general_self_ref_impossible
plain-language theorem explainer
General self-referential queries are impossible in Recognition Science because the correctness and negation-encoding conditions on a query q force RSStab(q.config) to be equivalent to its own negation. Researchers formalizing cost-minimization accounts of physical closure cite the result to reclassify Gödel sentences as non-configurations outside the ontology. The proof assumes existence of q, composes the two biconditionals into a single contradictory equivalence, and derives an immediate falsehood by case analysis on stabilization.
Claim. No real number $c$ and proposition $A$ exist such that $A$ is equivalent to the negation of RSStab$(c)$ and RSStab$(c)$ is equivalent to $A$.
background
The Gödel Dissolution module translates self-reference into stabilization queries under Recognition Science dynamics. RSStab$(c)$ is the predicate that holds exactly when defect$(c) = 0$. A GeneralSelfRefQuery packages a configuration $c$ with a proposition $A$ that the query asserts, together with the two conditions that $A$ is equivalent to the negation of RSStab$(c)$ and that RSStab$(c)$ is equivalent to $A$. The module setting is that Gödel sentences become queries asserting non-stabilization, and the framework shows they cannot possess a fixed point under cost minimization.
proof idea
The term-mode proof assumes such a query $q$ exists. It extracts the correctness equivalence RSStab$(q.config) ↔ q.asserts$ and the encodes_negation equivalence $q.asserts ↔ ¬$RSStab$(q.config)$. Transitivity produces the contradictory biconditional RSStab$(q.config) ↔ ¬$RSStab$(q.config)$. Case analysis on whether RSStab$(q.config)$ holds then yields an immediate falsehood in each branch.
why it matters
The theorem supplies the general-self-ref-impossible field of the GodelDissolutionTheorem structure, which records that self-referential stabilization queries are contradictory and therefore lie outside the RS ontology. It supports the paper's claim that Gödel's theorem does not obstruct physical closure because RS closure requires only a unique cost minimizer rather than arithmetic completeness. In the T0-T8 forcing chain it confirms that self-reference cannot produce a fixed point under the J-cost dynamics.
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