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Internal Logic: Foundations of Mathematics from Kronecker to Hilbert: Synthese Library, cartea 310

Autor Y. Gauthier
en Limba Engleză Hardback – 30 iun 2002
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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Specificații

ISBN-13: 9781402006890
ISBN-10: 1402006896
Pagini: 268
Ilustrații: X, 251 p.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.54 kg
Ediția:2002
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Synthese Library

Locul publicării:Dordrecht, Netherlands

Public țintă

Research

Cuprins

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.

Notă biografică

Yvon Gauthier was born in Drummondville, Québec in 1941. He has studied in Heidelberg and has been Research Fellow in Berkeley and Leningrad (St-Petersburg). He has taught at the University of Sudbury (Ontario) and at the University of Toronto. Since 1973, he is Professor of Logic and Foundations of Mathematics at the University of Montréal. Author of ten books, he has published numerous papers on foundations of mathematics and foundations of physics in specialized journals.

Caracteristici

Includes supplementary material: sn.pub/extras