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Internal Logic : Foundations of Mathematics from Kronecker to Hilbert

Author: Yvon Gauthier
Publisher: Dordrecht : Springer Netherlands, 2002.
Series: Synthese library, 310.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Yvon Gauthier
ISBN: 9789401700832 9401700834
OCLC Number: 851370723
Description: 1 online resource (x, 251 pages).
Contents: 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.
Series Title: Synthese library, 310.
Responsibility: by Yvon Gauthier.

Abstract:

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.

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