Integrated Information Theory offers a rigorously defined measure of informational integration. The ambition is genuine: an objective, intrinsic criterion for consciousness that does not depend on behavioral report or functional role. This paper takes that ambition seriously. What follows is not an attack on IIT's mathematics, nor a dismissal of integration as relevant to consciousness. It is a critique of what Φ is permitted to explain. Φ quantifies the irreducibility of a system's causal structure at a time slice. It measures how tightly coupled the parts are, how much the whole exceeds the sum of its partitions. Grant that this measure is well-defined. Grant that it tracks something real. The question remains: what does integration at a moment have to do with persistence across time? The paper argues that IIT commits a category error: treating a state scalar as sufficient for explaining what is fundamentally a trajectory phenomenon. Φ is a function of states; identity is a function of trajectories. A system can have high Φ and collapse immediately; moderate Φ and persist robustly; oscillating Φ while remaining the same identity. The measure and the phenomenon come apart in explanatory scope. Φ presupposes identity—a bounded, integrated system must already exist for the measure to apply—without explaining how identity is achieved or maintained. The critique traces consequences: IIT cannot see failure (the measure samples only systems that achieve integration), cannot theorize boundaries (Φ-maximization identifies boundaries without explaining how they are maintained), and cannot accommodate the regime structure of consciousness (thresholds, fragility, sudden disappearance). These limitations are structural, not computational; better Φ cannot fix them. The paper repositions IIT within a broader framework: Φ measures the integration of systems that persist; Identology explains why persistence is rare. Measuring what persists is not explaining why.
C.S. Thomas (Thu,) studied this question.