Do Or Do Not. There Is No Be.
What the most famous theory of consciousness gets wrong
Last time, I told you about the unfolding argument — the most powerful objection to any theory of consciousness that says recurrent processing matters. We showed that it doesn’t apply to systems with plasticity or ongoing process, which means it doesn’t apply to biological brains or anything else we’d seriously consider as a candidate for consciousness.
The unfolding argument hits one specific target with the greatest force. Today we’re going to take a break from the series to talk about that target: Integrated Information Theory, usually shortened to IIT. It was developed by Giulio Tononi, has been championed by Christof Koch, and it has generated more debate, more funding, and more philosophical heat than any other theory in the field. It has also produced one of the field’s most powerful clinical tools — the Perturbational Complexity Index, or PCI — which has a great deal of promise in allowing assessment of consciousness in patients who can’t tell us whether they’re awake.
I think IIT has a problem. Not the problems other people have raised — not the unfolding problem, not the computational intractability of calculating Φ for real systems, not the panpsychism implications, not the accusations of pseudoscience that have made headlines. A different problem. A problem with IIT’s own math.
As far as I know, this is a problem nobody has clearly identified before. Let me try to explain it in plain language and let me know what you think.
What IIT claims
IIT says consciousness is identical to something called Φ (phi) — a quantity computed from a system’s “cause-effect structure.” Unpacking all of that:
Don’t get scared off by the Greek letter. It’s just a fancy mathy way to label a variable. We could just call it P.
You can just think of cause-effect structure as a network — a set of nodes with connections between some of them, where the connections tell you how one node influences the next.
IIT is fundamentally axiomatic. It starts from certain first principles, the properties of experience: it exists, it’s structured, it’s unified, it’s specific, it’s definite). IIT then reasons backward to what a physical system would need to look like in order to account for those properties.
So what is Φ? First, again, it’s a quantity, a number. It is an expression of how “internally connected” the network is. If a network has no internal connections, Φ is 0.1 The degree of “internal connectedness” has, you guessed it, a formal mathematical definition. This is a central mathematical object in IIT and it usually doesn’t get the same headline attention as Φ.
This object is the transition probability matrix, or TPM. The TPM describes, for every possible state a system could be in, the probability that it transitions to every other possible state. If you have a network of neurons, the TPM captures its complete “causal dynamics” in one object — how each node causes effects within the network.
It is from this TPM that IIT computes Φ. High Φ means lots of integrated information. Consciousness, on IIT’s account, just is this integrated information. It’s not caused by it, not correlated with it, not produced by it. It is it.
And here’s the philosophical commitment that matters for what follows. IIT explicitly claims that consciousness is about being, not doing. The title of a 2021 paper by Albantakis and Tononi says it directly: “What we are is more than what we do.” Consciousness is a property of the system’s structure — its cause-effect architecture — not of any process the system performs. The TPM is a static object. Φ is computed from that static object. And that’s the whole story.
How IIT builds its central object
Here’s where it gets interesting. How do you actually construct a TPM?
IIT 4.0 is explicit about this. You use Judea Pearl’s do-operator2. This is a piece of mathematical machinery that formalizes what it means to intervene on a system rather than merely observe it. The TPM entry for “what happens when the system is in a specific state” is not observational. It is not computed by watching the system and recording what happens to it. It’s computed by setting the system to a particular state — forcing it there by fiat or external intervention — and then recording what happens.
The formal notation used by IIT is p(u′|do(u)). You don’t need to remember that. What is important is that it represents the probability of the system transitioning to the next state (u′), given that we intervened to place it in state u.
Pearl’s great insight — the one that won him the Turing Award — was that you cannot, in general, figure out causal structure just by watching a system. Correlation is not causation, and the reason it’s not is mathematically precise: multiple different causal structures can produce exactly the same patterns of observed correlation. To determine which causal structure you’re actually dealing with, you have to intervene. You have to reach in and change something and see what happens downstream.
IIT understood this. That’s why IIT 4.0 defines the TPM using the do-operator rather than passive observation. This is, in fact, one of IIT’s most sophisticated formal moves.
The tension
Now look at what the do-operator actually requires.
Each entry in the TPM answers the question: “What does the system do when set to state u?” There is an intervention (set the system; do(U=u) under Pearl’s notation. There is a temporal succession (time passes). There is a dynamical response (the system transitions to some u′ with some probability). Without the “before” of the intervention and the “after” of the response, there is no transition probability to record. The do-operator is, formally and irreducibly, a description of something happening.
IIT’s notation helps obscure this. The theory writes it with a clean, compact, and almost atemporal-looking notation (the p…do… equation above). But if you unpack equation, that little apostrophe (') tells you what the equation is actually doing: it is looking at what happens at the next state (u’) given an intervention now (do(u)). The temporal content is right there. IIT’s own prose confirms it: “the probability of a subsequent state given the current state.” Subsequent. Given. These are temporal words describing a temporal operation. The notation compresses the time. It doesn’t eliminate it.
The TPM is not a photograph of a structure. It is a complete catalogue of one-step dynamics. Every cell in the matrix describes an action: what the system does under a specific intervention. The matrix is, from top to bottom, a description of doing.
So when IIT computes Φ from this matrix and declares that consciousness is about being, not doing — that the static structure is what matters and the temporal process is irrelevant — it is making a claim that is in tension with the mathematical object the claim is about. IIT is stripping away the temporality and the intervention needed to define the object in the first place.
This bears repeating. IIT is not merely using a processual method to measure a static structure, the way you might use a thermometer (a dynamic instrument) to measure temperature (a static property). That is observational. The TPM is the dynamic — it is constituted entirely by transition probabilities, which are defined by what happens when you intervene on the system and wait. Strip away the doing — remove the interventions, the temporal succession, the dynamical responses — and you don’t have a TPM with the process removed. You have nothing. There is no matrix left. The entries are undefined.
IIT constructs its central object out of process and then declares process irrelevant to what the object describes. This is not an external critique. It is a tension internal to the formalism. The call is coming from within the house.
Where it bites
This tension has a concrete consequence, and it shows up the moment you consider a system that changes over time.
Your brain is not a fixed network. Every time you learn something, your synaptic connections change. The network that processes your experience of reading this sentence is not the same network that processed your experience of the previous sentence — because reading the previous sentence changed the network. This is called plasticity, and it is one of the most fundamental properties of biological neural systems.
For a plastic system, the TPM now is not the same as the TPM a moment ago. The causal structure changes because the system’s own operation changes it. There is no single, time-invariant TPM to compute Φ from.
IIT can accommodate this by recalculating Φ for the updated system at each moment. In fact, it already does — one of the theory’s own predictions is that cutting the corpus callosum (the massive bundle of fibers connecting the brain’s two hemispheres) should split a single high-Φ entity into two lower-Φ entities. That prediction requires recalculating Φ for the new system. Fair enough.
But the accommodation is revealing. It makes explicit that the supposedly timeless intrinsic property is actually temporally situated and malleable. Φ isn’t a fixed feature of the system. It’s a snapshot that has to be retaken every time the system changes. And in a plastic brain, the system is always changing.
The question then becomes: if you have to keep re-entering the world of interventions and temporal dynamics every time you want to know what Φ is, why insist that the temporal dynamics don’t matter? If the “being” requires constant reference to the “doing,” maybe the doing is the point.
For a system with plasticity, “being not doing” requires the being to hold still. Plastic systems don’t hold still. That’s what makes them plastic.
This isn’t a limitation of current measurement technology. It’s a formal property of any system whose constitutive parameters change as a function of its own operation. And biological brains are exactly such systems.
Recent IIT work by Findlay and colleagues has made a related point from a different direction: functionally equivalent systems with different causal architectures can produce different values of Φ. That’s exactly the kind of puzzle you’d expect if the theory is measuring the wrong thing — if Φ is capturing something about how a system is wired rather than what it’s doing, and the wiring isn’t what matters. This is, in fact, precisely the point made by Adrien Doerig and colleagues in their unfolding argument.
What about PCI?
Here’s the part that should make IIT proponents uncomfortable — not because it attacks their empirical work, but because it may suggest their empirical work is better than their theory.
The Perturbational Complexity Index works like this. You deliver a TMS pulse — a magnetic zap — to someone’s brain while they’re either conscious or unconscious (under anesthesia, in a coma, in deep sleep, awake). You record the EEG response over the next 300 milliseconds or so. You quantify how complex and differentiated that response is. Conscious brains produce rich, spatiotemporally complex responses. Unconscious brains produce simple, stereotyped responses or nothing at all.
PCI is one of the most impressive tools in consciousness science. It reliably distinguishes conscious from unconscious states across wakefulness, sleep, anesthesia, and disorders of consciousness. It works.
On IIT’s interpretation, PCI works because it’s probing the TPM — revealing the integrated cause-effect structure that is consciousness.
But look at what PCI actually measures. It delivers a perturbation during ongoing processing and records how the system responds as it evolves through time. It is measuring the integrity of a temporally extended dynamical process — how recurrent neural dynamics integrate and differentiate a perturbation over hundreds of milliseconds. It is not measuring a static structural property. It is measuring what the brain does when you poke it.
A process-based interpretation is available, and it may fit the data better than the static one. Conscious brains respond with rich, differentiated dynamics because recurrent processing integrates the perturbation into a complex trajectory. Unconscious brains don’t — because anesthesia, sleep, or injury has disrupted the temporal dynamics, not because the “structure” has changed in some static sense.
IIT may have built a brilliant tool for measuring dynamic process and then attributed its success to a theoretical object — static integrated information — that can’t fully account for why the tool works.
The structure that isn’t
This tension isn’t just abstract. It shows up in arguments offered by IIT’s own defenders.
A recent paper by Chen Song responds to an ongoing, lively philosophical debate in consciousness science about structuralism (to be covered in a future post). That paper provides a vivid illustration. Imagine two neural systems with identical patterns of activity at a single instant — every neuron firing at the same rate, same spatial pattern, a perfect snapshot match. But the wiring is different. Different connections under the hood.
IIT says these two systems should have different conscious experiences. Different structure, different Φ, different consciousness. And that might be right. But here’s the question: how would you ever know the structures are different? You can’t tell from the snapshot — the activity is identical. You’d have to do something. Perturb the system. Wait. Watch how one responds differently from the other over time. The structural difference that IIT says matters for consciousness is only detectable through dynamics.
The property doing the explanatory work is processual, even when the theoretical label says “structure.” Notably, Marlo Paßler and Adrien Doerig — the architect of the unfolding argument — have recently made a related observation in the structuralism debate: that for any neural structure to count as genuinely representing something, it has to be used by downstream processes over time. Structure without process isn't structure that matters. Again, we'll return to this debate in a future post as I think it’s one of the most interesting discussions in modern consciousness science.
Why this matters
I want to be clear about what I’m not saying. I’m not saying Φ is meaningless. I’m not saying Tononi and colleagues haven’t made profound contributions to consciousness science. They have. The axiomatic approach — starting from properties of experience and reasoning to physical constraints — is methodologically powerful. PCI is a genuine clinical achievement. And the insistence on mathematical precision, even when the math gets hard, has raised the standard for the whole field.
What I am saying is that there’s a specific tension between IIT’s mathematical formalism and its philosophical interpretation. The do-operator is not a neutral measurement tool. It is a processual formalism — it requires intervention, temporal succession, and dynamical response. Building your theory’s central object out of do-operator entries and then declaring that “doing” is irrelevant to consciousness is a philosophical commitment that requires defense, not a consequence of the mathematics.
The mathematics, if anything, points the other way: information is always lost when you collapse a finer-grained description into a coarser-grained one. That’s just math. The question is whether the lost information matters. IIT’s founding abstraction collapses the temporally extended, intervention-defined, dynamically constituted TPM into a static structural property and computes Φ from the result. That abstraction may be defensible. But it cannot be defended by asserting “being not doing” as though it were a theorem rather than a choice.
Others have noticed pieces of this problem. A 2022 paper in Philosophy and the Mind Sciences argued that IIT needs an axiom for time. Critics have pointed out that IIT struggles with temporal phenomenology — the flow of experience, the specious present, the felt continuity of consciousness. But those critiques are external: they say IIT is missing something.
The argument here is internal. The do-operator is already inside IIT’s formalism. The processual commitment is already there, in every entry of the matrix the theory is built on. The question is whether a theory can coherently build its central object out of dynamics and then declare dynamics irrelevant.
I think it can’t. Do, or do not. There is no be.
Vikas O’Reilly-Shah is a Professor of Anesthesiology & Pain Medicine at the University of Washington and Seattle Children’s Hospital. His work on the State Space Theory of consciousness is published in the Journal of Consciousness Studies and Nonlinear Dynamics, Psychology, and the Life Sciences. Further work is under review at several additional journals. All the papers can be found here. He can be reached at voreill@uw.edu.
This definition of internal connectedness is why the unfolding argument has such force against IIT. Adrien Doerig and colleagues proved with the unfolding argument that for the a specific input-output function (a specific ‘connectedness structure’), you can generate another network that perform the exact same function but has no internal connections: Φ = 0. You can also construct other networks that have the same input-output function but with arbitrary degrees of internal connectedness structure: same Φ. In other words, the starting consciousness-ness in a specific structure would have, under IIT, zero or infinitely variable degrees of consciousness-ness while doing exactly the same thing. As Doerig et al. put it, this makes the theory either false (internal contradiction) or unscientific (you can’t test for differences in consciousness if they have the same input-output function but variable internal structure).
Judea Pearl is a computer scientist and philosopher at UCLA who won the Turing Award in 2011 for developing the mathematics of causal reasoning. His framework solved a problem that had plagued statistics for a century: how to distinguish causation from correlation using formal tools rather than intuition. His do-operator — the mathematical notation for “what happens if I intervene?” as opposed to “what do I observe?” — is now foundational across medicine, economics, and AI. His book The Book of Why (2018) provides an excellent introduction. IIT 4.0 builds its central mathematical object using Pearl’s formalism, which is part of why the tension I’m describing matters: the tool IIT chose to build its foundation is inherently about doing, not being.