Internal Logic: Foundations of Mathematics from Kronecker to Hilbert

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Internal logic is the logic of content. This text deals with arithmetic, with emphasis on the 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 covers a 50-year span, from 1880 to 1930, a period of importance for foundational debates on the subject and its subsequent development.