Hilbert's Program : An Essay on Mathematical Instrumentalism

Language: English

Published by Springer, 2010

9048184207 / 9789048184200

Series: Book 152 of 304 - Synthese Library

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Druck auf Anfrage Neuware - Printed after ordering - 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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Title
Hilbert's Program : An Essay on Mathematical Instrumentalism
Author
M. Detlefsen
Publisher
Springer
Publication year
2010
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
9048184207
ISBN 13
9789048184200
Item weight
264 grams
Dimensions
216x140x12 mm
Series
Book 152 of 304: Synthese Library

AHA-BUCH GmbH

Einbeck, Germany

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