What is Mathematics, Really?

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Oxford University Press, 1997 - Medical - 343 pages
2 Reviews
Virtually all philosophers treat mathematics as isolated, timeless, ahistorical, inhuman. In What Is Mathematics, Really? renowned mathematician Reuben Hersh argues the contrary. In a subversive attack on traditional philosophies of mathematics, most notably Platonism and formalism, he shows 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. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. 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. The humanist standpoint helps him to resolve ancient controversies about proof, certainty, and invention versus discovery. The second half of the book provides a fascinating history of the "mainstream" of philosophy - ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, Hilbert, Carnap, and Quine. Then come the mavericks who saw mathematics as a human artifact - Aristotle, Locke, Hume, Mill, Peirce, Dewey, Wittgenstein. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. Platonism and elitism fit together naturally. Humanism, on the other hand, links mathematics with people, with society, and with history. It fits with liberal anti-elitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge and culture. Thus Hersh's argument has educational and political consequences.
  

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What is mathematics, Really?

User Review  - Not Available - Book Verdict

Hersh, mathematician and coauthor of The Mathematical Experience (1983), attempts to answer here the philosophical question, "What is mathematics?" Many practitioners think of themselves as ... Read full review

Review: What Is Mathematics, Really?

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A great book for a philosophical nerd. Read full review

Contents

Survey and Proposals
3
Criteria for a Philosophy of Mathematics
24
MythsMistakesMisunderstandings
35
IutuitionProofCertniuty
48
Five Classical Puzzles
72
Mainstream Before the Crisis
91
Mainstream Philosophy at Its Peak119
119
Mainstream Since the Crisis
137
Humanists and Mavericks of Old
182
Modern Humanists and Mavericks
198
Coutemporary Humanists and Mavericks
220
mathematics
235
Mathematical NotesCommeuts
251
Mathematical issues from chapters 113 A simple account of square
314
Index
335
Copyright

Foundationism DicsMainstream Lives
165

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About the author (1997)


Reuben Hersh taught at several distinguished colleges and universities around the country. Now retired, he resides in Santa Fe, New Mexico.

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