Premise decomposition: 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 Register: claim Central commitment (one sentence): Naur's inference from the inexpressibility of program theory to its being bound to humans depends on an unargued exhaustive partition between human insight and formulable rule-following, and a learned nonhuman interpreter outside that partition leaves only acquisition, retention, and dispositional conditions rather than a human-only conclusion.

Premises and counterexamples

  1. A deployed LLM is outside “what can be determined by rules” in Naur's sense because its similarity criteria were learned rather than written by a person. — DOUBTFUL — A deployed model's outputs are produced by a finite executable architecture and parameter tensor, while Naur introduces computing as formal symbol manipulation and later says the judgment is outside everything “determined by rules.” The absence of hand-authored semantic criteria does not settle whether the implemented decision function belongs to that broader rule pole; if it does, the note's proposed third category disappears. — GLOBAL — instance
  2. Naur's exhaustive human-insight/formulable-rule partition is the premise through which his human-binding conclusion is reached, rather than one of several independent anthropocentric restrictions in the essay. — DOUBTFUL — Naur also introduces theory as “knowledge a person must have,” says relevance to the world can only be decided by someone who understands it and must be contributed by the programmer, and calls theory by its nature the programmer's mental possession. Those passages do not establish human exclusivity, but they supply person-bound premises not obviously reducible to the machine-as-rule-follower partition, denting the note's identification of that partition as the sole bridge. — GLOBAL — instance
  3. Acquisition from examples rather than direct human specification is sufficient to distinguish a recognizer from a follower of formulable rules. — DEFEATED — A decision tree induced from labelled examples is acquired through training rather than by a person choosing its predicates, yet the learned tree is an explicit finite rule set; acquisition history therefore does not determine whether the resulting recognizer follows formulable rules. The note can retain its trained-interpreter witness only by adding a separate representational or behavioral distinction. — LOCAL — instance
  4. Inexpressibility in terms of criteria or rules does not by itself entail that only humans can possess the inexpressible capacity; some additional premise must exclude every eligible nonhuman, non-rule candidate. — HOLDS — The active hunt considered Naur's person-centered definition of theory and his assertions about programmers, but each functions as just such an additional human-exclusion premise; no case made the human-only conclusion follow from rule-inexpressibility alone.
  5. Naur supplies no separate argument that the relevant similarity judgment is noncomputable or unrealizable by every formally implemented interpreter. — HOLDS — The source repeatedly asserts that the judgment cannot be reduced to criteria or determined by rules and describes computers as formal symbol manipulators, but the active hunt found no computation-level argument connecting those claims to every learned implementation; the broader human-only assertion is a conclusion, not that missing argument.
  6. Showing that Naur's stated premises leave an eligible nonhuman interpreter unexcluded is enough to contest the argument's reach without first showing that a current LLM actually possesses a program's theory. — HOLDS — A random generator or fixed lookup table would not be an eligible interpreter because it lacks the explanatory and modification capacities under discussion, but the hunt found no need to establish actual theory possession once the witness is limited to a coherent candidate whose competence remains an open empirical question.
  7. A theory of a particular program requires program-specific acquisition, and general language-and-world competence plus access to artifacts does not by itself establish that acquisition. — HOLDS — The hunt considered models trained on the repository and very small self-explanatory programs, but the former adds program-specific acquisition and the latter can make acquisition easy rather than unnecessary; neither makes general competence alone sufficient for possession of this program's theory.
  8. If a decision premise is required for coherent modification and the interpreter cannot regenerate it from available artifacts and general knowledge, some component of the claimed theory-holding composite must retain or otherwise supply it. — HOLDS — On-demand advice, additional training, and an external decision record can each supply the premise, but each adds a retaining or supplying component to the composite; the active hunt found no case in which a premise remains both necessary and unavailable while the composite reliably uses it.
  9. Possession of a program's theory is a disposition to explain, justify, and respond coherently across later demands, so one successful extension does not establish possession. — HOLDS — A memorized patch or lucky completion can succeed once without supporting a novel later modification or an explanation of the structure; active hunting found no single occasion that demonstrates the cross-occasion capacity as stated.
  10. Naur's reported transfer failures do not exclude every retained-rationale or trained-interpreter route not tested in those cases. — HOLDS — The compiler case used one documented artifact set and successor group, and the fault-diagnosis case reports what its programmers could conceive; the active hunt found no comparison against decision-time rationale selected for a specified interpreter, so the cases cannot eliminate that untested route.

For the human

Look first at premise 1: until “formulable rules” is separated from a learned model's finite executable implementation, the LLM witness has not been shown to stand outside Naur's machine pole.