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Towards an arithmetical logicthe ari...

Gauthier, Yvon.

Towards an arithmetical logicthe arithmetical foundations of logic /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Towards an arithmetical logicby Yvon Gauthier.
其他題名:	the arithmetical foundations of logic /
作者:	Gauthier, Yvon.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xi, 184 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Logic, Symbolic and mathematical.
電子資源:	http://dx.doi.org/10.1007/978-3-319-22087-1
ISBN:	9783319220871$q(electronic bk.)

Towards an arithmetical logicthe arithmetical foundations of logic /
Gauthier, Yvon.

Towards an arithmetical logicthe arithmetical foundations of logic /[electronic resource] :by Yvon Gauthier. - Cham :Springer International Publishing :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$q(electronic bk.)

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

180452
Logic, Symbolic and mathematical.

LC Class. No.: QA9

Dewey Class. No.: 511.3

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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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