20*. Wittgenstein on Rules and Private Language

At article 6 of the Discours de métaphysique, Leibniz says that God does nothing disorderly. In the same breath he makes clear that he means an impossibility of even imagining any ‘absolutely irregular happening’. To illustrate or persuade us of this he says:

For let us suppose for example that someone were to make a lot of points on a piece of paper quite randomly, as is done by people practising the ridiculous art of geomancy. I say that a geometric line can be found, the notion of which is constant and uniform following a certain rule, such that this line passes through all those points, in the same order as that in which the hand marked them. And if someone were quite quickly tracing a line, now straight, now circular, now of some other kind, it is possible to find a notion or rule or equation common to all the points on that line, in virtue of which those very alterations would have to occur. And there isn’t, for example, a single face whose contour would not make part of a geometric line and could not be traced at one go by a particular movement governed by a rule.

I believe this to be a first in philosophy and would be much obliged if anyone who knows better could point to any earlier author who had this thought. (We find echoes of it later in Russell’s Principles of Mathematics and Wittgenstein’s Tractatus.)

What Leibniz says has a particular consequence: I don’t know whether he drew it or would have liked it. If what he says is true, an indefinite number of rules should be discoverable for a line passing through all these points in that order; and, given one particular line that so passes through them all, an indefinite number of rules producing it and continuing it in different ways. This sort of fact is of course familiar to Saul Kripke:

Given my past intentions regarding the symbol ‘+’, one and only one answer is dictated as the one appropriate to ‘68 + 57’. On the other hand, although an intelligence tester may suppose that there is only one possible continuation to the sequence 2, 4, 6, 8,..., mathematical and philosophical sophisticates know that an indefinite number of rules (even rules stated in terms of mathematical functions as conventional as ordinary polynomials) are compatible with any such finite initial segment. So if the tester urges me to respond, after 2, 4, 6, 8, ..., with the unique appropriate next number, the proper response is that no such unique number exists, nor is there any unique (rule determined) infinite sequence that continues the given one. (pp. 17–18)

The intelligence tester has arbitrarily fixed on one answer as the correct one.

Kripke goes on to ask: since the process of explaining which function we mean must eventually stop, with ‘ultimate’ functions and rules stipulated ‘only by a finite number of examples’, isn’t our procedure arbitrary after all? ‘In what sense is my actual computation procedure, following an algorithm that yields “125”, more justified by my past instructions than an alternative procedure that would have resulted in “5”?’ (p.18) At this point he has a footnote which opens with: ‘Few readers ... will by this time be tempted to appeal a determination to “go on in the same way” as before.’ (p. 18, n. 13) I think it a pity that he did not actually discuss this. His footnote was concerned principally to say that questions of ‘relative’ or ‘absolute’ identity have nothing to do with the matter. But the question: ‘What is going on in the same way?’ has everything to do with it.

At the faint risk of being unfair to Leibniz I will attach his name to the point that an infinite number of rules are compatible with, say, an initial segment of a series, for example, 1, 5, 11, 19, 29; or with such as he himself sketches. I don’t call it a Wittgenstein point because I don’t know if he ever so much as referred to it. (Perhaps §213— ‘this segment of a series obviously admitted of various interpretations’—is a partial reference to it.)[1] But since it is true, there is no use in giving a stretch of a series and suggesting that that gives you with mathematical certainty or logical necessity the function to use in developing that series further. I take it that it is this fact that leads Kripke to his account of ‘Wittgenstein’s sceptical question’ as a question whether there is any such fact as ‘my having an intention to mean one function rather than another by “+”.’ (p. 28) Or again, he speaks of himself as asserting that he definitely means addition by ‘plus’ and insists that in asserting this ‘I assert that the present meaning I give to “+” determines values for arbitrarily large amounts’. (p. 29, n. 21) He invents a name, ‘quus’, for a function whose values coincide with those of plus up to a point and thereafter are always 5. Given that the previous examples in which I have computed n + m are within the range of coincidence, ‘The sceptic argues that there is no fact as to what I meant, whether plus or quus’. (p. 39) ‘There can be no fact as to what I meant by “plus”, or any other word at any time.’ (p. 21)

This last sentence ends a paragraph. The next begins:

This, then, is the sceptical paradox. When I respond in one way rather than another to such a problem as ‘68 + 57’, I can have no justification for one response rather than another. Since the sceptic who supposes that I meant quus cannot be answered, there is no fact about me that distinguishes between my meaning plus and my meaning quus. (p. 21)

I am not sure whether the ‘This’ at the beginning of this quotation looks backward to the previous sentence or forward to the next one. Perhaps it does not matter, for Kripke has previously said that the questions whether there is ‘such a fact’ and whether I am justified in giving 125 as the answer are related.

Neither the accuracy of my computation nor of my memory is under dispute. So it ought to be agreed that if I meant plus, then unless I wish to change my usage, I am justified in answering (indeed compelled to answer) ‘125’ not ‘5’. An answer to the sceptic must satisfy two conditions. First, it must give an account of what fact it is (about my mental state) that constitutes my meaning plus, not quus. But further, there is a condition that any putative candidate for such a fact must satisfy. It must, in some sense, show how I am justified in giving the answer ‘125’ to ‘68 + 57’. (p. 11)

He has previously said:

... I do not simply make an unjustified leap in the dark. I follow directions I previously gave myself that uniquely determine that in this new instance I should say ‘125’. What are these directions? By hypothesis, I never explicitly told myself I should say ‘125’ in this very instance. Nor can I say that I should simply ‘do the same thing I always did’, if this means ‘compute according to the rule exhibited by my previous examples’. That rule could just as well have been the rule for quaddition ... The idea that quaddition is what I meant, that in a sudden frenzy I have changed my previous usage, dramatizes the problem. (pp. 10–11)

Now I will justify my regret that Kripke did not discuss ‘going on in the same way’. It is a matter that the Leibniz point makes problematic in an elementary way. What is necessarily the next term in the series, or point which the traced line has to reach, beyond the points already on the paper? It seems that there is no such thing without the formula, rule, or equation. For this reason the aforementioned footnote of Kripke’s (pp. 18–19, n. 13) sins against what I have quoted from his page 18. For in the footnote he says:

If someone who computed ‘+’ as we do for small arguments gave bizarre responses, in the style of ‘quus’ for larger arguments, and insisted that he was ‘going on in the same way as before’ we would not acknowledge his claim that he was ‘going on in the same way’ as for the small arguments. What we call the ‘right’ response determines what we call ‘going on in the same way’. (my italics)

It is possible—even probable—that Kripke wrote these lines as it were adopting the mask of Wittgenstein, speaking with the intention of expressing a view of Wittgenstein’s. In that case he is not himself sinning against what he said on page 18, but making as if Wittgenstein does so. Now I think he could not quote anything from Wittgenstein to justify the last sentence (in spite of its sounding more ‘Wittgensteiny’ than ‘Kripkeish’). And as for the previous, long sentence, the only evidence we have about what Wittgenstein would say is adverse or neutral. The sentence itself is (strictly) true: we would probably think such a person dotty or shake our heads and say we couldn’t make him out. But so might we too for Wittgenstein’s example: the man who first learns the decimal system of numerals (Investigations, §143) and then does exercises in writing down series at an order of the form +n (Investigations, §185). His exercises have been in the domain of numbers up to 1000. Now, asked to go on from 1000 with +2, he writes 1004, 1008, 1012. When we exclaim to him, shout: ‘You were meant to add two: look how you began the series!’ he says ‘But surely I’m doing it right? I thought that was what I was to do!’ and ‘But I went on in the same way, didn’t I?’ Wittgenstein sketches the case and says: ‘It will now be useless to say “‘But can’t you see ... ?” and repeat the old examples and explanations’.

The passage is famous; I quote it for the sake of the way it ends: ‘In such a case we might say, perhaps: It comes natural to this human being to understand that order, given our explanations, as we would understand the order “Add 2 up to 1000, 4 up to 2000, 6 up to 3000, etc.” ‘

That is, there is here a different understanding—and a weird one. For Wittgenstein straightway compares it to a human being’s naturally reacting to a pointing gesture of the hand by looking in the direction from fingertips to wrist.

In this there is no suggestion that we would say: ‘He is not going on as he began!’ Of course the example is so strange—and not meant not to be—that one doesn’t exactly think of practicalities: of how ‘we’ would actually react. Probably we’d never carry it far enough to make the suggested remark, but just say he was hopeless, seemed all right at first, but for some reason it was no good teaching him beyond 1000. There are people who can’t learn to tell the time, we may reflect. We don’t take trouble to find out what they are doing when they ‘try’. And remember how late (apparently) colour blindness was noted, how late brought to the attention of the learned world. Before then, it seems likely that, say, red-green colour-blind people just seemed stupid on various occasions.

As Wittgenstein imagines the case, however, we do go on with it long enough to find out that there is something like rule-governed reaction; the pupil understood the rule, together with the instructions, differently. If we go this far, could we say he wasn’t going on in the same way as he began? It is a different same way from our ‘same way’. That doesn’t mean that ‘same’ means something different, except in the sense that if I had a beer and you had a whisky and we both said ‘same again’ my ‘same’ would mean beer and yours whisky. (Kripke has a pleasing footnote on objects of the verb ‘to mean’ on p. 9.)

The relevance of the Leibniz point is obvious. Is the imagined pupil applying the same rule? As we? No, not as we understand it; the rule is reinterpreted or changed by us in order to describe his way of going on. So he is applying the same rule—as he began with? Or is he applying the +2 rule—but wrong? Here Wittgenstein imagines the comment: ‘What you are saying comes to this: a new insight—an intuition—is needed at each step to carry out the order +n right.’ He explodes:

To carry it out right! How does it get decided what the right step is at a particular point? ‘The right step is the one that agrees with the order—as it was meant.’ So, when you gave the order, you meant him to write 1002 after 1000—and did you also mean him to write 1868 after 1866, and 100036 after 100034 and so on—an infinite number of such propositions?—’No, I meant him to write the next but one number after each number that he wrote; and from that all those propositions follow in their place.’—But [Wittgenstein replies] that is just the question: what, at any particular place, does follow from that proposition. Or again—what are we to call agreement with that proposition (and also with the mind [intention] you were putting into it then—whatever that may have consisted in). (Investigations, §186)

(I have here made a new effort to translate Meinung, which in this sentence is appallingly difficult to render in English. N.B. this use of ‘mind’ is a bit old-fashioned. We might say ‘That was not his mind’ in discussing how something in someone’s ‘last will and testament’ was actually carried out.)

What is ‘just the question’ is evidently: ‘What is the next-but-one number here?’ The pupil has only done exercises and tests up to 1000. So he has learned to write the four digit number 1000 after 999.—If he didn’t know what to write next after 999, there’d be nothing surprising about that. I have sometimes given a series (see Fig. 1)

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Fig. 1

and asked a class to suggest ‘the’ next row; thus no doubt behaving like the intelligence tester. I suppose if I gave them ?!!! to start the new row it would help. I personally find it difficult to go on as I mean to except by actually recalling the development of numerals in the decimal notation—my intention being to produce something on those lines. Children have no such model. Yet they learn!—and eventually can go on beyond anything they’ve been given! Wittgenstein doesn’t tell us anything about his pupil of §143 and §185, which definitely implies that he has developed the basic cardinal numbers beyond 1000, so we don’t know whether he would go on with that series: 1002, 1004, 1006, etc., or whether we are to assume he has done it in the ordinary way. Probably the latter; but note that if the former were the case, his way of taking ‘the next but one’ would be perfectly intelligible. If the latter, it is his way of going on with +2 that is strange (just as we would find his development of the cardinal numbers strange in the former case). Why do the numbers 1001 and 1003 not count as determining what is the next but one? Well, the fact that something is a two-digit numeral in the decimal system ‘doesn’t matter’ if we are speaking of the ‘next but one’ there. If that were an insurmountable obstacle to someone, we’d think him incompetent to learn, perhaps mentally defective.

Kripke quotes from Remarks on the Foundations of Mathematics (pt.1, §3): ‘How do I know that in working out the series +2 I must write “20,004, 20,006” and not “20,004, 20,008”? (The question “How do I know that this colour is red?” is similar.)’ In Philosophical Investigations, §381, we find: ‘How do I tell that this colour is red?—It would be an answer to say “I have learnt English”.’ Can we not infer that that would also answer the other question? A completer answer to the colour question might be: ‘I am not blind and not colour-blind and have learnt English’. So too with the former question: ‘I have learned that much English’.—But it doesn’t seem important which language one has learnt. I have that much mastery of a language which includes this sort of thing.

It seems more obvious that one is ‘doing something new’ in answering a simple new arithmetical question or developing a new bit of a series—say of the cardinal numbers—than when one calls a new object ‘red’. What about this?

Wittgenstein seems to set no value on it. For he says: ‘If an intuition is necessary to develop the series 1 2 3 4 ..., then so it is to develop the series 2222… (Investigations, §214). Here one wants to say: ‘But merely repeating is different!’ This will be why he goes on at once to ask: ‘But isn’t the same at least the same?’ (Investigations, §215), which leads on to some considerations about identity, rules, and agreement. These, however, don’t concern us for the moment. §214 might not definitely show that Wittgenstein regards 2 2 2 2 in the same light as123 4, for in no case has he any respect for the idea of intuition which is suggested. ‘Intuition an unnecessary dodge.’ (Investigations, §213). So §214 may just be a coup de grace for intuition. This, however, can only work if those who want to invoke an intuition are struck by the idea that you are doing something new, something else or different, all the time in developing (say) the cardinal number series but would feel that you were not in just going on with 2s—as we may feel you are not in calling something of this colour ‘red’ again.

But now: Wittgenstein speaks not just of going on writing down 2 but of developing the series 2 2 2 2 .... Suppose I were a child developing the decimal series 10∕3, no one could say this wasn’t finding out what it was at each step I took. To be sure, Wittgenstein is not giving us a formula for 2 2 2 2 ..., but then neither do we use a formula for 1 2 3 4 .... If writing 2 2 2 2 ... is developing a series, the invoker of intuition should accept §214 and say an intuition is just as necessary for 2 2 2 2 .... And so this example does show that Wittgenstein sees what we might call ‘mere repetition - nothing new’ in just the same light as the case of development of a series where we feel it is always ‘something new’ that one is doing. To repeat from §186, ‘The question is, what, at any particular place, does follow from that proposition. Or what we are to call agreement with it (and with the mind you are uttering it with).’ The ‘new’ thing is that this is the answer at this place. The place is new. And that can be seen for each place in 2 2 2 2 ... if it is the development of a series. But we are also to see it, it seems, if ‘red’, ‘red’, ‘red’, ‘red’ is a string of applications of the word ‘red’. To different objects?—Not necessarily if these are utterances, for example; they are temporally distinct. (This brings out a way in which an ostensive definition of the word ‘red’ doesn’t ‘have everything in it’. Think of a German wondering what type of word is being explained. ‘This is red’ I say, holding up a little red book. ‘And is it still red?’ he asks as I lay it down. ‘Yes’. He is content: for he had been hesitating between ‘rot’ and ‘aufrecht’.) And the question ‘what to do at this place’ arises even for the order ‘Keep on writing 2’.

A new place in the series, a new occasion, another time—all these, it seems, are assimilated under one heading. The questions ‘How do I know that 1197 is the next odd number after 1195?’ ‘How do I know that this taste is sweet?’ and ‘How do I know that this note is high?’ can all be answered by ‘I have learned English—that part of English’. Compare and contrast ‘How do I know that this is a cockroach? a premise? a novel? oak? satire? a rainbow? a hole? laughter?’

The comparison between red and working out the series of +2 at the number 20,004 is extremely interesting. Kripke’s explanation is ‘a central thesis of this essay’ (p. 20): namely that Wittgenstein has propounded an irrefutable sceptical paradox and come up with a ‘sceptical solution’—a ‘sceptical conclusion about rules and the attendant rejection of private rules’. This ‘is hard enough to swallow in general, but it seems especially unnatural in two areas. The first is mathematics ... another is that of a sensation or mental image ... Because these two cases, mathematics and inner experience, seem so obviously to be counter-examples to Wittgenstein’s view of rules, Wittgenstein treats each in detail.’ (pp. 79–80)

The exegesis is wrong. Wittgenstein was not putting forward sceptical arguments: the ‘new sceptical problem’ about which Kripke expresses such great admiration on page 60—is Kripke’s.

Superficially it is easy to prove that Wittgenstein had no such sceptical problem as Kripke credits him with. At §§84-86, where he considers how the application of a rule, and a doubt about it, may be taken care of by another, and it in turn by another, and so on, he says, ‘That is not to say that we doubt because we can imagine a doubt’. Also, he asks whether a table one consults by looking across from a word to a picture is incomplete without a schema to tell one this; the answer is evidently no. We have already examined §185 and §186, where indeed the idea of the right way of going on with a series under an order ‘+2’ is questioned because (a) the explanations and examples are useless for demonstrating the rightness of our way to someone who has an abnormal response to them, even though the response is the expression of some systematic understanding and (b) what one is to do at each place of the series, in order to obey the rule, is exactly what is in question when we are considering someone who does something different from us and is not in any ordinary sense making a mistake.

This is, I think, the best passage for Kripke to call ‘sceptical’. But what is the doubt? Kripke thinks—apparently—that an argument that a stretch of a series can’t tell you the continuation of it is correct enough; and he seems to accept the argument that, since a rule can be reinterpreted ad lib., you cannot simply point like Leibniz to the rule or formula or equation. But he is sure that there is the right answer to a sum, though this now can’t depend either on previous examples or on the formula n + m with an interpretation. Hence he is driven, as far as I can make out, to think that the required guarantee resides in what he meant or had the ‘intention to mean’ by the plus symbol— that being the example which he chooses for discussion. He might seize joyfully on Leibniz’s word ‘notion’.

Wittgenstein’s discussions several times emphasize something which Kripke does not mention: the teacher cannot succeed in teaching unless the pupil has certain reactions which he is not obliged to have and which the teacher can’t teach him; is responsive in certain ways in which he does not have to be. And this does not mean that the teacher can’t teach, for example, an inattentive pupil. Rather, he won’t be able to teach him unless, for example, he does get the basic cardinal numbers by heart and in order and does go on in a new stretch, after the examples and the practice, like this and not in some other way. This is something that cannot be taught; it is a prerequisite of teaching. The ancients and medievals had a problem whether and how teaching is possible; the point I have been making—which is in Wittgenstein—is a contribution to that discussion; the matter, I believe, is not discussed nowadays. I have never heard of its being a question discussed in philosophy departments: Is it possible for one human being to teach another? You can tell him histories; can you teach him to calculate? You can do something which is called teaching; but he only ends up knowing, if he has had these reactions, not those, in the course of the teaching.

However, what is called teaching does end up, if successful, with the pupil able to do what in a certain sense he cannot be taught. And then, the pupil—take him to be Kripke—means addition by ‘+’, and what he means is a function ‘that determines values for arbitrarily large amounts’, that is, arbitrarily large finite cardinals. Whether for anything else, we do not know, for Kripke does not tell us. But he insists that ‘the sceptic’ argues that there can be no such fact as that he meant addition in the past by ‘+’ and that the sceptic’s argument is not only invented but accepted by Wittgenstein. Kripke could not, however, quote anything to the effect that ‘there can be no such fact, etc’. It is his deduction from the past procedures’ having been ‘only finite in number’ and variously continuable and from rules’ being indefinitely reinterpretable.

Wittgenstein, however, does not say or imply that there can be no such fact.

Is it correct for someone to say ‘When I gave you this rule, I meant you to ... in this case’? Even if he did not think of this case at all as he gave the rule? Of course it is correct. For ‘meaning it’ did not mean: thinking of it. But now the question is: how are we to judge whether someone meant this?—That he mastered a particular technique of arithmetic and algebra and gave the other the usual instruction in the development of series, is such a criterion. (Investigations, §692)

Nor do we have to look away from our passages §§185 and following to get this information; it is not an afterthought, nor does it belong to a movement of thought in Wittgenstein: ‘How can I cope with this ghastly sceptical problem?’ I have discussed §185 and §186; §187 begins:

‘But I already knew, at the time when I gave the order, that he ought to write 1002 after 1000.’—Certainly; and you can also say you meant it then; only you should not let yourself be misled by the grammar of the words ‘know’ and ‘mean’. For you don’t think that you thought of the step from 1000 to 1002 then—and even if you did, you didn’t think of others. Your ‘I already knew then …’ means something like: ‘If anyone had asked me then what number he ought to write after 1000, I’d have answered ‘1002’.’ And that I don’t doubt. This is an assumption of the same kind as, say, the following: ‘If he had fallen into the water then, I’d have jumped in after him.’—Now, where was the mistake in your idea?

On pages 69–70 Kripke indicates that Wittgenstein does not state broad philosophical theses: it is easier so to avoid the danger of denial of any ordinary belief.

Whenever our opponent insists on the perfect propriety of an ordinary form of expression (e.g. that ‘the steps are determined by the formula’, ‘the future application is already present’ [!]) we can insist that if these expressions are properly understood, we agree. The danger comes when we try to give a precise formulation of what we are denying—what ‘erroneous interpretation’ our opponent is placing on ordinary means of expression.

What Kripke doesn’t seem to recognise here is that correctly attacking a philosophical idea—at any rate of the kind which gets a grip on us as nonsensical is likely to involve difficulties about characterising it. ‘The steps are determined by the formula’—one may be contrasting formulas in saying this; and that is harmless. But—there is something else one may be saying, something difficult to distinguish; and which may have a sense which is not what one supposes.

All the same, we should note that Wittgenstein does not fail to give expression to what he is attacking. He says that the first thing he would like to say (having asked ‘Where did your idea go wrong?’) is: ‘Your idea was that meaning the order had already, in its own way, taken all those steps: that your mind, in meaning the order, as it were flew ahead and made all the transitions before you physically reached this or that one.’ (Investigations, §188) He adds: ‘So you were inclined to use expressions like “The steps are really already taken, even before I take them in writing, or orally, or in thought”. And it seemed as if they were in a peculiar way determined beforehand, anticipated—as only meaning can anticipate reality.’ Kripke does not mention some of these formulations by Wittgenstein of what he is attacking. It is possible that this is because he himself would want to embrace them but would not—could not—deny their absurdity.

At §190 Wittgenstein imagines someone using an unfamiliar sign in a formula, and our saying, ‘If with “x!2” your intention is x2, you get this value for y, but if you mean 2x, you get that one.’ He then invites us to ask ourselves ‘How does one have the one or the other intention in using “x!2’?” He declares that that will be how one’s meaning can determine the steps in advance. This is an interesting example because it involves the use of a sign not in common use. How could one train someone who knew neither ‘x2’ nor ‘2x’, in the use of ‘x!2’ with the meaning of one of them? How (assuming one’s own innocence of both ‘x2’ and ‘2x’) would one explain ‘x!2’, when it does have one of these meanings for oneself?

The passage implies that, whatever intending such a meaning as x2 for an unfamiliar sign would be, that will be how one’s intention for a sign can determine steps in advance. This seems to be a somewhat roundabout way of saying that the criteria for N.N.’s having meant the pupil to do this in this place of this series include N.N.’s possession of a certain technique of arithmetic. I only say ‘include’ because I am obviously not sketching the rest of the situation of N.N. and the pupil. But this part of the total set of criteria is the business part for Kripke’s problem.

At this point we should stress that Wittgenstein does not think, as Kripke does, that a stretch of a series can’t rightly be taken as to be continued so. It can: either from familiarity with it or by guessing at a formula or principle of development and having one’s guess confirmed by the next number one is given. (See Investigations, §151) To the objection: ‘You must have chosen one out of the various possible interpretations’, he replies: ‘Not a bit of it! In some circumstances a doubt was possible. But that is not to say that I did have, or even could have had, any doubt.’ (Investigations, §213) Neither the Leibniz point nor the reinterpretability of a formula or rule makes Wittgenstein fault the exclamation ‘Now I can go on!’

They make Kripke fall back on a mental state of meaning and want an account of ‘the fact about his mental state’ which constitutes his meaning whatever he does mean. It has got to be an account which will justify, for example, his computations of n + m. What he will allow as justification has got to be formally (not merely in practice) immune to objections based on the Leibniz point or the reinterpretability of rules.

Wittgenstein’s accounts, which I have quoted, of the sort of thing it is for you to have meant me to give 1868 as successor of 1866 in the +2 series, Kripke would no doubt count as a bit of ‘the sceptical solution’ (though I fear he doesn’t actually attend to it).

Kripke can’t prove the existence of the fact that ‘the sceptic’ denies. Now scepticism cannot endure the imaginability of doubt. You ought to doubt if you can think of a doubt. So Kripke is faced with a dreadful threat if he can’t answer the sceptic. How can he say he knows?—Knows what?—That he has ‘reason to be so confident that he should answer “125” and not “5”.’ (See p. 11) Clearly he does not feel justified in replying like Wittgenstein, ‘I do not doubt’. And ‘My eyes are shut’. I do not know if he has gravely considered this possibility as anything but a sort of bluff.

And yet he said that the problem ‘is not [A] “How do I know that 68 plus 57 is 125?”, which should be answered by giving an arithmetical computation, but rather [C] “How do I know that 68 plus 57 as I meant ‘plus’ in the past should denote 125?” ‘ (p. 12) But: only if A cannot be settled as it is and as he says it is, does C relevantly arise. The demand that whatever mental state was meaning plus should in some sense show how Kripke is justified in giving the answer ‘125’ means that he wants some account of his past mental state to justify saying that 68 plus 57 is 125—contrary to what he says on p. 12. Why not simply give the computation as the justification and leave it at that? The answer must be: because after all Kripke thinks that you can raise a doubt about the computation itself if the sceptical question about past meaning cannot be answered.

Let us accept it that the sceptical doubt turns into a doubt about present as well as past meaning, and about meaning any word; and that this is necessarily a doubt about whether ‘125’ is the right answer to the sum.

Then we can scrutinise Kripke’s ‘condition that any putative candidate for such a fact must satisfy’, that is, such a fact about one’s mental state as constitutes one’s meaning plus. This was that it must in some sense show how one is justified in giving the answer ‘125’ to ‘68 + 57’. This demand seems to be an impossible one for any ‘fact about a mental state’ to satisfy unless one is to be extremely generous about what is to count as a ‘fact about a mental state’. For example, Wittgenstein, replying to the question ‘How are we to judge whether someone meant such and such?’ says: ‘The fact that he has, for example, mastered a particular technique in arithmetic and algebra, and that he taught someone else the expansion of a series in the usual way, is such a criterion.’ (Investigations, §692) Now can we say: There you are, there’s the fact about the mental state he was in or was having or which was his mental state—when he told that pupil to go on adding 2? All of those italicised phrases sound queer; they seem to express something different from what we want. But never mind that: my present point is that calling that ‘a fact about a mental state’ is like calling ‘somebody had been playing chess in the next room five minutes before’ a description of a ‘fact about my physical state’ at a certain time. What one would naturally mean by ‘a fact about one’s mental state’ (taking this in the way philosophers in the empiricist tradition have taken it) would be some current feature of one’s (possibly momentary) mental posture. Of course if one says that some mental state terms are ‘dispositional’, one may not mean just that. Kripke devotes a lot of space to dealing with this suggestion, made to him as a solution to his sceptical problem; he deals with what I gather was meant by his interlocutors in making it, very efficiently. They do on the whole seem to have meant something like the set of an alarm clock; something which theoretically could be directly inspected by someone looking directly inside the mechanism. Such is not the sense in which knowledge, for example, is a dispositional concept. In neither sense is having meant plus by ‘+’ dispositional. So I will say no more on this part of the book. It is worth noting, with some curiosity, that Kripke speaks of a mental state rather than of a mental act; possibly he would accept Wittgenstein’s remark that it is thoroughly wrongheaded to think of the verb ‘to mean’ (with personal subject) as the name of an intellectual (or mental) activity. (Investigations, §693)

This leads me to Kripke’s good observations on the difficulty of arguing ‘that meaning addition by “plus” denotes an irreducible experience, with its own special quale, known directly to each of us by introspection. (Headaches, tickles, nausea are examples of inner states with such qualia)’. (p. 41) If one did argue thus, one would say that ‘the fact that I mean addition by “plus” is to be identified with my possession of experience of this quality’.

He criticises this idea as being ‘Off target as an answer to the original challenge of the sceptic’. For the sceptic wanted to know why he was so sure that he ought to say ‘125’ when asked about 68 + 57. But, he asks, how could an experience with a very special quality help him figure out whether he ought to answer ‘125’ or ‘5’. (p. 42)

Quite so. Such is the difficulty. What sort of mental somewhat meets it?

Kripke’s problem: how do I know I meant plus? is indeed interesting, if sceptical problems ever are.

More interesting is the problem with which he is implicitly confronting himself: what is the fact that he knows, namely that he meant, and means, plus? His account of Wittgenstein as giving a ‘sceptical solution’ to the first problem is far less interesting and is I fear affected by his not letting himself be épris by this problem.

The sceptical question about past meaning is not supposed to be part of a general sceptical question about memory of mental events, states and processes. One might wonder why it matters for the justification of Kripke’s answer to the sum. If he meant plus and has not changed his usage, he says, he is justified. But ‘if’ is not ‘only if’. For this reason, one might well think that the sceptic’s challenge: ‘You are making a mistake about the meaning of “+”; going by what you have meant before, your answer should be “5”,’ was merely a device for arousing us to the essential problem: ‘What is the mental fact of meaning?’ with the attendant considerations about rules and the Leibniz point.

But the sceptical question about past meaning has a peculiar interest: one says ‘I meant such and such’ as a direct memory of a fact. One is not recalling one’s possession of such-and-such techniques, previous training of the pupil, et cetera, though one might refer to these if one were arguing with the sceptic. At the same time ‘I meant …’ is not, surely, the expression of a Cartesian cogitatio. This problem, about the first person past indicative of psychological verbs, was barely scratched by Wittgenstein.

My friend Yorick Smythies once said to me that what was needed was an attack on Wittgenstein. Such as there have been are no use at all, as far as I have seen them. Kripke’s express intention was not to attack but to expound the argument which he, Kripke, got out of Wittgenstein. In my opinion it ought to be useful in the way Smythies thought a serious attack would be. The great chapter for this purpose is the one called ‘The Wittgensteinian Paradox’. For this reason I have simply tackled its main line. I hope it may lead readers (partly in perceiving what is wrong with it) to a stronger perception of and further enquiry into the questions involved. And I say to Kripke, Much thanks.

 

* A review of Saul A Kripke, Wittgenstein: On Rules and Private Language (Cambridge, Mass: Harvard University Press, 1982) published in Ethics 95 (January 1985): 342–352, and reprinted by permission of the publishers, Chicago University Press. This is one of two quite distinct reviews of the Kripke volume by Anscombe published in 1985. The other appeared in the Canadian Journal of Philosophy 15 (1985): 103–109.

1 Ludwig Wittgenstein, Philosophische Untersuchungen (Frankfurt am Main: Suhrkamp Verlag, 1977).