Naturalism in Mathematics

by Penelope Maddy

Overview

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem—realism—is examined and rejected in favor of another approach—naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Product Details

ISBN-13:	9780198235736
Publisher:	Oxford University Press
Publication date:	02/26/1998
Pages:	264
Product dimensions:	8.74(w) x 5.74(h) x 0.81(d)

About the Author

Penelope Maddy is Professor of Philosophy at the University of California, Irvine, having previously held positions at the University of Illinois, Chicago, and the University of Notre Dame, Indiana.

Table of Contents

PART I: THE PROBLEM1. The origins of set theory2. Set theory as a foundation3. The standard axioms4. Independent questions5. New axiom candidates6. V = LPART II: REALISM1. Godelian realism2. Quinean realism3. Set-theoretic realism4. A realist's case against V = L5. Hints of trouble6. Indispensability and scientific practice7. Indispensability and mathematical practicPART III: NATURALISM1. Wittgensteinian anti-philosophy2. A second Godelian theme3. Quinean naturalism4. Mathematical naturalism5. The problem revisited6. A naturalist's case against V = LConclusionBibliographyIndex

Editorial Reviews

"Maddy's knowledge of early and contemporary set theory, and of philosophically significant parts of the history of mathematics generally, is impressively wide and deep, and her discussions of these matters are illuminating and rewarding. She writes in a clear, forthright and challenging style. Her book is eminently readable, instructive, and thought-provoking."—The Journal of Symbolic Logic

From the Publisher