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Doubting the Truth of Hume's Principle

Hume’s Principle (HP) states that for any two (sortal) 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 (such as “the number of the forks on the table is identical to the number of the knives on the table iff the forks are one-one correlated with the knives”) 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 (as occur in instances of HP) 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.

Hume's principle; logical truth; neo-logicism; numerical identity; platonism; reference

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