The Boundary Problem

Introduction:

In this article we will examine a problem in the philosophy of mind known as the boundary problem. To develop an intuitive grasp of what the boundary problem is, we will look at how a theory of consciousness called Integrated Information Theory (IIT) attempts to address it.

The Boundary Problem

Let us begin with the boundary problem itself and how it arises. The problem emerges once we assume that there are distinct conscious subjects whose experiences differ—either qualitatively or quantitatively. If “you” and “I” have non-identical conscious experiences, we need an account of what separates one stream of experience from another. Without some principle that enforces “this experience belongs here, not there,” the default position collapses into monopsychism: a single universal consciousness. This issue arises regardless of whether one adopts a materialist, functionalist, or panpsychist worldview.

The intuitive response is simply to appeal to the brain. We assume that consciousness emerges from neural processes—or that the brain functions as some kind of receiver—and that its structural or functional organization creates the boundaries between subjects. Conceptually, this works well enough: we acknowledge the boundary problem, admit that we do not yet know the precise mechanism, and assume that the brain provides the answer.

The problem resurfaces, however, when we attempt to construct a serious theory of consciousness, since any such theory must explain local boundedness rather than merely presupposing it.

A Thought Experiment: Functional Equivalence and Disconnection

To clarify why some sort of binding mechanism is required, let us turn to a thought experiment.

On Lex Fridman’s podcast, Karl Deisseroth presents a thought experiment involving optogenetics, a technique in which cells are modified by introducing light-sensitive proteins called opsins. These allow researchers to turn cells on and off using light—neurons, in this case. While the technology is still relatively primitive, it is already advanced enough to motivate a future scenario in which optogenetic stimulation could fully emulate the brain’s complete electrochemical signaling.

Imagine showing a person a red piece of paper and recording all of their neural activity for one second. We then reproduce that activity using optogenetics, stimulating the same neurons in the same temporal pattern. Does the person have the same experience of seeing the red piece of paper?

To many of us, this seems plausible. It is the same brain, and the same neural activity is being instantiated.

Now imagine spreading those neurons out over a much larger distance and connecting them with fiber-optic cables. We repeat the stimulation. Does the person still have the same experience? This already feels far more questionable.

If one’s theory of consciousness depends exclusively on functional or computational patterns, however, the two scenarios are equivalent.

Let us push the thought experiment further. Suppose we sever all of the fiber-optic connections entirely and instead stimulate each neuron locally. The system is now fully disconnected. No neuron communicates with any other. Each neuron is stimulated according to a preprogrammed schedule, synchronized by a shared clock. Nevertheless, the overall firing pattern across the population of neurons is identical to the original one-second recording.

Does the person still have the same conscious experience?

This is a poisonous bullet. Biting it leads to serious problems. But why, exactly? After all, the original function of the neural pathways was simply to propagate signals. If we bypass that propagation by stimulating each neuron directly, why should the result differ?

Once this bullet is bitten, spatial boundaries evaporate entirely. Neurons across millions of brains could, in principle, participate in a single conscious pattern. Worse still, if one relies on a broadly computational model, neurons themselves are no longer privileged. Atoms would suffice. Conscious systems could then span arbitrarily large regions of space, up to and including the entire universe.

In such a scenario, why is your consciousness tied to your brain at all? It may seem obvious that the brain generating the pattern is attached to your body, but this appeal quietly reintroduces spatial boundaries that the theory itself has abandoned. Why does your experience not borrow neurons—or atoms—from those around you? Within this framework, spatial proximity is not merely unprivileged; it is irrelevant.

IIT’s Initial Response to the Boundary Problem

This brings us to the next stage of the discussion: how specific theories of consciousness attempt to solve the boundary problem rather than assuming it away.

IIT addresses the decoupled-brain scenario through its irreducibility postulate, which examines the effect of severing any given element—or set of elements—from a system. If removing an element has negligible impact on the rest of the system, that element is considered reducible. Only irreducible systems count as candidates for consciousness. In practice, this means that under IIT’s postulates, the decoupled brain would be reduced to individual neurons.

Let us now take a closer look at IIT itself, to understand how it attempts to handle boundary problems and what difficulties arise.

Integrated Information Theory

Integrated Information Theory is a framework that uses a computational-style formalism to explain consciousness in terms of causal integration. Fully understanding IIT requires engaging with its mathematical machinery, but since our focus is the boundary problem, we will remain at an intuitive level.

IIT measures causal integration using a quantity called Φ (phi), intended to capture the strength of causal constraints within a system.

A helpful way to think of Φ is as a measure of how tightly the elements of a system constrain one another. If a small intervention in one part of the system barely affects anything else, the system has low Φ. If even a minor change significantly alters the system’s cause–effect structure, the system has high Φ. Crucially, IIT requires bidirectional causal influence. A purely feed-forward chain (A → B → C) has very low Φ because changes downstream do not constrain upstream states. Without mutual constraint, the system lacks intrinsic causal power.

You can think of Φ as analogous to a loaded spring: it represents the system’s intrinsic cause–effect power at a given moment. Unlike a physical spring, this power does not propagate outward; it consists in how the system constrains its own possible states through bidirectional relations.

The XOR Grid and the Absence of Temporality

To illustrate what IIT means by causal integration, consider Scott Aaronson’s well-known critique of the theory. He imagines a massive two-dimensional grid of XOR gates, all connected and all initialized to zero. The system is entirely static; nothing happens. Yet according to IIT, it has enormous Φ, because flipping any single bit would produce a massive bidirectional cascade across the network.

IIT proponents accept this implication. A frozen but maximally sensitive XOR grid would count as conscious—a kind of “loud hum,” locked into a single state with enormous intrinsic causal constraint.

An intuitive response is to introduce something like Shannon entropy, or a dependence on realized states over time, which would exclude the static grid. But this is precisely what IIT seeks to avoid. Proponents insist that consciousness must exist in the “here and now,” independent of temporal unfolding, and they are careful to avoid drifting toward functionalism.

The benefit of excluding temporality, however, remains unclear. Calculating Φ already relies on hypothetical interventions that unfold over time. Moreover, any system whose actual history unfolded in a particular way necessarily possessed, at every moment, the causal structure that enabled those transitions. It is not obvious that introducing an explicit temporal component would undermine IIT’s commitment to present-moment consciousness.

Irreducibility and the Main Complex

Another central concept in IIT is irreducibility. Consciousness, according to the theory, resides only in the “main complex”: the subset of elements whose causal power cannot be reduced without loss. If removing a component does not significantly alter the system’s cause–effect structure, that component is excluded.

The standard example is the brain. While computing the Φ of a real brain is infeasible, the main complex is thought to lie primarily in posterior cortical regions. The cerebellum, by contrast, is largely feed-forward. Including it would lower Φ, so it is excluded. This is IIT’s explanation for why we experience a unified field of consciousness rather than fragmentation across many parallel subsystems.

However, the same logic gives rise to deeper puzzles.

The Two-Person Fusion Problem

Imagine two people interacting. Suppose person A’s brain has a higher Φ than person B’s.

We begin with A. We evaluate A’s brain as a candidate system, identify the main complex in the posterior cortex, and exclude the cerebellum because including it would lower Φ. This follows standard IIT procedure: include what increases irreducibility and exclude what does not.

Now expand the candidate system to include both A and B together. This step is mandatory under IIT, which requires evaluating all possible candidate systems rather than restricting attention to intuitively defined ones. When we do this, we encounter a massive bottleneck. Communication between two brains is low-bandwidth, indirect, and largely feed-forward. Severing the connection barely alters the cause–effect structure of either brain. As a result, the combined A+B system is reducible, and A’s brain remains its own main complex. No fused consciousness emerges.

So far, this is unproblematic.

Now consider B. When B is treated as the candidate system under the same global, non-perspectival IIT rules, we again evaluate all supersets that include B. The combined A+B system contains a subsystem—A’s brain—with a higher Φ than B’s entire brain. By IIT’s exclusion principle, a subsystem contained within a larger, more irreducible complex is excluded. On these rules, B’s brain becomes an unintegrated appendage of A’s complex. In other words, person B would lose consciousness when interacting with person A.

This is not a shift in subjective perspective. “From B’s perspective” here simply means that B is treated as the candidate system under exactly the same evaluation procedure used everywhere else in IIT. No additional assumptions are introduced.

Scaling this reasoning up produces a winner-take-all outcome: the highest-Φ complex dominates, excluding all others and collapsing consciousness into a single subject.

One might object that the combined A+B system was already ruled out as a unified complex due to the communication bottleneck. That is correct; no fused super-system emerges. But the same logic IIT uses to exclude the cerebellum as an unintegrated subsystem applies equally here. Just as including the cerebellum lowers Φ when evaluating A, including B’s brain lowers Φ relative to the larger A-complex when evaluating candidate systems that contain B. By IIT’s own criteria, B is excluded in exactly the same way the cerebellum is.

The natural response is to insist that two separate brains are distinct systems, whereas the cerebellum is part of A’s brain. But without a principled, theory-driven criterion for what counts as “the same system,” this distinction is not supported by IIT’s formalism. Anatomically they differ, but under IIT’s rules they are both simply subsystems whose inclusion lowers Φ.

Another possible move would be to allow multiple complexes—local maxima that coexist. But IIT forbids this through its exclusion postulate: only the single maximally irreducible complex counts as conscious. Allowing secondary complexes would resurrect exactly the issues IIT sought to avoid, since structures like the cerebellum would then qualify as conscious subsystems.

Granularity, Elements, and Circularity

IIT ultimately attempts to avoid these boundary-collapse problems by imposing strict criteria on what counts as an element and which candidate systems are even allowed.

To see how these additional criteria operate, let us return to the Two-Person Fusion Problem and attempt to break the boundary again.

The most obvious way to do so is by examining the “weak connection” between the two brains—the air that transmits oral communication, carries odorants, and serves as the medium through which photons travel, creating auditory, olfactory, and visual cause–effect bridges.

IIT proponents argue that this connection is mostly feed-forward and chaotic. Air molecules interact with one another, but the effect is largely propagation rather than bidirectional constraint. The messiness leads to low causal integration, and severing the connection does not meaningfully impact the cause–effect structure of either brain A or B. This is why the system is reducible and no combined super-system emerges.

However, we can observe that the “weak link” is analyzed at a different granularity than the brains themselves. When we examine the brain at the granularity of neurons, we find high causal integration. The system appears clean: a neuron either fires and sends a signal—causally affecting other neurons—or it remains dormant. The relative lack of noise is precisely what makes the system so tightly integrated; every element is strongly constrained by the others.

But what happens if we zoom in further—if we analyze the same neuronal mechanisms at a finer granularity, such as ion channels or molecular interactions? Suddenly the system becomes noisy and chaotic, and causal integration plummets. This leads to a natural question: if the neuron occupies a granularity at which causal integration is uniquely large, what prevents us from identifying a granularity and boundary at which the communication bridge between the two brains is uniquely large? If we can do that, then according to IIT’s formalism the boundary between the two brains collapses once again, yielding a fused system with a higher Φ than either brain individually. What if, for example, we defined the entire communicational bridge between the two brains as a single element with an enormous number of inputs and outputs?

IIT accepts this challenge but imposes an additional criterion: elements themselves must be irreducible local maxima. Under IIT’s rules, our attempt to treat the entire communication channel as a single element fails. Airwaves, lightwaves, and odorants are largely independent streams of information and therefore do not meet the criteria for an element.

IIT effectively bets that if we were to evaluate all possible systems at all possible granularities, neurons and the brain would yield the highest Φ.

As you may have noticed, however, an element is defined by the same rules as the main complex itself. This creates a circular nesting problem: the only way to determine what counts as an element is by identifying what yields the highest-Φ main complex. The same winner-take-all dynamic seen in the Two-Person Fusion Problem reappears. This makes even simple toy systems extremely difficult to calculate and renders real systems effectively intractable.

Models, Simplifications, and Temporality

All of this is further complicated by the fact that our models are highly simplified. Neurons are often treated as binary or near-binary on/off switches in IIT calculations. This is not how neurons actually behave, and it further complicates how we analyze different granularities and where we draw boundaries.

As if these difficulties were not already substantial, an additional problem looms: temporality. Because IIT does not incorporate a genuine notion of time into its formalism—aside from discrete counterfactual transitions between states—we can, in principle, examine cause–effect structures at any timescale. Atomic timescales are not privileged over milliseconds, nor are milliseconds privileged over millennia. If it was not already clear that one could gerrymander one’s way to a higher Φ than neurons and brains, the possibility now borders on the absurd.

Assessment and Motivation

IIT is one of the few theories of consciousness that confronts the boundary problem directly and attempts to solve it. While this article is critical of IIT, the aim is not dismissal but illumination. The theory’s rigorous attempt to impose principled boundaries highlights just how severe the conceptual difficulties are. In doing so, IIT paves the way for deeper understanding and challenges our common intuitions about consciousness.

To conclude, let us consider an analogy that illustrates why the boundary problem is so elusive.

Intelligence, Computation, and Observable Boundaries

Functionalist accounts of intelligence rely on abstract computational patterns similar to those invoked by many theories of consciousness. However, they have one major advantage: intelligence can be demonstrated.

I can wire the outputs of a computer’s internal computations to a monitor and verify that the system is performing something we might reasonably call intelligent behavior. Unplugging the monitor does not remove the intelligence; it merely removes our ability to observe it.

I can place two computers next to one another and, because our theory of intelligence appeals to abstract computational patterns, I might worry about the computers “borrowing” states from one another in the same way consciousness theories worry about boundary leakage. The difference is that I can plug the monitor back in and verify that nothing of the sort occurs. The boundaries remain exactly where we expect them. There is no mysterious interaction because the systems are not causally connected. This might suggest that the boundary problem is illusory.

The argument seems compelling, but it misses a crucial fact. While unplugging the monitor does not remove intelligence, scrambling the wires does. If nobody knows how the wires are meant to connect—or even what they are meant to do—the intelligence disappears. The internal states of a computer carry no inherent semantic meaning. Semantics are something we ascribe. The computer merely transitions syntactically between states, and coherence arises only because those states are coupled to specific mechanisms that interact with the world.

A monitor produces pixels that yield images. A trained driving system produces steering commands that move a car. In each case, there is a specific, non-arbitrary way in which outputs are coupled to mechanisms that make the system intelligent. Abstract computation alone does not suffice; it must be embedded in the right causal structure. Decouple it, and the intelligence vanishes. For any given computational system, there is a specific wiring between inputs and outputs that yields intelligence, and the mechanisms it connects to are essential, not optional.

Consciousness, by contrast, is often treated as an intrinsic property of an abstract computational pattern itself. This removes substrate dependence and, with it, the kinds of observable boundaries we rely on in the case of intelligence.

A Final Thought Experiment

Consider the millions of brains distributed across Tokyo, each containing billions of neurons. At any given moment, one could in principle identify a computational pattern across these neurons that corresponds to a digital computer outputting a cube on a monitor. We could even imagine connecting wires to those neurons and attaching them to a monitor, briefly producing that cube.

What would follow is complete incoherence. There would be no stable continuation, no meaningful sequence of states. We would not obtain intelligence; we would obtain noise. The pattern exists, and it could in principle represent a cube, but it lacks coherence. The absence of intelligence is observable.

If consciousness is instead treated as an intrinsic property of that abstract pattern, then the pattern simply is a cube. Selecting those neurons as our system yields a momentary stream of consciousness of a cube, followed by randomness. This provides no principled boundaries. The pattern does not depend on output wiring or causal embedding, and so there is no reason why the neurons in my brain are privileged for my consciousness. Spatial proximity does not matter for abstract computation; it matters only for our practical ability to instantiate and maintain coherent causal structures.

If, on the other hand, our theory of consciousness is substrate-dependent, the boundaries become observable. They are given by physics itself.