Abstract

Hume’s Principle states that for any two concepts, F and G, the number of Fs is identical to the number of Gs iff the Fs are one-one correlated with the Gs. Backed by second-order logic HP is supposed to be the starting point for the neo-logicist program of the foundations of arithmetic. The principle brings a number of formal and philosophical controversies. In this paper I discuss some arguments against it brought out by Trobok, as well as by Potter and Smiley, designed to undermine a claim that HP and its instances are true. Their criticism starts from distinguishing the objective truth from a weak or stipulative one, and focusing on fictional identities such as “Hamlet = Hamlet” or “Jekyll = Hyde.” They argue that numerical identities are much the same as fictional identities; that we can attribute them only a weak or stipulative truth; and, consequently, that neo-logicists are not entitled to ontological conclusions concerning numbers they derive from HP and its instances. As opposed to that, I argue that such a criticism is ill-conceived. The analogy between the numerical and fictional identities is far-fetched. So, relative to such a criticism, HP has more prospects than some authors are prepared to admit