Following a Rule

1. The Puzzle

Ask someone to continue the series 2, 4, 6, 8 and they will write 10 without hesitation.¹ Yet nothing in the four numbers already given forces that answer. This is the puzzle Wittgenstein presses in the Philosophical Investigations: how can a rule settle in advance what counts as following it?

A rule is learned inside a language-game, not read off a formula. Compare the earlier essay on meaning, where the same thought appears.

2. Interpretations

2.1. The regress

If every application of a rule needed an interpretation, the interpretation would need one too. Wittgenstein’s answer:

There is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call “obeying the rule” and “going against it” in actual cases.²

2.2. A formal version

Write the rule as a function $f(n) = 2n$. The first four values fix $f(1), \dots, f(4)$, but infinitely many functions agree on them, for instance

which gives $g(5) = 34$ instead of $10$.

3. Practice

What fixes the rule is a shared practice: training, correction, and agreement in what we do. Several language-games can share a rule without any one of them defining it. The practice has three parts:

• learning from examples,
• being corrected by others,
• agreeing in our reactions.

Such a practice is what Wittgenstein calls a custom.

Works Cited

• Kripke, Saul A. Wittgenstein on Rules and Private Language. Harvard UP, 1982.
• Wittgenstein, Ludwig. Philosophical Investigations. Translated by G. E. M. Anscombe, Blackwell, 1953.