Defending the Axioms: On the Philosophical Foundations of Set Theory

Penelope Maddy

OUP Oxford, Jan 27, 2011 - Mathematics - 162 pages

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.

About the author

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).

Bibliographic information

• Title: Defending the Axioms: On the Philosophical Foundations of Set Theory
• Author: Penelope Maddy
• Edition: reprint
• Publisher: OUP Oxford, 2011
• ISBN: 0199596182, 9780199596188
• Length: 162 pages
• Subjects: Mathematics / History & Philosophy; Philosophy / Logic; Science / Philosophy & Social Aspects