Table of Contents

PrefaceIntroductionPt. IChallenging Foundations1Some Proposals for Reviving the Philosophy of Mathematics9A Renaissance of Empiricism in the Recent Philosophy of Mathematics?29What Is Mathematical Truth?49"Modern" Mathematics: An Educational and Philosophic Error?67Mathematics as an Objective Science79Interlude95From the Preface of Induction and Analogy in Mathematics99Generalization, Specialization, Analogy103Pt. IIMathematical Practice125Theory and Practice in Mathematics129What Does a Mathematical Proof Prove?153Fidelity in Mathematical Discourse: Is One and One Really Two?163The Ideal Mathematician177The Cultural Basis of Mathematics185Is Mathematical Truth Time-Dependent?201Mathematical Change and Scientific Change215The Four-Color Problem and Its Philosophical Significance243Social Processes and Proofs of Theorems and Programs267Information-Theoretic Computational Complexity and Godel's Theorem and Information287Pt. IIICurrent Concerns313Proof as a Source of Truth317On Proof and Progress in Mathematics337Does V Equal L?357Afterword385Bibliography399Supplemental Bibliography of Recent Work411

About the Author

Thomas Tymoczko was Professor of Philosophy at Smith College. He was the author of numerous papers in philosophy and coauthor, with Jim Henle, of Sweet Reason: A Field Guide to Modern Logic. He died in 1996.