Hilbert's program : an essay on mathematical instrumentalism
著者
書誌事項
Hilbert's program : an essay on mathematical instrumentalism
（Synthese library, v. 182）
Springer Science+Business Media, c1986
- : pbk.
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注記
Includes bibliographical references (p. 179-182) and index
"Originally published by D. Reidel publishing company, Dordrecht, holland in 1986"--T.p verso
"Softcover reprint of the hardcover 1st edition 1986"--T.p verso
内容説明・目次
内容説明
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.
目次
I: The Philosophical Fundamentals of Hilbert's Program.- II: A Closer Look at the Problems.- III: The Goedelian Challenge.- IV: The Stability Problem.- V: The Convergence Problem and the Problem of Strict Instrumentalism.- Appendix: Hilbert's Program and the First Theorem.- References.
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