What is Mathematics, Really?
Oxford University Press, 1999 - 343 páginas
Virtually 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. 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. The humanist standpoint helps him to resolve ancient controversies about proof, certainty, and invention versus discovery. The 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. In 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.
Comentarios de usuarios - Escribir una reseña
What is mathematics, Really?Reseña de usuario - Not Available - Book Verdict
Hersh, mathematician and coauthor of The Mathematical Experience (1983), attempts to answer here the philosophical question, "What is mathematics?" Many practitioners think of themselves as ... Leer reseña completa
Criteria for a Philosophy of Mathematics
Five Classical Puzzles
Mainstream Philosophy at Its Peak
Mainstream Since the Crisis
Foundationism DiesMainstream Lives
Otras ediciones - Ver todo
abstract algebra analytic angles answer arithmetic axiomatic set theory axioms believe Bertrand Russell Brouwer calculation called certainty Chapter complex numbers concepts construction constructivist contradiction David Hilbert definition derivative Descartes empty set entities equation Euclid Euclidean Euclidean geometry example exist experience finite formal formalist formula foundationist foundations Frege function gazillion Gödel graph Hilbert human humanist idea ideal indubitable integral intuition intuitionism Kant Kitcher Kurt Gödel Lakatos Leibniz logic logicist mathe mathematical knowledge mathematical objects mathematical proof mathematicians matics meaning mental method mind myth natural numbers nature of mathematics non-Euclidean geometry notion number system philosophy of mathematics physical Platonism Platonist polynomials possible problem properties proved pure Pythagorean question rational numbers real numbers reality reasoning rigorous rules Russell Russell's paradox sense set theory set-theoretic space Spinoza square statement theorem There's things thought tion triangle true understand universe What's Wittgenstein zero
Todos los resultados de la Búsqueda de libros »
TIMSS/III. 2. Mathematische und physikalische Kompetenzen am Ende der ...
Jürgen Baumert,Wilfried Bos,Rainer Lehmann
Vista previa restringida - 2000