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＜電子ブック＞
Internal Logic : Foundations of Mathematics from Kronecker to Hilbert / by Y. Gauthier
(Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science. ISSN:25428292 ; 310)

版	1st ed. 2002.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	X, 251 p : online resource
著者標目	*Gauthier, Y author SpringerLink (Online service)
件　名	LCSH:Mathematical logic LCSH:Mathematics LCSH:Logic LCSH:Science -- Philosophy  全ての件名で検索 FREE:Mathematical Logic and Foundations FREE:Mathematics FREE:Logic FREE:Philosophy of Science
一般注記	1. Introduction. Foundations of Mathematics -- 2. From Hilbert to Kronecker -- 3. The Consistency of Arithmetic Revisited -- 4. The Internal Consistency of Arithmetic with Infinite Descent -- 5. From Kronecker to Brouwer -- 6. Hilbert and the Foundations of Physics -- 7. Conclusion. Internal logic: From Kronecker to Hilbert and Beyond -- References -- Name Index Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene HTTP:URL=https://doi.org/10.1007/978-94-017-0083-2

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