New Directions in the Philosophy of Mathematics: An Anthology - Revised and Expanded Edition
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.


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.

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New Directions in the Philosophy of Mathematics: An Anthology - Revised and Expanded Edition
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.


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.

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New Directions in the Philosophy of Mathematics: An Anthology - Revised and Expanded Edition

New Directions in the Philosophy of Mathematics: An Anthology - Revised and Expanded Edition

by Thomas Tymoczko (Editor)
New Directions in the Philosophy of Mathematics: An Anthology - Revised and Expanded Edition

New Directions in the Philosophy of Mathematics: An Anthology - Revised and Expanded Edition

by Thomas Tymoczko (Editor)

Paperback(Revised and Expanded Edition)

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Overview

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.


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.


Product Details

ISBN-13: 9780691034980
Publisher: Princeton University Press
Publication date: 02/01/1998
Edition description: Revised and Expanded Edition
Pages: 456
Product dimensions: 6.00(w) x 9.25(h) x (d)

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.

Table of Contents

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


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