Wittgenstein versus Turing: spelling of the second order

In 1939 both Wittgenstein and Turing were lecturing in Cambridge.  They were both lecturing on the same subject: the foundations of mathematics.  But their approaches couldn’t have been more different.  Not being a mathematician, I don’t know what Turing was on about.  But Wittgenstein was attempting to demolish the philosophical project that had been the lodestar of analytic philosophy since… well, since Bertrand Russell’s ‘Principles of Mathematics’.  That was the book that first turned Wittgenstein on to philosophy, about 1910 or so, and which served, in part, as the manifesto for the establishment of ‘analytic’ philosophy.  Analytic philosophy was born in those heady years when ‘Principia Mathematica’, and Frege’s ‘Basic Laws of Arithmetic’ promised to set the whole damn edifice of modern maths on the rock solid foundation of formal logic.  As the project collapsed (wounded almost before it began to breathe by Russell’s paradox; then killed and buried by Godel’s incompleteness theorem)… as the project collapsed the methodology survived, in a peculiar zombie state – free from any justification, but firmly rooted in the rich soil of Anglo-American academic practice.  Analytic philosophers can’t tell you why formal logic should have any kind of privileged status as the discourse of true reason; but they’ll sure as hell insist we all speak this strange, cramped language.  (An enforcement, in a way, of the same demand that Plato made in the Republic: the banishment of poetry from the world of truth.)

Anyway, Wittgenstein, in 1939, was having none of it.  He didn’t just turn against his own earlier project; he also turned against any attempt to give mathematics anything like the status he’d earlier aspired to explain.  When Turing started attending Wittgenstein’s lectures, the ‘lectures’ rapidly developed into a dialogue, with Turing defending mathematical propositions’ claim to truth, and Wittgenstein insisting again and again that it all comes down to nothing more than grammar, social conventions, practical demands, and so on.

“WITTGENSTEIN: I won’t say anything which anyone can dispute. Or if anyone does dispute it, I will let that point drop and pass on to say something else.”

“TURING: I understand but I don’t agree that it is simply a question of giving new meanings to words.

WITTGENSTEIN: Turing doesn’t object to anything I say. He agrees with every word.”

“TURING: I see your point.

WITTGENSTEIN: I don’t have a point.”

This kind of thing goes on quite a bit in the lectures: Wittgenstein trying to rebut Turing’s suggestion that he’s advancing a philosophical thesis – Turing insisting that they disagree on philosophical matters; Wittgenstein insisting that no – no philosophy, in the sense that Turing means, is taking place.

It’s very difficult not to feel sympathy with Turing; he comes across as extremely likeable – and it’s nice to see someone who actually understands the issues disagreeing with Wittgenstein, in real time. But I think it all also sheds an interesting light on the continuity in Wittgenstein’s thought – something that a lot of his readers (me, for one) perhaps tend to underestimate. Let me make a few wild claims, that require backtracking to beyond the beginning of analytic philosophy.

When Russell, Moore, the early Wittgenstein et al were trying to establish a new way of philosophising, part of the project was a more or less complete rejection of everything that had happened since, say, Hume. Analytic philosophy understood itself from the beginning as a reaction against modern continental thought. In particular, it was a reaction against German idealism – the transcendental philosophy established by Kant, and developed by his successors. A lot of English philosophers at the turn of the century were Hegelians of a sort. Analytic philosophy wanted to return to empiricism; but a new empiricism bolstered by the resources of modern logic.

I suggest that we see this return as associated with a rejection of the distinction that inaugurates Kant’s transcendental philosophy: the two fold distinction between analytic and synthetic judgements, on the one hand, and a priori and a posteriori judgements, on the other. Analytic philosophy (I’m aware it’s incredibly problematic to use this term as if it refers to an easily identifiable and homogenous tradition; but fuck it)… analytic philosophy, in almost all the forms I’m aware of, tends to obliterate this distinction, by assimilating the a priori to the analytic, and the a posteriori to the synthetic. What’s really baffling about the way in which this is done, is that it’s done so casually. Perhaps the most striking example I’ve read is Strawson’s ‘The Bounds of Sense’ – a work of Kant exegesis that simply declares the distinction non-sensical, and proceeds as if it didn’t exist. This tendency persists even in more recent analytic philosophy that supposedly makes some kind of contact with the continental tradition – see McDowell’s ‘Mind and World’.

Anyway – I think what’s striking about the Tractatus is that it’s totally candid about the double-imperative analytic philosophy faces once it’s attempted to abolish this distinction. The Tractatus is really an analysis of the a priori conditions of thought, in the Kantian tradition – but it insists that the logical propositions it discusses are tautologous; and that the propositions which discuss these propositions are worse than tautologous – they’re nonsensical. It seems to me that the early Wittgenstein, in trying to provide some kind of solution to the calamitous problems Russell’s paradox created for the analytic project went as far as he could in this direction: the need to create an infinite regress of meta-languages is abolished because there is no meta-language; the nonsensical, meaningless propositions of Wittgenstein’s early thought contain all the sense and meaning his project needs.

Dammit; I didn’t mean to discuss the Tractatus, and it’s so long since I read it. What I want to emphasise in this post is that Wittgenstein carries over from his early work this commitment to propositions without sense, content, or meaning; propositions that are not propositions. In the Tractatus these propositions are the foundations of logic; in the Investigations they’re the grammar of our language-games. (Though of course Wittgenstein hardly uses the phrase ‘language games’; I agree with the reading of the Wittgenstein that sees the pervasive discussion of ‘language games’ in the literature as an attempt to find an ‘ontological’ foundation for his later thought; an attempt antithetical to Wittgenstein’s project.) But in both his earlier and his later thought Wittgenstein’s own discourse occupies an incredibly paradoxical position. A position summarised in his lectures on the foundations of mathematics by the maxim “I don’t have a point.” Or, still more pointedly… “Obviously the whole point is that I must not have an opinion.”

Right at the start of the lectures, Wittgenstein uses a favourite analogy. “Compare the fact that when we learn spelling we learn the spelling of the word ‘spelling’ but we do not call that ‘spelling of the second order’.” It seems to me that this example is capable of carrying a double-investment in Wittgenstein’s work. On the one hand, it folds back the discourse of philosophy into the discourse of ordinary language; of empirical, everyday endeavours. But this folding back can also serve to conceal the massive philosophical investment Wittgenstein places in certain locations of ordinary language. Wittgenstein’s entire later project could, in a way, be called “spelling of the second order”; a discourse that keeps its nose to the ground and its feet on the earth; a discourse that refuses to engage in any philosophical speculation, but precisely in this refusal manages to evade many of the most important ways in which ordinary language is actually used – for an investigation into the rules of the grammar of our language must and always does involve opinions – the very modesty of Wittgenstein’s endeavour is, in a way, an attempt to preserve its transcendental status. For Wittgenstein is still searching for the conditions of possibility of thought. And, like his earlier self, and (crucially) unlike the transcendental philosophy his earlier thought reacted against, those conditions of possibility of thought must not themselves be any part of thought.

I write all this because I find Wittgenstein’s project – the attempt to fold the ambitions of transcendental philosophy back into everyday life – incredibly appealling. But I think his project is also, probably, doubly flawed: flawed because certain aspects of everyday life are given covert philosophical weight that Wittgenstein himself can’t justify; and also flawed because the thought he is reacting against in his later work (i.e. his own earlier work) is already a reaction against transcendental philosophy. Wittgenstein’s later work still bears the marks of that initial reaction – and it’s this, I think, that undermines his attempt to give philosophy peace. Wittgenstein’s later work can only be honest if he acknowledges that he is advancing opinions… and that is apparently only possible if he brings back the synthetic a priori: which is the one thing that Wittgenstein, from first to last, refuses to do.

Ahem.

Did I mention something about writing on the fly? My word, I’ll be amazed if this blog has any readers left by the end of the week.

I should probably mention that I think the above is probably wrong. I’m trying to get my thoughts out of my head, the better to assess them. I can already see a number of very dubious things in what I’ve just said – in addition to the simple carelessness. Oh me oh my. Keep on truckin’