Naturalism in Mathematics

Naturalism in Mathematics

by Penelope Maddy
     
 

ISBN-10: 0198235739

ISBN-13: 9780198235736

Pub. Date: 02/26/1998

Publisher: Oxford University Press

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

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:
5.50(w) x 8.60(h) x 0.90(d)

Table of Contents

PART I: THE PROBLEM
1. The origins of set theory
2. Set theory as a foundation
3. The standard axioms
4. Independent questions
5. New axiom candidates
6. V = L
PART II: REALISM
1. Godelian realism
2. Quinean realism
3. Set-theoretic realism
4. A realist's case against V = L
5. Hints of trouble
6. Indispensability and scientific practice
7. Indispensability and mathematical practic
PART III: NATURALISM
1. Wittgensteinian anti-philosophy
2. A second Godelian theme
3. Quinean naturalism
4. Mathematical naturalism
5. The problem revisited
6. A naturalist's case against V = L
Conclusion
Bibliography
Index

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