The Contemporary Interest of an Old Doctrine

Abstract

We call Frege's discovery that, in the context of second-order logic, Hume's principle-viz., The number of Fs = the number of Gs if, and only if, Fa G, where Fa G (the Fs and the Gs are in one-to-one correspondence) has its usual, second-order, explicit definition-implies the infinity of the natural numbers, Frege's theorem. We discuss whether this theorem can be marshalled in support of a possibly revised formulation of Frege's logicism.