Friction check: Naur's rule-inexpressibility argument does not by itself bind program theory to humans
Note: kb/notes/naur-binds-theory-to-humans-via-premise-that-machines-follow-rules.md Central claim (one sentence): Even if Naur establishes that program theory cannot be expressed as rules, human exclusivity follows only with an independently warranted premise that excludes every eligible nonhuman theory-holder.
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Verdict: SURVIVES The claim asks rule-inexpressibility, agnosticism about whether a current LLM possesses a program's theory, and the non-entailment of human exclusivity to hold at once. They can coexist: limiting what Naur's premise entails neither denies that premise nor supplies a nonhuman theory-holder.
Signal — thinnest joints
- “Following a rule can itself be done well or badly, so an intelligence-as-rule-following account requires further rules for following the first rules” — UNSUPPORTED — Variation in how well a rule is followed does not by itself require a distinct meta-rule. The regress also needs the unstated premise that a rule-complete account must represent every standard of correct rule application as another rule.
- “The essay also makes broader person-bound claims … Those claims may provide additional exclusions” — THIN — Calling theory a programmer's mental possession and assigning relevance to a programmer locates the capacity in the humans under discussion, but it does not exclude a nonhuman bearer unless the person-bound language is independently accepted as exhaustive. The note recognizes that independence but does not show how these descriptions could establish it.
- “The case shows that the supplied artifact package did not convey enough program-specific understanding to this successor group” — THIN — The successor group's structure-destroying proposals are evidence of failed exercise, but the inference treats that performance as evidence of insufficiently conveyed understanding and accepts the original group's structural judgment as the standard. The note's restriction to this group and package prevents the inference from carrying more than the case supports.
- “Read alongside Naur's account of theory possession, the case suggests three necessary tests” — THIN — Program-specific acquisition and repeated competent exercise follow from the capacities the note attributes to theory possession, but the compiler case does not establish that coherent modification always depends on an unregenerable decision premise. That middle test holds only under its stated conditional and gets its broader force from the linked recovery-test note, not from this case.
- “Even if this inexpressibility claim succeeds, it rules out only a rule-complete account of the judgment. It does not identify the species of every possible bearer of the capacity” — HOLDS — A constraint on how a capacity can be constituted does not classify all entities capable of bearing it. Human exclusivity therefore needs a further exclusionary premise, independently of whether any actual nonhuman meets Naur's capacity conditions.
For the human
Look first at the hidden premise that turns variable-quality rule application into an infinite regress of meta-rules; the note's central missing-premise diagnosis survives without that step, but its account of what Naur has established does not yet concretize the step.