Frege, Dedekind, and the philosophy of mathematics

Philip Kitcher

pp. 299-343

in: Leila Haaparanta, Jaakko Hintikka (eds), Frege synthesized, Berlin, Springer, 1986

Abstract

In the 1880s, two men who had both been trained as mathematicians wrote short books defending the idea that arithmetic has an intimate relation with logic. Neither work was exactly a commercial or intellectual success. Frege's Grundlagen (Frege 1884) went virtually unnoticed, and Frege recorded his disappointment and frustration in the introduction to his Grundgesetze (Frege, 1893, p. xi; Furth, 1967, p. 8). Dedekind's monograph, Was Sind und was Sollen die Zahlen? (Dedekind, 1888), fared only a little better. Before Dedekind published it, he had been encouraged by the interest of other mathematicians in his project. In 1878, for example, Heinrich Weber urged him not to postpone his planned study on the number concept (Dugac, 1976, p. 273). However, when the book appeared, it made comparatively little stir: certainly, Dedekind's discussion of the natural numbers aroused nothing like the interest excited by his study of the real numbers (Dedekind, 1872). Although many of Dedekind's contemporaries viewed him as an important mathematician, they did not rank Was Sind und was Sollen die Zahlen? among his major achievements.¹

Cited authors

Frege Gottlob

Dedekind Richard

Weber Heinrich