This book is well known for its proof that many mathematical systems - including lattice theory and closure algebras - are undecidable. It consists of three treatises from one of the greatest logicians of all time: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups.".

Provides a comprehensive introduction to the major philosophical theories attempting to explain the workings of language.

This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...

A collection of all but two of the author's philosophical essays and lectures originally published or presented before August 1976.

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.

INTRODUCTION Before Kant almost every philosopher subscribed to the view that truth is some kind of correspondence between ideas and 'what is the case'. ...

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

The dream of a community of philosophers engaged in inquiry with shared standards of evidence and justification has long been with us. It has led some thinkers puzzled by our mathematical experience to look to mathematics for adjudication between competing views. I am skeptical of this approach and consider Skolem's philosophical uses of the Löwenheim-Skolem Theorem to exemplify it. I argue that these uses invariably beg the questions at issue. I say ?uses?, because I claim further that Skolem shifted his (...) position on the philosophical significance of the theorem as a result of a shift in his background beliefs. The nature of this shift and possible explanations for it are investigated. Ironically, Skolem's own case provides a historical example of the philosophical flexibility of his theorem. Our suspicion ought always to be aroused when a proof proves more than its means allow it. Something of this sort might be called ?a puffed-up proof?. Ludwig Wittgenstein, Remarks on the foundations of mathematics (revised edition), vol. 2, 21. (shrink)

The doctrines of scientific realism have enjoyed a close and enduring, if not always harmonious, association with Tarski's semantic conception of truth and theories of formal semantics generally. From its inception Tarski's theory received unqualified support from some realists, like Karl Popper, who saw it as legitimizing the use of semantic notions in epistemology and the philosophy of science.