information content of the objective concept\nitself, considered not insofar as it is in the mind as its object, but\nin itself, disregarding whatever may carry it, is distinguished from\nits carriers both in the mind and in the ultimate objects of the mind,\nthe singular things, as the nature of these things in its absolute\nconsideration.", "\nHowever, the common nature as such cannot exist on its own any more\nthan a book could exist without any copies of it or any minds\nconceiving of it. So, this common nature has real existence only in\nthe singulars, informing them, and giving them their recognizably\ncommon characteristics. However, these common characteristics can be\nrecognized as such only by a mind capable of abstracting the common\nnature from experiencing it in its really existing singular instances.\nBut it is on account of the real existence of these individualized\ninstances in the singulars that the common nature can truly be\npredicated of the singulars, as long as they are actually informed by\nthese individualized instances.", "\nThe items thus distinguished and their interconnections can be\nrepresented by the following block-diagram. The dashed frames indicate\nthat the items enclosed by them have a certain reduced ontological\nstatus, a “diminished” mode of being, while the boxes\npartly sharing a side indicate the (possible) partial identities of\nthe items they\n enclose.[41]\n The arrows pointing from the common term to the singulars, their\nindividualized natures and items in the mind on this diagram represent\nsemantic relations, which I am going to explain later, in connection\nwith Ockham’s innovations. The rest of the arrows indicate the\nflow of information from experience of singulars through the sensory\nfaculties to the abstractive mind, and to the application of the\nuniversal information abstracted by the mind to further singular\nexperiences in acts of judgment.", "\nObviously, this is a rather complicated picture. However, its\ncomplexity itself should not be regarded as problematic or even\nsurprising, for that matter. After all, this diagram merely\nsummarizes, and distinguishes the main stages of, how the human mind\nprocesses the intelligible, universal information received from a\nmultitude of singular experiences, and then again, how it applies this\ninformation in classifying further experiences. This process may\nreasonably be expected to be complex, and should not be expected to\ninvolve fewer stages than, e.g., setting up, and retrieving\ninformation from, a computer database.", "\nWhat renders this picture more problematic is rather the difficulties\ninvolved in identifying and distinguishing these stages and the\ncorresponding items. Further complications were also generated by the\nvariations in terminology among several authors, and the various\ncriteria of identity and distinctness applied by them in introducing\nvarious different notions of identity and distinctness. In fact, many\nof the great debates of the authors working within this framework can\nbe characterized precisely as disputing the identity or distinctness\nof the items featured here, or the very criteria of identifying or\ndistinguishing them.", "\nFor example, already Abelard raised the question whether the concept\nor mental image, which we may identify in the diagram as the objective\nconcept of later authors, should be identified with the act of\nthought, which we may identify as the subjective concept, or perhaps a\nfurther act of the mind, called formatio, namely, the\npotential intellect’s act of forming the concept, using the\nintelligible species as the principle of its action. Such distinctions\nwere later on severely criticized by authors such as John Peter Olivi\nand others, who argued for the elimination of intelligible species,\nand, in general, of any intermediaries between an act of the intellect\nand its ultimate objects, the singulars conceived in a universal\n manner.[42]", "\nAgain, looking at the diagram on the side of the singulars, most\n13th century authors agreed that what accounts for the\nspecific unity of several individuals of the same species, namely,\ntheir specific nature, should be something other than what accounts\nfor their numerical distinctness, namely, their principle of\nindividuation. However, one singular entity in a species of several\nco-specific individuals has to contain both the principle of the\nspecific unity of these individuals and its own principle of\nindividuation. Therefore, this singular entity, being a composite at\nleast of its specific nature and its principle of individuation, has\nto be distinct from its specific nature. At any rate, this is the\nsituation with material substances, whose principle of individuation\nwas held to be their matter. However, based on this reasoning,\nimmaterial substances, such as angels, could not be regarded as\nnumerically distinct on account of their matter, but only on account\nof their form. But since form is the principle of specific unity,\ndifference in form causes specific diversity. Therefore, on this\nbasis, any two angels had to be regarded as different in species. This\nconclusion was explicitly drawn by Aquinas and others, but it was\nrejected by Augustinian theologians, and it was condemned in Paris in\n 1277.[43]", "\nSo, no wonder authors such as Henry of Ghent and Duns Scotus worked\nout alternative accounts of individuation, introducing not only\ndifferent principles of individuation, such as the Scotists’\nfamous (or infamous) haecceity, but also different criteria\nof distinctness and identity, such as those grounding Henry of\nGhent’s intentional distinction, or Scotus’s\nformal\n distinction,[44]\n or even later Suarez’ modal\n distinction.[45]", "\nBut even further problems arose from considering the identity or\ndistinctness of the individualized natures signified by several common\nterms in one and the same individual. The metaphysical debate over the\nreal distinction of essence and existence from this point of view is\nnothing but the issue whether the individualized common nature\nsignified by the definition of a thing is the same as the act of being\nsignified by the verb ‘is’ in the same thing. In fact, the\nfamous problem of the plurality vs. unity of substantial forms may\nalso be regarded as a dispute over whether the common natures\nsignified by the substantial predicates on the Porphyrian tree in the\ncategory of substance are distinct or the same in the same individual\n(cf. Callus 1967). Finally, and this appears to be the primary\nmotivation for Ockham’s innovations, there was the question\nwhether one must regard all individualized common natures signified in\nthe same individual by several predicates in the ten Aristotelian\ncategories as distinct from one another. For the affirmative answer\nwould involve commitment to a virtually limitless multiplication of\nentities.", "\nIndeed, according to Ockham, the via antiqua conception would\nentail that", "\na column is to the right by to-the-rightness, God is creating by\ncreation, is good by goodness, just by justice, mighty by might, an\naccident inheres by inherence, a subject is subjected by subjection,\nthe apt is apt by aptitude, a chimera is nothing by nothingness,\nsomeone blind is blind by blindness, a body is mobile by mobility, and\nso on for other, innumerable\n cases.[46]\n ", "\nAnd this is nothing, but “multiplying beings according to the\nmultiplicity of terms… which, however, is erroneous and leads\nfar away from the\n truth”.[47]" ], "section_title": "8. Universals in the Via Antiqua", "subsections": [] }, { "main_content": [ "\nTo be sure, as the very debates within the via antiqua\nframework concerning the identity or non-identity of various items\ndistinguished in that framework indicate, Ockham’s charges are\nnot quite\n justified.[48]\n After all, several via antiqua authors did allow\nthe identification of the significata of terms belonging to\nvarious categories, so their “multiplication of beings”\ndid not necessarily match the multiplicity of terms. Furthermore,\nsince via antiqua authors also distinguished between various\nmodes or senses of being, allowing various sorts of\n“diminished” kinds of being, such as beings of\nreason, their ontological commitments were certainly not as\nunambiguous as Ockham would have us believe in this passage. However,\nif we contrast the diagram of the via antiqua framework above\nwith the following schematic representation of the via\nmoderna framework introduced by Ockham, we can immediately\nappreciate the point of Ockham’s innovations.", "\nWithout a doubt, it is the captivating simplicity of this picture,\nespecially as compared with the complexity of the via antiqua\npicture, that was the major appeal of the Ockhamist approach. There\nare fewer items here, equally on the same ontological footing,\ndistinguished from one another in terms of the same unambiguous\ndistinction, the numerical distinction between individual real\nentities.", "\nTo be sure, there still are universals in this picture. But these\nuniversals are neither common natures “contracted” to\nindividuals by some really or merely formally distinct principle of\nindividuation, nor some universal objects of the mind, which exist in\na “diminished” manner, as beings of reason.\nOckham’s universals, at least in his mature\n theory,[49]\n are just our common terms and our common concepts. Our common terms,\nwhich are just singular utterances or inscriptions, are common in\nvirtue of being subordinated to our common concepts. Our common\nconcepts, on the other hand, are just singular acts of our singular\nminds. Their universality consists simply in the universality of their\nrepresentative function. For example, the common term\n‘man’ is a spoken or written universal term of English,\nbecause it is subordinated to that concept of our minds by which we\nconceive of each man indifferently. (See Klima, 2011) It is this\nindifference in its representative function that enables the singular\nact of my mind to conceive of each man in a universal manner, and the\nsame goes for the singular act of your mind. Accordingly, there is no\nneed to assume that there is anything in the individual humans,\ndistinct from these humans themselves, a common yet individualized\nnature waiting to be abstracted by the mind. All we need to assume is\nthat two humans are more similar to each other than either of them to\na brute animal, and all animals are more similar to each other than\nany of them to a plant, etc., and that the mind, being able to\nrecognize this similarity, is able to represent the humans by means of\na common specific concept, the animals by means of a common generic\nconcept, all living things by means of a more general generic concept,\n etc.[50]\n In this way, then, the common terms subordinated to these concepts\nneed not signify some abstract common nature in the mind, and\nconsequently its individualized instances in the singulars, for they\ndirectly signify the singulars themselves, just as they are directly\nconceived by the universally representative acts of the mind. So, what\nthese common terms signify are just the singulars themselves, which\nare also the things referred to by these terms when they are used in\npropositions. Using the customary rendering of the medieval logical\nterminology, the things ultimately signified by a common term are its\nsignificata, while the things referred to by the same term\nwhen it is used in a proposition are their (personal)\n supposita.[51]", "\nNow if we compare the two diagrams representing the respective\nconceptions of the two viae, we can see just how radically\nOckham’s innovations changed the character of the semantic\nrelations connecting terms, concepts and things. In both\nviae, common terms are subordinated to common concepts, and\nit is in virtue of this subordination that they ultimately signify\nwhat their concepts represent. In the via moderna, a concept\nis just an act of the mind representing singulars in a more or less\nindifferent manner, yielding a more or less universal signification\nfor the term. In the via antiqua, however, the act of the\nmind is just one item in a whole series of intermediary\nrepresentations, distinguished in terms of their different functions\nin processing universal information, and connected by their common\ncontent, ultimately representing the common, yet individualized\nnatures of their\n singulars.[52]\n Accordingly, a common term, expressing this common content, is\nprimarily subordinated to the objective concept of the mind. But of\ncourse, this objective concept is only the common content of the\nsingular representative acts of singular minds, their subjective\nconcepts, formed by means of the intelligible species, abstracted by\ntheir active intellects. On the other hand, the objective concept,\nabstracting from all individuating conditions, expresses only what is\ncommon to all singulars, namely, their nature considered absolutely.\nBut this absolutely considered nature is only the common content of\nwhat informs each singular of the same nature in its actual real\nexistence. So, the term’s ultimate significata will\nhave to be the individualized natures of the singulars. But these\nultimate significata may still not be the singulars\nthemselves, namely, when the things informed by these\nsignificata are not metaphysically simple. In the via\nmoderna conception, therefore, the ultimate significata\nof a term are nothing but those singular things that can be the\nterm’s supposita in various propositions, as a matter\nof semantics. By contrast, in the via antiqua conception, a\nterm’s ultimate significata may or may not be the same\nthings as the term’s (personal) supposita, depending on\nthe constitution of these supposita, as a matter of\nmetaphysics. The singulars will be the supposita of the term\nwhen it is used as the subject term of a proposition in which\nsomething is predicated about the things informed by these ultimate\nsignificata (in the case of metaphysically simple entities,\nthe term’s significata and supposita\n coincide).[53]", "\nNevertheless, despite the nominalists’ charges to the contrary,\nthe via antiqua framework, as far as its semantic\nconsiderations are concerned, was no more committed to the real\ndistinction of the significata and supposita of its\ncommon terms than the via moderna framework was. For if the\nsemantic theory in itself had precluded the identification of these\nsemantic values, then the question of possible identity of these\nvalues could not have been meaningfully raised in the first place.\nFurthermore, in that case such identifications would have been\nprecluded as meaningless even when talking about metaphysically simple\nentities, such as angels and God, whereas the metaphysical simplicity\nof these entities was expressed precisely in terms of such\nidentifications. But also in the mundane cases of the\nsignificata and supposita of concrete and abstract\nuniversal terms in the nine accidental categories, several via\nantiqua authors argued for the identification of these semantic\nvalues both within and across categories. First of all there was\nAristotle’s authority for the claim that action and passion are\nthe same\n motion,[54]\n so the significata of terms in these two categories could not be\nregarded as really distinct entities. But several authors also argued\nfor the identification of relations with their foundations, that is to\nsay, for the identity of the significata of relative terms with the\nsignificata of terms in the categories quantity and quality. (For\nexample, on this conception, my equality in height to you would be\njust my height, provided you were of the same height, and not a\ndistinct “equality-thing” somehow attached to my height,\ncaused by our equal\n heights.)[55]", "\nBy contrast, what makes the via moderna approach simpler is\nthat it “automatically” achieves such identifications\nalready on the basis of its semantic principles. Since in this\napproach the significata of concrete common terms are just\nthe singulars directly represented by the corresponding concepts, the\nsignificata and (personal) supposita of terms are\ntaken to be the same singulars from the beginning. So these common\nterms signify and supposit for the same things\neither absolutely, provided the term is absolute, or in\nrelation to other singulars, provided the term is\nconnotative. But even in the case of connotative terms, such\nas relative terms (in fact, all terms in the nine accidental\ncategories, except for some abstract terms in the category quality,\naccording to Ockham) we do not need to assume the existence of some\nmysterious relational entities informing singular substances. For\nexample, the term ‘father’ need not be construed as\nsignifying in me an inherent relation, my fatherhood, somehow\nconnecting me to my son, and suppositing for me on that account in the\ncontext of a proposition; rather, it should merely be construed as\nsignifying me in relation to my son, thereby suppositing for me in the\ncontext of a proposition, while connoting my son." ], "section_title": "9. Universals in the Via Moderna", "subsections": [] }, { "main_content": [ "\nThe appeal of the simplicity of the via moderna approach,\nespecially as it was systematically articulated in the works of John\nBuridan and his students, had a tremendous impact on late-medieval\nphilosophy and theology. To be sure, many late-medieval scholars, who\nwere familiar with both ways, would have shared the sentiment\nexpressed by the remark of Domingo Soto (1494–1560, describing\nhimself as someone who was “born among nominalists and raised by\n realists”)[56]\n to the effect that whereas the realist doctrine of the via\nantiqua was more difficult to understand, still, the nominalist\ndoctrine of the via moderna was more difficult to\n believe.[57]\n Nevertheless, the overall simplicity and internal consistency of the\nnominalist approach were undeniable, gathering a strong following by\nthe 15th century in all major universities of Europe, old\nand newly established\n alike.[58]", "\nThe resulting separation and the ensuing struggle of the medieval\nviae did not end with the victory of the one over the other.\nInstead, due to the primarily semantic nature of the\nseparation, getting the parties embroiled in increasingly complicated\nways of talking past each other, thereby generating an ever growing\ndissatisfaction, even contempt, in a new, lay, humanist\n intelligentsia,[59]\n it ended with the demise of the characteristically medieval\nconceptual frameworks of both viae in the late-medieval and\nearly modern period.", "\nThese developments, therefore, also put an end to the specifically\nmedieval problem of universals. However, the increasingly\nrarified late-medieval problem eventually vanished only to give way to\nseveral modern variants of recognizably the same\nproblem, which keeps recurring in one form or another in contemporary\nphilosophy as well. Indeed, one may safely assert that as long as\nthere is interest in the questions of how a human language obviously\nabounding in universal terms can be meaningfully mapped onto a world\nof singulars, there is a problem of universals, regardless of\nthe details of the particular conceptual framework in which the\nrelevant questions are articulated. Clearly, in this sense, the\nproblem of universals is itself a universal, the universal problem of\naccounting for the relationships between mind, language, and\nreality." ], "section_title": "10. The Separation of the Viae, and the Breakdown of Scholastic Discourse in Late-Medieval Philosophy", "subsections": [] } ]

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Werbeck, et al.\n(eds.), Tübingen: J.C.B. Mohr (Paul Siebeck), 1973.", "Cajetan, T., Commentary on Being and Essence, tr. L. J.\nKendzierski and F. C. Wade, Milwaukee: Marquette University Press,\n1964.", "Giles of Rome, In Primum Librum Sententiarum,\nFrankfurt/Main: Minerva, 1968 (Venetiis, 1521).", "Henry of Ghent, Summae quaestionum ordinariarum theologi\nrecepto praeconio solennis Henrici a Gandavo, (Parisiis In\naedibus Jodoci Badii Ascensii 1520), New York: Franciscan Institute,\n1953.", "John Duns Scotus, B. Ioannis Duns Scoti Commentaria Oxoniensia\nad IV libros Magistri Sententiarum, novis curis edidit p.\nMarianus Fernandez Garcia, Ad Claras Aquas (Quaracchi) prope\nFlorentiam, ex typographia Collegii s. Bonaventurae,\n1912–1914.", "John of Salisbury, Metalogicon, Oxford: Clarendon Press,\n1929.", "John Wyclif, Tractatus de Universalibus, I. J. Mueller\n(ed.), Oxford: Clarendon Press, 1985.", "Plato, Collected Dialogues, E. Hamilton and H. Cairns\n(eds.), Princeton: Princeton University Press, 1982.", "Seneca, Ad Lucilium Epistulae Morales, Loeb classical\nlibrary: Latin authors, Cambridge, MA: Harvard University Press,\n1962–1967.", "Soto, D., In Porphyrii Isagogen, Aristotelis Categorias,\nlibrosque de Demonstratione, Commentaria, Venice, ex officina\nDominici Guarraei, et Io. Baptistae, fratrum, 1587, reprint,\nFrankfurt: Minerva, 1967.", "Spade, P. V., (tr.), Five Texts on the Mediaeval Problem of\nUniversals: Porphyry, Boethius, Abelard, Duns Scotus, Ockham,\nIndianapolis: Hackett, 1994.", "Suarez, F., Disputaciones Metafisicas, Madrid: Editorial\nGredos, 1960.", "Suarez, F., On the Various Kinds of Distinctions\n(Disputationes metaphysicae, Disputatio VII, de variis\ndistinctionum generibus), tr. intro. C. Vollert, Milwaukee:\nMarquette University Press: 1947.", "Thomas of Sutton, Quodlibeta, München: Bayerische\nAkademie, 1969.", "Vincent Ferrer, Tractatus de Suppositionibus,\nStuttgart-Bad Cannstatt: Fromman Holzboog, 1977.", "Vives, J. L., Against the Pseudodialecticians, tr. R.\nGuerlac, Dordrecht-Boston-London: D. Reidel Publishing Company,\n1979.", "William Ockham, Summa Logicae, Ph. Boehner, et\nal. (eds.), Opera Philosophica, vol. I., St.\nBonaventure, NY: The Franciscan Institute, 1974.", "William Ockham, Ordinatio: Guillelmi de Ockham\nScriptum in librum primum sententiarum ordinatio: distinctiones\nXIX-XLVIII, G. I. Etzkorn and F. E. Kelley (eds.), Opera\nTheologica, vol. IV, St. Bonaventure, NY: The Franciscan\nInstitute, 1979.", "Adams, M. M., 1987, William Ockham, 2 volumes, Notre\nDame: University of Notre Dame Press.", "Amerini, F. and Cesalli, L. (eds.), 2017, Universals in the\nFourteenth Century, Pisa: Scuola Normale Superiore.", "Ashworth, E. J., 1974, Language and Logic in the Post-Medieval\nPeriod (Synthese Historical Library: Volume 12), Dordrecht: D.\nReidel.", "Callus, D. A., 1967, “Unicity and Plurality of Forms”,\nin New Catholic Encyclopedia, New York: McGraw-Hill,\n1967–79.", "Cross, R., 2014, “Medieval Theories of Haecceity”,\n The Stanford Encyclopedia of Philosophy (Summer 2014\nEdition), Edward N. Zalta (ed.), URL =\n<https://plato.stanford.edu/archives/sum2014/entries/medieval-haecceity/>.", "Gracia, J., 1994, Individuation in Scholasticism: The Later\nMiddle Ages and the Counter Reformation (1150–1650),\nAlbany, NY: SUNY Press.", "Gracia, J., 1984, Introduction to the Problem of Individuation\nin the Early Middle Ages (Analytica Series), München and\nWashington, D.C.: Philosophia Verlag and Catholic University of\nAmerica Press; 2nd edition, 1988.", "Henninger, M., 1989, Relations: Medieval Theories\n1250–1325, Oxford: Clarendon Press.", "Hissette, R., 1977, Enquête sur les 219 articles\ncondamnés à Paris le 7 Mars 1277,\n“Philosophes médiévaux,” Volume 22, Louvain:\nPublications Universitaires.", "Hyman, A., and Walsh, J. J., (eds.), 1973, Philosophy of the\nMiddle Ages, Indianapolis: Hackett.", "Klima, G., 2011, “Indifference vs. Universality of Mental\nRepresentation in Ockham, Buridan, and Aquinas”, in Amerini, F.\n– Marrone, F. – Porro, P. (eds.) Later Medieval\nPerspectives on Intentionality (Quaestio 10/2010), Brepols\nPublishers/Pagina soc. Coop., Turnhout/Bari, 2010, pp. 99–110.", "–––, 2000a, “Thomas of Sutton on the\nNature of the Intellective Soul and the Thomistic Theory of\nBeing”, in J. Aertsen, et al. (eds.), Nach der\nVerurteilung von 1277. Philosophie und Theologie an der\nUniversität von Paris im letzten Viertel des\n13. Jahrhunderts, Studien und Texte (Miscellanea Mediaevalia 28),\nBerlin-New York, 2000, pp. 436-455.\n [Author preprint of Klima 2000a available online]", "–––, 2000b, “Aquinas on One and Many”,\nDocumenti e Studi sulla Tradizione Filosofica Medievale (An\nInternational Journal on the Philosophical Tradition from Late\nAntiquity to the Late Middle Ages of the Società Internazionale\nper lo Studio del Medioevo Latino), 11: 195–215.\n[Author preprint of Klima 2000b available online]", "–––, 1999, “Ockham’s Semantics and\nMetaphysics of the Categories”, in P. V. Spade (ed.), The\nCambridge Companion to Ockham, Cambridge: Cambridge University\nPress, pp. 118–142. \n [Author preprint of Klima 1999 available online]", "–––, 1996a, “The Semantic Principles\n Underlying Saint Thomas Aquinas’s Metaphysics of\n Being”,\n Medieval Philosophy and Theology, 5: 87–141.\n [Author preprint of Klima 1996a available online]", "–––, 1993a, “‘Socrates est\nspecies’: Logic, Metaphysics and Psychology in St. Thomas\nAquinas’ Treatment of a Paralogism”, in K. Jacobi (ed.),\nArgumentationstheorie: Scholastische Forschungen zu den logischen\nund semantischen Regeln korrekten Folgerns, Leiden: Brill, pp.\n489–504.", "–––, 1993b, “The Changing Role\nof Entia Rationis in Medieval Philosophy: A Comparative Study\nwith a Reconstruction”, Synthese, 96: 25–59.\n [Author preprint\nof Klima 1993b available online]", "–––,\n and Hall, A.W. (eds.) 2011, Medieval Metaphysics, or is it\n“Just Semantics”?, Newcastle upon Tyne: Cambridge\nScholars Publishing.", "Kretzmann, N.,\nand A. Kenny and J. Pinborg (eds.), 1982, The Cambridge History\nof Later Medieval Philosophy, Cambridge: Cambridge University\nPress.", "Libera, A. de,\n1996, La querelle des universeaux: De Platon à la fin du\nMoyen Age, Paris: Éditions du Seuil, 1996.", "Marrone, S.,\n2001, The light of Thy countenance: science and knowledge of God\nin the thirteenth century, Leiden-Boston: Brill.", "Panaccio, C.,\n2004, Ockham on Concepts, Aldershot: Ashgate.", "Pasnau, R.,\n2002, Thomas Aquinas on Human Nature: A Philosophical Study of\nSumma Theologiae 1a 75–89, Cambridge: Cambridge University\nPress.", "–––, 1999a,\n“Peter John Olivi”,\nin The Stanford Encyclopedia of Philosophy. (Winter 1999\nEdition), Edward N. Zalta (ed.), URL =\n<https://plato.stanford.edu/archives/win1999/entries/olivi/>", "–––, 1999b,\n“Divine Illumination”,\nin The Stanford Encyclopedia of Philosophy. (Winter 1999\nEdition), Edward N. Zalta (ed.), URL =\n <https://plato.stanford.edu/archives/win1999/entries/illumination/>", "–––,\n1997, Theories of Cognition in the Later Middle Ages,\nCambridge: Cambridge University Press.", "Read, S. L., 1977, “The Objective Being of Ockham’s\nFicta”, The Philosophical Quarterly, 27:\n14–31.", "–––, 2015, “Medieval Theories: Properties\nof Terms”, in The Stanford Encyclopedia of Philosophy.\n(Spring 2015 Edition), Edward N. Zalta (ed.), URL =\n <https://plato.stanford.edu/archives/spr2015/entries/medieval-terms/>", "Schmidt, R. W., 1966, The Domain of Logic according to Saint\nThomas Aquinas, The Hague: Martinus Nijhoff.", "Spade, P. V., 1982, “The Semantics of Terms”, in\nKretzmann, et al., 1982,\npp. 188–196.", "Tweedale, M., 1982, “Abelard and the Culmination of Old\nLogic”, in\nKretzmann, et al., 1982,\npp. 142–157.", "Wood, A., 2011, “Aquinas, Scotus, and Cajetan on\n‘Horseness is just Horseness’”, in\nKlima, et al., 2011,\npp. 69–84." ]

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[ "\n\nUtilitarianism is one of the most powerful and persuasive approaches\nto normative ethics in the history of philosophy. Though not\nfully articulated until the 19th century, proto-utilitarian\npositions can be discerned throughout the history of ethical\ntheory.", "\n\nThough there are many varieties of the view discussed,\nutilitarianism is generally held to be the view that the morally right\naction is the action that produces the most good. There are many\nways to spell out this general claim. One thing to note is that\nthe theory is a form of consequentialism: the right action is\nunderstood entirely in terms of consequences produced. What\ndistinguishes utilitarianism from egoism has to do with the scope of\nthe relevant consequences. On the utilitarian view one ought to\nmaximize the overall good — that is, consider the good of others\nas well as one's own good.", "\n\nThe Classical Utilitarians, Jeremy Bentham and John Stuart Mill,\nidentified the good with pleasure, so, like Epicurus, were hedonists\nabout value. They also held that we ought to maximize the good,\nthat is, bring about ‘the greatest amount of good for the\ngreatest number’.", "\n\nUtilitarianism is also distinguished by impartiality and\nagent-neutrality. Everyone's happiness counts the\nsame. When one maximizes the good, it is the good\nimpartially considered. My good counts for no more than\nanyone else's good. Further, the reason I have to promote\nthe overall good is the same reason anyone else has to so promote the\ngood. It is not peculiar to me.", "\n\nAll of these features of this approach to moral evaluation and/or\nmoral decision-making have proven to be somewhat controversial and\nsubsequent controversies have led to changes in the Classical version\nof the theory." ]

[ { "content_title": "1. Precursors to the Classical Approach", "sub_toc": [] }, { "content_title": "2. The Classical Approach", "sub_toc": [ "2.1 Jeremy Bentham", "2.2 John Stuart Mill" ] }, { "content_title": "3. Henry Sidgwick", "sub_toc": [] }, { "content_title": "4. Ideal Utilitarianism", "sub_toc": [] }, { "content_title": "5. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nThough the first systematic account of utilitarianism was developed\nby Jeremy Bentham (1748–1832), the core insight motivating the theory\noccurred much earlier. That insight is that morally appropriate\nbehavior will not harm others, but instead increase happiness or\n‘utility.’ What is distinctive about utilitarianism\nis its approach in taking that insight and developing an account of\nmoral evaluation and moral direction that expands on it. Early\nprecursors to the Classical Utilitarians include the British Moralists,\nCumberland, Shaftesbury, Hutcheson, Gay, and Hume. Of these,\nFrancis Hutcheson (1694–1746) is explicitly utilitarian when it comes\nto action choice.", "\n\nSome of the earliest utilitarian thinkers were the\n‘theological’ utilitarians such as Richard Cumberland\n(1631–1718) and John Gay (1699–1745). They believed that\npromoting human happiness was incumbent on us since it was approved by\nGod. After enumerating the ways in which humans come under\nobligations (by perceiving the “natural consequences of\nthings”, the obligation to be virtuous, our civil obligations\nthat arise from laws, and obligations arising from “the authority\nof God”) John Gay writes: “…from the consideration\nof these four sorts of obligation…it is evident that a full and\ncomplete obligation which will extend to all cases, can only be that\narising from the authority of God; because God only can in all\ncases make a man happy or miserable: and therefore, since we are\nalways obliged to that conformity called virtue, it is evident\nthat the immediate rule or criterion of it is the will of God”\n(R, 412). Gay held that since God wants the happiness of mankind,\nand since God's will gives us the criterion of virtue,\n“…the happiness of mankind may be said to be the criterion\nof virtue, but once removed” (R, 413). This view\nwas combined with a view of human motivation with egoistic\nelements. A person's individual salvation, her eternal\nhappiness, depended on conformity to God's will, as did virtue\nitself. Promoting human happiness and one's own coincided,\nbut, given God's design, it was not an accidental\ncoincidence.", "\n\nThis approach to utilitarianism, however, is not theoretically clean\nin the sense that it isn't clear what essential work God does, at\nleast in terms of normative ethics. God as the source of\nnormativity is compatible with utilitarianism, but utilitarianism\ndoesn't require this.", "\n\nGay's influence on later writers, such as Hume, deserves\nnote. It is in Gay's essay that some of the\nquestions that concerned Hume on the nature of virtue are\naddressed. For example, Gay was curious about how to explain our\npractice of approbation and disapprobation of action and\ncharacter. When we see an act that is vicious we disapprove of\nit. Further, we associate certain things with their effects, so\nthat we form positive associations and negative associations that also\nunderwrite our moral judgments. Of course, that we view happiness,\nincluding the happiness of others as a good, is due to God's\ndesign. This is a feature crucial to the theological approach,\nwhich would clearly be rejected by Hume in favor of a naturalistic view\nof human nature and a reliance on our sympathetic engagement with\nothers, an approach anticipated by Shaftesbury (below). The\ntheological approach to utilitarianism would be developed later by\nWilliam Paley, for example, but the lack of any theoretical necessity\nin appealing to God would result in its diminishing appeal.", "\n\nAnthony Ashley Cooper, the 3rd Earl of Shaftesbury\n(1671–1713) is generally thought to have been the one of the earliest\n‘moral sense’ theorists, holding that we possess a kind\nof “inner eye” that allows us to make moral\ndiscriminations. This seems to have been an innate sense of right\nand wrong, or moral beauty and deformity. Again, aspects of this\ndoctrine would be picked up by Francis Hutcheson and David Hume\n(1711–1776). Hume, of course, would clearly reject any robust\nrealist implications. If the moral sense is like the other\nperceptual senses and enables us to pick up on properties out there in\nthe universe around us, properties that exist independent from our\nperception of them, that are objective, then Hume clearly was not a\nmoral sense theorist in this regard. But perception picks up on\nfeatures of our environment that one could regard as having a\ncontingent quality. There is one famous passage where Hume likens moral\ndiscrimination to the perception of secondary qualities, such as\ncolor. In modern terminology, these are response-dependent\nproperties, and lack objectivity in the sense that they do not exist\nindependent of our responses. This is radical. If an\nact is vicious, its viciousness is a matter of the human\nresponse (given a corrected perspective) to the act (or its perceived\neffects) and thus has a kind of contingency that seems unsettling,\ncertainly unsettling to those who opted for the theological option.", "\n\nSo, the view that it is part of our very nature to make moral\ndiscriminations is very much in Hume. Further — and what is\nrelevant to the development of utilitarianism — the view of\nShaftesbury that the virtuous person contributes to the good of the\nwhole — would figure into Hume's writings, though\nmodified. It is the virtue that contributes to the good of the\nwhole system, in the case of Hume's artificial virtues.", "\n\nShaftesbury held that in judging someone virtuous or good in a moral\nsense we need to perceive that person's impact on the systems of\nwhich he or she is a part. Here it sometimes becomes difficult to\ndisentangle egoistic versus utilitarian lines of thought in\nShaftesbury. He clearly states that whatever guiding force there is has\nmade nature such that it is “…the private\ninterest and good of every one, to work towards the\ngeneral good, which if a creature ceases to promote, he is\nactually so far wanting to himself, and ceases to promote his own\nhappiness and welfare…” (R, 188). It is hard, sometimes,\nto discern the direction of the ‘because’ — if one\nshould act to help others because it supports a system in which\none's own happiness is more likely, then it looks really like a\nform of egoism. If one should help others because that's the\nright thing to do — and, fortunately, it also ends up promoting\none's own interests, then that's more like utilitarianism,\nsince the promotion of self-interest is a welcome effect but not what,\nall by itself, justifies one's character or actions.", "\n\nFurther, to be virtuous a person must have certain psychological\ncapacities — they must be able to reflect on character, for example,\nand represent to themselves the qualities in others that are either\napproved or disapproved of.", "\n…in this case alone it is we call any creature worthy or\nvirtuous when it can have the notion of a public interest, and can\nattain the speculation or science of what is morally good or ill,\nadmirable or blameable, right or wrong….we never say\nof….any mere beast, idiot, or changeling, though ever so\ngood-natured, that he is worthy or virtuous. (Shaftesbury IVM; BKI,\nPII, sec. iii)\n", "\n\nThus, animals are not objects of moral appraisal on the view, since\nthey lack the necessary reflective capacities. Animals also lack\nthe capacity for moral discrimination and would therefore seem to lack\nthe moral sense. This raises some interesting questions. It\nwould seem that the moral sense is a perception that something\nis the case. So it isn't merely a discriminatory sense that\nallows us to sort perceptions. It also has a propositional\naspect, so that animals, which are not lacking in other senses are\nlacking in this one.", "\n\nThe virtuous person is one whose affections, motives, dispositions\nare of the right sort, not one whose behavior is simply of the right\nsort and who is able to reflect on goodness, and her own goodness [see\nGill]. Similarly, the vicious person is one who exemplifies the\nwrong sorts of mental states, affections, and so forth. A person\nwho harms others through no fault of his own “…because he\nhas convulsive fits which make him strike and wound such as approach\nhim” is not vicious since he has no desire to harm anyone and his\nbodily movements in this case are beyond his control.", "\n\nShaftesbury approached moral evaluation via the virtues and vices.\nHis utilitarian leanings are distinct from his moral sense approach,\nand his overall sentimentalism. However, this approach highlights the\nmove away from egoistic views of human nature — a trend picked\nup by Hutcheson and Hume, and later adopted by Mill in criticism of\nBentham's version of utilitarianism. For writers like Shaftesbury and\nHutcheson the main contrast was with egoism rather than\nrationalism.", "\n\nLike Shaftesbury, Francis Hutcheson was very much interested in\nvirtue evaluation. He also adopted the moral sense\napproach. However, in his writings we also see an emphasis\non action choice and the importance of moral deliberation to action\nchoice. Hutcheson, in An Inquiry Concerning Moral Good and\nEvil, fairly explicitly spelled out a utilitarian principle of\naction choice. (Joachim Hruschka (1991) notes, however, that it was\nLeibniz who first spelled out a utilitarian decision procedure.)", "\n\n….In comparing the moral qualities of actions…we are led\nby our moral sense of virtue to judge thus; that in equal\ndegrees of happiness, expected to proceed from the action, the\nvirtue is in proportion to the number of persons to whom the\nhappiness shall extend (and here the dignity, or moral\nimportance of persons, may compensate numbers); and, in\nequal numbers, the virtue is the quantity of the\nhappiness, or natural good; or that the virtue is in a compound ratio of the\nquantity of good, and number of enjoyers….so\nthat that action is best, which procures\nthe greatest happiness for the greatest numbers; and\nthat worst, which, in like manner, occasions\nmisery. (R, 283–4)\n", "\n\nScarre notes that some hold the moral sense approach incompatible\nwith this emphasis on the use of reason to determine what we ought to\ndo; there is an opposition between just apprehending what's\nmorally significant and a model in which we need to reason to figure\nout what morality demands of us. But Scarre notes these are not\nactually incompatible:", "\nThe picture which emerges from Hutcheson's discussion is of a\ndivision of labor, in which the moral sense causes us to look with\nfavor on actions which benefit others and disfavor those which harm\nthem, while consequentialist reasoning determines a more precise\nranking order of practical options in given situations. (Scarre,\n53–54)", "\n\nScarre then uses the example of telling a lie to illustrate: lying\nis harmful to the person to whom one lies, and so this is viewed with\ndisfavor, in general. However, in a specific case, if a lie is\nnecessary to achieve some notable good, consequentialist reasoning will\nlead us to favor the lying. But this example seems to\nput all the emphasis on a consideration of consequences in\nmoral approval and disapproval. Stephen Darwall notes (1995,\n216 ff.) that the moral sense is concerned\nwith motives — we approve, for example, of the motive of\nbenevolence, and the wider the scope the better. It is the motives\nrather than the consequences that are the objects of approval and\ndisapproval. But inasmuch as the morally good person cares about what\nhappens to others, and of course she will, she will rank order acts in\nterms of their effects on others, and reason is used in calculating\neffects. So there is no incompatibility at all.", "\n\nHutcheson was committed to maximization, it seems. However, he\ninsisted on a caveat — that “the dignity or moral\nimportance of persons may compensate numbers.” He added\na deontological constraint — that we have a duty to others in\nvirtue of their personhood to accord them fundamental dignity\nregardless of the numbers of others whose happiness is to be affected\nby the action in question.", "\n\nHume was heavily influenced by Hutcheson, who was one of his\nteachers. His system also incorporates insights made by\nShaftesbury, though he certainly lacks Shaftesbury's confidence\nthat virtue is its own reward. In terms of his place in the\nhistory of utilitarianism we should note two distinct effects his\nsystem had. Firstly, his account of the social utility of the\nartificial virtues influenced Bentham's thought on utility.\nSecondly, his account of the role sentiment played in moral judgment\nand commitment to moral norms influenced Mill's thoughts about\nthe internal sanctions of morality. Mill would diverge from\nBentham in developing the ‘altruistic’ approach to\nUtilitarianism (which is actually a misnomer, but more on that\nlater). Bentham, in contrast to Mill, represented the egoistic\nbranch — his theory of human nature reflected Hobbesian\npsychological egoism." ], "section_title": "1. Precursors to the Classical Approach", "subsections": [] }, { "main_content": [ "\n\nThe Classical Utilitarians, Bentham and Mill, were concerned with\nlegal and social reform. If anything could be identified as the\nfundamental motivation behind the development of Classical\nUtilitarianism it would be the desire to see useless, corrupt laws and\nsocial practices changed. Accomplishing this goal required a\nnormative ethical theory employed as a critical tool. What is the\ntruth about what makes an action or a policy a morally good one, or\nmorally right? But developing the theory itself was also\ninfluenced by strong views about what was wrong in their society.\nThe conviction that, for example, some laws are bad resulted in\nanalysis of why they were bad. And, for Jeremy Bentham, what made\nthem bad was their lack of utility, their tendency to lead to\nunhappiness and misery without any compensating happiness. If a\nlaw or an action doesn't do any good, then it\nisn't any good." ], "section_title": "2. The Classical Approach", "subsections": [ { "content": [ "\n\nJeremy Bentham (1748–1832) was influenced both by Hobbes'\naccount of human nature and Hume's account of social\nutility. He famously held that humans were ruled by two sovereign\nmasters — pleasure and pain. We seek pleasure and the avoidance\nof pain, they “…govern us in all we do, in all we say, in\nall we think…” (Bentham PML, 1). Yet he also promulgated the\nprinciple of utility as the standard of right action on the part of\ngovernments and individuals. Actions are approved when they\nare such as to promote happiness, or pleasure, and disapproved of when\nthey have a tendency to cause unhappiness, or pain (PML). Combine\nthis criterion of rightness with a view that we should be actively\ntrying to promote overall happiness, and one has a serious\nincompatibility with psychological egoism. Thus, his apparent\nendorsement of Hobbesian psychological egoism created problems in\nunderstanding his moral theory since psychological egoism rules out\nacting to promote the overall well-being when that it is incompatible\nwith one's own. For the psychological egoist, that is not\neven a possibility. So, given ‘ought implies can’ it\nwould follow that we are not obligated to act to promote overall\nwell-being when that is incompatible with our own. This generates\na serious tension in Bentham's thought, one that was drawn to his\nattention. He sometimes seemed to think that he could reconcile\nthe two commitments empirically, that is, by noting that when people\nact to promote the good they are helping themselves, too. But\nthis claim only serves to muddy the waters, since the standard\nunderstanding of psychological egoism — and Bentham's own\nstatement of his view — identifies motives of action which are\nself-interested. Yet this seems, again, in conflict with his own\nspecification of the method for making moral decisions which is not to\nfocus on self-interest — indeed, the addition of extent as a\nparameter along which to measure pleasure produced distinguishes this\napproach from ethical egoism. Aware of the difficulty, in later\nyears he seemed to pull back from a full-fledged commitment to\npsychological egoism, admitting that people do sometimes act\nbenevolently — with the overall good of humanity in mind.", "\n\nBentham also benefited from Hume's work, though in many ways\ntheir approaches to moral philosophy were completely different. Hume\nrejected the egoistic view of human nature. Hume also focused on\ncharacter evaluation in his system. Actions are significant as\nevidence of character, but only have this derivative significance. In\nmoral evaluation the main concern is that of character. Yet Bentham\nfocused on act-evaluation. There was a tendency — remarked on by\nJ. B. Schneewind (1990), for example — to move away from focus on\ncharacter evaluation after Hume and towards act-evaluation. Recall\nthat Bentham was enormously interested in social reform. Indeed,\nreflection on what was morally problematic about laws and policies\ninfluenced his thinking on utility as a standard. When one legislates,\nhowever, one is legislating in support of, or against, certain\nactions. Character — that is, a person's true\ncharacter — is known, if known at all, only by that person. If one\nfinds the opacity of the will thesis plausible then character, while\ntheoretically very interesting, isn't a practical focus for\nlegislation. Further, as Schneewind notes, there was an increasing\nsense that focus on character would actually be disruptive, socially,\nparticularly if one's view was that a person who didn't\nagree with one on a moral issues was defective in terms of his or her\ncharacter, as opposed to simply making a mistake reflected in\naction.", "\n\nBut Bentham does take from Hume the view that utility is the measure\nof virtue — that is, utility more broadly construed than\nHume's actual usage of the term. This is because Hume made\na distinction between pleasure that the perception of virtue generates\nin the observer, and social utility, which consisted in a trait's\nhaving tangible benefits for society, any instance of which may or may\nnot generate pleasure in the observer. But Bentham is not simply\nreformulating a Humean position — he's merely been\ninfluenced by Hume's arguments to see pleasure as a measure or\nstandard of moral value. So, why not move from pleasurable\nresponses to traits to pleasure as a kind of\nconsequence which is good, and in relation to which, actions\nare morally right or wrong? Bentham, in making this move, avoids a\nproblem for Hume. On Hume's view it seems that the\nresponse — corrected, to be sure — determines the trait's\nquality as a virtue or vice. But on Bentham's view the action\n(or trait) is morally good, right, virtuous in view of the\nconsequences it generates, the pleasure or utility it produces, which\ncould be completely independent of what our responses are to the\ntrait. So, unless Hume endorses a kind of ideal observer test for\nvirtue, it will be harder for him to account for how it is people make\nmistakes in evaluations of virtue and vice. Bentham, on the other\nhand, can say that people may not respond to the actions good\nqualities — perhaps they don't perceive the good\neffects. But as long as there are these good effects which are, on\nbalance, better than the effects of any alternative course of action,\nthen the action is the right one. Rhetorically, anyway, one can see\nwhy this is an important move for Bentham to be able to make. He was a\nsocial reformer. He felt that people often had responses to certain\nactions — of pleasure or disgust — that did not reflect anything\nmorally significant at all. Indeed, in his discussions of\nhomosexuality, for example, he explicitly notes that\n‘antipathy’ is not sufficient reason to legislate against\na practice:", "\n\nThe circumstances from which this antipathy may have taken its rise\nmay be worth enquiring to…. One is the physical antipathy to\nthe offence…. The act is to the highest degree odious and\ndisgusting, that is, not to the man who does it, for he does it only\nbecause it gives him pleasure, but to one who thinks [?] of it. Be it\nso, but what is that to him? (Bentham OAO, v. 4, 94)", "\n\nBentham then notes that people are prone to use their physical\nantipathy as a pretext to transition to moral antipathy, and the\nattending desire to punish the persons who offend their taste.\nThis is illegitimate on his view for a variety of reasons, one of which\nis that to punish a person for violations of taste, or on the basis of\nprejudice, would result in runaway punishments, “…one\nshould never know where to stop…” The prejudice in\nquestion can be dealt with by showing it “to be\nill-grounded”. This reduces the antipathy to the act in\nquestion. This demonstrates an optimism in Bentham. If a\npain can be demonstrated to be based on false beliefs then he believes\nthat it can be altered or at the very least ‘assuaged and\nreduced’. This is distinct from the view that a pain or\npleasure based on a false belief should be discounted. Bentham\ndoes not believe the latter. Thus Bentham's hedonism is a\nvery straightforward hedonism. The one intrinsic good is\npleasure, the bad is pain. We are to promote pleasure and act to\nreduce pain. When called upon to make a moral decision one\nmeasures an action's value with respect to pleasure and pain\naccording to the following: intensity (how strong the pleasure or pain\nis), duration (how long it lasts), certainty (how likely the pleasure\nor pain is to be the result of the action), proximity (how close the\nsensation will be to performance of the action), fecundity (how likely\nit is to lead to further pleasures or pains), purity (how much\nintermixture there is with the other sensation). One also\nconsiders extent — the number of people affected by the\naction.", "\n\nKeeping track of all of these parameters can be complicated and time\nconsuming. Bentham does not recommend that they figure into every\nact of moral deliberation because of the efficiency costs which need to\nbe considered. Experience can guide us. We know that the\npleasure of kicking someone is generally outweighed by the pain\ninflicted on that person, so such calculations when confronted with a\ntemptation to kick someone are unnecessary. It is reasonable to\njudge it wrong on the basis of past experience or consensus. One\ncan use ‘rules of thumb’ to guide action, but these rules\nare overridable when abiding by them would conflict with the promotion\nof the good.", "\n\nBentham's view was surprising to many at the time at least in part\nbecause he viewed the moral quality of an action to be determined\ninstrumentally. It isn't so much that there is a particular kind of\naction that is intrinsically wrong; actions that are wrong are wrong\nsimply in virtue of their effects, thus, instrumentally wrong. This\ncut against the view that there are some actions that by their very\nnature are just wrong, regardless of their effects. Some may be wrong\nbecause they are ‘unnatural’ — and, again, Bentham\nwould dismiss this as a legitimate criterion. Some may be wrong\nbecause they violate liberty, or autonomy. Again, Bentham would view\nliberty and autonomy as good — but good instrumentally, not\nintrinsically. Thus, any action deemed wrong due to a violation of\nautonomy is derivatively wrong on instrumental grounds as well. This\nis interesting in moral philosophy — as it is far removed from\nthe Kantian approach to moral evaluation as well as from natural law\napproaches. It is also interesting in terms of political philosophy\nand social policy. On Bentham's view the law is not monolithic and\nimmutable. Since effects of a given policy may change, the moral\nquality of the policy may change as well. Nancy Rosenblum noted that\nfor Bentham one doesn't simply decide on good laws and leave it at\nthat: “Lawmaking must be recognized as a continual process in\nresponse to diverse and changing desires that require\nadjustment” (Rosenblum 1978, 9). A law that is good at one point\nin time may be a bad law at some other point in time. Thus, lawmakers\nhave to be sensitive to changing social circumstances. To be fair to\nBentham's critics, of course, they are free to agree with him that\nthis is the case in many situations, just not all — and that\nthere is still a subset of laws that reflect the fact that some\nactions just are intrinsically wrong regardless of\nconsequences. Bentham is in the much more difficult position of\narguing that effects are all there are to moral evaluation of action\nand policy." ], "subsection_title": "2.1 Jeremy Bentham" }, { "content": [ "\n\nJohn Stuart Mill (1806–1873) was a follower of Bentham, and, through\nmost of his life, greatly admired Bentham's work even though he\ndisagreed with some of Bentham's claims — particularly on\nthe nature of ‘happiness.’ Bentham, recall, had\nheld that there were no qualitative differences between pleasures, only\nquantitative ones. This left him open to a variety of\ncriticisms. First, Bentham's Hedonism was too\negalitarian. Simple-minded pleasures, sensual pleasures, were\njust as good, at least intrinsically, than more sophisticated and\ncomplex pleasures. The pleasure of drinking a beer in front of\nthe T.V. surely doesn't rate as highly as the pleasure one gets\nsolving a complicated math problem, or reading a poem, or listening to\nMozart. Second, Bentham's view that there were no\nqualitative differences in pleasures also left him open to the\ncomplaint that on his view human pleasures were of no more value than\nanimal pleasures and, third, committed him to the corollary that the\nmoral status of animals, tied to their sentience, was the same as that\nof humans. While harming a puppy and harming a person are both\nbad, however, most people had the view that harming the person was\nworse. Mill sought changes to the theory that could accommodate\nthose sorts of intuitions.", "\n\nTo this end, Mill's hedonism was influenced by perfectionist\nintuitions. There are some pleasures that are more fitting than\nothers. Intellectual pleasures are of a higher, better, sort than\nthe ones that are merely sensual, and that we share with animals.\nTo some this seems to mean that Mill really wasn't a hedonistic\nutilitarian. His view of the good did radically depart from\nBentham's view. However, like Bentham, the good still\nconsists in pleasure, it is still a psychological state. There is\ncertainly that similarity. Further, the basic structures of the\ntheories are the same (for more on this see Donner 1991). While it is\ntrue that Mill is more comfortable with notions like\n‘rights’ this does not mean that he, in actuality, rejected\nutilitarianism. The rationale for all the rights he recognizes is\nutilitarian.", "\n\nMill's ‘proof’ of the claim that intellectual\npleasures are better in kind than others, though, is highly\nsuspect. He doesn't attempt a mere appeal to raw\nintuition. Instead, he argues that those persons who have experienced\nboth view the higher as better than the lower. Who would rather be a\nhappy oyster, living an enormously long life, than a person living a\nnormal life? Or, to use his most famous example — it is better to\nbe Socrates ‘dissatisfied’ than a fool\n‘satisfied.’ In this way Mill was able to solve a problem\nfor utilitarianism.", "\n\nMill also argued that the principle could be proven, using another\nrather notorious argument:", "\nThe only proof capable of being given that an object is visible is\nthat people actually see it…. In like manner, I apprehend, the\nsole evidence it is possible to produce that anything is desirable is\nthat people do actually desire it. If the end which the utilitarian\ndoctrine proposes to itself were not, in theory and in practiced,\nacknowledged to be an end, nothing could ever convince any person that\nit was so. (Mill, U, 81)", "\n\nMill then continues to argue that people desire happiness — the\nutilitarian end — and that the general happiness is “a good\nto the aggregate of all persons.” (81)", "\n\nG. E. Moore (1873–1958) criticized this as fallacious. He\nargued that it rested on an obvious ambiguity:", "\n\nMill has made as naïve and artless a use of the naturalistic\nfallacy as anybody could desire. “Good”, he tells us,\nmeans “desirable”, and you can only find out what is\ndesirable by seeking to find out what is actually desired….\nThe fact is that “desirable” does not mean “able to\nbe desired” as “visible” means “able to be\nseen.” The desirable means simply what ought to be\ndesired or deserves to be desired; just as the detestable means not\nwhat can be but what ought to be detested… (Moore, PE, 66–7)\n", "\n\nIt should be noted, however, that Mill was offering this as an\nalternative to Bentham's view which had been itself criticized as\na ‘swine morality,’ locating the good in pleasure in a kind\nof indiscriminate way. The distinctions he makes strike many as\nintuitively plausible ones. Bentham, however, can accommodate\nmany of the same intuitions within his system. This is because he\nnotes that there are a variety of parameters along which we\nquantitatively measure pleasure — intensity and duration are just two\nof those. His complete list is the following: intensity,\nduration, certainty or uncertainty, propinquity or remoteness,\nfecundity, purity, and extent. Thus, what Mill\ncalls the intellectual pleasures will score more highly than the\nsensual ones along several parameters, and this could give us reason to\nprefer those pleasures — but it is a quantitative not a qualitative\nreason, on Bentham's view. When a student decides to\nstudy for an exam rather than go to a party, for example, she is making\nthe best decision even though she is sacrificing short term\npleasure. That's because studying for the exam, Bentham\ncould argue, scores higher in terms of the long term pleasures doing\nwell in school lead to, as well as the fecundity of the pleasure in\nleading to yet other pleasures. However, Bentham will have to\nconcede that the very happy oyster that lives a very long time could,\nin principle, have a better life than a normal human.", "\n\nMill's version of utilitarianism differed from Bentham's\nalso in that he placed weight on the effectiveness of internal\nsanctions — emotions like guilt and remorse which serve to\nregulate our actions. This is an off-shoot of the different view\nof human nature adopted by Mill. We are the sorts of beings that\nhave social feelings, feelings for others, not just ourselves. We\ncare about them, and when we perceive harms to them this causes painful\nexperiences in us. When one perceives oneself to be the agent of\nthat harm, the negative emotions are centered on the self. One\nfeels guilt for what one has done, not for what one sees another\ndoing. Like external forms of punishment, internal sanctions are\ninstrumentally very important to appropriate action. Mill also\nheld that natural features of human psychology, such as conscience and\na sense of justice, underwrite motivation. The sense of justice,\nfor example, results from very natural impulses. Part of this\nsense involves a desire to punish those who have harmed others, and\nthis desire in turn “…is a spontaneous outgrowth from two\nsentiments, both in the highest degree natural…; the impulse of\nself-defense, and the feeling of sympathy.” (Chapter 5,\nUtilitarianism) Of course, he goes on, the justification\nmust be a separate issue. The feeling is there naturally, but it\nis our ‘enlarged’ sense, our capacity to include the\nwelfare of others into our considerations, and make intelligent\ndecisions, that gives it the right normative force.", "\n\nLike Bentham, Mill sought to use utilitarianism to inform law and\nsocial policy. The aim of increasing happiness underlies his\narguments for women's suffrage and free speech. We can be\nsaid to have certain rights, then — but those rights are\nunderwritten by utility. If one can show that a purported right\nor duty is harmful, then one has shown that it is not genuine.\nOne of Mills most famous arguments to this effect can be found in his\nwriting on women's suffrage when he discusses the ideal marriage\nof partners, noting that the ideal exists between individuals of\n“cultivated faculties” who influence each other\nequally. Improving the social status of women was important\nbecause they were capable of these cultivated faculties, and denying\nthem access to education and other opportunities for development is\nforgoing a significant source of happiness. Further, the men who\nwould deny women the opportunity for education, self-improvement, and\npolitical expression do so out of base motives, and the resulting\npleasures are not ones that are of the best sort.", "\n\nBentham and Mill both attacked social traditions that were justified\nby appeals to natural order. The correct appeal is to utility\nitself. Traditions often turned out to be “relics”\nof “barbarous” times, and appeals to nature as a form\nof justification were just ways to try rationalize continued deference\nto those\nrelics.", "In the latter part of the 20th century some writers criticized\nutilitarianism for its failure to accommodate virtue evaluation.\nHowever, though virtue is not the central normative concept in Mill's\ntheory, it is an extremely important one. In Chapter 4 of\nUtilitarianism Mill noted ", "… does the utilitarian doctrine deny that people\ndesire virtue, or maintain that virtue is not a thing to be desired?\nThe very reverse. It maintains not only that virtue is to be desired,\nbut also that it is to be desired disinterestedly, for\nitself. Whatever may be the opinion of utilitarian moralists as to the\noriginal conditions by which virtue is made virtue … they not only\nplace virtue at the very head of things which are good as a means to\nthe ultimate end, but they also recognize as a psychological fact the\npossibility of its being, to the individual, a good in itself, without\nlooking to any end beyond it; and hold, that the mind is not in a\nright state, not in a state conformable to Utility, not in the state\nmost conducive to the general happiness, unless it does love virtue in\nthis manner …", "In Utilitarianism Mill argues that virtue not only has\ninstrumental value, but is constitutive of the good life. A person\nwithout virtue is morally lacking, is not as able to promote the good.\nHowever, this view of virtue is someone complicated by rather cryptic\nremarks Mill makes about virtue in his A System of Logic in\nthe section in which he discusses the “Art of Life.” There he seems\nto associate virtue with aesthetics, and morality is reserved for the\nsphere of ‘right’ or ‘duty‘. Wendy Donner\nnotes that separating virtue from right allows Mill to solve another\nproblem for the theory: the demandingness problem (Donner 2011). This\nis the problem that holds that if we ought to maximize utility, if\nthat is the right thing to do, then doing right requires enormous\nsacrifices (under actual conditions), and that requiring such\nsacrifices is too demanding. With duties, on Mill's view, it is\nimportant that we get compliance, and that justifies coercion. In the\ncase of virtue, however, virtuous actions are those which it is\n“…for the general interest that they remain free.”" ], "subsection_title": "2.2 John Stuart Mill" } ] }, { "main_content": [ "\n\nHenry Sidgwick's (1838–1900) The Methods of Ethics (1874) is\none of the most well known works in utilitarian moral philosophy, and\ndeservedly so. It offers a defense of utilitarianism, though some\nwriters (Schneewind 1977) have argued that it should not primarily be\nread as a defense of utilitarianism. In The Methods Sidgwick\nis concerned with developing an account of “…the\ndifferent methods of Ethics that I find implicit in our common moral\nreasoning…” These methods are egoism, intuition based\nmorality, and utilitarianism. On Sidgwick's view, utilitarianism is\nthe more basic theory. A simple reliance on intuition, for example,\ncannot resolve fundamental conflicts between values, or rules, such as\nTruth and Justice that may conflict. In Sidgwick's words\n“…we require some higher principle to decide the\nissue…” That will be utilitarianism. Further, the rules\nwhich seem to be a fundamental part of common sense morality are often\nvague and underdescribed, and applying them will actually require\nappeal to something theoretically more basic — again,\nutilitarianism. Yet further, absolute interpretations of rules seem\nhighly counter-intuitive, and yet we need some justification for any\nexceptions — provided, again, by utilitarianism. Sidgwick\nprovides a compelling case for the theoretical primacy of\nutilitarianism.", "\n\nSidgwick was also a British philosopher, and his views developed out\nof and in response to those of Bentham and Mill. His\nMethods offer an engagement with the theory as it had been\npresented before him, and was an exploration of it and the main\nalternatives as well as a defense.", "\n\nSidgwick was also concerned with clarifying fundamental features of\nthe theory, and in this respect his account has been enormously\ninfluential to later writers, not only to utilitarians and\nconsequentialists, generally, but to intuitionists as well.\nSidgwick's thorough and penetrating discussion of the theory\nraised many of the concerns that have been developed by recent moral\nphilosophers.", "\n\nOne extremely controversial feature of Sidgwick's views\nrelates to his rejection of a publicity requirement for moral\ntheory. He writes:", "\n\nThus, the Utilitarian conclusion, carefully stated, would seem to be\nthis; that the opinion that secrecy may render an action right which\nwould not otherwise be so should itself be kept comparatively secret;\nand similarly it seems expedient that the doctrine that esoteric\nmorality is expedient should itself be kept esoteric. Or, if this\nconcealment be difficult to maintain, it may be desirable that Common\nSense should repudiate the doctrines which it is expedient to confine\nto an enlightened few. And thus a Utilitarian may reasonably desire,\non Utilitarian principles, that some of his conclusions should be\nrejected by mankind generally; or even that the vulgar should keep\naloof from his system as a whole, in so far as the inevitable\nindefiniteness and complexity of its calculations render it likely to\nlead to bad results in their hands. (490)", "\n\nThis accepts that utilitarianism may be self-effacing; that is, that\nit may be best if people do not believe it, even though it is\ntrue. Further, it rendered the theory subject to Bernard\nWilliams' (1995) criticism that the theory really simply\nreflected the colonial elitism of Sidgwick's time, that it was\n‘Government House Utilitarianism.’ The elitism in his\nremarks may reflect a broader attitude, one in which the educated are\nconsidered better policy makers than the uneducated.", "\n\nOne issue raised in the above remarks is relevant to practical\ndeliberation in general. To what extent should proponents of a\ngiven theory, or a given rule, or a given policy — or even\nproponents of a given one-off action — consider what they think\npeople will actually do, as opposed to what they think those\nsame people ought to do (under full and reasonable reflection,\nfor example)? This is an example of something that comes up in\nthe Actualism/possibilism debate in accounts of practical\ndeliberation. Extrapolating from the example used above, we have\npeople who advocate telling the truth, or what they believe to be the\ntruth, even if the effects are bad because the truth is somehow misused\nby others. On the other hand are those who recommend not telling\nthe truth when it is predicted that the truth will be misused by others\nto achieve bad results. Of course it is the case that the truth\nought not be misused, that its misuse can be avoided and is not\ninevitable, but the misuse is entirely predictable. Sidgwick\nseems to recommending that we follow the course that we predict will\nhave the best outcome, given as part of our calculations the data that\nothers may fail in some way — either due to having bad desires,\nor simply not being able to reason effectively. The worry\nWilliams points to really isn't a worry specifically with\nutilitarianism (Driver 2011). Sidgwick would point out\nthat if it is bad to hide the truth, because ‘Government\nHouse’ types, for example, typically engage in self-deceptive\nrationalizations of their policies (which seems entirely plausible),\nthen one shouldn't do it. And of course, that heavily\ninfluences our intuitions.", "\n\nSidgwick raised issues that run much deeper to our basic\nunderstanding of utilitarianism. For example, the way earlier\nutilitarians characterized the principle of utility left open serious\nindeterminacies. The major one rests on the distinction between\ntotal and average utility. He raised the issue in the context of\npopulation growth and increasing utility levels by increasing numbers\nof people (or sentient beings):", "\n\nAssuming, then, that the average happiness of human beings is a\npositive quantity, it seems clear that, supposing the average\nhappiness enjoyed remains undiminished, Utilitarianism directs us to\nmake the number enjoying it as great as possible. But if we foresee as\npossible that an increase in numbers will be accompanied by a decrease\nin average happiness or vice versa, a point arises which has\nnot only never been formally noticed, but which seems to have been\nsubstantially overlooked by many Utilitarians. For if we take\nUtilitarianism to prescribe, as the ultimate end of action, happiness\non the whole, and not any individual's happiness, unless\nconsidered as an element of the whole, it would follow that, if the\nadditional population enjoy on the whole positive happiness, we ought\nto weigh the amount of happiness gained by the extra number against\nthe amount lost by the remainder. (415)", "\n\nFor Sidgwick, the conclusion on this issue is not to simply strive\nto greater average utility, but to increase population to the point\nwhere we maximize the product of the number of persons who are\ncurrently alive and the amount of average happiness. So it seems\nto be a hybrid, total-average view. This discussion also raised\nthe issue of policy with respect to population growth, and both would\nbe pursued in more detail by later writers, most notably Derek Parfit\n(1986)." ], "section_title": "3. Henry Sidgwick", "subsections": [] }, { "main_content": [ "\n\nG. E. Moore strongly disagreed with the hedonistic value theory\nadopted by the Classical Utilitarians. Moore agreed that we ought\nto promote the good, but believed that the good included far more than\nwhat could be reduced to pleasure. He was a pluralist, rather\nthan a monist, regarding intrinsic value. For example, he\nbelieved that ‘beauty’ was an intrinsic good. A\nbeautiful object had value independent of any pleasure it might\ngenerate in a viewer. Thus, Moore differed from Sidgwick who\nregarded the good as consisting in some consciousness. Some objective\nstates in the world are intrinsically good, and on Moore's view,\nbeauty is just such a state. He used one of his more notorious\nthought experiments to make this point: he asked the reader to\ncompare two worlds, one was entirely beautiful, full of things which\ncomplemented each other; the other was a hideous, ugly world, filled\nwith “everything that is most disgusting to us.” Further,\nthere are not human beings, one imagines, around to appreciate or be\ndisgusted by the worlds. The question then is, which of these worlds is\nbetter, which one's existence would be better than the\nother's? Of course, Moore believed it was clear that the\nbeautiful world was better, even though no one was around to appreciate\nits beauty. This emphasis on beauty was one facet of\nMoore's work that made him a darling of the Bloomsbury\nGroup. If beauty was a part of the good independent of its\neffects on the psychological states of others — independent of,\nreally, how it affected others, then one needn't sacrifice\nmorality on the altar of beauty anymore. Following beauty is not\na mere indulgence, but may even be a moral obligation. Though\nMoore himself certainly never applied his view to such cases, it does\nprovide the resources for dealing with what the contemporary literature\nhas dubbed ‘admirable immorality’ cases, at least some of\nthem. Gauguin may have abandoned his wife and children, but it\nwas to a beautiful end.", "\n\nMoore's targets in arguing against hedonism were the earlier\nutilitarians who argued that the good was some state of consciousness\nsuch as pleasure. He actually waffled on this issue a bit, but\nalways disagreed with Hedonism in that even when he held that beauty\nall by itself was not an intrinsic good, he also held that for the\nappreciation of beauty to be a good the beauty must actually be there,\nin the world, and not be the result of illusion.", "\n\nMoore further criticized the view that pleasure itself was\nan intrinsic good, since it failed a kind of isolation test that he\nproposed for intrinsic value. If one compared an empty universe\nwith a universe of sadists, the empty universe would strike one as\nbetter. This is true even though there is a good deal of\npleasure, and no pain, in the universe of sadists. This would\nseem to indicate that what is necessary for the good is at least the\nabsence of bad intentionality. The pleasures of sadists, in\nvirtue of their desires to harm others, get discounted — they are\nnot good, even though they are pleasures. Note this radical\ndeparture from Bentham who held that even malicious pleasure was\nintrinsically good, and that if nothing instrumentally bad attached to the\npleasure, it was wholly good as well.", "\n\nOne of Moore's important contributions was to put forward an\n‘organic unity’ or ‘organic whole’ view of\nvalue. The principle of organic unity is vague, and there is some\ndisagreement about what Moore actually meant in presenting it.\nMoore states that ‘organic’ is used “…to\ndenote the fact that a whole has an intrinsic value different in amount\nfrom the sum of the values of its parts.” (PE, 36) And, for\nMoore, that is all it is supposed to denote. So, for example, one\ncannot determine the value of a body by adding up the value of its\nparts. Some parts of the body may have value only in relation to\nthe whole. An arm or a leg, for example, may have no value at all\nseparated from the body, but have a great deal of value attached to the\nbody, and increase the value of the body, even. In the section of\nPrincipia Ethica on the Ideal, the principle of organic unity\ncomes into play in noting that when persons experience pleasure through\nperception of something beautiful (which involves a positive emotion in\nthe face of a recognition of an appropriate object — an emotive\nand cognitive set of elements), the experience of the beauty is better\nwhen the object of the experience, the beautiful object, actually\nexists. The idea was that experiencing beauty has a small positive\nvalue, and existence of beauty has a small positive value, but\ncombining them has a great deal of value, more than the simple addition\nof the two small values (PE, 189 ff.). Moore noted:\n“A true belief in the reality of an object greatly increases the\nvalue of many valuable wholes…” (199).", "\n\nThis principle in Moore — particularly as applied to the\nsignificance of actual existence and value, or knowledge and value,\nprovided utilitarians with tools to meet some significant\nchallenges. For example, deluded happiness would be severely\nlacking on Moore's view, especially in comparison to happiness\nbased on knowledge." ], "section_title": "4. Ideal Utilitarianism", "subsections": [] }, { "main_content": [ "\n\nSince the early 20th Century utilitarianism has undergone a variety\nof refinements. After the middle of the 20th Century it has\nbecome more common to identify as a ‘Consequentialist’\nsince very few philosophers agree entirely with the view proposed by\nthe Classical Utilitarians, particularly with respect to the hedonistic\nvalue theory. But the influence of the Classical Utilitarians has\nbeen profound — not only within moral philosophy, but within\npolitical philosophy and social policy. The question Bentham\nasked, “What use is it?,” is a cornerstone of policy\nformation. It is a completely secular, forward-looking\nquestion. The articulation and systematic development of this\napproach to policy formation is owed to the Classical Utilitarians." ], "section_title": "5. Conclusion", "subsections": [] } ]

[ "Bentham, Jeremy, 1789 [PML]. An Introduction to the Principles of\nMorals and Legislation., Oxford: Clarendon Press, 1907.", "–––, 1785 [OAO]. “Offences Against\nOneself.” Louis Compton (ed.), The Journal of\nHomosexuality, 3(4) (1978): 389–406, 4(1): 91–107..", "Cooper, Anthony Ashley (3rd Earl of\nShaftesbury), 1711 [IVM]. Inquiry Concerning Virtue or\nMerit, in Characteristics of Men, Manners, Opinions and\nTimes, excerpts reprinted in Raphael 1969. ", "Cumberland, Richard, 1672. De Legibus Naturae Disquisitio\nPhilosophica, London. English translation by John Maxwell, A\nTreatise of the Laws of Nature, 1727, reprinted New York,\nGarland, 1978.", "Gay, John, 1731. A Dissertation Concerning the Fundamental\nPrinciple and Immediate Criterion of Virtue in Frances\nKing's An Essay on the Origin of Evil, London.", "Hume, David, 1738. A Treatise of Human Nature, edited by\nL. A. Selby-Bigge, Oxford: Oxford University Press, 1978.", "Hutcheson, Francis, 1725. An Inquiry into the Original of\nour Ideas of Beauty and Virtue, London; excerpts reprinted in\nRaphael 1969.", "Mill, John Stuart, 1843. A System of Logic, London: John\nW. Parker.", "–––, 1859. On Liberty, London: Longman,\nRoberts & Green.", "–––, 1861 [U]. Utilitarianism, Roger\nCrisp (ed.), Oxford: Oxford University Press, 1998.", "Moore, G. E., 1903 [PE]. Principia Ethica, Amherst, New\nYork: Prometheus Books, 1988.", "Price, Richard, 1758 [PE]. A Review of the Principle Questions\nin Morals, London: T. Cadell in the Strand, 1787.", "Raphael, D. D., 1969 [R]. British Moralists, in two\nvolumes, London: Oxford, Clarendon Press.", "Crisp, Roger, 1997. Mill on Utilitarianism., London:\nRoutledge.", "Darwall, Stephen, 1995. Hume and the Invention of\nUtilitarianism, University Park, PA: Penn State University\nPress.", "Donner, Wendy, 1991. The Liberal Self: John Stuart Mill's\nMoral and Political Philosophy, Ithaca, NY: Cornell University\nPress.", "–––, 2011. “Morality, Virtue, and\nAesthetics in Mill's Art of Life,” in Ben Eggleston, Dale\nE. Miller, and David Weinstein (eds.) John Stuart Mill and the Art\nof Life, Oxford: Oxford University Press.", "Driver, Julia, 2004. “Pleasure as the Standard of Virtue\nin Hume's Moral Philosophy.” Pacific Philosophical\nQuarterly., 85: 173–194.", "–––, 2011. Consequentialism,\nLondon: Routledge.", "Gill, Michael, 2006. The British Moralists on Human Nature\nand the Birth of Secular Ethics, New York: Cambridge University\nPress.", "Hruschka, Joachim, 1991. “The Greatest Happiness Principle\nand Other Early German Anticipations of Utilitarian\nTheory,” Utilitas, 3: 165–77.", "Long, Douglas, 1990. “‘Utility’ and the\n‘Utility Principle’: Hume, Smith, Bentham, Mill,”\nUtilitas, 2: 12–39.", "Rosen, Frederick, 2003. “Reading Hume Backwards: Utility as\nthe Foundation of Morals,” in Frederick Rosen (ed.),\nClassical Utilitarianism from Hume to Mill, London: Routledge,\n29–57.", "Rosenblum, Nancy, 1978. Bentham's Theory of the Modern\nState, New York: Cambridge University Press.", "Ryan, Alan, 1990. The Philosophy of John Stuart\nMill, Amherst, NY: Prometheus Books.", "Scarre, Geoffrey, 1996. Utilitarianism, London:\nRoutledge.", "Schneewind, J. B., 1977. Sidgwick's Ethics and Victorian\nMoral Philosophy, Oxford: Clarendon Press.", "–––, 1990. “The Misfortunes of\nVirtue,” Ethics, 101: 42–63.", "Schofield, Philip, 2006. Utility and Democracy: the Political\nThought of Jeremy Bentham, Oxford: Oxford University Press.", "Schultz, Bart, 2004. Henry Sidgwick, Eye of the\nUniverse, New York: Cambridge University Press.", "Skorupski, John, 1989. John Stuart Mill, London:\nRoutledge & Kegan Paul." ]

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[ "\nIntrinsic value has traditionally been thought to lie at the heart of\nethics. Philosophers use a number of terms to refer to such value. The\nintrinsic value of something is said to be the value that that thing\nhas “in itself,” or “for its own sake,” or\n“as such,” or “in its own right.” Extrinsic\nvalue is value that is not intrinsic.", "\nMany philosophers take intrinsic value to be crucial to a variety of\nmoral judgments. For example, according to a fundamental form of\nconsequentialism, whether an action is morally right or wrong\nhas exclusively to do with whether its consequences are intrinsically\nbetter than those of any other action one can perform under the\ncircumstances. Many other theories also hold that what it is right or\nwrong to do has at least in part to do with the intrinsic value of the\nconsequences of the actions one can perform. Moreover, if, as is\ncommonly believed, what one is morally responsible for doing\nis some function of the rightness or wrongness of what one does, then\nintrinsic value would seem relevant to judgments about responsibility,\ntoo. Intrinsic value is also often taken to be pertinent to judgments\nabout moral justice (whether having to do with moral rights\nor moral desert), insofar as it is good that justice is done and bad\nthat justice is denied, in ways that appear intimately tied to\nintrinsic value. Finally, it is typically thought that judgments about\nmoral virtue and vice also turn on questions of intrinsic\nvalue, inasmuch as virtues are good, and vices bad, again in ways that\nappear closely connected to such value.", "\nAll four types of moral judgments have been the subject of discussion\nsince the dawn of western philosophy in ancient Greece. The Greeks\nthemselves were especially concerned with questions about virtue and\nvice, and the concept of intrinsic value may be found at work in their\nwritings and in the writings of moral philosophers ever since. Despite\nthis fact, and rather surprisingly, it is only within the last one\nhundred years or so that this concept has itself been the subject of\nsustained scrutiny, and even within this relatively brief period the\nscrutiny has waxed and waned." ]

[ { "content_title": "1. What Has Intrinsic Value?", "sub_toc": [] }, { "content_title": "2. What Is Intrinsic Value?", "sub_toc": [] }, { "content_title": "3. Is There Such a Thing As Intrinsic Value At All?", "sub_toc": [] }, { "content_title": "4. What Sort of Thing Can Have Intrinsic Value?", "sub_toc": [] }, { "content_title": "5. How Is Intrinsic Value to Be Computed?", "sub_toc": [] }, { "content_title": "6. What Is Extrinsic Value?", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [ "Cited works", "Other works" ] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nThe question “What is intrinsic value?” is more\nfundamental than the question “What has intrinsic value?,”\nbut historically these have been treated in reverse order. For a long\ntime, philosophers appear to have thought that the notion of intrinsic\nvalue is itself sufficiently clear to allow them to go straight to the\nquestion of what should be said to have intrinsic value. Not even a\npotted history of what has been said on this matter can be attempted\nhere, since the record is so rich. Rather, a few representative\nillustrations must suffice.", "\nIn his dialogue Protagoras, Plato [428–347 B.C.E.]\nmaintains (through the character of Socrates, modeled after the real\nSocrates [470–399 B.C.E.], who was Plato’s teacher) that,\nwhen people condemn pleasure, they do so, not because they take\npleasure to be bad as such, but because of the bad consequences they\nfind pleasure often to have. For example, at one point Socrates says\nthat the only reason why the pleasures of food and drink and sex seem\nto be evil is that they result in pain and deprive us of future\npleasures (Plato, Protagoras, 353e). He concludes that\npleasure is in fact good as such and pain bad, regardless of what\ntheir consequences may on occasion be. In the Timaeus, Plato\nseems quite pessimistic about these consequences, for he has Timaeus\ndeclare pleasure to be “the greatest incitement to evil”\nand pain to be something that “deters from good” (Plato,\nTimaeus, 69d). Plato does not think of pleasure as the\n“highest” good, however. In the Republic,\nSocrates states that there can be no “communion” between\n“extravagant” pleasure and virtue (Plato,\nRepublic, 402e) and in the Philebus, where Philebus\nargues that pleasure is the highest good, Socrates argues against\nthis, claiming that pleasure is better when accompanied by\nintelligence (Plato, Philebus, 60e).", "\nMany philosophers have followed Plato’s lead in declaring\npleasure intrinsically good and pain intrinsically bad. Aristotle\n[384–322 B.C.E.], for example, himself a student of\nPlato’s, says at one point that all are agreed that pain is bad\nand to be avoided, either because it is bad “without\nqualification” or because it is in some way an\n“impediment” to us; he adds that pleasure, being the\n“contrary” of that which is to be avoided, is therefore\nnecessarily a good (Aristotle, Nicomachean Ethics, 1153b).\nOver the course of the more than two thousand years since this was\nwritten, this view has been frequently endorsed. Like Plato, Aristotle\ndoes not take pleasure and pain to be the only things that are\nintrinsically good and bad, although some have maintained that this is\nindeed the case. This more restrictive view, often called hedonism,\nhas had proponents since the time of Epicurus [341–271\n B.C.E.].[1]\n Perhaps the most thorough renditions of it are to be found in the\nworks of Jeremy Bentham [1748–1832] and Henry Sidgwick\n[1838–1900] (see Bentham 1789, Sidgwick 1907); perhaps its most\nfamous proponent is John Stuart Mill [1806–1873] (see Mill\n1863).", "\nMost philosophers who have written on the question of what has\nintrinsic value have not been hedonists; like Plato and Aristotle,\nthey have thought that something besides pleasure and pain has\nintrinsic value. One of the most comprehensive lists of intrinsic\ngoods that anyone has suggested is that given by William Frankena\n(Frankena 1973, pp. 87–88): life, consciousness, and activity;\nhealth and strength; pleasures and satisfactions of all or certain\nkinds; happiness, beatitude, contentment, etc.; truth; knowledge and\ntrue opinions of various kinds, understanding, wisdom; beauty,\nharmony, proportion in objects contemplated; aesthetic experience;\nmorally good dispositions or virtues; mutual affection, love,\nfriendship, cooperation; just distribution of goods and evils; harmony\nand proportion in one’s own life; power and experiences of\nachievement; self-expression; freedom; peace, security; adventure and\nnovelty; and good reputation, honor, esteem, etc. (Presumably a\ncorresponding list of intrinsic evils could be provided.) Almost any\nphilosopher who has ever addressed the question of what has intrinsic\nvalue will find his or her answer represented in some way by one or\nmore items on Frankena’s list. (Frankena himself notes that he\ndoes not explicitly include in his list the communion with and love\nand knowledge of God that certain philosophers believe to be the\nhighest good, since he takes them to fall under the headings of\n“knowledge” and “love.”) One conspicuous\nomission from the list, however, is the increasingly popular view that\ncertain environmental entities or qualities have intrinsic value\n(although Frankena may again assert that these are implicitly\nrepresented by one or more items already on the list). Some find\nintrinsic value, for example, in certain “natural”\nenvironments (wildernesses untouched by human hand); some find it in\ncertain animal species; and so on.", "\nSuppose that you were confronted with some proposed list of intrinsic\ngoods. It would be natural to ask how you might assess the accuracy of\nthe list. How can you tell whether something has intrinsic value or\nnot? On one level, this is an epistemological question about which\nthis article will not be concerned. (See the entry in this\nencyclopedia on moral epistemology.) On another level, however, this\nis a conceptual question, for we cannot be sure that something has\nintrinsic value unless we understand what it is for something to have\nintrinsic value." ], "section_title": "1. What Has Intrinsic Value?", "subsections": [] }, { "main_content": [ "\nThe concept of intrinsic value has been characterized above in terms\nof the value that something has “in itself,” or “for\nits own sake,” or “as such,” or “in its own\nright.” The custom has been not to distinguish between the\nmeanings of these terms, but we will see that there is reason to think\nthat there may in fact be more than one concept at issue here. For the\nmoment, though, let us ignore this complication and focus on what it\nmeans to say that something is valuable for its own sake as\nopposed to being valuable for the sake of something else to\nwhich it is related in some way. Perhaps it is easiest to grasp this\ndistinction by way of illustration.", "\nSuppose that someone were to ask you whether it is good to help others\nin time of need. Unless you suspected some sort of trick, you would\nanswer, “Yes, of course.” If this person were to go on to\nask you why acting in this way is good, you might say that it is good\nto help others in time of need simply because it is good that their\nneeds be satisfied. If you were then asked why it is good that\npeople’s needs be satisfied, you might be puzzled. You might be\ninclined to say, “It just is.” Or you might accept the\nlegitimacy of the question and say that it is good that people’s\nneeds be satisfied because this brings them pleasure. But then, of\ncourse, your interlocutor could ask once again, “What’s\ngood about that?” Perhaps at this point you would answer,\n“It just is good that people be pleased,” and thus put an\nend to this line of questioning. Or perhaps you would again seek to\nexplain the fact that it is good that people be pleased in terms of\nsomething else that you take to be good. At some point, though, you\nwould have to put an end to the questions, not because you would have\ngrown tired of them (though that is a distinct possibility), but\nbecause you would be forced to recognize that, if one thing derives\nits goodness from some other thing, which derives its goodness from\nyet a third thing, and so on, there must come a point at which you\nreach something whose goodness is not derivative in this way,\nsomething that “just is” good in its own right, something\nwhose goodness is the source of, and thus explains, the goodness to be\nfound in all the other things that precede it on the list. It is at\nthis point that you will have arrived at intrinsic goodness (cf.\nAristotle, Nicomachean Ethics, 1094a). That which is\nintrinsically good is nonderivatively good; it is good for its\nown sake. That which is not intrinsically good but\nextrinsically good is derivatively good; it is good, not (insofar as\nits extrinsic value is concerned) for its own sake, but for the sake\nof something else that is good and to which it is related in some way.\nIntrinsic value thus has a certain priority over extrinsic value. The\nlatter is derivative from or reflective of the former and is to be\nexplained in terms of the former. It is for this reason that\nphilosophers have tended to focus on intrinsic value in\nparticular.", "\nThe account just given of the distinction between intrinsic and\nextrinsic value is rough, but it should do as a start. Certain\ncomplications must be immediately acknowledged, though. First, there\nis the possibility, mentioned above, that the terms traditionally used\nto refer to intrinsic value in fact refer to more than one concept;\nagain, this will be addressed later (in this section and the next).\nAnother complication is that it may not in fact be accurate to say\nthat whatever is intrinsically good is nonderivatively good; some\nintrinsic value may be derivative. This issue will be taken up (in\nSection 5) when the computation of intrinsic value is discussed; it\nmay be safely ignored for now. Still another complication is this. It\nis almost universally acknowledged among philosophers that all value\nis “supervenient” or “grounded in” on certain\nnonevaluative features of the thing that has value. Roughly, what this\nmeans is that, if something has value, it will have this value in\nvirtue of certain nonevaluative features that it has; its value can be\nattributed to these features. For example, the value of helping\nothers in time of need might be attributed to the fact that such\nbehavior has the feature of being causally related to certain pleasant\nexperiences induced in those who receive the help. Suppose we accept\nthis and accept also that the experiences in question are\nintrinsically good. In saying this, we are (barring the complication\nto be discussed in Section 5) taking the value of the experiences to\nbe nonderivative. Nonetheless, we may well take this value, like all\nvalue, to be supervenient on, or grounded in, something. In this case,\nwe would probably simply attribute the value of the experiences to\ntheir having the feature of being pleasant. This brings out the subtle\nbut important point that the question whether some value is derivative\nis distinct from the question whether it is supervenient. Even\nnonderivative value (value that something has in its own right; value\nthat is, in some way, not attributable to the value of\nanything else) is usually understood to be supervenient on certain\nnonevaluative features of the thing that has value (and thus to be\nattributable, in a different way, to these features).", "\nTo repeat: whatever is intrinsically good is (barring the complication\nto be discussed in Section 5) nonderivatively good. It would be a\nmistake, however, to affirm the converse of this and say that whatever\nis nonderivatively good is intrinsically good. As “intrinsic\nvalue” is traditionally understood, it refers to a\nparticular way of being nonderivatively good; there are other\nways in which something might be nonderivatively good. For example,\nsuppose that your interlocutor were to ask you whether it is good to\neat and drink in moderation and to exercise regularly. Again, you\nwould say, “Yes, of course.” If asked why, you would say\nthat this is because such behavior promotes health. If asked what is\ngood about being healthy, you might cite something else whose goodness\nwould explain the value of health, or you might simply say,\n“Being healthy just is a good way to be.” If the latter\nwere your response, you would be indicating that you took health to be\nnonderivatively good in some way. In what way, though? Well, perhaps\nyou would be thinking of health as intrinsically good. But perhaps\nnot. Suppose that what you meant was that being healthy just is\n“good for” the person who is healthy (in the sense that it\nis in each person’s interest to be healthy), so that\nJohn’s being healthy is good for John, Jane’s being\nhealthy is good for Jane, and so on. You would thereby be attributing\na type of nonderivative interest-value to John’s being healthy,\nand yet it would be perfectly consistent for you to deny that\nJohn’s being healthy is intrinsically good. If John\nwere a villain, you might well deny this. Indeed, you might want to\ninsist that, in light of his villainy, his being healthy is\nintrinsically bad, even though you recognize that his being\nhealthy is good for him. If you did say this, you would be\nindicating that you subscribe to the common view that intrinsic value\nis nonderivative value of some peculiarly moral\n sort.[2]", "\nLet us now see whether this still rough account of intrinsic value can\nbe made more precise. One of the first writers to concern himself with\nthe question of what exactly is at issue when we ascribe intrinsic\nvalue to something was G. E. Moore [1873–1958]. In his book\nPrincipia Ethica, Moore asks whether the concept of intrinsic\nvalue (or, more particularly, the concept of intrinsic goodness, upon\nwhich he tended to focus) is analyzable. In raising this question, he\nhas a particular type of analysis in mind, one which consists in\n“breaking down” a concept into simpler component concepts.\n(One example of an analysis of this sort is the analysis of the\nconcept of being a vixen in terms of the concepts of being a fox and\nbeing female.) His own answer to the question is that the concept of\nintrinsic goodness is not amenable to such analysis (Moore\n1903, ch. 1). In place of analysis, Moore proposes a certain kind of\nthought-experiment in order both to come to understand the concept\nbetter and to reach a decision about what is intrinsically good. He\nadvises us to consider what things are such that, if they existed by\nthemselves “in absolute isolation,” we would judge their\nexistence to be good; in this way, we will be better able to see what\nreally accounts for the value that there is in our world. For example,\nif such a thought-experiment led you to conclude that all and only\npleasure would be good in isolation, and all and only pain bad, you\nwould be a\n hedonist.[3]\n Moore himself deems it incredible that anyone, thinking clearly,\nwould reach this conclusion. He says that it involves our saying that\na world in which only pleasure existed—a world without any\nknowledge, love, enjoyment of beauty, or moral qualities—is\nbetter than a world that contained all these things but in which there\nexisted slightly less pleasure (Moore 1912, p. 102). Such a view he\nfinds absurd.", "\nRegardless of the merits of this isolation test, it remains unclear\nexactly why Moore finds the concept of intrinsic goodness to be\nunanalyzable. At one point he attacks the view that it can be analyzed\nwholly in terms of “natural” concepts—the view, that\nis, that we can break down the concept of being intrinsically good\ninto the simpler concepts of being A, being B, being\nC…, where these component concepts are all purely\ndescriptive rather than evaluative. (One candidate that Moore\ndiscusses is this: for something to be intrinsically good is for it to\nbe something that we desire to desire.) He argues that any such\nanalysis is to be rejected, since it will always be intelligible to\nask whether (and, presumably, to deny that) it is good that something\nbe A, B, C,…, which would not be the\ncase if the analysis were accurate (Moore 1903, pp. 15–16). Even\nif this argument is successful (a complicated matter about which there\nis considerable disagreement), it of course does not establish the\nmore general claim that the concept of intrinsic goodness is not\nanalyzable at all, since it leaves open the possibility that this\nconcept is analyzable in terms of other concepts, some or all of which\nare not “natural” but evaluative. Moore apparently thinks\nthat his objection works just as well where one or more of the\ncomponent concepts A, B, C,…, is\nevaluative; but, again, many dispute the cogency of his argument.\nIndeed, several philosophers have proposed analyses of just this sort.\nFor example, Roderick Chisholm [1916–1999] has argued that\nMoore’s own isolation test in fact provides the basis for an\nanalysis of the concept of intrinsic value. He formulates a view\naccording to which (to put matters roughly) to say that a state of\naffairs is intrinsically good or bad is to say that it is possible\nthat its goodness or badness constitutes all the goodness or badness\nthat there is in the world (Chisholm 1978). ", "\nEva Bodanszky and Earl Conee have attacked Chisholm’s proposal,\nshowing that it is, in its details, unacceptable (Bodanszky and Conee\n1981). However, the general idea that an intrinsically valuable state\nis one that could somehow account for all the value in the world is\nsuggestive and promising; if it could be adequately formulated, it\nwould reveal an important feature of intrinsic value that would help\nus better understand the concept. We will return to this point in\nSection 5. Rather than pursue such a line of thought, Chisholm himself\nresponded (Chisholm 1981) in a different way to Bodanszky and Conee.\nHe shifted from what may be called an ontological version of\nMoore’s isolation test—the attempt to understand the\nintrinsic value of a state in terms of the value that there would be\nif it were the only valuable state in existence—to an\nintentional version of that test—the attempt to\nunderstand the intrinsic value of a state in terms of the kind of\nattitude it would be fitting to have if one were to\ncontemplate the valuable state as such, without reference to\ncircumstances or consequences.", "\nThis new analysis in fact reflects a general idea that has a rich\nhistory. Franz Brentano [1838–1917], C. D. Broad\n[1887–1971], W. D. Ross [1877–1971], and A. C. Ewing\n[1899–1973], among others, have claimed, in a more or less\nqualified way, that the concept of intrinsic goodness is analyzable in\nterms of the fittingness of some “pro” (i.e., positive)\nattitude (Brentano 1969, p. 18; Broad 1930, p. 283; Ross 1939, pp.\n275–76; Ewing 1948, p. 152). Such an analysis, which has come to\nbe called “the fitting attitude analysis” of value, is\nsupported by the mundane observation that, instead of saying that\nsomething is good, we often say that it is valuable, which\nitself just means that it is fitting to value the thing in question.\nIt would thus seem very natural to suppose that for something to be\nintrinsically good is simply for it to be such that it is fitting to\nvalue it for its own sake. (“Fitting” here is often\nunderstood to signify a particular kind of moral fittingness, in\nkeeping with the idea that intrinsic value is a particular kind of\nmoral value. The underlying point is that those who value for its own\nsake that which is intrinsically good thereby evince a kind of\nmoral sensitivity.)", "\nThough undoubtedly attractive, this analysis can be and has been\nchallenged. Brand Blanshard [1892–1987], for example, argues\nthat the analysis is to be rejected because, if we ask why\nsomething is such that it is fitting to value it for its own sake, the\nanswer is that this is the case precisely because the thing\nin question is intrinsically good; this answer indicates that the\nconcept of intrinsic goodness is more fundamental than that of the\nfittingness of some pro attitude, which is inconsistent with analyzing\nthe former in terms of the latter (Blanshard 1961, pp. 284–86).\nEwing and others have resisted Blanshard’s argument, maintaining\nthat what grounds and explains something’s being valuable is not\nits being good but rather its having whatever non-value property it is\nupon which its goodness supervenes; they claim that it is because of\nthis underlying property that the thing in question is\n“both” good and valuable (Ewing 1948, pp. 157 and 172. Cf.\nLemos 1994, p. 19). Thomas Scanlon calls such an account of the\nrelation between valuableness, goodness, and underlying properties a\nbuck-passing account, since it “passes the buck” of\nexplaining why something is such that it is fitting to value it from\nits goodness to some property that underlies its goodness (Scanlon\n1998, pp. 95 ff.). Whether such an account is acceptable has recently\nbeen the subject of intense debate. Many, like Scanlon, endorse\npassing the buck; some, like Blanshard, object to doing so. If such an\naccount is acceptable, then Ewing’s analysis survives\nBlanshard’s challenge; but otherwise not. (Note that one might\nendorse passing the buck and yet reject Ewing’s analysis for\nsome other reason. Hence a buck-passer may, but need not, accept the\nanalysis. Indeed, there is reason to think that Moore himself is a\nbuck-passer, even though he takes the concept of intrinsic goodness to\nbe unanalyzable; cf. Olson 2006).", "\nEven if Blanshard’s argument succeeds and intrinsic goodness is\nnot to be analyzed in terms of the fittingness of some pro\nattitude, it could still be that there is a strict\ncorrelation between something’s being intrinsically good\nand its being such that it is fitting to value it for its own sake;\nthat is, it could still be both that (a) it is necessarily true that\nwhatever is intrinsically good is such that it is fitting to value it\nfor its own sake, and that (b) it is necessarily true that whatever it\nis fitting to value for its own sake is intrinsically good. If this\nwere the case, it would reveal an important feature of intrinsic\nvalue, recognition of which would help us to improve our understanding\nof the concept. However, this thesis has also been challenged.", "\nKrister Bykvist has argued that what he calls solitary goods may\nconstitute a counterexample to part (a) of the thesis (Bykvist 2009,\npp. 4 ff.). Such (alleged) goods consist in states of affairs that\nentail that there is no one in a position to value them. Suppose, for\nexample, that happiness is intrinsically good, and good in such a way\nthat it is fitting to welcome it. Then, more particularly, the state\nof affairs of there being happy egrets is intrinsically good; so too,\npresumably, is the more complex state of affairs of there being happy\negrets but no welcomers. The simpler state of affairs would appear to\npose no problem for part (a) of the thesis, but the more complex state\nof affairs, which is an example of a solitary good, may pose a\nproblem. For if to welcome a state of affairs entails that that state\nof affairs obtains, then welcoming the more complex state of affairs\nis logically impossible. Furthermore, if to welcome a state of affairs\nentails that one believes that that state of affairs obtains, then the\npertinent belief regarding the more complex state of affairs would be\nnecessarily false. In neither case would it seem plausible to say that\nwelcoming the state of affairs is nonetheless fitting. Thus, unless\nthis challenge can somehow be met, a proponent of the thesis must\nrestrict the thesis to pro attitudes that are neither truth- nor\nbelief-entailing, a restriction that might itself prove unwelcome,\nsince it excludes a number of favorable responses to what is good\n(such as promoting what is good, or taking pleasure in what is good)\nto which proponents of the thesis have often appealed.", "\nAs to part (b) of the thesis: some philosophers have argued that it\ncan be fitting to value something for its own sake even if that thing\nis not intrinsically good. A relatively early version of this argument\nwas again provided by Blanshard (1961, pp. 287 ff. Cf. Lemos 1994, p.\n18). Recently the issue has been brought into stark relief by the\nfollowing sort of thought-experiment. Imagine that an evil demon wants\nyou to value him for his own sake and threatens to cause you severe\nsuffering unless you do. It seems that you have good reason to do what\nhe wants—it is appropriate or fitting to comply with his demand\nand value him for his own sake—even though he is clearly not\nintrinsically good (Rabinowicz and Rønnow-Rasmussen 2004, pp.\n402 ff.). This issue, which has come to be known as “the wrong\nkind of reason problem,” has attracted a great deal of\nattention. Some have been persuaded that the challenge succeeds, while\nothers have sought to undermine it.", "\nOne final cautionary note. It is apparent that some philosophers use\nthe term “intrinsic value” and similar terms to express\nsome concept other than the one just discussed. In particular,\nImmanuel Kant [1724–1804] is famous for saying that the only\nthing that is “good without qualification” is a good will,\nwhich is good not because of what it effects or accomplishes but\n“in itself” (Kant 1785, Ak. 1–3). This may seem to\nsuggest that Kant ascribes (positive) intrinsic value only to a good\nwill, declaring the value that anything else may possess merely\nextrinsic, in the senses of “intrinsic value” and\n“extrinsic value” discussed above. This suggestion is, if\nanything, reinforced when Kant immediately adds that a good will\n“is to be esteemed beyond comparison as far higher than anything\nit could ever bring about,” that it “shine[s] like a jewel\nfor its own sake,” and that its “usefulness…can\nneither add to, nor subtract from, [its] value.” For here Kant\nmay seem not only to be invoking the distinction between intrinsic and\nextrinsic value but also to be in agreement with Brentano et\nal. regarding the characterization of the former in terms of the\nfittingness of some attitude, namely, esteem. (The term\n“respect” is often used in place of “esteem”\nin such contexts.) Nonetheless, it becomes clear on further inspection\nthat Kant is in fact discussing a concept quite different from that\nwith which this article is concerned. A little later on he says that\nall rational beings, even those that lack a good will, have\n“absolute value”; such beings are “ends in\nthemselves” that have a “dignity” or\n“intrinsic value” that is “above all price”\n(Kant 1785, Ak. 64 and 77). Such talk indicates that Kant believes\nthat the sort of value that he ascribes to rational beings is one that\nthey possess to an infinite degree. But then, if this were understood\nas a thesis about intrinsic value as we have been understanding this\nconcept, the implication would seem to be that, since it contains\nrational beings, ours is the best of all possible\n worlds.[4]\n Yet this is a thesis that Kant, along with many others, explicitly\nrejects elsewhere (Kant, Lectures in Ethics). It seems best\nto understand Kant, and other philosophers who have since written in\nthe same vein (cf. Anderson 1993), as being concerned not with the\nquestion of what intrinsic value rational beings have—in the\nsense of “intrinsic value” discussed above—but with\nthe quite different question of how we ought to behave toward such\ncreatures (cf. Bradley 2006)." ], "section_title": "2. What Is Intrinsic Value?", "subsections": [] }, { "main_content": [ "\nIn the history of philosophy, relatively few seem to have entertained\ndoubts about the concept of intrinsic value. Much of the debate about\nintrinsic value has tended to be about what things actually do have\nsuch value. However, once questions about the concept itself were\nraised, doubts about its metaphysical implications, its moral\nsignificance, and even its very coherence began to appear.", "\nConsider, first, the metaphysics underlying ascriptions of intrinsic\nvalue. It seems safe to say that, before the twentieth century, most\nmoral philosophers presupposed that the intrinsic goodness of\nsomething is a genuine property of that thing, one that is no less\nreal than the properties (of being pleasant, of satisfying a need, or\nwhatever) in virtue of which the thing in question is good. (Several\ndissented from this view, however. Especially well known for their\ndissent are Thomas Hobbes [1588–1679], who believed the goodness\nor badness of something to be constituted by the desire or aversion\nthat one may have regarding it, and David Hume [1711–1776], who\nsimilarly took all ascriptions of value to involve projections of\none’s own sentiments onto whatever is said to have value. See\nHobbes 1651, Hume 1739.) It was not until Moore argued that this view\nimplies that intrinsic goodness, as a supervening property, is a very\ndifferent sort of property (one that he called\n“nonnatural”) from those (which he called\n“natural”) upon which it supervenes, that doubts about the\nview proliferated.", "\nOne of the first to raise such doubts and to press for a view quite\ndifferent from the prevailing view was Axel Hägerström\n[1868–1939], who developed an account according to which\nascriptions of value are neither true nor false (Hägerström\n1953). This view has come to be called “noncognitivism.”\nThe particular brand of noncognitivism proposed by\nHägerström is usually called “emotivism,” since\nit holds (in a manner reminiscent of Hume) that ascriptions of value\nare in essence expressions of emotion. (For example, an emotivist of a\nparticularly simple kind might claim that to say “A is\ngood” is not to make a statement about A but to say\nsomething like “Hooray for A!”) This view was\ntaken up by several philosophers, including most notably A. J. Ayer\n[1910–1989] and Charles L. Stevenson [1908–1979] (see Ayer\n1946, Stevenson 1944). Other philosophers have since embraced other\nforms of noncognitivism. R. M. Hare [1919–2002], for example,\nadvocated the theory of “prescriptivism” (according to\nwhich moral judgments, including judgments about goodness and badness,\nare not descriptive statements about the world but rather constitute a\nkind of command as to how we are to act; see Hare 1952) and Simon\nBlackburn and Allan Gibbard have since proposed yet other versions of\nnoncognitivism (Blackburn 1984, Gibbard 1990).", "\nHägerström characterized his own view as a type of\n“value-nihilism,” and many have followed suit in taking\nnoncognitivism of all kinds to constitute a rejection of the very idea\nof intrinsic value. But this seems to be a mistake. We should\ndistinguish questions about value from questions about\nevaluation. Questions about value fall into two main groups,\nconceptual (of the sort discussed in the last section) and\nsubstantive (of the sort discussed in the first section).\nQuestions about evaluation have to do with what precisely is going on\nwhen we ascribe value to something. Cognitivists claim that\nour ascriptions of value constitute statements that are either true or\nfalse; noncognitivists deny this. But even noncognitivists must\nrecognize that our ascriptions of value fall into two fundamental\nclasses—ascriptions of intrinsic value and ascriptions of\nextrinsic value—and so they too must concern themselves with the\nvery same conceptual and substantive questions about value as\ncognitivists address. It may be that noncognitivism dictates or rules\nout certain answers to these questions that cognitivism does not, but\nthat is of course quite a different matter from rejecting the very\nidea of intrinsic value on metaphysical grounds.", "\nAnother type of metaphysical challenge to intrinsic value stems from\nthe theory of “pragmatism,” especially in the form\nadvanced by John Dewey [1859–1952] (see Dewey 1922). According\nto the pragmatist, the world is constantly changing in such a way that\nthe solution to one problem becomes the source of another, what is an\nend in one context is a means in another, and thus it is a mistake to\nseek or offer a timeless list of intrinsic goods and evils, of ends to\nbe achieved or avoided for their own sakes. This theme has been\nelaborated by Monroe Beardsley, who attacks the very notion of\nintrinsic value (Beardsley 1965; cf. Conee 1982). Denying that the\nexistence of something with extrinsic value presupposes the existence\nof something else with intrinsic value, Beardsley argues that all\nvalue is extrinsic. (In the course of his argument, Beardsley rejects\nthe sort of “dialectical demonstration” of intrinsic value\nthat was attempted in the last section, when an explanation of the\nderivative value of helping others was given in terms of some\nnonderivative value.) A quick response to Beardsley’s misgivings\nabout intrinsic value would be to admit that it may well be that, the\nworld being as complex as it is, nothing is such that its value is\nwholly intrinsic; perhaps whatever has intrinsic value also has\nextrinsic value, and of course many things that have extrinsic value\nwill have no (or, at least, neutral) intrinsic value. Far from\nrepudiating the notion of intrinsic value, though, this admission\nwould confirm its legitimacy. But Beardsley would insist that this\nquick response misses the point of his attack, and that it really is\nthe case, not just that whatever has value has extrinsic value, but\nalso that nothing has intrinsic value. His argument for this view is\nbased on the claim that the concept of intrinsic value is\n“inapplicable,” in that, even if something had such value,\nwe could not know this and hence its having such value could play no\nrole in our reasoning about value. But here Beardsley seems to be\noverreaching. Even if it were the case that we cannot know\nwhether something has intrinsic value, this of course leaves open the\nquestion whether anything does have such value. And even if\nit could somehow be shown that nothing does have such value,\nthis would still leave open the question whether something\ncould have such value. If the answer to this last question is\n“yes,” then the legitimacy of the concept of intrinsic\nvalue is in fact confirmed rather than refuted.", "\nAs has been noted, some philosophers do indeed doubt the legitimacy,\nthe very coherence, of the concept of intrinsic value. Before we turn\nto a discussion of this issue, however, let us for the moment presume\nthat the concept is coherent and address a different sort of doubt:\nthe doubt that the concept has any great moral significance. Recall\nthe suggestion, mentioned in the last section, that discussions of\nintrinsic value may have been compromised by a failure to distinguish\ncertain concepts. This suggestion is at the heart of Christine\nKorsgaard’s “Two Distinctions in Goodness”\n(Korsgaard 1983). Korsgaard notes that “intrinsic value”\nhas traditionally been contrasted with “instrumental\nvalue” (the value that something has in virtue of being a means\nto an end) and claims that this approach is misleading. She contends\nthat “instrumental value” is to be contrasted with\n“final value,” that is, the value that something has as an\nend or for its own sake; however, “intrinsic value” (the\nvalue that something has in itself, that is, in virtue of its\nintrinsic, nonrelational properties) is to be contrasted with\n“extrinsic value” (the value that something has in virtue\nof its extrinsic, relational properties). (An example of a\nnonrelational property is the property of being round; an example of a\nrelational property is the property of being loved.) As an\nillustration of final value, Korsgaard suggests that gorgeously\nenameled frying pans are, in virtue of the role they play in our\nlives, good for their own sakes. In like fashion, Beardsley wonders\nwhether a rare stamp may be good for its own sake (Beardsley 1965);\nShelly Kagan says that the pen that Abraham Lincoln used to sign the\nEmancipation Proclamation may well be good for its own sake (Kagan\n1998); and others have offered similar examples (cf. Rabinowicz and\nRønnow-Rasmussen 1999 and 2003). Notice that in each case the\nvalue being attributed to the object in question is (allegedly) had in\nvirtue of some extrinsic property of the object. This puts\nthe moral significance of intrinsic value into question,\nsince (as is apparent from our discussion so far) it is with the\nnotion of something’s being valuable for its own sake that\nphilosophers have traditionally been, and continue to be, primarily\nconcerned.", "\nThere is an important corollary to drawing a distinction between\nintrinsic value and final value (and between extrinsic value and\nnonfinal value), and that is that, contrary to what Korsgaard herself\ninitially says, it may be a mistake to contrast final value with\ninstrumental value. If it is possible, as Korsgaard claims, that final\nvalue sometimes supervenes on extrinsic properties, then it might be\npossible that it sometimes supervenes in particular on the property of\nbeing a means to some other end. Indeed, Korsgaard herself suggests\nthis when she says that “certain kinds of things, such as\nluxurious instruments, … are valued for their own sakes under\nthe condition of their usefulness” (Korsgaard 1983, p. 185).\nKagan also tentatively endorses this idea. If the idea is coherent,\nthen we should in principle distinguish two kinds of instrumental\nvalue, one final and the other\n nonfinal.[5]\n If something A is a means to something else B and\nhas instrumental value in virtue of this fact, such value will be\nnonfinal if it is merely derivative from or reflective of\nB’s value, whereas it will be final if it is\nnonderivative, that is, if it is a value that A has in its\nown right (due to the fact that it is a means to B),\nirrespective of any value that B may or may not have in\nits own right.", "\nEven if it is agreed that it is final value that is central to the\nconcerns of moral philosophers, we should be careful in drawing the\nconclusion that intrinsic value is not central to their concerns.\nFirst, there is no necessity that the term “intrinsic\nvalue” be reserved for the value that something has in virtue of\nits intrinsic properties; presumably it has been used by many writers\nsimply to refer to what Korsgaard calls final value, in which case the\nmoral significance of (what is thus called) intrinsic value has of\ncourse not been thrown into doubt. Nonetheless, it should probably be\nconceded that “final value” is a more suitable term than\n“intrinsic value” to refer to the sort of value in\nquestion, since the latter term certainly does suggest value that\nsupervenes on intrinsic properties. But here a second point can be\nmade, and that is that, even if use of the term “intrinsic\nvalue” is restricted accordingly, it is arguable that, contrary\nto Korsgaard’s contention, all final value does after all\nsupervene on intrinsic properties alone; if that were the case, there\nwould seem to be no reason not to continue to use the term\n“intrinsic value” to refer to final value. Whether this is\nin fact the case depends in part on just what sort of thing\ncan be valuable for its own sake—an issue to be taken\nup in the next section.", "\nIn light of the matter just discussed, we must now decide what\nterminology to adopt. It is clear that moral philosophers since\nancient times have been concerned with the distinction between the\nvalue that something has for its own sake (the sort of nonderivative\nvalue that Korsgaard calls “final value”) and the value\nthat something has for the sake of something else to which it is\nrelated in some way. However, given the weight of tradition, it seems\njustifiable, perhaps even advisable, to continue, despite\nKorsgaard’s misgivings, to use the terms “intrinsic\nvalue” and “extrinsic value” to refer to these two\ntypes of value; if we do so, however, we should explicitly note that\nthis practice is not itself intended to endorse, or reject, the view\nthat intrinsic value supervenes on intrinsic properties alone.", "\nLet us now turn to doubts about the very coherence of the concept of\nintrinsic value, so understood. In Principia Ethica and\nelsewhere, Moore embraces the consequentialist view, mentioned above,\nthat whether an action is morally right or wrong turns exclusively on\nwhether its consequences are intrinsically better than those of its\nalternatives. Some philosophers have recently argued that ascribing\nintrinsic value to consequences in this way is fundamentally\nmisconceived. Peter Geach, for example, argues that Moore makes a\nserious mistake when comparing “good” with\n “yellow.”[6]\n Moore says that both terms express unanalyzable concepts but are to\nbe distinguished in that, whereas the latter refers to a natural\nproperty, the former refers to a nonnatural one. Geach contends that\nthere is a mistaken assimilation underlying Moore’s remarks,\nsince “good” in fact operates in a way quite unlike that\nof “yellow”—something that Moore wholly overlooks.\nThis contention would appear to be confirmed by the observation that\nthe phrase “x is a yellow bird” splits up\nlogically (as Geach puts it) into the phrase “x is a\nbird and x is yellow,” whereas the phrase\n“x is a good singer” does not split up in the\nsame way. Also, from “x is a yellow bird” and\n“a bird is an animal” we do not hesitate to infer\n“x is a yellow animal,” whereas no similar\ninference seems warranted in the case of “x is a good\nsinger” and “a singer is a person.” On the basis of\nthese observations Geach concludes that nothing can be good in the\nfree-standing way that Moore alleges; rather, whatever is good is good\nrelative to a certain kind.", "\nJudith Thomson has recently elaborated on Geach’s thesis\n(Thomson 1997). Although she does not unqualifiedly agree that\nwhatever is good is good relative to a certain kind, she does claim\nthat whatever is good is good in some way; nothing can be “just\nplain good,” as she believes Moore would have it. Philippa Foot,\namong others, has made a similar charge (Foot 1985). It is a charge\nthat has been rebutted by Michael Zimmerman, who argues that\nGeach’s tests are less straightforward than they may seem and\nfail after all to reveal a significant distinction between the ways in\nwhich “good” and “yellow” operate (Zimmerman\n2001, ch. 2). He argues further that Thomson mischaracterizes\nMoore’s conception of intrinsic value. According to Moore, he\nclaims, what is intrinsically good is not “just plain\ngood”; rather, it is good in a particular way, in keeping with\nThomson’s thesis that all goodness is goodness in a way. He\nmaintains that, for Moore and other proponents of intrinsic value,\nsuch value is a particular kind of moral value. Mahrad\nAlmotahari and Adam Hosein have revived Geach’s challenge\n(Almotahari and Hosein 2015). They argue that if, contrary to Geach,\n“good” could be used predicatively, we would be able to\nuse the term predicatively in sentences of the form ‘a is\na good K’ but, they argue, the linguistic evidence\nindicates that we cannot do so (Almotahari and Hosein 2015,\n1493–4). " ], "section_title": "3. Is There Such a Thing As Intrinsic Value At All?", "subsections": [] }, { "main_content": [ "\nAmong those who do not doubt the coherence of the concept of intrinsic\nvalue there is considerable difference of opinion about what sort or\nsorts of entity can have such value. Moore does not explicitly address\nthis issue, but his writings show him to have a liberal view on the\nmatter. There are times when he talks of individual objects (e.g.,\nbooks) as having intrinsic value, others when he talks of the\nconsciousness of individual objects (or of their qualities) as having\nintrinsic value, others when he talks of the existence of individual\nobjects as having intrinsic value, others when he talks of types of\nindividual objects as having intrinsic value, and still others when he\ntalks of states of individual objects as having intrinsic value.", "\nMoore would thus appear to be a “pluralist” concerning the\nbearers of intrinsic value. Others take a more conservative,\n“monistic” approach, according to which there is just one\nkind of bearer of intrinsic value. Consider, for example,\nFrankena’s long list of intrinsic goods, presented in Section 1\nabove: life, consciousness, etc. To what kind(s) of entity do\nsuch terms refer? Various answers have been given. Some (such as\nPanayot Butchvarov) claim that it is properties that are the\nbearers of intrinsic value (Butchvarov 1989, pp. 14–15). On this\nview, Frankena’s list implies that it is the properties of being\nalive, being conscious, and so on, that are intrinsically good. Others\n(such as Chisholm) claim that it is states of affairs that\nare the bearers of intrinsic value (Chisholm 1968–69, 1972,\n1975). On this view, Frankena’s list implies that it is the\nstates of affairs of someone (or something) being alive, someone being\nconscious, and so on, that are intrinsically good. Still others (such\nas Ross) claim that it is facts that are the bearers of\nintrinsic value (Ross 1930, pp. 112–13; cf. Lemos 1994, ch. 2).\nOn this view, Frankena’s list implies that it is the facts that\nsomeone (or something) is alive, that someone is conscious, and so on,\nthat are intrinsically good. (The difference between Chisholm’s\nand Ross’s views would seem to be this: whereas Chisholm would\nascribe intrinsic value even to states of affairs, such as that of\neveryone being happy, that do not obtain, Ross would ascribe such\nvalue only to states of affairs that do obtain.)", "\nOntologists often divide entities into two fundamental classes, those\nthat are abstract and those that are concrete. Unfortunately, there is\nno consensus on just how this distinction is to be drawn. Most\nphilosophers would classify the sorts of entities just mentioned\n(properties, states of affairs, and facts) as abstract. So understood,\nthe claim that intrinsic value is borne by such entities is to be\ndistinguished from the claim that it is borne by certain other closely\nrelated entities that are often classified as concrete. For example,\nit has recently been suggested that it is tropes that have intrinsic\n value.[7]\n Tropes are supposed to be a sort of particularized property, a kind\nof property-instance (rather than simply a property). (Thus the\nparticular whiteness of a particular piece of paper is to be\ndistinguished, on this view, from the property of whiteness.) It has\nalso been suggested that it is states, understood as a kind of\ninstance of states of affairs, that have intrinsic value (cf.\nZimmerman 2001, ch. 3).", "\nThose who make monistic proposals of the sort just mentioned are aware\nthat intrinsic value is sometimes ascribed to kinds of entities\ndifferent from those favored by their proposals. They claim that all\nsuch ascriptions can be reduced to, or translated into, ascriptions of\nintrinsic value of the sort they deem proper. Consider, for example,\nKorsgaard’s suggestion that a gorgeously enameled frying pan is\ngood for its own sake. Ross would say that this cannot be the case. If\nthere is any intrinsic value to be found here, it will, according to\nRoss, not reside in the pan itself but in the fact that it plays a\ncertain role in our lives, or perhaps in the fact that something plays\nthis role, or in the fact that something that plays this role exists.\n(Others would make other translations in the terms that they deem\nappropriate.) On the basis of this ascription of intrinsic value to\nsome fact, Ross could go on to ascribe a kind of extrinsic\nvalue to the pan itself, in virtue of its relation to the fact in\nquestion.", "\nWhether reduction of this sort is acceptable has been a matter of\nconsiderable debate. Proponents of monism maintain that it introduces\nsome much-needed order into the discussion of intrinsic value,\nclarifying just what is involved in the ascription of such value and\nsimplifying the computation of such value—on which point, see\nthe next section. (A corollary of some monistic approaches is that the\nvalue that something has for its own sake supervenes on the intrinsic\nproperties of that thing, so that there is a perfect convergence of\nthe two sorts of values that Korsgaard calls “final” and\n“intrinsic”. On this point, see the last section;\nZimmerman 2001, ch. 3; Tucker 2016; and Tucker (forthcoming).)\nOpponents argue that reduction results in distortion and\noversimplification; they maintain that, even if there is intrinsic\nvalue to be found in such a fact as that a gorgeously enameled frying\npan plays a certain role in our lives, there may yet be\nintrinsic, and not merely extrinsic, value to be found in the\npan itself and perhaps also in its existence (cf. Rabinowicz and\nRønnow-Rasmussen 1999 and 2003). Some propose a compromise\naccording to which the kind of intrinsic value that can sensibly be\nascribed to individual objects like frying pans is not the same kind\nof intrinsic value that is the topic of this article and can sensibly\nbe ascribed to items of the sort on Frankena’s list (cf. Bradley\n2006). (See again the cautionary note in the final paragraph of\nSection 2 above.)" ], "section_title": "4. What Sort of Thing Can Have Intrinsic Value?", "subsections": [] }, { "main_content": [ "\nIn our assessments of intrinsic value, we are often and understandably\nconcerned not only with whether something is good or bad but\nwith how good or bad it is. Arriving at an answer to the\nlatter question is not straightforward. At least three problems\nthreaten to undermine the computation of intrinsic value.", "\nFirst, there is the possibility that the relation of intrinsic\nbetterness is not transitive (that is, the possibility that something\nA is intrinsically better than something else B,\nwhich is itself intrinsically better than some third thing C,\nand yet A is not intrinsically better than C).\nDespite the very natural assumption that this relation is transitive,\nit has been argued that it is not (Rachels 1998; Temkin 1987, 1997,\n2012). Should this in fact be the case, it would seriously complicate\ncomparisons, and hence assessments, of intrinsic value.", "\nSecond, there is the possibility that certain values are\nincommensurate. For example, Ross at one point contends that it is\nimpossible to compare the goodness of pleasure with that of virtue.\nWhereas he had suggested in The Right and the Good that\npleasure and virtue could be measured on the same scale of goodness,\nin Foundations of Ethics he declares this to be impossible,\nsince (he claims) it would imply that pleasure of a certain intensity,\nenjoyed by a sufficient number of people or for a sufficient time,\nwould counterbalance virtue possessed or manifested only by a small\nnumber of people or only for a short time; and this he professes to be\nincredible (Ross 1939, p. 275). But there is some confusion here. In\nclaiming that virtue and pleasure are incommensurate for the reason\ngiven, Ross presumably means that they cannot be measured on the same\nratio scale. (A ratio scale is one with an arbitrary unit but\na fixed zero point. Mass and length are standardly measured on ratio\nscales.) But incommensurability on a ratio scale does not imply\nincommensurability on every scale—an ordinal scale, for\ninstance. (An ordinal scale is simply one that supplies an ordering\nfor the quantity in question, such as the measurement of arm-strength\nthat is provided by an arm-wrestling competition.) Ross’s\nremarks indicate that he in fact believes that virtue and pleasure\nare commensurate on an ordinal scale, since he appears to\nsubscribe to the arch-puritanical view that any amount of virtue is\nintrinsically better than any amount of pleasure. This view is just\none example of the thesis that some goods are “higher”\nthan others, in the sense that any amount of the former is better than\nany amount of the latter. This thesis can be traced to the ancient\nGreeks (Plato, Philebus, 21a-e; Aristotle, Nicomachean\nEthics, 1174a), and it has been endorsed by many philosophers\nsince, perhaps most famously by Mill (Mill 1863, paras. 4 ff).\nInterest in the thesis has recently been revived by a set of intricate\nand intriguing puzzles, posed by Derek Parfit, concerning the relative\nvalues of low-quantity/high-quality goods and\nhigh-quantity/low-quality goods (Parfit 1984, Part IV). One response\nto these puzzles (eschewed by Parfit himself) is to adopt the thesis\nof the nontransitivity of intrinsic betterness. Another is to insist\non the thesis that some goods are higher than others. Such a response\ndoes not by itself solve the puzzles that Parfit raises, but, to the\nextent that it helps, it does so at the cost of once again\ncomplicating the computation of intrinsic value.", "\nTo repeat: contrary to what Ross says, the thesis that some goods are\nhigher than others implies that such goods are commensurate, and not\nthat they are incommensurate. Some people do hold, however, that\ncertain values really are incommensurate and thus cannot be compared\non any meaningful scale. (Isaiah Berlin [1909–1997], for\nexample, is often thought to have said this about the values of\nliberty and equality. Whether he is best interpreted in this way is\ndebatable. See Berlin 1969.) This view constitutes a more radical\nthreat to the computation of intrinsic value than does the view that\nintrinsic betterness is not transitive. The latter view presupposes at\nleast some measure of commensurability. If A is better than\nB and B is better than C, then A\nis commensurate with B and B is commensurate with\nC; and even if it should turn out that A is not\nbetter than C, it may still be that A is\ncommensurate with C, either because it is as good as\nC or because it is worse than C. But if A\nis incommensurate with B, then A is neither better\nthan nor as good as nor worse than B. (Some claim, however,\nthat the reverse does not hold and that, even if A is neither\nbetter than nor as good as nor worse than B, still A\nmay be “on a par” with B and thus be roughly\ncomparable with it. Cf. Chang 1997, 2002.) If such a case can arise,\nthere is an obvious limit to the extent to which we can meaningfully\nsay how good a certain complex whole is (here, “whole” is\nused to refer to whatever kind of entity may have intrinsic value);\nfor, if such a whole comprises incommensurate goods A and\nB, then there will be no way of establishing just how good it\nis overall, even if there is a way of establishing how good it is with\nrespect to each of A and B.", "\nThere is a third, still more radical threat to the computation of\nintrinsic value. Quite apart from any concern with the\ncommensurability of values, Moore famously claims that there is no\neasy formula for the determination of the intrinsic value of complex\nwholes because of the truth of what he calls the “principle of\norganic unities” (Moore 1903, p. 96). According to this\nprinciple, the intrinsic value of a whole must not be assumed to be\nthe same as the sum of the intrinsic values of its parts (Moore 1903,\np. 28) As an example of an organic unity, Moore gives the case of the\nconsciousness of a beautiful object; he says that this has great\nintrinsic value, even though the consciousness as such and the\nbeautiful object as such each have comparatively little, if any,\nintrinsic value. If the principle of organic unities is true, then\nthere is scant hope of a systematic approach to the computation of\nintrinsic value. Although the principle explicitly rules out only\nsummation as a method of computation, Moore’s remarks strongly\nsuggest that there is no relation between the parts of a whole and the\nwhole itself that holds in general and in terms of which the value of\nthe latter can be computed by aggregating (whether by summation or by\nsome other means) the values of the former. Moore’s position has\nbeen endorsed by many other philosophers. For example, Ross says that\nit is better that one person be good and happy and another bad and\nunhappy than that the former be good and unhappy and the latter bad\nand happy, and he takes this to be confirmation of Moore’s\nprinciple (Ross 1930, p. 72). Broad takes organic unities of the sort\nthat Moore discusses to be just one instance of a more general\nphenomenon that he believes to be at work in many other situations, as\nwhen, for example, two tunes, each pleasing in its own right, make for\na cacophonous combination (Broad 1985, p. 256). Others have furnished\nstill further examples of organic unities (Chisholm 1986, ch. 7; Lemos\n1994, chs. 3 and 4, and 1998; Hurka 1998).", "\nWas Moore the first to call attention to the phenomenon of organic\nunities in the context of intrinsic value? This is debatable. Despite\nthe fact that he explicitly invoked what he called a “principle\nof summation” that would appear to be inconsistent with the\nprinciple of organic unities, Brentano appears nonetheless to have\nanticipated Moore’s principle in his discussion of\nSchadenfreude, that is, of malicious pleasure; he condemns\nsuch an attitude, even though he claims that pleasure as such is\nintrinsically good (Brentano 1969, p. 23 n). Certainly Chisholm takes\nBrentano to be an advocate of organic unities (Chisholm 1986, ch. 5),\nascribing to him the view that there are many kinds of organic unity\nand building on what he takes to be Brentano’s insights (and,\ngoing further back in the history of philosophy, the insights of St.\nThomas Aquinas [1225–1274] and others).", "\nRecently, a special spin has been put on the principle of organic\nunities by so-called “particularists.” Jonathan Dancy, for\nexample, has claimed (in keeping with Korsgaard and others mentioned\nin Section 3 above), that something’s intrinsic value need not\nsupervene on its intrinsic properties alone; in fact, the\nsupervenience-base may be so open-ended that it resists\ngeneralization. The upshot, according to Dancy, is that the intrinsic\nvalue of something may vary from context to context; indeed, the\nvariation may be so great that the thing’s value changes\n“polarity” from good to bad, or vice versa (Dancy\n2000). This approach to value constitutes an endorsement of the\nprinciple of organic unities that is even more subversive of the\ncomputation of intrinsic value than Moore’s; for Moore holds\nthat the intrinsic value of something is and must be constant, even if\nits contribution to the value of wholes of which it forms a part is\nnot, whereas Dancy holds that variation can occur at both levels.", "\nNot everyone has accepted the principle of organic unities; some have\nheld out hope for a more systematic approach to the computation of\nintrinsic value. However, even someone who is inclined to measure\nintrinsic value in terms of summation must acknowledge that there is a\nsense in which the principle of organic unities is obviously true.\nConsider some complex whole, W, that is composed of three\ngoods, X, Y, and Z, which are wholly\nindependent of one another. Suppose that we had a ratio scale on which\nto measure these goods, and that their values on this scale were 10,\n20, and 30, respectively. We would expect someone who takes intrinsic\nvalue to be summative to declare the value of W to be (10 +\n20 + 30 =) 60. But notice that, if X, Y, and\nZ are parts of W, then so too, presumably, are the\ncombinations X-and-Y, X-and-Z, and\nY-and-Z; the values of these combinations, computed\nin terms of summation, will be 30, 40, and 50, respectively. If the\nvalues of these parts of W were also taken into consideration\nwhen evaluating W, the value of W would balloon to\n180. Clearly, this would be a distortion. Someone who wishes to\nmaintain that intrinsic value is summative must thus show not only how\nthe various alleged examples of organic unities provided by Moore and\nothers are to be reinterpreted, but also how, in the sort of case just\nsketched, it is only the values of X, Y, and\nZ, and not the values either of any combinations of these\ncomponents or of any parts of these components, that are to be taken\ninto account when evaluating W itself. In order to bring some\nsemblance of manageability to the computation of intrinsic value, this\nis precisely what some writers, by appealing to the idea of\n“basic” intrinsic value, have tried to do. The general\nidea is this. In the sort of example just given, each of X,\nY, and Z is to be construed as having basic\nintrinsic value; if any combinations or parts of X,\nY, and Z have intrinsic value, this value is not\nbasic; and the value of W is to be computed by appealing only\nto those parts of W that have basic intrinsic value.", "\nGilbert Harman was one of the first explicitly to discuss basic\nintrinsic value when he pointed out the apparent need to invoke such\nvalue if we are to avoid distortions in our evaluations (Harman 1967).\nHowever, he offers no precise account of the concept of basic\nintrinsic value and ends his paper by saying that he can think of no\nway to show that nonbasic intrinsic value is to be computed in terms\nof the summation of basic intrinsic value. Several philosophers have\nsince tried to do better. Many have argued that nonbasic intrinsic\nvalue cannot always be computed by summing basic intrinsic\nvalue. Suppose that states of affairs can bear intrinsic value. Let\nX be the state of affairs of John being pleased to a certain\ndegree x, and Y be the state of affairs of Jane\nbeing displeased to a certain degree y, and suppose that\nX has a basic intrinsic value of 10 and Y a basic\nintrinsic value of −20. It seems reasonable to sum these values\nand attribute an intrinsic value of −10 to the conjunctive state\nof affairs X&Y. But what of the disjunctive state of\naffairs XvY or the negative state of affairs ~X? How\nare their intrinsic values to be computed? Summation seems to\nbe a nonstarter in these cases. Nonetheless, attempts have been made\neven in such cases to show how the intrinsic value of a complex whole\nis to be computed in a nonsummative way in terms of the basic\nintrinsic values of simpler states, thus preserving the idea that\nbasic intrinsic value is the key to the computation of all intrinsic\nvalue (Quinn 1974, Chisholm 1975, Oldfield 1977, Carlson 1997). (These\nattempts have generally been based on the assumption that states of\naffairs are the sole bearers of intrinsic value. Matters\nwould be considerably more complicated if it turned out that entities\nof several different ontological categories could all have intrinsic\nvalue.)", "\nSuggestions as to how to compute nonbasic intrinsic value in terms of\nbasic intrinsic value of course presuppose that there is such a thing\nas basic intrinsic value, but few have attempted to provide an account\nof what basic intrinsic value itself consists in. Fred Feldman is one\nof the few (Feldman 2000; cf. Feldman 1997, pp. 116–18).\nSubscribing to the view that only states of affairs bear intrinsic\nvalue, Feldman identifies several features that any state of affairs\nthat has basic intrinsic value in particular must possess. He\nmaintains, for example, that whatever has basic intrinsic value must\nhave it to a determinate degree and that this value cannot be\n“defeated” by any Moorean organic unity. In this way,\nFeldman seeks to preserve the idea that intrinsic value is summative\nafter all. He does not claim that all intrinsic value is to be\ncomputed by summing basic intrinsic value, but he does insist that the\nvalue of entire worlds is to be computed in this way.", "\nDespite the detail in which Feldman characterizes the concept of basic\nintrinsic value, he offers no strict analysis of it. Others have tried\nto supply such an analysis. For example, by noting that, even if it is\ntrue that only states have intrinsic value, it may yet be that not all\nstates have intrinsic value, Zimmerman suggests (to put matters\nsomewhat roughly) that basic intrinsic value is the intrinsic value\nhad by states none of whose proper parts have intrinsic value\n(Zimmerman 2001, ch. 5). On this basis he argues that disjunctive and\nnegative states in fact have no intrinsic value at all, and thereby\nseeks to show how all intrinsic value is to be computed in terms of\nsummation after all.", "\nTwo final points. First, we are now in a position to see why it was\nsaid above (in Section 2) that perhaps not all intrinsic value is\nnonderivative. If it is correct to distinguish between basic and\nnonbasic intrinsic value and also to compute the latter in terms of\nthe former, then there is clearly a respectable sense in which\nnonbasic intrinsic value is derivative. Second, if states with basic\nintrinsic value account for all the value that there is in the world,\nsupport is found for Chisholm’s view (reported in Section 2)\nthat some ontological version of Moore’s isolation test is\nacceptable." ], "section_title": "5. How Is Intrinsic Value to Be Computed?", "subsections": [] }, { "main_content": [ "\nAt the beginning of this article, extrinsic value was said\nsimply—too simply—to be value that is not intrinsic.\nLater, once intrinsic value had been characterized as nonderivative\nvalue of a certain, perhaps moral kind, extrinsic value was said more\nparticularly to be derivative value of that same kind. That\nwhich is extrinsically good is good, not (insofar as its extrinsic\nvalue is concerned) for its own sake, but for the sake of something\nelse to which it is related in some way. For example, the goodness of\nhelping others in time of need is plausibly thought to be extrinsic\n(at least in part), being derivative (at least in part) from the\ngoodness of something else, such as these people’s needs being\nsatisfied, or their experiencing pleasure, to which helping them is\nrelated in some causal way.", "\nTwo questions arise. The first is whether so-called extrinsic value is\nreally a type of value at all. There would seem to be a sense in which\nit is not, for it does not add to or detract from the value in the\nworld. Consider some long chain of derivation. Suppose that the\nextrinsic value of A can be traced to the intrinsic value of\nZ by way of B, C, D… Thus\nA is good (for example) because of B, which is good\nbecause of C, and so on, until we get to Y’s\nbeing good because of Z; when it comes to Z,\nhowever, we have something that is good, not because of something\nelse, but “because of itself,” i.e., for its own sake. In\nthis sort of case, the values of A, B, …,\nY are all parasitic on the value of Z. It is\nZ’s value that contributes to the value there is in the\nworld; A, B, …, Y contribute no\nvalue of their own. (As long as the value of Z is the only\nintrinsic value at stake, no change of value would be effected in or\nimparted to the world if a shorter route from A to Z\nwere discovered, one that bypassed some letters in the middle of the\nalphabet.)", "\nWhy talk of “extrinsic value” at all, then? The answer can\nonly be that we just do say that certain things are good, and others\nbad, not for their own sake but for the sake of something else to\nwhich they are related in some way. To say that these things are good\nand bad only in a derivative sense, that their value is merely\nparasitic on or reflective of the value of something else, is one\nthing; to deny that they are good or bad in any respectable sense is\nquite another. The former claim is accurate; hence the latter would\nappear unwarranted.", "\nIf we accept that talk of “extrinsic value” can be\nappropriate, however, a second question then arises: what sort of\nrelation must obtain between A and Z if A\nis to be said to be good “because of” Z? It is\nnot clear just what the answer to this question is. Philosophers have\ntended to focus on just one particular causal relation, the means-end\nrelation. This is the relation at issue in the example given earlier:\nhelping others is a means to their needs being satisfied, which is\nitself a means to their experiencing pleasure. The term most often\nused to refer to this type of extrinsic value is “instrumental\nvalue,” although there is some dispute as to just how this term\nis to be employed. (Remember also, from Section 3 above, that on some\nviews “instrumental value” may refer to a type of\nintrinsic, or final, value.) Suppose that A is a\nmeans to Z, and that Z is intrinsically good. Should\nwe therefore say that A is instrumentally good? What if\nA has another consequence, Y, and this consequence\nis intrinsically bad? What, especially, if the intrinsic badness of\nY is greater than the intrinsic goodness of Z? Some\nwould say that in such a case A is both instrumentally good\n(because of Z) and instrumentally bad (because of\nY). Others would say that it is correct to say that\nA is instrumentally good only if all of A’s\ncausal consequences that have intrinsic value are, taken as a whole,\nintrinsically good. Still others would say that whether something is\ninstrumentally good depends not only on what it causes to happen but\nalso on what it prevents from happening (cf. Bradley 1998). For\nexample, if pain is intrinsically bad, and taking an aspirin puts a\nstop to your pain but causes nothing of any positive intrinsic value,\nsome would say that taking the aspirin is instrumentally good despite\nits having no intrinsically good consequences.", "\nMany philosophers write as if instrumental value is the only type of\nextrinsic value, but that is a mistake. Suppose, for instance, that\nthe results of a certain medical test indicate that the patient is in\ngood health, and suppose that this patient’s having good health\nis intrinsically good. Then we may well want to say that the results\nare themselves (extrinsically) good. But notice that the results are\nof course not a means to good health; they are simply indicative of\nit. Or suppose that making your home available to a struggling artist\nwhile you spend a year abroad provides him with an opportunity he\nwould otherwise not have to create some masterpieces, and suppose that\neither the process or the product of this creation would be\nintrinsically good. Then we may well want to say that your making your\nhome available to him is (extrinsically) good because of the\nopportunity it provides him, even if he goes on to squander the\nopportunity and nothing good comes of it. Or suppose that\nsomeone’s appreciating the beauty of the Mona Lisa\nwould be intrinsically good. Then we may well want to say that the\npainting itself has value in light of this fact, a kind of value that\nsome have called “inherent value” (Lewis 1946, p. 391; cf.\nFrankena 1973, p. 82). (“Inherent value” may not\nbe the most suitable term to use here, since it may well suggest\nintrinsic value, whereas the sort of value at issue is\nsupposed to be a type of extrinsic value. The value\nattributed to the painting is one that it is said to have in virtue of\nits relation to something else that would supposedly be intrinsically\ngood if it occurred, namely, the appreciation of its beauty.) Many\nother instances could be given of cases in which we are inclined to\ncall something good in virtue of its relation to something else that\nis or would be intrinsically good, even though the relation in\nquestion is not a means-end relation.", "\nOne final point. It is sometimes said that there can be no extrinsic\nvalue without intrinsic value. This thesis admits of several\ninterpretations. First, it might mean that nothing can occur that is\nextrinsically good unless something else occurs that is intrinsically\ngood, and that nothing can occur that is extrinsically bad unless\nsomething else occurs that is intrinsically bad. Second, it might mean\nthat nothing can occur that is either extrinsically good or\nextrinsically bad unless something else occurs that is either\nintrinsically good or intrinsically bad. On both these\ninterpretations, the thesis is dubious. Suppose that no one ever\nappreciates the beauty of Leonardo’s masterpiece, and that\nnothing else that is intrinsically either good or bad ever occurs;\nstill his painting may be said to be inherently good. Or suppose that\nthe aspirin prevents your pain from even starting, and hence inhibits\nthe occurrence of something intrinsically bad, but nothing else that\nis intrinsically either good or bad ever occurs; still your taking the\naspirin may be said to be instrumentally good. On a third\ninterpretation, however, the thesis might be true. That interpretation\nis this: nothing can occur that is either extrinsically good or\nextrinsically neutral or extrinsically bad unless something else\noccurs that is either intrinsically good or intrinsically neutral or\nintrinsically bad. This would be trivially true if, as some maintain,\nthe nonoccurrence of something intrinsically either good or bad\nentails the occurrence of something intrinsically neutral. But even if\nthe thesis should turn out to be false on this third interpretation,\ntoo, it would nonetheless seem to be true on a fourth interpretation,\naccording to which the concept of extrinsic value, in all its\nvarieties, is to be understood in terms of the concept of intrinsic\nvalue." ], "section_title": "6. What Is Extrinsic Value?", "subsections": [] } ]

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B., 1918, General Theory of Value, New York:\nLongmans, Green.", "Persson, Ingmar, 1996, “Benevolence, Identification and\nValue”, Uppsala Philosophical Studies, 45:\n58–71.", "–––, 1997, “Ambiguities in Feldman’s\nDesert-adjusted Values”, Utilitas, 9: 319–27.", "–––, 2003, “The Badness of Unjust\nInequality”, Theoria, 69: 109–24.", "Pettit, Philip, 1993, “Consequentialism”, in A\nCompanion to Ethics, Peter Singer (ed.), Oxford: Blackwell.", "Phillips, David, 2003, “Thomson and the Semantic Argument\nagainst Consequentialism”, Journal of Philosophy, 100:\n475–86.", "Pianalto, Matthew, 2009, “Against the Intrinsic Value of\nPleasure”, Journal of Value Inquiry, 23:\n33–39.", "Pitcher, George, 1970, “The Awfulness of Pain”,\nJournal of Philosophy, 67: 481–92.", "Quinn, Philip, 1977, “Improved Foundations for a Logic of\nIntrinsic Value”, Philosophical Studies, 32:\n73–81.", "–––, 1978, Divine Commands and Moral\nRequirements, Oxford: Clarendon Press.", "Quinn, Warren S., 1990, “The Puzzle of the\nSelf-Torturer”, Philosophical Studies, 59: 79–90.", "Rabinowicz, Wlodek, (ed.), 2000, Value and Choice, vol.\n1, Lund: Lund Philosophy Reports.", "–––, (ed.), 2001, Value and Choice,\nvol. 2, Lund: Lund Philosophy Reports.", "–––, 2003a, “Ryberg’s Doubts about\nHigher Pleasures—Put to Rest?”, Ethical Theory and\nMoral Practice, 6: 231–35.", "–––, 2003b, “The Size of Inequality and\nIts Badness: Some Reflections around Temkin’s\nInequality”, Theoria, 69: 60–84.", "–––, 2008, “Value Relations”,\nTheoria, 74: 18–49.", "–––, 2009, “Incommensurability and\nVagueness”, Proceedings of the Aristotelian Society,\nsuppl. vol. 83: 71–94.", "–––, 2012, “Value Relations\nRevisited”, Economics and Philosophy, 28:\n133–64.", "Rabinowicz, Wlodek, and Österberg, Jan, 1996, “Value\nBased on Preferences”, Economics and Philosophy, 12:\n1–27.", "Rabinowicz, Wlodek, and Rønnow-Rasmussen, Toni, (ed.),\n2003, Patterns of Value, vol. 1, Lund: Lund Philosophy\nReports.", "–––, (ed.), 2004, Patterns of Value,\nvol. 2, Lund: Lund Philosophy Reports.", "–––, 2006, “Buck-Passing and the Right\nKind of Reasons”, Philosophical Quarterly, 56:\n114–20.", "Rachels, Stuart, 2003, “A Defense of Two Optimistic Claims\nin Ethical Theory”, Philosophical Studies, 112:\n1–30.", "Rashdall, Hastings, 1907, The Theory of Good and Evil,\nLondon: Oxford University Press.", "Raz, Joseph, 1985–86, “Value Incommensurability: Some\nPreliminaries”, Proceedings of the Aristotelian\nSociety, 86: 117–34.", "–––, 1999, Engaging Reason, Oxford:\nOxford University Press.", "–––, 2001, Value, Respect and\nAttachment, Cambridge: Cambridge University Press.", "Reeve, Andrew F., 1997, “Incommensurability and Basic\nValues”, Journal of Value Inquiry, 31:\n545–52.", "Regan, Donald H., 2002, “The Value of Rational\nNature”, Ethics, 112: 267–91.", "–––, 2003, “How to Be a Moorean”,\nEthics, 113: 651–77.", "Regan, Tom, (ed.), 1984, Earthbound: New Introductory Essays\nin Environmental Ethics, Philadelphia: Temple University\nPress.", "–––, 1986, Bloomsbury’s Prophet,\nPhiladelphia: Temple University Press.", "–––, 1992, “Does Environmental Ethics Rest\non a Mistake?”, Monist, 75: 161–82.", "Reisner, Andrew E., 2009, “Abandoning the Buck Passing\nAnalysis of Final Value”, Ethical Theory and Moral\nPractice, 12: 379–95.", "–––, forthcoming, “Fittingness, Value, and\nTrans-World Attitudes”, Philosophical Quarterly.", "Rescher, Nicholas, 1967, “Semantic Foundations for the Logic\nof Preference”, in The Logic of Decision and Action,\nNicholas Rescher (ed.), Pittsburgh: University of Pittsburgh\nPress.", "–––, 1993, The Validity of Values,\nPrinceton: Princeton University Press.", "Rolston, Holmes, III, 1992, “Disvalues in Nature”,\nMonist, 75: 250–78.", "Rønnow-Rasmussen, Toni, 2002, “Hedonism,\nPreferentialism, and Value Bearers”, Journal of Value\nInquiry, 36: 463–72.", "–––, 2011, Personal Value, Oxford:\nOxford University Press.", "Rønnow-Rasmussen, Toni and Zimmerman, Michael J. (ed.),\n2005, Recent Work on Intrinsic Value, Dordrecht:\nSpringer.", "Rosati, Connie, 2003, “Agency and the Open Question\nArgument”, Ethics, 113: 490–527.", "Rowland, Richard, 2016, “In Defence of Good\nSimpliciter”, Philosophical Studies, 173:\n1371–91.", "Ryberg, Jesper, 2002, “Higher and Lower\nPleasures—Doubts on Justification”, Ethical Theory and\nMoral Practice, 5: 415–29.", "Schaber, Peter, 1999, “Value Pluralism: Some\nProblems”, Journal of Value Inquiry, 33:\n71–78.", "Schilpp, P. A., (ed.), 1942, The Philosophy of G. E.\nMoore, Evanston: Northwestern University Press.", "Schroeder, Mark, 2007, “Teleology, Agent-Relative Value, and\n‘Good’”, Ethics, 117: 265–95.", "–––, 2009, “Buck-Passers’ Negative\nThesis”, Philosophical Explorations, 12:\n341–47.", "–––, 2010, “Value and the Right Kind of\nReason”, Oxford Studies in Metaethics, 5:\n25–55.", "Schroth, Jörg, 2003, “Particularism and\nUniversalizability”, Journal of Value Inquiry, 37:\n455–61.", "Schumm, George, 1987, “Transitivity, Preference and\nIndifference”, Philosophical Studies, 52:\n435–37.", "Sinnott-Armstrong, Walter, 2003, “For Goodness’\nSake”, Southern Journal of Philosophy, 41:\n83–91.", "Slote, Michael, 1983, Goods and Virtues, Oxford:\nClarendon Press.", "Smith, Holly M., 1991, “Varieties of Moral Credit and Moral\nWorth”, Ethics, 101: 279–303.", "Smith, James Ward, 1948, “Intrinsic and Extrinsic\nGood”, Ethics, 58: 195–208.", "Smith, Michael, 2003, “Neutral and Relative Value after\nMoore”, Ethics, 113: 576–98.", "Smith, Tara, 1998, “Intrinsic Value: Look-Say Ethics”,\nJournal of Value Inquiry, 32: 539–53.", "Sobel, David, 2002, “Varieties of Hedonism”,\nJournal of Social Philosophy, 33: 240–56.", "Sobel, J. Howard, 1970, “Utilitarianisms: Simple and\nGeneral”, Inquiry, 13: 394–449.", "Stocker, Michael, 1990, Plural and Conflicting Values,\nOxford: Clarendon Press.", "Stratton-Lake, Philip, 2000, Kant, Duty, and Moral Worth,\nLondon: Routledge.", "–––, 2005, “How to Deal with Evil Demons:\nComment on Rabinowicz and Rønnow-Rasmussen”,\nEthics, 115: 788–98.", "–––, 2009, “Roger Crisp on Goodness and\nReasons”, Mind, 118: 1081–94.", "Stratton-Lake, Philip and Hooker, Brad, 2006, “Scanlon\nversus Moore on Goodness”, in Metaethics after Moore,\nTerence Horgan and Mark Timmons (ed.), New York: Oxford University\nPress.", "Sturgeon, Nicholas, 1996, “Anderson on Reason and\nValue”, Ethics, 106: 509–24.", "–––, 2003, “Moore on Ethical\nNaturalism”, Ethics, 113: 528–56.", "Suikkanen, Jussi, 2005, “A Defence of the Buck-Passing\nAccount”, Ethical Theory and Moral Practice, 7:\n513–35.", "–––, 2009, “Buck-Passing Accounts of\nValue”, Philosophy Compass, 4: 768–79.", "Sumner, L. W., 1996, Welfare, Happiness, and Ethics,\nOxford: Clarendon Press.", "Svavarsdóttir, Sigrún, 2014, “Having Value and\nBeing Worth Valuing”, Journal of Philosophy, 111(2):\n84–109.", "Swanton, Christine, 1995, “Profiles of the Virtues”,\nPacific Philosophical Quarterly, 27: 335–44.", "Tännsjö, Torbjörn, 1996, “Classical\nHedonistic Utilitarianism”, Philosophical Studies, 81:\n97–115.", "–––, 1999, “A Concrete View of Intrinsic\nValue”, Journal of Value Inquiry, 33:\n531–36.", "Taylor, Paul, 1961, Normative Discourse, New York:\nPrentice-Hall.", "Taylor, Timothy E., 2010, “Does Pleasure Have Intrinsic\nValue?”, Journal of Value Inquiry, 44:\n313–19.", "Temkin, Larry S., 1993, Inequality, Oxford: Oxford\nUniversity Press.", "–––, 1994, “Weighted Goods: Some Questions\nand Comments”, Philosophy and Public Affairs, 23:\n361–63.", "–––, 1997, “Rethinking the Good, Moral\nIdeals and the Nature of Practical Reasoning”, in Reading\nParfit, Jonathan Dancy (ed.), Oxford: Blackwell.", "–––, 2003a, “Personal versus Impersonal\nPrinciples: Reconsidering the Slogan”, Theoria, 69:\n21–31.", "–––, 2003b, “Determining the Scope of\nEgalitarian Concern: A Partial Defense of Complete Lives\nEgalitarianism”, Theoria, 69: 46–59.", "–––, 2003c, “Measuring Inequality’s\nBadness: Does Size Matter? If So, How, If Not, What Does?”,\nTheoria, 69: 85–108.", "–––, 2003d, “Exploring the Roots of\nEgalitarian Concerns”, Theoria, 69: 125–51.", "Thomson, Judith Jarvis, 1992, “On Some Ways in Which a Thing\nCan Be Good”, in Paul, 1992.", "–––, 1994, “Goodness and\nUtilitarianism”, Proceedings and Addresses of the American\nPhilosophical Association, 67: 7–21.", "–––, 2001, Goodness and Advice,\nPrinceton: Princeton University Press.", "–––, 2003a, “The Legacy of\nPrincipia”, Southern Journal of Philosophy,\n41: 62–82.", "–––, 2003b, “Reply to\nSinnott-Armstrong”, Southern Journal of Philosophy, 41:\n92–94.", "–––, 2008, Normativity, Chicago: Open\nCourt.", "–––, 2010, “Reply to Critics”,\nAnalysis, 70: 753–64.", "Tolhurst, William, 1983, “On the Nature of Intrinsic\nValue”, Philosophical Studies, 43: 383–95.", "Tucker, Miles, 2016, “Two Kinds of Value Pluralism”,\nUtilitas, 28: 333–46.", "–––, 2018, “Simply Good: A Defence of the\nPrincipia”, Utilitas, 30: 253–70.", "Vallentyne, Peter, 2009, “Broome on Moral Goodness and\nPopulation Ethics”, Philosophy and Phenomenological\nResearch, 78: 739–46.", "Vallentyne, Peter and Kagan, Shelly, 1997, “Infinite Value\nand Finitely Additive Value Theory”, Journal of\nPhilosophy, 94: 5–26.", "Van Willigenburg, Theo, 1999, “Is the Consumer Always Right?\nIntrinsic Value and Subject-Relativity”, in Ethics and the\nMarket, R. Norman (ed.), Aldershot: Ashgate Press.", "–––, 2004, “Understanding Value as Knowing\nHow to Value, and for What Reasons”, Journal of Value\nInquiry, 38: 91–104.", "Väyrynen, Pekka, 2006, “Resisting the Buck-Passing\nAccount of Value”, Oxford Studies in Metaethics, 1:\n295–324.", "Velleman, J. David, 2008, “A Theory of Value”,\nEthics, 118: 410–36.", "Vendler, Zeno, 1963, “The Grammar of Goodness”,\nPhilosophical Review, 72: 446–65.", "Voorhoove, Alex, 2013, “Vaulting Intuition: Temkin’s\nCritique of Transitivity”, Economics and Philosophy,\n29: 409–23.", "Wallace, James D., 1978, Virtues and Vices, Ithaca:\nCornell University Press.", "Way, Jonathan, 2013, “Value and Reasons to Favor”,\nOxford Studies in Metaethics, 8. doi:\n10.1093/acprof:oso/9780199678044.001.0001", "Wedgwood, Ralph, 2009a, “Intrinsic Values and Reasons for\nAction”, Philosophical Issues, 19: 342–63.", "–––, 2009b, “The ‘Good’ and\nthe ‘Right’ Revisited”, Philosophical\nPerspectives, 23: 499–519.", "Weston, Anthony, 1985, “Beyond Intrinsic Value: Pragmatism\nin Environmental Ethics”, Environmental Ethics, 7:\n321–39.", "–––, 1992, “Between Means and Ends”,\nMonist, 75: 236–49.", "White, Heath, 2009, “Fitting Attitudes, Wrong Kinds of\nReasons, and Mind-Independent Goodness”, Journal of Moral\nPhilosophy, 6: 339–64.", "Wielenberg, E., 1998, “Goodness without\nQualification”, Journal of Value Inquiry, 32:\n93–104.", "Williams, Bernard, 1972, Morality, New York: Harper and\nRow.", "Wolf, Susan, 1982, “Moral Saints”, Journal of\nPhilosophy, 79: 419–39.", "–––, 1997, “Happiness and Meaning: Two\nAspects of the Good Life”, Social Philosophy and\nPolicy, 14: 207–25.", "Wright, Georg Henrik von, 1963, The Varieties of\nGoodness, London: Routledge and Kegan Paul.", "–––, 1972, “The Logic of Preference\nReconsidered”, Theory and Decision, 3:\n140–69.", "Yarnell, Patrick H., 2001, “The Intrinsic Goodness of Pain,\nAnguish, and the Loss of Pleasure”, Journal of Value\nInquiry, 35: 449–54.", "Zimmerman, Michael J., 1983, “Mill and the Consistency of\nHedonism”, Philosophia, 13: 317–35.", "–––, 2007, “The Good and the Right”,\nUtilitas, 19: 326–53.", "–––, 2009, “Understanding What’s\nGood for Us”, Ethical Theory and Moral Practice, 12:\n429–39.", "–––, 2011, “Partiality and Intrinsic\nValue”, Mind, 120: 447–83." ]

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[ "\n\nThe word ‘pluralism’ generally refers to the view that\nthere are many of the things in question (concepts, scientific world\nviews, discourses, viewpoints etc.) The issues arising from there\nbeing many differ widely from subject area to subject area. This entry\nis concerned with moral pluralism—the view that there are many\ndifferent moral values.", "\n\nMoral value pluralism should be distinguished from political\npluralism. Political pluralism, which, like moral value pluralism, is\noften referred to as ‘value pluralism’, is a view\nassociated with political liberalism. Political pluralism is concerned\nwith the question of what sort of restrictions governments can put on\npeople’s freedom to act according to their values. One version\nof political pluralism is based on moral value pluralism, claiming\nthat there are irreducibly plural moral values and that this justifies\na liberal political system. (See Isaiah Berlin, 1969; George Crowder,\n2002; William Galston, 2002, and for a more detailed discussion of\nthis see the entry on\n Isaiah Berlin). Political Liberalism need\nnot be based on value pluralism: a defence of toleration of different\nvalue systems need not rely on the claim that there are plural moral\nvalues. We shall leave political pluralism aside for the purposes of\nthis entry, and concentrate on moral value pluralism.", " It is also worth emphasising that moral value pluralism does not\nentail relativism. The idea is not that all values or value systems\nare equally true. Value pluralism is independent of any particular\nmeta-ethical view. It is a claim about the normative domain: about\nwhat value looks like. ", "\nCommonsensically we talk about lots of\ndifferent values—happiness, liberty, friendship, and so\non. The question about pluralism in moral theory is whether these\napparently different values are all reducible to one supervalue, or\nwhether we should think that there really are several distinct\nvalues.", "\nThere are different ways that value might be conceived, but\nthe debate about pluralism should be able to cut across different\nsorts of moral theory. Traditionally, moral philosophers recognize\nthree different ways of thinking about morality: the deontological\nway, the consequentialist way, and the virtue ethics way, although there\nis debate about the cogency of these\n distinctions.[1]\nThe term ‘value’ as it appears in ‘value\npluralism’ is neutral between these three\ntheories. Deontologists think of morality as being fundamentally about\nmoral principles. Thus the question of whether a deontological theory\nis pluralist is a question about how many fundamental principles there\nare. The consequentialist, by contrast, tends to see value as being\nrealized by goods in the world, such as friendship, knowledge, beauty\nand so on, and the question of pluralism is thus a question about how\nmany fundamental goods there are. Virtue ethicists focus on how agents\nshould be, so are interested both in principles of action (or\nmotivation) and the pursuit of goods, such as friendship.\n", "\n\nDeontologists can clearly be monists or pluralists. Kant can be\nunderstood as a monist—arguing that there is one overarching\nprinciple, and that all other principles are derived from it. Ross, by\ncontrast, is a  pluralist, because he thinks that\nthere is a plurality of prima facie duties. (See Kant (1948), Ross\n(1930).)[2]\n", " \n\nMany utilitarians are monists, arguing that there is only one\nfundamental value and that is well-being or pleasure or happiness, or\nsomething of that sort. In other words, some utilitarians are\ncommitted to hedonism. Monist utilitarians must claim that all other\nputative values, such as friendship, knowledge and so on, are only\ninstrumental values, which are valuable in so far as they contribute\nto the foundational value. But utilitarians need not be\nmonists. Amartya Sen, for example, argues that utilitarians can take a\n‘vector view of utility’, according to which there are\ndifferences in the qualities as well of the quantites of utility in\ngoods in the world. According to Sen, we should interpet Mill as a\npluralist in this way. (I return to Mill below: it is not entirely\nclear how we should understand his view). Sen points out that desire\nsatisfaction theorists can be pluralists too. Just as different sorts\nof pleasure might have different sorts of value, so different desires\nmight have different sorts of value. (Sen, 1981). Even utilitarians\nwho claim that the value to be maximized is well-being can be\npluralist: a prominent view of well-being is that well-being itself is\nplural, an objective list of things that are fundamentally\nplural. (See Finnis 1980; Griffin 1986; for recent defences see\nFletcher, 2013, Lin, 2014). Another reason to think that hedonistic\nutilitarians should be pluralists is that it seems essential to say\nsomething about the disvalue of pain. As Shelly Kagan points out\n(2014), we need an account of ill-being in addition to an account of\nwell-being. ", "\nIn what follows I will be as neutral as possible between different\ntheoretical approaches to morality, and will focus on the debate\nbetween monists and pluralists. Monists claim that there is only one\nultimate value. Pluralists argue that there really are several\ndifferent values, and that these values are not reducible to each\nother or to a supervalue. Monism has the advantage of relative\nsimplicity: once it has been determined what the supervalue is\n(whether we think of the super value in terms of the goods approach or\nany other approach) much of the hard work has been done. On the other\nhand, monism may be too simple: it may not capture the real texture of\nour ethical lives. However, pluralism faces the difficulty of\nexplaining how different fundamental values relate to each other, and\nhow they can be compared.\n" ]

[ { "content_title": "1. Some Preliminary Clarifications", "sub_toc": [ "1.1 Foundational and Non-foundational Pluralism", "1.2 A Purely Verbal Dispute?" ] }, { "content_title": "2. The Attraction of Pluralism", "sub_toc": [ "2.1 Discontinuities", "2.2 Value Conflicts and Rational Regret", "2.3 Appropriate Responses to Value" ] }, { "content_title": "3. Monist Solutions", "sub_toc": [ "3.1 Different Bearers of Value", "3.2 Diminishing Marginal Value", "3.3 Theoretical Virtues", "3.4 Preference Satisfaction Views" ] }, { "content_title": "4. Pluralism and Rational Choice", "sub_toc": [ "4.1 Practical Wisdom", "4.2 Super Scales", "4.3 Basic Preferences", "4.4 Accepting Incomparability" ] }, { "content_title": "5. Conclusion", "sub_toc": [] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [], "section_title": "1. Some Preliminary Clarifications", "subsections": [ { "content": [ "\n\nIt is important to clarify the levels at which a moral theory might be\npluralistic. Let us distinguish between two levels of pluralism:\nfoundational and non-foundational. Foundational pluralism is the view\nthat there are plural moral values at the most basic level—that\nis to say, there is no one value that subsumes all other values, no\none property of goodness, and no overarching principle of\naction. Non-foundational pluralism is the view that there are plural\nvalues at the level of choice, but these apparently plural values can\nbe understood in terms of their contribution to one more fundamental\nvalue.[3]", "\nJudith Jarvis Thomson, a foundational pluralist, argues that when we\nsay that something is good we are never ascribing a property of\ngoodness, rather we are always saying that the thing in question is\ngood in some way. If we say that a fountain pen is good we mean\nsomething different from when we say that a logic book is good, or a\nfilm is good. As Thomson puts it, all goodness is a goodness in a\nway. Thomson focusses her argument on Moore, who argues that when we\nsay ‘x is good’ we do not mean ‘x\nis conducive to pleasure’, or ‘x is in accordance\nwith a given set of rules’ and nor do we mean anything else that\nis purely descriptive. As Moore points out, we can always query\nwhether any purely descriptive property really is good—so he\nconcludes that goodness is simple and\nunanalyzable.[4]\nMoore is thus a foundational monist, he thinks that there is one\nnon-natural property of goodness, and that all good things are good in\nvirtue of having this property. Thomson finds this preposterous. In\nThomson’s own words:\n", "\n\nMoore says that the question he will be addressing himself to in what\nfollows is the question ‘What is good?’, and he rightly\nthinks that we are going to need a bit of help in seeing exactly what\nquestion he is expressing in those words. He proposes to help us by\ndrawing attention to a possible answer to the question he is\nexpressing—that is, to something that would be an answer to it,\nwhether or not it is the correct answer to it. Here is what he offers\nus: “Books are good.” Books are good? What would you mean if you said\n‘Books are good’? Moore, however, goes placidly on:\n“though [that would be] an answer obviously false; for some books are\nvery bad indeed”. Well some books are bad to read or to look at, some\nare bad for use in teaching philosophy, some are bad for\nchildren. What sense could be made of a person who said, “No. no. I\nmeant that some books are just plain bad things”? (Thomson 1997,\npp. 275-276)  ", "\n\nAccording to Thomson there is a fundamental plurality of ways of being\ngood. We cannot reduce them to something they all have in common, or\nsensibly claim that there is a disjunctive property of goodness (such\nthat goodness is ‘goodness in one of the various ways’. Thomson\nargues that that could not be an interesting property as each disjunct\nis truly different from every other disjunct. Thomson (1997), p. 277).\nThomson is thus a foundational pluralist—she does not think\nthat there is any one property of value at the most basic\nlevel. ", "\n\nW.D. Ross is a foundational pluralist in a rather complex way. Most\nstraightforwardly, Ross thinks that there are several prima facie\nduties, and there is nothing that they all have in common: they are\nirreducibly plural. This is the aspect of Ross’s view that is referred\nto with the phrase, ‘Ross-style pluralism’. However, Ross also thinks\nthat there are goods in the world (justice and pleasure, for example),\nand that these are good because of some property they share. Goodness\nand rightness are not reducible to one another, so Ross is a pluralist\nabout types of value as well as about principles.", "\n\nWriters do not always make the distinction between foundational\nand other forms of pluralism, but as well as Thomson and Ross, at least Bernard\nWilliams (1981), Charles Taylor (1982), Charles Larmore (1987), John\nKekes (1993), Michael Stocker (1990 and 1997), David Wiggins (1997)\nand Christine Swanton (2001) are all committed to foundational\npluralism.", "\n\nNon-foundational pluralism is less radical—it posits a plurality\nof bearers of value. In fact, almost everyone accepts that there are\nplural bearers of value. This is compatible with thinking that there\nis only one ultimate value. G.E. Moore (1903), Thomson’s\ntarget, is a foundational monist, but he accepts that there are\nnon-foundational plural values. Moore thinks that there are many\ndifferent bearers of value, but he thinks that there is one property\nof goodness, and that it is a simple non-natural property that bearers\nof value possess in varying degrees. Moore is clear that comparison\nbetween plural goods proceeds in terms of the amount of goodness they\nhave. ", "\n\nThis is not to say that the amount of goodness is always a matter of\nsimple addition. Moore thinks that there can be organic unities, where\nthe amount of goodness contributed by a certain value will vary\naccording to the combination of values such as love and\nfriendship. Thus Moore’s view is pluralist at the level of\nordinary choices, and that is not without interesting consequences. (I\nshall return to the issue of how a foundational monist like Moore can\naccount for organic unities in section 2.1.) ", "\n\nMill, a classic utilitarian, could be and often has\nbeen interpreted as thinking that there are irreducibly different\nsorts of pleasure. Mill argues that there are higher and lower\npleasures, and that the higher pleasures (pleasures of the intellect\nas opposed to the body) are superior, in that higher pleasures can\noutweigh lower pleasures regardless of the quantity of the latter. As\nMill puts it: “It is quite compatible with the principle of utility to\nrecognize the fact, that some kinds of pleasure are more desirable and\nmore valuable than others.” (2002, p. 241). On the foundational\npluralist interpretation of Mill, there is not one ultimate good, but\ntwo (at least): higher and lower pleasures. Mill goes on to give an\naccount of what he means:", "\n\nIf I am asked, what I mean by difference in quality in pleasures, or\nwhat makes one pleasure more valuable than another, merely as a\npleasure, except its being greater in amount, there is but one\npossible answer. Of two pleasures, if there be one to which all or\nalmost all who have experience of both give a decided preference,\nirrespective of any feeling of moral obligation to prefer it, that is\nthe more desirable pleasure. (2002, p. 241). \n", "\n\nThe passage is ambiguous, it is not clear what role the expert\njudges play in the theory. On the pluralist interpretation of this\npassage we must take Mill as intending the role of the expert judges\nas a purely heuristic device: thinking about what such people\nwould prefer is a way of discovering which pleasures are higher and\nwhich are lower, but the respective values of the pleasure is\nindependent of the judges’ judgment. On a monist interpretation we\nmust understand Mill as a preference utilitarian: the\npreferences of the judges determine value. On this interpretation\nthere is one property of value (being preferred by expert judges) and\nmany bearers of value (whatever the\n judges\n prefer).[5]\n", "\n\nBefore moving on, it is worth noting that a theory might be\nfoundationally monist in its account of what values there are, but not\nrecommend that people attempt to think or make decisions on the basis\nof the supervalue. A distinction between decision procedures and\ncriteria of right has become commonplace in moral philosophy. For\nexample, a certain form of consequentialism has as its criterion of\nright action: act so as to maximize good consequences. This might\ninvite the complaint that an agent who is constantly trying to\nmaximize good consequences will often, in virtue of that fact, fail to\ndo so. Sometimes concentrating too hard on the goal will make it less\nlikely that the goal is achieved. A distinction between decision\nprocedure and right action can provide a response—the\nconsequentialist can say that the criterion of right action, (act so\nas to maximize good consequences) is not intended as a decision\nprocedure—the agent should use whichever decision procedure is\nmost likely to result in success. If, then, there is some attraction\nor instrumental advantage from the point of view of a particular\ntheory to thinking in pluralist terms, then it is open to that theory\nto have a decision procedure that deals with apparently plural values,\neven if the theory is monist in every other way.\n [6]\n \n" ], "subsection_title": "1.1 Foundational and Non-foundational Pluralism" }, { "content": [ "\n\nOne final clarification about different understandings of pluralism\nought to be made. There is an ambiguity between the name for a group\nof values and the name for one unitary value. There are really two\nproblems here: distinguishing between the terms that refer to groups\nand the terms that refer to individuals (a merely linguistic problem)\nand defending the view that there really is  a candidate for a\nunitary value (a metaphysical problem). The linguistic problem comes\nabout because in natural language we may use a singular term as\n‘shorthand’: conceptual analysis may reveal that surface\ngrammar does not reflect the real nature of the concept. For example,\nwe use the term ‘well-being’ as if it refers to one single\nthing, but it is not hard to see that it may \nnot. ‘Well-being’ may be a term that we use to refer to\na group of things such as pleasure, health, a sense of achievement and\nso on. A theory that tells us that well-being is the only value may only\nbe nominally monist. The metaphysical question is more\ndifficult, and concerns whether there are any genuinely unitary values\nat all.", "\n\nThe metaphysical question is rather different for naturalist and\nnon-naturalist accounts of value. On Moore’s non-naturalist account,\ngoodness is a unitary property but it is not a natural \nproperty: it is not empirically available to us, but is known by a\nspecial faculty of intuition. It is very clear that Moore thinks that\ngoodness is a genuinely unitary property:", "\n\n‘Good’, then, if we mean by it that quality which we assert to belong\nto a thing, when we say that the thing is good, is incapable of any\ndefinition, in the most important sense of that word. The most\nimportant sense of ‘definition’ is that in which a definition states\nwhat are the parts which invariably compose a certain whole; and in\nthis sense ‘good’ has no definition because it is simple and has no\nparts. (Moore, 1903, p. 9)\n", " The question of whether there could be such a thing is no more\neasy or difficult than any question about the existence of non-natural\nentities. The issue of whether the entity is genuinely unitary\nis not an especially difficult part of that issue.", "\n\nBy contrast, naturalist views do face a particular difficulty in\ngiving an account of a value that is genuinely unitary. On the goods\napproach, for example, the claim must be that there is one good that\nis genuinely singular, not a composite of other goods. So for example,\na monist hedonist must claim that pleasure really is just one\nthing. Pleasure is a concept we use to refer to something we take to\nbe in the natural world, and conceptual analysis may or may not\nconfirm that pleasure really is one thing. Perhaps, for example, \nwe refer both to intellectual and sensual experiences as\npleasure. Or, take another good often suggested by proponents of the\ngoods approach to value, friendship. It seems highly unlikely that\nthere is one thing that we call friendship, even if there are good\nreasons to use one umbrella concept to refer to all those different\nthings. Many of the plausible candidates for the good seem plausible\nprecisely because they are very broad terms. If a theory is to be\nproperly monist then, it must have an account of the good that is\nsatisfactorily unitary.", "\n\nThe problem applies to the deontological approach to value too. It is\noften relatively easy to determine whether a principle is really two\nor more principles in disguise—the presence of a conjunction\nor a disjunction, for example, is a clear giveaway. However,\nprinciples can contain terms that are unclear. Take for example\na deontological theory that tells us to respect friendship. As mentioned previously,\nit is not clear whether there is one thing that is friendship or more\nthan one, so it is not clear whether this is one principle about one\nthing, or one principle about several things, or whether it is really\nmore than one principle.", "\n\nQuestions about what makes individuals individuals and what the\nrelationship is between parts and wholes have been discussed in the\ncontext of metaphysics but these issues have not been much discussed in the\nliterature on pluralism and monism in moral philosophy. However, these issues are\nimplicit in discussions of the well-being, nature of friendship and pleasure, and\nin the literature on Kant’s categorical imperative, or on Aristotelian\naccounts of eudaimonea. Part of an investigation into the nature of\nthese things is an investigation into whether there really is one\nthing or not. [7]\n", "\n\nThe upshot of this brief discussion is that monists must be able to\ndefend their claim that the value they cite is genuinely one\nvalue. There may be fewer monist theories than it first\nappears. Further, the monist must accept the implications of a\ngenuinely monist view. As Ruth Chang points out, (2015, p. 24) the\nsimpler the monist’s account of the good is, the less likely it\nis that the monist will be able to give a good account of the various\ncomplexities in choice that seem an inevitable part of our experience\nof value. But on the other hand, if the monist starts to admit that\nthe good is complex, the view gets closer and closer to being a\npluralist view.\n", "\nHowever, the dispute between monists and pluralists is not merely\nverbal: there is no prima facie reason to think that there are no\ngenuinely unitary properties, goods or principles. " ], "subsection_title": "1.2 A Purely Verbal Dispute?" } ] }, { "main_content": [ "\n\nIf values are plural, then choices between them will be complex.\nPluralists have pressed the point that choices are complex, and so we\nshould not shy away from the hypothesis that values are plural. In\nbrief, the attraction of pluralism is that it seems to allow for the\ncomplexity and conflict that is part of our moral experience. We do\nnot experience our moral choices as simple additive\npuzzles. Pluralists have argued that there are incommensurabilities\nand discontinuities in value comparisons, value remainders (or\nresidues) when choices are made, and complexities in appropriate\nresponses to value. Recent empirical work confirms\nthat our ethical experience is of apparently irreducible plural\nvalues. (See Gill and Nichols, 2008.) " ], "section_title": "2. The Attraction of Pluralism", "subsections": [ { "content": [ "\n\nJohn Stuart Mill suggested that there are higher and lower pleasures\n(Mill, 2002, p. 241), the idea being that the value of higher and lower\npleasures is measured on different scales. In other words, there are\ndiscontinuities in the measurement of value. As mentioned previously, it is unclear\nwhether we should interpret Mill as a foundational pluralist, but the\nnotion of higher and lower pleasures is a very useful one to\nillustrate the attraction of thinking that there are discontinuities\nin value. The distinction between higher and lower pleasures allows us\nto say that no amount of lower pleasures can outweigh some amount of\nhigher pleasures. As Mill puts it, it is better to be an unhappy\nhuman being than a happy pig. In other words, the distinction allows\nus to say that there are discontinuities in value addition. As James\nGriffin (1986, p. 87) puts it: “We do seem, when informed, to rank a\ncertain amount of life at a very high level above any amount of life\nat a very low level.” Griffin’s point is that there are\ndiscontinuities in the way we rank values, and this suggests that\nthere are different\n values.[8]\n The phenomenon of\ndiscontinuities in our value rankings seems to support pluralism: if\nhigher pleasures are not outweighed by lower pleasures, that suggests\nthat they are not the same sort of thing. For if they were just the\nsame sort of thing, there seems to be no reason why lower pleasures\nwill not eventually outweigh higher pleasures.\n", "\n\nThe most extreme form of discontinuity is incommensurability or\nincomparability, when two values cannot be ranked at\nall. Pluralists differ on whether pluralism entails\nincommensurabilities, and on what incommensurability entails for the\npossibility of choice. Griffin denies that pluralism entails\nincommensurability (Griffin uses the term incomparability) whereas\nother pluralists embrace incommensurability, but deny that it entails\nthat rational choice is impossible. Some pluralists accept that there\nare sometimes cases where incommensurability precludes rational\nchoice. We shall return to these issues in Section 4." ], "subsection_title": "2.1 Discontinuities" }, { "content": [ "\n\nMichael Stocker (1990) and Bernard Williams (1973 and 1981) and others\nhave argued that it can be rational to regret the outcome of a correct\nmoral choice. That is,  even when the right choice has been made,\nthe rejected option can reasonably be regretted, and so the choice\ninvolves a genuine value conflict. This seems strange if the options\nare being compared in terms of a supervalue. How can we regret having\nchosen more rather than less of the same thing? Yet the phenomenon\nseems undeniable, and pluralism can explain it. If there are plural\nvalues, then one can rationally regret not having chosen something which\nthough less good, was different.", "\n\nIt is worth noting that the pluralist argument is not that all cases\nof value conflict point to pluralism. There may be conflicts because\nof ignorance, for example, or because of irrationality, and these do\nnot require positing plural values. Stocker argues that there are (at\nleast) two sorts of value conflict that require plural values. The\nfirst is conflict that involves choices between doing things at\ndifferent times. Stocker argues that goods become different values in\ndifferent temporal situations, and the monist cannot accommodate this\nthought. The other sort of case (which Williams also points to) is\nwhen there is a conflict between things that have different advantages\nand disadvantages. The better option may be better, but it does not\n‘make up for’ the lesser option, because it isn’t the same\nsort of thing. Thus there is a remainder—a moral value that is\nlost in the choice, and that it is rational to regret. ", "\n\nBoth Martha Nussbaum (1986) and David Wiggins (1980) have argued for\npluralism on the grounds that only pluralism can explain akrasia, or\nweakness of will. An agent is said to suffer from weakness of will\nwhen she knowingly chooses a less good option over a better one. On\nthe face of it, this is a puzzling thing to do—why would\nsomeone knowingly do what they know to be worse? A pluralist has a\nplausible answer—when the choice is between two different\nsorts of value, the agent is preferring A to B, rather than preferring\nless of A to more of A. Wiggins explains the akratic choice by\nsuggesting that the agent is ‘charmed’ by some aspect of\nthe choice, and is swayed by that to choose what she knows to be worse\noverall (Wiggins 1980, p. 257). However, even Michael Stocker, the arch\npluralist, does not accept that this argument works. As Stocker points\nout, Wiggins is using a distinction between a cognitive and an\naffective element to the choice, and this distinction can explain\nakrasia on a monist account of value too. Imagine that a monist\nhedonist agent is faced with a choice between something that will give\nher more pleasure and something that will give her less pleasure. The\ncognitive aspect to the choice is clear—the agent knows that\none option is more pleasurable than the other, and hence on her theory\nbetter. However, to say that the agent believes that more pleasure is\nbetter is not to say that she will always be attracted to the option\nthat is most pleasurable. She may, on occasion, be attracted to the\noption that is more unusual or interesting. Hence she may act\nakratically because she was charmed by some aspect of the less good\nchoice—and as Stocker says, there is no need to posit plural\nvalues to make sense of this—being charmed is not the same as\nvaluing. (Stocker 1990, p.219)." ], "subsection_title": "2.2 Value Conflicts and Rational Regret" }, { "content": [ "\n\nAnother argument for pluralism starts from the observation that there\nare many and diverse appropriate responses to value. Christine Swanton\n(2003, ch. 2) and Elizabeth Anderson (1993) both take this line. As\nSwanton puts it:", "\n\nAccording to value centered monism, the rightness of moral\nresponsiveness is determined entirely by degree or strength of\nvalue…I shall argue, on the contrary, that just how things are\nto be pursued, nurtured, respected, loved, preserved, protected, and so\nforth may often depend on further general features of those things, and\ntheir relations to other things, particularly the moral agent. (Swanton\n2003, p. 41).\n", "\n\nThe crucial thought is that there are various bases of moral\nresponsiveness, and these bases are irreducibly plural. A monist could\nargue that there are different appropriate responses to value, but the\nmonist would have to explain why there are different appropriate\nresponses to the same value. Swanton’s point is that the only\nexplanation the monist has is that different degrees of value merit\ndifferent responses. According to Swanton, this does not capture what\nis really going on when we appropriately honor or respect a value\nrather than promoting it. Anderson and Swanton both argue that the\ncomplexity of our responses to value can only be explained by a\npluralistic theory.", "\n\nElizabeth Anderson argues that it is a mistake to understand moral\ngoods on the maximising model. She uses the example of parental love\n(Anderson 1997, p. 98). Parents should not see their love for their\nchildren as being directed towards an “aggregate child\ncollective”. Such a view would entail that trade offs were\npossible, that one child could be sacrificed for another. On\nAnderson’s view we can make rational choices between conflicting\nvalues without ranking values: “…choices concerning those\ngoods or their continued existence do not generally require that we\nrank their values on a common scale and choose the more valuable good;\nthey require that we give each good its due” (Anderson 1997,\np. 104).\n\n" ], "subsection_title": "2.3 Appropriate Responses to Value" } ] }, { "main_content": [ "\n\nI began the last section by saying that if foundational values are\nplural, then choices between them will be complex. It is clear that\nour choices are complex. However, it would be invalid to conclude from\nthat that values are plural—the challenge for monists is to\nexplain how they too can make sense of the complexity of our value\nchoices. " ], "section_title": "3. Monist Solutions", "subsections": [ { "content": [ "\n\nOne way for monists to make sense of complexity in value choice is to\npoint out that there are different bearers of value, and this makes a\nbig difference to the experience of choice. (See Hurka, 1996; Schaber,\n1999; Klocksiem 2011). Here is the challenge to monism in Michael\nStocker’s words (Stocker, 1990, p. 272): “[if monism is\ntrue] there is no ground for rational conflict because the better\noption lacks nothing that would be made good by the lesser.” In\nother words, there are no relevant differences between the better and\nworse options except that the better option is better. Thomas Hurka\nobjects that there can be such differences. For example, in a choice\nbetween giving five units of pleasure to A and ten units\nto B, the best option (more pleasure for B) involves\ngiving no pleasure at all to A. So there is something to\nrationally regret, namely, that A had no pleasure. The\nargument can be expanded to deal with all sorts of choice situation:\nin each situation,  a monist can say something sensible about an\nunavoidable loss, a loss that really is a loss. If, of two options one\nwill contribute more basic value, the monist must obviously choose\nthat one. But the lesser of the options may contribute value via\npleasure, while the superior option contributes value via knowledge,\nand so there is a loss in choosing the option with the greater value\ncontribution—a loss in pleasure— and it is rational for us\nto regret this.", "\n\nThere is one difficulty with this answer. The loss described by Hurka\nis not a moral loss, and so the regret is not moral regret. In Hurka’s\nexample, the relevant loss is that A does not get any\npleasure. The agent doing the choosing may be rational to regret this\nif she cares about A, or even if she just feels sorry for\nA, but there has been no moral loss, as ‘pleasure for\nA’ as opposed to pleasure itself is not a moral\nvalue. According to the view under consideration, pleasure itself is\nwhat matters morally, and so although A’s pleasure matters\nqua pleasure, the moral point of view takes B’s pleasure into\naccount in just the same way, and there is nothing to regret, as there\nis more pleasure than there would otherwise have been. Stocker and\nWilliams would surely insist that the point of their argument was not\njust that there is a loss, but that there is a moral loss. The monist\ncannot accommodate that point, as the monist can only consider the\nquantity of the value, not its distribution, and so we are at an\nimpasse.", "\n\nHowever, the initial question was whether the monist has succeeded in\nexplaining the phenomenon of ‘moral regret’, and perhaps\nHurka has done that by positing a conflation of moral and non-moral\nregret in our experience. From our point of view, there is regret, and\nthe monist can explain why that is without appealing to\nirrationality. On the other hand the monist cannot appeal to anything\nother than quantity of value in appraising the morality of the\nsituation. So although Hurka is clearly right in so far as he is\nsaying that a correct moral choice can be regretted for non-moral\nreasons, he can go no further than that." ], "subsection_title": "3.1 Different Bearers of Value" }, { "content": [ "\n\nAnother promising strategy that the monist can use in order to explain\nthe complexity in our value choices is the appeal to\n‘diminishing marginal value’. The value that is added to\nthe sum by a source of value will tend to diminish after a certain\npoint—this phenomenon is known as diminishing marginal value\n(or, sometimes, diminishing marginal utility). Mill’s higher and lower\npleasures, which seem to be plural values, might be accommodated by\nthe monist in this way. The monist makes sense of discontinuities in\nvalue by insisting on the distinction between sources of value, which\nare often ambiguously referred to as ‘values’, and the super\nvalue. Using a monist utilitarian account of value, we can distinguish\nbetween the non-evaluative description of options, the intermediate\ndescription, and the evaluative description as follows:", "\n\nOn this account, painting produces beauty, and beauty (which is not a\nvalue but the intermediate source of value) produces value. Similarly,\nreading a book produces knowledge, and gaining knowledge produces\nvalue. Now it should be clear how the monist can make sense of\nphenomena like higher and lower pleasures. The non-evaluative options\n(e.g. eating donuts) have diminishing marginal non-basic value.", "\n\nOn top of that, the intermediate effect, or non-basic value,\n(e.g. experiencing pleasure) can have a diminishing contribution to\nvalue. Varying diminishing marginal value in these cases is easily\nexplained psychologically. It is just the way we are—we get\nless and less enjoyment from donuts as we eat more and more (at least\nin one sitting). However, we may well get the same amount of enjoyment\nfrom the tenth Johnny Cash song that we did from the first. In order\nto deal with the higher and lower pleasures case the monist will have\nto argue that pleasures themselves can have diminishing marginal\nutility—the monist can argue that gustatory pleasure gets\nboring after a while, and hence contributes less and less to the super\nvalue—well being, or whatever it\n is.[9]", "\n\nThis picture brings us back to the distinction between foundational\nand non-foundational pluralism. Notice that the monist theories being\nimagined here are foundationally monist, because they claim that\nthere is fundamentally one value, such as pleasure, and they are\npluralist at the level of ordinary choice because they claim that there are intermediate\nvalues, such as knowledge and beauty, which are valuable because of\nthe amount of pleasure they produce (or realize, or \ncontain—the exact relationship will vary from theory to\ntheory). " ], "subsection_title": "3.2 Diminishing Marginal Value" }, { "content": [ "\nThe main advantage of pluralism is that it seems true to our\nexperience of value. We experience values as plural, and pluralism\ntells is that values are indeed plural. The monist can respond, as we\nhave seen, that there are ways to explain the apparent plurality of\nvalues without positing fundamentally plural values. Another,\ncomplementary strategy that the monist can pursue is to argue that\nmonism has theoretical virtues that pluralism lacks. In general, it\nseems that theories should be as simple and coherent as possible, and\nthat other things being equal, we should prefer a more coherent theory\nto a less coherent one. Thus so long as monism can make sense of\nenough of our intuitive judgments about the nature of value, then it\nis to be preferred to pluralism because it does better on the\ntheoretical virtue of coherence.\n", "\nAnother way to put this point is in terms of explanation. The monist\ncan point out that the pluralist picture lacks explanatory depth. It\nseems that a list of values needs some further explanation: what makes\nthese things values? (See Bradley, 2009, p.16). The monist picture is\nsuperior, because the monist can provide an explanation for the value\nof the (non-foundational) plurality of values: these things are values\nbecause they contribute to well-being, or pleasure, or whatever the\nfoundational monist value is. (See also the discussion of this in the\nentry on\n value theory).", "Patricia Marino argues against this strategy (2016). She argues\nthat ‘systematicity’ (the idea that it is better to have\nfewer principles) is not a good argument in favour of monism. Marino\npoints out that explanation in terms of fewer fundamental principles\nis not necessarily better explanation. If there are plural\nvalues, then the explanation that appeals to plural values is a better\none, in the sense that it is the true one: it doesn’t deny the\nplurality of values. (2016, p.124-125). Even if we could give a monist\nexplanation without having to trade off against our pluralist\nintuitions, Marino argues, we have no particular reason to think that\nexplanations appealing to fewer principles are superior. " ], "subsection_title": "3.3 Theoretical Virtues" }, { "content": [ "\n\nThere is a different account of value that we ought to consider here:\nthe view that value consists in preference or desire satisfaction. On\nthis view, knowledge and pleasure and so on are valuable when they are\ndesired, and if they are not desired anymore they are not valuable\nanymore. There is no need to appeal to complicated accounts of\ndiminishing marginal utility: it is uncontroversial that we sometimes\ndesire something and sometimes don’t. Thus complexities in choices are\nexplained by complexities in our desires, and it is uncontroversial\nthat our desires are complex.", "\n\nImagine a one person preference satisfaction account of value that\nsays simply that what is valuable is what P desires.\nApparently this view is foundationally monist: there is only one thing\nthat confers value (being desired by P), yet at the\nnon-foundational level there are many values (whatever P\ndesires). Let us say that P desires hot baths, donuts and\nknowledge. The structure of P’s desires is such that\nthere is a complicated ranking of these things, which will vary from\ncircumstance to circumstance. The ranking is not explained by the\nvalue of the objects,rather, her desire explains the ranking and\ndetermines the value of the objects. So it might be that P\nsometimes desires a hot bath and a donut equally, and cannot choose\nbetween them; it might be that sometimes she would choose knowledge\nover a hot bath and a donut, but sometimes she would choose a hot bath\nover knowledge. On James Griffin’s slightly more complex view,\nwell-being consist in the fulfillment of informed desire, and Griffin\npoints out that his view can explain discontinuities in value without\nhaving to appeal to diminishing marginal utility:", "\n\nthere may well turn out to be cases in which, when informed, I want,\nsay, a certain amount of one thing more than any amount of another, and\nnot because the second thing cloys, and so adding to it merely produces\ndiminishing marginal values. I may want it even though the second thing\ndoes not, with addition, lose its value; it may be that I think that no\nincrease in that kind of value, even if constant and positive, can\novertake a certain amount of this kind of value. (1986, p. 76).\n", "\n\nThis version of foundational monism/normative pluralism escapes some\nof the problems that attend the goods approach. First, this view can\naccount for deep complexities in choice. The plural goods that P is\nchoosing between do not seem merely instrumental. Donuts are not good\nbecause they contribute to another value, and P does not desire donuts\nfor any reason other than their donuty nature. On this view, if it is\nhard to choose between donuts and hot baths it is because of the\nintrinsic nature of the objects. The key here is that value is\nconferred by desire, not by contribution to another value. Second,\nthis view can accommodate incomparabilities: if P desires a hot bath\nbecause of its hot bathy nature, and a donut because of its donuty\nnature, she may not be able to choose between them.", " However, it is not entirely clear that a view like Griffin’s is\ngenuinely monist at the foundational level: the question arises, what\nis constraining the desires that qualify as value conferring? If the\nanswer is ‘nothing’, then the view seems genuinely monist,\nbut is probably implausible. Unconstrained desire accounts of value\nseem implausible because our desires can be for all sorts of \nthings—we may desire things that are bad for us, or we may desire\nthings because of some mistake we have made. If the answer is that\nthere is something constraining the desires that count as value\nconferring, then of course the question is, ‘what?’ Is it\nthe values of the things desired? A desire satisfaction view that\nrestricts the qualifying desires must give an account of what\nrestricts them, and obviously, the account may commit the view to\nfoundational pluralism. ", " Griffin addresses this question at the very beginning of his book\non well being (Griffin, 1986,\n ch.2).[10]\n As he puts it,", "\n\nThe danger is that desire accounts get plausible only by, in effect,\nceasing to be desire accounts. We had to qualify desire with informed,\nand that gave prominence to the features or qualities of the objects of\ndesire, and not to the mere existence of desire. (1986, p. 26).\n", "\n\nGriffin’s account of the relationship between desire and value is\nsubtle, and (partly because Griffin himself does not distinguish\nbetween foundational and normative pluralism) it is difficult to say\nwhether his view is foundationally pluralist or not. Griffin argues\nthat it is a mistake to see desire as a blind motivational \nforce—we desire things that we perceive in a favorable light- we\ntake them to have a desirability feature. When we try to explain what\ninvolved in seeing things in a favorable light, we cannot, according\nto Griffin, separate understanding from desire: ", "\n\n…we cannot, even in the case of a desirability feature such as\naccomplishment, separate understanding and desire. Once we see\nsomething as ‘accomplishment’, as ‘giving weight and\nsubstance to our lives’, there is no space left for desire to follow\nalong in a secondary subordinate position. Desire is not\nblind. Understanding is not bloodless. Neither is the slave of the\nother. There is no priority. (1986, p. 30)", "\n\nThis suggests that the view is indeed pluralist at the\nfoundation—values are not defined entirely by desire, but partly\nby other features of the situation, and so at the most fundamental\nlevel there is more than one value making feature. Griffin himself\nsays that “the desire account is compatible with a strong form of\npluralism about values” (p. 31).", "\n\nI shall not pursue further the question whether or not Griffin is a\nfoundational pluralist, my aim in this section is to show first, that\nmonist preference satisfaction accounts of value may have more\ncompelling ways of explaining complexities in value comparison than\nmonist goods approaches, but second, to point out that any constrained\ndesire account may well actually be foundationally pluralist. As soon\nas something is introduced to constrain the desires that qualify as\nvalue conferring, it looks as though another value is operating.\n" ], "subsection_title": "3.4 Preference Satisfaction Views" } ] }, { "main_content": [ "\n\nThe big question facing pluralism is whether rational choices can be\nmade between irreducibly plural values. Irreducible plurality appears\nto imply incommensurability—that is to say, that there is no\ncommon measure which can be used to compare two different values. (See\nthe entry on\n incommensurable values.)\n Value incommensurability seems worrying: if values are incommensurable, then\neither we are forced into an ad hoc ranking, or we cannot rank the\nvalues at all. Neither of these are very appealing options. ", "\nHowever, pluralists reject this dilemma. \nBernard Williams argues that it is a mistake to think that pluralism\nimplies that comparisons are impossible. He says:", "\n\nThere is one motive for reductivism that does not operate simply on the\nethical, or on the non-ethical, but tends to reduce every consideration\nto one basic kind. This rests on an assumption about rationality, to\nthe effect that two considerations cannot be rationally weighed against\neach other unless there is a common consideration in terms of which\nthey can be compared. This assumption is at once very powerful and\nutterly baseless. Quite apart from the ethical, aesthetic\nconsiderations can be weighed against economic ones (for instance)\nwithout being an application of them, and without their both being an\nexample of a third kind of consideration. (Williams 1985, p. 17)\n", "\nMaking a similar point, Ruth Chang points out that incommensurability\nis often conflated with incomparability. She provides clear\ndefinitions of each: incommensurability is the lack of a common unit\nof value by which precise comparisons can be made. Two items are\nincomparable, if there is no possible relation of comparison, such as\n‘better than’, or ‘as good as’ (1997,\nIntroduction). Chang points out that incommensurability is often\nthought to entail incomparability, but it does not. ", "\nDefenders of pluralism have used various strategies to show that it is\npossible to make rational choices between plural values. " ], "section_title": "4. Pluralism and Rational Choice", "subsections": [ { "content": [ "\n\nThe pluralist’s most common strategy in the face of worries about\nchoices between incommensurable values is to appeal to practical\nwisdom—the faculty described by Aristotle—a faculty of\njudgment that the wise and virtuous person has, which enables him to\nsee the right answer. Practical wisdom is not just a question of being\nable to see and collate the facts, it goes beyond that in some\nway—the wise person will see things that only a wise person\ncould see. So plural values can be compared in that a wise person will\n‘just see’ that one course of action rather than another\nis to be taken. This strategy is used (explicitly or implicitly) by\nMcDowell (1979), Nagel (1979), Larmore (1987), Skorupski (1996),\nAnderson (1993 and 1997) Wiggins (1997 and 1998), Chappell (1998),\nSwanton (2003). Here it is in Nagel’s words:", " \n\nProvided one has taken the process of practical justification as far\nas it will go in the course of arriving at the conflict, one may be\nable to proceed without further justification, but without\nirrationality either. What makes this possible is \njudgment—essentially the faculty Aristotle described as\npractical wisdom, which reveals itself over time in individual\ndecisions rather than in the enunciation of general principles. (1979,\np. 135)", "\n\nThe main issue for this solution to the comparison problem is to come\nup with an account of what practical wisdom is. It is not easy to\nunderstand what sort of thing the faculty of judgment might be, or how\nit might work. Obviously pluralists who appeal to this strategy do not\nwant to end up saying that the wise judge can see which of the options\nhas more goodness, as that would constitute collapsing back into\nmonism. So the pluralist has to maintain that the wise judge makes a\njudgment about what the right thing to do is without making any\nquantitative judgment. The danger is that the faculty seems entirely\nmysterious: it is a kind of magical vision, unrelated to our\nnatural senses. As a solution to the comparison problem, the appeal to\npractical wisdom looks rather like way of shifting the problem to\nanother level. Thus the appeal to practical wisdom cannot be left at\nthat. The pluralist owes more explanation of what is involved\nin practical wisdom. What follows below are various pluralists’\naccounts of how choice between plural values is possible, and whether\nsuch choice is rational." ], "subsection_title": "4.1 Practical Wisdom" }, { "content": [ "\nOne direction that pluralists have taken is to argue that although\nvalues are plural, there is nonetheless an available scale on which to\nrank them. This scale is not rationalized by something that the values\nhave in common (that would be monism), but by something over and above\nthe values, which is not itself a super value. Williams sometimes\nwrites as if this is his intention, as do Griffin (1986 and 1997),\nStocker (1990), Chang (1997 and 2004), Taylor (1982 and 1997). James\nGriffin (1986) develops this suggestion in his discussion of plural\nprudential values. According to Griffin, we do not need to have a\nsuper-value to have super-scale. Griffin says:", "\n\n…it does not follow from there being no super-value that there\nis no super-scale. To think so would be to misunderstand how the notion\nof ‘quantity’ of well-being enters. It enters through ranking;\nquantitative differences are defined on qualitative ones. The quantity\nwe are talking about is ‘prudential value’ defined on informed\nrankings. All that we need for the all-encompassing-scale is the\npossibility of ranking items on the basis of their nature. And we can,\nin fact, rank them in that way. We can work out trade-offs between\ndifferent dimensions of pleasure or happiness. And when we do, we rank\nin a strong sense: not just choose one rather than the other, but\nregard it as worth more. That is the ultimate scale here: worth to\none’s life. (Griffin 1986, p. 90)", "\n \nThis passage is slightly hard to interpret (for more on why see my\nearlier discussion of Griffin in the section on preference\nsatisfaction accounts). On one interpretation, Griffin is in fact\nespousing a sophisticated monism. The basic value is ‘worth to\none’s life’, and though it is important to talk about non-basic\nvalues, such as the different dimensions of pleasure and happiness,\nthey are ultimately judged in terms of their contribution to the worth\nof lives.", "\n\nThe second possible interpretation takes Griffin’s claim that worth to\nlife is not a supervalue seriously. On this interpretation, it is\nhard to see what worth to life is, if not a supervalue. Perhaps it is\nonly a value that we should resort to when faced with\nincomparabilities. However, this interpretation invites the criticism\nthat Griffin is introducing a non-moral value, perhaps prudential\nvalue, to arbitrate when moral values are incommensurable. In other\nwords, we cannot decide between incommensurable values on moral\ngrounds, so we should decide on prudential grounds. This seems\nreasonable when applied to incommensurabilities in aesthetic\nvalues. One might not be able to say whether Guernica is better than\nWar and Peace, but one might choose to have Guernica displayed on the\nwall because it will impress one’s friends, or because it is worth\nmore money, or even because one just enjoys it more. In the case of\nmoral choices this is a less convincing strategy: it introduces a\nlevel of frivolity into morality that seems out of place.", "\n\nStocker’s main strategy is to argue that values are plural, and\ncomparisons are made, so it must be possible to make rational\ncomparisons. He suggests that a “higher level synthesizing category”\ncan explain how comparisons are made (1990, p. 172). According to\nStocker these comparisons are not quantitative, they are evaluative:\n", "\n\nSuppose we are trying to choose between lying on a beach\nand discussing philosophy—or more particularly, between the\npleasure of the former and the gain in understanding from the latter.\nTo compare them we may invoke what might be called a higher-level\nsynthesizing category. So, we may ask which will conduce to a more\npleasing day, or to a day that is better spent. Once we have fixed upon\nthe higher synthesizing category, we can often easily ask which option\nis better in regard to that category and judge which to choose on the\nbasis of that. Even if it seems a mystery how we might ‘directly’\ncompare lying on the beach and discussing philosophy, it is a\ncommonplace that we do compare them, e.g. in regard to their\ncontribution to a pleasing day. (Stocker 1990, p. 72)", " Stocker claims that goodness is just the highest level\nsynthesizing category, and that lower goods are constitutive means to\nthe good. Ruth Chang’s approach to comparisons of plural values is\nvery similar (Chang 1997 (introduction) and 2004). Chang claims that\ncomparisons can only be made in terms of a covering value—a\nmore comprehensive value that has the plural values as parts.", "\n\nThere is a problem in understanding quite what a ‘synthesizing\ncategory’ or ‘covering value’ is. How does the\ncovering value determine the relative weightings of the constituent\nvalues? One possibility is that it does it by pure \nstipulation—as a martini just is a certain proportion of gin and\nvermouth. However, stipulation does not have the right sort of\nexplanatory power. On the other hand, if a view is to remain\npluralist, it must avoid conflating the super scale with a super\nvalue. Chang argues that her covering values are sufficiently unitary\nto provide a basis for comparison, and yet preserve the separateness\nof the other values. Chang’s argument goes as follows: the values at\nstake in a situation (for example, prudence and morality) cannot on\ntheir own determine how heavily they weigh in a particular choice\nsituation—the values weigh differently depending on the\ncircumstances of the choice. However, the values plus the\ncircumstances cannot determine relevant weightings \neither—because (I am simplifying here) the internal circumstances of the\nchoice will affect the weighting of the values differently depending\non the external circumstances. To use Chang’s own example, when the\nvalues at stake are prudence and morality (specifically, the duty to\nhelp an innocent victim), and the circumstances include the fact that\nthe victim is far away, the effect this circumstance will have on the\nweighting of the values depends on external circumstances, which fix\nwhat matters in the choice. So, as Chang puts it, “‘What\nmatters’ must therefore have content beyond the values and the\ncircumstances of the choice” (2004, p. 134).", "\n\nStocker is aware of the worry that appeal to something in terms of\nwhich comparisons can be made reduces the view to monism: Stocker\ninsists that the synthesizing category (such as a good life) is not a\nunitary value—it is at most ‘nominal monism’ in my\nterminology. Stocker argues that it is a philosophical prejudice to\nthink that rational judgment must be quantitative, and so he claims\nthat he does not need to give an account of how we form and use the\nhigher level synthesizing categories." ], "subsection_title": "4.2 Super Scales" }, { "content": [ "\n\nAnother approach to the comparison problem appeals to basic\npreferences. Joseph Raz takes the line that we can explain choice\nbetween irreducibly plural goods by talking about basic preferences.\nRaz approaches the issue of incommensurability by talking about the\nnature of agency and rationality instead of about the nature of value.\nHe distinguishes between two conceptions of human agency: the\nrationalist conception, and the classical conception. The rationalist\nconception corresponds to what we have called the stronger use of the\nterm rational. According to the rationalist conception, reasons\nrequire action. The classical conception, by contrast, “regards\nreasons as rendering options eligible” (Raz 1999, p. 47). Raz favors\nthe classical conception, which regards the will as something separate\nfrom desire: ", "\n\nThe will is the ability to choose and perform intentional actions. We\nexercise our will when we endorse the verdict of reason that we must\nperform an action, and we do so, whether willingly, reluctantly, or\nregretting the need, etc. According to the classical conception,\nhowever, the most typical exercise or manifestation of the will is in\nchoosing among options that reason merely renders eligible. Commonly\nwhen we so choose, we do what we want, and we choose what we want, from\namong the eligible options. Sometimes speaking of wanting one option\n(or its consequences) in preference to the other eligible ones is out\nof place. When I choose one tin of soup from a row of identical tins in\nthe shop, it would be wrong and misleading to say that I wanted that\ntin rather than, or in preference to, the others. Similarly, when faced\nwith unpalatable but unavoidable and incommensurate options (as when\nfinancial need forces me to give up one or another of incommensurate\ngoods), it would be incorrect to say that I want to give up the one I\nchoose to give up. I do not want to do so. I have to, and I would\nequally have regretted the loss of either good. I simply choose to give\nup one of them. (Raz, 1999, p. 48)\n", "\n\nRaz’s view about the nature of agency is defended in great detail over\nthe course of many  articles, and all of those arguments cannot\nbe examined in detail here. What is crucial in the context of this\ndiscussion of pluralism is whether Raz gives us a satisfactory account\nof the weaker sense of rational. Raz’s solution to the problem of\nincommensurability hangs on the claim that it can be rational (in the\nweak sense) to choose A over B  when there are no further reasons\nfavouring A over B. We shall restrict ourselves to mentioning one\nobjection to the view in the context of moral choices between plural\ngoods. Though Raz’s account of choice may seem plausible in cases\nwhere we choose between non-moral values, it seems to do violence to\nthe concept of morality. Consider one of Raz’s own examples, the\nchoice between a banana and a pear. It may be that one has to choose\nbetween them, and there is no objective reason to choose one or the\nother. In this case, it seems Raz’s account of choice is plausible. If\none feels like eating a banana, then in this case, desire does provide\na reason. As Raz puts it, “A want can never tip the balance of\nreasons in and of itself. Rather, our wants become relevant when\nreasons have run their course.” In the example where we choose\nbetween a banana and a pear, this sounds fine. However, if we apply it\nto a moral choice it seems a lot less plausible. Raz admits that\n“If of the options available to agents in typical situations of\nchoice and decision, several are incommensurate, then reason can\nneither determine nor completely explain their choices or\nactions” (Raz, 1999, p. 48). Thus many moral choices are not\ndirected by reason but by a basic preference. It is not fair to call\nit a desire, because on Raz’s account we desire things for\nreasons—we take the object of our desire to be desirable. On\nRaz’s picture then, when reasons have run their course, we are\nchoosing without reasons. It doesn’t matter hugely whether we call\nthat ‘rational’ (it is not rational in the strong sense,\nbut it is in the weak sense). What matters is whether this weak\nsense of rational is sufficient to satisfy our concept of moral choice\nas being objectively defensible. The problem is that choosing without\nreasons look rather like plumping. Plumping may be an intelligible\nform of choice, but it is questionable whether it is a satisfactory\naccount of moral choice." ], "subsection_title": "4.3 Basic Preferences" }, { "content": [ "\n\nOne philosopher who is happy to accept that there may be situations\nwhere we just cannot make reasoned choices between plural values is\nIsaiah Berlin, who claimed that goods such as liberty and equality\nconflict at the fundamental level. Berlin is primarily concerned with\npolitical pluralism, and with defending political liberalism, but his\nviews about incomparability have been very influential in\ndiscussions on moral pluralism. Bernard Williams (1981), Charles\nLarmore (1987), John Kekes (1993), Michael Stocker (1990 and 1997),\nDavid Wiggins (1997) have all argued that there are at least some\ngenuinely irresolvable conflicts between values, and that to expect a\nrational resolution is a mistake. For Williams this is part of a more\ngeneral mistake made by contemporary moral philosophers—he\nthinks that philosophy tries to make ethics too easy, too much like\narithmetic. Williams insists throughout his writings that ethics is a\nmuch more complex and multi-faceted beast than its treatment at the\nhands of moral philosophers would suggest, and so it is not surprising\nto him that there should be situations where values conflict\nirresolvably. Stocker (1990) discusses the nature of moral conflict at\ngreat length, and although he thinks that many apparent conflicts can\nbe dissolved or are not serious, like Williams, he argues that much of\ncontemporary philosophy’s demand for simplicity is mistaken. Stocker\nargues that ethics need not always be action guiding, that value is\nmuch more complex than Kantians and utilitarians would have us think,\nand that as the world is complicated we will inevitably face\nconflicts. Several pluralists have argued that accepting the\ninevitability of value conflicts does not result in a  breakdown\nof moral argument, but rather the reverse. Kekes (1993), for example,\nclaims that pluralism enables us to see that irresolvable\ndisagreements are not due to wickedness on the part of our\ninterlocutor, but may be due to the plural nature of values." ], "subsection_title": "4.4 Accepting Incomparability" } ] }, { "main_content": [ "\n\nThe battle lines in the debate between pluralism and monism are not\nalways clear. In this entry I have outlined some of them, and\ndiscussed some of the main arguments. Pluralists need to be clear\nabout whether they are foundational or non-foundational pluralists. Monists must defend\ntheir claim that there really is a unitary value. Much of the debate\nbetween pluralists and monists has focussed on the issue of whether\nthe complexity of moral choice implies that values really are \nplural—a pattern emerges in which the monist claims to be able to\nexplain the appearance of plurality away, and the pluralist insists\nthat the appearance reflects a pluralist reality. Finally, pluralists\nmust explain how comparisons between values are made, or defend the\nconsequence that incommensurability is widespread. " ], "section_title": "5. Conclusion", "subsections": [] } ]

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[ { "href": "../berlin/", "text": "Berlin, Isaiah" }, { "href": "../ethics-virtue/", "text": "ethics: virtue" }, { "href": "../hedonism/", "text": "hedonism" }, { "href": "../liberalism/", "text": "liberalism" }, { "href": "../metaethics/", "text": "metaethics" }, { "href": "../mill/", "text": "Mill, John Stuart" }, { "href": "../moore-moral/", "text": "Moore, George Edward: moral philosophy" }, { "href": "../moral-dilemmas/", "text": "moral dilemmas" }, { "href": "../moral-epistemology/", "text": "moral epistemology" }, { "href": "../moral-particularism/", "text": "moral particularism" }, { "href": "../reasoning-moral/", "text": "reasoning: moral" }, { "href": "../value-incommensurable/", "text": "value: incommensurable" }, { "href": "../value-theory/", "text": "value theory" }, { "href": "../williams-bernard/", "text": "Williams, Bernard" } ]

[ "\nA fundamental problem faced by any group of people is how to arrive at\na good group decision when there is disagreement among its members.\nThe difficulties are most evident when there is a large number of\npeople with diverse opinions, such as, when electing leaders in a\nnational election. But it is often not any easier with smaller groups,\nsuch as, when a committee must select a candidate to hire, or when a\ngroup of friends must decide where to go for dinner. Mathematicians,\nphilosophers, political scientists and economists have devised various\nvoting methods that select a winner (or winners) from a set of\nalternatives taking into account everyone’s opinion. It is not hard to\nfind examples in which different voting methods select different\nwinners given the same inputs from the members of the group. What\ncriteria should be used to compare and contrast different voting\nmethods? Not only is this an interesting and difficult theoretical\nquestion, but it also has important practical ramifications. Given the\ntumultuous 2016 election cycle, many people (both researchers and\npoliticians) have suggested that the US should use a different voting\nmethod. However, there is little agreement about which voting method\nshould be used. ", "\nThis article introduces and critically examines a number of different\nvoting methods. Deep and important results in the theory of social\nchoice suggest that there is no single voting method that is best in\nall situations (see List 2013 for an overview). My objective in this\narticle is to highlight and discuss the key results and issues that\nfacilitate comparisons between voting methods. " ]

[ { "content_title": "1. The Problem: Who ", "sub_toc": [ "1.1 Notation" ] }, { "content_title": "2. Examples of Voting Methods ", "sub_toc": [ "2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods", "2.2 Voting by Grading", "2.3 Quadratic Voting and Liquid Democracy", "2.4 Criteria for Comparing Voting Methods" ] }, { "content_title": "3. Voting Paradoxes", "sub_toc": [ "3.1 Condorcet’s Paradox", "3.2 Failures of Monotonicity", "3.3 Variable Population Paradoxes", "3.4 The Multiple Elections Paradox" ] }, { "content_title": "4. Topics in Voting Theory", "sub_toc": [ "4.1 Strategizing", "4.2 Characterization Results", "4.3 Voting to Track the Truth", "4.4 Computational Social Choice" ] }, { "content_title": "5. Concluding Remarks", "sub_toc": [ "5.1 From Theory to Practice", "5.2 Further Reading" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\nSuppose that there is a group of 21 voters who need to make a decision\nabout which of four candidates should be elected. Let the names of the\ncandidates be \\(A\\), \\(B\\), \\(C\\) and \\(D\\). Your job, as a social\nplanner, is to determine which of these 4 candidates should win the\nelection given the opinions of all the voters. The first step\nis to elicit the voters’ opinions about the candidates. Suppose that\nyou ask each voter to rank the 4 candidates from best to worst (not\nallowing ties). The following table summarizes the voters’ rankings of\nthe candidates in this hypothetical election scenario. ", "\nRead the table as follows: Each row represents a ranking for a group of voters\nin which candidates to the left are ranked higher. The numbers in the first column\n indicate the number of voters with that particular\nranking. So, for example, the third row in the table indicates that\n7 voters have the ranking \\(B\\s D\\s C\\s A\\) which means that each of the 7 voters \nrank \\(B\\) first, \\(D\\) second, \\(C\\) third and \\(A\\) last.\nSuppose that, as the social planner, you do not have any personal\ninterest in the outcome of this election. Given the voters’ expressed\nopinions, which candidate should win the election? Since the voters\ndisagree about the ranking of the candidates, there is no obvious\ncandidate that best represents the group’s opinion. If there were\nonly two candidates to choose from, there is a very straightforward\nanswer: The winner should be the candidate or alternative that is supported\nby more than 50 percent of the voters (cf. the discussion below about\nMay’s Theorem in Section 4.2). However, if there are more than two\ncandidates, as in the above example, the statement “the\ncandidate that is supported by more than 50 percent of the\nvoters” can be interpreted in different ways, leading to\ndifferent ideas about who should win the election. ", "\nOne candidate who, at first sight, seems to be a good choice to win\nthe election is \\(A\\). Candidate \\(A\\) is ranked first by more voters\nthan any other candidate. (\\(A\\) is ranked first by 8 voters,\n\\(B\\) is ranked first by 7; \\(C\\) is ranked first by 6; and\n\\(D\\) is not ranked first by any of the voters.) Of course, 13 people\nrank \\(A\\) last. So, while more voters rank \\(A\\) first than\nany other candidate, more than half of the voters rank \\(A\\) last.\nThis suggests that \\(A\\) should not be elected. ", "\nNone of the voters rank \\(D\\) first. This fact alone does not rule out\n\\(D\\) as a possible winner of the election. However, note that\nevery voter ranks candidate \\(B\\) above candidate \\(D\\). While this\ndoes not mean that \\(B\\) should necessarily win the election, it does\nsuggest that \\(D\\) should not win the election. ", "\nThe choice, then, boils down to \\(B\\) and \\(C\\). It turns out that there are good\narguments for each of \\(B\\) and \\(C\\) to be elected. The debate about\nwhich of \\(B\\) or \\(C\\) should be elected started in the 18th-century\nas an argument between the two founding fathers of voting theory,\nJean-Charles de Borda (1733–1799) and M.J.A.N. de Caritat,\nMarquis de Condorcet (1743–1794). For a history of voting theory\nas an academic discipline, including Condorcet’s and Borda’s writings,\nsee McLean and Urken (1995). I sketch the intuitive arguments for the\nelection of \\(B\\) and \\(C\\) below.", "\nCandidate \\(C\\) should win. Initially, this might seem like\nan odd choice since both \\(A\\) and \\(B\\) receive more first place\nvotes than \\(C\\) (only 6 voters rank \\(C\\) first while 8 voters rank \\(A\\) \nfirst and 7 voters rank \\(B\\) first). However, note \nhow the population would vote in the various two-way elections comparing \n\\(C\\) with each of the other candidates: ", "\nCondorcet’s idea is that \\(C\\) should be declared the winner since she beats\nevery other candidate in a one-on-one election. A candidate with this\nproperty is called a Condorcet winner. We can similarly define\na Condorcet loser. In fact, in the above example, candidate\n\\(A\\) is the Condorcet loser since she loses to every other candidate\nin a one-on-one election.", "\nCandidate \\(B\\) should win. Consider \\(B\\)’s performance in\nthe one-on-one elections. ", "\nCandidate \\(B\\) performs the same as \\(C\\) in a head-to-head election\nwith \\(A\\), loses to \\(C\\) by only one vote and beats \\(D\\) in a\nlandslide (everyone prefers \\(B\\) over \\(D\\)). Borda suggests that we should\ntake into account all of these facts when determining which\ncandidate best represents the overall group opinion. To do this, Borda \nassigns a score to each candidate that reflects how much support he or she has \namong the electorate. Then, the\ncandidate with the largest score is declared the winner. One way to\ncalculate the score for each candidate is as follows (I will give an\nalternative method, which is easier to use, in the next section): ", "\nThe candidate with the highest score (in this case, \\(B\\)) is the one\nwho should be elected. ", "Both Condorcet and Borda suggest comparing candidates in\none-on-one elections in order to determine the winner. While Condorcet\ntallies how many of the head-to-head races each candidate wins, Borda\nsuggests that one should look at the margin of victory or loss. \nThe debate about whether to elect the Condorcet winner or the Borda\nwinner is not settled. Proponents of electing the Condorcet winner\ninclude Mathias Risse (2001, 2004, 2005) and Steven Brams (2008);\nProponents of electing the Borda winner include Donald Saari (2003,\n2006) and Michael Dummett (1984). See Section 3.1.1\nfor further issues comparing the Condorcet and Borda winners. \n", "\nThe take-away message from this discussion is that in many election\nscenarios with more than two candidates, there may not always be one\nobvious candidate that best reflects the overall group opinion. The\nremainder of this entry will discuss different methods, or procedures,\nthat can be used to determine the winner(s) given the a group of\nvoters’ opinions. Each of these methods is intended to be an answer to\nthe following question: ", "\nGiven a group of people faced with some decision, how should a central\nauthority combine the individual opinions so as to best reflect the\n“overall group opinion”?\n", "\nA complete analysis of this question would incorporate a number of\ndifferent issues ranging from central topics in political philosophy\nabout the nature of democracy and the “will of the people”\nto the psychology of decision making. In this article, I focus on one\naspect of this question: the formal analysis of algorithms that aggregate \nthe opinions of a group of voters (i.e., voting methods). Consult, for \nexample, Riker 1982, Mackie 2003, and Christiano 2008 for a more comprehensive \nanalysis of the above question, incorporating many of the issues raised in \nthis article. " ], "section_title": "1. The Problem: Who Should be Elected? ", "subsections": [ { "content": [ "\nIn this article, I will keep the formal details to a minimum; however,\nit is useful at this point to settle on some terminology. Let \\(V\\)\nand \\(X\\) be finite sets. The elements of \\(V\\) are called voters and\nI will use lowercase letters \\(i, j, k, \\ldots\\) or integers \\(1, 2,\n3, \\ldots\\) to denote them. The elements of \\(X\\) are called\ncandidates, or alternatives, and I will use uppercase letters \\(A, B,\nC, \\ldots \\) to denote them. ", "\nDifferent voting methods require different types of information from\nthe voters as input. The input requested from the voters are called\nballots. One standard example of a ballot is a ranking\nof the set of candidates. Formally, a ranking of \\(X\\) is a relation\n\\(P\\) on \\(X\\), where \\(Y\\mathrel{P} Z\\) means that “\\(Y\\) is\nranked above \\(Z\\),” satisfying three constraints: (1) \\(P\\) is\ncomplete: any two distinct candidates are ranked (for all\ncandidates \\(Y\\) and \\(Z\\), if \\(Y\\ne Z\\), then either \\(Y\\mathrel{P}\nZ\\) or \\(Z\\mathrel{P} Y\\)); (2) \\(P\\) is transitive: if a\ncandidate \\(Y\\) is ranked above a candidate \\(W\\) and \\(W\\) is\nranked above a candidate \\(Z\\), then \\(Y\\) is ranked above\n\\(Z\\) (for all\ncandidates \\(Y, Z\\), and \\(W\\), if \\(Y\\mathrel{P} W\\) and \\(W\\mathrel{P} Z\\), then \\(Y\\mathrel{P} Z\\)); and (3) \\(P\\) is irreflexive: no candidate is ranked\nabove itself (there is no candidate \\(Y\\) such that \\(Y\\mathrel{P}\nY\\)). For example, suppose that there are three candidates \\(X =\\{A,\nB, C\\}\\). Then, the six possible rankings of \\(X\\) are listed in the\nfollowing table: ", "\nI can now be more precise about the definition of a Condorcet winner\n(loser). Given a ranking from each voter, the majority\nrelation orders the candidates in terms of how they perform in\none-on-one elections. More precisely, for candidates \\(Y\\) and \\(Z\\),\nwrite \\(Y \\mathrel{>_M} Z\\), provided that more voters rank candidate\n\\(Y\\) above candidate \\(Z\\) than the other way around. So, if the\ndistribution of rankings is given in the above table, we have: ", "\nA candidate \\(Y\\) is called the Condorcet winner in an election\nscenario if \\(Y\\) is the maximum of the majority ordering \\(>_M\\) for\nthat election scenario (that is, \\(Y\\) is the Condorcet winner if\n\\(Y\\mathrel{>_M} Z\\) for all other candidates \\(Z\\)). The Condorcet\nloser is the candidate that is the minimum of the majority\nordering. ", "\nRankings are one type of ballot. In this article, we will see examples\nof other types of ballots, such as selecting a single candidate,\nselecting a subset of candidates or assigning grades to candidates.\nGiven a set of ballots \\(\\mathcal{B}\\), a profile for a set of\nvoters specifies the ballot selected by each voter. Formally, a\nprofile for set of voters \\(V=\\{1,\\ldots, n\\}\\) and a set of ballots\n\\(\\mathcal{B}\\) is a sequence \\(\\bb=(b_1,\\ldots, b_n)\\), where\nfor each voter \\(i\\), \\(b_i\\) is the ballot from \\(\\mathcal{B}\\)\nsubmitted by voter \\(i\\). ", "\nA voting method is a function that assigns to each possible\nprofile a group decision. The group decision may be a single\ncandidate (the winning candidate), a set of candidates (when ties are\nallowed), or an ordering of the candidates (possibly allowing ties). \nNote that since a profile identifies the voter associated with each ballot, a\n voting method may take this information into account. This means that\n voting methods can be designed that select a winner (or winners) based only\n on the ballots of some subset of voters while ignoring all the other voters’ ballots. \n An extreme example of this is the so-called Arrovian dictatorship for voter \\(d\\) \n that assigns to each profile the candidate ranked first by \\(d\\). \n A natural way to rule out these types of voting methods is to require that \n a voting method is anonymous: the group decision should \n depend only on the number of voters that chose each ballot. This means that \n if two profiles are permutations of each other, then a voting method that is \n anonymous must assign the same group decision to both profiles. When studying \n voting methods that are anonymous, it is convenient to assume the inputs are anonymized\nprofiles. An anonymous profile for a set of ballots\n\\(\\mathcal{B}\\) is a function from \\(\\mathcal{B}\\) to the set of\nintegers \\(\\mathbb{N}\\). The election scenario discussed in the\nprevious section is an example of an anonymized profile (assuming that\neach ranking not displayed in the table is assigned the number 0). In\nthe remainder of this article (unless otherwise specified), I will\nrestrict attention to anonymized profiles. \n ", "\nI conclude this section with a few comments on the relationship\nbetween the ballots in a profile and the voters’ opinions about the\ncandidates. Two issues are important to keep in mind. First, the\nballots used by a voting method are intended to reflect some\naspect of the voters’ opinions about the candidates. Voters may choose\na ballot that best expresses their personal preference about the set\nof candidates or their judgements about the relative strengths of the\ncandidates. A common assumption in the voting theory literature is\nthat a ranking of the set of candidates expresses a voter’s\nordinal preference ordering over the set of candidates (see\nthe entry on preferences, Hansson and Grüne-Yanoff 2009, for an\nextended discussion of issues surrounding the formal modeling of\npreferences). Other types of ballots represent information that cannot\nbe inferred directly from a voter’s ordinal preference\nordering, for example, by describing the intensity of a\npreference for a particular candidate (see Section 2.3). Second, it is\nimportant to be precise about the type of considerations voters take\ninto account when selecting a ballot. One approach is to assume that\nvoters choose sincerely by selecting the ballot that best\nreflects their opinion about the the different candidates. A second\napproach assumes that the voters choose strategically. In\nthis case, a voter selects a ballot that she expects to lead\nto her most desired outcome given the information she has about how\nthe other members of the group will vote. Strategic voting is an\nimportant topic in voting theory and social choice theory (see Taylor\n2005 and Section 3.3 of List 2013 for a discussion and pointers to the \nliterature), but in this article, unless otherwise stated, I assume \nthat voters choose sincerely (cf. Section 4.1)." ], "subsection_title": "1.1 Notation" } ] }, { "main_content": [ "\nA quick survey of elections held in different democratic societies\nthroughout the world reveals a wide variety of voting methods. In this\nsection, I discuss some of the key methods that have been analyzed in\nthe voting theory literature. These methods may be of interest because\nthey are widely used (e.g., Plurality Rule or Plurality Rule with\nRunoff) or because they are of theoretical interest (e.g., Dodgson’s\nmethod). ", "\nI start with the most widely used method:", "\nPlurality Rule:\n\nEach voter selects one candidate (or none if voters can abstain), and\nthe candidate(s) with the most votes win.\n", "\nPlurality rule (also called First Past the Post) is a very\nsimple method that is widely used despite its many problems. The most\npervasive problem is the fact that plurality rule can elect a\nCondorcet loser. Borda (1784) observed this phenomenon in the 18th\ncentury (see also the example from Section 1). ", "\nCandidate \\(A\\) is the Condorcet loser (both \\(B\\) and \\(C\\) beat\ncandidate \\(A\\), 13 – 8); however, \\(A\\) is the plurality rule\nwinner (assuming the voters vote for the candidate that they rank first). \nIn fact, the plurality ranking (\\(A\\) is first with 8\nvotes, \\(B\\) is second with 7 votes and \\(C\\) is third with 6\nvotes) reverses the majority ordering \\(C\\mathrel{>_M} B\\mathrel{>_M}\nA\\). See Laslier 2012 for further criticisms of Plurality Rule and\ncomparisons with other voting methods discussed in this article. One\nresponse to the above phenomenon is to require that candidates pass a\ncertain threshold to be declared the winner. ", "\nQuota Rule:\n\nSuppose that \\(q\\), called the quota, is any number between 0\nand 1. Each voter selects one candidate (or none if voters can\nabstain), and the winners are the candidates that receive at least\n\\(q \\times \\# V\\) votes, where \\(\\# V\\) is the number of voters. \nMajority Rule is a quota rule with \\(q=0.5\\) (a candidate is the\nstrict or absolute majority winner if that candidate\nreceives strictly more than \\(0.5 \\times \\# V\\) votes). Unanimity\nRule is a quota rule with \\(q=1\\).\n", "\nAn important problem with quota rules is that they do not identify a\nwinner in every election scenario. For instance, in the above election\nscenario, there are no majority winners since none of the candidates\nare ranked first by more than 50% of the voters. ", "\nA criticism of both plurality and quota rules is that they severely\nlimit what voters can express about their opinions of the candidates.\nIn the remainder of this section, I discuss voting methods that use\nballots that are more expressive than simply selecting a single\ncandidate. Section 2.1 discusses voting methods that require voters to\nrank the alternatives. Section 2.2 discusses voting methods that\nrequire voters to assign grades to the alternatives (from some fixed\nset of grades). Finally, Section 2.3 discusses two voting methods in\nwhich the voters may have different levels of influence on the group\ndecision. In this article, I focus on voting methods that either are\nfamiliar or help illustrate important ideas. Consult Brams and\nFishburn 2002, Felsenthal 2012, and Nurmi 1987 for discussions of\nvoting methods not covered in this article. " ], "section_title": "2. Examples of Voting Methods ", "subsections": [ { "content": [ "\nThe voting methods discussed in this section require the voters to\nrank the candidates (see section 1.1 for the definition of a\nranking). Providing a ranking of the candidates is much more\nexpressive than simply selecting a single candidate. However,\nranking all of the candidates can be very demanding,\nespecially when there is a large number of them, since it can be\ndifficult for voters to make distinctions between all the\ncandidates. The most well-known example of a voting method that uses\nthe voters’ rankings is Borda Count: ", "\nBorda Count:\n\nEach voter provides a ranking of the candidates. Then, a score (the\nBorda score) is assigned to each candidate by a voter as follows: If\nthere are \\(n\\) candidates, give \\(n-1\\) points to the candidate ranked\nfirst, \\(n-2\\) points to the candidate ranked second,…, 1 point to\nthe candidate ranked second to last and 0 points to candidate ranked\nlast. So, the Borda score of candidate \\(A\\), denoted \\(\\BS(A)\\), is\ncalculated as follows (where \\(\\#U\\) denotes the number elements in\nthe set \\(U)\\):\n\n\\[\\begin{align}\n\\BS(A) =\\ &(n-1)\\times \\# \\{i\\ |\\ i \\text{ ranks \\(A\\) first}\\}\\\\\n &+ (n-2)\\times \\# \\{i\\ |\\ i \\text{ ranks \\(A\\) second}\\} \\\\\n &+ \\cdots \\\\\n &+ 1\\times \\# \\{i\\ |\\ i \\text{ ranks \\(A\\) second to last}\\}\\\\\n &+ 0\\times \\# \\{i\\ |\\ i \\text{ ranks \\(A\\) last}\\} \n\\end{align}\\]\n\nThe candidate with the highest Borda score wins.\n", "\nRecall the example discussed in the introduction to Section 1. For\neach alternative, the Borda scores can be calculated using the above\nmethod: ", "\nBorda Count is an example of a scoring rule. A scoring rule is\nany method that calculates a score based on weights assigned to\ncandidates according to where they fall in the voters’ rankings. That\nis, a scoring rule for \\(n\\) candidates is defined as follows: Fix a\nsequence of numbers \\((s_1, s_2, \\ldots, s_n)\\) where \\(s_k\\ge\ns_{k+1}\\) for all \\(k=1,\\ldots, n-1\\). For each \\(k\\),  \\(s_k \\)\nis the score assigned to a alternatives ranked in position \\(k\\).\nThen, the score for alternative \\(A\\), denoted \\(Score(A)\\), is\ncalculated as follows:", "\nBorda count for \\(n\\) alternatives uses scores \\((n-1, n-2, \\ldots,\n0)\\) (call \\(\\BS(X)\\) the Borda score for candidate \\(X\\)). \nNote that Plurality Rule can be viewed as a scoring rule that\nassigns 1 point to the first ranked candidate and 0 points to the\nother candidates. So, the plurality score of a candidate \\(X\\) is the number \nof voters that rank \\(X\\) first. Building on this idea, \\(k\\)-Approval Voting\nis a scoring method that gives 1 point to each candidate that is\nranked in position \\(k\\) or higher, and 0 points to all other\ncandidates. To illustrate \\(k\\)-Approval Voting, consider the\nfollowing election scenario: ", "\n Note that the Condorcet winner is \\(A\\), so none of the above\nmethods guarantee that the Condorcet winner is elected\n(whether \\(A\\) is elected using 1-Approval or 3-Approval depends on\nthe tie-breaking mechanism that is used). ", "\nA second way to make a voting method sensitive to more than the\nvoters’ top choice is to hold “multi-stage” elections. The\nidea is to successively remove candidates that perform poorly in the\nelection until there is one candidate that is ranked first by more\nthan 50% of the voters (i.e., there is a strict majority winner). The\ndifferent stages can be actual “runoff” elections in which\nvoters are asked to evaluate a reduced set of candidates; or they can\nbe built in to the way the winner is calculated by asking voters to\nsubmit rankings over the set of all candidates. The first example of a\nmulti-stage method is used to elect the French president. ", "\nPlurality with Runoff:\n\nStart with a plurality vote to determine the top two candidates (the\ncandidates ranked first and second according to their plurality scores).\nIf a candidate is ranked first by more than 50% of the voters, then\nthat candidate is declared the winner. If there is no candidate with\na strict majority of first place votes, then there is a runoff\nbetween the top two candidates (or more if there are ties). The\ncandidate(s) with the most votes in the runoff elections is(are) declared the\nwinner(s).\n", "\nRather than focusing on the top two candidates, one can also\niteratively remove the candidate(s) with the fewest first-place votes:\n", "\nThe Hare Rule:\n\nThe ballots are rankings of the candidates. If a candidate is ranked\nfirst by more than 50% of the voters, then that candidate is declared\nthe winner. If there is no candidate with a strict majority of first\nplace votes, repeatedly delete the candidate or candidates that\nreceive the fewest first-place votes (i.e., the candidate(s) with the lowest plurality \nscore(s)). The first candidate to be ranked\nfirst by strict majority of voters is declared the winner (if there is\nno such candidate, then the remaining candidate(s) are declared the\nwinners).\n", "\n\t\nThe Hare Rule is also called Ranked-Choice Voting, Alternative Vote, and \nInstant Runoff. If there are only three candidates, then the above two voting methods\nare the same (removing the candidate with the lowest plurality score is\nthe same as keeping the two candidates with highest and second-highest plurality score). The following example\nshows that they can select different winners when there are more than\nthree candidates: ", "\nCandidate \\(A\\) is the Plurality with Runoff winner: Candidates \\(A\\)\nand \\(B\\) are the top two candidates, being ranked first by 7 and 5\nvoters, respectively. In the runoff election (using the rankings from\nthe above table), the groups voting for candidates \\(C\\) and \\(D\\)\ntransfer their support to candidates \\(B\\) and \\(A,\\) respectively,\nwith \\(A\\) winning 10 – 9. ", "\nCandidate \\(D\\) is the Hare Rule winner: In the first round, candidate\n\\(C\\) is eliminated since she is only ranked first by 3 voters. This\ngroup’s votes are transferred to \\(D\\), giving him 7 votes. This means\nthat in the second round, candidate \\(B\\) is ranked first by the\nfewest voters (5 voters rank \\(B\\) first in the profile with candidate\n\\(C\\) removed), and so is eliminated. After the elimination of\ncandidate \\(B\\), candidate \\(D\\) has a strict majority of the\nfirst-place votes: 12 voters ranking him first (note that in this\nround the group in the second column transfers all their votes to\n\\(D\\) since \\(C\\) was eliminated in an earlier round). ", "\nThe core idea of multi-stage methods is to successively remove\ncandidates that perform \"poorly\" in an election. For the Hare Rule,\nperforming poorly is interpreted as receiving the fewest first place\nvotes. There are other ways to identify \"poorly performing\" candidates\nin an election scenario. For instance, the Coombs Rule successively\nremoves candidates that are ranked last by the most voters (see\nGrofman and Feld 2004 for an overview of Coombs Rule). ", "\nCoombs Rule:\n\nThe ballots are rankings of the candidates. If a candidate is ranked\nfirst by more than 50% of the voters, then that candidate is declared\nthe winner. If there is no candidate with a strict majority of first\nplace votes, repeatedly delete the candidate or candidates that\nreceive the most last-place votes. The first candidate to be ranked\nfirst by a strict majority of voters is declared the winner (if there is\nno such candidate, then the remaining candidate(s) are declared the\nwinners).\n", "\nIn the above example, candidate \\(B\\) wins the election using Coombs\nRule. In the first round, \\(A\\), with 9 last-place votes, is\neliminated. Then, candidate \\(B\\) receives 12 first-place votes, which\nis a strict majority, and so is declared the winner. ", " There is a technical issue that is important to keep in mind regarding \n\tthe above definitions of the multi-stage voting methods. When identifying \n\tthe poorly performing candidates in each round, there may be ties (i.e., there \nmay be more than one candidate with the lowest plurality score or more than one candidate\nranked last by the most voters). In the above definitions, I assume that all of the poorly \nperforming candidates will be removed in each round. An alternative approach would use a tie-breaking rule to select one of the poorly performing candidates to be removed at each round. \n" ], "subsection_title": "2.1 Ranking Methods: Scoring Rules and Multi-Stage Methods" }, { "content": [ "\nThe voting methods discussed in this section can be viewed as\ngeneralizations of scoring methods, such as Borda Count. In a scoring\nmethod, a voter’s ranking is an assignment of grades (e.g.,\n\"1st place\", \"2nd place\", \"3rd place\", ... , \"last place\") to the\ncandidates. Requiring voters to rank all the candidates means that (1)\nevery candidate is assigned a grade, (2) there are the same number of\npossible grades as the number of candidates, and (3) different\ncandidates must be assigned different grades. In this section, we drop\nassumptions (2) and (3), assuming a fixed number of grades for every\nset of candidates and allowing different candidates to be assigned the\nsame grade. ", "\nThe first example gives voters the option to either select a candidate\nthat they want to vote for (as in plurality rule) or to\nselect a candidate that they want to vote against.", "\nNegative Voting:\n\nEach voter is allowed to choose one candidate to either vote\nfor (giving the candidate one point) or to vote\nagainst (giving the candidate –1 points). The winner(s)\nis(are) the candidate(s) with the highest total number of points (i.e., the candidate\nwith the greatest score, where the score is the total number of positive votes minus the total \nnumber of negative votes).\n", "\nNegative voting is tantamount to allowing the voters to support either\na single candidate or all but one candidate (taking a point away from\na candidate \\(C\\) is equivalent to giving one point to all candidates\nexcept \\(C\\)). That is, the voters are asked to choose a set of\ncandidates that they support, where the choice is between sets\nconsisting of a single candidate or sets consisting of all except one\ncandidate. The next voting method generalizes this idea by allowing\nvoters to choose any subset of candidates: ", "\nApproval Voting:\n\nEach voter selects a subset of the candidates (where the\nempty set means the voter abstains) and the candidate(s) with selected by \nthe most voters wins. \n", "\nIf a candidate \\(X\\) is in the set of candidates selected by \na voter, we say that the voter approves of candidate \\(X\\). Then, the approval winner is the \ncandidate with the most approvals. Approval voting has been extensively discussed by Steven Brams and Peter Fishburn (Brams and Fishburn 2007; Brams 2008). See, also, the\nrecent collection of articles devoted to approval voting (Laslier and\nSanver 2010). ", "\nApproval voting forces voters to think about the decision problem\ndifferently: They are asked to determine which candidates they\napprove of rather than selecting a single candidate to voter\nfor or determining the relative ranking of the candidates.\nThat is, the voters are asked which candidates are above a certain\n“threshold of acceptance”. Ranking a set of candidates and\nselecting the candidates that are approved are two different aspects\nof a voters overall opinion about the candidates. They are related but\ncannot be derived from each other. See Brams and Sanver 2009, for\nexamples of voting methods that ask voters to both select a set of\ncandidates that they approve and to (linearly) rank the\ncandidates. ", "\nApproval voting is a very flexible method. Recall the election\nscenario illustrating the \\(k\\)-Approval Voting methods: ", "\nIn this election scenario, \\(k\\)-Approval for \\(k=1,2,3\\) cannot\nguarantee that the Condorcet winner \\(A\\) is elected. The Approval\nballot \\((\\{A\\},\\{B\\}, \\{A, C\\})\\) does elect the Condorcet winner. In\nfact, Brams (2008, Chapter 2) proves that if there is a unique\nCondorcet winner, then that candidate may be elected under approval\nvoting (assuming that all voters vote sincerely: see Brams\n2008, Chapter 2, for a discussion). Note that approval voting may also\nelect other candidates (perhaps even the Condorcet loser). Whether\nthis flexibility of Approval Voting should be seen as a virtue or a\nvice is debated in Brams, Fishburn and Merrill 1988a, 1988b and Saari\nand van Newenhizen 1988a, 1988b. ", "\nApproval Voting asks voters to express something about their\nintensity of preference for the candidates by assigning one\nof two grades: \"Approve\" or \"Don’t Approve\". Expanding on this idea,\nsome voting methods assume that there is a fixed set of grades, or a\ngrading language, that voters can assign to each candidate.\nSee Chapters 7 and 8 from Balinksi and Laraki 2010 for examples and a\ndiscussion of grading languages (cf. Morreau 2016). ", "\nThere are different ways to determine the winner(s) given a profile of\nballots that assign grades to each candidate. The main approach is to\ncalculate a \"group\" grade for each candidate, then select the\ncandidate with the best overall group grade. In order to calculate a\ngroup grade for each candidate, it is convenient to use numbers for\nthe grading language. Then, there are two natural ways to determine\nthe group grade for a candidate: calculating the mean, or average, of\nthe grades or calculating the median of the grades.", "\nCumulative Voting:\n\nEach voter is asked to distribute a fixed number of points, say ten,\namong the candidates in any way they please. The candidate(s) with the\nmost total points wins the election.\n", "\nScore Voting (also called Range Voting):\n\nThe grades are a finite set of numbers. The ballots are an assignment\nof grades to the candidates. The candidate(s) with the largest average\ngrade is declared the winner(s).\n", "\nCumulative Voting and Score Voting are similar. The important\ndifference is that Cumulative Voting requires that the sum of the\ngrades assigned to the candidates by each voter is the same. The next\nprocedure, proposed by Balinski and Laraki 2010 (cf. Bassett and\nPersky 1999 and \n the discussion of this method at rangevoting.org),\n selects the candidate(s) with the largest median grade rather\nthan the largest mean grade. ", "\nMajority Judgement:\n\nThe grades are a finite set of numbers (cf. discussion of common grading languages). \nThe ballots are an assignment of grades to the candidates. The candidate(s) \nwith the largest median grade is(are) declared the winner(s). See \nBalinski and Laraki 2007 and 2010 for further refinements of this voting method \nthat use different methods for breaking ties when there are multiple candidates \nwith the largest median grade.\n", "\nI conclude this section with an example that illustrates Score Voting\nand Majority Judgement. Suppose that there are 3 candidates \\(\\{A, B,\nC\\}\\), 5 grades \\(\\{0,1,2,3,4\\}\\) (with the assumption that the larger\nthe number, the higher the grade), and 5 voters. The table below\ndescribes an election scenario. The candidates are listed in the first row.\n Each row describes an assignment of grades to a candidate by a set of voters. ", "\nThe bottom two rows give the mean and median grade for each\ncandidate. Candidate \\(A\\) is the score voting winner with the greatest\nmean grade, and candidate \\(B\\) is the majority judgement winner with\nthe greatest median grade. \n\n", "\nThere are two types of debates about the voting methods introduced in this section. \nThe first concerns the choice of the grading language that voters use \nto evaluate the candidates. Consult Balinski and Laraki 2010 amd Morreau 2016 for an extensive discussion of the types of considerations that influence the choice of a grading language. Brams and Potthoff 2015 argue that two grades, as in Approval Voting, is best to avoid certain paradoxical outcomes. To illustrate, note that, in the above example, if the candidates are ranked by\nthe voters according to the grades that are assigned, then candidate\n\\(C\\) is the Condorcet winner (since 3 voters assign higher grades to\n\\(C\\) than to \\(A\\) or \\(B\\)). However, neither Score Voting nor Majority Judgement selects candidate \\(C\\). \n\n", "\n\nThe second type of debate concerns the method used to calculate the group grade for each candidate (i.e., whether to use the mean as in Score Voting or the median as in Majority Judgement). One important issue is whether voters have an incentive to misrepresent their evaluations of the candidates. Consider the voter in the middle column that assigns the grade of 2 to \\(A\\), 0 to \\(B\\), and 3 to \\(C\\). Suppose that these grades represents the voter’s true evaluations of the candidates. If this voter increases the grade for \\(C\\) to 4 and decreases the grade for \\(A\\) to 1 (and the other voters do not change their grades), then the average grade for \\(A\\) becomes 2.4 and the average grade for \\(C\\) becomes 2.6, which better reflects the voter’s true evaluations of the candidates (and results in \\(C\\) being elected according to Score Voting). Thus, this voter has an incentive to misrepresent her grades. Note that the median grades for the candidates do not change after this voter changes her grades. Indeed, Balinski and Laraki 2010, chapter 10, argue that using the median to assign group grades to candidates encourages voters to submit grades that reflect their true evaluations of the candidates. The key idea of their argument is as follows: If a voter’s true grade matches the median grade for a candidate, then the voter does not have an incentive to assign a different grade. If a voter’s true grade is greater than the median grade for a candidate, then raising the grade will not change the candidate’s grade and lowering the voter’s grade may result in the candidate receiving a grade that is lowering than the voter’s true evaluation. Similarly, if a voter’s true grade is lower than the median grade for a candidate, then lowering the grade will not change the candidate’s grade and raising the voter’s grade may result in the candidate receiving a grade that is higher than the voter’s true evaluation. Thus, if voters are focused on ensuring that the group grades for the candidates best reflects their true evaluations of the candidates, then voters do not have an incentive to misrepresent their grades. However, as pointed out in Felsenthal and Machover 2008 (Example 3.3), voters can manipulate the outcome of an election using Majority Judgement to ensure a preferred candidate is elected (cf. the discussion of strategic voting in Section 4.1 and Section 3.3 of List 2013). Suppose that the voter in the middle column assigns the grade of 4 to candidate \\(A\\), 0 to candidate \\(B\\) and 3 to candidate \\(C\\). Assuming the other voters do not change their grades, the majority judgement winner is now \\(A\\), which the voter ranks higher than the original majority judgement winner \\(B.\\) Consult Balinski and Laraki 2010, 2014 and Edelman 2012b for arguments in favor of electing candidates with the greatest median grade; and Felsenthal and Machover 2008, Gehrlein and Lepelley 2003, and Laslier 2011 for arguments against electing candidates with the greatest median grade. \n \n\n" ], "subsection_title": "2.2 Voting by Grading" }, { "content": [ "\nIn this section, I briefly discuss two new approaches to voting that\ndo not fit nicely into the categories of voting methods introduced in\nthe previous sections. While both of these methods can be used to\nselect representatives, such as a president, the primary application\nis a group of people voting directly on propositions, or referendums.\n", "\nQuadratic Voting: When more than 50% of the voters support an\nalternative, most voting methods will select that alternative. Indeed,\nwhen there are only two alternatives, such as when voting for or\nagainst a proposition, there are many arguments that identify majority\nrule as the best and most stable group decision method (May 1952;\nMaskin 1995). One well-known problem with always selecting the\nmajority winner is the so-called tyranny of the majority. A\ncomplete discussion of this issue is beyond the scope of this article.\nThe main problem from the point of view of the analysis of voting\nmethods is that there may be situations in which a majority of the\nvoters weakly support a proposition while there is a sizable minority\nof voters that have a strong preference against the proposition. ", "\nOne way of dealing with this problem is to increase the quota required\nto accept a proposition. However, this gives too much power to a small\ngroup of voters. For instance, with Unanimity Rule a single voter can\nblock a proposal from being accepted. Arguably, a better solution is\nto use ballots that allow voters to express something about their\nintensity of preference for the alternatives. Setting aside issues\nabout interpersonal comparisons of utility (see, for instance, Hausman\n1995), this is the benefit of using the voting methods discussed in\nSection 2.2, such as Score Voting or Majority Judgement. These voting\nmethods assume that there is a fixed set of grades that the\nvoters use to express their intensity of preference. One challenge is\nfinding an appropriate set of grades for a population of voters. Too\nfew grades makes it harder for a sizable minority with strong\npreferences to override the majority opinion, but too many grades\nmakes it easy for a vocal minority to overrule the majority opinion.\n", "\nUsing ideas from mechanism design (Groves and Ledyard 1977; Hylland and\nZeckhauser 1980), the economist E. Glen Weyl developed a voting method\ncalled Quadratic Voting that mitigates some of the above issues\n(Lalley and Weyl 2018a). The idea is to think of an election as a\nmarket (Posner and Weyl, 2018, Chapter 2). Each voter can purchase\nvotes at a costs that is quadratic in the number of votes. For\ninstance, a voter must pay $25 for 5 votes (either in favor or against\na proposition). After the election, the money collected is distributed\non a pro rata basis to the voters. There are a variety of\neconomic arguments that justify why voters should pay \\(v^2\\) to\npurchase \\(v\\) votes (Lalley and Weyl 2018b; Goeree and Zhang 2017).\nSee Posner and Weyl 2015 and 2017 for further discussion and a\nvigorous defense of the use of Quadratic Voting in national elections. \nConsult Laurence and Sher 2017 for two arguments against the use of Quadratic Voting. \nBoth arguments are derived from the presence of wealth inequality. The first \nargument is that it is ambiguous whether the Quadratic Voting decision really outperforms a decision using majority rule from the perspective of utilitarianism \n(see Driver 2014 and Sinnott-Armstrong 2019 for overviews of utilitarianism). \nThe second argument is that any vote-buying mechanism will have a hard \ntime meeting a legitimacy requirement, familiar from the theory of democratic \ninstitutions (cf. Fabienne 2017). \n\n\n", "\nLiquid Democracy: Using Quadratic Voting, the voters’ opinions\nmay end up being weighted differently: Voters that purchase more of a\nvoice have more influence over the election. There are other reasons\nwhy some voters’ opinions may have more weight than others when making\na decision about some issue. For instance, a voter may have been\nelected to represent a constituency, or a voter may be recognized as\nan expert on the issue under consideration. An alternative approach to\ngroup decision making is direct democracy in which every\ncitizen is asked to vote on every political issue. Asking the citizens\nto vote on every issue faces a number of challenges, \n nicely explained by Green-Armytage (2015, pg. 191):", "\nDirect democracy without any option for representation is problematic.\nEven if it were possible for every citizen to learn everything they\ncould possibly know about every political issue, people who did this\nwould be able to do little else, and massive amounts of time would be\nwasted in duplicated effort. Or, if every citizen voted but most\npeople did not take the time to learn about the issues, the results\nwould be highly random and/or highly sensitive to overly simplistic\npublic relations campaigns. Or, if only a few citizens voted,\nparticular demographic and ideological groups would likely be\nunder-represented\n", "\nOne way to deal with some of the problems raised in the above quote is to \nuse proxy voting, in which voters can delegate their vote \non some issues (Miller 1969). Liquid Democracy is a form of proxy voting \nin which voters can delegate their votes to other voters (ideally, to voters that are\nwell-informed about the issue under consideration). What distinguishes\nLiquid Democracy from proxy voting is that proxies may further\ndelegate the votes entrusted to them. For example, suppose that there\nis a vote to accept or reject a proposition. Each voter is given the\noption to delegate their vote to another voter, called a proxy. The\nproxies, in turn, are given the option to delegate their votes to yet\nanother voter. The voters that decide to not transfer their votes cast\na vote weighted by the number of voters who entrusted them as a proxy,\neither directly or indirectly. ", "\nWhile there has been some discussion of proxy voting in the political\nscience literature (Miller 1969; Alger 2006; Green-Armytage 2015),\nmost studies of Liquid Democracy can be found in the computer science\nliterature. A notable exception is Blum and Zuber 2016 that justifies\nLiquid Democracy, understood as a procedure for democratic\ndecision-making, within normative democratic theory. An overview of\nthe origins of Liquid Democracy and pointers to other online\ndiscussions can be found in Behrens 2017. Formal studies of Liquid\nDemocracy have focused on: the possibility of delegation cycles and\nthe relationship with the theory of judgement aggregation (Christoff\nand Grossi 2017); the rationality of delegating votes (Bloembergen,\nGrossi and Lackner 2018); the potential problems that arise when many\nvoters delegate votes to only a few voters (Kang et al. 2018; Golz et\nal. 2018); and generalizations of Liquid Democracy beyond binary\nchoices (Brill and Talmon 2018; Zhang and Zhou 2017). " ], "subsection_title": "2.3 Quadratic Voting and Liquid Democracy" }, { "content": [ "\nThis section introduced different methods for making a group decision.\nOne striking fact about the voting methods discussed in this section\nis that they can identify different winners given the same collection\nof ballots. This raises an important question: How should we\ncompare the different voting methods? Can we argue that some\nvoting methods are better than others? There are a number of different\ncriteria that can be used to compare and contrast different voting\nmethods: " ], "subsection_title": "2.4 Criteria for Comparing Voting Methods" } ] }, { "main_content": [ "\nIn this section, I introduce and discuss a number of voting\nparadoxes — i.e., anomalies that highlight problems with\ndifferent voting methods. Consult Saari 1995 and Nurmi 1999 for\npenetrating analyses that explain the underlying mathematics behind\nthe different voting paradoxes. " ], "section_title": "3. Voting Paradoxes", "subsections": [ { "content": [ "\nA very common assumption is that a rational preference\nordering must be transitive (i.e., if \\(A\\) is preferred to\n\\(B\\), and \\(B\\) is preferred to \\(C\\), then \\(A\\) must be preferred\nto \\(C\\)). See the entry on preferences (Hansson and Grüne-Yanoff\n2009) for an extended discussion of the rationale behind this\nassumption. Indeed, if a voter’s preference ordering is not\ntransitive, for instance, allowing for cycles (e.g., an ordering of \\(A, B, C\\) with \n\\(A \\succ B \\succ C \\succ A\\), where \\(X\\succ Y\\) means \\(X\\) is strictly preferred to \\(Y\\)), then there is no alternative that the voter can be said to actually support (for each\nalternative, there is another alternative that the voter strictly prefers). Many\nauthors argue that voters with cyclic preference orderings have\ninconsistent opinions about the candidates and should be\nignored by a voting method (in particular, Condorcet\nforcefully argued this point). A key observation of Condorcet (which\nhas become known as the Condorcet Paradox) is that the majority ordering\nmay have cycles (even when all the voters submit rankings of the alternatives). ", "\nCondorcet’s original example was more complicated, but the following\nsituation with three voters and three candidates illustrates the\nphenomenon:", "\nNote that we have: ", "\nThat is, there is a majority cycle \\(A>_M B >_M C >_M A\\). This\nmeans that there is no Condorcet winner. This simple, but fundamental\nobservation has been extensively studied (Gehrlein 2006; Schwartz\n2018). ", "\nThe Condorcet Paradox shows that there may not always be a Condorcet\nwinner in an election. However, one natural requirement for a voting\nmethod is that if there is a Condorcet winner, then that candidate\nshould be elected. Voting methods that satisfy this property are\ncalled Condorcet consistent. Many of the methods introduced\nabove are not Condorcet consistent. I already presented an example\nshowing that plurality rule is not Condorcet consistent (in fact,\nplurality rule may even elect the Condorcet loser). ", "\nThe example from Section 1 shows that Borda Count is not Condorcet\nconsistent. In fact, this is an instance of a general phenomenon that\nFishburn (1974) called Condorcet’s other paradox. Consider the\nfollowing voting situation with 81 voters and three candidates from\nCondorcet 1785. ", "\nThe majority ordering is \\(A >_M B >_M C\\), so \\(A\\) is the Condorcet\nwinner. Using the Borda rule, we have: ", "\nSo, candidate \\(B\\) is the Borda winner. Condorcet pointed out\nsomething more: The only way to elect candidate \\(A\\) using\nany scoring method is to assign more points to candidates\nranked second than to candidates ranked first. Recall that a scoring\nmethod for 3 candidates fixes weights \\(s_1\\ge s_2\\ge s_3\\), where\n\\(s_1\\) points are assigned to candidates ranked 1st, \\(s_2\\) points\nare assigned to candidates ranked 2nd, and \\(s_3\\) points are assigned\nto candidates ranked last. To simplify the calculation, assume that\ncandidates ranked last receive 0 points (i.e., \\(s_3=0\\)). Then, the\nscores assigned to candidates \\(A\\) and \\(B\\) are: ", "\nSo, in order for \\(Score(A) > Score(B)\\), we must have \\((s_1 \\times\n31 + s_2 \\times 39) > (s_1 \\times 39 + s_2 \\times 31)\\), which implies\nthat \\(s_2 > s_1\\). But, of course, it is counterintuitive to give\nmore points for being ranked second than for being ranked first. Peter\nFishburn generalized this example as follows: ", "\nTheorem (Fishburn 1974).\n\nFor all \\(m\\ge 3\\), there is some voting situation with a Condorcet\nwinner such that every scoring rule will have at least\n\\(m-2\\) candidates with a greater score than the Condorcet winner.\n", "\nSo, no scoring rule is Condorcet consistent, but what about other\nmethods? A number of voting methods were devised specifically to\nguarantee that a Condorcet winner will be elected, if one\nexists. The examples below give a flavor of different types of\nCondorcet consistent methods. (See Brams and Fishburn, 2002, and\nFishburn, 1977, for more examples and a discussion of \nCondorcet consistent methods.) ", "\nThe last method was proposed by Charles Dodgson (better known by the\npseudonym Lewis Carroll). Interestingly, this is an example of a\nprocedure in which it is computationally difficult to compute the\nwinner (that is, the problem of calculating the winner is\nNP-complete). See Bartholdi et al. 1989 for a discussion.\n", "\nThese voting methods (and the other Condorcet consistent methods)\nguarantee that a Condorcet winner, if one exists, will be elected.\nBut, should a Condorcet winner be elected? Many people argue\nthat there is something amiss with a voting method that does not\nalways elect a Condorcet winner (if one exists). The idea is that a\nCondorcet winner best reflects the overall group opinion and is\nstable in the sense that it will defeat any challenger in a one-on-one\ncontest using Majority Rule. The most persuasive argument that the\nCondorcet winner should not always be elected comes from the work of\nDonald Saari (1995, 2001). Consider again Condorcet’s example of 81\nvoters. ", "\nThis is another example that shows that Borda’s method need not elect\nthe Condorcet winner. The majority ordering is", "\nwhile the ranking given by the Borda score is ", "\nHowever, there is an argument that candidate \\(B\\) is the best choice\nfor this electorate. Saari’s central observation is to note that the\n81 voters can be divided into three groups:", "\nGroups 1 and 2 constitute majority cycles with the voters evenly\ndistributed among the three possible rankings. Such profiles are\ncalled Condorcet components. These profiles form a\nperfect symmetry among the rankings. So, within each of these groups,\nit is natural to assume that the voters’ opinions cancel each other out; therefore, the decision\nshould depend only on the voters in group 3. In group 3, candidate\n\\(B\\) is the clear winner. ", "\nBalinski and Laraki (2010, pgs. 74–83) have an interesting spin on\nSaari’s argument. Let \\(V\\) be a ranking voting method (i.e., a voting\nmethod that requires voters to rank the alternatives). Say that \\(V\\)\ncancels properly if for all profiles \\(\\bR\\), if \\(V\\)\nselects \\(A\\) as a winner in \\(\\bP\\), then \\(V\\) selects \\(A\\) as\na winner in any profile \\(\\bP+\\bC\\), where \\(\\bC\\) is a\nCondorcet component and \\(\\bP+\\bC\\) is the profile that\ncontains all the rankings from \\(\\bP\\) and \\(\\bC\\). Balinski\nand Laraki (2010, pg. 77) prove that there is no Condorcet consistent\nvoting method that cancels properly. (See the discussion of the\nmultiple districts paradox in Section 3.3 for a proof of a closely\nrelated result.) " ], "subsection_title": "3.1 Condorcet’s Paradox" }, { "content": [ "\nA voting method is monotonic provided that receiving more\nsupport from the voters is always better for a candidate. There are\ndifferent ways to make this idea precise (see Fishburn, 1982, Sanver\nand Zwicker, 2012, and Felsenthal and Tideman, 2013). For instance,\nmoving up in the rankings should not adversely affect a\ncandidate’s chances to win an election. It is easy to see that\nPlurality Rule is monotonic in this sense: The more voters that rank a\ncandidate first, the better chance the candidate has to\nwin. Surprisingly, there are voting methods that do not satisfy this\nnatural property. The most well-known example is Plurality with\nRunoff. Consider the two scenarios below. Note that the only\ndifference between the them is the ranking of the fourth group of\nvoters. This group of two voters ranks \\(B\\) above \\(A\\) above \\(C\\)\nin scenario 1 and swaps \\(B\\) and \\(A\\) in scenario 2 (so, \\(A\\) is\nnow their top-ranked candidate; \\(B\\) is ranked second; and \\(C\\) is\nstill ranked third).\n", "\nIn scenario 1, candidates \\(A\\) and \\(B\\) both have a plurality score\nof 6 while candidate \\(C\\) has a plurality score of 5. So, \\(A\\) and\n\\(B\\) move on to the runoff election. Assuming the voters do not\nchange their rankings, the 5 voters that rank \\(C\\) transfer their\nsupport to candidate \\(A\\), giving her a total of 11 to win the runoff\nelection. However, in scenario 2, even after moving up in the\nrankings of the fourth group (\\(A\\) is now ranked first by this\ngroup), candidate \\(A\\) does not win this election. In fact,\nby trying to give more support to the winner of the election in\nscenario 1, rather than solidifying \\(A\\)’s win, the last\ngroup’s least-preferred candidate ended up winning the election!\nThe problem arises because in scenario 2, candidates \\(A\\) and \\(B\\)\nare swapped in the last group’s ranking. This means that\n\\(A\\)’s plurality score increases by 2 and \\(B\\)’s\nplurality score decreases by 2. As a consequence, \\(A\\) and \\(C\\) move\non to the runoff election rather than \\(A\\) and \\(B\\). Candidate\n\\(C\\) wins the runoff election with 9 voters that rank \\(C\\) above\n\\(A\\) compared to 8 voters that rank \\(A\\) above \\(C\\).\n", "\nThe above example is surprising since it shows that, when using\nPlurality with Runoff, it may not always be beneficial for a candidate\nto move up in some of the voter’s rankings. The other voting methods\nthat violate monotonicity include Coombs Rule, Hare Rule, Dodgson’s\nMethod and Nanson’s Method. See Felsenthal and Nurmi 2017 for further \ndiscussion of voting methods that are not monotonic. " ], "subsection_title": "3.2 Failures of Monotonicity" }, { "content": [ "\nIn this section, I discuss two related paradoxes that involve changes\nto the population of voters. ", "\nNo-Show Paradox: One way that a candidate may receive\n“more support” is to have more voters show up to an\nelection that support them. Voting methods that do not satisfy this\nversion of monotonicity are said to be susceptible to the no-show\nparadox (Fishburn and Brams 1983). Suppose that there are 3\ncandidates and 11 voters with the following rankings: \n", "\nIn the first round, candidates \\(A\\) and \\(C\\) are both ranked first\nby 4 voters while \\(B\\) is ranked first by only 3 voters. So, \\(A\\)\nand \\(C\\) move to the runoff round. In this round, the voters in the\nsecond column transfer their votes to candidate \\(C\\), so candidate\n\\(C\\) is the winner beating \\(A\\) 7-4. Suppose that 2 voters in the\nfirst group do not show up to the election: ", "\nIn this election, candidate \\(A\\) has the lowest plurality score in\nthe first round, so candidates \\(B\\) and \\(C\\) move to the runoff\nround. The first group’s votes are transferred to \\(B\\), so \\(B\\) is\nthe winner beating \\(C\\) 5-4. Since the 2 voters that did not show up\nto this election rank \\(B\\) above \\(C\\), they prefer the outcome of\nthe second election in which they did not participate! ", "\nPlurality with Runoff is not the only voting method that is\nsusceptible to the no-show paradox. The Coombs Rule, Hare Rule and\nMajority Judgement (using the tie-breaking mechanism from Balinski and Laraki 2010)\nare all susceptible to the no-show paradox. It turns out that always\nelecting a Condorcet winner, if one exists, makes a voting method\nsusceptible to the above failure of monotonicity.", "\nTheorem (Moulin 1988).\n\nIf there are four or more candidates, then every Condorcet consistent\nvoting method is susceptible to the no-show paradox.\n", "\nSee Perez 2001, Campbell and Kelly 2002, Jimeno et al.\n2009, Duddy 2014, Brandt et al. 2017, 2019, and Nunez and Sanver 2017\nfor further discussions and generalizations of this result. ", "\nMultiple Districts Paradox: Suppose that a population is\ndivided into districts. If a candidate wins each of the districts, one\nwould expect that candidate to win the election over the entire\npopulation of voters (assuming that the two districts divide the set of voters \ninto disjoint sets). This is certainly true for Plurality Rule: If a\ncandidate is ranked first by the most voters in each of\nthe districts, then that candidate will also be ranked first by a\nthe most voters over the entire population. Interestingly, this is\nnot true for all voting methods (Fishburn and Brams 1983). The example\nbelow illustrates the paradox for Coombs Rule. ", "\nCandidate \\(B\\) wins both districts: ", "\nCombining the two districts gives the following table:", "\nThere are 15 total voters in the combined districts. None of the\ncandidates are ranked first by 8 or more of the voters. Candidate\n\\(C\\) receives the most last-place votes, so is eliminated in the\nfirst round. In the second round, candidate \\(A\\) is beats candidate\n\\(B\\) by 1 vote (8 voters rank \\(A\\) above \\(B\\) and 7 voters rank\n\\(B\\) above \\(A\\)), and so is declared the winner. Thus, even though\n\\(B\\) wins both districts, candidate \\(A\\) wins the election when the\ndistricts are combined. ", "\nThe other voting methods that are susceptible to the\nmultiple-districts paradox include Plurality with Runoff, The Hare\nRule, and Majority Judgement. Note that these methods are also\nsusceptible to the no-show paradox. As is the case with the no-show\nparadox, every Condorcet consistent voting method is susceptible to\nthe multiple districts paradox (see Zwicker, 2016, Proposition 2.5). I\nsketch the proof of this from Zwicker 2016 (pg. 40) since it adds to\nthe discussion at the end of Section 3.1 about whether the Condorcet\nwinner should be elected. ", "\nSuppose that \\(V\\) is a voting method that always selects the\nCondorcet winner (if one exists) and that \\(V\\) is not susceptible to\nthe multiple-districts paradox. This means that if a candidate \\(X\\)\nis among the winners according to \\(V\\) in each of two districts, then\n\\(X\\) must be among the winners according to \\(V\\) in the combined\ndistricts. Consider the following two districts.", "\nNote that in district 2 candidate \\(B\\) is the Condorcet winner, so\nmust be the only winner according to \\(V\\). In district 1, there are\nno Condorcet winners. If candidate \\(B\\) is among the winners\naccording to \\(V\\), then, in order to not be susceptible to the\nmultiple districts paradox, \\(B\\) must be among the winners in the\ncombined districts. In fact, since \\(B\\) is the only winner in\ndistrict 2, \\(B\\) must be the only winner in the combined districts.\nHowever, in the combined districts, candidate \\(A\\) is the Condorcet\nwinner, so must be the (unique) winner according to \\(V\\). This is a\ncontradiction, so \\(B\\) cannot be among the winners according to \\(V\\)\nin district 1. A similar argument shows that neither \\(A\\) nor \\(C\\)\ncan be among the winners according to \\(V\\) in district 1 by swapping\n\\(A\\) and \\(B\\) in the first case and \\(B\\) with \\(C\\) in the second\ncase in the rankings of the voters in district 2. Since \\(V\\) must\nassign at least one winner to every profile, this is a contradiction;\nand so, \\(V\\) is susceptible to the multiple districts paradox. ", "\nOne last comment about this paradox: It is an example of a more\ngeneral phenomenon known as Simpson’s Paradox (Malinas and Bigelow\n2009). See Saari (2001, Section 4.2) for a discussion of Simpson’s\nParadox in the context of voting theory. " ], "subsection_title": "3.3 Variable Population Paradoxes" }, { "content": [ "\nThe paradox discussed in this section, first introduced by Brams,\nKilgour and Zwicker (1998), has a somewhat different structure from\nthe paradoxes discussed above. Voters are taking part in a\nreferendum, where they are asked their opinion directly about\nvarious propositions (cf. the discussion of Quadratic Voting and Liquid Democracy\n in Section 2.3). So, voters must select either “yes”\n(Y) or “no” (N) for each proposition. Suppose that there\nare 13 voters who cast the following votes for the three propositions (so\nvoters can cast one of eight possible votes): ", "\nWhen the votes are tallied for each proposition separately, the\noutcome is N for each proposition (N wins 7–6 for all three\npropositions). Putting this information together, this means that NNN\nis the outcome of this election. However, there is no support\nfor this outcome in this population of voters. This raises an important \nquestion about what outcome reflects the group opinion: Viewing each proposition \nseparately, there is clear support for N on each proposition; however, \nthere is no support for the entire package of N for all propositions. \nBrams et al. (1998, pg. 234) nicely summarise the issue as follows: ", "\nThe paradox does not just highlight problems of aggregation and\npackaging, however, but strikes at the core of social\nchoice—both what it means and how to uncover it. In our view,\nthe paradox shows there may be a clash between two different meanings\nof social choice, leaving unsettled the best way to uncover what this\nelusive quantity is.\n", "\nSee Scarsini 1998, Lacy and Niou 2000, Xia et al. 2007, and Lang and Xia 2009 for further discussion of this paradox. \n", "\nA similar issue is raised by Anscombe’s paradox (Anscombe\n1976), in which: ", "\nIt is possible for a majority of voters to be on the losing side of a\nmajority of issues.\n", "\nThis phenomenon is illustrated by the following example with five\nvoters voting on three different issues (the voters either vote\n‘yes’ or ‘no’ on the different issues).", "\nHowever, a majority of the voters (voters 1, 2 and 3) do not\nsupport the majority outcome on a majority of the issues (note that\nvoter 1 does not support the majority outcome on issues 2 and 3; voter\n2 does not support the majority outcome on issues 1 and 3; and voter 3\ndoes not support the majority outcome on issues 1 and 2)! ", "\nThe issue is more interesting when the voters do not vote directly on\nthe issues, but on candidates that take positions on the different\nissues. Suppose there are two candidates \\(A\\) and \\(B\\) who take the\nfollowing positions on the three issues: ", "\nCandidate \\(A\\) takes the majority position, agreeing with a majority\nof the voters on each issue, and candidate \\(B\\) takes the opposite,\nminority position. Under the natural assumption that voters will vote\nfor the candidate who agrees with their position on a majority of the\nissues, candidate \\(B\\) will win the election (each of the voters 1, 2\nand 3 agree with \\(B\\) on two of the three issues, so \\(B\\) wins the\nelection 3–2)! This version of the paradox is known as\nOstrogorski’s Paradox (Ostrogorski 1902). See Kelly 1989; Rae\nand Daudt 1976; Wagner 1983, 1984; and Saari 2001, Section 4.6, for\nanalyses of this paradox, and Pigozzi 2005 for the relationship with \n\tthe judgement aggregation literature (List 2013, Section 5)." ], "subsection_title": "3.4 The Multiple Elections Paradox" } ] }, { "main_content": [], "section_title": "4. Topics in Voting Theory", "subsections": [ { "content": [ "\nIn the discussion above, I have assumed that voters select ballots\nsincerely. That is, the voters are simply trying to\ncommunicate their opinions about the candidates under the constraints\nof the chosen voting method. However, in many contexts, it makes sense to \nassume that voters choose strategically. One need only look to recent\nU.S. elections to see concrete examples of strategic voting. The most\noften cited example is the 2000 U.S. election: Many voters who ranked\nthird-party candidate Ralph Nader first voted for their second choice\n(typically Al Gore). A detailed overview of the literature on\nstrategic voting is beyond the scope of this article (see Taylor 2005 and \nSection 3.3 of List 2013 for discussions and pointers to the relevant literature; also see\nPoundstone 2008 for an entertaining and informative discussion of the\noccurrence of this phenomenon in many actual elections). I will\nexplain the main issues, focusing on specific voting rules. ", "\nThere are two general types of manipulation that can be studied in the\ncontext of voting. The first is manipulation by a moderator or outside\nparty that has the authority to set the agenda or select the voting\nmethod that will be used. So, the outcome of an election is not\nmanipulated from within by unhappy voters, but, rather, it is\ncontrolled by an outside authority figure. To illustrate this\ntype of control, consider a population with three voters whose\nrankings of four candidates are given in the table below: ", "\nNote that everyone prefers candidate \\(B\\) over candidate \\(D\\).\nNonetheless, a moderator can ask the right questions so that candidate\n\\(D\\) ends up being elected. The moderator proceeds as follows: First,\nask the voters if they prefer candidate \\(A\\) or candidate \\(B\\).\nSince the voters prefer \\(A\\) to \\(B\\) by a margin of 2 to 1, the\nmoderator declares that candidate \\(B\\) is no longer in the running.\nThe moderator then asks voters to choose between candidate \\(A\\) and\ncandidate \\(C\\). Candidate \\(C\\) wins this election 2–1, so\ncandidate \\(A\\) is removed. Finally, in the last round the chairman\nasks voters to choose between candidates \\(C\\) and \\(D\\).\nCandidate \\(D\\) wins this election 2–1 and is declared the\nwinner. ", "\nA second type of manipulation focuses on how the voters themselves can\nmanipulate the outcome of an election by misrepresenting\ntheir preferences. Consider the following two election scenarios \nwith 7 voters and 3 candidates:", "\nThe only difference between the two election scenarios is that the third voter\nchanged the ranking of the bottom three candidates. In election scenario 1, the third \nvoter has candidate \\(A\\) ranked first, then \\(C\\) ranked second, \\(B\\) ranked third \nand \\(D\\) ranked last. In election scenario 2, this voter still has \\(A\\) ranked\nfirst, but ranks \\(B\\) second, \\(D\\) third and \\(C\\) last. In election scenario 1, candidate \\(C\\) is the Borda Count winner (the Borda scores are \\(\\BS(A)=9, \\BS(B)=5, \\BS(C)=10\\), and \\(\\BS(D)=6\\)). In the election scenario 2, candidate \\(A\\) is \nthe Borda Count winner (the Borda scores are \\(\\BS(A)=9, \\BS(B)=6, \\BS(C)=8\\), and \\(\\BS(D)=7\\)). \nAccording to her ranking in election scenario 1, this voter prefers the outcome in election scenario 2 (candidate \\(A\\), the Borda winner in election scenario 2, is ranked above candidate \\(C\\), the Borda winner in election scenario 1). So, if we assume that\nelection scenario 1 represents the “true” preferences of the\nelectorate, it is in the interest of the third voter to misrepresent\nher preferences as in election scenario 2. This is an instance of a general result known as the\nGibbard-Satterthwaite Theorem (Gibbard 1973; Satterthwaite\n1975): Under natural assumptions, there is no voting method that\nguarantees that voters will choose their ballots sincerely\n(for a precise statement of this theorem \nsee Theorem 3.1.2 from Taylor 2005 or Section 3.3 of List 2013). " ], "subsection_title": "4.1 Strategizing" }, { "content": [ "\nMuch of the literature on voting theory (and, more generally, social\nchoice theory) is focused on so-called axiomatic characterization\nresults. The main goal is to characterize different voting\nmethods in terms of abstract principles of collective decision making.\nSee Pauly 2008 and Endriss 2011 for interesting discussions of\naxiomatic characterization results from a logician’s point-of-view.\n", "\nConsult List 2013 and Gaertner 2006 for introductions to \nthe vast literature on axiomatic characterizations in social choice theory. \nIn this article, I focus on a few key axioms and results and how they \nrelate to the voting methods and paradoxes discussed above. I start with \nthree core principles. ", "\nThese properties ensure that the outcome of an election depends only\non the voters’ ballots, with all the voters and candidates being treated equally.\nOther properties are intended to rule out some of the paradoxes and\nanomalies discussed above. In section 4.1, there is an example of a\nsituation in which a candidate is elected, even though all\nthe voters prefer a different candidate. The next principle rules out\nsuch situations: ", "\nUnanimity (also called the Pareto Principle): If candidate\n\\(A\\) is ranked above candidate \\(B\\) by all voters, then\ncandidate \\(B\\) should not win the election. ", "\nThese are natural properties to impose on any voting method. A\nsurprising consequence of these properties is that they rule out\nanother natural property that one may want to impose: Say that a\nvoting method is resolute if the method always selects one\nwinner (i.e., there are no ties). Suppose that \\(V\\) is a voting\nmethod that requires voters to rank the candidates and that there are\nat least 3 candidates and enough voters to form a Condorcet\ncomponent (a profile generating a majority cycle with voters evenly\ndistributed among the different rankings). First, consider the situation when \nthere are exactly 3 candidates (in this case, we do not need to assume Unanimity). \nDivide the set of voters into \nthree groups of size \\(n\\) and consider the Condorcet component: \n", "\nBy Universal Domain and resoluteness, \\(V\\) must select exactly one of \n\\(A\\), \\(B\\), or \\(C\\) as the winner. Assume that \\(V\\) select \\(A\\) \nas the winner (the argument when \\(V\\) selects the other candidates is similar). \nNow, consider the profile in which every voter swaps candidate \\(A\\) \nand \\(B\\) in their rankings: \n", "\nBy Neutrality and Universal Domain, \\(V\\) must elect candidate \\(B\\) in this election scenario. Now, consider the profile in which every voter in the above election scenario swaps candidates \\(B\\) and \\(C\\): \n", "\nBy Neutrality and Universal Domain, \\(V\\) must elect candidate \\(C\\)\nin this election scenario. Notice that this last election scenario\ncan be generated by permuting the voters in the first election\nscenario (to generate the last election scenario from the first\nelection scenario, move the first group of voters to the 2nd position,\nthe 2nd group of voters to the 3rd position and the 3rd group of\nvoters to the first position). But this contradicts Anonymity since\nthis requires \\(V\\) to elect the same candidate in the first and third\nelection scenario. To extend this result to more than 3 candidates,\nconsider a profile in which candidates \\(A\\), \\(B\\), and \\(C\\) are all\nranked above any other candidate and the restriction to these three\ncandidates forms a Condorcet component. If \\(V\\) satisfies Unanimity,\nthen no candidate except \\(A\\), \\(B\\) or \\(C\\) can be elected. Then,\nthe above argument shows that \\(V\\) cannot satisfy Resoluteness,\nUniversal Domain, Neutrality, and Anonymity. That is, there are no\nResolute voting methods that satisfy Universal Domain, Anonymity,\nNeutrality, and Unanimity for 3 or more candidates (note that I have\nassumed that the number of voters is a multiple of 3, see Moulin 1983\nfor the full proof).\n", "\nSection 3.2 discussed examples in which candidates end up losing an\nelection as a result of more support from some of the voters. There\nare many ways to state properties that require a voting method to be\nmonotonic. The following strong version (called Positive\nResponsiveness in the literature) is used to characterize majority\nrule when there are only two candidates: ", "\nPositive Responsiveness: If candidate \\(A\\) is a winner or\ntied for the win and moves up in some of the voter’s rankings, then\ncandidate \\(A\\) is the unique winner. ", "\nI can now state our first characterization result. Note that in all of\nthe example discussed above, it is crucial that there are three or\nmore candidates (for example, stating Condorcet’s paradox requires there \nto be three or more candidates). When there are only two\ncandidates, or alternatives, Majority Rule (choose the alternative ranked\nfirst by more than 50% of the voters) can be singled out as “best”: ", "\nTheorem (May 1952).\n\n A voting method for choosing between two candidates satisfies\nNeutrality, Anonymity, Unanimity and Positive Responsiveness if and only if the\nmethod is majority rule.\n", "\nSee May 1952 for a precise statement of this theorem and Asan and\nSanver 2002, Maskin 1995, and Woeginger 2003 for \nalternative characterizations of majority rule. \n", "\nA key assumption in the proof May’s theorem and subsequent results is the \nrestriction to voting on two alternatives. When there are only two \nalternatives, the definition of a ballot can be simplified since a \nranking of two alternatives boils down to selecting the alternative \nthat is ranked first. The above characterizations of Majority \nRule work in a more general setting since they also allow \nvoters to abstain (which is ambiguous between not voting \nand being indifferent between the alternatives). So, if the alternatives \nare \\(\\{A,B\\}\\), then there are three possible ballots: selecting \\(A\\), \nselecting \\(B\\), or abstaining (which is treated as selecting both \\(A\\) and \\(B\\)). \nA natural question is whether there are May-style characterization theorems \nfor more than two alternatives. A crucial issue is that rankings of more than \ntwo alternatives are much more informative than selecting an alternative or abstaining. By restricting the information required \nfrom a voter to selecting one of the alternatives or abstaining, \nGoodin and List 2006 prove that the axioms used in May’s Theorem characterize \nPlurality Rule when there are more than two alternatives. They also show that a\n minor modification of the axioms characterize Approval Voting when voters are allowed to \n select more than one alternative. \n", "\n Note that focusing on voting methods that limit the information required from \n the voters to selecting one or more of the alternatives hides all the interesting \n phenomena discussed in the previous sections, such as the existence of a Condorcet paradox. \nReturning to the study of voting methods that require voters to rank the alternatives, \nthe most important characterization result is Ken Arrow’s celebrated impossibility \ntheorem (1963). Arrow showed that there is no social welfare function (a social\nwelfare function maps the voters’ rankings (possibly allowing ties) to\na single social ranking) satisfying universal domain, unanimity,\nnon-dictatorship (there is no voter \\(d\\) such that for all profiles,\nif \\(d\\) ranks \\(A\\) above \\(B\\) in the profile, then the social\nordering ranks \\(A\\) above \\(B\\)) and the following key property: \n", "\nIndependence of Irrelevant Alternatives: The social ranking\n(higher, lower, or indifferent) of two candidates \\(A\\) and \\(B\\)\ndepends only on the relative rankings of \\(A\\) and \\(B\\) for each\nvoter. ", "\nThis means that if the voters’ rankings of two candidates \\(A\\) and\n\\(B\\) are the same in two different election scenarios, then the\nsocial rankings of \\(A\\) and \\(B\\) must be the same. This is a very\nstrong property that has been extensively criticized (see Gaertner,\n2006, for pointers to the relevant literature, and Cato, 2014, for a\ndiscussion of generalizations of this property). It is beyond the\nscope of this article to go into detail about the proof and the\nramifications of Arrow’s theorem (see Morreau, 2014, for this\ndiscussion), but I note that many of the voting methods we have\ndiscussed do not satisfy the above property. A striking example of a\nvoting method that does not satisfy Independence of Irrelevant\nAlternatives is Borda Count. Consider the following two election\nscenarios:", "\nNotice that the relative rankings of candidates \\(A\\), \\(B\\) and \\(C\\)\nare the same in both election scenarios. In the election scenario 2, the\nranking of candidate \\(X\\), that is uniformly ranked in last place in\n election scenario 1, is changed. The ranking according to the\nBorda score of the candidates in election scenario 1 puts \\(A\\) first with 15\npoints, \\(B\\) second with 14 points, \\(C\\) third with 13 points, and\n\\(X\\) last with 0 points. In election scenario 2, the ranking of \\(A\\), \\(B\\)\nand \\(C\\) is reversed: Candidate \\(C\\) is first with 13 voters;\ncandidate \\(B\\) is second with 12 points; candidate \\(A\\) is third\nwith 11 points; and candidate \\(X\\) is last with 6 points. So, even\nthough the relative rankings of candidates \\(A\\), \\(B\\) and \\(C\\) do\nnot differ in the two election scenarios, the position of candidate \\(X\\)\nin the voters’ rankings reverses the Borda rankings of these candidates. ", "\nIn Section 3.3, it was noted that a number of methods (including all\nCondorcet consistent methods) are susceptible to the multiple\ndistricts paradox. An example of a method that is not susceptible to\nthe multiple districts paradox is Plurality Rule: If a candidate\nreceives the most first place votes in two different districts, then\nthat candidate must receive the most first place votes in the combined\nthe districts. More generally, no scoring rule is susceptible to the\nmultiple districts paradox. This property is called reinforcement:\n", "\nReinforcement:\nSuppose that \\(N_1\\) and \\(N_2\\) are\ndisjoint sets of voters facing the same set of candidates. Further,\nsuppose that \\(W_1\\) is the set of winners for the population \\(N_1\\),\nand \\(W_2\\) is the set of winners for the population \\(N_2\\). If there\nis at least one candidate that wins both elections, then the winner(s)\nfor the entire population (including voters from both \\(N_1\\) and\n\\(N_2\\)) is the set of candidates that are in both \\(W_1\\) and \\(W_2\\)\n(i.e., the winners for the entire population is \\(W_1\\cap W_2\\)).", "\nThe reinforcement property explicitly rules out the multiple-districts\nparadox (so, candidates that win all sub-elections are guaranteed to\nwin the full election). In order to characterize all scoring rules,\none additional technical property is needed: ", "\nContinuity: Suppose that a group of voters \\(N_1\\) elects a\ncandidate \\(A\\) and a disjoint group of voters \\(N_2\\) elects a\ndifferent candidate \\(B\\). Then there must be some number \\(m\\) such\nthat the population consisting of the subgroup \\(N_2\\) together with\n\\(m\\) copies of \\(N_1\\) will elect \\(A\\).\n", "We then have:", "\nTheorem (Young 1975).\n\nSuppose that \\(V\\) is a voting method that requires voters to rank the\ncandidates. Then, \\(V\\) satisfies Anonymity, Neutrality, Reinforcement\nand Continuity if and only if the method is a scoring rule.\n", "\nSee Merlin 2003 and Chebotarev and Smais 1998 for surveys of other\ncharacterizations of scoring rules. Additional axioms single out Borda\nCount among all scoring methods (Young 1974; Gardenfors 1973; Nitzan\nand Rubinstein 1981). In fact, Saari has argued that “any fault\nor paradox admitted by Borda’s method also must be admitted by all\nother positional voting methods” (Saari 1989, pg. 454). For\nexample, it is often remarked that Borda Count (and all scoring rules)\ncan be easily manipulated by the voters. Saari (1995, Section 5.3.1)\nshows that among all scores rules Borda Count is the least susceptible\nto manipulation (in the sense that it has the fewest profiles where a\nsmall percentage of voters can manipulate the outcome). ", "\nI have glossed over an important detail of Young’s characterization of\nscoring rules. Note that the reinforcement property refers to the\nbehavior of a voting method on different populations of voters. To\nmake this precise, the formal definition of a voting method must allow for \ndomains that include profiles (i.e., sequences of ballots) of different\nlengths. To do this, it is convenient to assume that the domain of a\nvoting method is an anonymized profile: Given a set of ballots\n\\(\\mathcal{B}\\), an anonymous profile is a function\n\\(\\pi:\\mathcal{B}\\rightarrow\\mathbb{N}\\). Let \\(\\Pi\\) be the set of\nall anonymous profiles. A variable domain voting method assigns\na non-empty set of voters to each anonymous profile—i.e., it is a function\n\\(V:\\Pi\\rightarrow \\wp(X)-\\emptyset\\)). Of course, this builds in the\nproperty of Anonymity into the definition of a voting method. For this\nreason, Young (1975) does not need to state Anonymity as a\ncharacterizing property of scoring rules. ", "\nYoung’s axioms identify scoring rules out of the set of all functions\ndefined from ballots that are rankings of candidates. In order to\ncharacterize the voting methods from Section 2.2, we need to change\nthe set of ballots. For example, in order to characterize Approval\nVoting, the set of ballots \\(\\mathcal{B}\\) is the set of non-empty\nsubsets of the set of candidates—i.e.,\n\\(\\mathcal{B}=\\wp(X)-\\emptyset\\) (selecting the ballot \\(X\\)\nconsisting of all candidates means that the voter abstains).\nTwo additional axioms are needed to characterize Approval Voting:", "We then have:", "\nTheorem (Fishburn 1978b; Alos-Ferrer 2006 ).\n\nA variable domain voting method where the ballots are non-empty sets\nof candidates is Approval Voting if and only if it satisfies\nFaithfulness, Cancellation, and Reinforcement.\n", "\nNote that Approval Voting satisfies Neutrality even though it is not\nlisted as one of the characterizing properties in the above\ntheorem. This is because Alos-Ferrer (2006) showed that Neutrality is\na consequence of Faithfulness, Cancellation and Reinforcement. See\nFishburn 1978a and Baigent and Xu 1991 for alternative\ncharacterizations of Approval Voting, and Xu 2010 for a survey of the\ncharacterizations of Approval Voting (cf. the characterization of\nApproval Voting from Goodin and List 2006). ", "\nMyerson (1995) introduced a general framework for characterizing\nabstract scoring rules that include Borda Count and Approval\nVoting as examples. The key idea is to think of a ballot, called a\nsignal or a vote, as a function from candidates to a set\n\\(\\mathcal{V}\\), where \\(\\mathcal{V}\\) is a set of numbers. That is,\nthe set of ballots is a subset of \\(\\mathcal{V}^X\\) (the set of functions\nfrom \\(X\\) to \\(\\mathcal{V}\\)). Then, an anonymous profile of signals\nassigns a score to each candidate \\(X\\) by summing the numbers\nassigned to \\(X\\) by each voter. This allows us to define voting methods \nby specifying the set of ballots: ", "\nMyerson (1995) showed that an abstract voting rule is an abstract\nscoring rule if and only if it satisfies Reinforcement, Universal\nDomain (i.e. it is defined for all anonymous profiles), a version of\nthe Neutrality property (adapted to the more abstract setting), and\nthe Continuity property, which is called Overwhelming Majority.\nPivato (2013) generalizes this result, and Gaertner and Xu (2012)\nprovide a related characterization result (using different\nproperties). Pivato (2014) characterizes Formal Utilitarian and Range\nVoting within the class of abstract scoring rules, and Mace (2018)\nextends this approach to cover a wider class of grading voting methods\n(including Majority Judgement). " ], "subsection_title": "4.2 Characterization Results" }, { "content": [ "\nThe voting methods discussed above have been judged on\nprocedural grounds. This “proceduralist approach to\ncollective decision making” is defined by Coleman and Ferejohn\n(1986, p. 7) as one that “identifies a set of ideals with which\nany collective decision-making procedure ought to comply. … [A]\nprocess of collective decision making would be more or less\njustifiable depending on the extent to which it satisfies them.”\nThe authors add that a distinguishing feature of proceduralism is that\n“what justifies a [collective] decision-making procedure is\nstrictly a necessary property of the procedure — one entailed by\nthe definition of the procedure alone.” Indeed, the\ncharacterization theorems discussed in the previous section can be\nviewed as an implementation of this idea (cf. Riker 1982). The general\nview is to analyze voting methods in terms of “fairness\ncriteria” that ensure that a given method is sensitive to\nall of the voters’ opinions in the right way. ", "\nHowever, one may not be interested only in whether a collective\ndecision was arrived at “in the right way,” but in whether\nor not the collective decision is correct. This\nepistemic approach to voting is nicely explained by Joshua\nCohen (1986, p. 34): ", "\nAn epistemic interpretation of voting has three main elements: (1) an\nindependent standard of correct decisions — that is, an account\nof justice or of the common good that is independent of current\nconsensus and the outcome of votes; (2) a cognitive account of voting\n— that is, the view that voting expresses beliefs about what the\ncorrect policies are according to the independent standard, not\npersonal preferences for policies; and (3) an account of decision\nmaking as a process of the adjustment of beliefs, adjustments that are\nundertaken in part in light of the evidence about the correct answer\nthat is provided by the beliefs of others. \n\n", "\nUnder this interpretation of voting, a given method is judged on how\nwell it “tracks the truth” of some objective fact (the\ntruth of which is independent of the method being used). A\ncomprehensive comparison of these two approaches to voting touches on\na number of issues surrounding the justification of democracy (cf.\nChristiano 2008); however, I will not focus on these broader issues\nhere. Instead, I briefly discuss an analysis of Majority Rule that\ntakes this epistemic approach. ", "\nThe most well-known analysis comes from the writings of Condorcet\n(1785). The following theorem, which is attributed to Condorcet and\nwas first proved formally by Laplace, shows that if there are only two\noptions, then majority rule is, in fact, the best procedure from an\nepistemic point of view. This is interesting because it also shows\nthat a proceduralist analysis and an epistemic analysis both single\nout Majority Rule as the “best” voting method when there\nare only two candidates. ", "\nAssume that there are \\(n\\) voters that have to decide between two\nalternatives. Exactly one of these alternatives is (objectively)\n“correct” or “better.” The typical example\nhere is a jury deciding whether or not a defendant is guilty. The two\nassumptions of the Condorcet jury theorem are: ", "\nSee Dietrich 2008 for a critical discussion of these two assumptions.\nThe classic theorem is: ", "\nCondorcet Jury Theorem.\n\nSuppose that Independence and Voter Competence are both satisfied.\nThen, as the group size increases, the probability that the majority\nchooses the correct option increases and converges to certainty.\n", "\nSee Nitzan 2010 (part III) and Dietrich and Spiekermann 2013 for modern\nexpositions of this theorem, and Goodin and Spiekermann 2018 for\nimplications for the theory of democracy. ", "\nCondorcet envisioned that the above argument could be adapted to\nvoting situations with more than two alternatives. Young (1975, 1988, 1995) \nwas the first to fully work out this\nidea (cf. List and Goodin 2001 who generalize the Condorcet Jury \nTheorem to more than two alternatives in a different framework). \nHe showed (among other things) that the Borda Count can be\nviewed as the maximum likelihood estimator for identifying\nthe best candidate. Conitzer and Sandholm (2005), Conitzer et\nal. (2009), Xia et al. (2010), and Xia (2016) take these ideas further\nby classifying different voting methods according to whether or not\nthe methods can be viewed as a maximum likelihood estimator\n(for a noise model). The most general results along these lines can be\nfound in Pivato 2013 which contains a series of results showing when\nvoting methods can be interpreted as different kinds of statistical\n‘estimators’. " ], "subsection_title": "4.3 Voting to Track the Truth" }, { "content": [ "\nOne of the most active and exciting areas of research that is focused,\nin part, on the study of voting methods and voting paradoxes is\ncomputational social choice. This is an interdisciplinary\nresearch area that uses ideas and techniques from theoretical computer\nscience and artificial intelligence to provide new perspectives and to\nask new questions about methods for making group decisions; and to use\nvoting methods in computational domains, such as recommendation\nsystems, information retrieval, and crowdsourcing. It is beyond the\nscope of this article to survey this entire research area. Readers are\nencouraged to consult the Handbook of Computational Social\nChoice (Brandt et al. 2016) for an overview of this field (cf.\nalso Endriss 2017). In the remainder of this section, I briefly\nhighlight some work from this research area related to issues\ndiscussed in this article. ", "\nSection 4.1 discussed election scenarios in which voters choose their\nballots strategically and briefly introduced the Gibbard-Satterthwaite\nTheorem. This theorem shows that every voting method satisfying\nnatural properties has profiles in which there is some voter, called a\nmanipulator, that can achieve a better outcome by selecting a\nballot that misrepresents her preferences. Importantly, in order to\nsuccessfully manipulate an election, the manipulator must not only\nknow which voting method is being used but also how the other members\nof society are voting. Although there is some debate about whether\nmanipulation in this sense is in fact a problem (Dowding and van Hees\n2008; Conitzer and Walsh, 2016, Section 6.2), there is interest in\nmechanisms that incentivize voters to report their\n“truthful” preferences. In a seminal paper, Bartholdi et\nal. (1989) argue that the complexity of computing which ballot will\nlead to a preferred outcome for the manipulator may provide a barrier\nto voting insincerely. See Faliszewski and Procaccia 2010, Faliszewski\net al. 2010, Walsh 2011, Brandt et al. 2013, and Conitzer and Walsh\n2016 for surveys of the literature on this and related questions, such\nas the the complexity of determining the winner given a voting method\nand the complexity of determining which voter or voters should be\nbribed to change their vote to achieve a given outcome. ", "\nOne of the most interesting lines of research in computational social\nchoice is to use techniques and ideas from AI and theoretical computer\nscience to design new voting methods. The main idea is to think of\nvoting methods as solutions to an optimization problem. Consider the\nspace of all rankings of the alternatives \\(X\\). Given a profile of\nrankings, the voting problem is to find an “optimal” group\nranking (cf. the discussion or distance-based\nrationalizations of voting methods from Elkind et al. 2015). What\ncounts as an “optimal” group ranking depends on\nassumptions about the type of the decision that the group is making.\nOne assumption is that the voters have real-valued utilities\nfor each candidate, but are only able to report rankings of the\nalternatives (it is assumed that the rankings represent the utility\nfunctions). The voting problem is to identify the candidates that\nmaximizes the (expected) social welfare (the average of the voters’\nutilities), given the partial information about the voters’\nutilities—i.e., the profile of rankings of the candidates. See\nPivato 2015 for a discussion of this approach to voting and Boutilier\net al. 2015 for algorithms that solve different versions of this\nproblem. A second assumption is that there is an objectively correct\nranking of the alternatives and the voters’ rankings are noisy\nestimates of this ground truth. This way of thinking about the voting\nproblem was introduced by Condorcet and discussed in Section 4.3.\nProcaccia et al. (2016) import ideas from the theory of\nerror-correcting codes to develop an interesting new approach to\naggregate rankings viewed as noisy estimates of some ground truth.\n" ], "subsection_title": "4.4 Computational Social Choice" } ] }, { "main_content": [], "section_title": "5. Concluding Remarks", "subsections": [ { "content": [ "\nAs with any mathematical analysis of social phenomena, questions\nabound about the “real-life” implications of the\ntheoretical analysis of the voting methods given above. The main\nquestion is whether the voting paradoxes are simply features of the\nformal framework used to represent an election scenario or\nformalizations of real-life phenomena. This raises a number of subtle\nissues about the scope of mathematical modeling in the social\nsciences, many of which fall outside the scope of this article. I\nconclude with a brief discussion of two questions that shed some light\non how one should interpret the above analysis. ", "\nHow likely is a Condorcet Paradox or any of the other\nvoting paradoxes? There are two ways to approach this question.\nThe first is to calculate the probability that a majority cycle will\noccur in an election scenario. There is a sizable literature devoted\nto analytically deriving the probability of a majority cycle occurring\nin election scenarios of varying sizes (see Gehrlein 2006, and\nRegenwetter et al. 2006, for overviews of this literature).\nThe calculations depend on assumptions about the distribution of\nrankings among the voters. One distribution that is\ntypically used is the so-called impartial culture, where each\nranking is possible and occurs with equal probability. For\nexample, if there are three candidates, and it is assumed that the\nvoters’ ballots are rankings of the candidates, then each possible ranking \ncan occur with probability 1/6. Under this assumption,\nthe probability of a majority cycle occurring has been calculated (see\nGehrlein 2006, for details). Riker (1982, p. 122) has a table of the\nrelevant calculations. Two observations about this data: First, as the\nnumber of candidates and voters increases, the probability of a\nmajority cycles increases to certainty. Second, for a fixed number of\ncandidates, the probability of a majority cycle still increases,\nthough not necessarily to certainty (the number of voters is the\nindependent variable here). For example, if there are five candidates\nand seven voters, then the probability of a majority cycle is 21.5\npercent. This probability increases to 25.1 percent as the number of\nvoters increases to infinity (keeping the number of candidates fixed)\nand to 100 percent as the number of candidates increases to infinity\n(keeping the number of voters fixed). Prima facie, this result\nsuggests that we should expect to see instances of the Condorcet and\nrelated paradoxes in large elections. Of course, this interpretation\ntakes it for granted that the impartial culture is a realistic\nassumption. Many authors have noted that the impartial culture is a\nsignificant idealization that almost certainly does not occur in\nreal-life elections. Tsetlin et al. (2003) go even further arguing\nthat the impartial culture is a worst-case scenario in the sense that\nany deviation results in lower probabilities of a majority\ncycle (see Regenwetter et al. 2006, for a complete discussion\nof this issue, and List and Goodin 2001, Appendix 3, for a related result). ", "\nA second way to argue that the above theoretical observations are\nrobust is to find supporting empirical evidence. For instance, is\nthere evidence that majority cycles have occurred in actual elections?\nWhile Riker (1982) offers a number of intriguing examples, the most\ncomprehensive analysis of the empirical evidence for majority cycles\nis provided by Mackie (2003, especially Chapters 14 and 15). The\nconclusion is that, in striking contrast to the probabilistic analysis\nreferenced above, majority cycles typically have not occurred in\nactual elections. However, this literature has not reached a consensus\nabout this issue (cf. Riker 1982): The problem is that the available\ndata typically does not include voters’ opinions about all\npairwise comparison of candidates, which is needed to determine if\nthere is a majority cycle. So, this information must be\ninferred (for example, by using statistical methods) from the\ngiven data. ", "\nA related line of research focuses on the influence of factors, \nsuch as polls (Reijngoud and Endriss 2012), \nsocial networks (Santoro and Beck 2017, Stirling 2016) and deliberation \namong the voters (List 2018), on the profiles of ballots that are actually \nrealized in an election. For instance, List et al. 2013 has evidence \nsuggesting that deliberation reduces the probability of a Condorcet cycle occurring. \n", "\nHow do the different voting methods compare in actual elections?\n In this article, I have analyzed voting methods under highly\nidealized assumptions. But, in the end, we are interested in a very\npractical question: Which method should a group adopt? Of\ncourse, any answer to this question will depend on many factors that\ngo beyond the abstract analysis given above (cf. Edelman 2012a). An interesting line of\nresearch focuses on incorporating empirical evidence into the\ngeneral theory of voting. Evidence can come in the form of a computer\nsimulation, a detailed analysis of a particular voting method in\nreal-life elections (for example, see Brams 2008, Chapter 1, which\nanalyzes Approval voting in practice), or as in situ\nexperiments in which voters are asked to fill in additional ballots\nduring an actual election (Laslier 2010, 2011). ", "\nThe most striking results can be found in the work of\nMichael Regenwetter and his colleagues. They have analyzed datasets\nfrom a variety of elections, showing that many of the usual voting\nmethods that are considered irreconcilable (e.g., Plurality Rule, Borda\nCount and the Condorcet consistent methods from Section 3.1.1) are, in fact, in\nperfect agreement. This suggests that the “theoretical\nliterature may promote overly pessimistic views about the likelihood\nof consensus among consensus methods” (Regenwetter et\nal. 2009, p. 840). See Regenwetter et al. 2006 for an\nintroduction to the methods used in these analyses and Regenwetter\net al. 2009 for the current state-of-the-art. \n" ], "subsection_title": "5.1 From Theory to Practice" } ] } ]

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[ "\n\nThe central idea of Wyclif's political philosophy is that the\ndominium defining God's primary relation to creation\njustifies all human dominium, whether it be the mastery of a\nking, a lesser civil lord, or a priest. But unlike predecessors who\nwere content to define God's mastery as foundational to human lordship\nin non-metaphysical terms, Wyclif made ready use of his realist\nontology to argue that God's dominium functions as a\nuniversal by causality for all instances of just human\ndominium. For medieval political theorists, this was not\ncommon practice; some, like\n Aquinas,\n can be argued to present unified systems of metaphysics, political\nthought, and ecclesiology, but many others, including\n Ockham,\n Marsilius of Padua, John of Paris, and\n Giles of Rome,\n did not. If, like Ockham or Giles, they had metaphysical positions,\nit is impossible to argue persuasively that their ontologies affected\ntheir politics. This makes Wyclif's political and ecclesiological\nthought notable, for it is one of the few cases where a distinguished\nmetaphysician used his ontology as a foundation for a detailed\nexamination of the just arrangement of authority in church and\nstate. An immediate corrollary to Wyclif's axiomatic position that all\njust human dominium derives from God is that no private\nproperty relations, which serve as the underpinnings for all human\nmastery, are just without grace. Because, following\n Augustine,\n private property is a direct result of the Fall of man, the ideal\nstate is one of communal ownership. Since the Church is the\nre-established ideal state, grace does not provide for its just\nownership of any property whatsoever. Because Wyclif saw the\nfourteenth-century church enjoying the lion's share of property\nownership in England, he argued that the king was bound by God to\nrelieve the church of its property, and to rule over it as a divinely\nappointed steward. The substance of this argument was realized by\nHenry VIII, and so Wyclif has been associated, if only as prophetic\nforerunner, with Tudor reformation. The form of Wyclif's arguments are\nin no way comparable to modern arguments, though, and are more\ndirectly associated with earlier Franciscan positions, like those of\n Ockham,\n than they are with later political theory. In this essay, the Latin\nterm dominium will be used to distinguish Wyclif's\ntheologically medieval view from its modern English correlate\n'dominion', which connotes absolute mastery." ]

[ { "content_title": "1. Wyclif's Later Works ", "sub_toc": [] }, { "content_title": "2. ", "sub_toc": [ "2.1 Augustine", "2.2 Giles of Rome", "2.3 The Franciscans and Their Opponents" ] }, { "content_title": "3. Divine ", "sub_toc": [ "3.1 Natural Dominium" ] }, { "content_title": "4. Types of Human ", "sub_toc": [ "4.1 Evangelical Dominium", "4.2 Civil Dominium", "4.3 Tyranny" ] }, { "content_title": "Bibliography", "sub_toc": [] }, { "content_title": "Academic Tools", "sub_toc": [] }, { "content_title": "Other Internet Resources", "sub_toc": [] }, { "content_title": "Related Entries", "sub_toc": [] } ]

[ { "main_content": [ "\n\nGovernment and the relation of divine justice to human law, both\nsecular and ecclesiastical, figure as occasional themes throughout the\ntreatises of the Summa de Ente. After receiving his doctorate\nin theology in 1373, his attention began to focus more completely on\nthese topics, and his realism continued to undergird his thought at\nleast through 1381, during which period he wrote the treatises that\nmake up the second of his great Summae, the Summa\nTheologie. In late 1373, he began De Dominio Divino,\nwhich serves as bridge from the later, formal theological treatises of\nthe Summa de Ente to the political, social, and\necclesiological subject matter of the Summa Theologie. He\nbegan royal service during this period, participating in an embassy to\nBruges for negotiations with papal envoys in 1374. Wyclif remained in\nthe service of John of Gaunt for the rest of his life; the Duke\nprotected him from the formal prosecution prompted by five bulls of\npapal condemnation in 1377. After being condemned for his views on the\nEucharist at Oxford in 1381, Wyclif withdrew to Lutterworth, where he\nremained until his death in December 1384. Though still protected by\nJohn of Gaunt, he was no longer in active service after 1379. During\nthese tumultuous years, Wyclif wrote the ten treatises of the\nSumma Theologie: four on just human government, two on the\nstructure and government of the church, one on scriptural\nhermeneutics, and three on specific problems afflicting the\nChurch. Our interest lies in De Mandatis Divinis (1375–76),\nDe Statu Innocencie (1376), and De Civili\nDominio (1375–76), where he provides the theological foundation\nfor the radical transformation of the church he prescribes in De\nEcclesia (1378–79) De Potestate Pape (1379), and De\nOfficio Regis (1379). Towards the end of his life, Wyclif\nsummarized his entire theological vision in Trialogus\n(1382–83), reiterating the connections between his earlier\nphilosophical works and later political treatises in a three-way\ndialogue written in language that would appeal to members of the royal\ncourt. " ], "section_title": "1. Wyclif's Later Works", "subsections": [] }, { "main_content": [ "\n\n Dominium and its generally accepted translation, 'lordship',\nsuggest the sovereignty exercised by one individual over another, but\nRoman law allowed for complexity in distinguishing between property\nownership, its primary referent, and jurisdiction, governance, and\npolitical power. When twelfth-century canon lawyers resurrected Roman\nlaw as the foundation for the ascendant papal monarchy, it was common\nto distinguish between jurisdictive authority, secular power, and the\nuse and possession of private\n property.[1]\n By the beginning of the fourteenth century, dominium largely\nconnoted property ownership, though this usually entailed jurisdictive\nauthority. Most political theorists agreed with Thomas Aquinas in saying that a civil lord who\nsupposed that his jurisdictive authority arose from property ownership\nrather than from a constitution would be a tyrant (Summa\nTheologiae IaIIae, Q.56, a.5; Q.58, a.2). Given that the legal\nuse of dominium referred to property ownership and not to the\nauthority to govern, it seems odd that Wyclif used the term to do so\nmuch more. The reason may be found in the connection of Augustinian\ntheology to theories of the justice of property ownership. As the\npapal monarchy developed, its theorists, such as\n Giles of Rome,\n found it useful to identify all earthly justice, including just\nproperty ownership, with the source of justice in creation." ], "section_title": "2. Dominium in Political Thought Before Wyclif", "subsections": [ { "content": [ "\n\n Augustine's\n De Civitate Dei was the basis for relating property\nownership and secular justice to divine authority. Here the division\nbetween two classes of men is clear: some are members of the City of\nMan, motivated by love of self, while others are motivated by the love\nof God and a contempt for self, placing them in the City of\n God.[2]\n There is really only one true Lord in creation. Mastery of one man\nover another is the result of Original Sin and is therefore unnatural\nexcept in the case of paternity, which is founded on parental love for\na child. Among members of the City of God, the relation of prince and\nsubject is not political and does not entail the sort of mastery we\nsee in the City of Man, but rather involves service and sacrifice, as\nexemplified by the parent/child relationship.", "\n\nProperty ownership has been united to mastery in the City of Man\nbecause of Original Sin, whereby man turned away from God in the\nmistaken belief that he could make claims of exclusive ownership on\ncreated beings. This is not to say that Augustine thought that all\nprivate property relations are wrong; indeed, he is famous for having\nargued that all things belong to the just (De Civitate Dei\n14, ch. 28). But people who own things are not de facto\njust. Those for whom ownership is not an end in itself but a means by\nwhich to do God's will are freed from the bondage of selfishness\nimposed by the Fall. They easily recognize the truth of the dictum\nthat one should abstain from the possession of private things, or if\none cannot do so, then at least from the love of property\n(Enarratio in Psalmam 132, ch.4).", "\n\nAugustine's thought on the relation of ownership to political\nauthority is open to interpretation. One can easily read him as\narguing that the Church, as the Body of Christ and earthly\ninstantiation of the City of God, can best exemplify loving\nlord/subject relations through its ecclesiastical structure, thereby\njustifying a top-down papal monarchy. Likewise, one can read him as\nhaving so separated secular political authority from the rule of love\nas to make political and ecclesiastical jurisdictive authority utterly\ndistinct. Again, one could interpret Augustine's 'all things belong to\nthe just' as meaning that the Church is the arbiter of all property\nownership in virtue of being the Body of Christ and seat of all\ncreated justice, or one could argue that the Church should abandon all\nclaims to property ownership, just as the Apostles abstained from the\npossession of private property. This ambiguity in interpretation was\nthe source of some of the competing theories that influenced Wyclif's\nposition." ], "subsection_title": "2.1 Augustine" }, { "content": [ "\n\nDuring the conflict between Philip IV of France and Pope Boniface VIII\nin 1301, Giles of Rome wrote De Ecclesiastica Potestate,\nestablishing the absolute secular superiority of the papacy. Giles'\nmaster Boniface VIII was responsible for the two famous Bulls,\nClericos laicos (1296), which forbade clergy to give up\nproperty without papal approval, and Unam sanctam (1302),\nwhich declared that secular power is in the service of, and subject\nto, papal authority. De Ecclesiastica Potestate is an\narticulation of the concept of power underlying these two Bulls and\narising from one of the two interpretations of Augustine described\nabove. In it, Giles describes all power “spiritual and secular” as\nrooted in the papacy, likening its structure to a papal river from\nwhich smaller, secular streams branch out. The source of this river,\nhe continues, is the sea, which is God: “God is a kind of font and a\nkind of sea of force and power, from which sea all forces and all\npowers are derived like\n streams.”[3]\n Not only is secular power reliant on papal authority; all property\nownership, insofar as it is just, is similarly dependent on an\necclesiastical foundation. The key element in just secular power and\nproperty ownership, he continues, is grace: without God's will\ndirectly moving in creation through the sacraments of the Church,\npower and ownership are empty claims, devoid of justice. Although\nGiles did not explicitly call the combination of ownership and\ntemporal power dominium, his uniting the two in a consistent,\nAugustinian fashion was sufficient for the next generation of\nAugustinian theorists." ], "subsection_title": "2.2 Giles of Rome" }, { "content": [ "\n\nThirty years earlier, in Bonaventure's\nApologia pauperum of 1269, the Franciscans had defined any\nproperty ownership, communal or individual, as inimical to the ideals\nof their Order. The Fall from paradise and the introduction of\nselfishness to human nature makes property ownership of any type,\nprivate or communal, an abberation. For the Franciscans, “all things\nbelong to the just” only in the sense that “belonging” entails\nnon-exclusive sharing (usus pauper), not ownership. Within\nthree decades, the Franciscans were divided on this issue: one party,\nthe Spirituals, demanded that the friars adopt usus pauper as\ntheir ideal of spiritual perfection, while the other, the Conventuals,\nargued for a more lenient interpretation of the Rule. The Spirituals,\nunder the guidance of the philosopher\n John Peter Olivi\n and his follower Ubertino de Casale, outnumbered the Conventuals by\ncentury's end, and had become sufficiently vocal to attract the\nattention of the\n pope.[4]\n John XXII was deeply suspicious of the Spiritual Franciscans'\narguments, perhaps fearing a reappearance of the communitarian\nWaldensian heresy. Private ownership, John argued, was not the result\nof Original Sin, but a gift from God that Adam enjoyed in Paradise and\nwhich the blessed still can enjoy, secure in the knowledge that their\nownership is sanctioned by God's dominium. This argument was\nto have notable consequences. John's eventual controversy with the\nSpiritual's champion,\n William Ockham,\n led to the first important use of the concept of natural right. But\nfor our analysis, the important thing is that iurisdictio and\nproprietas were united in the concept of\ndominium. Wyclif would make use of the Franciscans' arguments\nfor apostolic poverty, as well as of John XXII's idea that divine\ndominium provides the basis for all human dominium,\nthough in a way that would certainly have displeased both\n parties.[5]", "\n\nBy the 1350s, opponents of the Franciscans had broadened their range\nof criticism to question the legitimacy of the Order itself. Richard\nFitzralph, (d. 1360) wrote De Pauperie Salvatoris, a\nsustained examination of the Franciscans' claim to function without\nsupervision by diocesan bishop in which he argues that if the friars\nrely on the justice of the owners of what they use, they are bound by\nthe same laws that bind the owners. Thus, if the owners of what the\nfriars use are ecclesiastical, it follows that the friars must obey\necclesiastical\n authority.[6]\n Fitzralph's position is important here because it argues that grace\nalone is the justification for any instance of dominium in\ncreation, and that all just dominium ultimately relies on\nGod's dominium. Both serve as cornerstones of Wyclif's\nposition. God's dominium is a natural consequence of the act\nof creating, and with it comes divine governance and conservation of\ncreated being. The rational beings in creation, angels and human\nbeings, enjoy the loan of elements of God's created universe, but this\nis not a divine abdication of ultimate authority since everything is\nstill directly subject to divine dominium. ", "\n\nWhen the nature of the dominium lent to Adam changed with the\nFall, the love defining our natural dominium was affected,\nbut not eradicated. Men devised political dominium to\nregulate property relations, and although sin keeps them from\nrecognizing the borrowed nature of any dominium, it does not\npreclude there being grace-justified property ownership. In some\ncases, God infuses the artificial property-relations that we call\ndominium with sufficient grace to make them generally\nequivalent to prelapsarian dominium. These grace-favored\ncases of human dominium do not replicate the authority of God's\ndominium, but can exhibit the love that characterizes\nit. Fitzralph's expression of the Augustinian papal position makes\ngrace the deciding factor in ownership relations and ultimately in\npolitical authority, both of which had become nested in the term\ndominium. Wyclif's interpretation of the Augustinian position\nwould stretch past arguments about papal authority and the friars,\neven past arguments between popes and kings, to stir the very nature\nof the church as Christ's earthly body. All of this begins, he would\nargue, with an understanding of God's dominium as the causal\nexemplar of created lordship. " ], "subsection_title": "2.3 The Franciscans and Their Opponents" } ] }, { "main_content": [ "\n\nThe relation of universal to particular defines Wyclif's conception of\nhow God's dominium causes all instances of dominium\nin creation. Divine dominium is “the standard prior to and\npresupposition of all other dominium; if a creature has\ndominium over anything, God already has dominium\nover it, so any created dominium follows upon divine\ndominium” (De Dominio Divino I, ch. 3,\np.16.18–22). This relation exceeds mere exemplarity, where human\ndominium only imitates God's dominium without divine\ncausal determination. God's dominium has causal efficacy over\nall instances of human mastery such that no true created\ndominium is possible without direct participation in and\nconstant reliance upon God's dominium. The instrument through\nwhich divine dominium moves is grace, which instills in human\nrulers an essential love defining their every ruling action. Thus,\nevery case of just human dominium entails a constant reliance\nupon grace as the hallmark of its being an instantiation of God's\nuniversal dominium. ", "\n\nGod's dominium has six aspects, three identifiable with\nlordship's ruling element (creation, sustenance, and governance), and\nthree that define lordship's proprietary nature (giving, receiving,\nand lending) (De Dominio Divino III, ch. 1,\n p.198.9).7\n The necessary precondition for an act of dominium is\ncreation, of which no created being is capable. This makes God's\ndominium the only true instance of dominium and the\nsource of all created instances of dominium. Because the\nDivine Ideas and their created correlates, the universals, are\nontologically prior to particular created beings, God's\ndominium over universals is prior to His dominium\nover particulars. This means that God creates, sustains, and governs\nthe human species prior to ruling over — and knowing —\nindividual people. This led to questions about determinism that served\nas a starting point for many refutations of Wyclif's theology. ", "\n\nThe second set of acts that define dominium — giving,\nreceiving, and lending — provides the foundation for Wyclif's\nargument that all created dominium necessarily requires\ngrace. God's giving of the divine essence in creating is the truest\nform of giving because God is giving of Himself through Himself, which\nno created being can do. Nor can any created being receive as God\nreceives; God truly receives only from Himself through His giving. God\ngives up nothing in His giving, and acquires nothing in His receiving;\ncreation is God's self-expression, an act in which the divine essence\nis neither decreased nor increased. The crucial act from the created\nstandpoint is God's lending, for here there is real interaction\nbetween Lord and subjects. What human beings as conscious participants\nin God's lending relation can claim as their own is lent to them by\ndivine authority, which they enjoy through grace. ", "\n\nIt is easy to confuse giving with lending because a lord who has only\nbeen “lent” a gift of God for use during his lifetime appears to have\nbeen “given” that gift. God's giving is communicative, not\ntranslative. For us, most giving is translative in that it involves\nthe giver's surrender of every connection to the gift, making it\nnatural for us to suppose that God renounces His authority over what\nHe gives us. In fact, God's giving is communicative, which does not\ninvolve surrender of the gift. Because all that God gives to creation\nwill ultimately return to Him, it makes more sense to speak of God's\ngiving as lending.", " With any instance of lending, Wyclif explains, the lender seeks\nassurance that the borrower truly deserves what is to be lent. Human\ndesert of the dominium they are lent is a matter of some\ncomplexity involving examination of the theological concept of grace.\nWhen a temporal lord lends his subject according to the subject's\nworthiness, the subject's merit is commensurable with the lord's, and\nthe mutual agreement defining the loan can be made according to the\nrespective merit of each party. The merit that allows the subject\ndesert of consideration for the loan is “condigna”, i.e.,\ngrounded in the dignitas shared by lender and\nsubject. Condign merit implies that the meritorious truly deserve the\nreward, requiring the giver to give it to the merited as something\ndue, as when an olympic athelete earns a gold medal by besting all her\nopponents. Such a loan is impossible between Creator and creature,\nbecause there is no way of placing a creature's merit on the same\nscale as God's perfect nature; all the creature has, including its\nworth, is from God, whereas God's perfection is per se. There is no\nway in which a creature can be considered to deserve anything from God\nin such a relation. Congruent merit obtains when the meritorious does\nnot have the power to require anything of the giver. In instances of\ncongruent merit, the goodness of the act does not require the giver to\nreward the agent, though it does provide sufficient cause for the\nreward to be given, as when one receives an Academy Award: although\nmany of the audience members may deserve an Oscar, the winner receives\nit because something about her performance is somehow pleasing to the\nAcademy. Still, Wyclif holds that “It is the invariable law of God\nthat nobody is awarded blessedness unless they first deserve it”\n(De Dominio Divino III, ch. 4, p.229.18). We can move our\nwills to the good, and from this, Wyclif says, grace may — but need\nnot — follow. Thus, we merit congruently thanks to God's generosity\ntowards a will in accord with His own. In effect, God lends merit.", "\n\nWyclif's theology of grace is the key to understanding how his theory\nof human dominium relates to divine dominium, its\ncausal paradigm. Man's lordship is at once ownership and jurisdictive\nmastery, but when a human lord governs, or gives, or receives, or\nlends, these acts are only just insofar as the lord recognizes that\nhis authority is that of a steward: “Any rational creature is only\nimproperly called a lord, and is rather a minister or steward of the\nsupreme Lord, and whatever he has to distribute, he has purely by\ngrace” ([De Dominio Divino III, ch. 6, p.250.25–29). The\nessential characteristic of every instance of human dominium\nis the grace God lends to the individual lord, which itself is\ngrounded in the grace of the Holy Spirit. The human lord appears to\nhave proprietary and juristictive authority by virtue of his own\nexcellence, but this is really only an instantiation of divine\ndominium, a grace-realized agent of God's lordship. This\nmakes the human lord both master and servant; from the divine\nperspective, the lord is God's servant, but from the viewpoint of the\nsubject, he is master. Wyclif is tireless in his emphasis on the\nillusory nature of this mastery; grace allows the human lord to\nrecognize that he is, in fact, the servant of his subjects,\nministering to them as a nurturing steward, not lording over them as\nwould a powerful sovereign. " ], "section_title": "3. Divine Dominium: Creating, Lending, and Grace", "subsections": [ { "content": [ "\n\nDe Civili Dominio begins with the motto, “Civil justice\npresupposes divine justice; civil dominium presupposes\nnatural dominium.” Man's dominium is threefold —\nnatural, civil, and evangelical — but comprehensible as an\ninstantiation of the justice of God's dominium. As he moved\ninto his general analysis of human dominium, Wyclif's\nthoughts turned to the most fundamental instance of God's loving\ngovernance, the Scriptural commandments. The foundation of all that is\nright (ius) in creation, he explains, is divine justice\n(iustitia), so we cannot begin to understand right and wrong\nin creation without understanding God's uncreated right. This was a\nsignificant departure from the Aristotelian position that unaided\nhuman reason is capable of justice, and Wyclif explicitly rejects any\nconception of justice that does not rely on uncreated\n right.[8]\n The laws of Scripture are the purest expression of uncreated right\navailable to human eyes, he explains, and are most clearly expressed\nin the Ten Commandments of Exodus 20, and again in the two greatest\ncommandments of Matthew 22: 37–40. Wyclif's analysis of Christ's law\nof love and of the Ten Commandments proceeds directly from his\ndisquisition on the relation of earthly justice to eternal right in\nDe Mandatis Divinis. That Wyclif uses the same title\n Robert Grosseteste\n had used in his analysis of the decalogue is no accident; Wyclif's\ndebt to Grosseteste's conceptions of sin, love of God, idolatry, and\nthe substance of true faith is obvious throughout the treatise. In\nDe Statu Innocencie, the innocence into which we were created\nbefore the Fall, he says, is the optimal condition for any rational\nbeing. In our prelapsarian state, our wills would have been in perfect\nconcord with the divine will, so that all human action would be just,\neffortlessly aligned with the natural order of creation. In this\ncondition, there would be no need for civil or criminal law, since we\nunderstood what is right naturally.", "\n\nThis denial of the need for human law is of special import, for Wyclif\nlater argues that the evangelical lord, or priest, as heir of Christ's\nrestoration of the possibility of natural dominium, should\nnever be concerned with such matters. In such a state, private\nproperty ownership was unknown. The natural dominium\ndescribed in Genesis 1:26 is characterized by lack of selfishness,\nownership, or any distinction between 'mine' and 'thine'. The true\nsense of Augustine's “All things belong to the just” is most fully\napparent in the prelapsarian natural disposition to share in the use\nof creation while acting as faithful steward to its perfect lord. The\nFall was brought about by the first sin, which Wyclif characterizes as\na privation of God's right in man's soul. We are left with wills prone\nto value the physical, material world above spiritual concerns, and\nthe unavoidable result is private property ownership. We no longer\nunderstand a given created good as a gift on loan from God, but can\nonly see it in terms of our own self-interest, and the unfortunate\nresult is civil dominium, an enslavement to material goods.\n" ], "subsection_title": "3.1 Natural Dominium" } ] }, { "main_content": [ "\n\nWyclif's definition of civil dominium as “proprietary\nlordship in a viator over the goods of fortune fully\naccording to human law” is centered not on legislative authority, but\non the private property ownership enjoyed by the viator, or\nwayfarer, along life's path (De Civili Dominio III ch. 11,\n p.178.9–17).[9]\n This is because all civil dominium is based on the use of\ngoods owned, which is the basis for all postlapsarian conceptions of\njustice (recall that for Wyclif, only God truly owns created things\nbecause creating a thing is necessary for owning it; hence, human\nbeings are only lent created things and can use them justly, or\nunjustly in case they appropriate them for themselves). Before the\nFall, our use of created goods was communal, unencumbered by the\ncomplexity that follows upon selfishness. But now, Wyclif explains,\nthere are three types of use: that directly consequent upon civil\nownership, civil use without ownership, and evangelical use. The first\ntwo are natural results of the Fall, and the third is the result of\nChrist's Incarnation. Before the Incarnation, civil ownership and\ncivil use were grounded in man-made laws designed primarily to\nregulate property ownership. These legal systems tended to have two\ngeneral structures: they were either monarchies, as in most cases, or\nelse they were aristocratic polities. The harmony of the aristocratic\npolity is certainly preferable because it most resembles the state\nenjoyed before the Fall; the benevolent aristocracy, as evidenced in\nthe time of the Biblical judges, would foster the contemplative life,\ncommunalism, and an absence of corruptible governmental apparatus.\n", "\n\nThe most common species of civil dominium is monarchy, in\nwhich a chief executive power holds ultimate legislative\nauthority. This centralized authority in one man is necessary to\nimplement order; there is no real possibility that the many are\ncapable of ruling on behalf of the many, given the prevalence of\nsin. The point of civil dominium is not, as with\n Aristotle,\n the sustenance of individual virtuous activity. Civil\ndominium is a phenomenon based on Original Sin, and is\ntherefore unlikely to produce justice per se. If the government of\nCaesar is occasionally just, it is because it has accidentally\nrealized divine justice. But if civil dominium that is not\ngrounded directly in divine dominium is incapable of\nsustained just governance, and if natural dominium is the\ninstantiation of divine dominium for which man was created,\nhow can any talk of just civil dominium be possible? To\nreturn to the opening dictum of De Civili Dominio, if natural\ndominium is free from private property ownership, how can\ncivil dominium rely upon it in any way? ", "\n\nBefore resolving this problem, we will need to address evangelical\ndominium as yet another factor in Wyclif's conception of\nman's postlapsarian state. " ], "section_title": "4. Types of Human Dominium", "subsections": [ { "content": [ "\n\nChrist restores the possibility of gaining our lost natural\ndominium both through His apostolic poverty and His\nredemptive sacrifice as described in Holy Scripture. Because of\nChrist's sinless nature, He was the first man since Adam capable of\nexhibiting the purity of natural dominium. This Christ shared\nwith His disciples, who were able to renounce all exclusive claims to\ncreated goods in a recreation of the communal caritas lost in\nthe Fall (De Civili Dominio III, 4, p. 51.17–24). This\npoverty is not simply the state of not owning things; one can live\nsinfully as easily in squalor as one can in luxury. The apostolic\npoverty of the early Church is a spiritual state, not an economic\nrejection of civil dominium. The similarity between Wyclif's\nconception of spiritual poverty as the ideal state for Christians and\nthe Franciscan ideal is noteworthy. Wyclif seems to make a case\nsimilar to the Spiritual Franciscans: Christ's life was exemplary for\nall Christians and Christ lived in apostolic poverty; therefore, all\nChristians ought follow His example, or at the least have that option\nopen to them. Wyclif's consonance with the Franciscan tradition is\nalso suggested in his use of\n Bonaventure's\n definition of apostolic poverty in the third book of De Civili\nDominio, but Wyclif's motives are distinctly different from the\nFriars' (De Civili Dominio III, 8, pp. 119–120). While the\nFranciscans argued that their rule allowed them to regain the\nownership-free purity enjoyed by the early Apostolic church, Wyclif\ncontended that Christ's redemptive sacrifice enabled all Christians to\nregain natural dominium itself, not just its purity. This\nsuggested that the Franciscan life was a pale imitation of true\nChristianity, which Wyclif's Franciscan colleagues were quick to point\nout. One of the first critics of Wyclif's dominium thought\nwas William Woodford, O.F.M., who argued that Wyclif had gone too far\nin equating apostolic, spiritual poverty with prelapsarian purity. The\nextensive third book of De Civili Dominio is Wyclif's\nresponse to Franciscan critics like Woodford, and in which lie the\nseeds of the antifraternalism that would characterize his later\nwritings. ", "\n\nWyclif describes apostolic poverty as a mode of having with love,\ncomprehensible in terms of the individual's use of a thing for the\ngreatest spiritual benefit. God alone can bring about the love\ninstantiating divine dominium, making grace necessary for\napostolic poverty. Because the church is founded not on the\nmaterially-based laws of man, but on the spiritually-grounded lex\nChristi, it must be absolutely free of property ownership, the\nbetter to realize the spiritual purity required by apostolic\npoverty. Any material riches that the church comes upon as “goods of\nfortune” must be distributed as alms for the poor, following the\npractice of Christ and the disciples, and the apostolic church. This\nis the ideal to which the Church must aspire through the example of\nChrist, and some of the harshest invective in Wyclif's prose is\ndirected against the Church's refusal to return to this apostolic\nstate. The turning point in Church history was the Donation of\nConstantine, on the basis of which the Church claimed to have the\ncivil dominium of a Caesar. Wyclif was vigorous in his\ncondemnation of the Donation, and would likely have been pleased had\nhe lived into the early fifteenth century, when\n Nicholas of Cusa\n argued persuasively that the document was a ninth-century forgery.\n" ], "subsection_title": "4.1 Evangelical Dominium" }, { "content": [ "\n\nGiven the deleterious influence civil dominium has had on the\nevangelical dominium of Christ's law, it is difficult to\nimagine how Wyclif would set aside some civil lords as capable of\ninstantiating divine justice. But apostolic poverty is not identical\nwith an absence of property ownership; it is having with love. While\nthe clergy as spiritual lords ought to follow Christ's example of\nmaterial poverty, it does not follow that all ownership precludes\nlove. God can certainly bestow grace on those whom He wills to be\nstewards of created goods. Wyclif envisions the just civil lord or\nking as the means by which the Church is relieved of its accumulated\nburden of property ownership. So long as the Church exists in\npostlapsarian society, it must be protected from thieves, heresy, and\ninfidels. Certainly no evangelical lord ought to be concerned with\nsuch matters, given their higher responsibility for the welfare of\nChristian souls. As a result, the Church needs a guardian to ward off\nenemies while caring for its own weel-being and administering alms to\nthe poor. This allows Wyclif to describe just, grace-favored civil\ndominium as different in kind from the civil lordship\npredicated on materialistic human concerns: “It is right for God to\nhave two vicars in His church, namely a king in temporal affairs, and\na priest in spiritual. The king should strongly check rebellion, as\ndid God in the Old Testament, while priests ought minister the\nprecepts mildly, as did Christ, who was at once priest and king.” When\nhe raises conventional topics in political thought, like the\nparticulars of just rule, the responsibilities of royal councillors to\ntheir king, the nature of just war, and royal jurisdiction in\ncommerce, his advice is priestly: “[A] lord ought not treat his\nsubjects in a way other than he would rationally wish to be treated in\nsimilar circumstances; the Christian lord should not desire subjects\nfor love of dominating, but for the correction and spiritual\nimprovement of his subjects, and so to the efficacy of the church”\n(De Officio Regis ch. 1, p. 13.4–8). The king ought provide\nfew and just laws wisely and accurately administered, and live subject\nto these laws, since just law is more necessary for the community than\nthe king. Also, the king should strive to protect the lower classes'\nclaims on temporal goods in the interests of social order, for\n“nothing is more destructive in a kingdom in its political life than\nimmoderately to deprive the lower classes of the goods of fortune”\n(De Officio Regis ch. 5, p.\n 96.9–27).[10]\n On occasion he discusses the king's need of reliable councillors,\ngenerally when discussing the king's need for sacerdotal advice in\ndirecting church reform, but he never mentions Parliament as a\nsignificant aspect of civil rule. ", "\n\nThe most immediate concern of a civil lord living in an age when the\nChurch is being poisoned by avarice should be the radical divestment\nof all ecclesiastical ownership. Wyclif is tireless in arguing for the\nking's right to take all land and goods, and indeed, even the\nbuildings themselves, away from the Church. Should the clergy protest\nagainst royal divestment, threatening the king with excommunication or\ninterdict, the king should proceed as a physician applies his lancet\nto an infected boil. No grace-favored civil lord will be disposed to\nsave up the divested goods of the Church for his own enrichment,\ndespite the obvious temptation. He will distribute the Church's\nill-gotten lands and goods to the people. This, Wyclif explains, will\nbe his continued responsibility even after the Church has been purged,\nfor he is the Church's custodian as well as its protector. ", "\n\nThe hereditary succession by which civil lordship passes from father\nto son is a problem for Wyclif. People cannot inherit the grace needed\nto ensure just ownership and jurisdiction. Primogeniture imperils\ngrace-founded civil lordship, making lords prone to rule on behalf of\ntheir own familial interests rather than in the interests of their\nsubjects. The only means by which Wyclif can envision hereditary\nsuccession operating is through spiritual filiation, in which a civil\nlord instructs a worthy successor. He suggests adoption as the basis\nfor the spiritual primogeniture by which lordship is passed on, which\nwould be preferable to general election, for Wyclif is clear about the\nimpossibility of widespread recognition of grace in a potential civil\nlord: “It does not follow, if all the people want Peter to be their\ncivil lord, that therefore it is just” (De Civili Dominio I,\n18, p. 130.6). Central to his ecclesiology is the impossibility of\ndetermining the presence of grace in another's soul, which militates\nagainst identifying members of the elect with certainty, and therefore\nagainst excommunicating any of them from the Church, as well as ruling\nout popular election as a means of instituting just civil\ndominium. Grants in perpetuity, commonly employed by civil\nlords to guarantee the ongoing obligation of subjects in return for a\ngift of land or political authority, are as impossible as hereditary\ninheritance. A lord might reward someone with a grant while acting as\nGod's steward, but he certainly cannot thereby make his subject's\nprogeny deserve the gift. " ], "subsection_title": "4.2 Civil Dominium" } ] } ]

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