How does FC relate to IIT?

The Short Answer

FC and IIT share the intuition that consciousness requires both differentiation (rich internal representations) and integration (those representations working together). In FC, differentiation maps onto R and integration onto P — specifically, how much reasoning power depends on self-models being cross-linked across subsystems.

FC defines a computable analogue of IIT's Φ:

Φ_FCS = P(S) − Σⱼ P(moduleⱼ)

where P(S) is the reasoning power of the integrated system and each P(moduleⱼ) is the reasoning power of subsystem j operating with only local, non-shared self-models. The difference measures how much integration contributes. Unlike IIT's Φ, which is computationally intractable even for systems with known architecture, Φ_FCS is directly computable for white-box systems. FC does not claim equivalence with IIT — but it captures its core functional intuition in a tractable form.

Longer discussion

IIT, developed by Giulio Tononi, proposes that consciousness is identical to integrated information — measured by Φ, roughly the amount of information generated by a system above and beyond its parts. A system is conscious to the degree that it cannot be decomposed into independent subsystems without information loss. IIT has been enormously influential but faces a fundamental practical problem: computing Φ exactly requires evaluating every possible partition of a system, which is computationally intractable even for small networks with known architecture (Aaronson 2014).

FC engages with IIT at the level of functional intuition rather than formal equivalence. IIT's two core requirements map naturally onto FC's components:

• Differentiation — the system must have rich, varied internal states — corresponds to R. A system with high representational capacity tracks many distinct aspects of its own state with high precision.
• Integration — those states must work together rather than in isolation — corresponds to the cross-linking of self-models under global reasoning. When self-models are shared across subsystems, reasoning power P grows multiplicatively (in the fully integrated case, P_agent = Πⱼ P(mⱼ)). Partitioning the system destroys this multiplicative gain.

This motivates the FC analogue of Φ:

Φ_FCS = P(S) − Σⱼ P(moduleⱼ)

A system where all self-models are independent would have Φ_FCS = 0 — no integration premium. A system with deep cross-linking would show a large gap between integrated and partitioned reasoning power. This is computable directly from architectural specifications for white-box systems, which is precisely what IIT's Φ cannot claim.

Key Differences

The key differences are worth being explicit about. IIT's Φ is defined over causal structure — it measures irreducibility in terms of cause-effect power. Φ_FCS is defined over reasoning power — it measures how much inferential capacity depends on integration. These are related but not identical. IIT also makes strong metaphysical claims (Φ just is consciousness); FC makes no such claim, treating Φ_FCS as an engineering-tractable proxy for one functional property IIT considers necessary. Think of it as IIT's insight with IIT's intractability removed — at the cost of some theoretical completeness.

ToDo: Make a table of concepts in IIT and FC.