In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

With his customary incisiveness, W. V. Quine presents logic as the product of two factors, truth and grammar-but argues against the doctrine that the logical truths are true because of grammar or language. Rather, in presenting a general theory of grammar and discussing the boundaries and possible extensions of logic, Quine argues that logic is not a mere matter of words.

The first complete English translation of a groundbreaking work. An ambitious account of the relation of mathematics to logic. Includes a foreword by Crispin Wright, translators' Introduction, and an appendix on Frege's logic by Roy T. Cook. The German philosopher and mathematician Gottlob Frege (1848-1925) was the father of analytic philosophy and to all intents and purposes the inventor of modern logic. Basic Laws of Arithmetic, originally published in German in two volumes (1893, 1903), is Freges magnum opus. It was (...) to be the pinnacle of Freges lifes work. It represents the final stage of his logicist project the idea that arithmetic and analysis are reducible to logic and contains his mature philosophy of mathematics and logic. The aim of Basic Laws of Arithmetic is to demonstrate the logical nature of mathematical theorems by providing gapless proofs in Frege's formal system using only basic laws of logic, logical inference, and explicit definitions. The work contains a philosophical foreword, an introduction to Frege's logic, a derivation of arithmetic from this logic, a critique of contemporary approaches to the real numbers, and the beginnings of a logicist treatment of real analysis. As is well-known, a letter received from Bertrand Russell shortly before the publication of the second volume made Frege realise that his basic law V, governing the identity of value-ranges, leads into inconsistency. Frege discusses a revision to basic law V written in response to Russells letter in an afterword to volume II. The continuing importance of Basic Laws of Arithmetic lies not only in its bearing on issues in the foundations of mathematics and logic but in its model of philosophical inquiry. Frege's ability to locate the essential questions, his integration of logical and philosophical analysis, and his rigorous approach to criticism and argument in general are vividly in evidence in this, his most ambitious work. Philip Ebert and Marcus Rossberg present the first full English translation of both volumes of Freges major work preserving the original formalism and pagination. The edition contains a foreword by Crispin Wright and an extensive appendix providing an introduction to Frege's formal system by Roy T. Cook. Readership: Scholars and advanced students in philosophy of logic, philosophy of mathematics, and early analytic philosophy. (shrink)

This is the first single-volume edition and translation of Frege's philosophical writings to include his seminal papers as well as substantial selections from ...

This volume reprints a dozen of the author’s papers, most with substantial postscripts, and adds one new one. The bulk of the material is on topics in philosophy of language, but there are also two papers on philosophy of mathematics written after the appearance of the author’s collected papers on that subject, and one on epistemology. As to the substance of Field’s contributions, limitations of space preclude doing much more below than indicating the range of issues addressed, and the general (...) orientation taken towards them. As to the style of his writing, it well exhibits the first of the two virtues, clarity and conciseness, that one looks for in philosophical prose. (shrink)

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

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)

I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...

This volume consists of the first of the John Dewey Lectures delivered under the auspices of Columbia University's Philosophy Department as well as other essays by the author. Intended to clarify the meaning of the philosophical doctrines propounded by Professor Quine in 'Word and Objects', the essays included herein both support and expand those doctrines.

The work of mathematician and logician Alfred Tarski (1901--1983) marks the transition from substantial to deflationary views about truth.

What is truth. Paul Horwich advocates the controversial theory of minimalism, that is that the nature of truth is entirely captured in the trivial fact that each proposition specifies its own condition for being true, and that truth is therefore an entirely mundane and unpuzzling concept. The first edition of Truth, published in 1980, established itself as the best account of minimalism and as an excellent introduction to the debate for students. For this new edition, Horwich has refined and developed (...) his treatment of the subject in the light of subsequent discussions, while preserving the distinctive format that made the earlier edition so successful. (shrink)

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

Presenting a selection of thirteen essays on various topics at the foundations of philosophy--one previously unpublished and eight accompanied by substantial new postscripts--this book offers outstanding insight on truth, meaning, and propositional attitudes; semantic indeterminacy and other kinds of "factual defectiveness;" and issues concerning objectivity, especially in mathematics and in epistemology. It will reward the attention of any philosopher interested in language, epistemology, or mathematics.

This volume presents a selection of essays by the leading philosopher Christopher S. Hill. Together, they address central philosophical issues related to four key concerns: the nature of truth; the relation between experiences and brain states; the relation between experiences and representational states; and problems concerning knowledge.

Paul Horwich gives the definitive exposition of a prominent philosophical theory about truth, `minimalism'. His theory has attracted much attention since the first edition of Truth in 1990; he has now developed, refined, and updated his treatment of the subject, while preserving the distinctive format of the book. This revised edition appears simultaneously with a new companion volume, Meaning; the two books demystify central philosophical issues, and will be essential reading for all who work on the philosophy of language.

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.