New Directions in the Philosophy of Mathematics: An AnthologyThomas 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. |
Índice
Challenging Foundations | 1 |
Reuben Hersh | 9 |
Hilary Putnam | 49 |
Philosophic Error? | 67 |
Goodman | 79 |
Interlude | 95 |
George Polya | 103 |
Mathematical Practice | 125 |
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 | 287 |
Current Concerns | 313 |
William P Thurston | 337 |
Afterword | 385 |
Imre Lakatos | 153 |
Really Two? | 163 |
Philip J Davis and Reuben Hersh | 177 |
THE EVOLUTion of Mathematical PraCTICE | 185 |
Bibliography | 399 |
Supplemental Bibliography of Recent Work | 411 |
Otras ediciones - Ver todo
New Directions in the Philosophy of Mathematics: An Anthology Thomas Tymoczko Vista previa restringida - 1998 |