Are There Mathematical Hinges?

Abstract

In this paper I argue that, contrary to what several prominent scholars of On Certainty have claimed, Wittgenstein did not maintain that simple mathematical propositions like “2 × 2 = 4” or “12 × 12 = 144,” much like G. E. Moore’s truisms, could be examples of hinge propositions. In particular, given his overall conception of mathematics, it was impossible for him to single out these simpler mathematical propositions from the rest of mathematical statements, to reserve only to them a normative function. I then maintain that these mathematical examples were introduced merely as objects of comparison to bring out some peculiar features of the only hinges he countenanced in On Certainty, which were all outside the realm of mathematics. I then close by gesturing at how the distinction between mathematical hinges and non-hinges could be exemplified and by exploring its consequences with respect to (Wittgenstein’s) philosophy of mathematics.