Defending the Axioms

Defending the Axioms : On the Philosophical Foundations of Set Theory

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Description

Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments.show more

Product details

  • Paperback | 162 pages
  • 139.7 x 213.36 x 10.16mm | 204.12g
  • Oxford University Press
  • Oxford, United Kingdom
  • English
  • Reprint
  • 0199671486
  • 9780199671489
  • 126,562

About Penelope Maddy

Penelope Maddy is Distinguished Professor of Logic and Philosophy of Science at the University of California, Irvine. She is the author of Naturalism in Mathematics (OUP, 1997), Realism in Mathematics (OUP, 1992), and Second Philosophy (OUP, 2007).show more

Table of contents

Introduction ; 1. The Problem ; 2. Proper Method ; 3. Thin Realism ; 4. Arealism ; 5. Morals ; Bibliographyshow more

Review quote

'an engaging contribution to an important philosophical debate [which] deserves to be read far beyond the ranks of philosophers of mathematics' * Journal of Philosophy *show more

Rating details

13 ratings
3.69 out of 5 stars
5 15% (2)
4 46% (6)
3 31% (4)
2 8% (1)
1 0% (0)
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