Wittgenstein on Rules and Private Language: An Elementary Exposition 
by Saul Kripke.
Blackwell, 150 pp., £9.50, September 1982, 0 631 13077 2
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The human mind is a measure of nature and, like all such devices, ought to maintain constancy. But it is also part of nature and so it may be affected by the kind of inconstancy that it often claims to detect in the other part which it measures. Wittgenstein in some of his later work was concerned with a fundamental form of this problem. Do the meanings of our words remain stable and unchanged through all the vicissitudes of our lives? If Crusoe talked to himself during his solitary period, may there not have been some slippage, not evident to him, in his use of his vocabulary? Ruskin believed that the growth of industry had dimmed the bright colours of nature that had surrounded him in his early years, and he might have gone further and suspected that the common use of colour-words was shifting in the same direction. The Gypsy Moth acquired a darker camouflage in the industrialised Midlands. Who knew how words would react? Would they remain unchanged and show up the change in the rest of nature or would they change with it?

We may be inclined to dismiss these questions without feeling the need for any very definite reason for dismissing them. We simply remember that we are using our vocabulary this year in the same way as last year and, of course, we are going to keep it up next year.

But do we really know what we are after when we ask ourselves whether our language is a constant and reliable measure of things? We have the standard metre, cast in platinum and kept in the cool of the Louvre, but such physical paradigms are rare. Do the majority of words then have to rely on mental paradigms? But there are so many minds, and, even if we could single out one and preserve it as a permanent repository, what do we suppose that it would house? And how would others gain access to it? Or perhaps this is not the right way to counter the sceptic’s insinuation of inconstancy in the last place where we would think of it, our own minds?

Professor Kripke takes Wittgenstein’s treatment of this unnerving form of scepticism, develops it at length and assesses the merits of what he supposes to be Wittgenstein’s answer to it. His presentation of the problem is characteristically profound and clear and it is likely to convince us of more than he may have intended at first. This is how the problem looks when it is developed in depth, and so this is how it must have struck Wittgenstein.

There are, however, reasons for doubting the inference. Kripke sees the problem as the sceptical paradox, that when someone uses a word, there is at the moment of his use of it no fact about him that distinguishes between his meaning one thing by it and his meaning another, quite different thing by it. If this is right, the speaker’s predicament is worse than his first, superficial encounter with the sceptic might suggest. It is not that his meaning on some earlier occasion was definite but difficult to remember now with certainty, but, rather, that it is never fixed on any occasion by any strictly contemporary fact. This is a deeper and more worrying suggestion. A craftsman might wonder whether his metal ruler had changed its length since he took a certain measurement, but if someone suggested to him that its length on that occasion was not a contemporary fact but a function of its later history, he would think that that way madness lies.

When Kripke develops this sceptical paradox, his target is the same as Wittgenstein’s. They both attack the idea that meaning is fixed and preserved by mental paradigms, and they both argue that the search for some analogue of a physical measuring device cannot possibly succeed. The point at which Kripke’s interpretation might be doubted comes before his exposition of the paradox, when we ask about its place in Wittgenstein’s philosophy rather than about its content.

The paradox strikes Kripke as one that arises immediately from a close investigation of meaning and has to be met on its own terms. Wittgenstein took a different view of its origin. He presented it as a consequence of a mistaken assumption: because we assume that meaning ought to be fixed and preserved by some omnicompetent mental paradigm, we fall into scepticism when we find that it is not. So the paradox that takes the stage throughout Kripke’s dramatisation is only the play within the play for Wittgenstein.

How much this matters will depend on what is sought from Kripke’s book. If we want a development of the paradox, we shall find it beautifully done. When the nervous speaker confronts the sceptic, he feels that all would be well if only there were something in his mind which set the standard for the use of the word that he had ventured, and set it not only in this case but also in every possible case in which it would be correctly applied. So on later occasions he would only have to remember this mental paradigm and refer to it.

This mistaken idea takes various forms, depending on the choice of paradigm. Perhaps it is an image which somehow prefigures every application of a colour-word and contains a ruling on borderline cases whose possibility has not yet even occurred to the speaker. Or the guidance may be supposed to be implicit in an act of meaning which somehow takes all its hurdles before it comes to them. What all the variations have in common is that they are very reassuring until we realise that they are too good to be true.

There is one way of asking for the moon which is given prominence quite early in Wittgenstein’s discussion. Suppose that a doubt is raised about the precise import of a rule governing the use of a word. A natural response would be to offer an interpretation of the rule to settle the doubt. That, of course, was the strategy of the school of analytic philosophers at the time when Wittgenstein was writing. His reaction to it was to point out that so long as we remain inside language, as we do when we offer an interpretation of a rule, nothing is really fixed. The only thing that fixes the import of a rule definitively is the actual practice of obeying it.

One way of expressing this version of the exorbitant demand would be to say that every rule must have a perfect interpretation, which would settle any conceivable doubt in advance. This all-powerful formula would combine the definitiveness of actual practice with the perspicuousness of anticipatory thought. Wittgenstein evidently takes this to be an incoherent demand. For at any given moment a speaker can only have thought of a limited number of cases in which he would apply a word. Beyond the horizon of his forethought he may feel that his future decisions are as good as taken, because they will have to be in line with what he has already done or decided to do. But the only thing that is quite as good as taking a decision is actually taking it, and no limited set of decisions will ever yield a line that can be prolonged in only one way over the horizon of his forethought into the limitless future.

For example, like all of us, he has only added up a limited set of columns of figures in his life and that achievement, helped out by a certain amount of reflection on what he would do if he ventured further out into the world of numbers and tried some really astronomical computations, would always leave him with a horizon beyond which the plus-sign could behave in some outrageous way without breaking any explicit prohibition. It is as if it could always claim that he had never told it how to behave with numbers beyond his horizon, and that nobody had ever told it how to behave beyond the collective horizon of all its users.

All this is explained very clearly by Kripke, who makes a powerful case for the sceptic’s paradox. But it is not until page 51 of his book that he gives any clue to the way in which the case struck Wittgenstein. Wittgenstein explicitly treats the idea of an omnicompetent mental paradigm or formula as an incoherent myth. Of course, it is not just a philosopher’s myth: it is one to which we are all prone. But how can the insatiability of a demand generated by an incoherent myth be represented as a paradox?

But Wittgenstein actually calls it ‘our paradox’ in §201 of Philosophical Investigations: ‘This was our paradox: no course of action could be determined by a rule, because every course of action can be made to accord with a rule.’ True, but he immediately explains that ‘our paradox’ developed from a misunderstanding of the facts and not from a realistic appreciation of them. If we insist on magic, the distinction between accord and conflict with a rule will collapse. So this is not a natural dénouement, but one which results from a completely unrealistic assumption which we bring to the phenomena. In Wittgenstein’s text the play within the play begins at the point where this assumption is made.

How much does it matter that Kripke mistakes the play within the play for the main drama? That depends on what we seek from his book. It will not matter much if our concern is simply with the paradox of scepticism about meaning. But if we want to understand Wittgenstein’s philosophy, it will matter. For Wittgenstein never puts the paradox in the centre of the stage or tries to meet it on its own terms. On the contrary, in all his writings he treats scepticism as the result of misunderstanding. But we do not have to rely on an inference from the general to the particular in order to settle the interpretation of his attitude to the sceptical paradox about meaning. He makes it quite clear that he believes that our ordinary practice can be seen to provide us with the resources needed to counter it, if only we renounce all hope of magic and assess them realistically without any heady prejudices.

After all, a speaker’s ordinary interpretations of the rule that he is following are very effective, because the words in which they are formulated are hardly likely to raise a real doubt about their application in the very gaps that they were designed to stop. Of course, nobody can produce interpretations to cover every conceivable doubt about the import of a rule, but those that a speaker does produce are a useful anticipatory fringe between his past applications of a word and the innumerable further interpretations that he would give if he were pushed beyond the limit set by the present horizon of his forethought. Admittedly, the fact that he would give these interpretations if asked is not the kind of fact sought by the sceptic, but there is not, and could not be any contemporary magic exerting an absolute constraint in every possible future contingency. So later, when he remembers what he meant, he does not have to recall any incantations, but what he does recall is sufficiently effective.

These are platitudes, but they are platitudes of the kind that Wittgenstein always used in order to neutralise a fantasy and call us back to the sublunary world. Kripke mentions this strategy and stresses the conservatism of Wittgenstein’s philosophy, but mostly in footnotes. In his text the drama rolls on through the acceptance of ‘our paradox’ to the ultimate attempt to meet it on its own terms.

But first we need to look at another part of the plot, which has been kept in the background so far in this review. Wittgenstein’s argument against the possibility of a ‘private language’ has usually been interpreted as a critique of the idea that our sensations are internal objects described in autobiographical statements which are true or false independently of public criteria. The argument has been taken to start at §243 of Philosophical Investigations and many theories of sense-data would be its obvious targets.

Kripke’s most radical proposal is that this interpretation should be rejected. According to him, the ‘private language argument’ is over before its supposed commencement at §243. The conclusion, that no such language is possible, is then applied to two cases in which it is especially hard to believe that ‘participation in a community’ is needed, the case of sensations in the passage beginning at §243 of Philosophical Investigations, and the case of mathematics in Remarks on the Foundations of Mathematics.

Here Kripke is exaggerating a good point. It is true that the ‘private language argument’ is far advanced before §243. However, it is not true that the case of sensations is brought on later simply because it looks like a counter-example to its conclusion. The importance of sensations in the sections following 243 is not that the language used to report them seems peculiarly independent of ‘participation in a community’, but rather that it tends to generate two connected myths. First, like any piece of reportage, it might seem to require an omnicompetent mental paradigm. Second, it is a special feature of sensations that they are readily construed as private mental objects. So the argument that follows §243 is not just a mopping-up operation after the main battle is over. On the contrary, the special feature of sensations has always been one of the two main reasons for regarding the language used to report them as private.

This may seem a captious point about what counts as a single argument, but in fact it is a substantial one, as can be seen from a brief examination of the two sources of the illusion that the language of sensations is private. The point has been made that the theory of the all-powerful mental paradigm is incoherent. But suppose that it were not only coherent but also true. Then nobody could be sure that anyone else was using a word with the same meaning that he attached to it, because each speaker’s mental paradigm would be inaccessible to every other speaker. Their languages, on this supposition, would be private in Wittgenstein’s sense, i.e. necessarily unteachable, and communication would break down.

Wittgenstein exorcised this fantasy by arguing that the supposition is incoherent and by reminding us that the meaning of a word is fixed by its actual application. Now it may look, at first sight, as if he is emptying speakers’ minds and assimilating their performance to somnambulism. In fact, he is only insisting that there is nothing magical in their minds. His philosophy is conservative.

Another common misinterpretation of his strategy is to mistake his reason for insisting that meaning is fixed by actual application. His reason is not that Crusoe would lose the meanings of his words without the checks provided by interlocutors. It is that his rules for applying them, like ours, would hang in the air if he did not actually apply them. Now in most cases it is a consequence of actual application that the checks provided by the give and take of communication are instantly available. But this is only a common consequence of actual application and, as Kripke is aware, Wittgenstein never claims that it is essential.

So far the question has been a general one about any descriptive language, but at this point the special feature of the language of sensations adds its pressure to the case for privacy. For sensations seem to be private objects and yet the application of words to them seems to be a practice that is just as good as Crusoe’s application of words to the trees and birds on his island. If the accidental unobservability of a practice is allowable, why not its necessary unobservability? This is not a question about a mental paradigm, but a question about the things which a mental paradigm is supposed to help us to recognise. This is the other end of the stick.

If these things are completely detached from any external criteria, Wittgenstein’s attitude to them is radically sceptical: there would be no difference between applying words to them correctly and being under the mistaken impression that one was doing so. He makes the same point about the comparison of trees, and birds with an all-powerful mental paradigm. Obviously, his reasoning cannot have been quite the same in the two cases. It follows that the special feature of the language of sensations is an independent, but perhaps equally formidable force adding its pressure to the case for privacy. Given the prevalence of sense-datum theories, that is how Wittgenstein might have been expected to analyse the strategic situation and it would have been surprising if the argument beginning at §243 had been a minor consequential skirmish.

It is not obvious how Wittgenstein connects the two sources of the idea that the language of sensations is private or why he uses the same formula to dismiss them both, albeit presumably with a difference in the reasoning behind the formula in the two cases. Certainly, traditional British empiricism, represented by Russell, completely detached sense-data from all external criteria, and then, in order to explain how they are recognised, brought in images to serve as mental paradigms. In this theory the paradigms would be natural replicas of the things requiring to be recognised. However, that does not really explain why both should be dismissed with the same formula. There is some evidence, analysed in an unpublished paper by Drs P. Hacker and G. Baker, for believing that Wittgenstein was not quite sure about the best way to link up his diagnoses of the two sources of the illusion that the language of sensation is private. But we need a deeper explanation of the structure of his critique.

Perhaps one can be found in the fact that in each case the target is a theory which treats a mental object like a physical one. More precisely, in each case the function of something mental is represented as the product of its intrinsic nature, when it ought to be represented as the result of its place in a larger system. So both criticisms are directed against self-contained atomism, and both replace it with a kind of holism which treats some of the features of interconnected things as the products of their interconnections. However, though it is easy to see how this change explains his critique of the all-powerful mental paradigm, its relevance to his critique of sense-data detached from external criteria is not nearly so obvious.

Let us put the language of sensations, with its special feature, on one side for the moment, and let us take another look at the general problem. Wittgenstein claims that meaning is fixed and preserved by the practice of applying words to things, and that, since language is a social phenomenon, its ultimate basis is agreement in judgments. But what about the further development of Ruskin’s suspicion? Might there not be a shift in the application of a word which produced universal agreement in mistaken judgments? Part of the answer to this is that the practice sets the standard of correctness and in certain cases it really is possible for communication across the ages to break down. But on what is the agreement of contemporaries based?

Surprisingly, Wittgenstein tells us that it is based on human nature. People are not forced to continue the application of a word or to develop a mathematical series in the way that they do: they only find a particular development natural. Here, as Kripke points out, Hume might be speaking. We are robbed of the comfortable assumption of an independent necessity and told that our habits of thought are just another part of nature, as changeable as any other. Kripke regards this as a sceptical and, therefore, unsatisfactory solution to ‘our paradox’.

It certainly seems to build on sand. Humpback whales make an annual visit to Hawaii and sing a song which changes from year to year. The group soon reaches agreement, which would not be possible if they were unable to hear each other. Evidently, it would not matter what the agreed song was, provided that they did not do anything with it but simply sang it. However, mathematics, logic and our descriptive vocabulary are not free improvisations. They have to be applied to the world and this puts them under a constraint to yield true predictions and intelligible laws. Now Wittgenstein hardly alludes to this constraint in Philosophical Investigations. Almost all his remarks are concerned with the learning and subsequent use of language in the give and take of social life. There is no doubt that this is the main source of the idea that the foundations of his theory of meaning are insecure.

It is an exaggerated idea. The truth is that he simply took the obvious constraint for granted when he was discussing our reactions to the world around us. However, our reactions to our sensations are another matter, because in their case there is a second, independent source of the illusion of privacy. Even when we have insisted on the importance of our actually reacting to them, it may still look as if we could do so in complete detachment from external criteria and, therefore, without the possibility of the operation of any external constraint.

So Wittgenstein reminds us that our sensations can be caught in the net of language only because they are placed in a larger system, and he then sets out to describe this delicate linguistic achievement. However, when he describes it, he still takes the obvious external constraint for granted and shows more interest in its special social effects. He is more concerned with the availability of checks applied by one person to another than in the ways in which Crusoe, alone on his island, might seek to reassure himself that there had not been any slippage in his recording of his sensations. Wittgenstein’s treatment of this subject is one-sided, because he does not approach it as a philosopher of science, like Mach or Quine, but as a philosopher of mind. But it is clear enough that here too he substitutes a naturalistic holism for his own earlier metaphysical atomism.

Finally, there is Kripke’s verdict, that Wittgenstein’s solution to the paradox of scepticism is itself unduly sceptical. The case for disagreeing with this verdict has been built up in this review stage by stage. ‘Our paradox’ is not Wittgenstein’s but a consequence of an assumption which he does not share. His philosophy is conservative and he does not try to discredit our ordinary resources for preserving constancy of meaning. Nor does his appeal to what we find natural imply that we are free improvisers like the whales. On the contrary, it is made under an external constraint which is simply taken for granted.

However, Kripke has another, more general reason for his verdict. Like many interpreters he argues that in his later work Wittgenstein rejected the realism of his Tractatus Logico-Philosophicus. Instead of linking the meaning of a sentence to its truth-conditions, he linked it to its assertibility-conditions. If someone finds it natural to assert a certain sentence and if all his peers agree with him, then he is justified in asserting it and the conditions of its assertibility exhaust its meaning.

This is not the place to enter the debate between realists and anti-realists and a single suggestion must suffice. It may be that it is only against the background of the metaphysical atomism of the Tractatus that the naturalistic holism of Philosophical Investigations looks as if it substituted assertibility-conditions for truth-conditions. Be that as it may, Kripke’s book is certainly the most scintillating reaction to Wittgenstein’s later philosophy that has yet appeared.

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