What Is Mathematics, Really?

What Is Mathematics, Really?

by Reuben Hersh
     
 

ISBN-10: 0195130871

ISBN-13: 9780195130874

Pub. Date: 07/28/1999

Publisher: Oxford University Press, USA

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,…  See more details below

Overview

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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Product Details

ISBN-13:
9780195130874
Publisher:
Oxford University Press, USA
Publication date:
07/28/1999
Edition description:
New Edition
Pages:
368
Sales rank:
707,106
Product dimensions:
9.00(w) x 6.10(h) x 1.10(d)
Lexile:
1090L (what's this?)

Table of Contents

Preface: Aims and Goals
Acknowledgments
Dialogue with Laura
1Survey and Proposals3
2Criteria for a Philosophy of Mathematics24
3Myths/Mistakes/Misunderstandings35
4Intuition/Proof/Certainty48
5Five Classical Puzzles72
6Mainstream Before the Crisis91
7Mainstream Philosophy at Its Peak119
8Mainstream Since the Crisis137
9Foundationism Dies/Mainstream Lives165
10Humanists and Mavericks of Old182
11Modern Humanists and Mavericks198
12Contemporary Humanists and Mavericks220
13Mathematics Is a Form of Life235
Mathematical Notes/Comments249
Bibliography317
Index335

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