Richard Gipps told me he’d come across an old paper of mine on Wittgenstein, McDowell and the problem in Kant’s schematism and had been thinking about the relation between the view I’d tried to articulate there and Hannah Ginsborg’s (pictured) views in her widely circulated pre-press paper ‘Primitive normativity and scepticism about rules’. That gave me the incentive to read her paper, which I’ve had on my to do list for a few months now. Hers is an interesting position.
If I follow it, the idea is that there is a middle path between, on the one hand, the kind of full blown (adult?) normativity of someone who, eg., intentionally adds 2 who thus continues ‘2, 4, 6, 8, … , 1000’ with ‘1002’ because those are the instances of the plus 2 rule and on the other, a clever parrot, trained to tap out those numbers for purely dispositional causes. The middle ground has some notion of correctness, unlike the latter, but not an explicit articulation of the rule. A child, eg., might continue offering a pattern of numbers taking them to be correct but unable to conceive them as the explicit rule plus 2. Here are a couple of accounts of this, the first from a review of Hattiangadi’s book, the second from the paper:
[T]here is a case to be made for the view that certain instances of behaviour, and in particular uses of linguistic expressions, can be intelligibly regarded as correct or appropriate in a way which does not presuppose our thinking of them as meaningful, or as subject to standards of correctness imposed by the speaker’s or community’s intentions. (I argue for this view in my ‘Primitive Normativity and Skepticism About Rules’ (forthcoming in Journal of Philosophy), and in sections four and five of my ‘Inside and Outside Language: Stroud’s Nonreductionism About Meaning’ (forthcoming, details given above).) For a simple example, we can consider the cases of ‘going on’ behaviour discussed by Wittgenstein in Philosophical Investigations, in particular the pupil at §185 who continues the ‘+2’ series with ‘1004, 1008’. As I see it, we do not first have to attach a determinate meaning to ‘+’ in order to deny that a pupil who goes on in this way is going on correctly or appropriately. There is something that is ‘primitively’ correct, or correct simpliciter about continuing the series ‘2, 4, 6, 8, … , 1000’ with ‘1002’, in that our taking ‘1002’ to be the appropriate continuation does not depend on our having specified a rule or standard with which ‘1002’ can be said to accord. An even simpler example is afforded by Wittgenstein’s case, also in §185, of the pointing hand. It strikes us as correct or appropriate to look in the direction of wrist to finger-tip rather than finger-tip to wrist, but this does not seem to depend on our antecedently having acknowledged a rule determining the correct response to a pointing hand, or having understood the pointing gesture as having one meaning rather than another. The point of these examples can be carried over to the use of linguistic expressions. If a child has been taught the use of the term ‘green’ in connection with an initial sample of green objects, and then goes on to apply the term in a novel case, we can think of her, and she can think of herself, as using ‘green’ appropriately in the new case, but this need not presuppose that we think of ‘green’ as having a determinate meaning, in particular as meaning green rather than grue. [Ginsborg 2011]
Imagine a child who is familiar with the numerals and able to recite them well into the hundreds, and who has just now learned to count by twos, that is to recite numerals in the sequence 2,4,6,8 and so on. Suppose that on one particular occasion she recites the numerals up to ‘40,’ and then goes on, as we expect, with ‘42.’ Moreover, she does so unhesitatingly, with an apparent assurance that this is the appropriate continuation. Now we stop her. ‘Why did you say ‘42’? Shouldn’t you have said ‘43’ instead?”
How we imagine her replying will depend on how we imagine that she learned her new skill. We might suppose that before learning to count by twos she was familiar not only with the numerals but also with the words ‘plus’ and ‘addition,’ and, relatedly, that she was able to give answers to simple addition problems. In that case she might have been taught to count by twos by being given successive addition problems: she was asked to add two to 2, then to 4, then to 6, and so on. A child who had learned counting by twos in this way could explain that she had said ‘42’ because she had been adding two and because two added to 40 makes 42. Although she might not use words like “rule” or “justification,” this would amount in effect to a justification of her response in terms of its according with a rule which she had antecedently adopted. She would be citing a rule which she had been following up to this point (the “add-two” rule) and claiming that, in this particular case, the number she had given was an application of that rule.
But we could also imagine the child’s having learned to count by twos without receiving any specific instructions, but rather in the same way that she learned to count by ones, that is to recite the series of natural numbers. A child does not learn to count by following instructions like ‘Add one to the previous number,’ but rather by following the example given by other people, and responding appropriately to their encouragement or correction. She learns initially by rote memorization, first of the numbers up to twenty, and then of the decades (“twenty,” “thirty,” and so on), but at a certain point she becomes able to recite sequences without relying exclusively on memory, at which point it becomes clear that she has acquired a capacity to count on her own.11 We could imagine a child learning to count by twos in much the same way, by listening to other people reciting ‘2,4,6,8..’ and following their example. Such a child could go on confidently with ‘42’ after ‘40’ , even if she had not heard this sequence before, or did not remember it, without being able to answer, or even understand, the question ‘what is 40 plus 2?’.
Now it is possible that a child who had learned to count by twos in this way could come up with an explanation of why she had said ‘42’ after ‘40.’ In particular, she might have arrived on her own at a conception of what she was doing at each step of the process, and she might now be able to articulate that conception by saying, for example, that each number she had said was ‘two more’ than the one before, and that 42 came next because it was ‘two more’ than 42. But it is at least equally likely that the child would be unable to say anything to explain or justify her having said ‘42,’ not just because she lacked the appropriate vocabulary, but because she lacked any conception of what her saying ‘42’ after ‘40’ had in common with her having said ‘40’ after ‘38.’ And yet this does not seem to rule out her reacting with surprise and puzzlement to the suggestion that she should have said ‘43’ instead. Rather, it seems plausible to imagine her insisting, with no less conviction than a child who was able to cite the add-two rule, that ‘42’ was the right thing to say after ‘40’: that it “came next” in the series, or “belonged” after 40, or “fit” what she had been doing previously.
It is part of my proposal that a child’s continuing the series with ‘42’ or applying the word ‘green’ to a green spoon can be explained in the same naturalistic way that we explain the parallel behaviour in the case of the parrot. But, I am suggesting, the situation of the child is different from that of the parrot in that she takes herself, in continuing the series with ‘42’ or saying ‘green’ when shown the green spoon, to be responding appropriately to her circumstances in the primitive sense of “appropriate” which I have described. [Ginsborg forthcoming]
This idea is in the same ball park as my paper on Wittgenstein, McDowell and Kant’s schematism because both are concerned with how one gets full blown normativity and conceptuality off the ground. The problem of the schematism is what guides a subject in bringing a concept (with its intrinsic universality) to bear on an individual? Whilst it seems clearer how one can draw out deductive consequences from more general claims to more specific consequences, the move from particulars to the general concepts that apply to them – a normative relation – is much less clear. That’s Kant’s problem of which he says:
[T]his schematism of our understanding, in its application to appearances and their mere form, is an art concealed in the depths of the human soul, whose real modes of activity nature is hardly likely ever to allow us to discover. [Kant 1929: 183]
But whilst it is in the same ball park, I am not sure how close the connection is (that I want to make a connection is my problem (and perhaps Richard’s) not Ginsborg’s, I hasten to add, but tempting given her cv). That, I suspect, turns on what the felt problem is. The problem of the schematism stems from the idea that it should be possible, at the very least, to gesture towards an account of how individuals or particulars come to be subsumed under general concepts. Ginsborg’s problem is not directly that. One motivation for it stems from a response to Kripke’s way of setting up the challenge, another as a response to Hattiangadi’s attack on idea of the normativity of content which has consequences for a response to Kripke. In fact, in the review of Hattiangadi, the idea is explicitly put forward as a defence of an essentially normative view of meaning. The dialectic runs something like this. A normative view might be defended on these lines:
The normativist, that is, can appeal to the intuition that we understand what it is for a term to be meaningful only by understanding that certain uses of it are correct and others are not correct. If the notion of a term’s being meaningful depends in this way on the notion of its having a correct use, then the dispositionalist is in trouble, since we can perfectly well make sense of a person’s being disposed to use a term in a certain way, and hence, on the dispositionalist view, of her using the term meaningfully, without helping ourselves to the thought that her uses can either be, or not be, correct.
But this faces an objection that actions or utterances are not correct tout court but rather correct as the actions they are or aim at. They are correct relative to an intentional description. But that undermines the project to explain meaning in independent terms of correct use.
The difficulty is, rather, that this non-descriptive element seems to depend on the prior assumption of an applicable standard. If this is so, then we cannot make sense of someone’s using an expression correctly on a given occasion unless we are already assuming a standard of correctness applying to uses of that expression. And that in turn requires, either that we assume that the expression has a meaning, or that we take the individual or her community to have determinate intentions with respect to the use of the expression. That would seem to put paid to the suggestion that we can think of facts of meaning, or intentional content more generally, as constituted in part by facts of correct use.
And at this point, primitive normativity comes to the rescue. I’m not sure why this should be a worry, however. It seems to suggest that the normativist is, like the dispositionalist, a kind of reductionist about meaning but with an unusual reduction base: primitively correct actions. I take it, by contrast, that the normativist typically objects that there’s something missing in the dispositionalist’s reduction, something normative about meaning, but not as saying that that normative element is itself independent of meaning and forming a rival reductionist project.** (That’s why one should object to the forced choices about the nature of normativity that Kusch offers, eg.) But what of the idea of primitive normativity as such?
Two thoughts. The first is that there is something like this in Diamond’s description of developing attitudes towards either order pencils by length or counting objects. One might, she suggests, acquire mastery of counting or length ordering without yet thinking of there as a number or an ordering which commands (thinking of Wright) or determines the process. One might recognise procedural rules without yet having the idea that, aside from a clear violation of these, there is a further standard in getting the number or the order right. She discusses this idea in the context of thinking that a proof establishes a necessity. Once, however, one makes the move to thinking that there is a correct number or order ‘out there’, there’s no going back and seeing the process in the initially less regulated way. Second, I'd need to do some more work to see the connection between this middle ground and what would be a middle ground in the schematism problem (a middle ground such as David Bell’s).
Still, I’m initially suspicious of Ginsborg’s middle position (and there’s no point in keeping a blog if I don’t ‘publish’ such initial thoughts: I can come back) for this reason. Correctness in making a move requires some conception of what it is that one is trying to do, some grasped normative standard (ie I’m stuck with the second part of her dialectic). The very same movement or utterance described in theory neutral terms might be incorrect in a different context. So I’d take Ginsborg’s example to be one in which the articulation of the conception is minimal and demonstrative. There’s no further articulation available to the child than saying that this! is the correct move after that! when doing this! kind of thing, the thing he is doing today and here. Tomorrow, he might reserve the right to be playing a different game (of which he may be able to give no name) and do thus something different. So sameness is still relative to a rule even if the rule is only picked out by what I am doing. To dig beneath this, I suspect, is not to point to a more primitive normativity but rather to lose the normativity.
Now it is possible that a child who had learned to count by twos in this way could come up with an explanation of why she had said ‘42’ after ‘40.’ In particular, she might have arrived on her own at a conception of what she was doing at each step of the process, and she might now be able to articulate that conception by saying, for example, that each number she had said was ‘two more’ than the one before, and that 42 came next because it was ‘two more’ than 42. But it is at least equally likely that the child would be unable to say anything to explain or justify her having said ‘42,’ not just because she lacked the appropriate vocabulary, but because she lacked any conception of what her saying ‘42’ after ‘40’ had in common with her having said ‘40’ after ‘38.’
But if the child has no conception that saying ‘42’ after ‘40’ has something in common with her having said ‘40’ after ‘38’ I do not see how this can be a normative practice. (One possibility: it is not one normative practive but as many practices as there are pairs of numbers. But what of the day when the child seems, as we might say, to add in 4s? Saying ‘44’ after ‘40’ is not always - primitively - wrong, surely? So if not many practices but just one then, I suspect, we do indeed need there to be some conception of the relevant similarity between the various moves for it to be a unitary normative practice.)
Ginsborg’ says ‘As I see it, we do not first have to attach a determinate meaning to ‘+’ in order to deny that a pupil who goes on in this way is going on correctly or appropriately.’ That may be true. The child may not know that in going on ‘2, 4, 6, 8, … , 1000’ and then ‘1002’ they are following the ‘plus 2’ rule or whatever codification might be offered from Peano’s axioms. Still, they do need to master a conception of what they are doing with a determinate enough meaning if it is to have normative consequences at a distance (even if they are gappy in the distance). Failing that, it is not a normatively governed practice at all.
(** I should perhaps not be so quick. One may, like Brandom, think that there is a point in reducing a normativist account of content to a more primitive normativity such as beating one another with sticks. But at this stage in her dialectic, Ginsborg does not seem to have motivated ruling out a whole hearted non-reductive normativism. She has not suggested why we must or should feel her pain, though there may be independent reasons for it, depending on what brand of naturalist one is.)
PS: I return to this here.
Ginsborg, H. (2011) ‘Oughts and Thoughts: Rule-Following and the Normativity of Content, by Anandi Hattiangadi’ Mind
Ginsborg, H. (forthcoming) ‘Primitive Normativity and Skepticism About Rules’ Journal of Philosophy
Thornton, T. (2007) ‘An aesthetic grounding for the role of concepts in experience in Kant, Wittgenstein and McDowell?’ Forum Philosophicum 12: 227-45