Readership: Philosophers, mathematicians, and logicians; graduate students in these subjects.
Penelope Maddy, Professor of Philosophy, University of California, Irvine
"An excellent book ... The philosopher's task is not to provide external criticism, but rather to clarify debates in this so-called mathematical community. And Ms Maddy makes some fascinating (and very technical) steps in this direction." - The Economist Review
"'This book represents the culmination of Penelope Maddy's recent work in the philosophy of mathematics. . . . The book is beautifully written, tightly argued and makes compelling reading. I believe the position Maddy introduces and defends - set theoretic naturalism - is a significant and original addition to the philosophy of mathematics landscape, and one that will certainly attract a great deal of attention. . . . In sum, this is a very important book covering some fascinating terrain on the border between philosophy and mathematics." - Mind
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
