New Directions in the Philosophy of Mathematics: An Anthology

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Thomas Tymoczko
Princeton University Press, 1998 - 436 páginas

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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Índice

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
An Educational and Philosophic Error?
67
Mathematics as an Objective Science
79
Interlude
95
From the Preface of Induction and Analogy in Mathematics
99
THE EVOLUTION OF MATHEMATICAL PRACTICE
185
Is Mathematical Truth TimeDependent?
201
Mathematical Change and Scientific Change
215
A CASE STUDY
243
Social Processes and Proofs of Theorems and Programs
267
InformationTheoretic Computational Complexity and Glodes Theorem and Information
287
Current Concerns
313
Proof as a Source of Truth
317

Generalization Specialization Analogy
103
Mathematical Practice
125
WHAT IS MATHEMATICAL PRACTICE?
129
What Does a Mathematical Proof Prove?
153
Is One and One Really Two?
163
The Ideal Mathematician
177
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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Sobre el autor (1998)

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.

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