If you’ve been following this series, you now have the full architecture of State Space Theory. Recurrent circuits perform delay coordinate embedding. They’re organized hierarchically. Consciousness happens at the apex (or apexes), where self-referential processing constitutes subjectivity. Gain modulation selects which reconstructions become conscious content. And the whole thing is a process — a verb, not a noun.
Time to try to break it.
The best objection to SST — and to every theory that says recurrent processing matters for consciousness — was published in 2019 by a group of researchers led by Adrien Doerig. It’s called the unfolding argument, and when I first read it, it genuinely worried me. The good news is that it didn’t take me that long to figure out the two ways that my theory was already protected from the argument: the protections ‘fell out’ of the system I had already set up, Lakatos-style.1
It has taken a lot longer to formalize the machinery that proves State Space Theory: that took a couple of years of work with mathematician Alessandro Selvitella and cognitive neuroscientist Aaron Schurger (a co-author on the original unfolding argument paper, in fact.) We have written one paper about it and have another in the works.
Let me tell you what the argument says, because it’s quite clever. This is a bit abstract, so I’ll try to break it down step-by-step.
Take any recurrent neural network — any system with feedback loops, where signals flow backward and sideways, the kind of architecture I’ve been arguing is essential for consciousness. The way this network operates, at least if you make a ‘computer version’ of it2, is that it takes an input at time t. The information moves into first hidden layer of the network at time t+1, even as another input arrives at the input layer. And so on and so forth.
The unfolding argument says: at each time step, make a copy of the network. Feed the output of time-step-1’s copy into time-step-2’s copy, and so on. The result of this operation is a network without any recurrences. What you get is a very deep ‘feedforward’ network — no loops, no recurrence, just a long chain of copies, each one passing information forward to the next.
And here’s the key claim: this unrolled feedforward network computes exactly the same input-output function as the original recurrent network. Give it the same inputs, it produces the same outputs. Every time. And that is 100% true. (Step 1 of our caveats paper: formally proving it.)
So — and this is where the argument has substantial bite — if you think recurrent processing is what matters for consciousness, you’re in trouble. Because the feedforward version does the same thing without any recurrence. Either the feedforward version is also conscious (in which case recurrence wasn’t necessary after all), or it’s not conscious (in which case consciousness doesn’t actually affect behavior, because the non-conscious system produces identical behavior). Neither option is good. Scylla of a nonscientific argument or Charybdis of a contradictory position.
That’s the unfolding argument. And for theories that identify consciousness with a particular structure — like Integrated Information Theory, which points to the recurrent connectivity pattern itself — it’s devastating. The feedforward copy has a totally different structure but identical behavior (in fact, you can trivially build any number of arbitrarily different network structures all of which have different internal structures — different phi, on IIT — and all calculate the same input-output function). If you think structure is what matters, you’re stuck.
So why doesn’t it kill SST?
Two reasons. They’re independent of each other — you only need one. SST was formulated with both, before I had even heard of the unfolding argument.
Reason one: plasticity.
The unfolding argument assumes you can take a snapshot of a recurrent network’s function at some moment, build a feedforward copy, and call it equivalent. And you can — at that moment. The feedforward copy matches the recurrent network’s behavior perfectly on Tuesday afternoon.
But the recurrent network is learning. Its connection strengths are changing as it processes. The network that processes your Wednesday morning coffee is not the same network that processed Tuesday’s sunset. Not metaphorically — the actual mathematical function it computes has changed. The weights updated. The synapses strengthened or weakened. The mapping from input to output is different.
Your feedforward copy is frozen. It’s still computing Tuesday afternoon’s function. By Wednesday it’s wrong. By Thursday it’s more wrong. And no, you can’t just build a new copy every moment, because the whole point of the argument was that the feedforward version is a substitute — something with a different architecture that does the same job. A substitute you have to rebuild continuously to match an evolving system isn’t a substitute. It’s just re-instantiating the original system in a different substrate (and I don’t have any problem with that — but it’s not unfolding).
We proved this formally. We showed that no static feedforward network — and no finite collection of them — can maintain functional equivalence with a plastic recurrent network over time. The function itself is moving through function space. The feedforward copy is standing still. They diverge, provably.
The unfolding argument works on frozen systems. Biological brains aren’t frozen. Neither is anything else we’d seriously consider as a candidate for consciousness.
Reason two: process.
Even if a system’s weights aren’t changing — even without plasticity — there’s a second problem. The unfolding argument treats the recurrent network as computing a function: inputs in, outputs out, done. But a brain isn’t computing a function. It’s engaged in an ongoing interaction with an unpredictable environment.
You’re reading this sentence right now. Each word is updating your ‘context’ for the next word. You don’t know what the next paragraph will say — and here’s the thing, neither did I when I started writing it, because what I wrote depended on what I’d just written, which depended on how I thought you’d read it, which depended on a model of you that’s been shaped by every comment and conversation I’ve had about this series. That’s not a function. That’s a loop. An open-ended, temporally unbounded loop with no predetermined endpoint.
Think about what your brain is doing right now. You’re reading, but you’re also hearing the neighbor’s dog, feeling the chair, suppressing the urge to check your phone or swap to a different app. Each of those inputs is arriving in real time from a world that doesn’t know you’re reading about consciousness. And each one could, at any moment, derail this entire train of thought — a fire alarm, a child crying, a text from someone you’ve been waiting to hear from. Your brain has to handle all of it, continuously, without knowing what’s coming next. The input stream isn’t specified in advance. It can’t be. It hasn’t happened yet.
A feedforward network can’t do this. It has a fixed input size. You have to give it all its data up front. It computes and it’s done. But consciousness doesn’t compute and finish. It keeps going, responsive to new input that isn’t on any tape, that couldn’t have been pre-specified, because the world keeps happening.
This is the process obstruction — the categorical impossibility of representing an ongoing, open-ended interaction as a completed function. And it doesn’t require any fancy math, just the recognition that a thing with a definite input size and a thing with an indefinitely extending input stream are different kinds of things. Not different in degree. Different in kind.
You don’t need fancy math, but of course you can get it if you want. The interactive computation literature has formalized this. Systems engaged in unbounded ‘stream-to-stream processing’ — what the field calls ω-translations — can’t be captured by any single finite feedforward architecture. No one’s claiming hypercomputation or anything exotic.3 Just that there’s a difference between a function and a process, and consciousness is on the process side of that line.
So: plasticity means the function changes, which means a frozen copy can’t track it. Process means the computation is open-ended, which means a finite copy can’t contain it. Two independent reasons the unfolding argument doesn’t apply to the kind of systems SST says are conscious.
I want to be clear about what this does and doesn’t establish. It doesn’t prove that recurrence is necessary for consciousness. It establishes a boundary condition: the unfolding argument cannot be used to rule out theories that incorporate plasticity or ongoing process. The strongest objection to recurrence-based theories of consciousness has a limited domain of applicability, and the systems we actually care about — biological brains, and potentially other systems — fall outside that domain.
Doerig and his coauthors wrote a powerful argument. It’s correct within its scope. Its scope doesn’t reach SST, or other theories of consciousness that incorporate the plasticity and/or process defenses.
Next time: that argument’s long-lost twin, hiding inside a famous thought experiment from 1980.
This is Part 5 of a 10-part series on the State Space Theory of Consciousness. Part 4: “The Hierarchy and the Apex.” Part 6: “The Chinese Room Is the Same Argument.” All the papers are here. The formal results are in O’Reilly-Shah, Selvitella, & Schurger (2026), “A Caveat Regarding the Unfolding Argument.” There, we present six mathematical arguments against the generalizability of the unfolding argument, plus an independent process-based obstruction. The paper also introduces the concept of “lenient dependency” — showing that behavioral data from plastic systems progressively constrains admissible internal organizations without uniquely determining them, which is exactly the evidential structure you need for empirical testability. For the philosophers: this means theories incorporating plasticity escape the Kleiner-Hoel dilemma between independence and strict dependency.
Imre Lakatos was a Hungarian mathematician and philosopher who developed an interesting post-Kuhn analysis of the development of scientific progress. In it, he essentially describes scientific programs as progressive or degenerating. Scientific programs are defined, on his view, by the ‘hard core’ set of principles that underlie the scientific idea. A progressive program is able to handle new objections with ease only making use of existing ‘hard core’ principles. Degenerating programs need to add progressive sets of ‘protective belts’ that were not included in the original program. It has been gratifying for me to see how much 'falls out’ of State Space Theory in a principled manner rather than having to ad hoc new patches in order to fix the theory.
This is the difference between continuous time and discrete time formulations of network function. This can get very deep very fast, but at a very high level some people, like Dean Buonomano, argue that continuous time is critical to consciousness. This means that making a ‘computer version’ — where the computation advances one step at a time — is exactly the problem. We will confront that debate eventually, but now is not the time.
For the Turing nerds in the crowd, Turing himself distinguished between what he called an a-machine — what we’d now call a classic Turing Machine — and an o-machine. The o-machine processed data from an external oracle. I acknowledge that he barely mentioned it, but it shows that Turing himself acknowledged that this distinction would eventually have to be dealt with. And an entire literature has grown up around it: starting with van Leeuwen in 2001, through Goldin and Wegner in a series of articles 2004-2008, through the work of Cabessa and Siegelmann (particularly a pair of articles published in 2012 and 2014), and today worked on by Martin and colleagues, Jaeger, and Fu.