Synopses & Reviews
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.
Synopsis
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.
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 |