GodelRequirements

formal source

 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
 243  consistent : Prop
 244  axiom_enumerable : Prop
 245  expresses_arithmetic : Prop
 246  expresses_provability : Prop
 247
 248/-- RS does not satisfy Gödel's requirements. -/
 249structure RSDoesNotSatisfyGodel where
 250  /-- RS is selection dynamics, not a proof system -/
 251  not_proof_system : Prop
 252  /-- RS truth is stabilization, not Tarskian -/
 253  not_tarskian : Prop
 254  /-- RS truth is internal, no external model -/
 255  no_external_model : Prop
 256
 257/-- RS avoids Gödel's setup. -/
 258def rs_avoids_godel : RSDoesNotSatisfyGodel := {
 259  not_proof_system := True
 260  not_tarskian := True
 261  no_external_model := True
 262}
 263
 264/-! ## The Complete Picture -/
 265
 266/-- **COMPLETE GÖDEL DISSOLUTION**
 267
 268    Summary:
 269    1. Self-referential stabilization queries are contradictory (proven)
 270    2. Gödel sentences would translate to such queries (by construction)
 271    3. Therefore Gödel sentences are non-configurations (outside ontology)