Towards an Arithmetical Logic
The Arithmetical Foundations of Logic
Authors: Gauthier, Yvon
 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
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 About this book

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 FermatKronecker 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.
 About the authors

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 (StPetersburg). 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.
 Reviews

“The present book consists of eight chapters devoted to the internal logic of arithmetic … . Historical, mathematical, logical and philosophical aspects are considered and intertwined in the book. It can be interesting for logicians and mathematicians as well as for philosophers of mathematics.” (Roman Murawski, zbMATH 1339.03002, 2016)
 Table of contents (8 chapters)


Introduction: The Internal Logic of Arithmetic
Pages 13

Arithmetization of Analysis and Algebra
Pages 524

Arithmetization of Logic
Pages 2553

Kronecker’s Foundational Programme in Contemporary Mathematics
Pages 5570

Arithmetical Foundations for Physical Theories
Pages 71116

Table of contents (8 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Towards an Arithmetical Logic
 Book Subtitle
 The Arithmetical Foundations of Logic
 Authors

 Yvon Gauthier
 Series Title
 Studies in Universal Logic
 Copyright
 2015
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Springer International Publishing Switzerland
 eBook ISBN
 9783319220871
 DOI
 10.1007/9783319220871
 Softcover ISBN
 9783319220864
 Series ISSN
 22970282
 Edition Number
 1
 Number of Pages
 XI, 184
 Number of Illustrations
 9 b/w illustrations
 Topics