© 2002

Internal Logic

Foundations of Mathematics from Kronecker to Hilbert


Part of the Synthese Library book series (SYLI, volume 310)

Table of contents

  1. Front Matter
    Pages i-x
  2. Yvon Gauthier
    Pages 1-21
  3. Yvon Gauthier
    Pages 22-49
  4. Yvon Gauthier
    Pages 50-80
  5. Yvon Gauthier
    Pages 118-147
  6. Yvon Gauthier
    Pages 148-185
  7. Back Matter
    Pages 215-251

About this book


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

Authors and affiliations

  1. 1.University of MontréalCanada

About the authors

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.

Bibliographic information

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