Collective Mediation Blocks Phenomenality (No-New-Closure Theorem)

A formal exclusion principle: mediated collectives do not instantiate phenomenality over and above their members.

0. Claim in One Line

If a collective’s evaluative steering is entirely implemented through intermediate phenomenal agents, then the collective has no phenomenal events not reducible to events in those agents.

Equivalently:

No emergent collective phenomenality without emergent collective closure.

This theorem makes precise what “mediation blocks phenomenality” means in closure terms.

1. Minimal Formal Setup

1.1 Systems, substrate, and control

A system S has:
- internal substrate ξ_t^S (its persisting internal state),
- internal control degrees u_t^S (its selection/routing/action),
- possible evaluation signals E_t^S.

A system exhibits a phenomenal event at time t only if it has internal evaluative closure at that time:
$$ \frac{\partial u^S_{t+1}}{\partial E^S_t} \neq 0 \quad\text{(closure / evaluative leverage).} $$
(Any equivalent closure condition is acceptable; the key is “evaluation steers control inside the system.”)

1.2 A collective as a mediated composition

Let a collective C be composed of:
- a non-phenomenal coordination substrate ξ_t^C (institutions, documents, norms, protocols, markets, networks),
- a set of intermediate agents {S_i}_i = 1^N that may themselves be phenomenal,
- communication channels between S_i and ξ^C.

The collective’s observable behavior arises from:
(ξ_t^C, {ξ_t⁽ⁱ⁾}) ↦ (ξ_t + 1^C, {ξ_t + 1⁽ⁱ⁾}).

1.3 Mediation assumption (the key condition)

We say the collective is fully mediated if every causal pathway by which evaluation affects collective control passes through individuals’ closures.

Formally:

The collective has no intrinsic evaluative signal E_t^C with direct leverage:
$$ \frac{\partial u^C_{t+1}}{\partial E^C_t} = 0. $$
Any effective evaluation impacting collective control arises only via agents:
u_t + 1^C = G (ξ_t^C, {a_t⁽ⁱ⁾}),
where each agent action a_t⁽ⁱ⁾ may be a function of their own internal evaluation E_t⁽ⁱ⁾:
a_t⁽ⁱ⁾ = π_i (ξ_t⁽ⁱ⁾, E_t⁽ⁱ⁾).

Intuitively: the collective’s “steering” happens because humans (or other phenomenal subsystems) read the situation, feel/assess, and act.

The collective substrate ξ^C itself is merely the medium that stores and transmits decisions.

2. Theorem (Collective Mediation Blocks Phenomenality)

Theorem (No-New-Closure).
Let C be a collective system composed of intermediate systems {S_i}.
If C is fully mediated—i.e., all evaluative steering of C is implemented through the closures of the S_i, and C has no intrinsic evaluative closure—then:

C instantiates no phenomenal events of its own:
Φ_t^C = 0 ∀t,

any phenomenal events attributable to “the collective” reduce to events in some S_i:
$$ \Phi^{collective} = \bigcup_{i=1}^N \Phi^{(i)}. $$

In short: there is no collective phenomenality over and above the individuals.

3. Proof (By Closure Localization)

3.1 Phenomenal events require internal closure

By the framework’s minimal criterion, a system S can only host phenomenal events at times when evaluation has internal leverage:
$$ \Phi^S_t > 0 \ \Rightarrow\ \frac{\partial u^S_{t+1}}{\partial E^S_t} \neq 0. $$
(Closure is a necessary condition for phenomenal instantiation.)

3.2 The collective lacks intrinsic closure

By the mediation assumption (1), the collective’s own evaluation has no internal leverage:
$$ \frac{\partial u^C_{t+1}}{\partial E^C_t} = 0. $$

Therefore, by necessity of closure for phenomenality:
Φ_t^C = 0 ∀t.

So C does not instantiate phenomenal events as a system.

3.3 All steering power resides in the intermediate phenomenal systems

Any evaluative effect on collective behavior occurs through individuals’ actions:
u_t + 1^C = G(ξ_t^C, {a_t⁽ⁱ⁾}), a_t⁽ⁱ⁾ = π_i(ξ_t⁽ⁱ⁾, E_t⁽ⁱ⁾).

So whenever “the collective changes course due to evaluation,” the evaluation is realized in some S_i, not in C.

Thus any phenomenal event that causally explains collective steering must be located in the set {S_i}:
$$ \Phi^{collective} \subseteq \bigcup_{i=1}^N \Phi^{(i)}. $$

Conversely, individuals’ phenomenal events trivially contribute to the global history of “what happened in the collective,” so:
$$ \Phi^{collective} = \bigcup_{i=1}^N \Phi^{(i)}. $$

Hence there is no additional phenomenal residue at the collective level.

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4. Intuition: Transmission Is Not Instantiation

A mediated collective can:
- coordinate actions,
- store plans,
- propagate norms,
- amplify signals,
- optimize outcomes,

without any place where evaluation closes onto a collective control loop internally.

It is:
- a medium of transmission and aggregation,
- not a substrate where “stakes burn.”

So the collective can have:
- intelligence-like behavior,
- coherent policy,
- even self-preservation tendencies at the group level,

without having a unified phenomenality.

5. Corollaries

5.1 “Group mind” requires emergent closure, not mere coordination

If you want a collective to be phenomenally conscious, it must not be fully mediated.
It must implement an internal evaluative loop of its own:
$$ \frac{\partial u^C_{t+1}}{\partial E^C_t} \neq 0 $$
in a substrate that is not reducible to individuals’ closures.

5.2 Collective self-preservation ≠ collective phenomenality

A collective can exhibit self-preservation behavior (institutions survive, firms protect themselves) via:
- incentives,
- enforcement,
- distributed action,
- selection mechanisms,

while remaining phenomenally null at the collective level under mediation.

5.3 Why SIP/TWCT generalizes to collectives

Even if the collective’s informational structure mirrors a conscious system (shared narratives, global states, “mood” metrics),
without intrinsic closure it remains in traversal-without-closure territory at the collective level.

6. Boundary Cases (Where the Theorem Does Not Apply)

This theorem does not rule out collective phenomenality in principle.
It rules it out for a specific architecture class: fully mediated collectives.

A collective might escape mediation if it has:

a genuinely shared substrate that updates via collective evaluation with direct leverage,
tight temporal coupling such that evaluation cannot be localized to individuals,
an integrated control system that binds distributed signals into one evaluative governor.

In those cases, the collective would no longer satisfy the mediation assumption.

7. One-Sentence Summary

If a collective’s evaluative steering only happens through its members, and the collective itself has no intrinsic closure, then the collective instantiates no phenomenality over and above the individuals.