Premise decomposition: Irreducibility to rules bounds text alone, not text plus an interpreter

Note: kb/notes/irreducibility-to-rules-bounds-text-alone-not-text-plus-interpreter.md Register: claim Central commitment (one sentence): At the undeclared and therefore universal modality, an argument that a capacity is irreducible to any limited rule set excludes finite text acting as the decider but does not by itself exclude retained text supplying premises to a separate world-competent interpreter, so Naur's human-only location requires an independent substrate premise.

Premises and counterexamples

1. Any argument that a capacity is irreducible to a limited rule set ranges only over a finite text's decision content, not over the end-to-end effective procedure formed by text plus interpreter. — DEFEATED — Take the capacity to decide, for every program and input, whether that program halts. The diagonal argument rules out every effective decider, including a system whose finite retained text is consumed by any computable interpreter; adding the interpreter does not move the composite outside the argument's quantified target. The reading rule therefore needs to be restricted to artifact-local irreducibility arguments rather than stated for irreducibility arguments without qualification. — GLOBAL — instance
2. For the Naur-to-LLM application, a deployed LLM's case judgment lies outside what "a limited set of criteria or rules" denotes rather than constituting another finite effective rule system. — DOUBTFUL — A fixed model's weights, inference program, and decoding procedure form a finite computable specification. If Naur's "rules" means effective procedures, that interpreter remains inside the prohibited class; if it means explicit criteria a person can state and consciously apply, learned distributed judgment may lie outside it. The note does not choose between those meanings, although the choice determines whether Naur's premise reaches the proposed composite. — GLOBAL — instance
3. When an executor supplies no case judgment, a finite text that decides the relevant cases is functionally a finite rule or criterion specification. — HOLDS — Executable code, a compressed lookup table, and a self-modifying program were the strongest apparent counterexamples, but each requires an execution semantics; if that executor contributes only mechanical semantics, the effective decider remains finitely specified, and if it contributes world-sensitive judgment the system has become the composite that the premise distinguishes.
4. When an interpreter genuinely contributes world knowledge and case judgment not determined by the retained text, text-as-input and text-as-decider are different causal arrangements. — HOLDS — A human judge applying a written contract and a situated programmer applying retained design rationale both supply discriminations not fixed by the words alone; attempts to collapse the two arrangements either put that judgment back into the text's decision procedure or deny that the interpreter has the stipulated competence.
5. The residue that a competent interpreter cannot supply on its own is always premise-shaped and expressible in retained text, so the text/interpreter division exhausts what the case requires. — DOUBTFUL — A maintenance decision can depend on a project-specific vibration signature learned beside a failing machine: a generally knowledgeable interpreter does not possess that discriminator, while a verbal proposition may not preserve the perceptual exemplar at the fidelity needed for the next case. Such cases require a non-text exemplar, sensor access, or guided participation, so the division can be rescued by limiting it to proposition-shaped residue. — LOCAL — instance
6. Naur's infinite-regress reasoning and similarity examples establish that open-ended program-modification judgment cannot in principle be reduced to any limited rule set. — DOUBTFUL — Finite learned face-verification systems provide a concrete rule-computable treatment of one similarity domain Naur offers as an analogy for criterion-inexpressibility. That does not establish a complete rule system for open-ended program modification, but it defeats the analogy's force as an in-principle demonstration, while the two maintenance cases show insufficiency of the supplied documentation rather than impossibility for every rule-carried representation. — LOCAL — instance
7. Naur supplies no independent conceptual premise that makes program theory human or mental by nature; the human bearer enters only because no non-human interpreter was available in 1985. — DEFEATED — Elsewhere in the essay Naur defines the relevant theory through knowledge a person has, calls it inextricably bound to human beings, and derives programmer status from theory being by its nature each programmer's mental possession. Those premises may themselves be challenged, but their presence is a concrete counterexample to describing the human location as an availability default alone. — LOCAL — instance
8. In 1985 no non-human interpreter actually possessed the open-world and program-specific judgment Naur requires. — HOLDS — Period expert systems and restricted-world language programs were the strongest counterexamples found, but their knowledge and judgments were narrow and predominantly rule-encoded; none supplied the open-ended relevance and modification judgment at issue, so they do not make the operational candidate set nonempty at the stated bar.
9. As a tendency, a program theory's justification capability is predominantly proposition-shaped and writable, its novel-demand similarity capability is predominantly judgment-shaped, and mapping combines the two. — DOUBTFUL — Naur says the final basis of every justification remains direct intuitive knowledge and that selecting which written principles are relevant is itself a judgment. That makes non-propositional judgment ordinary in his own justification population, while the note gives no comparison or rate that says when "largely premise-shaped" has lost predominance. — LOCAL — prevalence

For the human

Look first at premise 1: a computability-style irreducibility argument already reaches a finite text plus any computable interpreter, so the opening commitment needs to name the artifact-local class of irreducibility arguments to which its reading rule applies.