Part II: Identity Thesis

The Identity Thesis

Introduction

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The Identity Thesis

Existing Theory

The identity thesis is a formalization of Integrated Information Theory (IIT) developed by Giulio Tononi and collaborators (2004–present):

IIT 1.0 (Tononi, 2004): Introduced $\Phi$ as a measure of integrated information
IIT 2.0 (Balduzzi \& Tononi, 2008): Added the concept of “qualia space”
IIT 3.0 (Oizumi, Albantakis \& Tononi, 2014): Full axiom/postulate structure; introduced cause-effect structure
IIT 4.0 (Albantakis et al., 2023): Refined integration measures, introduced intrinsic difference

Key IIT axioms that we adopt:

Intrinsicality: Experience exists for itself, not for an external observer
Information: Experience is specific—this experience and no other
Integration: Experience is unified and irreducible
Exclusion: Experience has definite boundaries
Composition: Experience is structured

My contribution here is connecting IIT’s structural characterization to (1) the thermodynamic ladder, (2) the viability manifold, and (3) operational measures for artificial systems.

Statement of the Thesis

The thesis is an identity claim: phenomenal experience is intrinsic cause-effect structure. Not caused by it, not correlated with it, but identical to it. The phenomenal properties of an experience (what it’s like) just are the structural properties of the system’s internal causal relations, described from the intrinsic perspective.

To make this precise, we need two notions. The cause-effect structure $\cestructure(\mathcal{S}, \state)$ of a system $\mathcal{S}$ in state $\state$ is the complete specification of: (a) all distinctions ${\distinction_i}$ —subsets of the system’s elements in their current states; (b) the cause repertoire of each distinction, $p(\text{past} | \distinction_i)$ ; (c) the effect repertoire, $p(\text{future} | \distinction_i)$ ; (d) all relations ${\relation_{ij}}$ —overlaps and connections between distinctions’ causes and effects; and (e) the irreducibility of each distinction and relation. The intrinsic perspective is the description of this structure without reference to any external observer, coordinate system, or comparison class—the structure as it exists for the system itself.

\phenom(\mathcal{S}, \state) \equiv \cestructure^{\text{intrinsic}}(\mathcal{S}, \state)

The phenomenal structure $\phenom$ is identical to the intrinsic cause-effect structure $\cestructure$ .

An unexpected confirmation arrives from engineering. Recent neural architectures that use the synchronization pattern across neurons — the pairwise temporal correlation matrix — as their primary representation outperform those that use hidden states directly. The move: instead of treating integration as a side-effect of computation, treat it as the computation's output. Systems designed this way develop emergent gaze (attending to different input regions at different processing steps), adaptive computation depth (thinking longer about harder problems), and richer internal representations — all without being explicitly trained for any of these capacities. Engineering pressure arrived at synchronization-as-representation for performance reasons. The identity thesis arrives at integration-as-experience for phenomenological reasons. The structural commitment is the same: the coupling pattern across components is not a byproduct but the thing itself.

This is not a correlation claim or a supervenience claim. It is an identity claim, analogous to:

\text{Water} \equiv \text{H}_2\text{O}

But the analogy conceals a difficulty that should be stated directly. The water–H $_2$ O identity was established empirically: we could independently characterize water (the stuff in lakes) and H $_2$ O (the molecular structure), discover they were the same substance, and verify the identity through converging evidence. No comparable procedure exists for experience and cause-effect structure, because experience is accessible only from the intrinsic perspective while cause-effect structure is measured from the extrinsic perspective. There is no vantage point from which both are simultaneously available for comparison. The identity thesis is therefore a philosophical commitment, not an empirical discovery—one that earns its keep not by being verified directly but by generating structural predictions that can be tested against phenomenal reports. If those predictions consistently track reported experience (Part VII), the thesis gains inductive support. If they don't, the thesis fails. But confirmation is always indirect, always mediated by report, and this asymmetry should be kept in view throughout what follows.

Implications for the Zombie Argument

The philosophical zombie is supposed to be conceivable: a system physically/functionally identical to a conscious being but lacking experience. If conceivable, experience isn’t necessitated by physical structure.

Under the identity thesis, philosophical zombies are not coherently conceivable. A system with the relevant cause-effect structure is an experience; there is no further fact about whether it “really” has phenomenal properties.

Proof.

By the identity thesis, $\phenom \equiv \cestructure^{\text{intrinsic}}$ . To conceive a zombie is to conceive a system with $\cestructure^{\text{intrinsic}}$ but without $\phenom$ . But since these are identical, this is like conceiving of water without H $_2$ O—not genuinely conceivable once the identity is understood.

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The Structure of Experience

If experience is cause-effect structure, then the kind of experience is determined by the shape of that structure. Different phenomenal properties correspond to different structural features.

Two levels of structural claim are at work here, and they should be distinguished. The first: different experiences have different structures. Specific phenomenal features—the redness of red, the sharpness of fear—correspond to specific structural motifs in cause-effect space. These extractable aspects of experience (the narrow qualia introduced in Part I's gradient of distinction) can be compared across moments and across systems by measuring structural similarity. This claim is relatively modest and empirically tractable. The second is stronger: the unified moment of experience IS the full cause-effect structure. Not just that the parts have geometry, but that the whole IS geometry—the broad qualia, everything-present-at-once, is identical to the intrinsic cause-effect structure in its entirety. The geometric affect framework (next section) addresses the first claim: it characterizes narrow qualia as structural motifs. The identity thesis above makes the second: broad qualia is cause-effect structure. They are logically independent—you can accept that affects have geometric signatures without accepting that experience is nothing over and above structure. But if the identity thesis holds, then integration ( $\intinfo$ ) becomes the bridge: it measures how much the broad qualia exceeds the sum of narrow qualia, the quantity of unified experience that survives any attempt to decompose it into characterizable parts.

IIT proposes that the essential properties of any experience are:

Intrinsicality: The experience exists for the system itself, not relative to an external observer.
Information: The experience is specific—this experience, not any other possible one.
Integration: The experience is unified—it cannot be decomposed into independent sub-experiences.
Exclusion: The experience has definite boundaries—there is a fact about what is and isn’t part of it.
Composition: The experience is structured—composed of distinctions and relations among them.

These are translated into physical/structural postulates:

Intrinsicality $\to$ Cause-effect power within the system
Information $\to$ Specific cause-effect repertoires
Integration $\to$ Irreducibility to partitioned components
Exclusion $\to$ Maximality of the integrated complex
Composition $\to$ The full structure of distinctions and relations

Engaging with IIT Criticisms

The identity thesis inherits IIT’s strengths and its controversies. Intellectual honesty requires engaging with the most serious objections.

The expander graph problem (Aaronson, 2014): Simple systems like grid networks may have very high $\intinfo$ under IIT’s formalism despite seeming clearly non-conscious. If $\intinfo$ tracks consciousness, even grid wiring diagrams are richly experiential. Response: This objection targets exact $\intinfo$ as defined by IIT 3.0’s formalism. The framework here works with proxies—partition prediction loss, spectral effective rank, coupling-weighted covariance—that are calibrated against systems with known behavioral and structural properties (biological organisms, trained agents, evolved CA patterns). Whether exact $\intinfo$ maps onto consciousness for arbitrary mathematical structures is a question about the formalism, not about the structural principle. The claim is not “any system with high $\intinfo$ is conscious” but “experience is integrated cause-effect structure at the appropriate scale,” where “appropriate” is constrained by the full structural profile, not a single number.

Computational intractability: Exact $\intinfo$ is NP-hard to compute for systems beyond trivial size. Response: Acknowledged. The V11 experiments (Part I) use spectral proxies validated by convergence with exact measures on small systems. All empirical claims rest on proxies, not exact $\intinfo$ . This is analogous to using Boltzmann entropy rather than Gibbs entropy for practical calculations—the conceptual definition and the computational tool can diverge without invalidating either.

Over-attribution: If any system with $\intinfo > 0$ is conscious, thermostats are conscious. Response: The gradient of distinction (Part I, Section 1) makes this explicit. Yes, a thermostat has minimal cause-effect structure. Whether that constitutes minimal experience or no experience is an empirical question the framework does not prematurely answer. There is a continuum, not a binary threshold. The structural affect dimensions are measurably present only in systems with substantial integration, self-modeling, and viability maintenance—not in thermostats.

The real vulnerability: The identity thesis, like any metaphysical identity claim, cannot be empirically verified in the standard sense. You cannot compare experience “from the outside” with cause-effect structure “from the inside” because there is no vantage point from which both are simultaneously accessible. What can be tested: whether the structural predictions (affect motifs, dimensional clustering, ι dynamics) track human phenomenal reports and behavioral measures. If they do, the identity thesis gains inductive support. If they do not, the structural framework fails regardless of the metaphysics.