Wittgenstein on mathematics and games
Abstract
Unlike his other major typescripts, the Big Typescript is divided into titled chapters, themselves divided into titled sections. But within a section we still get a collection of remarks typically without connecting tissue and lacking any transparently significant ordering or helpful signposting. So we still encounter the usual difficulties in trying to think our way through into what Wittgenstein might be wanting to say. Some enthusiasts like to try to persuade us that the aphoristic style is really of the essence. But I’ve always wondered how true that is. So I here propose an experiment. Let’s take §108 of the ‘Big Typescript’ (the first of the sections in the part of the book titled ‘The Foundations of Mathematics’). There are four and a bit pages of remarks. I’m going to try to render them into rather more conventional prose. In the section that follows, then, I have embedded almost every sentence Wittgenstein wrote in his §108 – or rather, of course, I’ve embedded almost every sentence from the well-regarded translation. I have, however, often changed the order in which remarks appear, omitted some ‘and’s and ‘but’s and the like, changed some punctuation, demoted some passages to footnotes, but not – I hope – in any way that radically changes the significance of any remark, or distorts what is going on. And I’ve added a lot of signposting. I’ll comment, necessarily very briefly, on the results of the exercise starting in §3 below. So here we go . .