The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and (...) Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

Mr. Sharp's resolution of the Einstein-Podolsky-Rosen paradox is, in my opinion, the right one. However, the resolution does not in my opinion show that “God's in his heaven; all's right with the world.” This is in no way a criticism of Sharp; rather, it is inevitable that any resolution of this paradox, dealing as it does with the quantum mechanical concept of “measurement”, must tangle with some of the real difficulties which are lurking in the notion. The purpose (...) of these comments is to use Mr. Sharp's remarks as a basis for bringing out one of the serious conceptual difficulties connected with measurement. (shrink)

Hilary Putnam's argument against metaphysical realism (commonly referred to as the "model theoretic argument") has now enjoyed two decades of discussion.(1) The text is rich and contains variously construable arguments against variously construed philosophical positions. David Lewis isolated one argument and called it "Putnam's Paradox".(2) That argument is clear and concise; so is the paradoxical conclusion it purports to demonstrate; and so is Lewis' paradox-avoiding solution. His solution involves a position I call "anti-nominalism": not only are (...) classes real, but they are divided into arbitrary and 'natural' classes. The natural classes 'carve nature at the joints', being (as other philosophers might say) the extensions of 'real' properties, universals, or Forms.(3) Thus the argument was turned, in effect, into support for a metaphysical realism stronger than Putnam envisaged. (shrink)

In "Unnatural Science"(1) Catherine Elgin examines the dilemma which David Lewis sees posed by Putnam's model-theoretic argument against realism. One horn of the dilemma commits us to seeing truth as something all too easily come by, a virtue to be attributed to any theory meeting relatively minimal conditions of adequacy. The other horn commits us to "anti-nominalism", some version of the ancient doctrine that language must "carve nature at the joints": that there are natural kinds or classes which alone (...) qualify as referents (extensions) for our predicates. Elgin offers a searching critique of Lewis' response (accepting the second horn) and an illuminating defence of its contrary: "we cannot construe (mere) truth as the end of scientific inquiry. Not ... because truth is too hard to come by, but because it is too easy" (p. 301). (shrink)

The model-theoretic argument known as Putnam´s paradox threatens our notion of truth with triviality: Almost any world can satisfy almost any theory. Formal argument and intuition are at odds. David Lewis devised a solution according to which the very stucture of the world fixes how it is to be divided into elite classes which determine the reference of any true theory. Three claims are defended: Firstly, Lewis´ proposal must be completed by an account of successful referential intentions. Secondly, contrary (...) to Catherine Elgin´s criticism of Lewis, natural properties corresponding to elite classes may play a role in sound scientific inquiry. Thirdly, despite Bas van Fraassen´s objection that the sceptic cannot consistently maintain doubts about reference, there is a promising sceptical strategy of exploiting Putnam´s results which is answered by Lewis´ account. (shrink)

Two of Hilary Putnam's model-theoretic arguments against metaphysical realism are examined in detail. One of them is developed as an extension of a model-theoretic argument against mathematical realism based on considerations concerning the so-called Skolem-Paradox in set theory. This argument against mathematical realism is also treated explicitly. The article concentrates on the fine structure of the arguments because most commentators have concentrated on the major premisses of Putnam's argument and especially on his treatment of metaphysical realism. It (...) is shown that the validity of Putnam's arguments is doubtful and that realists are by no means forced to accept the theses Putnam ascribes to them. It is concluded that Putnam fails to give convincing arguments for rejecting mathematical or metaphysical realism. Furthermore, Putnam's internal realism is discussed critically. (shrink)

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

This collection of essays by Hilary Putnam, one of the very few contemporary grand masters of philosophy, presents the last development of Putnam's reflections regarding the core issue of his entire career: how to develop a form of philosophical realism able to account for both the scientific and the humanistic view of the world - that is, a conception in which the naturalistic view of the world can be reconciled with the acknowledgment that normative phenomena are a fundamental part (...) of our lives. Many great philosophers, from Hume to Kant, from Mill to Sellars, from Quine to Davidson, have faced this challenge."--Provided by publisher. (shrink)

The question of truth is perhaps a perennial question of philosophy. Is truth “merely” epistemological, a function of contingent human practices and conventions, or should we adopt a stonger, metaphysical conception of truth along realist lines, understood as correspondence with objectively existing reality? In this paper I examine a famous debate in the analytic philosophy of language that hinges on the status of truth – specifically, the challenge to traditional or metaphysical realism posed by Hilary Putnam’s model-theoretic argument and the (...) “paradox” that David Lewis derived from it. In the end, I will argue that metaphysical realism is a theoretically excessive position with regards to truth, and that a pragmatic or epistemological understanding of realism is, in Putnam’s words, “all the realism we want or need.”. (shrink)

Hilary Putnam, one of America’s most distinguished philosophers, surveys an astonishingly wide range of issues and proposes a new, clear-cut approach to philosophical questions—a renewal of philosophy. He contests the view that only science offers an appropriate model for philosophical inquiry. His discussion of topics from artificial intelligence to natural selection, and of reductive philosophical views derived from these models, identifies the insuperable problems encountered when philosophy ignores the normative or attempts to reduce it to something else.

The Lowenheim-Skolem theorems say that if a first-order theory has infinite models, then it has models which are only countably infinite. Cantor's theorem says that some sets are uncountable. Together, these theorems induce a puzzle known as Skolem's Paradox: the very axioms of set theory which prove the existence of uncountable sets can be satisfied by a merely countable model. ;This dissertation examines Skolem's Paradox from three perspectives. After a brief introduction, chapters two and three examine several formulations (...) of Skolem's Paradox in order to disentangle the roles which set theory, model theory, and philosophy play in these formulations. In these chapters, I accomplish three things. First, I clear up some of the mathematical ambiguities which have all too often infected discussions of Skolem's Paradox. Second, I isolate a key assumption upon which Skolem's Paradox rests, and I show why this assumption has to be false. Finally, I argue that there is no single explanation as to how a countable model can satisfy the axioms of set theory ;In chapter four, I turn to a second puzzle. Why, even though philosophers have known since the early 1920's that Skolem's Paradox has a relatively simple technical solution, have they continued to find this paradox so troubling? I argue that philosophers' attitudes towards Skolem's Paradox have been shaped by the acceptance of certain, fairly specific, claims in the philosophy of language. I then tackle these philosophical claims head on. In some cases, I argue that the claims depend on an incoherent account of mathematical language. In other cases, I argue that the claims are so powerful that they render Skolem's Paradox trivial. In either case, though, examination of the philosophical underpinnings of Skolem's Paradox renders that paradox decidedly unparadoxical. ;Finally, in chapter five, I turn away from "generic" formulations of Skolem's Paradox to examine Hilary Putnam's "model-theoretic argument against realism." I show that Putnam's argument involves mistakes of both the mathematical and the philosophical variety, and that these two types of mistake are closely related. Along the way, I clear up some of the mutual charges of question begging which have characterized discussions between Putnam and his critics. (shrink)

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox, a challenge to 'classical' mathematics from a world-famous mathematician, a new foundational school, and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present (...) collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

This book brings together key players in the current debate on positive and normative science and philosophy and value judgements in economics. Both editors have engaged in these debates throughout their careers from its early foundations; Putnam as a doctorial student of Hans Reichenbach at UCLA and Walsh a junior member of Lord Robbinsâe(tm)s department at the London School of Economics, both in the early 1950s. This book collects recent contributions from Martha Nussbaum and Harvey Gram, as well as a (...) new chapter from the editors. (shrink)

A fictionalist attitude towards an area of discourse encourages us to assent to certain sentences of that discourse without believing that they are true. Prima facie, this amounts to a suggestion that we should also assent to sentences of the form 'S but I don't believe that S'. Traditional versions of fictionalism have an answer to this challenge, but I argue that the answer is unavailable for a currently popular type of fictionalism. This is bad news for fictionalism in general (...) because the currently popular variety is the one that deals best with the Quine-Putnam indispensability argument. (shrink)

The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory of which (...) the green-hypothesis is a part has an unintended model in which the grue-hypothesis is equally confirmed; and there are no meaning-facts that determine reference, because the objects referred to by the referring terms of any language or set of intentional mental states are permutable in a way that is consistent with the truth-values of all other sentences in that language or beliefs in that set. The upshot is that the three paradoxes need to be solved in a unified way. (shrink)

"There are no paradoxes in mathematics," says Kurt Gödel. Moreover, Gödel seems to be right on this count. That is, there are no paradoxes, in the strict sense of the word, internal to the known and available body of mathematical knowledge. But while there are no paradoxes in mathematics, there certainly is an embarrassing bag of difficulties when we come to the application of mathematical concepts to the physical world. Of these, perhaps the most unruly offenders of all are the (...) problems proposed about 2500 years ago by Zeno and which, in modern idiom, have to do with the proper mathematical treatment of phenomena involving change and motion, and the physical meaning—if any—which may be assigned to convergent infinite series. At each stage in the growth of mathematical knowledge since their formulation Zeno's paradoxes have been the subject of some alleged resolution. Now Grünbaum contributes to this tradition, and it must be said that he makes a strong case. The weapons in the intellectual arsenal which Grünbaum brings to bear upon Zeno include such sophisticated devices as measure theory, but the weak link in the argument is in the first chapter where the author presents his somewhat psychologistic theory of temporal becoming. Grünbaum has a great many interesting things to say in later chapters about infinite processes, quantum mechanics, and Hilary Putnam. This is a first-rate contribution to the philosophy of physics.—H. P. K. (shrink)

In a series of articles Christopher Cowie has provided what he calls a ‘Master Argument’ against the Companions in Guilt (CG) defence of moral objectivity. In what follows I defend the CG strategy against Cowie. I show, firstly, that epistemic judgements are relevantly similar to moral judgements, and secondly, that it is not possible coherently to deny the existence of irreducible and categorically normative epistemic reasons. My argument for the second of these claims exploits an analogy between the thesis that (...) epistemic norms are non-categorical and G.E. Moore’s paradox concerning first personal belief ascriptions. I argue that the absurdity of the assertion “I have evidence that p but no reason to believe it” shows that the norms of belief are categorical. I then consider the counter-argument that this categoricity is a ‘conceptual’ rather than an ‘objective’ requirement. By drawing on the work of Hilary Putnam and Charles Travis, I show that this counter-argument is unsuccessful. Putnam is one of the original proponents of the Companions in Guilt strategy. Thus, by supporting the CG argument through appeal to other Putnamian theses, I show that its insights can only fully be appreciated in the context of broader metaphysical and semantic lessons. (shrink)

This lecture, given at Beijing University in 1984, presents a remarkable (previously unpublished) proof of the Gödel Incompleteness Theorem due to Kripke. Today we know purely algebraic techniques that can be used to give direct proofs of the existence of nonstandard models in a style with which ordinary mathematicians feel perfectly comfortable--techniques that do not even require knowledge of the Completeness Theorem or even require that logic itself be axiomatized. Kripke used these techniques to establish incompleteness by means that could, (...) in principle, have been understood by nineteenth-century mathematicians. The proof exhibits a statement of number theory--one which is not at all "self referring"--and constructs two models, in one of which it is true and in the other of which it is false, thereby establishing "undecidability" (independence). (shrink)

Putnam's goal is to embed philosophy in social life. The first part of this book is dedicated to metaphysical questions.

This is the third volume of Hilary Putnam's philosophical papers, published in paperback for the first time. The volume contains his major essays from 1975 to 1982, which reveal a large shift in emphasis in the 'realist'_position developed in his earlier work. While not renouncing those views, Professor Putnam has continued to explore their epistemological consequences and conceptual history. He now, crucially, sees theories of truth and of meaning that derive from a firm notion of reference as inadequate.

First published in 1978, this reissue presents a seminal philosophical work by professor Putnam, in which he puts forward a conception of knowledge which makes ethics, practical knowledge and non-mathematic parts of the social sciences just as much parts of 'knowledge' as the sciences themselves. He also rejects the idea that knowledge can be demarcated from non-knowledge by the fact that the former alone adheres to 'the scientific method'. The first part of the book consists of Professor Putnam's John (...) Locke lectures, delivered at the University of Oxford in 1976, offering a detailed examination of a 'physicalist' theory of reference against a background of the works of Tarski, Carnap, Popper, Hempel and Kant. The analysis then extends to notions of truth, the character of linguistic enquiry and social scientific enquiry in general, interconnecting with the great metaphysical problem of realism, the nature of language and reference, and the character of ourselves. (shrink)

"The first two lectures place the alternative I defend -- a kind of pragmatic realism -- in a historical and metaphysical context. Part of that context is provided by Husserl's remark that the history of modern philosophy begins with Galileo -- that is, modern philosophy has been hypnotized by the idea that scientific facts are all the facts there are. Another part is provided by the analysis of a very simple example of what I call 'contextual relativity'. The position I (...) defend holds that truth depends on conceptual scheme and it is nonetheless 'real truth'. "In my third lecture I turn to the Kantian antecedents of this view, explaining what I think should be retained of the Kantian idea of autonomy as the central theme of morality, and extracting from Kant's work a 'moral image of the world' that connects the ideals of equality and intellectual liberty. In this lecture I defend the idea that moral images are an indispensible part of our moral and cultural heritage. "In the final lecture I defend the idea of moral objectivity. I compare our epistemological positions in ethics, history, analysis of human character, and science, and I argue that in no area can we hope for a 'foundation' which is more ultimate than the beliefs that actually, at a given time, function as foundational in the area, the beliefs concerning which one has to say 'this is where my spade is turned'. In ethics such beliefs are represented in moral images of the world.". (shrink)

What is the relationship between our perceptions and reality? What is the relationship between the mind and the body? These are questions with which philosophers have grappled for centuries, and they are topics of considerable contemporary debate as well. Hilary Putnam has approached the divisions between perception and reality and between mind and body with great creativity throughout his career. Now, in _The Threefold Cord: Mind, Body, and World,_ he expounds upon these issues, elucidating both the strengths and weaknesses of (...) current schools of thought. With his characteristic wit and acuity, Putnam offers refreshing solutions to some of philosophy's most vexing problems. Putnam first examines the problem of realism: is objective truth possible? He acknowledges the deep impasse between empirical and idealist approaches to this question, critiquing them both, however, by highlighting the false assumption they share, that we cannot perceive the world directly. Drawing on the work of J. L. Austin and William James, Putnam develops a subtle and creative alternative, which he calls "natural realism." The second part of the book explores the mind-body question: is the mind independent of our interactions with the physical world? Again, Putnam critically assesses two sharply antithetical contemporary approaches and finds them both lacking. _The Threefold Cord_ shows the entire mind-body debate to be miscast and draws on the later work of Wittgenstein, once more advancing original views on perception and thought and their relationship with both the body and the external world. Finally, Putnam takes up two related problems--the role of causality in human behavior and whether or not thoughts and sensations have an "existence" all their own. With Putnam's lucid prose and insightful examples, _The Threefold Cord_ loosens the Gordian knots into which philosophy has bound itself over the issue of epistemology. (shrink)

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

In this book, one of the world's preeminent philosophers takes issue with an idea that has found an all-too-prominent place in popular culture and philosophical ...

UNCLEAR as it is, the traditional doctrine that the notion "meaning" possesses the extension/intension ambiguity has certain typical consequences. The doctrine that the meaning of a term is a concept carried the implication that mean- ings are mental entities. Frege, however, rebelled against this "psy- chologism." Feeling that meanings are public property-that the same meaning can be "grasped" by more than one person and by persons at different times-he identified concepts (and hence "intensions" or meanings) with abstract entities rather than (...) mental entities. However, "grasping" these abstract entities was still an individual psychological act. None of these philosophers doubted that understanding a word (knowing its intension) was just a matter of being in a certain psychological state (somewhat in the way in which knowing how to factor numbers in one's head is just a mat- ter of being in a certain very complex psychological state). (shrink)