Meaning and Rule-following Research Paper

1. Introduction

It is a common thought that an individual’s words mean what they do because the individual is following a rule for the use of that word: a rule that determines what is a correct, and what is an incorrect, use of the term. This idea has been challenged in a cluster of arguments given by Wittgenstein, which in turn have received great impetus in the interpretation given by Saul Kripke. According to Kripke, the central problem is this: there does not seem to be any set of facts that determines that a speaker is following one rule rather than another. In a little more detail: suppose that, in using a certain word, an individual seems to be following a certain rule, R. Then we can always come up with a different rule, R′, which fits all the facts about the individual’s use of the word just as well as R. Why is the individual following R rather than R′?

According to Kripke there is no straightforward answer to this question. The ordinary conception of what it is to follow a rule is simply mistaken; so, in turn, is the ordinary conception of what it is for a word to be meaningful. The best that is available is a surrogate for the ordinary conception; what Kripke calls a ‘skeptical solution.’ This takes the form of a social criterion of rule-following: an individual follows a rule in so far as their behavior conforms to that of the other members of their community. A mistake simply consists in deviation from what the others do. Thus an individual’s words mean whatever the other members of their community use them to mean. This, in turn, can be seen as providing the basis for Wittgenstein’s famous denial of the possibility of a private language. A private language is impossible since there would be no community-wide use to provide the correct use of its words, and hence the words would have no meaning.

Kripke’s presentation of the rule-following worries has engendered a large literature. His skeptical solution has not been widely accepted. Responses have typically fallen into one of two classes. Either it has been argued that there are further facts about an individual, overlooked by Kripke that determine which rule they are following. Or it has been argued that Kripke’s whole presentation is vitiated by an over reductionism approach. These responses will be examined in what follows; first it is necessary to examine the nature of the rule-following problem itself.

2. The Rule-following Problem

The passages of Wittgenstein that provide the inspiration for the argument appear, in typically compressed and gnomic form, in Wittgenstein (1953, pp. 138–242) and Wittgenstein (1978, Chap. 6). Kripke’s account was published in its final form in Kripke (1980), having been widely presented and discussed before; a similar interpretation was given independently in Fogelin 1987 (first edition 1976). There has been some controversy as to how accurate Kripke’s presentation of Wittgenstein’s views are; a number of authors have embraced the term ‘Kripkenstein’ to refer to the imaginary proponent of the views discussed by Kripke. The exegetical issue will not be of concern here. Kripke will only with the argument present the concern. (For discussion of the exegetical issues see Boghossian 1991.)

The central idea is easily put. Imagine an individual who makes statements using the sign ‘ +.’ For instance, they say ‘14 + 7 = 21,’ ‘3 + 23 = 26.’ It might be thought that they are following the rule that ‘ + ’ denotes the plus function. But consider the sums using ‘ + ’ that they have never performed before (there must be infinitely many of these, since they can only have performed a finite number of sums). Suppose that ’68 + 57’ is one such sum. Now consider the quus function, which is stipulated to be just like the plus function, except that 68 quus 57 is 5. What is it about the individual that makes it true that they have been using ‘ + ’ to denote the plus function rather than the quus function? By hypothesis it cannot be that they have returned the answer ‘125’ to the question ‘what is 68 + 57?,’ since they have never performed that sum before.

The immediate response is that the individual meant plus in virtue of having mastered some further rule: for instance, the rule that, to obtain the answer to the question ‘what is 68 + 57?’ one counts out a heap of 68 marbles, counts out another of 57, combines the two heaps, and then counts the result. But now reapply the worry. How can it be known that by ‘count’ the individual did not mean ‘quount,’ where, of course, this means the same as ‘count’ except when applied to a heap constructed from two piles, one containing 68 objects, the other containing 57, in which case one correctly quounts the pile if one simply returns the answer 5? One might try to fix the meaning of ‘count’ by some further rule; but this will just invite further worries about what is meant by the words occurring in that rule. Clearly there is a regress. Any rule that is offered to fix the interpretation of a rule will always be open to further interpretations itself.

At this point it might be suggested that it is a fact about the individual’s dispositions that determines that they meant plus: the relevant fact is that they would have answered ‘125’ if one had asked them the question ‘what is 68 + 57?’ But that response falls foul of the normativity constraint on rules. Rules are things that tell us what we ought to do; dispositions are simply facts about what we would do. To think that facts about the rules we follow can be derived from facts about our dispositions is to try, illegitimately, to derive an ‘ought’ from an ‘is.’ Thus even if, due to some cognitive blip, the individual would in fact have answered ‘5’ to the question ‘what is 68 + 57?,’ one would still want to say that by ‘ + ’ they meant plus, but that they simply made a mistake. If one identifies what their rule requires them to do with what they would in fact do, no possibility is left that they might go wrong. Yet it is part of the very idea of a rule that one can make sense of the idea of breaking it. So one cannot identify the rule that an individual would follow with what they are disposed to do. No answer has been found to the question of what the individual means by their words.

It is important to see just how wide the repercussions of this are. First, note that although Kripke presents the problem as an epistemic one (how can one know that the individual meant plus rather than quus), the deeper problem is constitutive: there seems to be nothing for meaning to consist in. Second, note that the problems do not arise just because Kripke restricts himself to behavioral evidence. The argument is that there is nothing in the individual’s mind, not just their behavior that can determine what they mean. (Here there is an important difference between Kripke’s arguments and the influential arguments for the indeterminacy of meaning given by Quine (1960); Quine does restrict himself to behavioral evidence.) Third, note that it is not just a matter of the meaning of words in a public language. The same considerations apply to the very contents of an individual’s thoughts themselves. How can an individual know that their thought that 2 + 2 = 4 is a thought about plus, and not a thought about quus? This makes the worry go much deeper; and it also makes Kripke’s skeptical solution much more shocking. For it is one thing to say that the meaning of words in a public language are determined by the behavior of the community; there is a sense in which, given the conventional nature of language, something like that is bound to be true. It is another thing to say that the very contents of an individual’s thoughts are somehow determined by the community around them. It is now time to examine the skeptical solution a little more deeply.

3. The Skeptical Solution

Recall that the basic problem that arose in identifying following a rule with having a disposition: it gives us no purchase on the idea of making a mistake. But once one identifies following a rule with conforming to the dispositions of the community, the idea of a mistake can come back: an individual makes a mistake in so far as they do not conform. What this approach can make no sense of is the idea of the whole community going wrong. In proposing this solution, Kripke is not suggesting that he has recaptured everything in the ordinary notion of meaning. After all, it is normally thought that the reason that the whole community gives the same answer to ‘what is 68 57?’ is because they have grasped the same concept. But as in Kripke (1982, p. 97), the skeptical solution does not allow us to say that; grasping the same concept isn’t some independent state that explains convergence in judgement. Rather, the skeptical solution is meant as a surrogate for our ordinary conception of meaning: it is the best that there is.

However, it is questionable whether it is good enough. It might be accepted that the ordinary philosophical picture of the nature of meaning is a false one, one that the skeptical solution corrects. It would be much worse if the skeptical solution were at odds with the ordinary practice of making judgements. Yet it seems that it is. As Paul Boghossian has noted, there are plenty of cases in which, for ordinary predictably reasons, the whole community tends to go wrong (Boghossian, 1990, pp. 535–6). Thus consider a good magician. With sleight of hand they can get us all to believe that they have put the egg into the hat; only they know that it is under the table. So the community agrees that the predicate ‘is in the hat’ applies to the egg; the magician is the odd one out. Yet it would be ridiculous to say, as it seems the skeptical solution must, that the community is right and the magician is wrong. The magician is the one who knows the truth. The rest of the community has simply been tricked.

A natural response to this is to say that not every disposition of the community should be respected. It is important to pick and choose. In this case, the disposition of the magician to say that the egg isn’t in the hat should count for far more than that of the rest of the community to say that it is. However, once that move is made, the primary motivation for the skeptical solution has been lost. The whole point was that using the actual dispositions of an individual could not give rise to the possibility of error; so it was necessary to look to the actual dispositions of the community instead. But once one starts to pick and choose amongst the dispositions of the community, saying that some must be given greater weight than others, the possibility of error is reintroduced into the individual case. Here too, if some dispositions are favored over others, then the individual can be thought of as falling into error: they will be in error whenever they go with a less favored over a more favored disposition. To say this is not to deny the role of the community altogether; for instance, it could be that in sorting out the preferred dispositions it will be necessary to have recourse to the dispositions of the experts, and this is a position conferred by the community. But the essential role of the community will have been lost, and with it, what is distinctive about the skeptical solution. Let us now turn to this alternative proposal, and examine in more detail the grounds on which some dispositions might be preferred to others.

4. Laundering the Dispositions

The central thought is that the correct application of a term cannot be identified with that which an individual is disposed to apply it to, nor with what the community is disposed to apply it to; but it might be possible to identify it with what the individual or the community is disposed to apply it to under certain circumstances. This is the device that enables some dispositions to be preferred to others. The proposal here parallels certain versions of the disposition theory of color, and useful lessons can be gained from considering that.

According to a crude dispositional theory of color, an object is, say, red, if and only if observers have the disposition to judge it as red. But that crude form of the theory is hopeless. Some observers are color-blind; some circumstances, for instance colored lighting, will distort the color judgements even of someone who is not. So, a more plausible dispositional account of red will say that an object is red if, and only if, competent observers in favorable circumstances have the disposition to judge it as red. This makes the account more plausible; and it reintroduces the possibility of error. Yet it raises a difficulty, that of specifying what competent observers and favorable circumstances are. For if all that can be said about them is that the are, respectively, the people who are good at identifying red things, and the circumstances that are good for such identifications, then the account will be circular. Parallel issues arise for the rule-following concerns. Suppose it were said that an individual means plus rather than quus by ‘ + ’ just in case, under favorable circumstances, they have the disposition to use it to denote the addition function i.e., to answer ‘125’ to ‘what is 68 + 57?’; ‘2’ to ‘what is 1 + 1?’ and so on. Now the possibility of error has been reintroduced, since sometimes the circumstances will not be favorable. But how should the favorable circumstances be specified? They cannot be specified as those circumstances in which the individual uses ‘ + ’ to denote the addition function; for that makes the proposal trivial. Worse, the proposal can provide no support for thinking that the individual does in fact use ‘ + ’ to mean plus, since it is equally true that they have a disposition to use ‘ + ’ to denote quus in those circumstances in which they use it to denote the quaddition function.

Moreover, it seems that it won’t do to say that favorable circumstances are those in which the individual is thinking hard, and has no distractions, for even here people make mistakes. Everyone does. Of course, in such cases the individual will not be thinking hard enough; but if that is shorthand for ‘not thinking hard enough to get it right,’ then the proposal has lapsed back to triviality.

What other ways might there be to launder dispositions without triviality? One response, stemming from those who seek to give a biological foundation to meaning, is to seek to spell out competent speakers and favorable circumstances in terms of proper functioning, where this, in turn, is spelled out in terms of the function that has been selected for. This is typically presented as part of a broader project of understanding semantics notions in terms of evolutionary ones. Whatever the merits of the broader project, it faces great difficulties in providing a response to the rulefollowing worries. One kind of problem arises when we try to give an account of highly abstract terms, terms that do not bring obvious evolutionary advantage to those who grasp them: the case of addition, discussed so far, provides a case in point, let alone the concepts of, say, algebraic topology. But suppose one were to consider more common concepts, like that of cow. Could it be argued that the reason a given individual means cow by ‘cow’ rather than, say, cow unless today is January 25, 2150 in which case horse is that they have been selected to do so? It appears not; for, since we have not yet reached January 25, 2150 it will be true of every cow that the individual has in fact met that they are: a cow unless today is January 25, in which case they are a horse. (This example makes clear the similarities that the rule-following problem bears to Goodman’s ‘New Riddle of Induction’ and the famous example of grue; see (Goodman 1973), and Kripke’s discussion 1982, pp. 20, 58–9.) Similar examples could be given using disjunctive concepts, for instance that of being a cow or a marshmallow: it is true of every cow that it is either a cow or a marshmallow. For discussion, and a suggested way of avoiding this latter problem, see Fodor (1990, Chaps. 3 and 4). It might be argued that the property of being a cow unless today is January 25, 2150 (in which case a horse), is not a very natural one. That is surely correct. But once that property is ruled out as an eligible referent for the term ‘cow’ on the grounds of its unnaturalness it is unclear that the talk of proper function is actually doing any work at all. (For an example of a teleological response to the rulefollowing problem, see Millikan (1990); for discussion of the problems with the approach in general see Boghossian (1989, pp. 537ff).) For a discussion of the advantages to be gained by treating naturalness as a primitive feature of properties, including an application to rule-following, see Lewis (1983, pp. 375–7).

A more promising approach to laundering dispositions is suggested by Philip Pettit (1999). Why not think of the ideal conditions as involving an idealization of our actual practices of correcting ourselves and others in the light of discrepancy and divergence? This reintroduces a social element: individuals mean plus rather than quus by ‘ + ’ just in case the process of correcting themselves and others in which they actually engage will, if taken as far as it can be taken, result in them using it to denote the addition function. However, there is in this proposal no unwanted guarantee that the community, as it now stands, is right in its use of terms; for the process of correction might not yet have been carried out. Provided that the idealization is not understood in a trivializing way (i.e., as the process that will bring individuals to apply their terms correctly according to what they mean by them) the proposal will not be trivial. Nonetheless a worry remains. It seems that there is no a priori guarantee that a community’s actual practices, even if idealized, will lead them to use their terms correctly. For couldn’t it be that their practices are prey to a deep and systematic error, such that however much they are idealized, the error will remain? Perhaps, to extend the example given before, nature itself is the magician, and the community will never see through its tricks. In such a case, following Pettit’s method of resolving differences and contradictions would perhaps lead them to a consistent theory, and one that they would be quite happy with; but it would be a theory involving misapplications of their own concepts—misapplications which, given their cast of mind, they would never be in a position to shake off. All this seems possible. Yet if what is meant by a word is what its users would be disposed to apply it to after they had resolved all discrepancies and divergences, no such errors would be possible. It might seem very implausible that communities are in fact prey to errors of this sort; but it is not clear that there should be an a priori guarantee that they are not.

5. Antireductionist Approaches

The rule-following worry consists in the thought that we cannot give a characterization of what following one linguistic rule rather than another amounts to. But what kind of characterization is required? It might appear that what Kripke has shown to be unobtainable is a characterization of facts about rule-following in terms of other sorts of facts. What it shows then is that a certain kind of reductionism is unavailable. So another response to the rule-following worries is just to give up on reductionism: conclude that meaning facts are simply not reducible to other sorts of facts, in particular, conclude that they are not reducible to facts about actual or possible behavior. This is the approach taken by McDowell (1984, 1993); see also Wright (1990).

The flight from reductionism has been a feature of much recent analytic philosophy; and social scientists schooled in the erstehen approach will find the response natural. But what exactly does a rejection of reductionism with respect to meaning consist in? One response would be to say that each individual meaning fact (that ‘plus’ means plus, for example) is sui generis and primitive; one simply grasps it or one doesn’t. Kripke (1982, p. 51) briefly discusses and rejects such an approach and he is surely right that it is most implausible. No matter how skeptical one might be about the existence of analytic equivalences, it cannot be denied that there are systematic connections between different meaning facts; how else could we explain the meanings of new words in terms of old ones? A more plausible claim is that, while there are connections between meaning facts, no meaning fact can be reduced to a nonmeaning fact. This is how proponents of anti reductionism typically conceive of it. The contention is that the rule-following worries only arise if one tries to give an account of meaning facts in terms of facts that make no reference to meaning. (Note: if this really is to be anti reductionism, the position had better be that there is no way whatsoever of deriving meaning facts from nonmeaning facts, not just that there are ways of formulating meaning facts that do not admit of reduction.) Thus, for instance, Paul Horwich denies that there is any reductive substitution for ‘F-ness’ in the sentence ‘‘‘Plus’’ means F-ness’; but he still claims that meaning facts are reducible to facts about use. As he correctly says, this is a rejection of the nonreductionist position. (See Horwich 1998).

An obvious difficulty with this antireductionist approach concerns how to fit it into a naturalistic world picture. Naturalism has been understood by many to require that every fact is ultimately reducible to a fact of natural science. This general issue of naturalistic reducibility is an enormous one, which cannot be pursued here. Clearly the success of a anti reductive response to the rule-following worries will depend on the success of anti reductive approaches more generally. However, the worry can be somewhat lessened by pointing out that whilst anti reductionists reject the idea that meaning facts are reducible to nonmeaning facts, it is not obvious that they need reject the idea that they super ene on natural facts. Reduction requires that, for every meaning fact, a corresponding nonmeaning fact can be given. Supervenience requires only the weaker theory that the class of meaning facts is somehow made true by the class of nonmeaning facts. That is, someone who embraces supervenience without reduction will accept that nonmeaning facts (in particular, facts about usage, belief, and the like) make true the meaning facts, in the sense that there could not be a change in the meaning facts without a change in the nonmeaning facts. Whether such a picture can really be made good, however, remains to be seen. (There is a gesture towards such a picture in McDowell 1984, p. 348; for a fuller discussion of supervenience of meaning on use, without reduction, see Williamson 1994, pp. 205–9.)

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