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Quine, New Foundations, and the Philosophy of Set Theory

AUD$136.95 inc GST

  • Author: Sean Morris, Metropolitan State University of Denver
  • Date Published: December 2018
  • availability: Available
  • format: Hardback
  • isbn: 9781107152502

AUD$ 136.95 inc GST
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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.

    • Presents the first book-length treatment on the interplay between Quine's technical work in logic and his general philosophy
    • Provides accessible accounts of the main technical results on Quine's set theory, New Foundations
    • Presents New Foundations in its historical and philosophical context and in the context of philosophy of set theory generally
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    Reviews & endorsements

    'Sean Morris's book fills a heretofore gaping hole in our understanding of the origins and history of set theory, explaining how Quine's New Foundations is not the isolated, idiosyncratic system it is sometimes taken to be, but is instead deeply connected - historically, philosophically, and mathematically - to other, now more mainstream, accounts of the nature of sets.' Roy T. Cook, University of Minnesota, Twin Cities

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    Product details

    • Date Published: December 2018
    • format: Hardback
    • isbn: 9781107152502
    • dimensions: 234 x 157 x 15 mm
    • weight: 0.47kg
    • availability: Available
  • Table of Contents

    Preface
    Introduction
    Part I:
    1. Cantor and the early development of set theory
    2. Cantor, Russell, and Zermelo and the set-theoretic paradoxes
    3. NF and the beginnings of Quine's philosophy of set theory
    Part II:
    4. Quine's philosophy of set theory
    5. Clarifying our conceptual scheme: set theory and the role of explication
    Part III:
    6. The iterative conception and set theory
    7. NF, the axiom of choice, and arithmetic
    Bibliography
    Index.

  • Author

    Sean Morris, Metropolitan State University of Denver
    Sean Morris is Associate Professor of Philosophy at the Metropolitan State University of Denver. He has written extensively on Quine and the history of analytic philosophy with a particular emphasis on Quine's work in the foundations of mathematics.

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