Towards an Arithmetical Logic, 1st ed. 2015
The Arithmetical Foundations of Logic
Studies in Universal Logic Series

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.

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.

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