GodelDissolutionTheorem

formal source

 209    These are different claims about different targets.
 210    Gödel constrains provability; RS constrains selection.
 211    Orthogonal. -/
 212structure GodelDissolutionTheorem where
 213  /-- Self-referential queries are impossible -/
 214  self_ref_impossible : ¬∃ q : SelfRefQuery, True
 215  /-- General self-ref queries are impossible -/
 216  general_self_ref_impossible : ¬∃ q : GeneralSelfRefQuery, True
 217  /-- Every real config has definite status -/
 218  definite_status : ∀ c : ℝ, RSStab c ∨ ¬RSStab c
 219  /-- RS closure is about unique minimizer, not arithmetic -/
 220  rs_closure_meaning : ∃! x : ℝ, RSExists x
 221
 222/-- The Gödel dissolution theorem holds. -/
 223theorem godel_dissolution_holds : GodelDissolutionTheorem := {
 224  self_ref_impossible := self_ref_query_impossible
 225  general_self_ref_impossible := general_self_ref_impossible
 226  definite_status := stab_decidable
 227  rs_closure_meaning := rs_exists_unique
 228}
 229
 230/-! ## Why Gödel Doesn't Apply -/
 231
 232/-- Gödel's theorem requires:
 233    1. A consistent formal system F
 234    2. Effective axiom enumeration
 235    3. Ability to express arithmetic and provability predicate
 236
 237    RS sidesteps by:
 238    - Not being primarily a proof system (selection dynamics)
 239    - Truth is stabilization, not Tarskian satisfaction
 240    - No external model needed (truth is internal to dynamics) -/
 241structure GodelRequirements where
 242  formal_system : Type