Proposition: Simulated Consciousness

Proposition 1 (Simulated consciousness). A simulation H′ that is physically and behaviourally indistinguishable from a conscious human H must itself instantiate subjective experience.

Proof.

Assumption for contradiction. Suppose H′ exists such that H′ ≡ H (physical and behavioural equivalence) but S(H′) = ∅ (lacks subjective experience):
$Behaviour(H′) = Behaviour(H ) and S(H ′) ⁄= S (H ).$
From A₄. The behaviour of H is a function of its physical inputs and its subjective experience:
$Behaviour(H ) = f (Inputs, S).$
Contradiction. If the behaviours are identical despite the difference in S, then S is not a necessary input to f. Subjective experience is causally inert.
Violation of A₄. Causal inertness of S directly contradicts Axiom 4. The assumption is therefore false.

Therefore S(H′)≠∅: the simulation instantiates subjective experience. □ □

This result, combined with the substrate independence established in Section 3, entails the full Internal Emergence Principle of Paper I: consciousness is a property of certain finite information structures, and any configuration space large enough to contain such structures contains consciousness, with no running process or external reader required.

4 Proposition: Simulated Consciousness