is_implies_ought

formal source

 144    - Moral progress = defect decrease
 145
 146    This is not a logical gap but an identification via cost semantics. -/
 147theorem is_implies_ought :
 148    -- IS (structural facts)
 149    (∀ x : ℝ, 0 < x → 0 ≤ defect x) ∧
 150    (∀ x : ℝ, 0 < x → (defect x = 0 ↔ x = 1)) ∧
 151    -- OUGHT (derived from IS via cost identification)
 152    -- Good = zero defect = x = 1
 153    (∀ a : EthicalAction, MorallyGood a ↔ a.after = 1) ∧
 154    -- Better = lower defect
 155    (∀ a b : EthicalAction, MorallyBetter a b ↔ moral_cost a ≤ moral_cost b) := by
 156  refine ⟨fun x hx => defect_nonneg hx, fun x hx => defect_zero_iff_one hx, ?_, fun _ _ => Iff.rfl⟩
 157  intro a
 158  constructor
 159  · intro h
 160    unfold MorallyGood moral_cost at h
 161    exact (defect_zero_iff_one a.after_pos).mp h
 162  · intro h
 163    unfold MorallyGood moral_cost
 164    rw [h]
 165    exact defect_at_one
 166
 167/-- **Theorem (Hume's Guillotine Dissolved)**:
 168    Hume's claim "no 'ought' from 'is'" is dissolved.
 169    In RS, the IS-OUGHT gap is bridged by identifying:
 170
 171        good(x) = (defect(x) = 0)
 172
 173    This identification is not arbitrary — it is forced by the RS framework:
 174    stable configurations (RSExists) are exactly those with zero defect.
 175    And "stable" in RS is the meaning of "real" and "good." -/
 176theorem hume_guillotine_dissolved :
 177    -- The moral ideal exists (is achievable)