SelfRefQuery

formal source

  70
  71    Formally: c is a SelfRefQuery if there exists a "decoder" function
  72    that maps c to the proposition ¬Stabilizes(c). -/
  73structure SelfRefQuery where
  74  /-- The configuration -/
  75  config : ℝ
  76  /-- The self-referential property: c encodes "I don't stabilize" -/
  77  self_ref : (defect config = 0) ↔ ¬(defect config = 0)
  78
  79/-- **THEOREM 1**: Self-referential stabilization queries are contradictory.
  80
  81    If c encodes "c ⟺ ¬Stab(c)", then assuming c has any definite
  82    stabilization status leads to contradiction.
  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 :