Rule-following

Rule-following is the puzzle of how a rule can tell you what to do in a case you have never met before. You learn "add 2" from a handful of examples. Nothing in those examples, and nothing in your head, seems to fix what you must write after 1000. Yet you know: 1002. Wittgenstein asks what that knowing consists in, and his answer is that following a rule is not a matter of interpreting it, but of taking part in a practice.

The discussion runs through roughly §138-242 of the Philosophical Investigations, one of the most debated passages in modern philosophy.

What the animation shows

In the animation above a pupil writes the series "+2": 2, 4, 6, and on to 996, 998, 1000. So far, so good. Then he continues: 1004, 1008, 1012. We tell him he went wrong. He looks at us, puzzled, and says that he went on in the same way (§185). Then a signpost appears. A rule, Wittgenstein says, stands there like a signpost (§85). But a signpost does not say whether you should follow it in the direction of the arrow or the opposite one, along the road or across the fields. It guides only because there is a custom of using signposts, a practice in which people are trained to react to them in a certain way (§198).

The pupil is not stupid. The point is that every explanation we gave him, and every example up to 1000, is consistent with what he did. He could have understood "+2" as "add 2 up to 1000, 4 up to 2000", and so on.

The paradox

Wittgenstein states the worry in its sharpest form:

Unser Paradox war dies: eine Regel könnte keine Handlungsweise bestimmen, da jede Handlungsweise mit der Regel in Übereinstimmung zu bringen sei.

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 the rule.

Philosophical Investigations §201

The tempting response is to add an interpretation: "add 2" means "always write the next number but one". But an interpretation is just another rule, which can itself be read in different ways. Interpretations, Wittgenstein says, hang in the air together with what they interpret (§198). Read on in §201 and he says the paradox rests on a misunderstanding: there is a way of grasping a rule which is not an interpretation, but which shows itself in what we call obeying the rule and going against it in actual cases.

A practice, not a private act

That leads to one of the most quoted remarks in the book:

Darum ist ‚der Regel folgen‘ eine Praxis. Und der Regel zu folgen glauben ist nicht: der Regel folgen.

That is why "following a rule" is a practice. And to think one is following a rule is not to follow a rule.

Philosophical Investigations §202

Following a rule, making a report, giving an order, playing a game of chess are customs, uses, institutions (§199). Understanding a sentence means mastering a technique. And at some point justifications run out. Wittgenstein's image for this is a spade hitting rock:

Habe ich die Begründungen erschöpft, so bin ich nun auf dem harten Felsen angelangt, und mein Spaten biegt sich zurück. Ich bin dann geneigt zu sagen: „So handle ich eben.“

Once I have exhausted the justifications, I have reached bedrock, and my spade is turned. Then I am inclined to say: "This is simply what I do."

Philosophical Investigations §217

A little later he adds that he follows the rule blindly (§219). Not carelessly, but without consulting anything further.

Kripke's sceptical reading

In 1982 Saul Kripke published Wittgenstein on Rules and Private Language, which made rule-following famous far beyond Wittgenstein scholarship. Kripke imagines a sceptic who asks how you know that by "plus" you meant addition and not "quus", a function that gives the same results as addition for small numbers but yields 5 for 68 + 57. Nothing in your past behaviour, your mental images or your dispositions seems to settle it. Kripke concludes that there is no fact about a person, considered in isolation, that makes it the case that they mean one thing rather than another.

His Wittgenstein offers a "sceptical solution", modelled on Hume: we cannot say what meaning consists in, but we can describe when we are entitled to say someone means addition. Roughly, when their answers agree with those of the community. Kripke himself said he was presenting Wittgenstein's argument "as it struck Kripke", and readers often call the resulting figure "Kripkenstein".

Why many readers disagree

Many Wittgenstein scholars think Kripke gets him wrong. John McDowell pointed out in 1984 that Kripke stops halfway through §201: Wittgenstein does not accept the paradox, he shows that it comes from thinking every grasp of a rule must be an interpretation. There is no sceptical gap to be bridged. G.P. Baker and P.M.S. Hacker (Scepticism, Rules and Language, 1984) argued that a rule and what accords with it are internally related, and that "practice" means a regular, repeated activity, not necessarily a social one. On their reading even a lifelong Robinson Crusoe could follow rules.

Others, such as Norman Malcolm and Meredith Williams, defend a community reading without Kripke's scepticism: rule-following needs a shared practice and training by others, as §198-199 suggest. So the honest summary is this. Almost everyone agrees that, for Wittgenstein, a rule is not a ghostly rail laid down in advance in the mind (§218). They disagree about whether the practice that replaces it must be shared with others. The Stanford Encyclopedia entry on rule-following maps the debate in detail; the main entry on Wittgenstein places it in his later work.

Why it matters

The argument feeds directly into the private language argument: if believing you follow a rule is not the same as following it, a language whose rules only you could check looks empty. It also underlies Wittgenstein's idea that language rests on shared forms of life, on agreement not in opinions but in what we do.

You meet the problem whenever you teach someone. A child learning to tie shoelaces, a new colleague learning how meetings "work here": at some point you stop explaining and say "like this", and show it again. That is not a failure of explanation. According to Wittgenstein, it is where explanation was always going to end.