A blocked transfer in Frazer Town

On a Monday morning in March, Philomena Fernandes, who is seventy-one and has banked with the same cooperative bank in Bengaluru for forty years, tries to send ₹4.8 lakh to her grandson's university in Dublin. It is the largest payment she has ever made, and the first to a beneficiary outside India. The transfer is blocked within two seconds. A message on her phone tells her to visit the branch.

The bank, which I will call Malnad Cooperative Bank, runs a fraud model its staff call Kavach. Kavach scores every outgoing payment and blocks the riskiest. It runs on two clusters of graphics processors, one in Pune and one in Chennai, and a compressed copy runs on tablets in the branches for when the network is down. The three copies use different chips, different number formats and different internal layouts. They agree on almost every decision.

Mrs Fernandes's son files a complaint with the banking ombudsman. The bank's model risk officer, Dr Ananya Rao, has to write a reply. Her draft says that the transfer was blocked because the amount was unusual for the account and the beneficiary was new and overseas. Both are true of the payment. Kavach's documentation says those are the two features that drive a block.

Before she sends it, a senior engineer, Farhan Siddiqui, stops by her desk. He has read some philosophy. "Strictly speaking," he says, "that is not what caused the block. What caused it was a particular pattern of voltages in a particular chip in Pune. Your 'unusual amount' is a story we tell about those voltages. If you want the real cause, it is in the logs, and it is about fourteen million numbers long."

Ananya, the bank, Kavach, Farhan and Mrs Fernandes are invented, a way to make an old argument concrete. They are never evidence for it. The argument Farhan is making is real. It belongs to the philosopher Jaegwon Kim, and for thirty years it has been the strongest challenge to the idea that anything above the level of physics causes anything.

Kim's challenge runs like this. Every event in Pune has a sufficient physical cause. If "unusual amount" is something over and above the physical state, it either does extra causal work, which would mean the physical cause was not sufficient after all, or it does none, in which case it is idle. Either way, the high-level explanation is in trouble. The usual reply is that high-level states are multiply realizable: the same feature can be carried by different physical states, as the same decision is carried by Pune, Chennai and a tablet. That, the reply says, is why the high level is real.

This paper asks a narrower question than the old debate. When does a high-level cause survive Kim's exclusion argument, and when does it fail? My answer is that it survives when the high-level variable is an exact causal abstraction of the low level. That means intervening on it has the same, well-defined effect however it is realised. It fails when the abstraction is lossy, or when an intervention on it can be carried out in different ways with different results. Those are properties of a model and its realisers, and they can be measured.

So Ananya's decision does not depend on winning an argument about metaphysics. It depends on a test she can run on Kavach. If "unusual amount and new beneficiary" is an exact abstraction of what Kavach does, her letter states the cause. If it is not, her letter is a story, and Farhan is right that the truth is somewhere in the fourteen million numbers.

Kim's squeeze

Start with the best-known argument for the reality of higher levels, because Kim built his challenge on its ruins. In 1967 Hilary Putnam argued in "Psychological predicates" that pain cannot be identical with any particular brain state. Mammals, birds, reptiles and perhaps octopuses all feel pain, and their brains are built very differently. If pain were a specific state of human neurons, an octopus could not be in pain. Since it plausibly can, pain must be something more abstract: a functional state that different physical systems can realise.

In 1974 Jerry Fodor generalised the point in "Special sciences". Economics has laws, such as Gresham's law that bad money drives out good. Monetary exchange can be realised by coins, shells, cheques, strings of wampum or electronic records. No physical description captures what all those have in common. So economics cannot be reduced to physics, not because money is magic, but because the physical realisations of money form a hopeless jumble. Fodor's slogan was that the special sciences carve nature at joints physics cannot see.

For a while this was the received view. Kim's work turned it around.

The jade problem

In 1992 Kim published "Multiple realization and the metaphysics of reduction". His central example was jade. The name "jade" was once thought to pick out one mineral. In the nineteenth century mineralogists found that it covers two quite different ones, jadeite and nephrite, with different chemical compositions and crystal structures. They look and feel similar, which is why they share a name.

Kim asked: is jade a natural kind? Can there be laws about jade? His answer was no. Any truth about jade as such is really a disjunction: either a truth about jadeite or a truth about nephrite. A generalisation confirmed by examining jadeite samples tells you nothing, by itself, about nephrite. So multiply realised kinds are not unified kinds at all. They are names for disjunctions of physical kinds.

Then he turned the point on minds. If pain is realised differently in humans, octopuses and machines, then "pain" is like "jade". There is human pain, octopus pain and machine pain, each a physical kind, and the general word adds nothing. Multiple realizability, which was supposed to save the higher level, ends by splitting it into local reductions.

The exclusion argument

Kim's second argument, set out most fully in his 1998 book Mind in a Physical World, is the one Farhan is making. It goes in steps. Suppose a mental property M causes some effect. M is realised by some physical property P, so whenever M is present, P is present. Physics is causally closed: every physical effect has a sufficient physical cause. So the effect has P as a sufficient cause. Unless the effect is systematically overdetermined, with two separate sufficient causes every time, M and P cannot both be causes. And since P is the physical one, closure says it is the one that does the work. M is excluded.

The argument is valid, and each premise is attractive. Closure is a working assumption of physics. Supervenience, the idea that higher-level facts are fixed by lower-level ones, is close to a definition of physicalism. Systematic overdetermination seems absurd: nobody thinks every action is caused twice. If you accept all three, you must either identify M with P, giving up multiple realizability, or accept that M is idle.

Kim called the dilemma a squeeze. Non-reductive physicalists, who want mental properties to be physical in some sense but not identical with physical properties, are squeezed between reduction and epiphenomenalism. There is no comfortable space in between.

A real case of multiple realisation

The two clusters are an engineering case. Brains provide a natural one, and the most striking was published in Nature in 2000.

The rewired ferret is close to a natural experiment in multiple realisation. Seeing, as a functional capacity, was carried by tissue that would normally have carried hearing. The same high-level state, "a light on the left", had two very different physical realisers in the same animal. And the animal's behaviour was explained at the level of the state, not the tissue.

But Kim's defenders have a reply, and it is a good one. William Bechtel and Jennifer Mundale argued in 1999 that neuroscientists in practice identify brain areas across species by their function and connections, and find them remarkably similar. Multiple realisation is less common than Putnam supposed. Thomas Polger and Lawrence Shapiro went further in The Multiple Realization Book in 2016. They argued that most supposed cases are not cases of genuinely different realisers. The rewired cortex, for example, came to work in visual ways: same kind of maps, same kind of cells. Different tissue, they would say, but the same mechanism.

That reply matters for Kavach. Pune and Chennai are not different mechanisms. They run the same network with different number formats. If multiple realisation means very different mechanisms, Kavach on two clusters is not a case of it at all. It is one mechanism, realised twice.

I think the reply is right about the label and wrong about the lesson. Whether we call it multiple realisation or not, the case shows something Kim's argument does not account for. There is a level of description at which Pune and Chennai do the same thing, and interventions at that level have the same effects on both. The question is not whether to call that level real. It is whether it is the level at which the causes are.

The tablet in the branch

Change one feature of the running example. On the day of Mrs Fernandes's complaint, the network in the Frazer Town branch went down for an hour, and payments were scored on the branch tablet instead. The tablet runs a compressed copy of Kavach. Its numbers are stored with far less precision, and some of its internal units have been pruned away altogether to make it fit.

The bank's own testing shows that the tablet agrees with the clusters on the great majority of decisions, but not all. Where they disagree, the tablet is more likely to block. Ananya now has three realisations of "Kavach's decision", and one of them behaves slightly differently.

This is where Kim's jade argument bites. Is there one kind here, "Kavach blocks the payment", realised three ways? Or are there three kinds, Pune-blocks, Chennai-blocks and tablet-blocks, sharing a name the way jadeite and nephrite share one? If the tablet's blocks follow different rules from the clusters' blocks, then a generalisation confirmed on Pune tells you nothing certain about the tablet. That is exactly Kim's point about jade. The high-level kind splits along the lines of its realisers.

I think Kim is right about the tablet, and that the tablet shows his argument's real scope. Where realisers differ in what makes a difference, the high-level kind does split. Where they agree in what makes a difference, it does not. Pune and Chennai agree; the tablet does not, on some inputs. So "Kavach's decision" is one kind across the clusters and a slightly different kind on the tablet. That is not a metaphysical verdict about all multiply realised kinds. It is a verdict about these three systems, and the next two parts show how to reach it.

Difference-makers

Change one feature of the running example. Ananya does not answer Farhan with metaphysics. She answers with a question every engineer understands. "If we had changed the amount to something ordinary, would the transfer have gone through?" Farhan says yes. "And if we had changed fourteen thousand of your numbers in Pune, keeping the features the same?" He says it would still have been blocked. "Then the amount made a difference and your numbers did not."

That exchange is the heart of a family of views about causation called interventionism. Its most developed statement is James Woodward's 2003 book Making Things Happen. The core idea is simple. X causes Y if there is some possible intervention on X that would change Y, holding fixed whatever needs holding fixed. An intervention is a clean manipulation: it sets X directly, without also changing Y through some other route. The idea grew out of work on causal models by Judea Pearl, Peter Spirtes, Clark Glymour and Richard Scheines, and it is how experimental scientists already think. To find out whether a drug works, you give it to some people and not to others, and see what changes.

Interventionism changes the question Kim asked. Kim asked which property is sufficient for the effect. Interventionists ask which property makes a difference to it. Sufficiency and difference-making come apart. The Pune activations are sufficient for the block, but changing most of them makes no difference. The feature "unusual amount" is not sufficient by itself, since the beneficiary matters too, but changing it changes the outcome.

Proportionality

Stephen Yablo gave the classic illustration in his 1992 paper "Mental causation". A pigeon is trained to peck at red things. It is shown a scarlet patch, and it pecks. What caused the peck: the patch being scarlet, or its being red? Both are true of the patch. Scarlet is more specific, and it is sufficient. But we would mislead anyone if we said the pigeon pecked because the patch was scarlet. That suggests a crimson patch would not have worked, and it would have. The right cause is red, because it is proportional: it is neither too specific nor too general for the effect.

Christian List and Peter Menzies made this precise in 2009 in "Nonreductive physicalism and the limits of the exclusion principle". On their account, a property F causes G when F makes a difference to G: if F were present G would be present, and if F were absent G would be absent. They showed that whether Kim's exclusion principle holds is then a contingent matter. It depends on how the high-level property is realised and how the effect depends on the realisers.

In some cases exclusion holds and the physical property wins. That is when the specific physical realiser matters: change it to another realiser of the same high-level property and the effect changes. In other cases exclusion holds the other way round. The high-level property wins, because the effect would have happened under any of its realisers, and so the specific physical state is not proportional to it. In the Kavach case, if any realisation of "unusual amount and new beneficiary" would have produced a block, then the feature, not the Pune activations, is the proportional cause.

This is the move my thesis builds on. Whether a high-level variable is a cause is not settled by metaphysics; it is settled by how the system responds to interventions at each level. That makes it an empirical question about particular systems, which is good news for Ananya and bad news for anyone who wants a general verdict on the mind.

Kim's reply, and why it does not settle the case

Kim anticipated something like the proportionality defence and had an answer. Higher-level properties, he said, inherit their causal powers from their realisers. Whatever difference "red" makes to the pigeon, it makes because scarlet, crimson and the rest each make that difference. The higher-level property has no causal powers that are not powers of its realisers. Call this the causal inheritance principle.

The principle is plausible, and I accept it as a constraint. The question is what follows. If the powers of "unusual amount" are inherited from the powers of its realisers, it does not follow that the realisers are the better causes. It follows that the realisers share something, and that what they share is what does the work. The shared thing is exactly what the high-level variable picks out. On the interventionist reading, inheritance and proportionality are compatible: the high-level variable inherits its powers from realisers that differ in many ways, and it is proportional because it names only the respect in which they agree.

Kim's deeper worry was that this makes the high-level property a disjunction of realisers, and disjunctions are not real properties. But a disjunction of realisers that all behave the same under intervention is not an arbitrary disjunction. It is a class of states unified by its causal role. That unity is what the jade case lacked. Jadeite and nephrite share colour and feel, but do not share the properties that matter to a mineralogist. Pune and Chennai share the properties that matter to the block.

Three analogies and their limits

Three analogies make the idea of a proportional cause vivid. Each breaks somewhere instructive.

The first is temperature. A kettle boils because the water reaches a hundred degrees, not because of the exact trajectory of each molecule. Countless arrangements of molecules realise the same temperature, and the boiling depends on the temperature, not the arrangement. That maps exact abstraction well. It breaks because temperature is a clean macro variable only in equilibrium, or near it. In a turbulent, rapidly heated liquid, local hot spots matter, and the single temperature reading stops being a good cause of where bubbles form.

The second is Fodor's money. A shop sells you bread because you paid, not because of whether you paid with a note, a card or a phone. The payment is the proportional cause. That maps multiple realisation across very different realisers. It breaks because what makes something money is not its physical make-up at all but a social agreement. When the agreement changes, as in a currency withdrawal, the same physical note stops being a cause of anything. The macro variable depends on facts outside the system.

The third is software. A program produces the same output on different computers, so the program, not the chip, explains the output. That maps Pune and Chennai exactly. It breaks because programs leak. Floating-point arithmetic gives slightly different results on different hardware, and a calculation that sits near a threshold can come out one way in Pune and the other in Chennai. When that happens, the chip is a difference-maker, and the program is not a complete cause.

Causal emergence

There is a quantitative version of the idea that higher levels can be better causes, and it is worth knowing about even though I do not rely on it. In 2013 Erik Hoel, Larissa Albantakis and Giulio Tononi published "Quantifying causal emergence" in the Proceedings of the National Academy of Sciences. They defined a measure of how much a system's state at one moment determines its next state, called effective information. They showed that, for some systems, a coarse-grained description has more effective information than the fine-grained one. The macro level is more deterministic and less degenerate than the micro level. In that sense, the macro level does more causal work.

The result is striking and contested. Critics have pointed out that the measure depends on choices about how interventions are distributed, and that the micro level always contains the information the macro level uses. I mention it because it shows that "higher levels can be better causes" is more than a philosopher's slogan. It has a measurable form. But the test in the next part asks a different and simpler question: not whether the macro level is more informative, but whether interventions on it are well defined.

Exact and lossy abstractions

So far the argument has a gap, and Farhan finds it. "Fine," he says. "If the features are proportional causes, the high level wins. But you have assumed that Kavach really carries 'unusual amount' and 'new beneficiary' as clean variables. Maybe it does. Maybe it carries something that only correlates with them. Your documentation was written by people who hoped it did." Change one feature of the running example: Ananya stops assuming and starts testing.

The tool for this comes from a body of work on causal abstraction. In 2017, Paul Rubenstein and colleagues asked when a simple causal model is a faithful summary of a more complex one, in a paper on the causal consistency of structural equation models. Their answer was that the two must agree on interventions as well as on observations. If you intervene on the simple model's variables, and carry out the corresponding intervention on the complex model, the outcomes should match. Sander Beckers and Joseph Halpern refined the definitions in 2019 in "Abstracting causal models", separating several grades of abstraction from loose to exact.

Then the idea moved into machine learning. In 2021, Atticus Geiger, Hanson Lu, Thomas Icard and Christopher Potts published "Causal abstractions of neural networks" at the NeurIPS conference. They proposed a way to test whether a network implements a hypothesised high-level causal model. The key move is the interchange intervention. Run the network on one input, the base. Run it on another, the source. Take the internal representation that is supposed to carry some high-level variable in the source run, and paste it into the base run in place of the base's own. If the representation really carries that variable, the network's output should now be what the high-level model predicts for the base input with that variable set to its source value.

Interchange interventions are exactly the test Kim's argument needs. They intervene on the realiser of the macro variable, using another realisation of a different value, and check that the result matches the macro model. If it does for every pair of inputs, the macro model is an exact abstraction of the network, at least on that set of inputs. If it does not, the macro model is lossy, and the failures show where.

The Abstraction Exactness Check

Here is the instrument of this paper. It combines interchange interventions with a check for ambiguous manipulation, and it reports two numbers and one judgement for any proposed high-level cause.

The minimal case

Start small. Strip Kavach down to a toy with three yes-or-no inputs: whether the amount is unusual for the account, call it a; whether the beneficiary is new and overseas, b; and a third input, n, that I will explain shortly. The toy network blocks a payment when both a and b are true. Inside it, two hidden units carry a and b. On the Pune version they sit in positions 3 and 7. On the Chennai version they sit in positions 1 and 2, in the opposite order and with their signs flipped. The proposed high-level model is the bank's documented rule: block if a and b.

I ran the check with a short program that enumerates every case exactly. There are eight possible inputs, so sixty-four base and source pairs, and no sampling. On both realisations, interchange accuracy was 1.000. The ambiguity spread was 0. The documented rule is an exact abstraction of the toy network, on both clusters, though the two clusters store the variables in completely different places.

That is the result Ananya hoped for, and it answers Farhan in the toy case. The rule is the proportional cause, and it is multiply realised in the sense that matters: interventions on it have the same effects whatever realises it. The specific positions and signs in Pune are sufficient for the block and make no difference to it, beyond carrying the variables.

The ambiguous risk score

Now the cholesterol problem. In 2004 Peter Spirtes and Richard Scheines published a paper called "Causal inference of ambiguous manipulations". Their illustration, which they deliberately simplified from the real history, involves total cholesterol. Suppose researchers observe that high total cholesterol goes with heart disease and recommend low-cholesterol diets. Unknown to them, total cholesterol is the sum of two kinds, one of which raises the risk and one of which lowers it. An intervention that sets total cholesterol to a medium value could be done with a lot of the harmful kind and little of the protective kind, or the other way round. The effect of "setting total cholesterol to medium" is not defined. It depends on how you do it.

The lesson generalises. A high-level variable that is a sum, or any many-to-one function, of lower-level variables with different effects is not a well-defined cause. Interventions on it are ambiguous manipulations.

For K2, what is the right high-level cause? The check says so directly. I ran it again with a different proposed variable, "unusual amount" alone, with the rule "block if a". For K2, interchange accuracy was 1.000. For K1 it was 0.750, because in K1 the beneficiary matters too. The exact abstraction exists in both models. It is a different variable in each.

The realistic case

The toy has three inputs, but it can be made less toy-like in the ways that matter. Put the two models side by side, give the proxy a moderate leak of 0.5, and run the full check on both clusters. This is the closest the program comes to Kavach as it would really be found: a documented rule, a dashboard score, two realisations and a pathway nobody wrote down.

The program's output, for K1 with a leak of 0.5, was as follows. The documented rule scored interchange accuracy 0.938 on Pune and 0.938 on Chennai. The risk score had the same accuracy, and an ambiguity spread of 0.25. "Unusual amount" alone scored 0.688. Realisation made no difference, which is by construction in the toy: the two clusters store the same variables in different places, and nothing else.

Read as a verdict, those numbers say four things. The documented rule is close to exact, but not exact. The risk score is worse than the rule, because one of its realisations now sometimes blocks and the other never does. "Unusual amount" alone is a poor cause for this model. And the failures, wherever they are, do not depend on which cluster made the decision. So Ananya can say that the high level wins against Farhan's hardware story, while losing to something else. That something else, as the next part shows, is a pathway through the third input.

The realistic case is less satisfying than the minimal one, and that is the point of running it. In real systems, high-level causes are rarely perfectly exact. The check turns "is the high level real?" into "how exact is this high-level variable, on which inputs, and where does it leak?" Those questions have answers.

The negative control

A test needs a case where it should fail, with only the tested thing removed. For the Abstraction Exactness Check, the negative control is the documented rule applied to the wrong model. I ran "block if a and b" on K2. Interchange accuracy fell to 0.750 on both clusters. The rule fails in exactly the cases where the amount is unusual and the beneficiary is old: K2 blocks, and the rule predicts it will not.

The control shows that the check is not a rubber stamp. It does not pass every plausible-sounding high-level story. It passes the story that matches the mechanism, and fails the same story on a mechanism it does not match, even when observed decisions are identical.

A counterexample: the drifting threshold

Here is a case where the check, run carelessly, gives the wrong answer. Kavach in Chennai uses a lower-precision number format than Kavach in Pune. For almost all payments, the difference is invisible. But a payment whose internal score sits within a hair of the blocking threshold can come out as a block in Pune and a pass in Chennai. Suppose the bank's test set happens to contain no such payments. The check reports interchange accuracy of 1 on both clusters, and Ananya concludes that the rule is multiply realised.

It is not, quite. For payments near the threshold, the hardware is a difference-maker. Change the cluster and the outcome changes, with the high-level variables fixed. On that slice of inputs, Farhan is right: the specific physical realiser matters, and the high-level rule is not the whole cause.

The repair is part of the instrument. Test the realisation probe on inputs chosen to sit near decision boundaries as well as on typical inputs. If the outcome there depends on the cluster, report the cause as "the rule, plus a hardware-dependent margin", and log which cluster made the decision. That is not a defeat for the high level. It is a precise statement of where the high level is exact and where it leaks into the low.

What exactness is not

It helps to be clear about three things the check does not show. It does not show that the high-level variable is the only cause. The low-level realisers still exist and still carry the variable; the check shows that, for this effect, their extra detail does not make a difference. It does not show that the variable is natural or simple. A variable defined by a strange function of fourteen million numbers could pass, and might still be hard to explain to Mrs Fernandes's son. And it does not show that the variable is the cause for every effect. A variable can be exact for the block decision and lossy for some other output of the same model, such as its confidence score.

Each of these limits is a reason to report the check's results with care. A high-level cause is exact relative to an effect, a set of inputs and a set of realisations. Change any of the three and the check must be run again.

The failure boundary

The check needs a hypothesised high-level model and a way to intervene on the internal units that carry it. For a toy with three inputs, both are easy. For Kavach in full, with fourteen million numbers per decision, neither is guaranteed. If the bank's engineers cannot find units that carry "unusual amount", there is nothing to interchange. If the true mechanism uses a hundred overlapping features, no short high-level story will be exact.

At that point the check stops working. What remains is the honest statement that the bank does not know a high-level cause of the decision. That is a real limit, and current interpretability research has not removed it for large models. Geiger and colleagues found that a BERT-based model trained on a demanding inference task realised parts of a hypothesised high-level structure. A simpler baseline model, trained on the same task, showed none of it. Exact abstractions exist in some networks and not in others, and finding them is hard.

When no exact abstraction can be found, Kim's exclusion argument wins by default. The only cause anyone can state is the low-level one, and the high-level story is a gloss. That is not because metaphysics forbids higher causes. It is because, for that system, no higher cause has been shown to exist.

Chariots, names and the floor

Change one feature of the running example again. Ananya's grandmother, who lives with her, finds her up late with the interchange results spread across the dining table. She asks what the trouble is. Ananya explains, badly, that she is trying to decide whether "unusual amount" is a real cause or just a name for a lot of numbers. Her grandmother laughs and says that a monk answered that question for a king two thousand years ago.

She is thinking of a famous dialogue. Indian Buddhist philosophy has argued about levels of reality, and what is real at each, for a very long time. Its central distinction, between conventional and ultimate truth, maps onto Kim's problem almost exactly.

The modern version of the same worry has a name. Ned Block asked, in a 2003 paper called "Do causal powers drain away?", what happens to Kim's argument if every level is realised by a lower one. If each higher level's causal powers are excluded by the level below, and there is no bottom, causation drains away entirely, and nothing causes anything. Jonathan Schaffer argued the same year, in "Is there a fundamental level?", that we have no good evidence that physics has a bottom. If Block and Schaffer are right, the exclusion argument proves too much. Since some things do cause others, something has gone wrong with exclusion in general.

I think this is a real point against Kim, but it is not the one I rely on. My argument does not need there to be no bottom. It needs only that, at a given level, the proportional cause can be identified by intervention. That is true whether or not physics has a floor. The Madhyamaka point helps only by removing Kim's assurance that the lowest level is where causes really live.

The name in the address

The next case is the one I least like writing, because it is about people like Mrs Fernandes.

The uncomfortable part is not confined to the bank. Psychological explanation has the same shape. We explain people's actions by their reasons: she hired him because he was the best candidate. That is a high-level cause. If the explanation is exact, it is the proportional cause of the hire. If it is lossy, and some low-level pathway sensitive to his accent or name also contributed, the reason-giving story is partly a cover. Studies that send identical job applications under different names have found such pathways in human hiring, in the United States in the work of Bertrand and Mullainathan and in India in the work of Sukhadeo Thorat and Paul Attewell. The high level is where we prefer to live. It is not always where the causes are.

[AUTHOR NOTE: an audit of a production model where the documented explanation did not match the mechanism. What you found, and how the documentation changed.]

Exclusion and the layers of RTM

This series tests a hypothesis about consciousness, the Recognitive Triadic Model, which I hold as a claim under test and not as a doctrine. RTM draws its vocabulary from the Pratyabhijñā school of Kashmir Śaivism. It describes five layers: L1, spanda, responsiveness or pulsation; L2, prakāśa, manifestation; L3, vimarśa, reflexive grasp; L4, pratyabhijñā, recognition; and L5, cit, consciousness as ground. RTM is a theory of levels. So Kim's argument is aimed at it as squarely as at any functionalist theory of mind, and possibly more.

Change one feature of the running example. Ananya, who has read some of this series, asks a pointed question. "If every physical event in a brain has a sufficient physical cause, what does your L5 do? Or your L2? Are they causes, or are they the voltages in Pune with a Sanskrit name?"

Where RTM has to choose

I think RTM should take both horns, for different layers. L1, spanda, is responsiveness, and responsiveness is a causal notion through and through. It should be modelled as a high-level variable, and it should be held to the exactness check. If L1 is realised in brains and in machines, interchange interventions on its realisers should show it. That is a testable commitment, and the coupling test in the previous paper was one form of it.

L5, cit, is the ground. It is not a variable. It does not take different values on different occasions, so no intervention can set it, and no interchange test applies. RTM should say plainly that cit is not a cause in the interventionist sense and is not in competition with neural causes. Kim's argument then does not touch it, but only because cit has been taken out of the causal order. That is a real cost. It means cit cannot be tested by any intervention, and it must earn its place in the theory some other way.

L2 and L3 are the hard cases, and the place where the theory is most exposed. If manifestation and reflexive grasp vary from moment to moment, as the meditator's report suggests, they are variables. Variables can be intervened on, and they must pass the check or be excluded. If they are constant features of any conscious moment, they are conditions, like cit, and they leave the causal story.

My verdict for this paper is that RTM is refined. It must now say, layer by layer, which of its layers are variables and which are conditions. Every layer it calls a variable must survive an exactness check against its realisers. Every layer it calls a condition must be justified without causal evidence. That is more than RTM has said so far, and it is a fair demand.

What a check of L1 would look like

Take the claim that a system has L1, spanda, in the sense RTM intends: a responsiveness that is the same high-level variable however it is realised. The check in this paper gives that claim a shape. Name the internal units that are supposed to carry the responsiveness in a brain, and in a machine. Run interchange interventions between states in which the system is responsive and states in which it is not. If the outcome matches the high-level model on every pair, and on both kinds of system, L1 is an exact abstraction and a multiply realised cause.

Nobody has run that test, and I do not want to pretend it is easy. Responsiveness in a brain is not two hidden units in a known position. But the shape of the test matters for RTM. It says that L1 can be wrong. It could turn out that what RTM calls spanda in a brain and what it calls spanda in a machine come apart under interchange, the way the risk score came apart between K1 and K2. Then RTM would have to say that L1 is a local kind, like jade, and not one layer realised many ways.

Ananya's question has a sting for the upper layers as well. If L2 and L3 are variables, they need realisers that can be found and interchanged, and RTM has not said what those are. If they are conditions, the theory must explain how a condition can differ between a meditator who notices the sound and one who does not. I do not yet have a good answer, and that is the part of this paper RTM is least comfortable with.

The strongest case against this paper

Here is the best objection I can build, stated as Kim's most careful defender would put it.

"The author has not answered the exclusion argument. He has changed the subject from causation to explanation. Interchange interventions show that a high-level model predicts the effects of low-level interventions. Of course it does: the high-level variable is defined by a mapping from low-level states. Every interchange intervention is a low-level intervention. Pasting units 3 and 7 from one run into another is a physical operation on a physical system. The fact that its results line up with a high-level description shows that the description is a good summary of the physics. It does not show that the description names anything with causal powers of its own.

"His proportionality argument fares no better. Yes, 'red' is a better explanation of the peck than 'scarlet'. But the pigeon's eye responded to particular wavelengths, and its brain to particular neural signals. Proportionality is a constraint on which explanations are informative to us. It says nothing about what is doing the work in the world. Kim always granted that higher-level explanations could be useful. His point was that their usefulness is borrowed from the physics they summarise.

"There is a second problem. The author's best natural case of multiple realisation, the rewired ferrets, is the kind of case Bechtel and Mundale, and Polger and Shapiro, have taken apart. The rewired cortex came to work like visual cortex. His engineering case is worse. Pune and Chennai run one network; only the number format differs. Where are the genuinely different realisers? If they do not exist, multiple realisation is a philosopher's fiction, and the exclusion argument has nothing to exclude."

"Finally, the author's own uncomfortable case gives the game away. When the bank's elegant high-level rule leaked, the truth was in the low level. It always is. High-level causes are low-level causes seen at a distance, and when you look closely enough, the distance disappears."

I accept that interchange interventions are physical interventions, and that the high-level variable is defined by a mapping. I accept that proportionality is partly a constraint on informative explanation. I do not accept the conclusion, for one reason. The objection assumes that "what is doing the work" is a fact independent of which differences make a difference. That is the very assumption interventionism denies. If causation is difference-making, then the variable that makes the difference is the cause. In an exact abstraction, that is the high-level one, and the low-level detail is not a difference-maker beyond carrying it.

On the second point, I agree that the clusters are not genuinely different mechanisms, and I said so in Part 1. But the argument does not need them to be. It needs only that interventions at one level have the same effect however the level below is arranged. Whether the arrangements are called different realisers or one mechanism realised twice, the interchange test treats them the same way. Where they differ in what makes a difference, as the branch tablet does, the test reports a local cause, and Kim gets the case.

The objection is right about the leak, and I said so. Exact abstractions are rare, and every high-level cause must earn its status by test. But an argument that high-level causes are always low-level causes seen at a distance must explain why the distance sometimes makes predictions the close view gets wrong, as in the risk score case. It has not.

What would change my mind

I would give up the central claim, that high-level causes survive exclusion when and only when they are exact abstractions, under any of the following.

First, a convincing argument that difference-making is not causation, but only evidence of it. If causation were production, the passing on of something physical from cause to effect, then the interchange test would measure explanation, not causation, and Kim would win. This bears on RTM's L1, spanda, which is defined by responsiveness.

Second, a case where a high-level variable passes the exactness check on every realisation and every input, and yet changing it by a clean intervention makes no difference to the effect. I cannot see how such a case could arise, which is why it would be decisive.

Third, evidence that exact abstractions do not exist in any trained system of realistic size. If interpretability research found only lossy high-level variables, then the high level would never win for large models, and my thesis would be true but empty for the systems that matter. This bears on L2 and L3, which would have nowhere to be realised as exact variables.

Fourth, a principled argument that cit, or any condition of manifestation, does make a difference to particular events. That would put RTM's L5 back into the causal order, and expose it to the check.

These are not idle possibilities. Interpretability groups are now running interchange interventions on models with billions of parameters, and their results will show within a few years whether exact high-level variables are common or rare in large systems.

Two dated predictions put the argument at risk.

• By the end of 2028, at least one published study will report a high-level causal variable in a production-scale language model with interchange intervention accuracy above 0.95 on held-out inputs. If none does, the claim that exact abstractions exist in large systems weakens.
• By the end of 2028, at least one financial regulator will publish guidance asking banks to test documented model explanations by intervention rather than by attribution scores. If none does, the decision rule in this paper will remain a recommendation without uptake.

Mahapatra, R. R. When the pattern does the causing: multiple realizability, Kim's exclusion argument and exact causal abstraction. Mind Frontier. DOI to be assigned. https://rajeshrmahapatra.com/papers/mind-frontier/u1041-when-the-pattern-does-the-causing.html

@article{mahapatra-mf47,
  author = {Mahapatra, Rajesh Ranjan},
  title = {When the pattern does the causing: multiple realizability, Kim's exclusion argument and exact causal abstraction},
  journal = {Mind Frontier},
  doi = {DOI to be assigned},
  url = {https://rajeshrmahapatra.com/papers/mind-frontier/u1041-when-the-pattern-does-the-causing.html}
}