Towards an Arithmetical Logic The Arithmetical Foundations of Logic /

• Main Author: Gauthier, Yvon (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Series: Studies in Universal Logic,
• Subjects: Mathematics.; Mathematical logic.; Mathematical Logic and Foundations.

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...

Table of Contents:

• 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.