{"product_id":"9789027721518","title":"Synthese Library: An Essay on Mathematical Instrumentalism","description":"\u003ch1\u003eSynthese Library\u003c\/h1\u003e\u003ch2\u003eAn Essay on Mathematical Instrumentalism\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003eContributors:\u003c\/strong\u003e Detlefsen, M.\u003c\/p\u003e\u003cp\u003eHilbert's Program was founded on a concern for the phenomenon of paradox in mathematics. To Hilbert, the paradoxes, which are at once both absurd and irresistible, revealed a deep philosophical truth: namely, that there is a discrepancy between the laws accord­ ing to which the mind of homo mathematicus works, and the laws governing objective mathematical fact. Mathematical epistemology is, therefore, to be seen as a struggle between a mind that naturally works in one way and a reality that works in another. Knowledge occurs when the two cooperate. Conceived in this way, there are two basic alternatives for mathematical epistemology: a skeptical position which maintains either that mind and reality seldom or never come to agreement, or that we have no very reliable way of telling when they do; and a non-skeptical position which holds that there is significant agree­ ment between mind and reality, and that their potential discrepan­ cies can be detected, avoided, and thus kept in check. Of these two, Hilbert clearly embraced the latter, and proposed a program designed to vindicate the epistemological riches represented by our natural, if non-literal, ways of thinking. Brouwer, on the other hand, opted for a position closer (in Hilbert's opinion) to that of the skeptic. Having decided that epistemological purity could come only through sacrifice, he turned his back on his classical heritage to accept a higher calling.\u003c\/p\u003e\u003ch3\u003eBook Details\u003c\/h3\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003ePublisher:\u003c\/strong\u003e Springer\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e 1986-04-30\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFormat:\u003c\/strong\u003e Hardcover\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eISBN-13:\u003c\/strong\u003e 9789027721518\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003ePages:\u003c\/strong\u003e 186\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":45416676720780,"sku":"9789027721518","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789027721518_c6bd8be4-27a2-481b-b932-5614e774e10f.jpg?v=1768917447","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9789027721518","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}