The Internal Contradictions in Integrated Information Theory 4.0

Abstract

The six postulates of Integrated Information Theory 4.0 (IIT) (Albantakis et al., 2023) are jointly unsatisfiable, and not because the theory ranks them: the exclusion postulate contradicts itself in successive clauses, integration forbids what composition requires, and the one conflict the theory does adjudicate it adjudicates against itself, excluding from the Φ-structure the determinations the postulate was written to secure. The postulates characterize consciousness through a zeroth axiom and the five essential properties of phenomenal experience, and are existence (P1), intrinsicality (P2), information (P3), integration (P4), exclusion (P5), and composition (P6), with all six claimed as jointly necessary for consciousness. The argument is conducted entirely in the theory's own vocabulary, which is granted in full so that no result below can be answered by redefinition. Three structural contradictions are developed in detail. The first is internal to a single postulate: P5 requires in one clause that the substrate be definite, this whole set of units, and supplies in the next the maximization over candidate systems and partitions that is to make it so, while P2 requires that the quality and quantity of existence be observer-independent. Four lines of evidence establish that the maximization's output depends on the investigator. The search space is the set-partitions of the units multiplied by a direction assignment per part, and the procedure defined over it terminates for no biological system, so the investigator's truncation is not a shortcut around the theory's procedure but what returns a substrate at all. The measure's claimed uniqueness is argued from its properties and never from the substrate it selects. The theory assigns the partition space, the distinctions, and the grain to one principle of maximal existence, and the three searches are nested rather than parallel, so they are one dependence. Where the procedure returns more than one answer, the theory resolves the tie in the first person plural. The second contradiction is between integration (P4) and composition (P6), which requires that consciousness be both undecomposable and structured into distinctions and relations, a pair the theory holds while stating that "causal distinctions have no inherent structure themselves" and reporting Φ-structures whose components it counts to the integer and bounds by formula. The third is between definiteness, the first clause of P5, and the joint demands of maximal information (P3) and structured composition (P6), which together require simultaneous specificity and variability. The available defenses, the discovery-property distinction, constitutive composition, and the aspect-distribution reading, each preserve the joint commitment by suspending one demand, and the three suspend three different demands, so the set is satisfiable at any moment only by not being the set the theory states. Two of the three suspensions fall on P5, which is the postulate that contradicts itself. Five results follow from the three. The observer-dependence of the maximization is the condition methodology names researcher degrees of freedom, and it is worse in IIT's case than in the standard one, because the choices reach the object the theory is about rather than the route to testing it. The theory records its own non-satisfaction cases: when the resolution of ties exhausts, the tied systems "do not comply with the exclusion postulate" and "do not qualify as complexes," so a system fails to be conscious because a computation returned two values rather than one. The rarity the theory offers as the reason ties can be set aside is itself a requirement of micro-level indeterminism, and the theory's worked examples require indeterminism to be absent for Φ to be high, with the cortex named as the substrate where both demands fall. The postulates specify what obtains and never what operates: where the theory names something at these seams it names a principle of maximal or minimal existence, offered as a good explanation of why outcomes are what they are, which supplies a reason and not an operator. The case of uncertainty, treated structurally rather than phenomenologically, is settled by the theory against itself, since the congruence condition on which distinctions compose a complex excludes incongruent cause-effect states from the structure, so the Φ-structure identified with the experience is not the structure of the state a system holding two incompatible determinations is in. No system therefore satisfies IIT 4.0 as stated, and which suspension is in force when a system is called conscious is settled outside the theory. The wider case against IIT's identity claim is developed in *Phi Without Phenomenology: The Compositional Failures of Integrated Information Theory (of "Consciousness")* (Stewart, 2026o). **Keywords:** integrated information theory, IIT 4.0, Phi, Φ-structure, consciousness, postulates, axioms, intrinsicality, information postulate, integration, exclusion postulate, composition, definiteness, maximal substrate, principle of maximal existence, intrinsic difference, causal distinctions, causal relations, congruence, tie resolution, degrees of freedom, theories of consciousness