Hilary Putnam
Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, and computer scientist, and a major figure in analytic philosophy in the second half of the 20th century. He made significant contributions to philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science. Outside philosophy, Putnam contributed to mathematics and computer science. Together with Martin Davis he developed the Davis–Putnam algorithm for the Boolean satisfiability problem and he helped demonstrate the unsolvability of Hilbert's tenth problem. Putnam was known for his willingness to apply equal scrutiny to his own  philosophical positions as to those of others, subjecting each position to rigorous analysis until he exposed its flaws. As a result, he acquired a reputation for frequently changing his positions. In philosophy of mind, Putnam is known for his argument against the type-identity of mental and physical states based on his hypothesis of the multiple realizability of the mental, and for the concept of functionalism, an influential theory regarding the mind–body problem. In philosophy of language, along with Saul Kripke and others, he developed the causal theory of reference, and formulated an original theory of meaning, introducing the  notion of semantic externalism based on a thought experiment called Twin Earth. In philosophy of mathematics, he and his mentor W. V. O. Quine developed the Quine–Putnam indispensability argument, an argument for the reality of mathematical entities, later espousing the view that mathematics is not purely logical, but "quasi-empirical". In epistemology, he is known for his critique of the well-known "brain in a vat" thought experiment. This thought experiment appears to provide a powerful argument for epistemological skepticism, but Putnam challenges its coherence. In metaphysics, he originally espoused a position called metaphysical realism, but eventually became one  of its most outspoken critics, first adopting a view he called "internal realism", which he later abandoned. Despite these changes of view, throughout his career he remained committed to scientific realism, roughly the view that mature scientific theories are approximately true descriptions of ways things are. In the philosophy of perception, Putnam came to endorse direct realism, according to which perceptual experiences directly present one with the external world. He once further held that there are no mental representations, sense data, or other intermediaries that stand between the mind and the world. By 2012, however, he rejected this commitment in  favor of "transactionalism", a view that accepts both that perceptual experiences are world-involving transactions, and that these transactions are functionally describable (provided that worldly items and intentional states may be referred to in the specification of the function). Such transactions can further involve qualia. In his later work, Putnam became increasingly interested in American pragmatism, Jewish philosophy, and ethics, engaging with a wider array of philosophical traditions. He also displayed an interest in metaphilosophy, seeking to "renew philosophy" from what he identified as narrow and inflated concerns. He was at times a politically controversial figure, especially for his involvement  with the Progressive Labor Party in the late 1960s and early 1970s. At the time of his death, Putnam was Cogan University Professor Emeritus at Harvard University. Life. Putnam was born in Chicago, Illinois, in 1926. His father, Samuel Putnam, was a scholar of Romance languages, columnist, and translator who wrote for the "Daily Worker", a publication of the American Communist Party, from 1936 to 1946 (when he became disillusioned with communism). As a result of his father's commitment to communism, Putnam had a secular upbringing, although his mother, Riva, was Jewish. The family lived in France until 1934 , when they returned to the United States, settling in Philadelphia. Putnam attended Central High School; there he met Noam Chomsky, who was a year behind him. The two remained friends—and often intellectual opponents—for the rest of Putnam's life. Putnam studied philosophy at the University of Pennsylvania, receiving his B.A. degree and becoming a member of the Philomathean Society, the country's oldest continually existing collegiate literary society. He did graduate work in philosophy at Harvard University and later at UCLA'S philosophy department, where he received his Ph.D. in 1951 for his dissertation, "The Meaning of the  Concept of Probability in Application to Finite Sequences". Putnam's dissertation supervisor Hans Reichenbach was a leading figure in logical positivism, the dominant school of philosophy of the day; one of Putnam's most consistent positions has been his rejection of logical positivism as self-defeating. After teaching at Northwestern University (1951–52), Princeton University (1953–61), and MIT (1961–65), Putnam moved to Harvard in 1965. His wife, the philosopher Ruth Anna Putnam, took a teaching position in philosophy at Wellesley College. Hilary and Ruth Anna were married on August 11, 1962. The Putnams, rebelling against the antisemitism they experienced during their  youth, decided to establish a traditional Jewish home for their children. Since they had no experience with the rituals of Judaism, they sought out invitations to other Jewish homes for Seder. They began to study Jewish ritual and Hebrew, and became more Jewishly interested, identified, and active. In 1994, Hilary Putnam celebrated a belated Bar Mitzvah service. In the 1960s and early 1970s, Putnam was an active supporter of the American Civil Rights Movement and opposition to the Vietnam War. In 1963, he organized one of MIT's first faculty and student committees against the war. After moving to Harvard  in 1965, he organized campus protests and began teaching courses on Marxism. Putnam became an official faculty advisor to the Students for a Democratic Society and in 1968 a member of the Progressive Labor Party (PLP). He was elected a Fellow of the American Academy of Arts and Sciences in 1965. After 1968, his political activities centered on the PLP. The Harvard administration considered these activities disruptive and attempted to censure Putnam, but two other faculty members criticized the procedures. Putnam permanently severed his relationship with the PLP in 1972. In 1997, at a meeting of former draft resistance activists  at Boston's Arlington Street Church, he called his involvement with the PLP a mistake. He said he had been impressed at first with the PLP's commitment to alliance-building and its willingness to attempt to organize from within the armed forces. In 1976, Putnam was elected president of the American Philosophical Association. The next year, he was selected as Walter Beverly Pearson Professor of Mathematical Logic in recognition of his contributions to the philosophy of logic and mathematics. While breaking with his radical past, Putnam never abandoned his belief that academics have a particular social and ethical responsibility  toward society. He continued to be forthright and progressive in his political views, as expressed in the articles "How Not to Solve Ethical Problems" (1983) and "Education for Democracy" (1993). Putnam was a Corresponding Fellow of the British Academy. He was elected to the American Philosophical Society in 1999. He retired from teaching in June 2000, but as of 2009 continued to give a seminar almost yearly at Tel Aviv University. He also held the Spinoza Chair of Philosophy at the University of Amsterdam in 2001. He was the Cogan University Professor Emeritus at Harvard University and a founding patron  of the small liberal arts college Ralston College. His corpus includes five volumes of collected works, seven books, and more than 200 articles. Putnam's renewed interest in Judaism inspired him to publish several books and essays on the topic. With his wife, he co-authored several books and essays on the late-19th-century American pragmatist movement. For his contributions in philosophy and logic, Putnam was awarded the Rolf Schock Prize in 2011 and the Nicholas Rescher Prize for Systematic Philosophy in 2015. Putnam died at his home in Arlington, Massachusetts, on March 13, 2016. Philosophy of mind. Multiple realizability . Putnam's best-known work concerns philosophy of mind. His most noted original contributions to that field came in several key papers published in the late 1960s that set out the hypothesis of multiple realizability. In these papers, Putnam argues that, contrary to the famous claim of the type-identity theory, it is not necessarily true that "Pain is identical to C-fibre firing." According to Putnam's papers, pain may correspond to utterly different physical states of the nervous system in different organisms even if they all experience the same mental state of "being in pain". Putnam cited examples  from the animal kingdom to illustrate his thesis. He asked whether it was likely that the brain structures of diverse types of animals realize pain, or other mental states, the same way. If they do not share the same brain structures, they cannot share the same mental states and properties, in which case mental states must be realized by different physical states in different species. Putnam then took his argument a step further, asking about such things as the nervous systems of alien beings, artificially intelligent robots and other silicon-based life forms. These hypothetical entities, he contended, should  not be considered incapable of experiencing pain just because they lack human neurochemistry. Putnam concluded that type-identity theorists had been making an "ambitious" and "highly implausible" conjecture that could be disproved by one example of multiple realizability. This is sometimes called the "likelihood argument". Putnam formulated a complementary argument based on what he called "functional isomorphism". He defined the concept in these terms: "Two systems are functionally isomorphic if 'there is a correspondence between the states of one and the states of the other that preserves functional relations'." In the case of computers, two machines are functionally isomorphic if  and only if the sequential relations among states in the first exactly mirror the sequential relations among states in the other. Therefore, a computer made of silicon chips and one made of cogs and wheels can be functionally isomorphic but constitutionally diverse. Functional isomorphism implies multiple realizability. This is sometimes called an ""a priori" argument". Putnam, Jerry Fodor, and others argued that, along with being an effective argument against type-identity theories, multiple realizability implies that any low-level explanation of higher-level mental phenomena is insufficiently abstract and general. Functionalism, which identifies mental kinds with functional kinds that are  characterized exclusively in terms of causes and effects, abstracts from the level of microphysics, and therefore seemed to be a better explanation of the relation between mind and body. In fact, there are many functional kinds, such as mousetraps, software and bookshelves, that are multiply realized at the physical level. Machine state functionalism. Putnam himself put forth the first formulation of such a functionalist theory. This formulation, now called "machine-state functionalism", was inspired by analogies Putnam and others made between the mind and Turing machines. The point for functionalism is the nature of the states of the Turing machine . Each state can be defined in terms of its relations to the other states and to the inputs and outputs, and the details of how it accomplishes what it accomplishes and of its material constitution are completely irrelevant. According to machine-state functionalism, the nature of a mental state is just like the nature of a Turing machine state. Just as "state one" simply is the state in which, given a particular input, such-and-such happens, so being in pain is the state which disposes one to cry "ouch", become distracted, wonder what the cause is, and so forth . Rejection of functionalism. In the late 1980s, Putnam abandoned his adherence to functionalism and other computational theories of mind. His change of mind was primarily due to the difficulties computational theories have in explaining certain intuitions with respect to the externalism of mental content. This is illustrated by Putnam's own Twin Earth thought experiment (see "Philosophy of language"). In 1988 he also developed a separate argument against functionalism based on Fodor's generalized version of multiple realizability. Asserting that functionalism is really a watered-down identity theory in which mental kinds are identified with functional kinds, Putnam argued that  mental kinds may be multiply realizable over functional kinds. The argument for functionalism is that the same mental state could be implemented by the different states of a universal Turing machine. Despite Putnam's rejection of functionalism, it has continued to flourish and been developed into numerous versions by Fodor, David Marr, Daniel Dennett, and David Lewis, among others. Functionalism helped lay the foundations for modern cognitive science and is the dominant theory of mind in philosophy today. By 2012 Putnam accepted a modification of functionalism called "liberal functionalism". The view holds that "what matters for consciousness and for mental  properties generally is the right sort of functional capacities and not the particular matter that subserves those capacities". The specification of these capacities may refer to what goes on outside the organism's "brain", may include intentional idioms, and need not describe a capacity to compute something or other. Philosophy of language. Semantic externalism. One of Putnam's contributions to philosophy of language is his claim that "meaning just ain't in the head". His views on meaning, first laid out in "Meaning and Reference" (1973), then in" The Meaning of "Meaning"" (1975), use his "Twin Earth" thought experiment to  illustrate that terms' meanings are determined by factors outside the mind. Twin Earth shows this, according to Putnam, since on Twin Earth everything is identical to Earth, except that its lakes, rivers and oceans are filled with XYZ rather than HO. Consequently, when an earthling, Fredrick, uses the Earth-English word "water", it has a different meaning from the Twin Earth-English word "water" when used by his physically identical twin, Frodrick, on Twin Earth. Since Fredrick and Frodrick are physically indistinguishable when they utter their respective words, and since their words have different meanings, meaning cannot be determined  solely by what is in their heads. This led Putnam to adopt a version of semantic externalism with regard to meaning and mental content. The philosopher of mind and language Donald Davidson, despite his many differences of opinion with Putnam, wrote that semantic externalism constituted an "anti-subjectivist revolution" in philosophers' way of seeing the world. Since Descartes's time, philosophers had been concerned with proving knowledge from the basis of subjective experience. Thanks to Putnam, Saul Kripke, Tyler Burge and others, Davidson said, philosophy could now take the objective realm for granted and start questioning the alleged "truths" of  subjective experience. Theory of meaning. Along with Kripke, Keith Donnellan, and others, Putnam contributed to what is known as the causal theory of reference. In particular, he maintained in "The Meaning of "Meaning"" that the objects referred to by natural kind terms—such as "tiger", "water", and "tree"—are the principal elements of the meaning of such terms. There is a linguistic division of labor, analogous to Adam Smith's economic division of labor, according to which such terms have their references fixed by the "experts" in the particular field of science to which the terms belong. So, for example, the  reference of the term "lion" is fixed by the community of zoologists, the reference of the term "elm tree" is fixed by the community of botanists, and chemists fix the reference of the term "table salt" as sodium chloride. These referents are considered rigid designators in the Kripkean sense and are disseminated outward to the linguistic community. Putnam specifies a finite sequence of elements (a vector) for the description of the meaning of every term in the language. Such a vector consists of four components: Such a "meaning-vector" provides a description of the reference and use of an expression  within a particular linguistic community. It provides the conditions for its correct usage and makes it possible to judge whether a single speaker attributes the appropriate meaning to it or whether its use has changed enough to cause a difference in its meaning. According to Putnam, it is legitimate to speak of a change in the meaning of an expression only if the reference of the term, and not its stereotype, has changed. But since no possible algorithm can determine which aspect—the stereotype or the reference—has changed in a particular case, it is necessary to consider the usage  of other expressions of the language. Since there is no limit to the number of such expressions to be considered, Putnam embraced a form of semantic holism. Philosophy of mathematics. Putnam made a significant contribution to philosophy of mathematics in the Quine–Putnam indispensability argument for mathematical realism. Stephen Yablo considers this argument one of the most challenging in favor of the existence of abstract mathematical entities, such as numbers and sets. The form of the argument is as follows. The justification for the first premise is the most controversial. Both Putnam and Quine invoke naturalism to justify the exclusion  of all non-scientific entities, and hence to defend the "only" part of "all and only". The assertion that "all" entities postulated in scientific theories, including numbers, should be accepted as real is justified by confirmation holism. Since theories are not confirmed in a piecemeal fashion, but as a whole, there is no justification for excluding any of the entities referred to in well-confirmed theories. This puts the nominalist who wishes to exclude the existence of sets and non-Euclidean geometry but include the existence of quarks and other undetectable entities of physics, for example, in a difficult position . Putnam holds the view that mathematics, like physics and other empirical sciences, uses both strict logical proofs and "quasi-empirical" methods. For example, Fermat's Last Theorem states that for no integer formula_1 are there positive integer values of "x", "y", and "z" such that formula_2. Before Andrew Wiles proved this for all formula_1 in 1995, it had been proved for many values of "n". These proofs inspired further research in the area, and formed a quasi-empirical consensus for the theorem. Even though such knowledge is more conjectural than a strictly proved theorem, it was still used in developing  other mathematical ideas. Mathematics and computer science. Putnam has contributed to scientific fields not directly related to his work in philosophy. As a mathematician, he contributed to the resolution of Hilbert's tenth problem in mathematics. This problem (now known as Matiyasevich's theorem or the MRDP theorem) was settled by Yuri Matiyasevich in 1970, with a proof that relied heavily on previous research by Putnam, Julia Robinson and Martin Davis. In computability theory, Putnam investigated the structure of the ramified analytical hierarchy, its connection with the constructible hierarchy and its Turing degrees. He showed that there are many levels  of the constructible hierarchy that add no subsets of the integers and later, with his student George Boolos, that the first such "non-index" is the ordinal formula_4 of ramified analysis (this is the smallest formula_5 such that formula_6 is a model of full second-order comprehension), and also, together with a separate paper with Richard Boyd (another of Putnam's students) and Gustav Hensel, how the Davis–Mostowski–Kleene hyperarithmetical hierarchy of arithmetical degrees can be naturally extended up to formula_4. In computer science, Putnam is known for the Davis–Putnam algorithm for the Boolean satisfiability problem (SAT), developed  with Martin Davis in 1960. The algorithm finds whether there is a set of true or false values that satisfies a given Boolean expression so that the entire expression becomes true. In 1962, they further refined the algorithm with the help of George Logemann and Donald W. Loveland. It became known as the DPLL algorithm. It is efficient and still forms the basis of most complete SAT solvers. Epistemology. In epistemology, Putnam is known for his "brain in a vat" thought experiment (a modernized version of Descartes's evil demon hypothesis). The argument is that one cannot coherently suspect  that one is a disembodied "brain in a vat" placed there by some "mad scientist". This follows from the causal theory of reference. Words always refer to the kinds of things they were coined to refer to, the kinds of things their user, or the user's ancestors, experienced. So, if some person, Mary, is a "brain in a vat", whose every experience is received through wiring and other gadgetry created by the mad scientist, then Mary's idea of a brain does not refer to a real brain, since she and her linguistic community have never encountered such a  thing. To her a brain is actually an image fed to her through the wiring. Nor does her idea of a vat refer to a real vat. So if, as a brain in a vat, she says, "I'm a brain in a vat", she is actually saying, "I'm a brain-image in a vat-image", which is incoherent. On the other hand, if she is not a brain in a vat, then saying that she is a brain in a vat is still incoherent, because she actually means the opposite. This is a form of epistemological externalism: knowledge  or justification depends on factors outside the mind and is not solely determined internally. Putnam has clarified that his real target in this argument was never skepticism, but metaphysical realism. Since realism of this kind assumes the existence of a gap between how one conceives the world and the way the world really is, skeptical scenarios such as this one (or Descartes's evil demon) present a formidable challenge. By arguing that such a scenario is impossible, Putnam attempts to show that this notion of a gap between one's concept of the world and the way it is is  absurd. One cannot have a "God's-eye" view of reality. One is limited to one's conceptual schemes, and metaphysical realism is therefore false. Metaphilosophy and ontology. In the late 1970s and the 1980s, stimulated by results from mathematical logic and by some of Quine's ideas, Putnam abandoned his long-standing defence of metaphysical realism—the view that the categories and structures of the external world are both causally and ontologically independent of the conceptualizations of the human mind. He adopted a rather different view, which he called "internal realism" or "pragmatic realism". Internal realism is the view  that, although the world may be "causally" independent of the human mind, the world's structure—its division into kinds, individuals and categories—is a function of the human mind, and hence the world is not "ontologically" independent. The general idea is influenced by Immanuel Kant's idea of the dependence of our knowledge of the world on the categories of thought. The problem with metaphysical realism, according to Putnam, is that it fails to explain the possibility of reference and truth. According to the metaphysical realist, our concepts and categories refer because they match up in some mysterious manner  with the categories, kinds and individuals inherent in the external world. But how is it possible that the world "carves up" into certain structures and categories, the mind carves up the world into its own categories and structures, and the two carvings perfectly coincide? The answer must be that the world does not come pre-structured but that the human mind and its conceptual schemes impose structure on it. In "Reason, Truth, and History", Putnam identified truth with what he termed "idealized rational acceptability." The theory, which owes something to C. S. Peirce, is that a belief is true if  it would be accepted by anyone under ideal epistemic conditions. Nelson Goodman formulated a similar notion in "Fact, Fiction and Forecast" (1956). "We have come to think of the actual as one among many possible worlds. We need to repaint that picture. All possible worlds lie within the actual one", Goodman wrote. Putnam rejected this form of social constructivism, but retained the idea that there can be many correct descriptions of reality. None of these descriptions can be scientifically proven to be the "one, true" description of the world. For Putnam, this does not imply relativism, because not all descriptions  are equally correct and correctness is not determined subjectively. Putnam renounced internal realism in his reply to Simon Blackburn in the volume "Reading Putnam". The reasons he gave up his "antirealism" are stated in the first three of his replies in "The Philosophy of Hilary Putnam", an issue of the journal "Philosophical Topics", where he gives a history of his use(s) of the term "internal realism", and, at more length, in his "The Threefold Cord: Mind, Body and World" (1999). Although he abandoned internal realism, Putnam still resisted the idea that any given thing or system of things can be  described in exactly one complete and correct way. He thus accepts "conceptual relativity"—the view that it may be a matter of choice or convention, e.g., whether mereological sums exist, or whether spacetime points are individuals or mere limits. In other words, having abandoned internal realism, Putnam came to accept metaphysical realism in the broad sense of rejecting all forms of verificationism and all talk of our "making" the world. Under the influence of Peirce and William James, Putnam also became convinced that there is no fact–value dichotomy; that is, normative (e.g., ethical and aesthetic) judgments often have a factual  basis, while scientific judgments have a normative element. Neopragmatism and Wittgenstein. At the end of the 1980s, Putnam became increasingly disillusioned with what he perceived as the "scientism" and the rejection of history that characterize modern analytic philosophy. He rejected internal realism because it assumed a "cognitive interface" model of the relation between the mind and the world. Putnam claimed that the very notion of truth would have to be abandoned by a consistent eliminative materialist. Under the increasing influence of James and the pragmatists, he adopted a direct realist view of this relation. For a time, under the influence  of Ludwig Wittgenstein, he adopted a pluralist view of philosophy itself and came to view most philosophical problems as nothing more than conceptual or linguistic confusions created by philosophers by using ordinary language out of context. A book of articles on pragmatism by Ruth Anna Putnam and Hilary Putnam, "Pragmatism as a Way of Life: The Lasting Legacy of William James and John Dewey" (Harvard UP, ), edited by David Macarthur, was published in 2017. Many of Putnam's last works addressed the concerns of ordinary people, particularly social problems. For example, he wrote about the nature of democracy, social justice  and religion. He also discussed Jürgen Habermas's ideas, and wrote articles influenced by continental philosophy. Criticism. Putnam himself may be his own most formidable philosophical adversary: his frequent changes of mind have led him to attack his previous positions. But many significant criticisms of his views have come from other philosophers and scientists. For example, multiple realizability has been criticized on the grounds that, if it were true, research and experimentation in the neurosciences would be impossible. According to William Bechtel and Jennifer Mundale, to be able to conduct such research in the neurosciences, universal consistencies must either exist  or be assumed to exist in brain structures. It is the similarity (or homology) of brain structures that allows us to generalize across species. If multiple realizability were an empirical fact, results from experiments conducted on one species of animal (or one organism) would not be meaningful when generalized to explain the behavior of another species (or organism of the same species). Jaegwon Kim, David Lewis, Robert Richardson and Patricia Churchland have also criticized metaphysical realism. Putnam himself formulated one of the main arguments against functionalism: the Twin Earth thought experiment. But there have been other criticisms. John Searle's  Chinese room argument (1980) is a direct attack on the claim that thought can be represented as a set of functions. The thought experiment is designed to show that it is possible to mimic intelligent action with a purely functional system, without any interpretation or understanding. Searle describes a situation in which a person who speaks only English is locked in a room with Chinese symbols in baskets and a rule book in English for moving the symbols around. The person is instructed, by people outside the room, to follow the rule book for sending certain symbols out of the  room when given certain symbols. The people outside the room speak Chinese and are communicating with the person inside via the Chinese symbols. According to Searle, it would be absurd to claim that the English speaker inside "knows" Chinese based on these syntactic processes alone. This argument attempts to show that systems that operate merely on syntactic processes cannot realize any semantics (meaning) or intentionality (aboutness). Searle thus attacks the idea that thought can be equated with following a set of syntactic rules and concludes that functionalism is an inadequate theory of the mind. Ned Block has advanced several  other arguments against functionalism. Despite the many changes in his other positions, Putnam consistently adhered to semantic holism. Michael Dummett, Jerry Fodor, Ernest Lepore, and others have identified problems with this position. In the first place, they suggest that, if semantic holism is true, it is impossible to understand how a speaker of a language can learn the meaning of an expression in the language. Given the limits of our cognitive abilities, we will never be able to master the whole of the English (or any other) language, even based on the (false) assumption that languages are static and immutable  entities. Thus, if one must understand all of a natural language to understand a single word or expression, language learning is simply impossible. Semantic holism also fails to explain how two speakers can mean the same thing when using the same expression, and therefore how any communication is possible between them. Given a sentence "P", since Fred and Mary have each mastered different parts of the English language and "P" is related in different ways to the sentences in each part, "P" means one thing to Fred and something else to Mary. Moreover, if "P" derives its meaning from its  relations with all the sentences of a language, as soon as the vocabulary of an individual changes by the addition or elimination of a sentence, the totality of relations changes, and therefore also the meaning of "P". As this is a common phenomenon, the result is that "P" has two different meanings in two different moments in the life of the same person. Consequently, if I accept the truth of a sentence and then reject it later on, the meaning of what I rejected and what I accepted are completely different and therefore I cannot change my opinions with  regard to the same sentences. Putnam's brain in a vat argument has also been criticized. Crispin Wright argues that Putnam's formulation of the brain-in-a-vat scenario is too narrow to refute global skepticism. The possibility that one is a recently disembodied brain in a vat is not undermined by semantic externalism. If a person has lived her entire life outside the vat—speaking the English language and interacting normally with the outside world—prior to her "envatment" by a mad scientist, when she wakes up inside the vat, her words and thoughts (e.g., "tree" and "grass ) will still refer to the objects or events in the external world that they referred to before her envatment. In another scenario, a brain in a vat may be hooked up to a supercomputer that randomly generates perceptual experiences. In that case, one's words and thoughts would not refer to anything: semantics would no longer exist and the argument would be meaningless. In philosophy of mathematics, Stephen Yablo has argued that the Quine–Putnam indispensability thesis does not demonstrate that mathematical entities are truly indispensable. The argumentation is sophisticated, but the upshot is that one can achieve the same 	Hilary Putnam
7472582	logical results by simply adding to any statement about an abstract object the assumption so-and-so is assumed (or hypothesized) to exist". For example, one can take the argument for indispensability described above and adjust it as follows: Finally, Curtis Brown has criticized Putnam's internal realism as a disguised form of subjective idealism, in which case it is subject to the traditional arguments against that position. In particular, it falls into the trap of solipsism. That is, if existence depends on experience, as subjective idealism maintains, and if one's consciousness ceased to exist, then the rest of  the universe would also cease to exist. Major works and bibliography. Vincent C. Müller compiled a detailed bibliography of Putnam's writings, citing 16 books and 198 articles, published in 1993 in PhilPapers.