Former library copy. Pages intact with possible writing/highlighting. Binding strong with minor wear. Dust jackets/supplements may not be included. Includes library markings. Stock photo provided. Product includes identifying sticker. Better World Books: Buy Books. Do Good.

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Bibliographic Details

Title: Hilbert's Program : An Essay on Mathematical Instrumentalism
Publisher: Springer Netherlands
Publication Date: 1986
Language: English
ISBN 10: 9027721513
ISBN 13: 9789027721518
Binding: Hardcover
Condition: Very Good
Weight: 2.271 pounds

About this title

Synopsis

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.

Review

`The book is well written and recommended reading for everyone interested in the philosophical dimensions of technical results from foundations of mathematics and pure logic.'
S. Gottwald, Zentralblatt f�r Mathematik und ihre Grenzgebiete, Vol. 641.

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