Why Simpler Arguments are Better Moti Mizrahi Florida Institute of Technology Forthcoming in Argumentation Abstract: In this paper, I argue that, other things being equal, simpler arguments are better. In other words, I argue that, other things being equal, it is rational to prefer simpler arguments over less simple ones. I sketch three arguments in support of this claim: an argument from mathematical proofs, an argument from scientific theories, and an argument from the conjunction rule. Keywords: argument; deduction; elegance; explanation; induction; parsimony; proof; simplicity; theory 1. Introduction It appears that many philosophers are often bedazzled by complex arguments. They admire the depth and complexity of a philosopher's arguments even though, when pressed, they might admit that the philosopher's arguments are often not of the highest argumentative standard. This is the impression one gets when it is said with approval of philosophy in general that it is "difficult" (Protevi 2001, p. 150), "hard" (Craig 2002, p. 100), or "complicated" (LeBon 1999, p. 17), and of particular philosophers, like Nietzsche and Hegel, that their "philosophy [is] hard to understand" (Danto 2005, p. 79) or "difficult" (Wood 2004, p. 197).1 As Kelly (2011, p. 106) puts it: To this day, great philosophers who embraced strange conclusions are praised in eulogies for their willingness to follow the argument where it leads, and the ideal is mentioned in faculty handbooks in the context of discussions of academic freedom. I think that this is a mistake. That is to say, I think that, instead of admiring complexity in philosophical argumentation, we should prefer simplicity. In this paper, then, I argue that, other things being equal, simpler arguments are better. In other words, if our goal in putting forth arguments is truth, or at least rational persuasion, then we should prefer simpler arguments, other things being equal.2 1 It is also worth noting that, against the attempt by some, like Simon Blackburn, to make philosophy public, i.e., more accessible to a general audience, others have argued that "philosophy is supposed to be difficult" (http://www.theguardian.com/books/booksblog/2011/feb/25/philosophy-technical-everyday-english). 2 On the use of arguments as tools of rational persuasion, see Hitchcock (2007), Johnson (2000), and Walton (1996). The notion of rational persuasion is supposed to exclude other forms of persuasion, such as threats and other kinds of blackmail. This is also meant to deal with alleged counterexamples where it seems rational to prefer complex 2 As far as arguments are concerned, it is common practice to distinguish between at least two kinds: deductive and inductive (i.e., non-deductive) arguments (see, e.g., Copi and Cohen 2005; Sinnott-Armstrong and Fogelin 2010). The premises of a valid deductive argument, if true, necessitate the truth of the conclusion. Hence, valid deductive arguments can be represented as follows: (Deduction) IF {Premise1, Premise2,..., Premisen} THEN necessarily {Conclusion} The premises of a strong inductive argument, if true, make the truth of the conclusion more probable, i.e., P(Conclusion | Premises) > P(¬Conclusion | Premises), but not guaranteed.3 Hence, strong inductive arguments can be represented as follows4: (Induction) IF {Premise1, Premise2,..., Premisen} THEN probably {Conclusion} With these basic characterizations of deductive and inductive arguments, I will argue in what follows that, of two competing arguments (either deductive or inductive), we should prefer the simpler one, other things being equal. Here is how I plan to proceed. In Section 2, I discuss two varieties of simplicity, namely syntactic simplicity (or elegance) and ontological simplicity (or parsimony). In Section 3, I sketch an argument from mathematical proofs for the claim that, other things being equal, simpler arguments are better. In Section 4, I sketch an argument from scientific theories for the claim that, other things being equal, simpler arguments are better. In Section 5, I sketch an argument from the conjunction rule for the claim that, other things being equal, simpler arguments are better. 2. Two varieties of simplicity Before I sketch my arguments for the claim that, other things being equal, simpler arguments are better, a few clarifications are in order. More specifically, I need to explain in more detail what is meant by simplicity. Philosophers usually identify two varieties of simplicity. In this section, I discuss these two varieties of simplicity. I am not concerned with the justification of simplicity principles.5 Rather, I am concerned with simplicity as a theoretical virtue of arguments.6 arguments. For example, suppose that an eccentric billionaire offers a cash prize for "Most Complex Argument." In this case, it seems rational to prefer more complex arguments, not for the sake of truth and/or rational persuasion, but rather for the sake of winning a cash prize. Thanks to Andrew Aberdein for this point. 3 Discussing the various concepts of probability and their interpretations is beyond the scope of this paper. For a useful overview, see Mellor (2005). 4 Note that this characterization of inductive arguments is broad enough to include non-deductive arguments like abductive arguments (or inferences to the best explanation) and conductive arguments (Govier 2010). For a useful overview, see McKeon (2013). 5 See, e.g., Sober (1988) and (1994). Sober argues that appeals to simplicity are local rather than global, i.e., they depend on local background assumptions and context for their rational justification. 3 2a. Syntactic simplicity According to Sober (1988), considerations of simplicity play a role in the so-called "curve-fitting problem." To use Sober's (1998) example, suppose that scientists want to discover general relations that might hold between independent variable x and dependent variable y. They gather the following set of observations, depicted as points in Figure 1 (adapted from Sober 1998). Figure 1. Curve-fitting and goodness-of-fit adapted from Sober (1998). They then evaluate competing hypotheses, A, B, and C, depicted as curves in Figure 1. In cases such as this one, given that the possibility of error is taken into account, the standard scientific practice, according to Sober (1998, p. 781), is to use the notion of "goodness-of-fit." For example, for each data point on curve A, the scientists compute the squared distance from the observed y-value to the y-value that curve A predicts. In this way, the "sum of squares" (SOS) 6 In this paper, I talk about simplicity as a theoretical virtue of arguments in much the same way that simplicity is taken to be a theoretical virtue of mathematical proofs and scientific theories. See, e.g., Baker (2011), Glynn (2010), and Sober (2001). On the virtues of arguers, rather than arguments, see Aberdein (2010). 4 measures how far the curve is from the data points. If SOS measures how well the data support the curve in question, then the data support curve A better than they support curve B. As Sober (1998, p. 781) puts it: Curves that are close to the data are more likely, in the technical sense defined by R. A. Fisher (1925). Curve A is more likely than Curve B (given standard assumptions about the probability of error) because A confers on the data a higher probability than B does: P(Data | Curve A) > P(Data | Curve B).7 At this point, simplicity becomes relevant, since curve A and curve C have the same SOS values. If the scientists are guided by considerations of simplicity, they will choose curve A over curve C, for curve A is smooth, whereas curve C is bumpy. As Sober (1998, p. 781) puts it, "Curve A seems more simple." In other words, curve A posits a simpler relationship between variables x and y than curve C does, and is thus preferable to curve C.8 This variety of simplicity, then, has to do with the number and complexity of hypotheses. As Baker (2011), puts it, "Syntactic simplicity, or elegance, measures the number and conciseness of the theory's basic principles." More explicitly: (Elegance) Other things being equal, if T1 is more syntactically simple than T2, then it is rational to prefer T1 over T2. As Gauch (2003, p. 270) notes, this is an epistemological conception of simplicity. 2b. Ontological simplicity Another variety of simplicity has to do with the number and complexity of postulated entities rather than hypotheses. Ockham's razor is perhaps the most famous formulation of this variety of simplicity. (Ockham's razor) Entities are not to be multiplied beyond necessity. As Gauch (2003, p. 270) notes, this is an ontological conception of simplicity, which is also known as the principle of parsimony. According to the principle of parsimony, hypotheses that postulate fewer entities, causes, and/or processes are better than hypotheses that postulate more.9 7 Note that this is different from saying that curve A is more probable, i.e., that P(Curve A | Data) > P(Curve B | Data). 8 As an anonymous reviewer helpfully pointed out, the assumption that smoothness is simpler than bumpiness can be operationalized in several ways. For example, the degree of a polynomial can be taken to indicate the number of bumps of the associated graph, in which case, a low degree is preferable to a high degree polynomial. As Armitage et al (2002, p. 378) put it: "Considerations of simplicity suggest that as low an order as possible should be used; for example, we should normally use linear regression unless there is any particular reason to use a higher-degree polynomial." 9 See also Sober (2001, p. 14) who calls this variety of simplicity "semantic simplicity." 5 As a principle of theory choice, then, the principle of parsimony states that, other things being equal, it is rational to prefer a theory that commits us to a limited ontology. More precisely: (Parsimony) Other things being equal, if T1 is more ontologically parsimonious than T2, then it is rational to prefer T1 over T2. According to this principle, if a theory, T1, has all the ontological commitments of a competing theory, T2, but T2 is also ontologically committed to Fs, whereas T1 is not, then T1 is more ontologically parsimonious than T2. Thus the notion of ontological parsimony is usually cashed out in terms of Quine's notion of ontological commitment. According to Quine (1981, p. 144), T is ontologically committed to Fs if and only if T entails that Fs exist.10 Like (Elegance), (Parsimony) is also a principle of theory choice. That is, (Elegance) states that, of two competing theories, we should choose the syntactically simpler one, other things being equal. Likewise, (Parsimony) states that, of two competing theories, we should choose the semantically simpler one, other things being equal. Einstein is said to have made a similar point by saying that "things should be made as simple as possible, but not simpler." According to Norman (2011, p. 50), what Einstein actually said was that "the grand aim of all science ... is to cover the greatest possible number of empirical facts by logical deductions from the smallest possible number of hypotheses or axioms." Accordingly, simplicity is a relative property; a theory is simple only relative to another competing theory. Applied to arguments, (Elegance) and (Parsimony) state that, of two competing arguments, we should prefer the simpler one, other things being equal. More explicitly, (Elegance) states that, of two competing arguments, we should choose the syntactically simpler one (i.e., the one with fewer inferences), other things being equal. Likewise, (Parsimony) states that, of two competing arguments, we should choose the semantically simpler one (i.e., the one with fewer premises), other things being equal. With these syntactic, i.e., (Elegance), and semantic or ontological, i.e., (Parsimony), conceptions of simplicity in hand, I now turn to my arguments for the claim that, other things being equal, simpler arguments are better. I outline three arguments in support of this claim: an argument from mathematical proofs, an argument from scientific theories, and an argument from the conjunction rule. 3. An argument from mathematical proofs My first argument for the claim that, other things being equal, simpler arguments are better is an argument from mathematical proofs. The argument runs as follows: (1.1) If, other things being equal, simpler mathematical proofs are better, then, other things being equal, simpler deductive arguments are better. (1.2) Other things being equal, simpler mathematical proofs are better. 10 In terms of ontological parsimony, a further distinction is often drawn between qualitative parsimony (the number of types of entities postulated) and quantitative parsimony (the number of individual entities postulated). See Baker (2003). 6 Therefore, (1.3) Other things being equal, simpler deductive arguments are better. In support of (1.2), consider what Russell (1918, p. 60) says about mathematics: Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.11 In general, mathematicians prefer mathematical proofs that are elegant and simple. For example (emphasis added): Here we want to discuss another bijection proof, due to Joyal, which is less known but of equal elegance and simplicity (Aigner and Ziegler 2004, p. 174). One proof stands out for its simplicity and elegance. It was found by Ernst Witt in 1931 and combines two elementary ideas towards a glorious finish (Aigner and Ziegler 2004, p. 23).12 If mathematicians' preference for simpler proofs is rational, then a preference for simpler deductive arguments more generally is rational as well. Why? Because mathematical proofs are arguments of the genus (Deduction) and species of the same genus usually share most of their properties in common except the property that makes them different species. For example, Homo sapiens, Homo habilis, and Homo erectus are species of the genus Homo. They share most of their properties in common except the property that makes them different species, which is taken to be primarily increased cranial capacity. If this is correct, then given that mathematical proofs are a species of the genus (Deduction) in virtue of being proofs (i.e., the sort of arguments whose premises, if true, necessitate the truth of the conclusion), it is reasonable to infer that they share most of their properties in common with other arguments of the genus (Deduction), such as the property of being better arguments when simpler than competing arguments. Now, granted that mathematicians prefer simpler proofs, and that their preference for simpler proofs is rational, it is reasonable to infer that, other things being equal, it is rational to prefer simpler arguments of the genus (Deduction). 11 Commenting on Dufour's Argument and Explanation in Mathematics (2013) at the conference of the Ontario Society for the Study of Argumentation (May 22-25, 2013), Aberdein mentions empirical results suggesting that "mathematicians who completed the study expected explanatory proofs to be precise, useful and not intricate. Or, in other words, simple, fruitful, and exact." Available at: http://www.academia.edu/3646529/Commentary_on_Michel_Dufour_Argument_and_explanation_in_mathematics. 12 See also the special issue of Foundations of Science on Mathematical Argumentation (vol. 14, issue 1-2), edited by Aberdein and Dove (2009). For example, according to Coleman (2009, p. 30), "One proof is better than another because it is more elegant, or informative, or shorter, or easier to follow, or less conceptually demanding, or more easily generalisable, or with less fuzzy details, or more direct, or more constructive, or even more novel..." (emphasis added). 7 To sum up, my argument in support of premise (1.1) runs as follows: (1.1a) If X and Y are species of genus G, then X and Y share most of their properties in common, except the property that makes them different species. (1.1b) Mathematical proofs and other deductive arguments are species of the genus (Deduction). Therefore, (1.1) If, other things being equal, simpler mathematical proofs are better, then, other things being equal, simpler deductive arguments are better.13 With this support for premises (1.1) and (1.2), I submit, the argument from mathematical proofs shows that, other things being equal, simpler arguments of the genus (Deduction) are better. 4. An argument from scientific theories According to Baker (2011), "Many philosophers believe that, other things being equal, simpler theories are better." This seems to be the case especially as far as scientific theories are concerned. For instance, as van Fraassen (1980, p. 87) writes: When a [scientific] theory is advocated, it is praised for many features other than empirical adequacy and strength: it is said to be mathematically elegant, simple, of great scope, complete in certain respects: also of wonderful use in unifying our account of hitherto disparate phenomena, and most of all, explanatory.14 Now, the important question for present purposes is the following: are simpler arguments better (in much the same way that simpler theories are better, other things being equal)? Here is an argument for an affirmative answer to this question: (2.1) If, other things being equal, simpler scientific theories are better, then, other things being equal, simpler deductive arguments are better. (2.2) Other things being equal, simpler scientific theories are better. Therefore, (2.3) Other things being equal, simpler deductive arguments are better. 13 As an anonymous reviewer helpfully pointed out, (1.1a) is consistent with there being a particular property F of species X but not Y, which are both species of genus G, that is not the property that makes X and Y different species of G. Perelman and Olbrechts-Tyteca call this kind of argument "argument a pari" (as opposed to argument a contrario). According to Perelman and Olbrechts-Tyteca (1969, p. 241), "These arguments deal with the application or nonapplication to another species of the same genus of what can be asserted about some particular species." 14 It is worth noting that, for van Fraassen, these features are merely pragmatic, not epistemic or truth-conducive. I will return to this point in Section 5. 8 In support of premise (2.2) consider how, like mathematicians' preference for simpler mathematical proofs, scientists' preference for simpler scientific theories is quite evident from scientific practice.15 If scientists' preference for simpler theories is rational, then a preference for simpler arguments more generally is rational as well. Why? Because scientific theories are a species of the genus (Deduction). To see why scientific theories are a species of the genus (Deduction), note that philosophers of science generally agree that successful scientific theories do not merely describe phenomena but rather explain them. In other words, successful scientific theories are explanations. As Godfrey-Smith (2003, p. 190) puts it: Science aims to tell us, and often succeeds in telling us, what the world is like. But it is also common to think that science tells us why things happen; we learn from science not just what goes on but why it does. Science apparently seeks to explain as well as describe (emphasis in original). For example, the Alvarez Asteroid Impact theory is supposed to be an explanation for the K-T extinction. The theory of evolution by natural selection is supposed to be an explanation for biological diversity. The general theory of relativity is supposed to be an explanation for what we call gravity. Now, the obvious question is this: what are explanations? Philosophers of science have proposed several answers. Which answer is the correct one is a matter of debate.16 Several philosophical accounts of scientific explanation, however, construe explanations deductively. Take, for example, the unification account of explanation. According to Kitcher (1989, p. 448), "all explanation is deductive." More explicitly, Kitcher argues that an explanation consists of an argument pattern, which is an ordered triple composed of a schematic argument (i.e., a sequence of schematic sentences, where a schematic sentence is a sentence in which non-logical terms have been replaced with letters), a set of filling instructions for each term in the schematic argument (i.e., instructions for filling in the letters in schematic sentences), and a classification of the schematic argument (i.e., a description of the premises, conclusions, and rules of inference used in the schematic argument).17 For instance, consider the argument pattern Kitcher (1993, p. 83) labels "Common Descent": Question: Why do the members of G, G` share P? Answer: (1) G, G` are descended from a common ancestor G0. (2) G0 members had P. 15 See, e.g., Baker (2007), Forster and Sober (1994), and Glynn (2010). 16 For a useful overview of philosophical accounts of scientific explanation, see Woodward (2011). 17 An earlier account that identifies scientific explanations with deductive arguments is the Deductive-Nomological account (Hempel 1965). 9 (3) P is heritable. (4) No factors intervened to modify P along the G0-G, G0-G` sequences. Therefore, (5) Members of G and G` have P. As Kitcher (1993, p. 83) explains: This consists of five schematic sentences. We could equip it with Filling Instructions by requiring that G, G`, G0 be replaced by names of groups of organisms, and that P be replaced by the name of a trait of organisms. Similarly, the classification would declare that (1)-(4) are premises and that (5) is deduced from them (emphasis added). If Kitcher is right, then to explain is to derive descriptions of various phenomena by using as few argument patterns as possible. As Kitcher (1989, p. 423) puts it, "Science advances our understanding of nature by showing us how to derive descriptions of many phenomena, using the same pattern of derivation again and again, and in demonstrating this, it teaches us how to reduce the number of facts we have to accept as ultimate" (emphasis added). To sum up, then, from the following claims: Scientific theories are explanations. Explanations are a species of the genus (Deduction). It follows that Scientific theories are a species of the genus (Deduction). If this is correct, then given that scientific theories are a species of the genus (Deduction) in virtue of being derivations (i.e., the sort of arguments whose premises, if true, necessitate the truth of the conclusion), it is reasonable to infer that they share most of their properties in common with other arguments of the genus (Deduction), such as the property of being better arguments when simpler than competing arguments. Now, granted that scientists prefer simpler explanations, and hence simpler scientific theories, and that their preference for simpler theories is rational, it is reasonable to infer that, other things being equal, it is rational to prefer simpler arguments of the genus (Deduction). To sum up, my argument for premise (2.1) runs as follows: (2.1a) If X and Y are species of genus G, then X and Y share most of their properties in common, except the property that makes them different species. (2.1b) Scientific theories and other deductive arguments are species of the genus (Deduction). Therefore, (2.1) If, other things being equal, simpler scientific theories are better, then, other things being equal, simpler deductive arguments are better. 10 With this support for premises (2.1) and (2.2), I submit, the argument from scientific theories shows that, other things being equal, simpler arguments of the genus (Deduction) are better. Some might object to the argument from scientific theories by insisting that, pace Kitcher, scientific explanations, and hence scientific theories, are not species of the genus (Deduction). They might point out that one form of non-deductive reasoning that is taken to be ubiquitous in scientific practice is Inference to the Best Explanation (IBE), which is a form of argument of the genus (Induction), given that the premises of an IBE, if true, do not guarantee the truth of its conclusion.18 In reply, I would like to suggest that this objection actually provides a way to extend the argument from scientific theories to arguments of the genus (Induction) as well.19 To see how, consider the general form of IBE (Govier 2010, p. 302): 1. D exists. 2. H1 would explain D. 3. H1 would offer the best available explanation of D. Therefore, probably, 4. H1 is true. [Where "D refers to data, and H1 refers to a hypothesis put forward in an attempt to explain that data" (Govier 2010, p. 298).]20 The key premise of an IBE, of course, is the third premise. What makes one explanation the best among several competing explanations? Philosophers of science have identified the following epistemic desiderata, the so-called "theoretical virtues," which make one explanation better than others: "accuracy, simplicity, internal and external consistency, breadth of scope, and fruitfulness" (Longino 1995, p. 383).21 Notice that one of those theoretical virtues is simplicity, which means that, of two competing explanations, H1 and H2, the simpler one is the best one, other things being equal. If this is correct, then the third premise of an IBE is true insofar as H1 is simpler than a competing explanation, H2. From this it follows that an IBE for H1 is better than an IBE for H2 insofar as the third premise of the former is true, whereas the third premise of the latter is not. In other words, arguments of the genus (Induction), namely IBEs, are better when the explanations they are arguments for are simpler than competing explanations. 18 On IBE, see Lipton (2004). Cf. Bird (2007) who argues that there is a form of IBE, namely, inference to the only explanation, in which the truth of the premises guarantees the truth of the conclusion. 19 Thanks to an anonymous reviewer for this point. 20 Cf. Psillos (2007, pp. 442-443). 21 Cf. Kuhn (1977, pp. 320-339). 11 Now, if IBEs are better when the explanations they are arguments for are simpler than competing explanations, and IBEs are a species of the genus (Induction), then it follows that simpler arguments of the genus (Induction) are better by (2.1a). More explicitly: (2.1a) If X and Y are species of genus G, then X and Y share most of their properties in common, except the property that makes them different species. (3.1) IBEs and other inductive arguments are species of the genus (Induction). Therefore, (3.2) If, other things being equal, simpler IBEs are better, then, other things being equal, simpler inductive arguments are better. With this argument for (3.2), it follows that simpler arguments of the genus (Induction) are better, since, other things being equal, simpler IBEs are better. That is: (3.2) If, other things being equal, simpler IBEs are better, then, other things being equal, simpler inductive arguments are better. (3.3) Other things being equal, simpler IBEs are better. Therefore, (3.4) Other things being equal, simpler inductive arguments are better. Given (2.3) and (3.4), then, it follows that simpler arguments are better. That is, of two competing arguments, A1 and A2, if A1 is simpler than A2, then A1 is a better argument than A2. So, from the following claims: Other things being equal, simpler deductive arguments are better. [(2.3)] Other things being equal, simpler inductive arguments are better. [(3.4)] It follows that Other things being equal, simpler arguments are better. Accordingly, of two competing arguments, A1 and A2, if A1 is simpler than A2, we should prefer A1 over A2. 5. An argument from the conjunction rule Some might object to the argument from mathematical proofs and the argument from scientific theories by insisting that simplicity-either (Elegance) or (Parsimony)-is a pragmatic, not an epistemic, virtue. For instance, in the philosophy of science, constructive empiricists distinguish between pragmatic and epistemic virtues of scientific theories and argue that simplicity is a pragmatic, not an epistemic, virtue of scientific theories. As van Fraassen (1985, p. 252) writes: 12 A person may believe that a certain theory is true and explain that he does so, for instance, because it is the best explanation he has of the facts or because it gives him the most satisfying world picture. This does not make him irrational, but I take it to be part of empiricism to disdain such reasons (emphasis added). In other words, according to constructive empiricists, pragmatic virtues, like simplicity, are not truth-conducive, unless one holds a metaphysical belief in the simplicity of the world. As empiricists, however, constructive empiricists think that such a metaphysical belief is unwarranted. As van Fraassen (1980, p. 90) puts it, "it is surely absurd to think that the world is more likely to be simple than complicated (unless one had certain metaphysics or theological views not usually accepted as legitimate factors in scientific inference)." Inspired by constructive empiricism, then, some might object to the argument from mathematical proofs and the argument from scientific theories by claiming that principles like (Elegance) and (Parsimony) are not truth-conducive because "it is surely absurd to think that the world is more likely to be simple than complicated" (van Fraassen 1980, p. 90). Although I have taken the rationality of mathematicians' preference for simpler mathematical proofs and scientists' preference for simpler scientific theories as basic premises in my arguments from mathematical proofs and scientific theories, respectively, I would like to offer another argument for the claim that, other things being equal, simpler arguments are better by way of a response to the aforementioned objection. This argument, if cogent, shows that one can accept that, other things being equal, simpler argument are better, without a commitment to a metaphysical belief in the simplicity of the world, a belief that constructive empiricists find unwarranted. To introduce this argument, I need to take a short detour through what Tversky and Kahneman (1983) call "the conjunction fallacy" in probability judgments. In their famous study, Tversky and Kahneman (1983) presented the following case to participants: Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable? (L1) Linda is a bank teller. (L2) Linda is a bank teller and is active in the feminist movement. Most participants choose (L2), even though (L2) is less probable than (L1), given that two conditions must hold in order for (L2) to be true, namely, that Linda is a bank teller and that she is active in the feminist movement, whereas only one of them must hold for (L1) to be true, namely, that she is a bank teller. More generally, for any two events, A and B, Pr(A & B) ≤ Pr(A) and Pr(A & B) ≤ Pr(B). Although (L2) is less probable, it appears that most people find (L2) more plausible. As Tversky and Kahneman's study show, an account rich in details often seems more plausible to people, even though the more details the account contains, the less probable it is, since the 13 probability of the conjunction of all the details is lower than the probability of each detail (by the conjunction rule). Accordingly, even though it may seem that an account rich in details is more probable, that is not the case. An account rich in details only seems more probable, because it is more plausible, but it is actually less probable, given that the more details the account contains, the less probable it is, since the probability of the conjunction of all the details is lower than the probability of each detail (by the conjunction rule). Likewise, an argument rich in details (i.e., rich in premises) might seem better than an argument with fewer premises, even though the more details (i.e., more premises) the argument contains, the probability that it is a sound argument (i.e., a valid argument with true premises) is lower, since the probability of the conjunction of all the details (i.e., all the premises) is lower than the probability of each premise (by the conjunction rule). With this understanding of the conjunction rule, and the distinction between probability and plausibility, the following argument from the conjunction rule for the claim that, other things being equal, simpler arguments are better can be made: (4.1) According to the conjunction rule, for any two competing arguments, A1 with premise P, and A2 with premises P and Q, Pr(P & Q) ≤ Pr(P) and Pr(P & Q) ≤ Pr(Q). (4.2) Given the conjunction rule, of two competing arguments, it is rational to prefer the simpler one (i.e., the argument with fewer premises), other things being equal. Therefore, (4.3) Of two competing arguments, it is rational to prefer the simpler one (i.e., the argument with fewer premises), other things being equal. In other words, other things being equal, it is rational to prefer simpler arguments, i.e., arguments with fewer premises. If A1 has fewer premises than A2, then we should prefer A1 over A2, other things being equal. The conclusion of this argument from the conjunction rule applies to arguments of the genus (Induction) as well as to arguments of the genus (Deduction) and there is no need to assume "that the world is more likely to be simple than complicated" (van Fraassen 1980, p. 90). 6. Conclusion In this paper, I have argued that, other things being equal, simpler arguments are better. In other words, I have argued that, other things being equal, it is rational to prefer simpler arguments over less simple ones. I have sketched three arguments in support of this claim. According to the first argument, if simpler mathematical proofs are better, other things being equal, then simpler argument of the genus (Deduction) are better, other things being equal. According to the second argument, if simpler scientific theories are better, other things being equal, then simpler arguments of the genus (Deduction) are better, other things being equal. I have extended this argument from scientific theories to arguments of the genus (Induction) as well on the grounds that, if simpler IBEs are better, other things being equal, then simpler arguments of the genus 14 (Induction) are better, other things being equal. According to the third argument, the conjunction rule implies that, other things being equal, it is rational to prefer simpler arguments, i.e., arguments with fewer premises. Admittedly, there are many questions that stem from the aforementioned arguments, which I have not addressed in this paper. For example, how do we rank arguments according to simplicity? How do we distinguish between simplicity of arguments and simplicity of statements that serve as premises and conclusions of arguments? There are more questions that need be addressed, I am sure, but that will have to wait for another occasion.22 Far from being a problem, I take this to be a virtue of the arguments put forth in this paper, since, in addition to simplicity, fruitfulness is often considered a theoretical virtue of both mathematical proofs and scientific theories. Acknowledgments I am grateful to Andrew Aberdein and three anonymous reviewers of Argumentation for helpful comments on earlier drafts. References Aberdein, A. and Dove, I. J. (Eds.). (2009). Mathematical Argumentation. Foundations of Science, 14, Issue 1-2, 1-152. Aberdein, A. (2010). Virtue in Argument. Argumentation, 24, 165-179. Aberdein, A. (2013). Commentary on Michel Dufour's Argument and Explanation in Mathematics. Ontario Society for the Study of Argumentation (May 22-25, 2013). Available at: http://www.academia.edu/3646529/Commentary_on_Michel_Dufour_Argument_and_ex planation_in_mathematics. Aigner, M. and Ziegler, G. M. (2004). Proofs from THE BOOK. Third Edition. Berlin: SpringerVerlag. Armitage, P., Berry, G., and Matthews, J. N. S. (2002). Statistical Methods in Medical Research. 4th Ed. Malden, MA: Blackwell Science. Baker, A. (2003). Quantitative Parsimony and Explanatory Power. British Journal for the Philosophy of Science, 54, 245-259. Baker, A. (2007). Occam's Razor in Science: A Case Study from Biogeography. Biology and Philosophy, 22, 193-215. 22 Another important question raised by an anonymous reviewer is the following: Is there a simpler argument than the ones sketched in this paper for the claim that simpler arguments are better? If we allow for zero-premise arguments, then perhaps the simplest argument for the claim that simpler arguments are better is this: simpler arguments are better. It must be noted, however, that zero-premise arguments are said to be valid "when and only when the conclusion is a tautology" (Corcoran 2001, p. 67). 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Philosophical Studies, 154, 105-124. Kitcher, P. (1989). Explanatory Unification and the Causal Structure of the World. In P. Kitcher and W. Salmon (Eds.), Scientific Explanation (pp. 410-505). Minneapolis: University of Minnesota Press. Kitcher, P. (1993). The Advancement of Science: Science Without Legend, Objectivity Without Illusions. New York: Oxford University Press. Kuhn, T. S. (1977). Objectivity, Value Judgment, and Theory Choice. In The Essential Tension: Selected Studies in Scientific Tradition and Change (pp. 320-339). Chicago: The University of Chicago Press. LeBon, T. (1999). Philosophy and the Perils of Popularisation. Practical Philosophy, 2, 15-17. Lipton, P. (2004). Inference to the Best Explanation. Second Edition. London: Routledge. Longino, H. E. (1995). Gender, Politics, and the Theoretical Virtues. Synthese, 104, 383-397. McKeon, M. (2013). Argument. In J. Fieser and B. Dowden (Eds.), Internet Encyclopedia of Philosophy (May 2013). http://www.iep.utm.edu/argument/. Mellor, D. H. (2005). Probability: A Philosophical Introduction. New York: Routledge. Norman, D. A. (2011). Living with Complexity. Cambridge, MA: The MIT Press. Perelman, C. and Olbrechts-Tyteca, L. (1969). The New Rhetoric: A Treatise on Argumentation. J. Wilkinson and P. Weaver (trans.). Notre Dame: University of Notre Dame Press. Protevi, J. (2001). Political Physics. New York: The Athlone Press. 16 Psillos, S. (2007). The Fine Structure of Inference to the Best Explanation. Philosophy and Phenomenological Research, 74, 441-448. Quine, W. V. O. (1981). Theories and Things. Cambridge, MA: Harvard University Press. Russell, B. (1918). Mysticism and Logic. London: Longmans, Green, and Co. Sinnott-Armstrong, W. and Fogelin, R. (2010). Understanding Arguments: An Introduction to Informal Logic. Eighth Edition. Belmont, CA: Wadsworth. Sober, E. (1988). Reconstructing the Past: Parsimony, Evolution and Inference. Cambridge, MA: MIT Press. Sober, E. (1994). Let's Razor Ockham's Razor. In E. Sober (Ed.). From a Biological Point of View (pp. 136-157). Cambridge: Cambridge University Press. Sober, E. (1998). Simplicity (in scientific theories). In E. Craig (Ed.). Routledge Encyclopedia of Philosophy (pp. 780-783). Volume 8. London: Routledge. Sober, E. (2001). What is the Problem of Simplicity? In A. Zellner, H. Keuzenkamp, & M. McAleer (Eds.). Simplicity, Inference, and Modeling: Keeping it Sophisticatedly Simple (pp. 13-31). Cambridge: Cambridge University Press. Tversky, A. and Kahneman, D. (1983). Extensional versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment. Psychological Review, 90, 293-315. van Fraassen, B. C. (1980). The Scientific Image. New York: Oxford University Press. van Fraassen, B. C. (1985). Empiricism in the Philosophy of Science. In P. M. Churchland and C. A. 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Debunking Objective Consequentialism: The Challenge of Knowledge-Centric Anti-Luck Epistemology Paul Silva Jr. University of Cologne It is a part of our commonsense perspective on the world that we know and have some justified beliefs about the moral status of our prospective actions. With these we also attempt to make our way towards a theoretical understanding of what makes these moral beliefs true, i.e. we attempt to home in on the correct normative theory of ethics. It is generally assumed that the search for the correct normative theory of ethics is not absolutely futile, i.e. at the very least we can find reasons to justifiedly increase to some degree our confidence in some normative theories over others. Certain versions of objective act consequentialism are widely thought to be among the normative theories of ethics that we should take most seriously and thus be comparatively more certain about. In a large part, this is due to its ability to explain important parts of our commonsense moral perspective. In what follows I will explain why this is mistaken from the perspective of knowledgecentric anti-luck epistemology. For according to it there are modal anti-luck demands on both knowledge and justification, and it turns out that our beliefs about the moral status of our prospective actions are almost never able to satisfy these demands if objective act consequentialism is true. Accordingly, if objective act consequentialism is true, we neither know nor have justified beliefs about the moral status of our prospective actions. So a problematic kind of applied moral skepticism obtains. As I will explain, this kind of applied moral skepticism introduces problematic limits on our ability to use objective act consequentialism's explanatory power to justifiedly increase our confidence in its truth. This is, in part, a product of higher-order defeat as I explain in the final section. There is, however, a silver lining for objective act consequentialists. For there is at least one type of objective act consequentialism, prior existence consequentialism, that is poised to avoid at least some of the epistemic problems discussed in this paper. Knowledge-Centric Anti-Luck Epistemology and Justificatory Defeat Take a standard lottery case: LOTTERY I have a ticket for a fair lottery with very long odds. The lottery has been drawn, although I have not heard the result yet. Reflecting on the odds involved I conclude that (L) my ticket is a loser. Besides my (accurate) assessment of the odds, I have no other reason to think my ticket is a loser. As it turns out, my belief that I own a losing ticket is true. It is widely thought that L cannot be known in these circumstances. The explanation for the unknowability of L in these circumstances is not that I lack strong evidence in favor of L. L is extremely probable on my evidence. Rather, the unknowability of L is thought to be owed to the fact that my belief, even if true, would be in some sense true by "epistemic luck"–a kind of luck that is incompatible with knowing. Generally, the nature of this epistemically problematic form of luck is thought to involve a modal defect in my believing L in these circumstances. The two leading accounts of this modal defect locate the problem with my belief not at the actual world where my belief is true, but in a relation I bear toward myself in nearby possible worlds where I falsely believe 2 L. The sensitivity account and the safety account are the leading accounts of that relation. Here is a common formulation of these proposed requirements on knowledge: SENSITIVITY Had it been that P, S would not still have believed that P (had S used the method that S actually used to determine whether P). SAFETY S could not have easily had a false belief as to whether or not P (using the method that S actually used to determine whether or not P).1 If either principle is correct, then L cannot be known in Lottery for neither principle is satisfied in that case. It is easy to see why Sensitivity fails in Lottery. My belief in L–that my ticket is a loser–is based solely on my statistical evidence. But I could have that same evidence even if my belief were false, i.e. even if there is some nearby world where my ticket is a winner. Because of this, I would still believe L on the basis of that same statistical evidence even were L false. So Sensitivity offers a straightforward explanation of the idea that L is unknowable in Lottery. It is a bit trickier to see how Safety explains the same fact. The idea that a belief could not have easily been false is the idea that the world would have to be significantly different in order for the target to belief to be false. For example, I truly believe that I will not become a US Navy Seal this year. And this belief could not have easily been false in the sense that in order for it to be false the world would have to be quite different in a variety of respects: the relevant governing bodies of the US Navy would have to decide that it's advisable to lower their fitness standards (dramatically) in order for me to be considered admissible as a Seal, or there would have to be some kind of conspiracy where all relevant individuals involved in assessing Seal candidates willingly lie about my admissibility, or something else equally unusual would have to happen. Given my age, my limited physical fitness, my limited ability to persevere through physical pain, my lack of political power to orchestrate a conspiracy, and my intention not to join the Seals, etc. it could not have easily been false that I will not become a Seal this year. So this belief satisfies Safety, and so is a candidate for knowledge. In contrast, as Pritchard (2008: section 4) explains, my belief in L in Lottery could easily have been false since "all that need be different in order for one's ticket to be a winning ticket is that a few numbered balls fall in a slightly different configuration." Intuitively, such worlds are not significantly different from the actual world and so my belief could not have easily been false.2 While the unknowability of L in Lottery is widely held, some hold out hope that L might never the less be justifiedly believable in Lottery (e.g. standard Lockean evidentialists about justification). But knowledge-centric theorists have generally argued for theses about the relation between knowledge and justification that are inconsistent with this view. While I cannot here go into the details, the general motivation connecting knowledge and justification has to do with the normative role of knowledge in our assessment of belief. First, not only does one intuitively fail to know in Lottery cases, one intuitively shouldn't hold, and so can't justifiedly hold, a lottery belief. If justification requires knowledge, this fact about lottery beliefs can easily be explained. Second, the idea that justification requires knowledge can explain why certain Moorean beliefs shouldn't be held, e.g. I believe P, but I do not know P. Third, a knowledge requirement on justification can explain our critical practices of assessing others' beliefs. For instance, if someone believes P, it's perfectly normal to object to their believing P on the basis of the fact that they don't know it. A knowledge requirement on justification would also explain this. 1 Pritchard (2005; 2008; 2012). 2 See Rabinowitz (2019) for further discussion of safety conditions. 3 It turns out there are different ways of putting knowledge at the center of the justification of belief. For example, some knowledge-centric theorists think that knowledge is necessary and sufficient (and to be token-identified with) justified belief (Williamson 2013; Sutton 2007; Littlejohn 2012): J↔K: S justifiedly believes that P iff S knows that P. If correct, then not only can L not be known in Lottery, it cannot be justifiedly believed in Lottery either. Alternatively, some knowledge-centric theorists have argued that justification requires something just shy of knowing: being in a position to know (Bird 2007; Ichikawa 2014; Rosenkranz 2018): J→PK: S justifiedly believes P only if S is in a position to know P. If correct, the impossibility of knowing L entails the impossibility of justifiedly believing L in Lottery also.3 Now, if it's possible to have justified false beliefs, then perhaps it's possible to fail to know L while never the less having justification for certain higher-order beliefs: the belief that one knows L (though one doesn't) or the belief that one is justified in believing L (though one isn't). But notice both J↔K and J→PK entail the defeat of these higher-order beliefs. For if either J↔K or J→PK are true, it's impossible to have justified false beliefs if they cannot ever constitute knowledge. Accordingly, it's not just first-order lottery beliefs that are unjustified, these higher-order beliefs are also unjustified. So justification for both first-order and higher-order beliefs are lost. Unsurprisingly, the idea that knowledge must be a bare possibility for one to have justification has seemed to some a difficult bullet to bite. Accordingly, some have sought to unify the intuitions driving knowledge-centric views of justification without committing themselves to the idea that knowledge or possible knowledge is required for justified belief. For example, Smithies (2012) has argued that justification for the belief that P requires that one enjoy justification to believe a higher-order claim about the knowability of P, i.e. that one have justification to believe that one is in a position to know P: J→JPK: S justifiedly believes P only if S has justification to believe that she's in a position to know P. If this is correct then there is room for both first-order and higher-order justified beliefs in L. But of course such justified beliefs are limited to those who are sufficiently ignorant of the fact that one cannot know L in Lottery, i.e. those who lack access to reasons sufficient to defeat the claim that one can know L in Lottery. Accordingly, J→JPK leaves many of us who are reflective about lottery cases in much the same position as J↔K and J→PK: we cannot know L, we cannot 3 Alternatively, some knowledge-centric theorists have argued that justification should be understood virtuetheoretically in terms of exercises of knowledge-yielding abilities, competences, or dispositions (Miracchi 2015; Silva 2017; Kelp 2018; Millar 2019): J→EKD: S justifiedly believe P only if S's belief is produced from an exercise of a knowledge-yielding ability (process, competence, disposition). Provided such competences are understood in an anti-luck fashion as requiring safety or sensitivity, then we will get the same result here as with J→PK. However, Silva, Miracchi, and Kelp all seem to allow for justified beliefs in standard gettier cases (where Safety and Sensitivity are not satisfied) and thus do not require for the exercise of those abilities that one believe safely or sensitively. Millar (2019) may be an exception to this. 4 justifiedly believe L, and we cannot even falsely justifiedly believe that we have justification to believe L. As formulated, each of the knowledge-centric principles of justification mentioned above concern only doxastic justification. It is typically important to keep in mind the difference between propositional justification (=having justification to φ) and doxastic justification (=justifiedly φing). I will not make much of this in what follows and switch freely between the two locutions. This will make no difference under the assumption that having propositional justification requires at least the bare possibility of doxastic justification. Since knowledge of lottery beliefs is impossible, this will make both doxastic and propositional justification impossible to come by on the knowledge-centric views mentioned above. In what follows I'll explain the surprising problem that anti-luck epistemology and knowledge-centric epistemology generate for ethical consequentialists. Objective Act Consequentialism For present purposes let a consequentialist about moral requirements be anyone who thinks that the truth of claims about what actions are morally required (forbidden, optional) depend solely on the long term consequences of that action in the following way: CONSEQUENTIALISM S is required to perform action A if the the long term net value of A-ing is greater than the long term net value of performing any alternative action. If the the long term net value of A-ing is less than the the long term net value of performing some alternative action, then A-ing is wrong. If the the long term net value of A-ing is the same as the the long term net value of some alternative and there is no other alternative action with a higher net value, then A-ing is optional. NET VALUE The net value of an action is the amount of value that results from that action in a specified period of time minus the disvalue that results from that action in that same period of time. This leaves open a number of dimensions along which to specify one's preferred version of (objective, act) consequentialism. One could take an egoist view on which all that matters is how one's present actions maximize the net amount of pleasure of one's experiences in their life– in which case 'the long term' is just the duration of one's life. Alternatively, one could take a classical utilitarian view on which right action is determined by actions maximizing the net pleasure for all sentient beings who stand to be impacted by one's actions–in which case 'the long term' is just the duration of the effects of one's potential actions. This could be 10 minutes from the time of action, 10 years, or 10,000 millennia. Alternatively, one could take a form of prior existence utilitarianism where all that matters for fixing right action is how one's prospective actions would impact people who already exist (our would come to exist irrespective of which action is performed)–in which case 'the long term' is limited to the lifespan of those individuals.4 While the forms of consequentialism I'm explicitly discussing are the maximizing varieties, satisficing varieties will have an equally difficult time avoiding the epistemic problem I develop for maximizing varieties.5 Also, while consequentialist views suffer perhaps the worst from 4 For critical discussion of prior existence utilitarianism see Singer (2011). 5 If Sensitivity is right, this will be because our view as to whether or not a prospective action satisfices net value will still have to rely on something like premise (1) of the CMR (see below). While if Safety is right, this will be 5 knowledge-centric anti-luck epistemology, any moral theory that creates space for the moral status of at least some actions to be determined by the net value of their consequences will face a version of this problem.6 Let's start by considering high-stakes moral beliefs about the actual world. The belief that it's actually wrong to murder the entire Rohingya population of Myanmar, the belief that it's actually wrong to steal large sums of money from effective charities that would use it to alleviate the suffering of many, the belief that it's actually wrong to euthanize every other baby in the world, the belief that it's actually wrong to drop an atomic bomb near a large population to observe it's negative effects across that population, etc. These are all claims about prospective actions in the actual world as opposed to merely possible worlds. When it comes to merely possible worlds, we can often a priori specify the net value of consequences of our potential actions more or less arbitrarily. Not so with the actual world. What I'm concerned with is the epistemic standing of our moral beliefs about actions we and others can perform in the actual world. One thing these moral beliefs have in common is that they concern foreseeablely high-stakes actions, i.e. these are prospective actions that are specified in such a way that it is assumed that the individual for whom they are prospective actions is in a position to know that in the near term an exceptionally bad moral state of affairs would result from performing them. Now, there can be prospective high-stakes actions in circumstances where every alternative action is also a high-stakes action (think of trolley cases where the numbers on the tracks are roughly equal). These are not the kind of circumstances I have in mind in what follows. Our moral beliefs about these kinds of high-stakes actions will be controversial and skepticism about them will be far less troubling. Rather, I'm limiting reflection to cases where a prospective high-stakes action has at least one prospective low-stakes alternative that one could easily perform. For example, a military leader's ability (a) to murder or displace all, or nearly all, of Myanmar's Rohingya population as well as his ability (b) to not murder or displace any of them. Ordinary moral judgements would affirm that performing (a) is morally wrong when–though perhaps not only when–(b) is an available prospective course of action. High-stakes moral beliefs are common, generally uncontroversial, and often function as starting points (and sometimes as fixed points) in non-skeptical moral theorizing. Their evidential usefulness in moral theorizing is owed to the fact that they seem to be justified and knowledgeable moral beliefs. But if our high-stakes moral beliefs are to be justified and knowledgeable from the consequentialist point of view, their justification and knowledgeability depends on induction in some way or other. Accordingly, we must inductively project in some way from past experience with a given action type to the conclusion that the target instance of that type will in one's present circumstances maximize net value in the long run. But the worry immediately arises: it's surely possible that a prospective action that would have horrendous near term consequences never the less maximizes net value in the long run. This is an old objection, and consequentialists have had something to say about this. For example, G. E. Moore (1903 [1988], 93) tentatively suggests the following: As we proceed further and further from the time at which alternative actions are open to us, the events of which either action would be part cause become because just as prospective actions could have easily failed to maximize net value, they could also have easily failed to satisfice net value (see below). 6 For example, one needn't be a consequentialist to endorse the following. Suppose it would otherwise be permissible either to help group A or to help group B by providing one with money. However, you know that group B would use a portion of that money to set in place a series of events whose outcomes would very likely severely and unnecessarily harm group A in the long run. Provided helping group A would not have comparably bad likely outcomes, intuitively, helping group B would (ceteris paribus) be wrong and it would be wrong because of the likely consequences of doing so. If that intuitive moral judgement is right, it is not one that could be known or justifiedly believed if the argument against consequentialism below is sound. 6 increasingly dependent on those other circumstances, which are the same, whichever action we adopt. The effects of any individual action seem, after a sufficient space of time, to be found only in trifling modifications spread over a very wide area, whereas its immediate effects consist in some prominent modification of a comparatively narrow area. Since, however, most of the things which have any great importance for good or evil are things of this prominent kind, there may be a probability that after a certain time all the effects of any particular action become so nearly indifferent, that any difference between their value and that of the effects of another action, is very unlikely to outweigh an obvious difference in the value of the immediate effects. J.J. C. (1973, 33) concisely reiterates the idea: [W]e do not normally in practice need to consider very remote consequences, as these in the end rapidly approximate to zero like the furthermost ripples on a pond after a stone has been dropped into it. Shelly Kagan (1998, 64) says that: Of course, it remains true that there will always be a very small chance of some totally unforeseen disaster resulting from your act. But it seems equally true that there will be a corresponding very small chance of your act resulting in something fantastically wonderful, although totally unforeseen. If there is indeed no reason to expect either, then the two possibilities will cancel each other out as we try to decide how to act. If Moore, Smart, and Kagan are right, then past experience allows us to reliably project the net value of a given action at least in a reasonable range of normal circumstances. For according to their suggestion, the long term effects of any prospective action will (or is objectively likely to) wash out in a way that tends to make its foreseeable near term net value representative of its long term net value. Accordingly, if any kind of action allows for this sort of projection, it's exactly the sort of high-stakes actions described above where the foreseeable near-term consequences are extremely high.7 Let's first clarify just how we can move from the informal assertions of projectability made above to outright claims about a given action being right or wrong. Here is an apparently cogent way of specifying the needed details: CONSEQUENTIALIST MORAL REASONING (CMR): (1) If up to the present A-ing in circumstances like the ones I'm in have (or would have) frequently enough maximized net value up till now, then A-ing in 7 Yet some have worried about this Moore-Smart-Kagan style response. For it's not hard to imagine a series events where, say, murdering lots of children has the highest net value in the long run, and it's not quite clear why we should think that the long term consequences will (or are objectively likely to) balance out (Greaves 2016), Moreover, Elgin (2015) points out that, under certain conditions, the mere fact that there are long term distant consequences statistically prohibits us from being able to reliably assess the net value of our prospective actions. But Elgin's criticism does not apply with equal force to all forms of consequentialism. For example, some forms of consequentialism give special place to the interests of beings that already exist (e.g. prior existence utilitarianism, ethical egoism). Once that is done, distant future consequences become irrelevant when it comes to undermining the the Moore-Smart-Kagan thesis. An upshot of the epistemic objection I present below is that one cannot retreat to something like prior existence utilitarianism to avoid it. 7 my present circumstances will very likely maximize net value in the long run. (suggested by Moore, Smart, and Kagan) (2) Up to the present A-ing in circumstances like the ones I'm in have (or would have) frequently enough maximized net value up till now. (3) Therefore, A-ing in my circumstances will very likely maximize net value in the long run. (from 1 and 2) (4) Therefore, given that I have no significant reason to think A-ing will fail to maximize net value in the long run, A-ing in my circumstances will maximize net value in the long run. (from 3 and contraction (see below)) (5) An action is wrong iff it fails to maximize net value the long run. (consequentialism) (6) Therefore, refraining from A-ing in my circumstances is wrong. (from 4 and 5) Let me say a few things about this pattern of reasoning before getting to the lottery problem for consequentialists. (1) offers us a way of specifying the underlying idea that Moore, Smart, and Kagan suggested on behalf of consequentialism. The parenthetical "would have" in (1) is to indicate that sometimes we can judge a possible past action's prospective net value in the near-term without the need of anyone having performed that specific action in the past. In no point in the past have 99.9% of earth's population suffered horribly unto death from the release of a virus. Yet we know (or can at any rate be reasonably certain) that if someone were to have done that five years ago, that action would have failed to maximize net value up to now–i.e. it's an action whose net value calculated up to the present moment is lower than some alternative prospective action's net value when calculated up to the present moment. Importantly, the justification for (1) is inductive: provided induction from past experience is sufficiently reliable in the case of high-stakes beliefs, then we have defeasible inductive justification for endorsing the conditional specified by (1). Of course, as noted above, the consequentialist application of (1) assumes that maximization of net value up to the present is a sufficiently reliable indicator of maximization of net value in the long run. Again, some versions of consequentialism will have a relatively easy time justifying this (prior existence utilitarianism) while other versions will have a comparatively difficult time doing so (classical utilitarianism). This is something that warrants further discussion, but I will pass it by to discuss other issues. For the most part, the justification of (1) becomes progressively easier the more high-stakes our potential actions are irrespective of the version of consequentialism one endorses. (2) stands to be justified by historical knowledge of the effects of such actions in suitably similar circumstances. (3) is a deductive conclusion from (1) and (2). (4) relies on what I'm calling a contraction principle, i.e. a principle that licenses transitioning from probabilistically qualified claims to probabilistically unqualified claims in the absence of defeating information. For example, when a radiologist examines an X-ray of your leg and concludes that you have a hairline fracture, they are (or can be) implicitly reasoning from a contraction principle. For while X-rays offer us highly reliable representations when interpreted by a trained professional, there is still some small margin of error; there is still some small chance that either the X-ray production involved some error in representation or the reader mistook something for a hair-line fracture that was not a hair-line fracture. Even so, a skilled radiologist can justifiedly judge that you in fact have a hair-line fracture, despite the small error possibilities so long as they have no reason to think the small error possibility is actual. Similarly, most of the time a jury judges (and sincerely believes) someone guilty of a crime on the basis of a body of evidence, they engage in a form of contractive reasoning from how things very likely are, to how things actually are. There is a lot to say about contractive reasoning and I will return to this below. 8 For now, it's enough to note that we regularly engage in (or could engage in) such reasoning, and that often enough such reasoning is justified. (5) is just a coarse-grained representation of the objective consequentialist thesis. If any of our high-stakes moral beliefs are to be justified on the assumption that some form of consequentialism is correct, then it has to be the case that something akin to a CMR argument underlies the justification our high-stakes moral beliefs. Applied Moral Skepticism Why think that our high-stakes moral beliefs are like lottery beliefs if consequentialism is true? The answer flows out of the different constraints that Sensitivity and Safety impose on knowledgeable belief. Take Sensitivity first. Suppose you believe A-ing is wrong on the basis of a CMR argument. Would you still hold this belief on the basis of a CMR argument even if your belief were false, i.e. even if A-ing were not wrong? You would. This is because CMR arguments are not "sensitive" to the falsity of the beliefs they support. The reason for this lies with premise (1), which is a conditional that relies on induction from past experience for its justification. But any reasoning that relies on the past as an indicator of the future will fail to satisfy Sensitivity. For example, believing the sun will rise tomorrow because it has always done so in the past will not count as knowledge since I would still have believed this even if, for whatever reason, the sun were destroyed or the rotation of the earth halted before it had a chance to rise tomorrow (Vogel 1987; Comesaña 2007). Similarly, it could improbably turn out to be the case that murdering all the local school children maximizes net value because that would lead to a distant future where many, many more children are saved from lethal harm they otherwise would have suffered. But even were that the unlikely truth, if my belief that it's wrong were based on a CMR argument I would still have believed that it's wrong to kill all the local school children just on the basis of the fact that such an action would foreseeably fail to maximize net value. Accordingly, if Sensitivity is true then premise (1) is unknown given its inductive justification. And if premise (1) is unknown then presumably we cannot know the moral status of an action on the basis of a CMR argument–at least not those that rely on induction for their justification of premise (1). Now, it's easy to see how little knowledge remains to us if Sensitivity is true since inductive knowledge becomes exceedingly difficult to come by in general (Vogel 1987; Comesaña 2007). For this reason, many philosophers have been reluctant to endorse Sensitivity and have turned to its contrapositive cousin, Safety, for help. Safety lacks the skeptical implications of Sensitivity for inductive beliefs. So if Safety is true, then premise (1) of CMR is not obviously in jeopardy. And if one can know premise (1) along with the rest of the premises, then it would seem that one could also come by moral knowledge and justified moral beliefs on the basis of CMR arguments also. The thing to note is that while Safety doesn't threaten premise (1), it does obstruct the derivation of it's conclusion by imposing limits on the ability of contractive reasoning to afford us knowledge. For recall that to reach (4) in the CMR we needed to rely on the idea that we can transition from claims about how things very likely are (/will be) to how things actually are (/will be). But if Safety is true, then we can only gain knowledge of actuality from knowledge of likelihoods when beliefs so based could not have easily been false. But if consequentialism is true, virtually all of our high-stakes moral beliefs are just that: they could easily have been false. To see this consider a variation on the Lottery case from above: AGENT-CAUSAL LOTTERY You're holding a lottery ticket whose number reads: 1524353214. Unlike a standard lottery, the winning ticket number is not determined through a nearrandom mechanical process. Rather, the winning ticket number is determined by the following process. Each day starting from tomorrow a new participant is selected to decide which number comes next in the series. It can be any 9 number between 1 and 5. Since there are 10 numbers on the ticket, this will take 10 days and will require 10 participants to select these numbers. Each participant is freely selected by the previous participant, while the first participant is chosen at random. And, excepting the first participant, each participant is informed as to the number selected by the previous participant and encouraged, but not forced, to choose a different number than the previous participant. Accordingly, the participants are influenced by that knowledge when selecting a number. Given this selection process, it's clear that the winning ticket number will not be chosen at random. So you know that, unlike a fair lottery, the exact chances that your ticket's number will be selected cannot be calculated in any precise way. But you do know that your chance of winning is obviously very small. So it's extremely likely that your ticket is a loser. Reflecting on the long odds involved you conclude (L*) that your ticket is a loser. Besides your rough assessment of the odds, you have no other reason to think your ticket is a loser. As it turns out, your number will not be selected in the following ten days and so your belief that you own a losing ticket is true. This is an "agent-causal lottery" in the sense that there is a clear non-random agent-causal path reaching from the first participant to the winning ticket number. For each participant (except for the first) is selected by the previous participant, and each participant's number selection is causally influenced by their knowledge of the previous participant's number selection (except for the first). Accordingly, the outcome of this lottery is casually produced by the actions performed by previous agents and the responses of the agents who are impacted by those past actions. Do you know (L*) that you have a losing ticket in Agent-Causal Lottery? I venture to claim that anyone convinced that you cannot know L in Lottery, will be likewise drawn to the conclusion that you cannot know L* in Agent-Causal Lottery. The parallels are too deep, and the differences are too superficial. But more to the point, if Safety is what we rely on in diagnosing what goes wrong with my belief in Lottery, then we must also rely on it in diagnosing this case. And given the parallels between this case and the original, it's easy to see where this is heading. For in the original case, my belief in L fails to satisfy Safety because it could easily have been false since "all that needs to be different in order for one's ticket to be a winning ticket is that a few numbered balls fall in a slightly different configuration" Pritchard (2008: section 4). And similarly, your belief in L* in Agent-Causal Lottery could easily have been false since all that needs to be different in order for your ticket to be a winning ticket is for a few people to have made a slightly different decisions about which number and subsequent participant to choose. So if Safety explains my failure to know in Lottery, it explains your failure to know in the Agent-Causal Lottery. The Agent-Causal Lottery is a trying case for non-skeptical consequentialists. For the outcomes of our high-stakes actions in the long run are a lot like the outcome in an Agent-Causal Lottery. For in both kinds of case there is an agent-causal path that produces the relevant outcome, and at each (or very many) node in that path things could easily have been otherwise. For there are almost always many alternative available prospective actions an agent might easily have performed, thereby leading to different outcomes with a plausibly different net value. Take, for example, the 2019 mass shooting in El Paso, Texas. 22 were killed and 24 were injured (if this is insufficiently high-stakes just imagine many more were killed and injured). By the lights of ordinary moral intuitions this was a wrong action and we know that this was a wrong action. But the knowledgeability of this as a wrong action doesn't just depend on (i) the known failure of this action to maximize net value in the near term, and (ii) the idea that (i) ensures that the shooting is also very likely to fail to maximize net value in the long run. For the lesson of the lottery cases is that beliefs that are highly likely to be true don't necessarily satisfy Safety. 10 According to Safety, for the belief that the shooting was wrong to constitute knowledge it has to be the case that the shooting could not have easily maximized net value in the long run. But just as in the Agent-Causal Lottery where it's easy to see how one could have easily beat the odds since each person could have easily chosen a slightly different number, in the mass shooting case too one could "easily have beat the odds" in at least some of the following ways. Consider that the El Paso shooting was the most lethal shooting in the US since 1949. And it comes just after a string of other disturbingly violent shootings. It is also a shooting that took place in a highly populated city in Texas–a state that ordinarily shows strong resistance to fire-arm restrictions. Now we know that, historically, social movements that bring about social change often erupt from tragic events. Could it not easily be the case that this shooting helps tip the balance in support of gunlaw reform in the US in such a way that future shootings are significantly reduced and thereby maximize net value in the long run? It's hard to see what grounds there could be for resisting this judgement in our present circumstances. But even if that fails to be the case, it could easily be the case that this shooting makes the general population much more vigilant and willing to report on people they know who might be at risk of committing a mass shooting, thus preventing many more shooting, and thereby maximizes net value in the long run. Further, it could easily be the case that this shooting has "identity-affecting" consequences that maximize net value, i.e. it impacts which people come into existence in long run and thereby impacts the net value of one's action. Perhaps, for example, by killing these people in El Paso the shooter has impacted history in a way that would prevent the births of what would otherwise have been the next massively genocidal dictator and thereby maximizes net value in the long run (cf. Lenman 2000). According to the thesis floated by Moore, Smart, and Kagan, these are very unlikely possibilities since they are possibilities where the near term consequences fail to accurately represent the long term consequences, but so too is my winning the lottery. And what the lottery teaches us is that the unlikelihood of an outcome doesn't ensure that the unlikely outcome could not have easily obtained. Recall that Sensitivity undermined the knowledgeability of premise (1). This was due to the fact that Sensitivity undermines inductive knowledge generally. But Safety is compatible with inductive knowledge and so it imposes no immediate threat to (1). Rather, Safety obstructs the justification of (4) by imposing a limit on knowledge-generating contractive reasoning. For recall that to reach (4) in the CMR we needed to rely on the idea that we can transition from claims about how things very likely are (/will be) to how things actually are (/will be). But if Safety is true, then we can only gain knowledge of actuality from knowledge of likelihoods when beliefs so based could not have easily been false. But, given the nature of the relation between our present actions and their outcomes (especially in the social world), consequentialism seems to imply that the vast majority of our high-stakes moral beliefs could easily have been false. This puts knowledge of our high-stakes moral beliefs out of reach. What impact might this have on the justificatory status of high-stakes moral beliefs if consequentialism is true? Well, if J↔K or J→PK are true, then our high-stakes moral beliefs are unjustified since both principles limit justified beliefs to those that are potential knowledge. If J→JPK is true, the justificatory status of our high-stakes moral beliefs fare a bit better. Since, so long as one is ignorant of the unknowability of our high-stakes moral beliefs it will be easier to have justification to believe that one is in a position to know them. This is in some sense "good news" for consequentialists since it carves out space for there to be some unknown yet justified highstakes moral beliefs. But the consequentialists for whom this is good news are only those who are ignorant of the fact that knowing requires either Sensitivity or Safety. Consequentialism and Self-Defeat According to many, the justification for believing (or assigning high credence to) consequentialism or any other general normative theory of ethics depends substantially on its ability to explain our "considered moral judgements", which includes our concrete case moral beliefs (or intuitions) that we reflectively endorse. Our high-stakes moral beliefs form an important subset of our considered 11 moral judgements about the actual world for they tend to be widely believed and are intuitively striking in the sense that their denials seem clearly to be false. This is doubtless due to the fact that, as defined, our high-stakes moral beliefs involve wantonly harming others in circumstances that have extremely bad effects in the near-term. Consequentialists have regularly argued that consequentialism can explain the truth of at least an important range of our (correct) considered moral judgements, while offering error theories for those it cannot explain. Let 'HSMBs' refer to our high-stakes moral beliefs about the moral status of prospective actions that consequentialism can explain. This will include only those HSMBs that are true by the lights of consequentialism. For example, if the HSMB is that it's wrong to murder Sam, it is an HSMB that consequentialism can explain only if killing Sam fails to maximize net value in the long run. Otherwise, it's just not true and so not the sort of HSMB that a consequentialist should expect their theory to explain. Explaining why people have false HSMBs is the job of an error theory. As is common, I interpret the evidential relevance of explanatory considerations in probabilistic terms. That is, we are to understand data that is explained by a hypothesis as increasing the likelihood of that hypothesis. Thus: Pr(Consequentialism|HSMBs) > Pr(Consequentialism) But this evidential inequality is only one part of the story of how we might be able to come to justifiedly increase our confidence in consequentialism in light of our HSMBs. For in order to justifiedly increase our confidence in consequentialism we must be able to update (e.g. conditionalize, jeffrey conditionalize, pseudo-conditionalize) on our HSMBs. But on all accounts, in order to update on some evidence, E, we have to stand in some epistemically significant relation to E. For example, standard update rules require that we have learned E. Now, it's an interesting question what it takes to "learn" that E. But at a minimum it should require that one have justification for believing E. The idea that one can justifiedly update on information that one doesn't even have justification to believe is very hard to make sense of. Now, the arguments of the previous section show that knowledge-centric anti-luck epistemology is inconsistent with having justification for believing our HSMBs, and so knowledgecentric anti-luck epistemology is inconsistent with the justification of updating on our HSMBs if consequentialism is true. This threatens to yield a form of standard first-order epistemic defeat for consequentialism since a crucial part of the evidence that is supposed to justify it, our HSMBs, are inaccessible to us. Yet consequentialism might be false. If consequentialism is false, then our HSMBs can be justified provided the correct normative theory of ethics doesn't give the long term consequences of our actions a role in determining right from wrong (and thereby run afoul of knowledge centric anti-luck epistemology). Generally, non-consequentialist theories of ethics and rule consequentialist theories don't do this, and thereby create a more hospitable environment for the justification of our HSMBs. Now, if our HSMBs can be justified then presumably they can also be justifiedly updated on, and therefore they can function as evidence for consequentialism! This is a surprising little fact, one that gives us a bit of higher-order information about our evidence for consequentialism, namely: HOE: Our evidence (constituted by our HSMBs) supports having an increased degree of confidence in consequentialism only if consequentialism is false. Now on the probabilistic outlook I began with the question of having a justified high credence in consequentialism depends on the evidential relation between our prior confidence in consequentialism and our prior confidence in consequentialism conditional on our HSMBs. 12 Having observed the way in which HOE follows from the arguments above, our evidence now includes both our HSMBs and HOE. Intuitively, HOE should have some evidential impact on our confidence in consequentialism. But what kind of impact, exactly? Surely it should not increase our confidence in consequentialism. Put in general terms, it's beyond credulity to think one can know/justifiedly believe that (i) E, and that (ii) E supports P only if ¬P, and think that one can justifiedly believe (or increase confidence in) P on the basis of (i) and (ii).8 That leaves two options with regard to the evidential impact of HOE: either HOE lowers our posterior confidence in consequentialism, or it screens off the relevance of our HSMBs. I don't know of an uncontroversial reason to prefer either disjunct. So let us remain neutral on this issue. Accordingly, we have the following inequality: Pr(Consequentialism|HSMBs & HOE) ≤ Pr(Consequentialism) That is to say, learning HOE at the very best screens off whatever justification our HSMBs afforded us for thinking that consequentialism is true; at worst it should lower our credence in consequentialism. So unless one has sufficient reason to believe (or at least increase confidence in) consequentialism that is wholly independent of our HSMBs, consequentialism is not a moral theory that we can justifiedly believe or have high confidence in. Put differently, if justifiedly believing consequentialism depends on its ability to explain our HSMBs, then consequentialism doesn't seem like the sort of ethical theory that can be justifiedly believed. It's a kind of blindspot, a truth about the structure of moral normativity that we would seem incapable of rationally recognizing as such. There are a number of questions this raises about the methodology of justifying normative theories. I think the most salient one it raises concerns the ability of concrete case judgments or intuitions about merely possible cases to justify normative theories. For when it comes to the merely possible cases we can generally specify in the very construction of the cases whether or not the prospective action under consideration maximizes net value in the long run. If ethical theorizing can function in an epistemically robust way with only such cases to work with, then the applied moral skepticism of consequentialism would not impose a limit on our ability to justifiedly increase our confidence in consequentialism. But, as others have worried, there seems to be something epistemically circular about this.9 Whether or not it is an epistemically problematic form of circularity is a discussion for another time. It's worth mentioning that there is one form of consequentialism that may evade these worries: prior existence consequentialism. For on such views whether or not an action is right or wrong just depends on it's impact on individuals who already exist (or would exist no matter which action were performed). Now, unlike our prospective actions, we have historical knowledge of the actual outcomes of people's past actions and how those actions impacted the people who existed (or doubtless would exist) at that time. Arguably, this historical knowledge can afford us knowledge of the moral status of past high-stakes actions if a version of prior existence consequentialism is correct. For example, the dropping of a second atomic bomb on a populated area like Nagasaki was gratuitous for quickly ending war with Japan. The war could have been brought to just as quick an end if it were not dropped or if it were dropped on an uninhabited area of Japan. We know this. So we know that this past action was wrong, even if at the time those who were making the decision were not–by the lights of knowledge-centric anti-luck epistemology–able to know or 8 If the evidential support relation involved some kind of standard conditional (material, indicative, counterfactual, strict), then (i) and (ii) would yield a contradiction. For whichever way the conditional is interpreted, it cannot be self-consistent and non-trivially true that: (E&(E → P)) → -P. But I'm here assuming evidential support is not essentially bound to such conditionals, and can often be understood in broadly probabilistic terms. 9 See Pust's (2013, Ch. 1) discussion of Rawls and the method of reflective equilibrium. 13 justifiedly believe it. The upshot is that prior existence consequentialist views may only imply a limited form of skepticism: we may not be able to know or justifiedly believe whether or not a prospective action of ours is wrong (due to the arguments of section 3), but at least we can justifiedly increase our confidence in prior existence consequentialist views in virtue of their explanatory power with respect to HSMBs about the past.1011 References Bird, Alexander. 2007. "Justified Judging." Philosophy and Phenomenological Research 74 (1): 81–110. https://doi.org/10.1111/j.1933-1592.2007.00004.x. Comesaña, Juan. 2007. "Knowledge and Subjunctive Conditionals." Philosophy Compass 2 (6): 781–91. https://doi.org/10.1111/j.1747-9991.2007.00076.x. Elgin, Samuel. 2015. "The Unreliability of Foreseeable Consequences: A Return to the Epistemic Objection." Ethical Theory and Moral Practice 18 (4): 759–66. https://doi.org/10.1007/s10677015-9602-8. Greaves, Hilary. 2016. "Cluelessness." 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Noûs 46 (2): 265–88. https://doi.org/10.1111/j.1468-0068.2010.00787.x. 10 For obvious reasons, this historical knowledge is not helpful for versions of consequentailism, like classical utilitarianism, which make the moral status of past actions depend on distant future outcomes. I'm grateful to Rik Peels for prompting me to reflect on whether our historical knowledge of outcomes could be useful in the justification of consequentialist views. 11 I'm grateful to the Alexander von Humboldt Foundation which funded this research as well as to Michael Blome-Tillmann, Michael Klenk, and Rik Peels who offered helpful feedback on this project. 14 Sutton, Jonathan. 2007. Without Justification. Bradford Books. Cambridge, MA: MIT Press. Vogel, J. 1987. "Tracking, Closure, and Inductive Knowledge." In the Possibility of Knowledge: Nozick and His Critics, edited by Steven Luper, 197–215. Lanham, MD: Rowman & Littlefield. Williamson, Timothy. 2013. "Knowledge First." 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