ISBN:
9789401577311
Language:
English
Pages:
1 Online-Ressource (xiv, 186 Seiten)
Edition:
Springer eBook Collection. Humanities, Social Sciences and Law
Series Statement:
Synthese library Volume182
Series Statement:
Springer eBook Collection
Parallel Title:
Erscheint auch als Detlefsen, Michael Hilbert's program
Keywords:
Philosophy (General)
;
Logic, Symbolic and mathematical
;
Logic
;
Mathematics.
;
History.
;
Mathematical logic.
;
Mathematik
;
Philosophie
;
Hilbert, David 1862-1943
;
Mathematik
;
Grundlage
;
Hilbertsche Probleme
Abstract:
I: The Philosophical Fundamentals of Hilbert’s Program -- II: A Closer Look at the Problems -- III: The Gödelian Challenge -- IV: The Stability Problem -- V: The Convergence Problem and the Problem of Strict Instrumentalism -- Appendix: Hilbert’s Program and the First Theorem -- References.
Abstract:
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.
Note:
Literaturverzeichnis: Seite 179-186
DOI:
10.1007/978-94-015-7731-1
URL:
Volltext
(lizenzpflichtig)
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