Naturalism in Mathematics [Paperback]

Naturalism in Mathematicsinvestigates 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.

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

Stylistically the book is an enjoyably readable and beautifully clear. In particular Maddy has a near-miraculous gift for explaining mathematical technicalities in a way that is comprehensible to the non-expert. The book is therefore well worth reading not just for the new and bold philosophical position it promotes, but also as a philosopher's guide to what is going on in contemporary set theory. The Philosophical Review

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 rewardinl3-