Towards an Arithmetical Logic The Arithmetical Foundations of 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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Gauthier, Yvon (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
Edición:1st ed. 2015.
Colección:Studies in Universal Logic,
Temas:
Mathematical logic.
Mathematical Logic and Foundations.
Acceso en línea:Texto Completo

MARC

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245 1 0 |a Towards an Arithmetical Logic  |h [electronic resource] :  |b The Arithmetical Foundations of Logic /  |c by Yvon Gauthier. 
250 |a 1st ed. 2015. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Birkhäuser,  |c 2015. 
300 |a XI, 184 p. 9 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
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490 1 |a Studies in Universal Logic,  |x 2297-0290 
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. 
650 0 |a Mathematical logic. 
650 1 4 |a Mathematical Logic and Foundations. 
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830 0 |a Studies in Universal Logic,  |x 2297-0290 
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950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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