Source
Barrett, Milinkovic, Mediano, Rosas, Bor, Barnett & Seth (2026), “Integrated information theory: the good, the bad and the misunderstood”, arXiv:2604.11482, LIT-185, read in full in NOTE-122.
What was actually shown
What the algorithm needs (§2). IIT 4.0 (Albantakis et al. 2023) computes system integrated information φs, the cause-effect structure and structure integrated information Φ from the probabilities of past and future states given the present states of parts, under a uniform prior, with spatial, temporal and state grainings chosen to maximise φs and Φ.
Ill-definedness (§5.1.1). The formulae need P(future | present) under each graining. For a non-Markovian graining that distribution is not fixed by the present state, so “the IIT algorithm is therefore not well-defined whenever there is at least one non-Markovian graining”, and it “does not produce an output for brains”. Two proposed fixes are said to fail: a uniform prior over the whole past does not converge for non-ergodic dynamics such as a random walk (Barrett & Mediano 2019), and Kleiner & Tull’s future trajectories leave one part’s evolution unspecified given no knowledge of another’s present state.
Further gaps (§5.1.2). The maximum-entropy prior is undefined for continuous state variables, such as membrane potential, without hard bounds. The maximisation over all grainings “has never been” investigated. Every application so far is to finite, binary, Markovian units assumed indivisible.
Proxies, not approximations (§5.2). A approximates B only if both are well defined and a bound on |A − B| can be given; Newton approximates general relativity in this sense, while GDP is a proxy for living standard. Since Φ is undefined for a brain, nothing approximates it. Existing measures, PCI included, are “operational proxies for at most two of the total set of six” axioms. Candidate empirical Φ measures disagree, “often moving in different directions under the same change of parameters” (Mediano et al. 2019).
What the evidence then supports (§3.1). TMS-EEG responses are local and stereotyped under anaesthesia, sleep and disorders of consciousness, and diverse and spreading in conscious states. These results are “equally compatible with alternative weaker versions of IIT, as well as, arguably, with other theories”.
What could have come out otherwise. A well-defined conditional distribution could have been specified for non-Markovian grainings, or Φ could have been computed for some real system. The paper reports that neither has been done.
What this does not say
- That IIT is false. The axioms are explicitly left uncontested (§6), and the authors recommend weak IIT, explanatory correlates without the identity claim, as a way to test its intuitions. What the paper denies is that strong IIT currently returns a verdict on any real system.
- That the formal case is established here. The non-Markovian argument is restated from Barrett & Mediano (2019), not proved in this paper, and the record does not hold that paper. The claim that brain dynamics are non-Markovian under the grainings IIT would use rests on one citation about ion-channel current fluctuations (Fuliński et al. 1998), and those grainings are not examined (NOTE-122, C2).
- That “high Φ = more consciousness” is a misreading. The paper concedes that “IIT does state that Φ corresponds to the quantity of consciousness” (§4.1). Its multi-dimensional global-state suite is a proposed revision. So is its verdict that an inactive expander grid is only minimally conscious: §4.1 grants that IIT gives the grid high Φ when first assembled (NOTE-122, Corrections).
- That IIT’s panpsychism is unproblematic. The paper derives a gapless, shifting tiling of space-time by non-overlapping substrates from the exclusion axiom (§4.2). Its defence is comparative: materialism has an explanatory gap too. It does not address the combination problem or the anti-nesting objections (THEORY-043, THEORY-644).
- That IIT has no achievements. The paper credits it with qualitative structure-to-phenomenology accounts on toy systems: a 2-D grid entails spatial extension, a directed chain temporal flow (§3.2). Those do not need Φ to be computed.
Connections
- IIT 3.0 (LIT-445) is the formal statement THEORY-043 cites for the exclusion postulate. THEORY-262 (Tononi, Sporns & Edelman’s neural complexity) and THEORY-240 (integrated information between default-mode gateways under propofol) report measures of the kind this paper calls proxies.
- THEORY-100 records the claim that PCI is a substitute for Φ; this account is the reason to read that as a proxy relation.
- THEORY-296 (no sustained posterior synchronization in the COGITATE test) tested a prediction IIT’s proponents made, not a Φ value; the paper’s Discussion says the same of COGITATE.
- The meta-problem challenge (THEORY-577) is an independent objection to Φ as the basis of consciousness: a zero-Φ simulation would report alike. Kleiner & Ludwig’s criterion (THEORY-498) is the test IIT’s toy structure-to-phenomenology results would have to pass.
- THEORY-023 cites this paper only as a defence against the expander-grid objection. Its §5 adds that IIT currently gives no verdict on any AI hardware, only on toy systems.