Phi Without Phenomenology The Compositional Failures of Integrated Information Theory (of "Consciousness")

Integrated Information Theory (IIT) proposes that consciousness is integrated information, quantified by a measure called Phi, with the proposal developed across four major versions (Tononi, 2004; Tononi, 2008; Oizumi, Albantakis, Albantakis et al., 2023). The variants share the central commitment that consciousness is identical with integrated information measured by Phi. This paper argues that IIT is not a theory of consciousness. It is a theory of mathematical potentials of brain function, with the consciousness label applied to instances of the measure exceeding zero. The formalism produces a number; the identity between the number and consciousness is asserted, not derived. The thesis rests on three structural absences in IIT's current form. Substrate-independence, the formalism describes any network with the right internal causal structure and commits to no specific physical substrate, so the central claim cannot pick out the human brain as the bearer of consciousness on its own terms. Computational inaccessibility, Phi at brain scale cannot be computed in practice or in principle for any actual brain, so the central measure has no operational application at the scale where conscious experience is. The constitutive bridge, the identity claim that consciousness is integrated information requires a mechanism showing how integration constitutes phenomenal experience, comparable to how molecular structure constitutes the macroscopic properties of water, and the framework's authors concede that the postulates are "unproven assumptions" and that the move from axiom to postulate is "an inference to a good explanation," neither of which derives the identity. The diagnosis predicts a recurring pattern in IIT's engagement with brain function and counterexamples. Where IIT's central claim is asked to do work, defenders import additional structure that the central claim itself does not contain, and the imports do the work the central claim cannot. The pattern is identified at operationalization, at the combining operations within the disambiguated quantities of IIT 4.0, at the response to Aaronson's counterexample, and at the auxiliary hypotheses tested by the Cogitate Consortium's preregistered adversarial collaboration (Cogitate Consortium et al., 2025), where the central prediction of sustained posterior-cortex synchronization was not supported and the supported predictions concerned imports rather than the identity claim itself. The diagnosis carries a forward-looking predictive commitment with explicit falsification conditions. IIT in its current form cannot generate brain-specific or consciousness-specific predictions from its central claim. The negative form of falsification is defeated by IIT supplying any of the three absences (substrate-independence, computational inaccessibility, the constitutive bridge). The positive form of falsification is defeated by a future version of IIT grounded strictly in the human brain rather than in a substrate-independent formalism applied to brain. The diagnosis is supported by direct verbatim quotations from each formulation of the framework (Tononi, 2004; Tononi, 2008; Oizumi, Albantakis, Tononi Albantakis et al., 2023), with the authors' own concessions across versions confirming the structural pattern at every stage. **Keywords:** integrated information theory, Phi, consciousness, panpsychism, computational ontology, identity claim, structural critique, IIT 4.0, exclusion postulate, axioms, postulates, inference to a good explanation, intrinsicality, phenomenological undeniability, falsifiability, substrate-independence