The Rule-Following Paradox

The paradox

You have added numbers correctly your entire life. Now someone asks: when you computed 68 + 57, were you doing addition or quaddition? Quaddition is defined as: give the normal sum for any pair of numbers you've encountered before, but give 5 for any pair where either number is larger than you've ever used.

Since you have never added numbers that large before, both rules are consistent with your entire past behavior. Every calculation you've ever done is compatible with quaddition as well as addition. And no matter what you find in your head, previous mental states or images or feelings of confidence, those facts are also consistent with having followed the quus rule all along.

The skeptical conclusion: there is no fact about you, behavioral or mental, that determines which rule you meant. And if there's no such fact for "plus," there's no such fact for any word. Meaning dissolves.

Kripke's skeptical solution

Kripke does not think Wittgenstein accepted the skeptical conclusion. Instead, Kripke attributes to Wittgenstein a skeptical solution: we give up looking for a private, inner fact that fixes meaning, and we locate meaning in social practice instead.

To say you mean addition by "plus" is not to describe a hidden mental state. It is to say that your dispositions fit into a community practice of using "plus" in the standard way, and that the community endorses your answers. Correctness is not a match between your use and some inner state; it is a match between your use and the community's norms.

Wittgenstein's own position

Scholars debate whether Kripke's interpretation is accurate. Wittgenstein himself did not frame the problem as a skeptical paradox to be solved. His treatment in the Philosophical Investigations is more deflationary: we were confused about what it would even mean for a rule to be "in the mind," and the confusion dissolves once we look at how rule-following actually works in practice.

For Wittgenstein, the question "what makes your use correct?" already assumes there must be a hidden fact doing the grounding. His move is to reject the assumption rather than answer the question. Forms of life, shared practical activity, ground meaning, not because they provide a better answer to the skeptic's question, but because they show the skeptic's question was never well-formed.