( From the graphic novel Logicomix, taken from this blog post by Richard Zach.)
“He doesn’t want to prove this or that, but to find out how things really are.” This is how Russell describes Wittgenstein in a letter to Lady Ottoline Morrell (as reported in M. Potter’s wonderful book Wittgenstein's Notes on Logic, p. 50 – see my critical note on the book). This may well be the most accurate characterization of Wittgenstein’s approach to philosophy in general, in fact a fitting description of the different phases Wittgenstein went through. Indeed, if there is a common denominator to the first, second, intermediate etc. Wittgensteins, it is the fundamental nature of the questions he asked: different answers, but similar questions throughout. So instead of proving ‘this or that’, for example, he asks what a proof is in the first place.
(My own take in my work on the philosophy of logic and mathematics is broadly Wittgensteinian (the later Wittgenstein, that is) in that I focus specifically on the human practices that fall under the heading of logic and mathematics — in particular the cognitive aspects of these activities.)
I’ve been toying around with the idea of putting together a master’s course on Wittgenstein, and now I’m thinking of something along the lines of ‘Wittgenstein on the nature of logic and mathematics'. (Btw, I highly recommend Juliet Floyd's chapter on Wittgenstein in the Oxford Handbook of Philosophy of Mathematics and Logic.) Half of it would be on the Tractatus, and the other half on later writings, in particular the Remarks on the Foundations of Mathematics.
The goal of the course would not be exclusively historical/exegetical; in fact, I am convinced that Wittgenstein asked all the right questions about logic and mathematics. So a systematic reflection on these topics does well to begin with the questions he asked and to engage with his answers, even if ultimately to reject the answers. The fact that he often focuses on very simple examples have led many to think that he did not really understand higher-level mathematics. But this is simply because for Wittgenstein, to understand the complex cases, we first need to understand the basics of the simple cases — which turn out to be everything but simple or straightforward.
And now, to my delight, it looks like I’ll be teaching such a course in the next academic year; can’t wait to go down to the barest essentials with Wittgenstein! (I anticipate an overflow of Wittgenstein-related blog posts in due course.)
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