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Kniha Hilbert's Program M. Detlefsen

Hilbert's Program

An Essay on Mathematical Instrumentalism

Autor: M. Detlefsen
Jazyk: Angličtina
Väzba: Pevná
Vydavateľ: Springer
Dostupnosť: Skladom u dodávateľa
Odosielame za 10-13 dní
99.76 €
Hilbert's Program was founded on a concern for the phenomenon of paradox in mathematics. To Hilbert,...

Informácie o knihe

Autor
M. Detlefsen
Jazyk
Angličtina
Väzba
Kniha - Pevná
Stránok
186
EAN
9789027721518
ISBN
9027721513
Enbook ID
02777051
Vydavateľ
Springer
Hmotnosť
1030
Rozmery
210 x 297 x 17

Kompletný popis

Hilbert'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.

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