Hilbert’s Program: An Essay on Mathematical Instrumentalism (Synthese Library, Band 182) - Softcover

Detlefsen, M.

Softcover

ISBN 10: 9048184207 ISBN 13: 9789048184200

Verlag: Springer, 2010

Inhaltsangabe

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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 9048184207
• ISBN 13: 9789048184200
• Einband: Taschenbuch
• Anzahl der Seiten: 204
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland