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Towards an arithmetical logic = the arithmetical foundations of logic /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Towards an arithmetical logic/ by Yvon Gauthier.
Reminder of title:	the arithmetical foundations of logic /
Author:	Gauthier, Yvon.
Published:	Cham :Imprint: Birkhauser, : 2015.,
Description:	xi, 184 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Mathematical Logic and Foundations. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-22087-1
ISBN:	9783319220871

Towards an arithmetical logic = the arithmetical foundations of logic /
Gauthier, Yvon.

Towards an arithmetical logicthe arithmetical foundations of logic /[electronic resource] :by Yvon Gauthier. - Cham :Imprint: Birkhauser,2015. - xi, 184 p. :ill., digital ;24 cm. - Studies in universal logic,2297-0282. - Studies in universal logic..

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.

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.

ISBN: 9783319220871

Standard No.: 10.1007/978-3-319-22087-1doiSubjects--Topical Terms:

669393
Mathematical Logic and Foundations.

LC Class. No.: QA9

Dewey Class. No.: 511.3

Towards an arithmetical logic = the arithmetical foundations of logic /
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505 0 $a 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.
520 $a 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.
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