Overview
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.
Full Product Details
Author: M. Detlefsen
Publisher: Springer
Imprint: Kluwer Academic Publishers
Edition: 1986 ed.
Volume: 182
Dimensions:
Width: 21.00cm
, Height: 1.20cm
, Length: 29.70cm
Weight: 1.030kg
ISBN: 9789027721518
ISBN 10: 9027721513
Pages: 186
Publication Date: 30 April 1986
Audience:
College/higher education
,
Professional and scholarly
,
Postgraduate, Research & Scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Reviews
'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 fur Mathematik und ihre Grenzgebiete, Vol. 641.
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 fA1/4r Mathematik und ihre Grenzgebiete, Vol. 641.
`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 fur Mathematik und ihre Grenzgebiete, Vol. 641.
