Saul Kripke (1940-) is a philosopher, with a particular interest in logic. People who are interested in formal logic do not, mostly, overlap very much with people who are interested in Wittgenstein’s later work; the Philosophical Investigations sometimes seems almost calculated to annoy people who like things to be neat in the mathematical way. (This could be the case. Wittgenstein wasn’t a huge fan of traditional analytic philosophy, although he was good at maths and had a great interest in philosophy of mathematics.) However, among many other interesting lines of work, Kripke wrote a book about Wittgenstein’s anti-private-language argument, Wittgenstein on Rules and Private Language.
It was actually through this book that Wittgenstein’s work first came to my attention. This book first came to my attention when a lecturer of mine used an example from it in one of my very first Elementary Logic lectures, which I was thoroughly enjoying. As far as I remember, the example was to illustrate a point of logic, and the book was only mentioned by way of a caution: remember, we were told, Kripke is wrong about everything else he says, especially about Wittgenstein.
Well, nothing makes me look up a book quicker than being told it’s all wrong, so naturally I hunted it out in the library. I don’t think I understood very much of it at the time – there are probably still parts I don’t fully appreciate. However, I didn’t see any particular reason to think that Kripke was wrong, and I thought the ideas he put forward were very interesting, especially those about rule-following. When I came to read Wittgenstein’s own work, a little later, I did come to agree that Kripke’s version of Wittgenstein is probably some distance – sometimes a long distance – from what, as far as we can tell, Wittgenstein himself had in mind. However, I do still think that some of Kripke’s key ideas are useful. Even his approach to Wittgenstein, which encourages a broad reading of the text rather than a narrow focus on one or two passages, is basically sound in method.
For me, the most striking part of Kripke’s argument is his ‘quus’ example, which poses the sceptical problem about rule-following in mathematics. In essence, this asks how we know that we are using the function ‘plus’ correctly. Can we tell whether we are really using ‘plus’, or its weird alternative, ‘quus’? There’s a clear explanation of this at the start of this paper, Kripke’s Skeptical Paradox [pdf].