Towards an Arithmetical Logic

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.

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.

"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)