Introduction to Special Issue: Dedekind and the Philosophy of Mathematics

Richard Dedekind (1831–1916) was a contemporary of Bernhard Riemann, Georg Cantor, and Gottlob Frege, among others. Together, they revolutionized mathematics and logic in the second half of the nineteenth century. Dedekind had an especially strong influence on David Hilbert, Ernst Zermelo, Emmy Noether, and Nicolas Bourbaki, who completed that revolution in the twentieth century. With respect to mainstream mathematics, he is best known for his contributions to algebra and number theory (his theory of ideals, the notions of algebraic number, field, module, etc.). With respect to logic and the foundations of mathematics, many of his technical results — his conceptualization of the natural and real numbers (the Dedekind-Peano axioms, Dedekind cuts, etc.), his analysis of proofs by mathematical induction and definitions by recursion (extended to the transfinite by Zermelo, John von Neumann, etc.), his definition of infinity for sets (Dedekind-infinite), etc. — have been built into the very fabric of twentieth- and twenty-first-century set theory, model theory, and recursion theory. And with some of his methodological innovations he even pointed towards category theory. (Cf. [Ferreirós, 1999; Corry, 2004; Reck, 2016] also for further references.)

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