# Towards an Arithmetical Logic

## The Arithmetical Foundations of Logic

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

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

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.

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

- 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
- Print ISBN 978-3-319-22086-4
- Online ISBN 978-3-319-22087-1
- Series Print ISSN 2297-0282
- Series Online ISSN 2297-0290
- About this book