A chord in Dharwad

On the last evening of a music festival in Dharwad, a choir of forty-eight voices sings a slow chorale in a school hall. The conductor, Kavita Kulkarni, has arranged the singers in an unusual way. The sopranos, altos, tenors and basses do not stand in blocks. They are scattered through the rows, so that every singer has neighbours from other sections. Kavita says it makes them listen harder.

At the back of the hall, a sound engineer named Imran Sheikh sits at a mixing desk. He has clipped a small microphone to every singer. His screen shows forty-eight separate tracks, each one a single voice, rising and falling in its own lane. On his headphones, when he pushes all the faders up, he hears what the audience hears: one chord, warm and full, that seems to come from the whole room.

In the third row of the audience sits Prakash Joshi, a retired physicist who has spent his retirement reading philosophy of mind. During the interval he catches Imran at the desk. "Each of those singers hears her own part," he says. "You can hear all forty-eight at once, and I hear a chord. My question is whether the choir hears the chord. Is there a forty-ninth listener, made of the other forty-eight?"

Imran laughs and says that is above his pay grade. But Prakash is serious, because he has been reading Philip Goff. Goff defends a view on which every fundamental particle has some tiny experience, and our own experience is built out of theirs. If that is right, Prakash says, then his own mind is a kind of choir. Billions of tiny listeners somehow make one person who hears one chord. Whatever makes that happen in his head, he wants to know why it does not happen in the hall.

Kavita, Imran, Prakash, the festival and the choir are invented. They are there to make an old problem concrete, and they are never evidence for an answer. The problem itself is real: philosophers call it the combination problem, and it is the main reason many people who are drawn to panpsychism do not accept it.

This paper asks how micro-level intrinsic natures could combine into one macro-subject without breaking the match between the structure of experience and the structure of the brain. My answer is that they cannot, on the assumptions constitutive panpsychism makes. I set out three conditions any combination must meet: it must preserve structure, it must yield exactly one subject built from the micro-subjects, and it must add no new primitive ingredient. I argue, and test in a small audit, that no combination function meets all three. The view must give one up, and the cheapest one to give up turns it into something its defenders did not intend: a theory on which the micro-subjects do no work.

What the physics leaves out

The view Prakash has been reading is called Russellian monism. It starts from a claim about physics that is less strange than it sounds. Physics tells us what things do. It describes mass by how a massive thing accelerates and attracts, charge by how charged things push and pull. It tells us the dispositions, the relations and the laws. What it does not tell us is what the things that have these dispositions are like in themselves.

Bertrand Russell put the point sharply in The Analysis of Matter in 1927. Our knowledge of the physical world, he argued, is knowledge of its structure. We know the pattern of relations among events, and we know it well. Of the intrinsic character of the events that stand in those relations, we know almost nothing, with one exception. We know the intrinsic character of our own experience, because we have it.

Philosophers now call the unknown intrinsic natures quiddities, from the Latin for "whatness". Russellian monism says that the quiddities of physical things are what ground their dispositions. It then adds a bold hypothesis: the quiddities are experiential, or proto-experiential. The one intrinsic nature we know, the nature of experience, is a sample of the kind of thing that fills in physics everywhere.

The appeal of the view is easy to state. It promises to put consciousness into the physical world without making it an extra ingredient. Experience is not added on top of physics, as in dualism. It is what physics was always describing from the outside. And because the quiddities are what make the physical dispositions what they are, experience is not idle. It does causal work, because it is the categorical base of the causal powers physics describes.

Galen Strawson gave the view a forceful argument in his 2006 paper Realistic monism, in the Journal of Consciousness Studies. Experience is real, he argued, and nothing is more certain. If experience is physical, and it arises from physical ultimates, then either it emerges from wholly non-experiential stuff or the ultimates are already experiential. Emergence of experience from the wholly non-experiential, he argued, would be a kind of magic. So the ultimates must be experiential.

Goff's version, defended at length in his 2017 book Consciousness and Fundamental Reality, is constitutive Russellian panpsychism. It says three things: fundamental physical entities have experiential quiddities, and those entities are subjects of experience, however simple. And our own experience is constituted by theirs, in the way a wall is constituted by bricks. Nothing new is added when the bricks are put together. The wall is just the bricks, suitably arranged.

[AUTHOR NOTE: if you wish, a sentence on where you first met Russellian monism and what drew you to it.]

That last claim is the one that makes the view attractive and the one that makes it vulnerable. If human experience is merely micro-experience suitably arranged, then explaining it requires saying what the arrangement is, and showing that it yields what we find. That is where the combination problem begins.

Return to the hall, where Imran's forty-eight tracks are, in Russell's sense, the structure. He can see when each voice rises and falls, how loud it is and how it relates to the others. What he cannot see on the screen is what it is like to be any singer. Each track's quiddity, if Goff is right, is the singer's own experience of singing her part. Now change one feature, and suppose the singers were not people but particles, each with a tiny experience no richer than a single tone. The question is the same: what turns forty-eight tones, each felt by its own tiny subject, into one chord heard by one subject?

James and the twelve men

The problem has a classic statement. In 1890, in chapter six of The Principles of Psychology, William James considered what he called the mind-stuff theory, the view that complex minds are made of simpler ones. His objection is one of the most quoted passages in the philosophy of mind.

The full passage, in the York University edition of chapter six, makes the point twice. Feelings packed together, he wrote, each remain "the same feeling it always was, shut in its own skin, windowless". And he offered the image that has stayed with the debate ever since: twelve men, each told one word of a sentence, with no consciousness of the whole sentence anywhere among them.

James's challenge is about subjects, and each man has his own perspective. Putting the perspectives side by side does not produce a new perspective that contains them. Something more would be needed, and nothing in the mere collection supplies it. Prakash's choir is James's twelve men with music instead of words.

Three conditions on combining

To make the problem precise, I want to state what a solution would have to do. Think of a combination function as a rule. It takes as input the micro-level facts, which on Russellian monism are of two kinds: the quiddities of the micro-entities and the structure of relations among them. It gives as output the macro-level experiential facts: which subjects exist, and what each of their experiences is like.

Constitutive panpsychism needs a combination function that meets three conditions. I state each informally first, then more precisely.

The first is structure preservation. The structure of a macro-subject's experience must match the relevant structure of the system that has it. When Prakash hears the chord, his experience has a structure. Some notes sound closer together than others, some louder, some higher. David Chalmers, in his 1995 paper Facing up to the problem of consciousness, called this match the principle of structural coherence. He wrote that it is "this isomorphism between the structures of consciousness and awareness" that the principle expresses. A combination function that yields an experience whose structure does not match what the brain is doing has got the wrong answer, however it got there.

The second is subject unification. The function must yield exactly one subject for a system like Prakash, and that subject must be built from the micro-subjects. Exactly one, because Prakash is one person, not a crowd. Built from the micro-subjects, because that is what constitutive panpsychism says: the macro-subject is constituted by them, and they persist as its parts. A function that replaced the micro-subjects with something new would not be combination. It would be emergence, or replacement.

The third is non-redundancy. The function must use only the inputs Russellian monism provides: the quiddities, the structure and the dynamics. It may not add a new fundamental ingredient, such as a special relation that exists only to make subjects combine. If it does, the view is no longer the economical one its defenders advertise. And, as I shall argue later, the new ingredient threatens the causal advantage that made the view attractive.

More precisely, let a world be a set of micro-units, each with a quiddity drawn from a small palette, related by a pattern of physical coupling. Call the macro-structure that experience must match the target structure. In a brain, this is the structure of functional states, such as the way colour processing places red nearer orange than blue. Then the three conditions are these. Structure preservation: the experience of the subject that spans the system has a structure that correlates closely with the target. Subject unification: exactly one subject spans the system, and the micro-subjects are its constituents. Non-redundancy: the function uses no primitive parameters beyond the couplings, quiddities and dynamics.

The trilemma

My central claim is that these three conditions cannot all be met. Any combination function that meets two will fail the third, and the argument for this has three steps.

The first step concerns structure. On Russellian monism, the micro-experiences mirror the micro-physical structure, because quiddities are the intrinsic side of what physics describes. If you combine them by aggregation, simply summing what is there, the result mirrors the micro-structure too. But the structure of Prakash's experience does not mirror the micro-structure of his brain. It mirrors the functional structure, which is a very selective coarse-graining of it. So aggregation fails structure preservation.

The second step concerns selection. A combination function can meet structure preservation without adding ingredients if it selects, from the many coarse-grainings definable from the micro-structure, the functional one. Selection can use only the inputs: couplings and dynamics. The most developed selection rule we have is the one used by integrated information theory: find the part of the system that is most integrated and treat it, and only it, as a subject. But a rule that picks out one maximal subject excludes every overlapping candidate, including the micro-subjects themselves. They do not survive as subjects inside the macro-subject. Their quiddities still feature, but their subjecthood does no work. So selection fails subject unification, in the constitutive sense that requires micro-subjects to be parts.

The third step concerns bonding. To keep the micro-subjects as constituents and also get exactly one structurally correct macro-subject, the function must say which micro-subjects unite, and in what pattern. If that pattern is not fixed by the couplings and dynamics, it must be stipulated as a further fact. That is a new primitive, so any function that meets the first two conditions fails non-redundancy.

This is an argument, not a proof. Each step relies on a premise a defender could reject. The first step assumes that aggregation mirrors micro-structure. The second assumes that the only principled selection uses something like maximal integration. The third assumes that any pattern not fixed by couplings and dynamics is a new primitive. In the parts that follow, I take each premise in turn, test it in a small model, and say what a defender would have to deny.

Where the structure goes wrong

Chalmers gave the first step its name. In his chapter The combination problem for panpsychism, he separated three versions of the problem: one about subjects, one about qualities and one about structure. Within the structural version he picked out what he called the structural mismatch problem. "Macrophysical structure (in the brain, say) seems entirely different from the macrophenomenal structure we experience," he wrote. Micro-experiences should mirror micro-physical structure, especially on a Russellian view, and their combination should mirror something like macro-physical structure. "How do these combine to yield macrophenomenal structure instead?"

The point is easy to miss, so return to the hall. Change one feature: the singers are now arranged as Kavita arranged them, scattered, with no section standing together. Look at the stage from above and you see forty-eight people in a grid, with sopranos, altos, tenors and basses mixed through it. That is the spatial structure. Listen with Prakash, though, and you hear four parts, each with its own line, and a harmony among them. That is the structure of the experience. The two structures do not match, and neighbours on the stage are often far apart in the harmony.

A brain is like Kavita's choir, only more so. The neurons that carry the colour of a flower are not laid out in the shape of the flower, nor in the order of the colour wheel. They are spread across several areas, interleaved with neurons doing other things. The structure of colour experience matches the structure of what those neurons do, their functional relations. It does not match where they are, or what they are made of.

A small audit

To test the argument, I built a toy world and ran several combination functions on it. I call the procedure the Combination Audit. It is deliberately simple, so that every number can be checked.

The world has twelve micro-units. Each has a micro-quality drawn from a palette of two, as Russellian monism expects few kinds of quiddity. Each has a place on a line. And each belongs to one of three functional modules, which fix what it contributes to the macro-experience. Here, the modules carry three colours: red, orange and blue. As in Kavita's choir, the modules are interleaved in space. Units inside a module are strongly coupled to one another, and units in different modules are coupled more weakly.

The target structure, the one experience should match, is the colour space: red is close to orange and far from blue. For each combination function, the audit measures three things. First, how closely the experience of the largest subject matches the target, as a rank correlation between the two patterns of distance. Second, how many subjects the function yields, and whether the micro-subjects persist inside them. Third, how many extra primitive parameters the function needs.

Integration needs a measure. Integrated information theory has one, called phi, but computing it is expensive and its details are disputed. I used a transparent stand-in: the weakest normalised cut. For any set of units, find the way of dividing it in two that severs the least coupling, relative to the size of the smaller side. That is the set's weak point, and a set with a strong weak point is well integrated. The audit computes it by brute force, over every possible division of every possible set.

The minimal case

Begin with the smallest world that shows anything: four units in two modules of two. Inside each module the coupling is 1. Between the modules every unit is coupled to every other at a strength c. This can be worked out by hand. A single module has a weakest cut of 1, the one link between its two units. The whole has several possible cuts. The cut between the two modules severs four links of strength c, divided by two, giving 2c, and every other cut costs more.

So the whole is more integrated than either module exactly when 2c exceeds 1, that is, when c is greater than 0.5. The audit agreed: at c of 0.3, the whole scored 0.600 and each module 1.000. At c of 0.7, the whole scored 1.400.

What do the combination functions say? Aggregation, which counts every connected set of two or more units as a subject, found eleven subjects in a four-unit world, at either coupling. Exclusion, which picks the most integrated set and discards everything overlapping it, found two subjects at c of 0.3, one per module, and one subject at c of 0.7.

The realistic case

The twelve-unit world is the realistic case, in the limited sense that it has interleaved modules, a small palette and a structure to match. With coupling between modules at 0.6, the audit gave these results.

Aggregation found 4,083 subjects, every connected set of two or more units. Its structural match was −0.181, because the experience it produces mirrors the micro-qualities and positions, and those have nothing to do with the colours. Like every function here except bonding and the control, it needed no extra primitives. It failed structure preservation and subject unification and passed non-redundancy.

Exclusion found one subject, all twelve units, with an integration score of 3.867. Its structural match was 0.968, because the subject's experience follows the functional states of the complex. It needed no extra primitives, but the micro-subjects do not persist inside it as subjects. It passed structure preservation and non-redundancy, and failed subject unification.

A tuned bonding relation, one that bonds the micro-subjects in exactly the pattern needed, found one subject with a match of 0.968, and kept the micro-subjects as constituents. It passed structure preservation and subject unification. But it needed sixty-six extra primitive parameters, one for every pair of units, to say which bond and which do not. It failed non-redundancy.

The negative control, a random function, found an arbitrary subject with a match of −0.079 and needed twelve arbitrary parameters. It failed everything except by luck. No function in the audit passed all three conditions, and every function that passed two failed a different third. The table in the figure above sets them out.

A counterexample: the crystal

The first step of the trilemma said that aggregation fails structure preservation because micro-structure and functional structure differ. That is a fact about brains, not a necessary truth. To check that the audit is not rigged, I ran it on a world where they coincide. In this crystal, the modules are spatial blocks, and each unit's micro-quality is its module's colour.

In the crystal, aggregation's structural match rose to 0.970, while exclusion stayed at 0.968. Aggregation still produced 4,083 subjects, so it still failed subject unification, but the mismatch was gone.

This matters for the argument. The structural mismatch problem is contingent. It arises because brains are built in a way that does not lay experience out in the shape of matter. In a world of crystals, summing would get the structure right. The counterexample also shows what the trilemma does and does not claim. It does not say that aggregation always fails on structure. It says that in any world like ours, it does, and that where it succeeds, it still fails on the number of subjects.

An analogy, and where it breaks

The choir itself is the first analogy. A chord is made of notes, and nothing is added to the notes to make the chord. That is the picture constitutive panpsychism wants. But a chord is a chord only for a listener. The air in the hall carries forty-eight overlapping pressure waves. Their sum is a single complicated wave, and that wave has the structure of the chord. Whether anyone hears the chord as a chord depends on Prakash, not on the air.

The analogy holds for structure: the chord's harmony is fixed by the notes and their relations, with no extra ingredient. It breaks for subjects, because the chord is unified in Prakash's experience, and the analogy borrows his unity to make the notes seem unified. That is exactly the step combination is supposed to explain.

The price of a bond

Goff has a response to the subject problem, and it is the most direct. In a paper titled Can the panpsychist get around the combination problem?, he proposed a relation he called phenomenal bonding. When micro-subjects stand in this relation, they constitute a further subject. Goff admitted that "neither introspection nor perception affords us experience of any such relation". But he argued that he could find "no principled reason" against supposing that some such relation exists.

The proposal answers James by adding the very thing James said was missing. The twelve men lacked a bond; give them one, and there is a consciousness of the sentence. It is a clean move, and Goff was candid about its cost. In the same paper, he wrote that the solution leaves the panpsychist ontologically committed to the phenomenal bonding relation, in addition to the experiences of particles. That is the cost the trilemma names. Bonding passes subject unification by violating non-redundancy.

How heavy is the cost? That depends on whether the bonding relation is fixed by something else. Goff's own suggestion, as I read his 2017 book, is that the bonding relation might be the intrinsic nature of a physical relation, perhaps spatial relatedness. That reading should be checked against the book's chapter on bonding, and I mark it to verify. If so, it would not be a new primitive. It would be the quiddity of a relation physics already describes, and the bonding pattern would follow from the physics.

That suggestion is the right one to test, and the audit can test it. If bonding is the intrinsic side of some physical relation, then the bonding pattern should follow the coupling pattern, or the spatial pattern, or whatever that relation is. The question is whether any such pattern produces one subject with the right structure.

Try spatial relations first, where a bond that follows space bonds neighbours. In Kavita's choir, that bonds sopranos to tenors and basses, because they stand together, and gives a subject whose experience mirrors the stage. That is aggregation again, with the same mismatch, so try causal coupling next. A bond that follows coupling strength, with a threshold, bonds units that interact strongly. That gives either the modules or the whole, depending on the threshold. To get the right answer, the threshold must be set where integration peaks. That is exclusion again, and the micro-subjects again stop being subjects.

To keep both the right structure and the persistence of micro-subjects, the bond pattern must be set by hand. In the audit, that took sixty-six parameters. How likely is a bond pattern to come out right by chance? I drew two thousand random bonding relations at a density of 0.3 and counted how many bonded every pair of units within the same module. None did, and the analytic chance is about four in ten billion.

Coleman's dilemma

Sam Coleman pressed a version of this point into a dilemma. In The real combination problem, published in Erkenntnis in 2014, he argued that "subjects cannot combine". Each subject has a point of view, and a point of view excludes other points of view in a way qualities do not. Two subjects can share a quality, but they cannot share a perspective without ceasing to be two.

So, Coleman argued, the panpsychist faces a choice: "giving up her explanatory ambitions, or of giving up the claim that the ultimates are subjects". He took the second option: on his view, the ultimates have phenomenal qualities but are not subjects, and subjects are built later, from qualities, by some functional arrangement. "So panpsychists should be neutral monists," he concluded.

The audit puts Coleman's view in a familiar place. If micro-qualities are not owned by micro-subjects, then nothing is lost when exclusion picks out a macro-subject. The micro-qualities feature in its experience, and there were never micro-subjects to be excluded. Exclusion with subjectless qualities passes all three conditions, if subject unification is relaxed to require only that one subject span the system. That relaxation is exactly what constitutive panpsychism cannot accept, and exactly what Coleman recommends.

Roelofs and combination without exclusion

Luke Roelofs offers the most developed defence of combination. In Combining Minds, published in 2019, he argues that we are too used to seeing the mind as an indivisible unity. Understanding our place in nature, he writes, requires seeing minds as composite systems, "simultaneously one conscious whole and many conscious parts".

Roelofs would reject the exclusion step. On his view, the parts of a mind can be subjects too, and their experiences can be shared with the whole. A part's experience is not hidden from the whole; the whole has it, as part of a larger experience. That answers the subject-summing worry by denying that subjects are exclusive in Coleman's sense.

This is the strongest form of constitution, and I take it seriously. But it pays at the structural step. If every part with enough integration is a subject, and its experience is shared with the whole, then the whole's experience includes the experiences of every part. In the audit, that is 4,083 overlapping subjects, most of them with experiences that mirror micro-structure. The whole must somehow have the right structure despite containing all of these. Roelofs must say how the shared experiences of overlapping parts combine into the one structure Prakash hears. That is the original problem again, one level up.

A second analogy: the mosaic

Think of a mosaic of a peacock on a temple floor. Each tile has its own colour, and the peacock is made of nothing but tiles. Look from far enough away and you see a bird, with a structure the tiles do not have: a neck, a fan of feathers, an eye.

The analogy holds in one respect. The peacock's structure is fixed by the tiles and their arrangement, with nothing added. It is a selective coarse-graining of the tile pattern, and many tile patterns would show no bird at all. That is what selection does in the trilemma.

It breaks in two places. The peacock appears only to a viewer at the right distance, so the analogy again borrows a subject. And the tiles are not subjects, which Coleman would say is the point: a mosaic is a picture of neutral monism, not of constitutive panpsychism.

Starting from the whole

If parts cannot combine into wholes without a price, perhaps the direction is wrong. Perhaps the whole comes first. That is the idea behind cosmopsychism, the view that the universe as a whole is the fundamental conscious subject, and that individual subjects like Prakash derive from it.

Itay Shani set out the view in a 2015 paper on cosmopsychism in Philosophical Papers. His starting point is "the assumption that an all pervading cosmic consciousness is the single ontological ultimate". Individual minds are not built up from particles. They are aspects or regions of the one cosmic mind.

The view does not escape the problem. It reverses it. Chalmers, in the same chapter on combination, called the reversed version the decomposition problem. "How does macroexperience give rise to microexperience?" he asked. "How does a single subject give rise to multiple dependent subjects?" He judged that "these problems seem just as hard as the original combination problem".

Miri Albahari pushed the view one step further. In a chapter in the Routledge Handbook of Panpsychism, she argued that cosmopsychism has "serious troubles" that come from treating the cosmos as a subject. She proposed instead that the world is grounded in a universal consciousness which, following Advaita Vedānta, "is not structured by subject or object". On her view, subjects are not carved out of a cosmic subject. They arise when a consciousness without a subject is structured by a point of view.

Contraction in the Pratyabhijñā

The Kashmiri non-dual Śaiva tradition, from which this series takes its test hypothesis, faced the decomposition problem a thousand years before Chalmers named it. Its answer has a precise vocabulary. Kṣemarāja's short treatise, the Pratyabhijñāhṛdayam, opens with a sūtra that, in the Mahānaya edition, reads "citiḥ svatantrā viśvasiddhihetuḥ". The edition translates it as: the self-dependent power of consciousness is the cause of the manifestation, maintenance and dissolution of the universe.

The individual enters at the fourth sūtra: "citisaṅkocātmā cetano'pi saṅkucitaviśvamayaḥ". Even the perceiver, characterised by the contraction of consciousness, is composed of a contracted universe. The fifth adds that consciousness itself, descending from the level of the conscious being, becomes the individual mind by contracting in the form of its objects.

The key word is saṅkoca, contraction. On this view, the individual subject is not a part of the cosmic subject, as a brick is part of a wall. It is the whole, contracted. Prakash is not one wave on a cosmic ocean. He is the ocean, narrowed to a point of view, and he contains the universe in a contracted form. Recognition, pratyabhijñā, is the reversal: the contracted subject coming to know itself as what it always was.

This is a top-down combination function, and the audit can run it. Start from one subject over the whole world. Choose a contraction mask, a rule that says which part of the world each individual subject is contracted to. The individual subject's experience is the cosmic experience restricted to its mask. The question is what sets the mask.

The audit tried two answers. If the mask follows place, contracting to spatial regions, the result was two subjects in a brain that should have one, with one extra parameter for the boundary. Each half happened to contain all three colours, so the structure within each was right, but the number of subjects was wrong. If the mask follows integration, contracting to the most integrated complexes, the result was identical to exclusion: one subject, with a match of 0.968 and no extra parameters.

So contraction by integration is exclusion read downward. It gets the structure and the number of subjects right without new primitives. And it does so because the mask is set by the same rule that set exclusion's complexes. The cosmic subject contributes nothing to where the boundaries fall. That is not a refutation of the Pratyabhijñā view. It is a demand on it: whatever sets the contraction must be something that tracks integration.

A third analogy: the ocean and the wave

The image of the ocean and its waves is common in writing on non-dual traditions. A wave is not a separate thing added to the ocean. It is the ocean, shaped for a while.

The analogy holds for dependence: a wave cannot exist without the ocean, and the ocean does not need any one wave. That is the direction of grounding cosmopsychism proposes. It holds for unity too: there is no question how waves combine into an ocean, because the ocean came first.

It breaks for privacy. Waves have no private contents. Two waves can merge without either losing anything it had kept from the other. Subjects are not like that. My toothache is not available to you, though on cosmopsychism we are both the one cosmic subject. The ocean image hides the very thing the decomposition problem is about.

Bridges and cuts

The audit's most useful output is not the table. It is the sweep. Return to the twelve-unit world and vary the coupling between modules, keeping everything else fixed. At low coupling, exclusion finds three subjects, one per module, each with a weakest cut of 2.000. As coupling rises, the whole becomes more integrated. At a coupling of 0.24 the whole scored 1.920, still below the modules. At 0.26 it scored 2.053, and exclusion found one subject.

In between, at exactly 0.25, the whole and each module tied at 2.000. Sixteen different sets shared the top score. The result depended entirely on the rule for breaking ties. The audit's rule, prefer the larger set, gave one subject. A rule preferring the smaller would have given three. Nothing in the integration measure decides between them.

That is the failure boundary of the exclusion approach. Where integration is balanced, the number of subjects is not fixed by the structure, and a tie-break rule must be added. A tie-break rule is a new primitive, though a small one. In real brains, exact ties may be rare. But near-ties are not, and near the boundary small changes in coupling switch the number of subjects.

Two real cases sit close to this boundary.

On exclusion, the Hogans should be either one subject or two, depending on whether the bridge makes the joined system more integrated than either brain alone. Sharing some contents while remaining two subjects is not an option the rule allows. On constitutive panpsychism, the twins should be two subjects and a third, the joint subject, made of both. The reporting fits neither cleanly. Two subjects who share some experiences is what Roelofs's view predicts, and it is the best evidence in his favour.

For exclusion, the split-brain finding is a warning. If the corpus callosum carries most of the coupling between hemispheres, cutting it should drop the whole below each hemisphere and produce two subjects. If Pinto is right, it did not. Either subcortical routes keep the whole more integrated than either half, or the number of subjects is not fixed by integration alone. The first is possible and testable. The second would undo the selection step of the trilemma.

Contraction and the layers of RTM

This series tests a five-layer hypothesis, the Recognition Theory of Mind, drawn from the Pratyabhijñā. L1 is spanda, the dynamic pulse of consciousness. L2 is prakāśa, the light by which anything appears. L3 is vimarśa, consciousness aware of itself. L4 is pratyabhijñā, recognition. L5 is cit, consciousness as the ground. The combination problem bears directly on three of them.

L5 is the hypothesis's cosmopsychism. If cit is the ground, then individual subjects are contractions of it, and the combination problem becomes the decomposition problem. The audit's result is that contraction can get the structure and the number of subjects right, but only if the mask follows integration. Cit, as the ground, explains why there is experience at all on this view. It does not explain where any subject's boundary falls.

L1 is where that work must go. Spanda is the tradition's name for the ceaseless activity of consciousness, its vibration or pulse. If RTM is to answer the decomposition problem, spanda must be what sets the contraction. That means it must be, or must correspond to, something like the dynamics whose integration structure fixes the complexes. This is a strong claim, and a testable one. It says that wherever integration peaks, there is a contracted subject, and nowhere else.

L4 is affected in a different way. Recognition is the reversal of contraction. If contraction follows integration, then recognition cannot be a widening of the boundary, since the boundary is fixed by the brain's dynamics. It must be a change in how the contracted subject takes itself, not in where its edges are. That fits the contemplative case: Kavita's widening, as reported, did not reach Imran's itch.

L2 and L3 are barely touched. Prakāśa, the light in which things appear, is not divided by contraction on this reading; what is divided is access to what appears. Vimarśa, self-awareness, belongs to each contracted subject, and the audit says nothing about it. I mention them only to mark that the combination problem is not a test of the whole hypothesis. It is a test of its outer and inner layers, the ground and the dynamics, and of how they are joined.

Why not simply adopt exclusion?

A reader might ask why RTM needs spanda at all. If exclusion does the work, why not adopt integrated information theory and leave the Kashmiri vocabulary aside? There are two reasons, one in each direction.

The first is that exclusion, on its own, is a postulate without a ground. Tononi and colleagues, in their 2016 review in Nature Reviews Neuroscience, state that the physical substrate of consciousness "must be a maximum of intrinsic cause-effect power". They derive this from what they take to be essential properties of experience, but they do not say why maxima, and only maxima, should be subjects. A view that grounds subjects in one consciousness and lets its dynamics set the boundaries at least offers an answer: the maximum is where contraction closes.

The second reason runs the other way, and it is a warning to RTM. If spanda is defined as whatever produces integration maxima, it explains nothing that exclusion does not. It earns its place only if it predicts something exclusion does not. One candidate is the behaviour of ties. Exclusion needs a rule to break them. A view on which contraction is an activity, not a static selection, might predict that near ties the boundary oscillates, and that subjects near the boundary report instability. That is a prediction a study could check, and it is the kind RTM must make if its first layer is to be more than a name.

What would test L1

A study that could put this at risk is easy to describe and hard to run. It needs cases where integration and subject count can be measured independently. Split-brain patients are one. The Hogans are another. Patients under anaesthesia, as integration falls, are a third.

The refined RTM predicts that the number of subjects tracks the number of integration maxima. Where integration is unified, as Pinto's findings may suggest for the split brain, there is one subject. Where it divides, there are two. Where it is near a tie, reports should be unstable, with patients sometimes behaving as one and sometimes as two.

If the number of subjects came apart from integration, that would count against L1 as RTM needs it. It would also count against exclusion and against contraction by integration. It would leave bonding and Roelofs's combination, both of which pay their own costs, as the remaining options.

The verdict for RTM is that the hypothesis is refined, not confirmed or refuted. Its top layer cannot carry the structural work cosmopsychism needs, and it should stop claiming to. Its first layer must carry it, and that turns an old metaphor into a claim about dynamics that a neuroscientist could test.

The strongest case against this paper

Here is the best objection I can build, in the voice of a careful constitutive panpsychist.

"The author's trilemma rests on a toy model with a made-up integration measure. Real combination, if it happens, happens in brains with billions of units and dynamics no one can compute. Nothing follows from twelve units and a normalised cut. The audit is a picture of the author's assumptions, not a test of the view.

"Worse, his subject unification condition is rigged. He requires that the micro-subjects persist as subjects inside the macro-subject. But constitution does not require that. A wall is constituted by bricks, and the bricks are still bricks, but they do not stand to the wall as bricks stand to each other. Micro-subjects can be constituents of a macro-subject without their perspectives showing up inside it. That is just what it is to be a constituent rather than a part in a heap.

"Finally, his charge against bonding is unfair. Every theory has primitives. Physicalism has its laws, IIT has its postulates, and the author's own favoured exclusion rule is a primitive too. If adding one relation to the fundamental inventory solves the oldest problem in panpsychism, that is a bargain, not a failure."

I accept the first point in part. The audit is a toy, and its integration measure is a stand-in. But the trilemma is not derived from the audit. It is an argument, and the audit only shows that its steps are not empty: a function can be built at each corner, and none at the centre. A bigger model would not remove the dilemma, because the steps do not depend on size.

I accept the second point as a fair challenge, and I think it is the best reply available. It amounts to saying that micro-subjects can constitute a macro-subject without their subjecthood contributing anything to it. But that is Coleman's conclusion, stated more gently. If the micro-subjects' perspectives play no role, then what does the work is their qualities and arrangement. The view is then neutral monism with an extra, idle claim that the ultimates are subjects.

I do not accept the third point. It is true that exclusion is a primitive principle. But it is a principle stated once, over all systems, using only couplings and dynamics. Bonding, as the audit shows, must be specified pair by pair, unless it is grounded in some physical relation, and then it collapses into aggregation or exclusion. The difference is between one law and a list.

What would change my mind

I would give up the central claim, that no combination function meets all three conditions, under any of the following.

First, a combination function that uses only couplings, quiddities and dynamics, yields exactly one subject for a brain-like system, matches its functional structure and keeps the micro-subjects as subjects. I have not found one, and I have argued that none exists. But the argument has premises, and a function that broke one would break the trilemma. This bears on RTM's L5 and L1.

Second, evidence that micro-structure and functional structure coincide in brains more than I have assumed. If experience were found to mirror the spatial and material layout of neural tissue, aggregation would be revived and the first step would fail.

Third, a principled account of phenomenal bonding that grounds it in a physical relation and still yields the right pattern. That would remove the charge of redundancy. It would need to explain why the relation bonds within functional modules and not within spatial neighbourhoods.

Fourth, evidence that the number of subjects in real systems does not track integration. That would not save constitution, but it would undo exclusion, and with it the refinement I have proposed for RTM's L1.

Two dated predictions put the argument at risk.

• By the end of 2029, no published constitutive panpsychist model will specify a combination function that meets all three conditions without an exclusion or maximum principle. If one does, my central claim is false.
• By the end of 2029, at least one formal paper on panpsychism or cosmopsychism will adopt an explicit maximum-of-integration principle to fix subject boundaries. If none does, the convergence I describe between exclusion and contraction is my construction, not the field's direction.

Mahapatra, R. R. The chord nobody hears: a formal trilemma for constitutive panpsychism and the contraction alternative. Mind Frontier. DOI to be assigned. https://rajeshrmahapatra.com/papers/mind-frontier/u0998-the-chord-nobody-hears.html

@article{mahapatra-mf49,
  author = {Mahapatra, Rajesh Ranjan},
  title = {The chord nobody hears: a formal trilemma for constitutive panpsychism and the contraction alternative},
  journal = {Mind Frontier},
  doi = {DOI to be assigned},
  url = {https://rajeshrmahapatra.com/papers/mind-frontier/u0998-the-chord-nobody-hears.html}
}