Naturalism in Mathematics / Edition 1

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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.

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Editorial Reviews

From the Publisher
"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
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Product Details

  • ISBN-13: 9780198250753
  • Publisher: Oxford University Press
  • Publication date: 9/14/2000
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 264
  • Product dimensions: 8.20 (w) x 5.20 (h) x 0.60 (d)

Meet 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.

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Table of Contents

Pt. I The Problem 1
1 The Origins of Set Theory 3
2 Set Theory as a Foundation 22
3 The Standard Axioms 36
4 Independent Questions 63
5 New Axioms Candidates 73
6 V = L 82
Pt. II Realism 87
1 Godelian Realism 89
2 Quinean Realism 95
3 Set Theoretic Realism 108
4 A Realist's Case against V = L 110
5 Hints of Trouble 130
6 Indispensability and Scientific Practice 133
7 Indispensability and Mathematical Practice 158
Pt. III Naturalism 161
1 Wittgensteinian Anti-Philosophy 162
2 A Second Godelian Theme 172
3 Quinean Naturalism 177
4 Mathematical Naturalism 183
5 The Problem Revisited 206
6 A Naturalist's Case against V = L 216
Conclusion 233
Bibliography 235
Index 249
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