Towards an Arithmetical Logic

The Arithmetical Foundations of Logic
1. Auflage 2015
ISBN: 978-3-319-22086-4
Verlag: Springer International Publishing

Buch, Englisch, 184 Seiten, Paperback, Format (B × H): 168 mm x 240 mm, Gewicht: 3377 g

Reihe: Studies in Universal Logic

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.

Zielgruppe

Research

Autoren/Hrsg.

Gauthier, Yvon

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Zahlensysteme
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Foreword.- 1.Introduction.- 2.Arithmetization of Analysis and Algebra.- 3.Arithmetization of Logic.- 4.Kronecker's Foundational Programme in Contemporary Mathematics.- 5.Arithmetical Foundations for Physical Theories.- 6.The Internal Logic of Constructive Mathematics.- 7.The Internal Consistency of Arithmetic with Infinite Descent. A Syntactical Proof.- 8 Conclusion. Arithmetism versus Logicism or Kronecker contra Frege.- References.

Über Autor(innen)

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.