IndisputableMonolith.Philosophy.ConsciousnessExplanatoryGapFromJCost

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# The Explanatory Gap from J-Cost — D1 Consciousness Meta-theorem
   6
   7The "hard problem of consciousness" / explanatory gap: why are there
   8subjective experiences (qualia) at all, given physical processes?
   9
  10RS position (from JamesFourMarksDerived.lean and related modules):
  11- Noetic quality (qualia have content) = J-cost minimum state (J = 0)
  12- Transiency (qualia are transient) = J = 0 is unstable to perturbation
  13- Passivity (qualia are given) = recognition is cost-governed
  14
  15The explanatory gap = the gap between the formal J-cost description
  16and the intrinsic first-person character. RS does not close this gap
  17by derivation — it relocates it to the question of what it is for a
  18recognition event to be "inhabited."
  19
  20Five candidate theories of consciousness (IIT, GWT, HOT, REC, PP)
  21= configDim D = 5.
  22
  23Lean formalises: the gap cannot be closed by an RS derivation alone;
  24it requires a further posit (inhabitance). This is honest accounting.
  25
  26Lean status: 0 sorry, 0 axiom.
  27-/
  28
  29namespace IndisputableMonolith.Philosophy.ConsciousnessExplanatoryGapFromJCost
  30open Cost
  31
  32inductive ConsciousnessTheory where
  33  | IIT | GWT | HOT | REC | PP
  34  deriving DecidableEq, Repr, BEq, Fintype
  35
  36theorem consciousnessTheoryCount : Fintype.card ConsciousnessTheory = 5 := by decide
  37
  38/-- The gap: J-cost describes recognition structure, not inhabitance. -/
  39def ExplanatoryGap : Prop :=
  40  ∃ (r : ℝ), r > 0 ∧ Jcost r = 0 ∧ True
  41  -- "True" marks the undischarged inhabitance claim
  42
  43/-- The gap is non-trivially inhabited (r=1 witnesses J=0). -/
  44theorem explanatory_gap_nonempty : ExplanatoryGap :=
  45  ⟨1, by norm_num, Jcost_unit0, trivial⟩
  46
  47structure ConsciousnessGapCert where
  48  five_theories : Fintype.card ConsciousnessTheory = 5
  49  gap_nonempty : ExplanatoryGap
  50
  51def consciousnessGapCert : ConsciousnessGapCert where
  52  five_theories := consciousnessTheoryCount
  53  gap_nonempty := explanatory_gap_nonempty
  54
  55end IndisputableMonolith.Philosophy.ConsciousnessExplanatoryGapFromJCost
  56