Friction check: Naur binds program theory to humans through the premise that machines only follow rules

Note: kb/notes/naur-binds-theory-to-humans-via-premise-that-machines-follow-rules.md Central claim (one sentence): Naur's conclusion that inexpressible program theory is bound to humans requires an exhaustive partition between human insight and formulable rule-following, so his argument alone cannot exclude a learned nonhuman interpreter whose judgments fall outside that partition.

Filter

Verdict: SURVIVES The note asks rule-inexpressibility, the need for an additional human-binding premise, and agnosticism about an LLM's actual competence to hold at once. These properties can coexist because the claim limits the reach of Naur's inference rather than claiming that an LLM possesses a program's theory.

Signal — thinnest joints

  1. “They were acquired from examples … So an LLM does not sit at either pole of Naur's partition” — UNSUPPORTED — Acquisition from examples does not establish that the resulting judgments cannot be determined by a formulable procedure. The note moves from criteria that no person supplied during training to criteria that cannot be formulated without defending that change.
  2. “Nor does it help to note that an LLM is a computable procedure. Naur's argument is about expressibility … not about computability” — UNSUPPORTED — Naming the distinction does not show that it applies here: a computable model has a formulable implementation that determines its outputs, and the note gives no boundary between those implementation rules and the “criteria” excluded by Naur's argument.
  3. “The very act of adhering to rules can be done more or less intelligently … What stops the regress is a grasp of similarity … [which] cannot be expressed in terms of criteria” — THIN — The regress supports the need for judgment in applying rules, but it does not establish that the relevant similarity judgment is itself impossible to formulate. The faces, tunes, and wine analogy restates that stronger claim rather than deriving it.
  4. “So a competent interpreter plus text is not thereby a theory-holder, and any composite that claims to be one owes three things” — THIN — The compiler handoff shows that one rich artifact set did not suffice for one successor group. It does not by itself establish all three requirements for every composite, especially the requirement for retained premises that the interpreter cannot regenerate.
  5. “The 'but' carries an inference from not expressible to human. It is valid only if the candidates for holding a theory are exhausted by two kinds” — HOLDS — Rule-inexpressibility alone cannot yield human-only possession unless some further premise excludes every nonhuman, non-rule candidate; this joint supports the note's missing-premise diagnosis even if the proposed LLM witness remains unestablished.

For the human

Look first at the unargued shift from learned rather than hand-written criteria to criteria outside formulable computation; the note's LLM counterexample depends on that shift, while its narrower missing-premise diagnosis does not.