Quine, New Foundations, and the Philosophy of Set Theory

Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.

Sean Morris (Author)

9781316606636, Cambridge University Press

Paperback / softback, published 21 January 2021

219 pages
23 x 15 x 1.2 cm, 0.33 kg

'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

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.

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.

Subject Areas: Philosophy: logic [HPL], Analytical philosophy & Logical Positivism [HPCF5], Western philosophy, from c 1900 - [HPCF], History of Western philosophy [HPC], Philosophy [HP], Humanities [H]