# Towards an Arithmetical Logic

## The Arithmetical Foundations of Logic

• Presents an original work on the foundations of logic and mathematics

• Covers many topics in logic, mathematics and physics that are relevant to formal logic and the philosophy of science

• Offers a new foundational and critical perspective in constructivist foundations

• The diverse range of topics will be of interest to a broad audience of scholars

Book

Part of the Studies in Universal Logic book series (SUL)

1. Front Matter
Pages i-xi
2. Yvon Gauthier
Pages 1-3
3. Yvon Gauthier
Pages 5-24
4. Yvon Gauthier
Pages 25-53
5. Yvon Gauthier
Pages 55-70
6. Yvon Gauthier
Pages 71-116
7. Yvon Gauthier
Pages 117-134
8. Yvon Gauthier
Pages 135-162
9. Yvon Gauthier
Pages 163-177
10. Back Matter
Pages 179-184

### Introduction

This book offers an original contribution to the foundations of logic and mathematics, and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic, and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of logic and mathematics.

### Keywords

Fermat’s infinite descent Kronecker’s general arithmetic arithmetical logic constructive logic foundations of mathematics

#### Authors and affiliations

Yvon Gauthier has taught formal logic and philosophy of science at the Universities of Sudbury, Toronto and Montreal for fifty years. He has studied philosophy in Heidelberg and he has been a Research Fellow in mathematics in Berkeley and Leningrad (St-Petersburg). Author of fifteen books, he has published extensively in foundations of mathematics and foundations of physics in specialized journals. The present book aims at a synthesis of his recent work.

### Bibliographic information

• Book Title Towards an Arithmetical Logic
• Book Subtitle The Arithmetical Foundations of Logic
• Authors Yvon Gauthier
• Series Title Studies in Universal Logic
• Series Abbreviated Title Stud. Universal Logic
• DOI https://doi.org/10.1007/978-3-319-22087-1
• Copyright Information Springer International Publishing Switzerland 2015
• Publisher Name Birkhäuser, Cham
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Softcover ISBN 978-3-319-22086-4
• eBook ISBN 978-3-319-22087-1
• Series ISSN 2297-0282
• Series E-ISSN 2297-0290
• Edition Number 1
• Number of Pages XI, 184
• Number of Illustrations 9 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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