Abstract

Frege's logicism consists of two theses: the truths of arithmetic are truths of logic; the natural numbers are objects. In this paper I pose the question: what conception of logic is required to defend these theses? I hold that there exists an appropriate and natural conception of logic in virtue of which Hume's principle is a logical truth. Hume's principle, which states that the number of Fs is the number of Gs iff the concepts F and G are equinumerous is the central plank in the neo-logicist argument for and. I defend this position against two objections Hume's principle canot be both a logical truth as required by and also have the ontological import required by ; and the use of Hume's principle by the logicist is in effect an ontological proof of a kind which is not valid.