1998•Unpublished venueRequires access

New directions in the philosophy of mathematics : an anthology

Thomas Tymoczko

Abstract

PrefaceIntroductionPt. IChallenging Foundations1Some Proposals for Reviving the Philosophy of Mathematics9A Renaissance of Empiricism in the Recent Philosophy of Mathematics?29What Is Mathematical Truth?49Modern 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

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Key concepts: Mathematical proof, Philosophy of mathematics, Analogy, Mathematical practice, Gödel, Mathematical induction, Gödel's incompleteness theorems, Epistemology