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What Is Mathematics, Really?by Reuben Hersh
Synopses & ReviewsPublisher Comments:Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, halfconscious 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 nineteenthcentury 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 What is Mathematics, Really?, renowned mathematician Rueben Hersh takes these eloquent words and this pervasive philosophy to task, in a subversive attack on traditional philosophies of mathematics, most notably, Platonism and formalism.
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 philosophyranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, David Hilbert, Rudolph Carnap, and Willard V.O. Quinefollowed 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 antielitism 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 coauthor of The Mathematical Experience, which won the American Book Award in 1983, this volume reflects an insider's view of mathematical life, based on twenty years of doing research on advanced mathematical problems, thirtyfive years of teaching graduates and undergraduates, and many long hours of listening, talking to, and reading philosophers. A clearly written and highly iconoclastic book, it is sure to be hotly debated by anyone with a passionate interest in mathematics or the philosophy of science. 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 philosophyranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnapfollowed 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. Description:Includes bibliographical references (p. [317]334) and index.
About the AuthorReuben Hersh taught at several distinguished colleges and universities around the country. Now retired, he resides in Santa Fe, New Mexico.
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