Foundation Universal Forcing Ethics Realization Ethics Realization

The ethical ledger

In the Recognition Science framework, ethicsRealization is a formal declaration that models ethical progress as a simple count. The carrier of this model is the set of natural numbers, where each number represents one morally meaningful improvement step. The cost of moving between two steps is defined as 0 if they are identical and 1 otherwise. This is a deliberately minimal structure: it establishes only the identity and step comparison needed by the broader Universal Forcing framework, not a full ethical theory.

The declaration proves two basic properties of this cost function. First, the cost of moving from a step to itself is always zero, which is immediate from the definition. Second, the cost is symmetric: the cost from step a to step b equals the cost from b to a. Both are proved in the machine-checked library of formal theorems. The declaration also provides an interpretation from the framework's internal logic numbers to these improvement steps, and an equivalence between the arithmetic of this realization and the natural numbers.

What ethicsRealization does not claim is substantial. It does not define what constitutes a morally meaningful improvement step; that content is left entirely unspecified. It does not provide a ranking of ethical states, a theory of obligation, or any guidance for moral decision-making. The cost function is not a measure of ethical value or goodness; it is only a structural device for counting distinct steps. The framework explicitly notes that the domain theory of ethics is not rebuilt here, only the identity and step comparison structure needed by Universal Forcing.

In plain terms, this declaration is a technical building block, not a moral philosophy. It says: if you can identify distinct morally meaningful improvements, then the framework can count them and compare them in a symmetric way. The philosophical question of what counts as an improvement is left entirely open, and the declaration makes no attempt to answer it.

/-- Ethical realization as morally meaningful improvement count. -/
def ethicsRealization : LogicRealization where
  Carrier := MoralImprovementStep
  Cost := Nat
  zeroCost := inferInstance
  compare := ethicsCost
  zero := 0
  step := Nat.succ
  Orbit := LogicNat
  orbitZero := LogicNat.zero
  orbitStep := LogicNat.succ
  interpret := ethicsInterpret
  interpret_zero := by rfl
  interpret_step := by
    intro n
    show LogicNat.toNat (LogicNat.succ n) = Nat.succ (LogicNat.toNat n)
    rfl
  orbit_no_confusion := by intro n h; exact LogicNat.zero_ne_succ n h
  orbit_step_injective := LogicNat.succ_injective
  orbit_induction := by
    intro P h0 hs n
    exact LogicNat.induction (motive := P) h0 hs n
  orbitEquivLogicNat := Equiv.refl LogicNat
  orbitEquiv_zero := rfl
  orbitEquiv_step := by intro n; rfl
  identity := ethicsCost_self
  nonContradiction := ethicsCost_symm
  excludedMiddle := True
  composition := True
  actionInvariant := True
  nontrivial := by
    refine ⟨1, ?_⟩
    simp [ethicsCost]

def ethicsCost (a b : MoralImprovementStep) : Nat :=
  if a = b then 0 else 1

theorem ethicsCost_symm (a b : MoralImprovementStep) : ethicsCost a b = ethicsCost b a := by
  by_cases h : a = b
  · subst h; simp [ethicsCost]
  · have h' : b ≠ a := by intro hb; exact h hb.symm
    simp [ethicsCost, h, h']

@[simp] theorem ethicsCost_self (a : MoralImprovementStep) : ethicsCost a a = 0 := by
  simp [ethicsCost]

What this page does not claim

This declaration does not define what constitutes a morally meaningful improvement step. The cost function is not a measure of ethical value or goodness. The declaration provides no theory of obligation or guidance for moral decision-making.

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/Foundation/UniversalForcing/EthicsRealization.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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