Defending the Axioms: On the Philosophical Foundations of Set Theory

Paperback | March 12, 2013

byPenelope Maddy

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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 abroadly 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, onerefreshingly free of metaphysical commitments.

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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 abroadly naturalistic or second-philosophical point...

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).
Format:PaperbackDimensions:162 pages, 8.5 × 5.51 × 0.07 inPublished:March 12, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199671486

ISBN - 13:9780199671489

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Table of Contents

Introduction1. The Problem2. Proper Method3. Thin Realism4. Arealism5. MoralsBibliography

Editorial Reviews

"an engaging contribution to an important philosophical debate [which] deserves to be read far beyond the ranks of philosophers of mathematics" --Journal of Philosophy