What Is Mathematics, Really?

Reuben Hersh9780195113686, 0-19-511368-3

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the “humanist” idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy – ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap – followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos.What is Mathematics, Really? reflects an insider’s view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.Hersh has a talent for exposition that makes me wish he had written most of the books on math Ive had to read….[His] fascinating…book should prove an enlightening and entertaining read for anyone who desires greater insight into the nature of the pursuit of fundamental knowledge. – Physics Today”

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Table of contents :
Contents……Page 10
Preface: Aims and Goals……Page 12
Acknowledgments……Page 18
Dialogue with Laura……Page 22
Part One……Page 26
1 Survey and Proposals……Page 28
2 Criteria for a Philosophy of Mathematics……Page 49
3 Myths/Mistakes/Misunderstandings……Page 60
4 Intuition/Proof/Certainty……Page 73
5 Five Classical Puzzles……Page 97
Part Two……Page 114
6 Mainstream Before the Crisis……Page 116
7 Mainstream Philosophy at Its Peak……Page 144
8 Mainstream Since the Crisis……Page 162
9 Foundationism Dies/Mainstream Lives……Page 190
10 Humanists and Mavericks of Old……Page 207
11 Modern Humanists and Mavericks……Page 223
12 Contemporary Humanists and Mavericks……Page 245
Summary and Recapitulation……Page 258
13 Mathematics Is a Form of Life……Page 260
Mathematical Notes/Comments……Page 276
Bibliography……Page 342
B……Page 360
C……Page 361
F……Page 362
H……Page 363
L……Page 364
P……Page 365
R……Page 366
T……Page 367
Z……Page 368