moral_cost
The moral cost of an ethical action is the defect of its resulting configuration. Researchers formalizing objective ethics from Recognition Science cost minimization cite this when ranking actions by ledger stability. It is a direct one-line abbreviation that applies the defect functional to the post-action state.
claimFor an ethical action $a$ with resulting configuration $y$, the moral cost is $J(y)$, where $J$ is the cost function satisfying the Recognition Composition Law and defect$(y) := J(y)$ for $y > 0$.
background
The ObjectiveMoralityStructure module derives objective ethics from J-cost minimization and resolves Hume's guillotine by equating goodness with stability. An EthicalAction is a structure carrying a before configuration and an after configuration, both positive reals. The defect functional, imported from LawOfExistence, equals $J(x)$ and vanishes only at unity.
proof idea
One-line definition that applies the defect function from LawOfExistence to the after field of the EthicalAction structure.
why it matters in Recognition Science
This definition supplies the numerical cost that drives the moral ordering in PH-004. It is used by better_action_exists (improvement always possible until defect zero), ethics_is_objective (deterministic comparisons), and is_implies_ought (the is-ought bridge). It realizes the framework identification that good configurations are exactly those with defect zero, i.e., $x=1$.
scope and limits
- Does not generate or enumerate ethical actions.
- Does not prove that J is the unique possible cost function.
- Does not address multi-agent or cultural extensions.
- Does not derive specific numerical values for defect beyond the J definition.
formal statement (Lean)
77noncomputable def moral_cost (a : EthicalAction) : ℝ := defect a.after
proof body
Definition body.
78
79/-- An action is **morally better** than another if it results in lower defect. -/