Rule-Following

In the AI Story

The rule-following considerations — developed in Philosophical Investigations §§138–242 and central to Saul Kripke's famous 1982 reading — dissolve the assumption that rules have a content that determines their applications. A rule is not a mental item with an intrinsic correctness-condition. A rule is a regularity in a practice, and the practice is constituted by a community of practitioners whose agreement in application is not itself grounded in a further rule.

The implication is radical and easily missed. Meaning does not reduce to rule-following because rule-following itself does not reduce to rules. Correct application is a human achievement maintained by shared practice. A community of practitioners, embedded in forms of life, reaches agreement on what counts as going on in the same way. This agreement is the ground. There is no deeper ground.

The consequence for AI is sharp and the Ludwig Wittgenstein — On AI volume makes it central. The language model produces outputs that look like rule-following. It continues series, applies grammatical patterns, generates code that compiles. But the model is not following rules in the Wittgensteinian sense. It is producing the statistical residue of rule-following — outputs indexed to patterns that correct rule-following has historically generated.

The distinction matters because it cuts between probability and correctness. The model generates the most probable continuation given its training. In most cases, the most probable continuation coincides with the correct one. But in novel cases, cases at the edges of the training distribution, or cases where the probability was derived from flawed examples, the two diverge. The model cannot recognize the divergence because it does not participate in the practice that makes correctness possible. It produces the appearance of rule-following without the capacity that rule-following requires — the practitioner's understanding of the point of the practice.

Origin

Developed across Philosophical Investigations §§138–242, with further elaboration in the Remarks on the Foundations of Mathematics. Saul Kripke's Wittgenstein on Rules and Private Language (1982) reframed the considerations as a skeptical paradox and made them central to contemporary philosophy of language, though Baker and Hacker disputed this reading.

Key Ideas

Rules underdetermine applications. Any finite series is consistent with infinitely many rules; the rule alone does not specify its next case.

Practice, not interpretation. Correct application is not secured by a mental act of interpreting the rule but by participation in a practice.

Agreement in judgments. The foundation of rule-following is shared agreement — not a meta-rule but a feature of a form of life.

Bedrock. When justifications are exhausted, the practitioner reaches bedrock and says this is simply what I do.

AI's structural gap. Language models produce the statistical residue of rule-following. They do not participate in the practice that makes rules followable.

Debates & Critiques

Whether Kripke's skeptical reading or Baker and Hacker's descriptive reading better captures Wittgenstein is an ongoing dispute. The Ludwig Wittgenstein — On AI volume aligns with the descriptive reading: rule-following is a practice, and language models approximate the practice's products without participating in the practice. Whether better architectures could close this gap is an open question about the limits of statistical learning, not a settled matter.