000			03226mam a2200325 a 4500
001			2006488
003			ARRUPE
005			20150121172710.0
008			960814s1997 nyua b 001 0 eng
010			_a 96038483
020			_a0195113683 (alk. paper)
035			_a(OCoLC)ocm35298635
040			_aDLC _cDLC _dYDX _dOrLoB-B
050	0	0	_aQA8.4 _b.H47 1997
082	0	0	_a510/.1 _220
100	1		_aHersh, Reuben, _d1927- _914015
245	1	0	_aWhat is mathematics, really? : _cReuben Hersh.
260			_aNew York : _bOxford University Press, _c1997.
300			_axxiv, 343 p. : _bill. ; _c25 cm.
504			_aIncludes bibliographical references (p. [317]-334) and index.
505	0	0	_tDialogue with Laura -- _g1. _tSurvey and Proposals -- _g2. _tCriteria for a Philosophy of Mathematics -- _g3. _tMyths/Mistakes/Misunderstandings -- _g4. _tIntuition/Proof/Certainty -- _g5. _tFive Classical Puzzles -- _g6. _tMainstream Before the Crisis -- _g7. _tMainstream Philosophy at Its Peak -- _g8. _tMainstream Since the Crisis -- _g9. _tFoundationism Dies/Mainstream Lives -- _g10. _tHumanists and Mavericks of Old -- _g11. _tModern Humanists and Mavericks -- _g12. _tContemporary Humanists and Mavericks -- _g13. _tMathematics Is a Form of Life -- _tMathematical Notes/Comments.
520			_aVirtually 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.
520	8		_aMathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life.
520	8		_aHersh 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.
520	8		_aThe 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.
520	8		_aIn 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.
650		0	_aMathematics _xPhilosophy. _914016
900			_bTOC
942			_2lcc _cMONOGRAPH
999			_c121690 _d121690