Internal Logic

Foundations of Mathematics from Kronecker to Hilbert

Nonfiction, Science & Nature, Mathematics, Logic, Religion & Spirituality, Philosophy
Cover of the book Internal Logic by Y. Gauthier, Springer Netherlands
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Y. Gauthier ISBN: 9789401700832
Publisher: Springer Netherlands Publication: March 9, 2013
Imprint: Springer Language: English
Author: Y. Gauthier
ISBN: 9789401700832
Publisher: Springer Netherlands
Publication: March 9, 2013
Imprint: Springer
Language: English

Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer.

The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer.

The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.

More books from Springer Netherlands

Cover of the book Surface Coatings—1 by Y. Gauthier
Cover of the book The Salton Sea by Y. Gauthier
Cover of the book Henry More (1614–1687) Tercentenary Studies by Y. Gauthier
Cover of the book Phenomenology and Intersubjectivity by Y. Gauthier
Cover of the book Nāgārjuna’s Twelve Gate Treatise by Y. Gauthier
Cover of the book The Visible and the Invisible in the Interplay between Philosophy, Literature and Reality by Y. Gauthier
Cover of the book Science between Europe and Asia by Y. Gauthier
Cover of the book African Climate and Climate Change by Y. Gauthier
Cover of the book Vegetation Dynamics by Y. Gauthier
Cover of the book Magnetic Resonance Detection of Explosives and Illicit Materials by Y. Gauthier
Cover of the book Reason, Democracy, Society by Y. Gauthier
Cover of the book The Convention on Biological Diversity and Developing Countries by Y. Gauthier
Cover of the book Knowing and the Mystique of Logic and Rules by Y. Gauthier
Cover of the book Government in Wanggulam by Y. Gauthier
Cover of the book Spatial Resilience in Social-Ecological Systems by Y. Gauthier
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy