TY  - BOOK
AU  - Detlefsen,M.
ED  - SpringerLink (Online service)
TI  - Hilbert’s Program: An Essay on Mathematical Instrumentalism 
T2  - Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,
SN  - 9789401577311
AV  - BC1-199 
U1  - 160 23
PY  - 1986///
CY  - Dordrecht
PB  - Springer Netherlands, Imprint: Springer
KW  - Logic
KW  - Mathematics
KW  - History
KW  - Mathematical logic
KW  - History of Mathematical Sciences
KW  - Mathematical Logic and Foundations
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-94-015-7731-1
ER  -