Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...) She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

This paper gives a new twist to already familia refutations of Putnam's "model-theoretic" argument against realism. Recent attempts to defend the model-theoretic argument in the face of those criticisms indicate that the main point of previous rebuttals of the argument can be easily missed. The paper expounds the same point again in a different guise, by having recourse to ideas on models and the model-theoretic account of the logical properties developed by the author in earlier work. Some writers appear to (...) think that the charge of previous criticisms is that Putnam's argument begs the question, by involving as premise a proposition which all too obviously entails the falsity of realism--precisely what the argument is designed to establish. They then defend it by claiming that Putnam does not simply _take for granted<D> the truth of the offending premise, but _argues for<D> it. This, however, does not defend Putnam's argument against the _pragmatic<D> charges of irrelevancy and potential for provoking confusion--which, the paper shows, can be taken as the main criticisms levelled against it by previous writers. The point is that, if Putnam has an independent argument for the question-begging premise, one not involving any model-theoretic considerations, then this is all that is needed; the specifically model-theoretic considerations are irrelevant and could lead to spurious debates. (shrink)

Putnam's Model-Theoretic argument purports to show that, contrary to what the metaphysical realist is committed to, an epistemically ideal theory which satisfies all operational and theoretical constraints can be guaranteed to be true. He draws the additional antirealist conclusion that there can be no single privileged relation of reference. I argue that the very possibility of a so-called ideal theory satisfying all operational constraints presupposes a determinate relation of reference, and hence Putnam must assume precisely what he denies.

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)

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

From the philosophy of mind and language, through physics and mathematics, to the philosophy of the human sciences, morality and religion, there is almost no area of philosophy to which Hilary Putnam has not made highly original and influential contributions. This wide-ranging collection of papers provides a critical assessment and exploration of Putnam's Seminal Work. Written by Philosophers themselves well known for their work in the field, each essay bears witness to the continuing influence and importance of Putnam's thought. Putnam's (...) reply constitutes an extensive new essay which clarifies, and develops further, central themes in his philosophy. This volume includes papers by Simon Blackburn, George Boolos, Michael Hallett, Michael Redhead, Thomas Ricketts, David Wiggins and Crispin Wright. (shrink)

In a recent article, James Van Cleve joins a growing throng who have argued that Hilary Putnam's model-theoretic argument (and his "just more theory" response) begs the question against those who hold externalist theories of reference. Van Cleve has misinterpreted Putnam's argument. Putnam does not demand that the statements which make up the causal theory of reference must, themselves, do the reference-fixing. That would be question-begging. Rather, Putnam's argument is a "reductio", which can only be blocked with a theory of (...) reference that is both substantive and plausible. Putnam argues that there is no interpretation of "causality" that meets both conditions. (shrink)