Internal logic : foundations of mathematics from Kronecker to Hilbert
Author(s)
Bibliographic Information
Internal logic : foundations of mathematics from Kronecker to Hilbert
（Synthese library, v. 310）
Kluwer Academic, c2002
Available at / 17 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science研究室
DC21:108/SY782070574200
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Note
Bibliography: p. [215]-229
Includes indexes
Description and Table of Contents
Description
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.
Table of Contents
Preface.
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. Subject Index. Name Index.
by "Nielsen BookData"
