{"product_id":"hilberts-program-an-essay-on-mathematical-instrumentalism-9789027721518","title":"Hilbert’s Program: An Essay on Mathematical Instrumentalism","description":"\u003cp\u003e • Author(s): M. Detlefsen\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: History \u0026amp; Philosophy\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","brand":"Springer","offers":[{"title":"Hardcover","offer_id":47658196828311,"sku":"9789027721518","price":7345.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9789027721518.webp?v=1775817727","url":"https:\/\/atlanticbooks.com\/products\/hilberts-program-an-essay-on-mathematical-instrumentalism-9789027721518","provider":"Atlantic Books","version":"1.0","type":"link"}