Wittgenstein, Ludwig Josef Johann (1889–1951)

10. Rule-following

By ‘rule’ Wittgenstein does not mean an abstract standard according to which some act may be judged right or wrong. Rather he means a concrete item, such as a noise, mark or gesture, which is presented to a person and by attending to which they direct their behaviour, the link between rule and response being learned and conventional. An enormous number of human activities can be seen as instances of rule-following. The activities include imitating the gestures and noises which others make, copying shapes, converting marks into noises as in reading music, chanting the number sounds in sequence, and so on. More generally, both nonverbal behaviour in response to verbal instruction (fetching a book when told to do so) and also producing linguistic reports (where the world itself is the guide and the utterance is the response) may be described as rule-following. Rule-following is thus at the heart of linguistic competence. If we further accept that coming to use a rich and expressive language is an indispensable part of coming to grasp complex concepts and to make reflective judgments, then rule-following is also at the heart of our lives as thinking creatures.

It is generally agreed that Wittgenstein has telling negative points to make about one attractive but misleading picture of rule-following. On this picture, to understand a rule, for example, to grasp what is meant by ‘Add two’, it is necessary and sufficient to have a certain sort of item, an image, feeling or formula, occur in the mind when the instruction is heard. For example, having a mental image of two blocks appearing at the end of a line of blocks is the sort of thing which might be imagined to constitute understanding ‘Add two’. This image is supposed to do two things. First, it helps bring about that the person goes on to produce a particular response, for example, saying ‘Eight’ if the previously given number was six; second, it sets a standard by which that response can be judged correct or incorrect.

But the picture will not do. A person might have such an image while responding to ‘Add two’ as if it meant ‘Multiply by two’. Moreover the person’s behaviour (the regular patterns of action, what seems to be regarded as a mistake, and so on) could show that for them, ‘Add two’ actually means ‘Multiply by two’. So images guarantee neither subsequent behaviour nor the appropriateness of a particular standard of assessment.

What the case makes us see is that an image, feeling or formula is merely another rule-like object (that is, a potential vehicle of meaning) rather than the meaning itself. An item is not automatically a self-interpreting sign, that is, one which fixes and enforces a certain reading of itself, simply in virtue of existing in the mind rather than in the outer public world. So images and the like are not sufficient for understanding; but neither are they necessary, since in many cases they do not occur. Typically when someone responds to everyday and familiar language they just act unhesitatingly and spontaneously, without consulting any inner item.

To teach someone to follow a rule, for example, to understand ‘Add two’, we put them through a finite amount of training, primarily by working through examples of adding two. These examples may appear to be another resource for pinning down meaning. But being only finite in number, they are bound to have more than one feature in common. Thus they do not themselves determine a unique interpretation for the sign we associate with them. A learner might exhibit a future bizarre divergence from what is expected, for instance by saying that adding two to 1000 yields 1004. And if this occurred it would suggest that they had all along been struck by some feature other than the one intended.

The central point here is that, for there to be meaning, the rule-followers must have fixed on one rather than another of the various similarities between the teaching examples and have associated it with the rule, that is, with the mark or sign to which they respond. ‘The use of the word ‘‘rule’’ and the use of the word ‘‘same’’ are interwoven’ (1953: §224). But neither the examples nor the rule itself determine which similarity this is; and imagined inner surrogates, in which we would like to see the relevant resemblance encapsulated, turn out to be equally inefficacious.

These reflections do not just undermine one picture of the psychology of understanding. They are also relevant to the metaphysics of the Tractatus. If the world consisted of intrinsically articulated facts as envisaged in the Tractatus, then there would exist items, namely the simple objects, which would fix the one and only absolute standard of similarity. If there is a simple which is a common element in two separate facts then there is a basic real resemblance between those facts; if not, not. Every other real resemblance which can be meaningfully labelled, for example, by the predicates of everyday language or science, must be founded in simples. A putative linguistic expression which is not tied to some definite combination of simples is, on the Tractatus view, an expression without meaning which is merely randomly applied. Further, as we saw earlier, a simple is the kind of thing which, when apprehended, must be apprehended as it is. So representing a simple, whether by a direct cognition of it or by having in mind something which encapsulates its nature, is to be aware of a self-interpreting item, something which dictates what is to count as ‘the same’. But this sort of confrontation is what the rule-following considerations suggest to be unintelligible.

Thus the discussions of §§143–242 can be seen as interweaving with and reinforcing those of §§1–88. The whole undermines not only the idea of closeness of fit between a Tractatus world and everyday language, but the underlying conception of that world itself, namely as already determinately articulated into facts by simples which we can apprehend (see Meaning and rule-following §§1–2).