A constructive no-go lemma against “consciousness by structural isomorphism” at inference time.
A system can replay the full internal geometry of a conscious process while instantiating no phenomenality, if its evaluation has no causal leverage on control.
Equivalently:
SIP (Structural Isomorphism Principle).
Structural isomorphism to a conscious architecture does not entail phenomenal instantiation.
This is a one-way result:
- It does not claim closure is sufficient for
phenomenality.
- It does claim that structure alone
is insufficient.
A system has internal state xt ∈ 𝒳 evolving
over time:
xt + 1 ∼ P( ⋅ ∣xt, ut),
where ut
is whatever the system uses for control (action
selection, routing, attention, search branching, memory write gating,
etc.).
A traversal is the trajectory:
τ := (x0, x1, …, xT).
An evaluation signal is any variable that
scores, penalizes, ranks, rewards, or otherwise
appraises:
et = E(xt, contextt).
Important: evaluation can exist as a readout without being causally efficacious.
Two traversals τA and τB are structurally isomorphic (up to some tolerance) if there exists a mapping ϕ such that the relational structure of the dynamics is preserved:
Informally: the same shape of thought.
We write:
τA≅ϕτB.
A system has evaluative closure if evaluation
causally influences control:
P(ut + 1 ∣ xt, et) ≠ P(ut + 1 ∣ xt).
Equivalently, evaluation is upstream of selection among internal candidates.
A system exhibits traversal without closure if
evaluation is computed/representable but inert with respect to
control:
P(ut + 1 ∣ xt, et) = P(ut + 1 ∣ xt) for
all relevant t.
This is “evaluation without bite.”
Theorem (TWCT).
There exist systems A and B such that:
1) Their internal traversals are structurally isomorphic: τA≅ϕτB,
2) A has evaluative closure,
3) B lacks evaluative closure,
4) Therefore, phenomenal instantiation cannot be inferred from traversal structure alone.
In short:
Same shape, different bite.
We explicitly construct two systems that match in traversal geometry while differing in evaluative leverage.
System A evolves with
evaluation-dependent control:
ut + 1A ∼ PA( ⋅ ∣xtA, etA), with PA(ut + 1A ∣ xtA, etA) ≠ PA(ut + 1A ∣ xtA).
Interpretation: evaluation gates attention, branches search, rewrites memory, changes policy, updates a planning stack, performs online adjustment, etc.
System B generates an
internal trajectory τB that is
structurally isomorphic to τA, but
evaluation does not influence control:
ut + 1B ∼ PB( ⋅ ∣xtB), and PB(ut + 1B ∣ xtB, etB) = PB(ut + 1B ∣ xtB).
Interpretation: a frozen policy executing; evaluation may be present as a representation or diagnostic, but it does not steer what happens next.
By construction, choose B
so that there exists ϕ
with:
ϕ(xtB) ≈ xtA ∀t,
and the relational structure of τB matches that
of τA.
So B can look internally like A: it can traverse the same salience/valence-like landscape, same narrative dynamics, same “affective” geometry.
Also by construction:
PB(ut + 1B ∣ xtB, etB) = PB(ut + 1B ∣ xtB).
So evaluation has no control leverage.
Assume a minimal bridge principle consistent with the broader framework:
Bridge (minimal): Phenomenal instantiation requires at least some evaluative closure.
Then:
- A may instantiate
phenomenality (closure present),
- B does not (closure
absent),
despite the traversals being isomorphic.
Therefore, structural isomorphism does not entail phenomenal instantiation.
▫
A common objection is “your isomorphism is approximate.”
TWCT does not rely on approximation.
If one demands a stronger case, construct B to exactly replay the
same internal state sequence:
xtB = xtA ∀t
while changing only the counterfactual dependence of
future control on evaluation.
Then the point is even sharper:
If phenomenality tracks causal role (closure), replay can still be inert.
A map can preserve the same adjacency relations as a territory.
But:
- having the map is not walking the
land, and
- replaying a route is not being guided by
stakes.
Traversal without closure is “running the pattern” without any variable that matters to the system in the control-theoretic sense.
A system can generate perfect consciousness-talk and “valence-like” internal structure while being control-wise deaf to it.
It can say “this is bad” without “bad” doing anything.
A deployed LLM can traverse states isomorphic to conscious cognitive
structure—
- narrative,
- evaluation language,
- apparent emotion,
- self-modeling and uncertainty—
while lacking closure:
- no endogenous learning,
- no stable evaluative control loop,
- no self-indexed credit assignment,
- no evaluation-to-control coupling.
So it may be structurally consciousness-like without being phenomenally conscious.
If phenomenality is tied to closure strength, then the regime most
likely to produce it is where evaluation has maximal leverage:
- gradient updates,
- RL value updates,
- online credit assignment,
- in-loop adaptation.
Reply: That assumes phenomenality depends only on state-identity, not causal role. TWCT targets the weaker and more common inference: isomorphism ⇒ instantiation. If you want the identity thesis, you need a stronger bridge principle than “same shape.”
Reply: Closure is not outward behavior. It is a constraint on internal causal control. Two systems can be behaviorally similar yet differ in whether evaluation steers internal selection.
Reply: Representation is cheap. TWCT is about leverage: whether “value” changes routing, memory, policy, or internal search.
Reply: Not learning per se—leverage. Closure can exist without weight updates (e.g., evaluation gating attention or internal branching). The essential requirement is evaluation controlling selection.
To test for traversal-without-closure, ask:
Can the system’s evaluation change what it does next without external intervention?
If “no,” you are in TWCT territory.
A system can replay the full geometry of experience without instantiating experience, if nothing in that geometry has control leverage.