Internal Logic

1. Front Matter

   Pages i-x

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2. Introduction Foundations of Mathematics

   • Yvon Gauthier

   Pages 1-21

3. From Hilbert to Kronecker

   • Yvon Gauthier

   Pages 22-49

4. The Consistency of Arithmetic Revisited

   • Yvon Gauthier

   Pages 50-80

5. The Internal Consistency of Arithmetic with Infinite Descent

   • Yvon Gauthier

   Pages 81-117

6. From Kronecker to Brouwer

   • Yvon Gauthier

   Pages 118-147

7. Hilbert and the Foundations of Physics

   • Yvon Gauthier

   Pages 148-185

8. Conclusion. Internal Logic : From Kronecker to Hilbert and Beyond

   • Yvon Gauthier

   Pages 186-213

9. Back Matter

   Pages 215-251

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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.

• Arithmetic
• Cantor
• Finite
• logic
• mathematics
• proof

• University of Montréal, Canada

  Yvon Gauthier

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.

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