ABSTRACT
According to P.M.S. Hacker, Wittgenstein’s central preoccupation was not to elucidate why the propositions of mathematics are necessary, but “the prior question”: [W]hat is it for a proposition to be a ‘necessary proposition’, i.e. to be a proposition of mathematics […]?” This point is of utmost importance for setting up the right direction in understanding Wittgenstein’s approach to mathematical necessity. Indeed, an interpretive reconstruction of Wittgenstein’s views should primarily aim to answer this question—and yet, despite the attention Wittgenstein’s philosophy of mathematics received among commentators, such an answer is still rather fragmentary articulated. Once this is done, the other task is to show how this answer enables us to deal with the traditional skeptical questions raised in relation to mathematics (e.g., what if we’re wrong that 25×25=625? is this revisable? etc.) In this paper, I hope to contribute to accomplishing the first task by sketching what I dub a ‘genealogical’ account of mathematics and its necessity; at the end, however, I’ll address in passing the second one too.
