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What Is Mathematics, Really?

โœ Scribed by Reuben Hersh

Publisher
Oxford University Press, USA
Year
1999
Tongue
English
Leaves
323
Category
Library
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โœฆ Synopsis

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.

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Contents; Preface: Aims and Goals; Acknowledgments; Dialogue with Laura; 1 Survey and Proposals; 2 Criteria for a Philosophy of Mathematics; 3 Myths/Mistakes/Misunderstandings; 4 Intuition/Proof/Certainty; 5 Five Classical Puzzles; 6 Mainstream Before the Crisis; 7 Mainstream Philosophy at Its Peak;

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What is Mathematics, Really?
๐Ÿ“ What is Mathematics, Really?
โœ Reuben Hersh ๐Ÿ“‚ Library ๐Ÿ“… 1997 ๐Ÿ› Oxford University Press ๐ŸŒ English

Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In