Wednesday, 14 February 2018

Two dimensions in the rule following considerations

Having a chat over coffee with Rupert Read last week, before giving a talk at UEA, I was struck by two distinct intuitions in critical responses to Wittgenstein’s rule following considerations. They seem unrelated or orthogonal. The first concerns how strongly determined are linguistic ‘moves’ which, nevertheless, accord with rules. The second concerns the nature of the determinacy whatever its degree: what underpins it. This makes me wonder whether they have any common motivation or, instead, whether running then together is confusing. I will try to distinguish them here though I will spend much more on one of them.

One expression of the former idea is that famous passage from Stanley Cavell:

We learn and teach words in certain contexts, and then we are expected, and expect others, to be able to project them into further contexts. Nothing insures that this projection will take place (in particular, not the grasping of universals nor the grasping of books of rules), just as nothing insures that we will make, and understand, the same projections. That on the whole we do is a matter of our sharing routes of interest and feeling, modes of response, senses of humor and of significance and of fulfillment, of what is outrageous, of what is similar to what else, what a rebuke, what forgiveness, of when an utterance is an assertion, when an appeal, when an explanation- all the whirl of organism Wittgenstein calls ‘forms of life’. Human speech and activity, sanity and community, rest upon nothing more, but nothing less, than this. It is a vision as simple as it is difficult, and as difficult as it is (and because it is) terrifying.

I think that this expresses this first aspect not because of the second half of the passage – which applies to the second, orthogonal view – but because of the claim that the projection is not ‘insured’ by the ‘grasping of universals nor the grasping of books of rules’. It is offered in part to undermine the assumption that language use is governed by formal rules. So it aims to correct the idea that linguistic usage just is rule following. Speaking a language isn’t to be modelled on grasp of universals or rule-books because they are not sufficient for the open-ended cut and thrust of language use. Language use is not so determined by formal rules but allows greater flexibility and improvisation. That’s, at least, how this seems to me.

Another expression of this sort of thought is Charles Travis’s mapping of the rule following considerations onto a Russellian distinction between knowledge by description and knowledge by acquaintance. This distinction underpins, according to his account, a 'prior' understanding of the meaning of an utterance and the 'novel' understanding one has when one becomes acquainted with the situation to which the prior understanding comes to apply. Thus one might have a prior understanding of the claim that ‘Pia’s shoes are under the bed’ and then, on seeing the situation in which they are directly alligned with and thus under a bed but three floors above, one comes to a potentially unexpected novel understanding (novel because situation-dependent). The potential slipperiness, the sense in which the prior understanding does not fully determine the novel understanding, is itself underpinned by Travis’ emphasis on occasion sensitivity. One is simply in no position to have the novel or situation-dependent thought in advance. That thought simply cannot come to mind, or be entertained, when one is framing a prior thought or understanding.

Elsewhere he gives this example:

A man in Ulan Bator is now standing before his yurt, sipping tea. (Make it ten o’clock his time.) I cannot think a thought, of him, that he is doing that—a thought which presents him as the one who must be some way for the thought to be true, and sipping tea before his yurt at ten as what he must be doing. I cannot do this, since I neither know, nor know of, anyone in Ulan Bator (though I am sure some people live there). I can, to be sure, think that everyone in Ulan Bator stands before his yurt at 10 and sips tea. What I thus think will be false if this man does not do that. The thought I thus think has a certain kind of generality which allows it to be true, or false, in this way. But as Frege points out (1914: 108-109, different example), that man falsifes my statement only given that he is in Ulan Bator—in present terms, only given that his being as he is participates in the instancing relation with that way for a thing to be. And it is just this last that I am not in a position to think—a corollary of not being able to think of him at all. Thinking a thought which is false, given his being as he is, is not the same thing as thinking a thought of him. [Travis 2011: 310-11]

This recalls another set of passages in Wittgenstein's Philosophical Investifations which also concern the apparent nor nativity of thought. Between paragraphs xx and yy Wittgenstein discusses connection between a prior the expectation of an explosion and the actual explosion which satisfies it. Clearly, one cannot have had a situation-dependent thought about that explosion (of the form: that! explosion) in advance of the explosion taking place. So what does connect a prior understanding (for example, of an expression of an expectation) and the novel understanding made available by having a situation dependent, demonstrative thought? There has to be some connection between prior and novel understandings. Tracks says:

[I]f an understanding of Sid’s words is one on which things being as they things being... as Sid says, then that understanding should contain some understanding which requires the corresponding novel understanding(s) relative to it. It should be an understanding relative to which understanding Sid’s words as speaking of what is instanced by this... is a novel understanding, but, moreover, one which that prior understanding mandates... The issue it raises is how prior understanding can require novel ones. [Travis 2006: 130-1] [W]ords can be true (or false) only where they bear a prior understanding that requires the right novel one. If they are made true by things being as they are, that is by virtue of an understanding available anyway... [131]

Travis then presents two rival accounts of this putative connection.

We...have two contrasting models of meaning and understanding. They differ importantly as to what it is to be prepared to make given translations of the sort of which §459 speaks. ...[ibid: 129]

The first account assumes that to mean words in some particular way is to be related to an explicit abstract or disembodied representation.

On that expansion [of what are in themselves, pre-philosophically, innocent banalities about meaning], an explicit specification of an understanding someone means words to bear is always possible in principle. To give it would be, inter alia, to produce a representation of things being as meant... That representation would be explicit, which is to say that it would have a very special property: unlike our ordinary representations, it would not admit of understandings (of things being as thus represented). [ibid: 121]

Travis puts initial pressure on this account by stressing that, in general, our words ‘admit of understandings’. So giving the example of Sid saying that the shoes are under the bed, Travis argues that this might mean any of many options. They might have to be completely under the bed. Or having their ends protruding might be allowed. Or, rather less likely for us or for Sid, ‘in a plumb line with the bed, but three floors down’ [ibid: 120]. So a condition of adequacy of the first account is that it singles out just one such interpretation.

One the first model... for Pia to understand the sign as she does is for her to relate in a particular way to a very special sort of (disembodied) representation. That representation requires the particular transitions it does independent of anything Pia is prepared to recognise, and independent of any understanding we may happen to share as to what it requires...[ibid: 129]

Such a representation would thus be a synopsis of the solutions to indefinitely many problems; a synopsis from which all those solutions are recoverable. One would not need Pia’s form of worldliness, or any other particular form, to manage the recovery. It might be a task for an idiot-savant. [ibid: 124]

Although initial pressure is put on this model, Travis goes on to introduce a rival, second account before assembling his key Wittgensteinian objections to the first. Those objections are that nothing could do the work that the disembodied representation is supposed to do. I’m less interested in those (which apply more to my second orthogonal thread / intuition) than with the novel set-up. So to the second model:

On the second model... for Pia to understand the sign as she does is for her to be positioned to see the solutions to an indefinite range of novel problems as to which translations it requires – problems as to whether it requires doing this to the door now. For her to be so positioned is for her to share a competence we have to see how to take the sign, except where, for one or another special reason, she deviates in her understanding from that. [ibid: 129]

On this second account, to mean something by one’s words depends on the contingencies of the situation, or the ‘occasions’, in Travis’ key word: that is, on the practical competences of speaker and hearer (‘Pia’s worldliness places her to deal with an indefinite range of potentially relevant, and sometimes unexpected, considerations’ [ibid: 124]) and the relation between the speaker and facts about what it would be reasonable to be taken to mean in the situation. That third point is one of the ways in which Travis is a kind of communitarian Wittgensteinian.

Now the idea that one is presented with the possibility of a ‘novel’ understanding when one has a situation-dependent singular thought seems to go hand in hand with the idea that the prior understandings do not go as far as we might have assumed in determining correct moves. Travis’ examples of occasion sensitivity suggest that gaps in the determined nature of correctness are filled on the hoof by the reasonable judgements of speakers as they go on.

But it also seems to me that this fits much better, or only, the application of empirical concepts to the empirical world than, say, the mathematical rules that Wittgenstein also discusses. In their case, there seems to be much less room for occasion sensitivity and hence the first thread in response to rule following: the idea that linguistic moves may not be as determined as we thought and hence less rule-like in nature.

So what is the second thread?

I think it is the nature of the determinacy, to whatever degree, of rule following. Take an area of human practice where the notion of a rule book does apply and ask: what is the nature of the way in which rules extend to so far unthought-about cases, such as Kripke’s hypothetical so-far-unadded 68 and 57 (or whatever is the smallest so far un-added pair)? I will say much less about this but it clearly concerns the failure of both platonic notions of already existing sequenc of numbers, or ideal machines (or depictions of ideal machine) or actual causal machinery to explain the way in which rules that are determined get determined. Now I had always taken this to be the main target of the rile following considerations but a conversation with Rupert, reflection on Stanley Cavell and Charles Travis' stimulating account in Thought's Footing suggest that other people think that the former line of thinking is central. But for the second dimension, considerations which support the former seem irrelevant. So why are both presented as a response to what Wittgenstein says about rules? And is there any relation?