Ethics Moral State Neutral Self Balanced

The meaning of neutrality

In the Recognition Science framework, a moral state is a mathematical snapshot of an agent's ethical position: it records the agent's local reciprocity skew and available energy, projected from the universal ledger, a discrete record of recognition events. The framework models ethics as grounded in physics rather than in arbitrary preferences. A moral state is neutral when its reciprocity skew, the log-multiplier imbalance between giving and receiving, is exactly zero. The theorem neutral_self_balanced establishes that any neutral moral state is balanced with itself, meaning its skew plus its own skew equals zero. This is a formal proof in the machine-checked library of formal theorems, derived directly from the definitions of neutral and balanced.

The proof itself is a simple algebraic identity: if a state's skew is zero, then adding zero to zero gives zero. The theorem is a foundational lemma within the framework's ethics module, not an empirical claim about human morality. It does not assert that neutrality is morally good, that balanced states are virtuous, or that any particular action is right or wrong. It only states a formal property of the framework's definitions. The framework's broader ethical structure includes additional concepts like virtue and admissibility, but this theorem alone does not address them.

What the theorem does provide is a precise, machine-checked starting point for ethical analysis within the framework. It ensures that the concept of neutrality is internally consistent: a neutral state is its own balance partner. This is a necessary condition for the framework's conservation law, which requires that admissible worldlines have zero total reciprocity skew. The theorem is a small but essential piece of the framework's claim that morality can be grounded in a physical-like ledger of recognition events.

/-- Neutral state is balanced with itself -/
theorem neutral_self_balanced (s : MoralState)
  (h : MoralState.neutral s) :
  MoralState.balanced s s := by
  unfold MoralState.neutral MoralState.balanced at *
  simp [h]

/-- A moral state is neutral if its local skew is zero -/
def neutral (s : MoralState) : Prop :=
  s.skew = 0

/-- A moral state represents an agent's projection of the universal ledger.

    This structure connects individual ethical analysis to the underlying
    recognition ledger, ensuring morality is grounded in physics rather than
    arbitrary preferences.
-/
structure MoralState where
  /-- Underlying ledger state (contains Z-patterns, channels, global phase, time) -/
  ledger : LedgerState

  /-- Bonds controlled by this agent (subset of ledger edges).
      These bonds define the agent's domain for action and responsibility. -/
  agent_bonds : Finset BondId

  /-- Agent's local reciprocity skew σ (log-space, must sum to zero globally).

      σ measures the log-multiplier imbalance in exchanges:
      - σ > 0: agent is extracting (moral debt)
      - σ < 0: agent is contributing (moral credit)
      - σ = 0: agent is balanced (reciprocity conserved)

      Global constraint: Σ_i σ_i = 0 (enforced by `valid` field)
  -/
  skew : ℝ

  /-- Recognition cost available for transformations (from RecognitionCost).

      This tracks the J-cost capacity for ethical actions. Virtues that
      transform states must respect positive energy constraints.
  -/
  energy : ℝ

  /-- Proof: global reciprocity net skew σ = 0 (admissibility condition).

      This enforces the conservation law from Morality-As-Conservation-Law.tex:
      admissible worldlines live on the manifold where total net skew is zero.
  -/
  valid : net_skew ledger = 0

  /-- Proof: energy is positive (physical viability).

      Ensures the state is physically realizable. Negative energy would
      violate the Positive Cost principle.
  -/
  energy_pos : 0 < energy

What this page does not claim

The theorem does not claim that neutrality is morally good or desirable. The theorem does not claim that balanced states are virtuous. The theorem does not claim that any particular action is right or wrong.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Ethics/MoralState.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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