GodelRequirements
plain-language theorem explainer
The GodelRequirements structure records the four standard conditions under which Gödel's incompleteness theorems apply to a formal system: consistency, effective enumerability of axioms, expressibility of arithmetic, and expressibility of a provability predicate. Recognition Science researchers cite this definition when showing that RS selection dynamics evade the incompleteness obstruction because truth is stabilization under cost minimization rather than Tarskian satisfaction. The definition is a direct packaging of these hypotheses with no附加
Claim. A record consisting of a type $F$ (formal system), a proposition asserting consistency of $F$, a proposition asserting effective enumerability of the axioms of $F$, a proposition asserting that $F$ can express arithmetic statements, and a proposition asserting that $F$ can express a provability predicate.
background
Recognition Science treats truth as stabilization under cost-minimizing dynamics (J-cost on the phi-ladder) rather than model-theoretic satisfaction. The module shows that self-referential stabilization queries have no fixed point: they neither stabilize (RSTrue) nor diverge (RSFalse) and therefore lie outside the ontology entirely. Gödel's theorem is about formal proof systems proving arithmetic sentences; RS is about selection by cost minimization, so the targets differ. The upstream consistent predicate from Backprop defines semantic consistency of a partial assignment with a CNF formula and XOR system as the existence of a total assignment that agrees on known bits and satisfies both.
proof idea
This is a structure definition that directly encodes the four hypotheses listed in the module documentation. No lemmas or tactics are applied; the record simply collects the propositions for later use in arguments about self-reference having no fixed point under RS dynamics.
why it matters
The definition sets up the contrast that lets RS achieve physical closure without Gödel obstruction: RS closure concerns a unique cost minimizer (T6 phi fixed point, T8 D=3) rather than provability of arithmetic truths. It fills the paper proposition that Gödel's theorem does not obstruct physical closure via a cost-theoretic resolution. No downstream uses are recorded, but the structure supports the main claim that self-referential queries are non-configurations.
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