The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form.<P>This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

	Preface
	Introduction
Pt. I	Challenging Foundations	1
	Some Proposals for Reviving the Philosophy of Mathematics	9
	A Renaissance of Empiricism in the Recent Philosophy of Mathematics?	29
	What Is Mathematical Truth?	49
	"Modern" Mathematics: An Educational and Philosophic Error?	67
	Mathematics as an Objective Science	79
	Interlude	95
	From the Preface of Induction and Analogy in Mathematics	99
	Generalization, Specialization, Analogy	103
Pt. II	Mathematical Practice	125
	Theory and Practice in Mathematics	129
	What Does a Mathematical Proof Prove?	153
	Fidelity in Mathematical Discourse: Is One and One Really Two?	163
	The Ideal Mathematician	177
	The Cultural Basis of Mathematics	185
	Is Mathematical Truth Time-Dependent?	201
	Mathematical Change and Scientific Change	215
	The Four-Color Problem and Its Philosophical Significance	243
	Social Processes and Proofs of Theorems and Programs	267
	Information-Theoretic Computational Complexity and Godel's Theorem and Information	287
Pt. III	Current Concerns	313
	Proof as a Source of Truth	317
	On Proof and Progress in Mathematics	337
	Does V Equal L?	357
	Afterword	385
	Bibliography	399
	Supplemental Bibliography of Recent Work	411