self_ref_query_impossible

formal source

  83
  84    This is the heart of the Gödel dissolution: such c cannot exist
  85    as consistent configurations. -/
  86theorem self_ref_query_impossible : ¬∃ q : SelfRefQuery, True := by
  87  intro ⟨q, _⟩
  88  -- q.self_ref says: (defect config = 0) ↔ ¬(defect config = 0)
  89  -- This is impossible: P ↔ ¬P has no model
  90  have h := q.self_ref
  91  -- Assume defect config = 0
  92  by_cases hd : defect q.config = 0
  93  · -- If defect = 0, then by self_ref, ¬(defect = 0)
  94    have : ¬(defect q.config = 0) := h.mp hd
  95    contradiction
  96  · -- If defect ≠ 0, then by self_ref.symm, defect = 0
  97    have : defect q.config = 0 := h.mpr hd
  98    contradiction
  99
 100/-- **COROLLARY**: No consistent configuration can be a self-referential
 101    stabilization query. Such "configurations" are syntactically expressible
 102    but ontologically empty. -/
 103theorem self_ref_not_configuration :
 104    ∀ c : ℝ, ¬((defect c = 0) ↔ ¬(defect c = 0)) := by
 105  intro c h
 106  by_cases hd : defect c = 0
 107  · exact (h.mp hd) hd
 108  · exact hd (h.mpr hd)
 109
 110/-! ## The Extended Analysis: RSTrue, RSFalse, and Outside -/
 111
 112/-- RS-truth predicate (stabilization). -/
 113def RSStab (c : ℝ) : Prop := defect c = 0
 114
 115/-- RS-falsity predicate (divergence). -/
 116def RSDiverge (c : ℝ) : Prop := ∀ C : ℝ, defect c > C