The Odd Couple: Wittgenstein and Quine on the Existence of Numbers

The aim of this talk is to sketch, then contrast later Wittgenstein's and Quine's views on the perennial, and central, question in the philosophy of mathematics: do numbers exist? By drawing on examples involving elementary arithmetic, I'll maintain that they are indeed an odd couple: their views are both very different from each other, but also related. I'll argue that one of them (easy to guess who) holds that 'the question contains a mistake', so can't even be meaningfully asked — which is disturbing news for both the realist and the antirealist projects in the traditional and contemporary philosophy of mathematics. Quine, on the other hand, contends that the answer to the question is affirmative; however, his justification to answer so is quite provocative as well. It is not metaphysical, as is traditionally assumed to be, but pragmatic. It relies on the contingent fact that mathematics is successfully applied -- that it is, in fact, indispensable in everyday life and to science. And it is this perspective, the paramount role assigned to the applicability of mathematics, that he and Wittgenstein share.