Frege, natural numbers, and arithmetic's umbilical cord

A central part of Frege's logicism is his reconstruction of the natural numbers as equivalence classes of equinumerous concepts or classes. In this paper, I examine the relationship of this reconstruction both to earlier views, from Mill all the way back to Plato, and to later formalist and structuralist views; I thus situate Frege within what may be called the “rise of pure mathematics” in the nineteenth century. Doing so allows us to acknowledge continuities between Frege's and other approaches, but also to understand better the motivation and the significance of his innovations, as well as their limits.