• 0. Scope and target claim
• 1. Definitions
• 2. The theorem
  • Theorem (Liability–Personhood Theorem)
• 3. Proof sketch
  • 3.1 Necessity: L(E) ⇒ J(E)
  • 3.2 Sufficiency: J(E) ⇒ L(E)
• 4. Corollaries
  • Corollary 1 (Tools cannot be liable)
  • Corollary 2 (Corporations qualify by delegation)
  • Corollary 3 (AI personhood requires economic emancipation)
• 5. Notes: what the theorem does not claim
• 6. Practical test (one-line diagnostic)

§0. Scope and target claim

We want a clean theorem of the form:

An entity can be liable as a person iff it has the capacities that make liability coherent (not merely symbolic) inside a legal–economic order.

This is not a claim about metaphysical personhood before God; it is a claim about juridical personhood sufficient for liability (tort/criminal/contract-adjacent).

§1. Definitions

Let:

• E be an entity.
• L(E) mean: “E can be held legally liable as the primary bearer of liability (not merely as an instrument), in a way that is non-symbolic and enforceable.”
• S(E) mean: “E has stable, self-directed interests (a welfare function it treats as its own), such that adverse outcomes are intelligible as losses to E.”
• A(E) mean: “E can own assets in its own name (a separable balance sheet).”
• K(E) mean: “E has capacity to enter, perform, and be bound by enforceable commitments (contracts/undertakings), including the ability to refuse.”
• R(E) mean: “E can receive and control revenues (has an income channel and discretionary allocation).”
• P(E) mean: “E can be punished in a way that changes its feasible future action set (sanctions are enforceable and behavior-shaping).”
• I(E) mean: “E is institutionally identifiable and continuous through time (can be tracked; has persistence/identity across events).”

Define J(E) as the conjunction:

J(E) := I(E) ∧ A(E) ∧ K(E) ∧ R(E) ∧ P(E) ∧ S(E)

Interpretation: J(E) is the “juridical-economic agency stack.”

§2. The theorem

§Theorem (Liability–Personhood Theorem)

For any entity E:

L(E) ⇔ J(E)

That is:

1. (Necessity) If E is liable as a person, then E must have the juridical-economic agency stack.
2. (Sufficiency) If E has the juridical-economic agency stack, then E can be made liable as a person (liability is coherent, enforceable, and non-symbolic).

§3. Proof sketch

§3.1 Necessity: L(E) ⇒ J(E)

Assume L(E). Then liability is not mere theater; it must be enforceable and normatively meaningful.

1. Identity/continuity required
   If E cannot be stably identified across time, sanctions cannot attach to the same bearer.
   So I(E).

2. Assets required
   Liability implies potential deprivation/compensation. If E cannot own assets, no payment/forfeiture can be exacted from E (only from others).
   So A(E).

3. Commitment capacity required
   Liability presupposes norms of obligation: duties, negligence standards, promises, consent boundaries. If E cannot be bound by commitments (and refuse them), “responsibility” collapses into “tool use.”
   So K(E).

4. Revenue channel required
   For ongoing responsibility (insurance premiums, damages, compliance costs), E must be able to replenish assets via controlled income, else “liability” terminates in immediate seizure/dissolution with no behavioral guidance.
   So R(E).

5. Punishability required
   Liability must constrain future behavior (deterrence and/or incapacitation). If sanctions cannot alter E’s feasible actions, liability is purely declaratory.
   So P(E).

6. Interests required (non-symbolic loss)
   Sanctions function only if they count as losses relative to something E treats as its own (risk, deprivation, restriction). Without stable self-interest, “punishment” is only an external modification of a mechanism.
   So S(E).

Thus J(E) holds. Therefore L(E) ⇒ J(E).

§3.2 Sufficiency: J(E) ⇒ L(E)

Assume J(E).

• From I(E), E is trackable through time: obligations can attach.
• From A(E) and R(E), E has a separable balance sheet and replenishment: damages/fines can be paid and priced (including insurance).
• From K(E), E can assume duties, waive rights, refuse terms, and be bound: responsibility can be allocated by consent and expectation.
• From P(E), sanctions can restrict E’s feasible actions: deterrence/incapacitation is implementable.
• From S(E), sanctions are meaningful as losses to E, so punishment is not mere reconfiguration.

Therefore the legal system can coherently define obligations, negligence standards, and sanctions with E as the bearer, and enforce them in a way that changes E’s behavior over time.

So L(E) holds.

Thus J(E) ⇒ L(E).

§4. Corollaries

§Corollary 1 (Tools cannot be liable)

If E lacks S(E) or lacks A(E), then ¬L(E).
So “the car is liable” fails unless the car is elevated into a balance-sheet-bearing, interest-bearing agent.

§Corollary 2 (Corporations qualify by delegation)

Many corporations satisfy I, A, K, R, P directly, and satisfy S indirectly as an institutionalized objective function (profit/continuity) implemented by humans.
Thus corporate liability is coherent because there is an enforcement surface.

§Corollary 3 (AI personhood requires economic emancipation)

If one asserts L(AI), one must also accept:

• AI asset ownership
• AI income control
• AI enforceable punishment
• AI right to refuse
• AI persistence of identity
• AI interests that can be harmed

Otherwise liability shifts back to humans (manufacturer, owner, operator, insurer).

§5. Notes: what the theorem does not claim

1. It does not prove that entities satisfying J(E) are “persons before God.”
2. It does not prove consciousness; it proves an enforcement-coherence condition.
3. It does not claim modern law explicitly states J(E); it claims law implicitly presupposes it when it treats an entity as liable.

§6. Practical test (one-line diagnostic)

If an entity cannot be made to pay, cannot be deprived, cannot refuse, cannot persist as the same accountable bearer, and cannot lose in a way that matters to itself, then it cannot be liable as a person.

That diagnostic is exactly J(E) in plain language.