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Tries to refine the philosophy of mathematics to reflect what mathematicians really do, and argues that mathematics must be understood in a social context

Hersh coauthored The Mathematical Experience which won the National Book Award in 1983, and has spent 20 years doing research on advanced mathematical problems; 35 years teaching graduates and undergraduates; and many hours listening to, talking to, and reading philosophers. He notes that although the 1950s saw a revolution in the philosophy of science bringing it in line with what scientists actually do, no such revolution occurred in the philosophy of math, which has remained out of touch with mathematicians, users of mathematics, and teachers of mathematics. Hersh is among the iconoclasts working to bring in new ideas, in particular an understanding that the activity of mathematics is intelligible only in a social context. Annotation c. by Book News, Inc., Portland, Or.

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 the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist there when the last of their radiant host shall have fallen from heaven." In

Virtually all philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. 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. 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. At the heart of the book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, David Hilbert, Rudolph Carnap, and Willard V.O. Quine--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, Peirce, Dewey, and Lakatos. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. He contends that Platonism and elitism fit well together, that Platonism in fact is used to justify the claim that "some people just can't learn math." The humanist philosophy, on the other hand, links mathematics with geople, 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 ramifications.

Written by the co-author of

Publisher:
New York : Oxford University Press, 1997

ISBN:
9780585356662

0585356661

9780195113686

0585356661

9780195113686

Characteristics:
1 online resource (xxiv, 343 pages) : illustrations

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