Internal Logic: Foundations of Mathematics from Kronecker to Hilbert

by Y. Gauthier

Overview

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.

Product Details

ISBN-13:	9789048160525
Publisher:	Springer Netherlands
Publication date:	12/08/2010
Series:	Synthese Library , #310
Edition description:	Softcover reprint of hardcover 1st ed. 2002
Pages:	251
Product dimensions:	6.30(w) x 9.45(h) x 0.02(d)

About the Author

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.

Table of 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.