Ethics Moral State Balanced Opposite Skews

The balance condition

In the Recognition Science framework, a moral state is a projection of the universal ledger, a discrete record of recognition events, onto an individual agent's domain. Each moral state carries a real number called its reciprocity skew, written σ, which measures the log-space imbalance between what the agent gives and receives. A skew of zero means the agent is perfectly neutral in its exchanges. The framework defines two moral states as balanced precisely when their skews sum to zero: σ₁ + σ₂ = 0.

The theorem balanced_opposite_skews states that if two moral states are balanced, then their skews are exact opposites: σ₁ = −σ₂. This is a direct consequence of the definition, proved in the machine-checked library by unfolding the balance condition and applying linear arithmetic. The statement is a formal theorem in the framework's library, meaning it is derived from the definitions with no additional assumptions. It establishes that the balance relation is not a loose or approximate notion; it is an exact arithmetic equality between the two skew values.

This balance condition connects to a broader conservation law in the framework. The valid field of a moral state enforces that global reciprocity skew must be zero for admissible states. A list of moral states is globally admissible when the sum of all their skews is zero. The balance relation between two states is the simplest case of this conservation: two states balance exactly when their combined skew cancels out. The framework also proves that the identity transformation preserves admissibility and that composing virtues preserves it, so balance is maintained under these operations.

What the theorem does not claim is important. It does not assert that any two states with opposite skews are morally equivalent, nor does it say that balance is sufficient for any ethical judgment. It only establishes the arithmetic consequence of the balance definition. The theorem does not prove that balanced states exist, nor does it specify what actions an agent should take. It is a structural fact about the framework's definitions, not a prescription for behavior.

/-- Balanced states have opposite skews -/
theorem balanced_opposite_skews {s₁ s₂ : MoralState}
  (h : MoralState.balanced s₁ s₂) :
  s₁.skew = -s₂.skew := by
  unfold MoralState.balanced at h
  linarith

/-- Two moral states are balanced if their skews sum to zero -/
def balanced (s₁ s₂ : MoralState) : Prop :=
  s₁.skew + s₂.skew = 0

/-- A collection of moral states is globally admissible if total skew is zero -/
def globally_admissible (states : List MoralState) : Prop :=
  total_skew states = 0

What this page does not claim

The theorem does not assert that balanced states are morally equivalent or that balance is sufficient for ethical judgment. The theorem does not prove that balanced states exist or specify what actions an agent should take. The balance condition is a definitional choice, not an empirical observation about human morality.

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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