Kronecker in contemporary mathematics. general arithmetic as a foundational programme

• Autorzy: Gauthier Y.
• Języki publikacji: EN

Abstrakty

EN

Kronecker called his programme of arithmetization "General Arithmetic" (Allgemeine Arithmetik). In his view, arithmetic is the building block of the whole edifce of mathematics. The aim of this paper is to show that Kronecker's arithmetical philosophy and mathematical practice have exerted a permanent in uence on a long tradition of mathematicians from Hilbert to Weil, Grothendieck and Langlands. The conclusion hints at a constructivist fnitist stance in contemporary mathematical logic, especially proof theory, beyond Hilbert's programme of fnitist foundations which can be seen as the continuation of Kronecker's arithmetization programme by metamathematical or logical means. It is fnally argued that the introduction of higher-degree polynomials by Kronecker inspired Hilbert's notion of functionals, which in turn in uenced Godel's functional Dialectica interpretation for his intuitionistic proof of the consistency of arithmetic.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2013
• Tom: Vol. 48
• Strony: 37--65
• Opis fizyczny: Bibliogr. 57 poz.

Twórcy

autor

Gauthier Y.

• Department of Philosophy University of Montreal C.P. 6128, Succ. Centre-Ville Montreal (Qc), Canada H3C 3J7

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