Quine, New Foundations, and the Philosophy of Set Theory

Quine, New Foundations, and the Philosophy of Set Theory PDF

Author: Sean Morris

Publisher: Cambridge University Press

Published: 2018-12-13

Total Pages: 221

ISBN-13: 1108604536

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Quine's set theory, New Foundations, has often been treated as an anomaly in the history and philosophy of set theory. In this book, Sean Morris shows that it is in fact well-motivated, emerging in a natural way from the early development of set theory. Morris introduces and explores the notion of set theory as explication: the view that there is no single correct axiomatization of set theory, but rather that the various axiomatizations all serve to explicate the notion of set and are judged largely according to pragmatic criteria. Morris also brings out the important interplay between New Foundations, Quine's philosophy of set theory, and his philosophy more generally. We see that his early technical work in logic foreshadows his later famed naturalism, with his philosophy of set theory playing a crucial role in his primary philosophical project of clarifying our conceptual scheme and specifically its logical and mathematical components.

Set Theory and its Philosophy

Set Theory and its Philosophy PDF

Author: Michael Potter

Publisher: Clarendon Press

Published: 2004-01-15

Total Pages: 362

ISBN-13: 0191556432

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Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Set Theory and Its Logic

Set Theory and Its Logic PDF

Author: Willard Van Orman Quine

Publisher: Harvard University Press

Published: 1969

Total Pages: 384

ISBN-13: 9780674802070

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This is an extensively revised edition of W. V. Quine’s introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.

Trading Ontology for Ideology

Trading Ontology for Ideology PDF

Author: L. Decock

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 282

ISBN-13: 9401735751

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Willard VanOrman Quine has probably been the most influential th American philosopher of the 20 century. His work spans over seven decades, and covers many domains in philosophy. He has made major contributions to the fields of logic and set theory, philosophy of logic and mathematics, philosophy of language, philosophy of science, epistemology and metaphysics. Quine's first work in philosophy was in the field of logic. His major contributions are the two set-theoretic systems NF (1936) and ML (1940). 1 These systems were alternatives to the type theory of Principia Mathematica or Zermelo's set theory, and are still being studied by 2 mathematicians. An indirect contribution to the field of logic is his strong resistance to moda110gic. Quine's objectIons to the notions of necessity and analyticity have influenced the development of moda110gic? Quine has had an enormous influence on philosophy of mathematics. When Quine entered philosophy there was a discussion on the foundations of mathematics between the schools of intuitionism, formalism, and conventionalism. Quine soon took issue with Carnap's conventionalism in "Truth by convention,,4 (1936). Quine has never joined one of the other schools, but has added new elements that are the basic ones of the 5 contemporary schools of nominalism, platonism, and structuralism. Quine has long been in the shadow of Benacerraf and Putnam in this field. At the moment there seems to be a renewed interest in Quine's work, and most philosophers explicitly refer to Quine's work.

Set Theory and Its Logic, Revised Edition

Set Theory and Its Logic, Revised Edition PDF

Author: Willard Van O QUINE

Publisher: Harvard University Press

Published: 2009-06-30

Total Pages: 381

ISBN-13: 0674042425

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This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.

A Profile of Mathematical Logic

A Profile of Mathematical Logic PDF

Author: Howard DeLong

Publisher: Courier Corporation

Published: 2012-09-26

Total Pages: 322

ISBN-13: 0486139158

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This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

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