March 5, 2008

Wittgenstein versus Turing: spelling of the second order

Filed under: Philosophy, Self indulgence, Unreadable — duncan @ 9:38 pm

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.


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’


  1. I had been going to tease you that you had promised to write things on the fly – and then saw that you are counting this as a post written on the fly: you shouldn’t be worrying – lovely post. I’ve also been struck by (perhaps slightly different?) continuities in Wittgenstein, but I’m far from an expert on his work. And I’m meant to be reviewing 100 pages of Hegel on Quantum, so I shouldn’t comment now :-)

    Comment by N Pepperell — March 5, 2008 @ 11:34 pm

  2. Interesting post — though there’s a number of little details about your characterisation of Wittgenstein that I don’t think I entirely agree with. I’ll limit myself to two short(ish) general queries here. Firstly, you say:

    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

    I was wondering whether you think that Wittgenstein is trying to directly resolve the problem of Russell’s paradox, or whether you think that something more roundabout is going on. As I read the early work, it is anti-logicist through-and-through, in the sense that at no point does it try to continue the project of providing a logical foundation for mathematics in the way that Frege and Russell thought was both desirable and possible. Wittgenstein was famously hostile to the Theory of Descriptions, but I see that hostility rooted in his rejection of the very project mathematical logicism more so than the specific objections he formulates against Russell.

    So, I suppose my question is, do you see the Tractatus as part of an attempt to give an alternative to Russell’s answer to how mathematics can be founded on logic, or as trying to draw a line under that whole program? For it seems that what I take to be your allusions to the showing/saying distinction as some sort of regress stopper (in relation to Russell’s paradox type problems), might be taken in either way. (I hope that makes some sense and is not too unclear.)

    Secondly, I was wondering if you would mind saying a little more about the idea that McDowell assimilates the a priori and the analytic?

    Anyway, I’m glad to have found my way to this blog since it looks good stuff all round!

    Comment by Tom (Grundlegung) — March 6, 2008 @ 1:40 am

  3. Oops… I meant that Wittgenstein was famously hostile to the Theory of Types, not the Theory of Descriptions. He loved the Theory of Descriptions, even in his latter years.

    Comment by Tom (Grundlegung) — March 6, 2008 @ 1:43 am

  4. N. – it was written on the fly! :) That explains (I hope) why I made such a mess of my description of the ‘Tractatus’. Tom – thanks for your brilliant comment. I’ve just clicked over to your site and am clearly going to have to be spending quite a lot of time there. :) My comments on the ‘Tractatus’ above are very confused, I think. Since I’m in a internet cafe, running out of time, I don’t think I can really respond at the length I ought to – but quickly.

    1) Certainly the early Wittgenstein isn’t trying to develop Russell’s or Frege’s project in anything like the way they’d want to. Say it like this: Russell and Frege were trying to found mathematics on logic – Wittgenstein’s work is an enquiry into the nature of logic. (R&F: What is the foundation of mathematics? Logic. W: What is the foundation of logic?) The enquiry is certainly motivated by the problems created for Russell & Frege’s project by Russell’s paradox; but it ends up going into far more ‘philosophical’ territory than Russell would dream of in its attempt to resolve those problems. And yes, I agree, this ends producing a philosophy that is in many ways anti-logicist. In a way, I think, the crucial move in Wittgenstein’s career comes very early, before the writing of the Tractatus, when he decides that logical propositions are tautologies, and that whatever meaning they convey (because Wittgenstein still thinks they convey important meaning) must be of a very special type. The early Wittgenstein calls this special type of meaning (meaning without propositional content) ‘mystical’ – the later Wittgenstein calls it social. But these are two different ways of approaching the same basic move. The reason I emphasise the a priori / analytic elision in the post is that I think Wittgenstein wants this special (tautological or grammatical) form of meaning to carry very substantial weight – the weight carried, in the post-Kantian tradition, by the transcendental constitutive forms of thought. (Whereas Wittgenstein’s more down-to-earth or positivist followers – early and late – tend to use Wittgenstein’s work to dismiss these ‘special’ (‘queer’) kinds of meaning). Obviously Wittgenstein’s conflicted – you can get plausible and strong ‘transcendental’ and ‘postivist’ readings from his work. And there’s a very good case to be made for a general move from ‘transcendental’ to (I don’t know what…) ‘grounded’ styles of philosophising. But that’s what I was trying to get at (I think and hope) when emphasising the continuity of his thought.

    So yeah – it’s definitely a roundabout response; but I think it is a response of sorts. [I think Wittgenstein's picture theory of meaning is an attempt to avoid the infinite regress of the Theory of Types. Probably. Perhaps.] Although – and I really can’t emphasise this strongly enough – it’s years since I read the Tractatus, and I’m a very long way out of this head-space (if I ever understood it at all – doubtful). So take all this – particularly the stuff about W’s relation to Russell – with a healthy dose of salt.

    2) On McDowell – I could write at great length about this. :) (I’ve only read ‘Mind and World’ – thoug I’ve read that reasonable carefully.) Ultra quickly – I think McDowell basically accepts Strawson’s (flawed) reading of the First Critique. Internet cafe, no books to hand – but don’t you think the way McDowell begins ‘Mind and World’ – with his opposition between form and content – is already an elision of the analytic/a priori distinction? Don’t you think McDowell misrepresents Kant’s distinction between concepts and intuitions? Looking at your site, though, it seems you’re pretty much a world authority on McDowell, so I probably shouldn’t risk saying much more on the fly. :)

    Really out of time now. Thanks again for your comment. (One last thing, if you want to answer… I’m not sure what you mean when you say that the later Wittgenstein loved the Theory of Descriptions. I would have said he didn’t – though I can’t remember any late discussions of it off hand. Hazy memory; insufficient reading.) Cheers.

    Comment by praxisblog — March 7, 2008 @ 9:57 pm

  5. (i) I think that the most historically accurate reading of the Tractatus is, as you say, as a work on the foundations of logic. FWIW, here’s how I place it in relation to Frege and Russell. Frege and Russell’s logicism requires them to employ a notion of logical truth, since their reductive project is one that seeks to ground the truths of maths in those of logic. But they never adequately defend or explicitly thematise this conception of logic. Wittgenstein was particularly irked by Russell’s appeal to a bunch of axioms as logical truths (e.g. the axiom of infinity) which — although dressed up in logical notation — seemed to have no more right to the status of logical truths than any formalised statements or rules. So, in steps Wittgenstein with his analysis of the proposition-form and his neat explanation of logical truths as tautologies. Now, with a criterion of logical truth in hand, some of the crucial technical apparatus which Russell appealed to in the Theory of Types appeared under-motivated. That is, Russell couldn’t appeal to them as logical truths (or as parts of the apparatus of logic, at least) that mathematical truths could be grounded upon because without a better explanation of what logic consisted in then they appeared totally ad hoc.

    Of course, that’s not the only criticism of Russell. One that might be a little closer to the criticism that you have in mind (i.e. the problem that Wittgenstein might be able to solve vis-a-vis Russell’s paradox) is that Russell has to appeal to the meaning of a term in order to say that, by the Theory of Types, it counts as meaningless. I think that one motivation for the showing/saying stuff might be to come in here as part of Wittgenstein escaping this problem. Like you, it’s been too long since I read the Tractatus for me to remember quite how I think all this stuff pans out though!

    (ii) I’m not sure exactly what to make of McDowell’s Kant, for a number of reasons. Firstly, I’m very sympathetic to McDowell in general, and I find his reading of Kant congenial for the place it plays in that wider project. Secondly, I tend to counterpose McDowell to Brandom a lot, and I find McDowell’s focus on experience as a rational constraint to be a welcome counter-weight to Brandom’s approach to Kant that tries to junk a lot of the talk of sensibility, receptivity, experience, etc. Neither of those are good scholarly reasons in favour of McDowell’s reading, but they exert some influence on my thinking about it.

    As for McDowell having a Strawsonian reading of Kant, I’m not so sure. In Mind and World, he explicitly says that he doesn’t know whether Strawson’s Kant is the real Kant, but nonetheless he seems to basically approve of the Strawsonian reading. So too, he says some ill-advised things about Kant and ‘the supersensible world’. So, on the basis of only having read Mind and World, it would seem fair to conclude that McDowell’s approach to Kant is basically Strawsonian. However, McDowell has since retracted many of the rather Strawsonian things he has said about Kant, and has defended himself against the claim that he has some sort of ‘two-worlds’ interpretation of him.

    The reading of Kant that he has developed post- Mind and World (e.g. in the Woodbridge lectures and, especially, in his more recent articles) is a lot more finessed. I think it falls somewhere in-between the sort of deflationary accounts given by Allison or Bird and the obviously unacceptable Strawsonian one. I’m not sure that I would nail my colours to the McDowellian mast on this one, but nor do I think the deflationary reading is without its major problems either though. (I wish I had the time to reread the First Critique!)

    It is not obvious to me that McDowell does mishandle the concept-intuition distinction in Kant, as you suggest. At least, I think that the Transcendental Deduction does begin to blur the distinction in a way that is congenial to McDowell’s story. (Presumably the worry is that concept and intuition are not kept separated enough?)

    I’m still not entirely clear what the elision of analytic and a priori is meant to amount to and why it is such a problem (although I am sympathetic to the idea that McDowell does not mark the distinction sufficiently). Is the problem that this ends up blurring semantic and epistemological concerns? Or is something else meant to go wrong?

    (iii) As for Wittgenstein’s attitude towards the Theory of Descriptions, I can’t remember where I formed that impression; and I agree that it doesn’t sit well with the tenor of the rest of his latter work. I have a dim recollection of Ray Monk mentioning it towards the end of his (brilliant!) biography of Wittgenstein, but there’s every chance that it comes up in some other secondary text (or maybe even one of Wittgenstein’s letters).

    Sorry about the length of this comment!

    Comment by Tom (Grundlegung) — March 10, 2008 @ 7:48 am

  6. Tom – no need to worry about comment length! I only apologise that I can’t respond at the length your thoughts deserve. (And sorry it’s taken me so long to respond…)

    Taking things backwards:

    1) My problem with McDowell’s treatment of Kant’s concepts and intuitions isn’t so much that he fails to keep them separate – it’s more that I don’t think he adequately describes what Kant means by the terms. Basically, McDowell maps concepts and intuitions onto the conceptual/empirical – or the scheme/content – distinction. Which is fine as far as it goes – but then McDowell suggests that, for Kant, intuitions = “representational” content of thought. [All this in the first page and a half or so of 'Mind and World', obviously.] McDowell doesn’t seem (at least in ‘Mind and World’) to have taken account of the fact that, for Kant, there are such things as pure intuitions – the intuitions of space and time – which do not possess what McDowell calls ‘representational content’. When glossing Kant’s phrase “concepts without intuitions are empty; intutions without concepts are blind” [hope I've got that right], McDowell says something along the lines of “Kant is not, absurdly, drawing our attention to a special kind of thoughts – the empty ones”. But that’s exactly what Kant’s doing. That’s what synthetic a priori judgements are – a special kind of empty thought. I’ve tried (I think) to read McDowell charitably – but he seems to me to just be misreading Kant.

    2) This is connected, I think, to what I see as the most general problem with ‘Mind and World’. McDowell seems to think that if he can show that ‘receptivity’ already involves ‘spontaneity’, he’ll have cut the Gordian knot of the Myth of the Given[/Coherentism]. He thinks he can use a Kantian theory of mind (properly supplemented by Hegelian Absolute Idealism) to do this. But he is only able to present the idea that ‘intuitions’ already involve some kind of ‘conceptual scheme’ as a departure from the tradition because he’s misrepresented what Kant means by ‘intutions’. Of course for Kant intuitions already involve the synthesising power of consciousness (that’s the point of the Transcendental Aesthetic). The question is: what is synthesised to produce ‘intuitions’? To put it bluntly: what does receptivity receive? McDowell, it seems to me, oscillates, in ‘Mind and World’, between two different perspectives, which map very well onto the ‘Myth of the Given’/’Coherentism’ opposition he analyses in the text. (McDowell’s text’s own oscillation equivalent to the oscillation of analytic philosophy he describes). On the one hand: the conceptual ends at the end of the human – at the end of ‘second nature’. On the other hand: the conceptual is unbounded. If the conceptual is unbounded, what sense can we make of the concept of receptivity? If it isn’t unbounded, aren’t we back with the Myth of the Given? I don’t think McDowell confronts the problems raised by his perspective. Though perhaps you can talk me round. :)

    3) McDowell certainly says that he doesn’t know whether Strawson’s Kant is the real Kant – but he seems to think it’s fine basically to use Strawson’s reading, on the grounds that it corresponds (better than Kant’s own work) to Kant’s true intentions. V. dubious, in my opinion.

    3) I haven’t read Brandom, so I can’t comment. Worth the time?

    4) Your comments on Wittgenstein seem spot on to me; but again, it’s been too long since I read the early work. Sorry.

    5) Finally – I should probably make it clear where I’m coming from Re: McDowell – which is (I guess obviously enough) that I’m pretty unsympathetic to him. This is for a variety of reasons. But I should probably mention that I’m particularly troubled by his humanism. Again, I’m (mis?)quoting from memory – but doesn’t he say in one of the later lectures that a human infant is not, strictly speaking, human – but only has the capacity to become human (through acquiring language, becoming socialised, etc.)? [Words to more or less that effect]. Anyone who can write that disturbs me…

    I should have brought the actual book with me; but I hope all that makes some kind of sense. Also, I hope it doesn’t come off as too belligerent. I do find McDowell interesting. I’m just… uh… unkeen. Thanks again for your very interesting comments. :)

    [Oh, and yeah, the Monk biography is terrific isn't it?]

    Comment by praxisblog — March 15, 2008 @ 6:22 pm

  7. A stream of consciousness experiment>? So you started with Turing and Wittgenstein. Then you regress to the Tractatus. Then some flies in a bottle. O, Kant about the a priori then the a posteriori. Maybe add the Private Language Argument next time? Sheesh!

    Comment by WHow — July 14, 2010 @ 2:04 am

  8. Loved it! Fantastic! Thanks!

    Comment by molloy2011 — June 15, 2013 @ 11:39 pm

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