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 |
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 |
Otras ediciones - Ver todo
New Directions in the Philosophy of Mathematics: An Anthology Thomas Tymoczko Vista previa restringida - 1998 |
Términos y frases comunes
Referencias a este libro
From Complexity to Life: On The Emergence of Life and Meaning Niels Henrik Gregersen Vista previa restringida - 2002 |
Multiple Perspectives on Mathematics Teaching and Learning Jo Boaler No hay ninguna vista previa disponible - 2000 |