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9780195130874

What Is Mathematics, Really?

by
  • ISBN13:

    9780195130874

  • ISBN10:

    0195130871

  • Edition: 1st
  • Format: Paperback
  • Copyright: 1999-07-08
  • Publisher: Oxford University Press
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Summary

Most philosophers of mathematics treat it as isolated, timeless,ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must beunderstood as a human activity, a social phenomenon, part of human culture,historically evolved, and intelligible only in a social context. Hersh pulls thescreen back to reveal mathematics as seen by professionals, debunking manymathematical myths, and demonstrating how the "humanist" idea of the nature ofmathematics more closely resembles how mathematicians actually work. At theheart of his book is a fascinating historical account of the mainstream ofphilosophy--ranging from Pythagoras, Descartes, and Spinoza, to BertrandRussell, David Hilbert, and Rudolph Carnap--followed by the mavericks who sawmathematics as a human artifact, including Aristotle, Locke, Hume, Mill, andLakatos.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 thephilosophy of science.

Author Biography


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

Table of Contents

Preface Aims and Goalsp. xi
Acknowledgmentsp. xvii
Dialogue with Laurap. xxi
p. 1
Survey and Proposalsp. 3
Criteria for a Philosophy of Mathematicsp. 24
Myths/Mistakes/ Misunderstandingsp. 35
Intuiton/Proof/Certaintyp. 48
Five Classical Puzzlesp. 72
p. 89
Mainstream Before the Crisisp. 91
Mainstream Philosophy at Its Peakp. 119
Mainstream Since the Crisisp. 137
Foundationism Dies/ Mainstream Livesp. 165
Humanists and Mavericks of Oldp. 182
Modern Humanists and Mavericksp. 198
Twelve Contemporary Humanists and Mavericksp. 220
Summary and Recapitulationp. 233
Thirteen Mathematics is a Form of Lifep. 235
Mathematical Notes/Commentsp. 251
Bibliographyp. 317
Indexp. 335
Table of Contents provided by Publisher. All Rights Reserved.

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