Thursday 3 February 2022

Kripke's sceptical solution

I’ve been chatting to Ali HosseinKhani about Kripke and despite his best endeavours, I seem to be in the grip of a confusion about Kripke’s sceptical solution that I’m finding it hard to shake. Here’s another attempt to make it clearer to me.

I assume that the dialectic goes something like this. Kripke deploys a sceptical argument against an intuitive picture of meaning. His argument aims to cast doubt on what appears, pre-philosophically, to be an everyday ‘metalinguistic’ fact: the fact that one can mean something by a word. He considers the case of meaning addition by the word ‘addition’ and asks: what justifies the claim that answering ‘125’ is the correct response to the question ‘what does 68 + 57 equal?’. Two simplifying assumptions are made:

  1. that ‘correct’ means in accordance with the standards of one’s previous usage of the signs involved: what one meant by them; and,
  2. that one has never calculated that particular result before. In fact, Kripke assumes that one has ‘added’ no number larger than 57.

Normally if called upon to justify the answer ‘125’ one might give either of two sorts of response. Arithmetically, one might ensure that one had carried out the computation correctly. Metalinguistically, one might assert: ‘that “plus”, as I intended to use that word in the past, denoted a function which, when applied to the numbers I call “68” and “57”, yields the value 125’ [Kripke 1982: 8].

Kripke now introduces the sceptical hypothesis that in the past one might have followed or meant a different mathematical function, the quus function. On the assumption that one has never previously encountered numbers greater than 57, this is defined to agree with the plus function for all pairs of numbers smaller than 57. For numbers greater or equal to 57 the output is 5. He now presses the question: what facts about one’s past performance show that one was calculating in accordance with the plus function rather than the quus function, that one meant plus rather than quus?

Kripke imposes two furthers condition on any satisfactory answer to the question. One is that it must show why it is correct to respond 125 rather than 5 and, in the dialectic at least, Kripke construes this as supporting normativism. A satisfactory answer should show why one ought to answer 125. This precludes citing facts about one’s education or training which now dispose one to answer 125. It may be true that one has such a disposition, but that will not show that one should answer 125. (One may equally be disposed to make mistakes when adding large columns of figures but that does not imply that one should, that that is what one meant to do.)

The other is that simply remembering what rules one was following or what one meant non-inferentially is cheating/spooky.

He then deploys arguments based on Wittgenstein’s Philosophical Investigations paragraphs 139-239 to show, apparently, that no facts about one’s past actions, utterances or dispositions can justify an answer [Kripke 1982: 7-54, Wittgenstein 1953]. Anything one did or said in the past could equally be interpreted as following or meaning the quus rule. For example, perhaps one said aloud that one was adding the numbers and by adding one meant counting up to the first number and then continuing counting by as many steps along the line of integers as the second number. However, as Kripke points out, perhaps the word ‘count’ meant quount which is defined as the same as counting but only as far as the number 57 [ibid: 108]. It appears that nothing that one said or did or thought to oneself can justify the claim that, now, answering ‘125’ is going on correctly in the same way one was before, in accord with what one previously meant.

In the face of this, he draws on an analogy with Hume to suggest a sceptical solution. This is partly based on the idea that while Hume denies a necessitating causal nexus from one singular event to another, so Kripke denies a necessitating meaning nexus from past intention to future performance. He suggests that a sceptical solution does not deny the force of the sceptical argument but attempts to re-establish everyday practice without it. I take it that it should be consistent with, ie not threatened by, the sceptical argument which is left intact, not undermined. (Undermining the argument is a ‘straight’ solution.)

So if Hume’s sceptical challenge is to find the impression that grounds the idea of a necessitating causal nexus, his sceptical solution of constant conjunction escapes scepticism’s force by a) denying that we need any such impression for such an idea and b) offering instead something of which we could form an impression of sorts. (OK: there are problems concerning how we even thought we had an idea of necessitating causal nexus but I’ll ignore that.)

The following passages suggest the basic idea of Kripke’s equivalent sceptical solution:

It is important to realize that we are not looking for necessary and sufficient conditions (truth conditions) for following a rule, or an analysis of what such rule-following ‘consists in’. Indeed such conditions would constitute a ‘straight’ solution to the sceptical problem, and have been rejected. (ibid: 87) 

If someone whom I judge to have been computing a normal addition function (that is, someone whom I judge to give, when he adds, the same answer I would give), suddenly gives answers according to procedures that differ bizarrely from my own, then I will judge that something must have happened to him, and that he is no longer following the rule he previously followed…From this we can discern rough assertability conditions for such a sentence as “Jones means addition by ‘plus’.” Jones is entitled, subject to correction by others, provisionally to say, “I mean addition by ‘plus’,” whenever he has the feeling of confidence -- “now I can go on!” -- that he can give ‘correct’ responses in new cases; and he is entitled, again provisionally and subject to correction by others, to judge a new response to be ‘correct’ simply because it is the response he is inclined to give. These inclinations… are not to be justified in terms of Jones’s ability to interpret his own intentions or anything else. But Smith need not accept Jones’s authority on these matters: Smith will judge Jones to mean addition by ‘plus’ only if he judges that Jones’s answers to particular addition problems agree with those he is inclined to give, or, if they occasionally disagree, he can interpret Jones as at least following the proper procedure. (ibid: 90-1). 

We can restate this in terms of a device that has been common in philosophy, inversion of a conditional. For example, it is important to our concept of causation that we accept some such conditional as: “If events of type A cause events of type B, and if an event e of type A occurs, then an event e’ of type B must follow… [H]ow do [Humeans] read the conditional? Essentially they concentrate on the assertability conditions of a contrapositive form of the conditional. It is not that any antecedent conditions necessitate that some event e’ must take place; rather the conditional commits us, whenever we know that an event e of type A occurs and is not followed by an event of type B, to deny that there is a causal connection between the two event types. If we did make such a claim, we must now withdraw it. Although a conditional is equivalent to its contrapositive, concentration on the contrapositive reverses our priorities. (ibid: 93-4) 

A similar inversion is used in the present instance. It is essential to our concept of a rule that we maintain some such conditional as “If Jones means addition by ‘+’, then if he is asked for ‘68+ 57’, he will reply ‘125’.”… As in the causal case, the conditional as stated makes it appear that some mental state obtains in Jones that guarantees his performance of particular additions such as ‘68 + 57’ – just what the sceptical argument denies. Wittgenstein’s picture of the true situation concentrates on the contrapositive, and on the justification conditions. If Jones does not come out with ‘125’ when asked about ‘68 + 57’, we cannot assert that he means addition by ‘+’. (ibid: 94-5). 

On Wittgenstein’s conception, a certain type of traditional -- and overwhelmingly natural -- explanation of our shared form of life is excluded. We cannot say that we all respond as we do to ‘68 + 57’ because we all grasp the concept of addition in the same way, that we share common responses to particular addition problems because we share a common concept of addition... For Wittgenstein, an ‘explanation’ of this kind ignores his treatment of the sceptical paradox and its solution. There is no objective fact -- that we all mean addition by ‘+’, or even that a given individual does – that explains our agreement in particular cases. Rather our license to say of each other that we mean addition by ‘+’ is part of a ‘language game’ that sustains itself only because of the brute fact that we generally agree. (ibid: 97)

Mulling this over, it is interesting that what is sufficient to justify Jones’s, albeit fallible, self-ascription of meaning addition by ‘plus’ is merely a feeling of confidence that he can give ‘correct’ responses in new cases; and he is entitled to judge a new response to be correct simply because it is the response he is inclined to give. Note also that this is not based on his ability to interpret his own intentions or anything else. It is, in other words, a brute inclination independent of any conception of what he took himself to be doing (cf Ginsborg’s primitive normativity straight solution).

This seems odd because what it justifies (contra Ginsborg’s primnitive normativity) is the following metalinguistic claim about meaning: “I mean addition by ‘plus’”. Suppose Jones has read Kripke’s book and knows all about quus and suppose he wonders whether he has always been adding or quadding. It turns out that he can justifiably, though fallibly, answer this question in favour of adding rather than quadding providing he is disposed confidently to give any answer (125 or 5!) and is justified, fallibly, in taking any answer to be the correct addition. This seems odd.

Suppose, in the past but post 1982, he has sometimes added and sometimes quadded, equally reliably though the latter only in philosophy classes. He further knows that signs are arbitrary and, in philosophical fun, has sometimes reacted to the ‘+’ sign as though it meant quus. Surely in order justifiably, though fallibly, to claim he now means addition, he needs to know which of these optional dispositional states he embodies? He might mean quaddition.

But perhaps this is illicit once the sceptical argument is in play. Perhaps we can no longer say anything about him meaning anything. Let’s call what remains after the sceptical argument and solution ‘meaning-K’. (I also think that this allows thinking about truth conditions for meaning-K. The truth about meaning-K is the truth about what justifies, albeit fallibly, claims to meaning.) By Kripke’s stipulation, if he has any shaped disposition, he means-K addition. (A reason for this might be that, prior to 1982, the second aspect of Kripke’s account of what justifies ascription to others of meaning-K would never have fitted meaning-K quaddition.) For it to be justifiable for others to ascribe meaning-K addition to Jones, Jones must be disposed to a particular pattern of responses and these must also be endorsed – ie not vetoed – by their peers.

So let’s put this account of meaning-K back through the sceptical argument. We will have to tweak Kripke’s original conditions, much as Hume’s requirement to find the impression of a necessitating causal nexus has to be given up once that is not part of the sceptical solution. Kripke’s stipulated conditions on a response were: (1) determine what we meant by our words in the past and (2) determine the correct use of them in the future.

I assume that the second has to go, as dependent on a picture of meaning (not meaning-K) which had a necessitating intentional nexus. Meaning is dispositional not normative so the best we can offer is a communal disposition. This is some sort of constraint because what a speaker is disposed to say, and which their community is disposed not to reject, rules out many possibilities. We can conjure up a Kripke-ised set of initially platonised variant meanings – take the various logically possible quus-like functions and put them through the sceptical argument - to get the slimmed down evidentially equivalent functions. It seems initially plausible that many of these will nevertheless be ruled out by the test of the sceptical solution (what a speaker is disposed to say, and which their community is disposed not to reject). Surely we do not generally even mean-K quaddition by ‘+’?

So the replacement answer for 2 isn’t what we ought to answer but what we will answer. But can Kripke answer 1? What facts about our/my past determine which Kripke-ised meaning-K is relevant for assessment of what I will do now and what my peers will not criticise?

Now we’ve read Kripke, we understand the quus rule as well as the plus rule. So I and also my peers might mean either by the English word ‘plus’. Which did I, and we, mean in the past? If my disposition is the plus disposition, I’ll do one thing. If the quus, I’ll do something else. Ditto my peers. So do I know, or can I justify a belief, either way in the face of the sceptical argument?

Given that there seem to be two elements to the sceptical solution, we can think of them independently. Asked of my own dispositions I’m inclined to offer two possibilities.

1) Prior to reading any philosophy, I will simply be disposed to give the addition of any two numbers with that cross sign between them. We all will! But surely that’s not the point of a sceptical argument? I am equally prone to disregard Cartesian sceptical possibilities until they are brought to my attention in a philosophy class. Further, I do not need to believe them either true or likely. They just have to be possible and evidentially indistinguishable from the normal picture. So now that I am offered, as a sceptical hypothesis, the idea that my past dispositions were quadditions, what is the evidence that they were not, bearing in mind that direct memory access of meanings was ruled out as spooky? So why should I be able to remember non-inferentially meaning-K either? But perhaps I simply try out my current disposition and see what I write? However...

2) Prior to being prompted, I do not know the shape of my current and future relevant dispositions partly because they will depend on a decision, now post 1982, of whether to add or whether to quad and that difference of meaning-intention will change what I am disposed to do. (I think I could write meaning-K-intention for that too.) Perhaps such dispositions are somehow self-intimating. Perhaps I can bind myself now to the norm (norm?!?) of addition not quaddition, even in fun! But that seems to require the resources of meaning not mere meaning-K if the latter is just brute disposition. (That is, I do need to take note of my intention to act a certain way even to rule out the quus meaning-K.)

I confess I don't find the options very clear because I am not sure what remains of such ideas as intending to use words with particular meanings or meanings-K once the sceptical argument is allowed. That might be the very nexus ruled out.

What of the community? Here I think Kripke’s previous scepticism does have a clear victory over his own sceptical solution. In the sceptical set-up, whether or not I have access to my own dispositions, I do not have access to the future dispositions of my peers. All evidence of what they have not vetoed in the past is consistent with quus. So if I am considering Jones and what he means-K, then I have no better evidence for whether Jones and his peers will add or quad. So Jones meaning-K plus rather than quus does not escape the sceptical argument, which is what it was supposed to do.

This I think should also cast doubt on the intuitive plausibility of Kripke’s account of the assertability condition, or Jones’ own justification, for Jones saying he means-K addition. He only means-K addition if both conjuncts are met. But, given Kripkean scepticism, he is never in a position to justify a belief that the second conjunct will hold: that his peers will not veto what he does. In the face of scepticism and its infinite quus-like sceptical ringers, he is never justified in singling out any meaning-K for himself, given how meaning-K is partly constituted by others.

So I’m confused. As a sceptical solution it seems far too vulnerable to the sceptical argument against which it was supposed to be inoculated.