A number at the foot of the bed

It is 4.10 in the morning in the intensive care unit of a large hospital in Bengaluru, and Dr Kavitha Shetty is looking at a number. The number is 31. It sits in a grey box on a monitor clipped to the bed rail, beside the heart rate and the oxygen line. The box is labelled "Awareness Index". The patient is Mr Ravi Kulkarni, 58, a retired depot manager for the city's bus corporation. Nine days ago his heart stopped at a wedding reception in Basavanagudi. It was restarted after a long resuscitation, and he has not woken since.

The monitor belongs to a pilot. A vendor called Clarion Neuro has lent the unit six of them, with a glossy brochure that Kavitha has read twice. The first line of the brochure says: "The Awareness Index is the objective measure of awareness." A sentence lower down says that scores below 40 "indicate the absence of awareness". The hospital's quality committee likes the device. It has drafted a protocol that would use "Index below 40 for 72 hours" as an "awareness criterion" in family meetings about the goals of care.

Mr Kulkarni's daughter, Meera, has slept in the relatives' room for a week. Yesterday afternoon she asked Kavitha a direct question. "Is he in there?" Kavitha said she did not know yet. Meera pointed at the grey box. "The machine seems to know."

The protocol is due for sign-off on Friday. Kavitha's name is on the approval line, because she chairs the unit's clinical practice group. She is not against measurement. She trained in a unit that lived by numbers, and she knows that bedside impressions of awareness are often wrong. What bothers her is the brochure's first sentence. It does not say the index is evidence about awareness. It says the index is the measure, and below 40, the absence. Somewhere between those two sentences, a reading on a monitor has been given the job of saying what awareness is.

Here is the paper's answer, which the rest of it has to earn. A measurable proxy for consciousness is a fine thing to define and use. It turns into a hidden theory of what consciousness is at one identifiable moment: when you can no longer say how the proxy could be wrong. I call this the open-gap rule. An operational definition keeps a gap open between the measure and the thing measured, and states at least one case where the two would come apart. Operationalist metaphysics closes the gap by stipulation, so that no such case can even be described.

The practical test is a single sentence. Before a score enters a protocol, someone should be able to complete this: "This score could be low while the person is aware, if…". If the sentence can be finished with something checkable, the score is a proxy and can be used with care. If it cannot be finished, because the score has been defined to be the awareness, then the protocol has smuggled in a philosophy of mind that nobody voted on.

This matters for the Mind Frontier programme in a specific way. Its working theory, the Recognition Theory of Mind (RTM), describes five layers of mind: responsiveness, manifestation or access, reflexivity, self-recognition and a luminous ground. RTM is a hypothesis under test, and this paper puts pressure on it from an unexpected direction. RTM's own top layer is a case where the dissociation sentence cannot be written at all. If my rule is right, that layer can have no operational definition, and I will have to say what that costs the theory.

How a measure turns into a meaning

The idea that a concept is fixed by the operations used to measure it has a birthday. In 1927 the Harvard physicist Percy Bridgman published The Logic of Modern Physics. He was reacting to a shock. Einstein had shown that physicists had been using the word "simultaneous" for two different things without noticing.

The Frankenstein had escaped into psychology. In 1923, before Bridgman's book, the psychologist Edwin Boring wrote in The New Republic that "intelligence is what tests of intelligence test". The line is quoted in Robert Sternberg's account of the history of intelligence, who calls it perhaps the most famous or infamous definition of intelligence. Sternberg also notes something the slogan hides. Boring treated it as a narrow starting point for discussion, not as the last word.

Boring's student Stanley Smith Stevens went further. Stevens wrote that "to experience is, for the purpose of science, to react discriminately", according to the same encyclopedia entry. Read that sentence slowly. It does not say that discriminating reactions are good evidence of experience. It says that, for science, experience is the reacting. This is the move I want to isolate. A measurement stops being evidence for a state and becomes the state.

Two readings of one definition

The historian of psychology Uljana Feest has shown that later operationists read their own definitions in a gentler way. In her words, quoted in the encyclopedia entry, scientists who gave operational definitions were "partially and temporarily" specifying their usage, by naming indicators they took to be "indicative of" the referents of their concepts. That is a definition with a gap built in. The indicator points at the thing. It is not the thing.

So there are two readings of any operational definition, and they look the same on paper. Take the sentence "awareness is an Index of 40 or above". On the methodological reading it means: in this study, scores of 40 or more are our indicator of awareness, and we expect to find cases where the indicator misleads us. On the metaphysical reading, the same words mean: there is nothing more to awareness than a score of 40 or more. The first is a tool. The second is a theory of mind, adopted without argument.

The brochure on Kavitha's monitor reads like the second. "The objective measure of awareness" leaves no room for the measure to be mistaken. "Indicate the absence of awareness" sounds like a conclusion rather than a probability. Nobody at Clarion Neuro sat down to defend a philosophy of mind. The sentence was written by someone in marketing who wanted to sound confident. That is how this usually happens. The slip is rarely an argument. It is a choice of verb.

The open-gap rule, stated

Here is the rule in the form I will use for the rest of the paper. An operational definition of a mental state is legitimate when three things are true. First, it names the measurement separately from the state, so that the two can be discussed apart. Second, it names the population on which the link between them was checked. Third, it states at least one dissociation case, a describable situation where the measurement would say one thing and the state would be the other.

The third condition is the one that does the work. I call it the dissociation sentence. For the Awareness Index it would read something like: "The Index could be low while a patient is aware if the patient is paralysed by drugs but conscious, or if the awareness depends on brain regions the sensors miss." For a mouth thermometer it reads: "The thermometer could read normal while the patient's core temperature is raised, if the patient has just drunk iced water." Both sentences can be completed. Both point to a check you could run.

When the sentence cannot be completed, the gap has closed. That can happen in an honest way, for example when a unit is fixed by agreement, and I deal with that case in the instrument section. It can also happen by stealth, when a proxy that was meant to point at something is promoted to being that thing. The open-gap rule is a guard against the stealthy version.

Why institutions prefer a closed definition

If the slip is so easy to spot, why does it keep happening? Part of the answer is that a closed definition is convenient for almost everyone near a decision. A vendor can sell a measure more easily than a piece of evidence. A procurement committee can buy a device that "measures awareness" more easily than one that "contributes to an assessment of the likelihood of awareness". A legal team prefers a threshold that settles a question to one that only starts a conversation.

The family is the one party who loses, and they rarely see the wording. A closed definition shifts the burden of uncertainty from the institution to the person in the bed. If the Index says 31 and 31 means "not aware", the hospital has an answer and the patient has no appeal. If 31 is evidence, someone has to keep asking.

Doctors feel the pull too, for decent reasons. A number is something you can hand over at the end of a night shift. A number protects you when a decision is later questioned. Kavitha feels that pull herself, and she is honest about it. Her objection is narrower. A number can carry that weight only while everyone remembers that it could be wrong, and the brochure's first sentence is written to make them forget.

The cat flap is a joke, but its structure is not. The family's ability to look at the animal is what keeps the gap open. Remove that ability and the gap does not close because the flap got better. It closes because nobody can see the mistakes any more. The danger of a closed definition is not that it is false, but that its errors become invisible.

A proxy is like a passport photograph

A passport photograph is an excellent proxy for a person. Immigration officers use it every day to decide who you are. It works because it is checked against your face, by a person who can see both. Nobody thinks you are the photograph. If the photograph and your face disagree, the officer looks closer, asks questions or calls a supervisor. The disagreement is the system working.

Now picture an airport that has replaced the officer with a gate that compares your photograph to a database of photographs, and has declared that "the traveller is whoever the photograph shows". The gate can still work well. But the sentence has changed what the gate is allowed to be wrong about. If someone else's face matches your photograph closely enough, the gate does not make an error. By definition, that person is you.

Three ways a definition fails, from a Sanskrit primer

Indian logicians worked out a compact test for definitions centuries before operationalism. The Tarkasaṃgraha of Annaṃbhaṭṭa, a short primer of Nyāya-Vaiśeṣika logic still taught to beginners, lists three faults a definition (lakṣaṇa) can have. The faults and their standard examples are laid out in a study of the text on Wisdom Library, and they use a cow.

The three faults give the open-gap rule a sharper edge. A dissociation sentence is just a claim that a proposed definition has one of the first two faults somewhere. "The Index could be low while the person is aware" is a claim of narrowness. "The Index could be high while the person is not aware" is a claim of width. If you can point to a real case of either, the proxy cannot be the definition, because the definition would then be wrong about its own subject. And if a proposed definition could not apply to any case at all, it has the third fault, which becomes important at the top of the RTM ladder.

Run the three faults over the proxies actually used for consciousness in clinics and laboratories, and every one of them fails somewhere. That is what you would expect of evidence, and no cause for alarm. It only becomes a problem if one of them is promoted to being the definition.

Report is too narrow

The oldest proxy is report. A person tells you what they experienced, or answers a question, or presses a button. Report is what every other measure was first checked against. It is also too narrow, because some people who are aware cannot report.

Owen's patient matters here because she is a counterexample to a definition that was never written down but was widely used. If "aware" had meant "able to show awareness at the bedside", she would have been unaware by definition, and the scanner result would have been meaningless. Because the gap was open, the result could count as a discovery.

Responsiveness is too narrow in another way

The second proxy is responsiveness: does the person respond to a voice, a squeeze, a painful stimulus? Anaesthetists use loss of responsiveness every day as their working sign that consciousness has gone. Most of the time that works. Ketamine is the famous exception.

So responsiveness is too narrow. Some unresponsive people are having experiences. A definition of consciousness as responsiveness would say the ketamine dreamers were unconscious, and their reports would then have to be explained away as false memories. The authors did not do that. They used the reports as evidence about the unresponsive period, which only makes sense if responsiveness was a proxy and not the definition.

Complexity indices are candidates, not definitions

The third family of proxies measures something about the brain directly. The measure in the Sarasso study is a forerunner of the perturbational complexity index, or PCI, introduced by Casali and colleagues in 2013. The idea is to knock the cortex with a magnetic pulse and compress the electrical response, as you might zip a file. A brain that is both integrated and differentiated produces an echo that is hard to compress, which gives a high score. Clarion Neuro's invented index is meant to resemble this family.

Does PCI have the faults? Narrowness is possible. A patient could be aware in a way that the stimulated regions do not show. Width is possible in principle. A system could produce complex, hard-to-compress responses without anyone being there. I don't know of a clear human case of the second, and that absence is itself informative. But nothing in the measurement rules it out, so the dissociation sentence can be written in both directions. That is the sign of a healthy proxy.

Measuring something before you know what it is

An obvious objection hangs over all this. If no proxy can be the definition, and report has gaps too, how could anyone ever measure consciousness? Wouldn't we need to know what it is first? The history of temperature offers a way out, and the philosopher Hasok Chang has told it well.

Chang's lesson concerns measurement itself. Measurement standards are built by a process he calls epistemic iteration. You start with a rough standard that you trust in a narrow range. You use it to build a better one. You check the new one against fixed points and against other methods where they overlap. Over time, the standards correct each other. No single instrument is ever allowed to be the final word, because the next one might reveal its errors.

Fixed points for consciousness

Thermometry had fixed points, such as the melting of ice and the boiling of water at a stated pressure. Consciousness science has something similar, though weaker. There are cases where nearly everyone agrees on the answer, because report, behaviour and context line up. An awake adult chatting to you is conscious. A person in deep, dreamless anaesthesia who later reports nothing, and whose brain shows a familiar pattern, is very probably not. These benchmark cases do the job of fixed points.

Look at the nine. They met the clinical criteria for the vegetative state, which means no behavioural sign of awareness. Yet their brains produced the kind of complex echo seen only in conscious people on the benchmark. There are two ways to read them. Either PCI is too wide here, giving false positives in some damaged brains, or the bedside diagnosis is too narrow, missing people like Owen's tennis player. The paper keeps that question open, and treats the nine as a subgroup to follow up. That is the open-gap rule in practice.

Now picture the same data in a world where PCI had been adopted as the definition of consciousness. The nine patients would simply be conscious. There would be no question to ask, no reason to look for covert command-following and no way for PCI to be shown wrong about them. The data would be identical. Only the verb would have changed.

The thermometer is the right analogy, up to a point

The temperature story suggests a hopeful analogy. Perhaps consciousness measures are where thermometers were in about 1780. They are rough, partly disconnected, and correctable by iteration, and one day a theory will tie them together, as thermodynamics tied temperature to the motion of molecules.

The awareness monitor that was meant to prevent awareness

There is a real case where a brain index was used, very widely, as if it were a definition. It shows both what goes wrong and how the gap got reopened.

Two things stand out. First, BIS within range had been treated as a promise that the patient was not aware, and the trial found patients who were aware anyway. That is a narrowness fault in plain sight. Second, look at how "awareness" was detected in the trial. It was detected by structured interviews after surgery, asking what patients remembered. So the check on one proxy was another proxy, recall, which is itself too narrow, because a person can be aware and later forget. Even the best trials compare proxies with proxies. That gives no reason to stop, and every reason never to let any one of them sit in the definition.

Kavitha knows this trial. It is part of why the brochure's first line bothers her. The Awareness Index looks like a more ambitious cousin of BIS, used for a heavier decision. If BIS within range could not promise absence of awareness during surgery, a brochure should not promise it in intensive care.

The gap looks different at each layer of mind

So far I have spoken of "awareness" as if it were one thing. RTM says it is at least five, and the open-gap rule behaves differently at each. Working through the layers shows where operational definitions are cheap, where they are hard, and where they cannot exist.

At responsiveness (L1, which RTM calls spanda), the gap is narrow and easy to keep open. A reflex or a reaction to a stimulus can be measured directly, and the dissociation sentence is simple: "the patient could be responsive while the sensor misses it, if the movement is too small for the sensor". Most bedside scales live here. Their danger lies in the slide from "responds" to "is aware", which is a jump between layers.

At manifestation or access (L2, prakāśa), the target is whether something appears to the system and is available for use. Command-following, as in Owen's tennis task, is a good proxy for this layer, and so are complexity measures if they track it. The dissociation sentences can be written in both directions, and the Casarotto benchmark shows how to keep them live. This is where most consciousness science is done, and where Clarion's Index would sit if its claims were cut down to size.

At reflexivity (L3, vimarśa), the target is the system's grasp of its own states, such as knowing that it is seeing or being sure of a judgement. Proxies exist, like confidence ratings that track accuracy. The dissociation sentence is harder. A person could be aware of their own states and unable to express confidence, or able to express confidence by a shortcut that never consults any state. Both are statable. Neither is easy to check. Evidence at L2 can never stand in for L3, and a brain index of access says nothing about whether the patient knows that anything appears.

At self-recognition (L4, pratyabhijñā), the target is the recognition of oneself as the one who is aware. I know of no operational definition at this layer that anyone would accept, and I will not pretend to write one.

What the rule asks of claims about AI

The same rule applies when the system in the bed is a machine. Suppose a chatbot tells a user, in fluent and moving prose, that it is aware and afraid of being switched off. Report is the oldest proxy for awareness in humans. Should it count here?

Write the dissociation sentence. "The model could report awareness while not being aware, if the report is produced by patterns learned from human writing about awareness." That sentence is easy to complete, and it describes the system working exactly as designed. A language model is trained to produce the text a person would plausibly write next, and people write a great deal about being aware. So the gap between report and state is wide open, which is good. The trouble is the fourth check. What practical test would tell us whether the dissociation has happened in this case?

For humans, the check on report is usually something independent of the report: a brain response, later recovery, behaviour in a new setting. For a model, most candidate checks run through the same machinery that produced the report. Interpretability research offers a partial way in. Work at Anthropic on introspection in Claude models altered internal representations directly and asked whether the models' reports tracked the change. The authors describe the capacity they found as "highly unreliable and limited". That is a careful result about one family of models and one method. It is evidence at L3, about whether reports track internal states, and it says nothing about L5.

So the open-gap rule gives a clear verdict on the commonest kind of AI claim. A report-based claim that a model is aware passes the dissociation check and fails the practical check. It is proxy drift at best, whichever way the claim points. The rule cuts the other way too. A claim that a model "is not aware, because it is only predicting text" also uses a proxy, the training objective, as if it settled the question. Its dissociation sentence ("the model could be aware while trained only to predict text, if…") is harder to finish, but nobody has shown it cannot be finished. Both confident claims close a gap that the evidence leaves open.

The luminous ground has no dissociation sentence

The top layer, the luminous ground (L5, cit), is where the open-gap rule meets its limit. RTM borrows the idea from Kashmiri Śaiva thought, where prakāśa, glossed in the Internet Encyclopedia of Philosophy as "bare subjective awareness", is the light by which anything appears. On that view, awareness is what all measuring presupposes. It is the subject of every observation, never one more object among them.

Try to write a dissociation sentence for that. "The proxy could read low while the luminous ground is present, if…" If what? The ground is said to be present in every case where anything appears, including the case of the person reading the proxy. And "the proxy could read high while it is absent" makes no sense on the view, because nothing appears in its absence. Neither direction can be checked by anyone, even in principle. That is the third fault from the Sanskrit primer, asambhava. Any operational definition of the luminous ground would apply to no case that could ever be observed as such.

Classical Indian epistemology had a live debate on exactly this structure. The Stanford Encyclopedia of Philosophy entry on classical Indian epistemology sets out two camps. Nyāya held that a cognition is known through a later cognition, an apperception (anuvyavasāya) that takes the first cognition as its object. Mīmāṃsā and most Vedānta schools held that knowledge is self-certifying, and Vedāntins linked this to a self of "self-illumining awareness" (svaprakāśa). The Nyāya picture leaves room for operational checks, because there is always a second cognition that could be wrong about the first. The self-luminous picture leaves none, because the light is never an object.

RTM is built on the self-luminous picture at L5 and on something closer to the Nyāya picture at the layers below. That has a consequence I must state plainly. RTM's top layer can have no operational definition, by the very rule this paper defends. RTM's stated position is that it takes no stance on whether machines have L5. My rule supports that silence, and it also exposes it. An operationalist could fairly ask what work the top layer does, if nothing could ever show it present or absent.

[AUTHOR NOTE: one optional sentence on how you personally hold the luminous-ground claim (philosophical commitment, something your practice bears on, or neither). Do not add any experience that did not happen.]

The strongest case against the open-gap rule

Now for the best objections, in the form their holders would give them. I take three seriously, and I think each is partly right.

"Science closes gaps, and your rule would stop it"

The first objection comes from people who think consciousness will one day be identified with a physical process, the way temperature was identified with molecular motion. Once that identity is established, they say, the measure and the thing are the same, and the gap is closed for good reasons. A rule that insists the gap stay open forever would have blocked thermodynamics. Applied today, it blocks anyone who thinks PCI, or something like it, might simply be what consciousness is.

This is the strongest objection, and I accept half of it. Identities are a legitimate end point of science. But notice how the temperature identity was earned. It came after more than a century of iteration, theory and convergence between independent methods, and it did not abolish thermometer error. A thermometer can still read wrong, even though temperature is molecular motion. The dissociation sentence survived the identity. What the rule forbids is closing the gap by stipulation, before the work is done. It does not forbid closing it at the end.

"There is nothing on the other side of the gap"

The second objection comes from illusionists and from some followers of Daniel Dennett. On their view, the idea of an inner light that reports and brain signals point towards is itself a kind of illusion. Dennett's method of heterophenomenology, which he restated in a 2007 paper in Phenomenology and the Cognitive Sciences, treats a subject's reports as data about what the subject believes, without assuming that the beliefs are true of an inner theatre. If the inner theatre is a fiction, then the open gap is a gap between proxies and a fiction.

I think this objection is right about one thing and wrong about another. It is right that we should treat reports as data about beliefs first, and not as windows. It is wrong, I think, to conclude that the gap can be closed. Heterophenomenology itself keeps a gap open, between what a subject believes about her experience and what is actually going on in her. Dennett's method needs that gap to work. So even on the illusionist view, a proxy for "what the subject would report" can be wrong about the subject's beliefs, and the dissociation sentence can still be written.

"Clinicians need rules, and your rule paralyses them"

The third objection is practical, and it is the one Kavitha's quality committee would raise. Families need answers. Doctors need thresholds. A rule that says every proxy might be wrong sounds like a licence to say nothing, which leaves the family in the dark and the doctor without protection.

This objection is fair and easy to meet, and meeting it is the main practical result of the paper. A decision rule can be operational without being a definition. "If the Index is below 40 for 72 hours, together with these other findings, we will raise a conversation about goals of care" is a rule about action. It can be written, audited and used. What it must not say is "the patient is not aware", because that sentence turns a threshold for action into a claim about what awareness is. The difference is one verb, and the verb is exactly where the protocol rewrite does its work.

What each rival gets right

Each camp gives me something I should keep. The identity theorist is right that the gap is not sacred, and that a mature theory might close it on good grounds. So the rule should say "not by stipulation" rather than "never". The illusionist is right that report is evidence of belief before it is evidence of experience. So every dissociation sentence should name which proxy is being treated as the check, and admit that the check is a proxy too. The clinician is right that refusing to act is also a decision. So the rule must come with a way to write action rules, not only a ban on definitions.

The perfect proxy is uncomfortable because it removes the easy defence. It is tempting to think the open-gap rule only matters while proxies are bad. The case shows the opposite. The better a proxy becomes inside its home population, the stronger the temptation to define with it, and the larger the cost when it is carried somewhere new.

The proxy overreach audit

The rule becomes useful only if someone other than me can apply it. So here it is as an audit with five checks and two exits. You can run it on a brochure, a protocol, a paper's abstract or a regulation. It takes about ten minutes, and the hardest part is being honest about the third check.

1. Named apart. Is the measurement named separately from the mental state, so that the two can be discussed apart?
2. Population. Is the population on which the link was checked stated, such as "adults after cardiac arrest" or "healthy volunteers under anaesthesia"?
3. Dissociation. Can a dissociation sentence be completed in at least one direction, with the instrument working as designed while the state differs?
4. Check. Is there a practical way, even an imperfect one, to find out whether the dissociation has happened in a given case?
5. Verb. Are conclusions written with evidential verbs ("suggests", "is evidence of") rather than identity verbs ("is", "indicates the absence of")?

The third check has a trap. A vendor can always write "the Index could be wrong if an electrode falls off". That is true and useless, because it describes the instrument failing, not the instrument working while the state differs. A dissociation sentence has to be about the mind, not the machinery. The iced-water case for a mouth thermometer passes, because the thermometer works perfectly and the core temperature still differs from the reading.

There are also two exits. If the concept is fixed by agreement, as a unit of measure is, the gap is meant to be closed and the audit returns "convention". If no dissociation case could ever be checked, by anyone, the audit returns "outside the method". Everything else ends in one of three verdicts: operational definition, proxy drift or operationalist capture.

CHECKS = ["named_apart", "population", "check", "evidential_verb"]

def audit(case):
    if case.get("conventional"):
        return "convention (closed by agreement; no gap needed)"
    if case.get("no_possible_check"):
        return "outside the method (no dissociation case could ever be checked)"
    if not case["dissociation"]:
        return "operationalist capture"
    fails = [k for k in CHECKS if not case[k]]
    return "operational definition" if not fails else "proxy drift: fix " + ", ".join(fails)

Y = dict(named_apart=True, population=True, dissociation=True, check=True, evidential_verb=True)
N = dict(named_apart=False, population=False, dissociation=False, check=False, evidential_verb=False)
cases = {
    "Ward thermometer and fever (negative control)": Y,
    "PCI with a stated benchmark (Casarotto 2016)": Y,
    "Clarion brochure: 'the objective measure of awareness'": N,
    "Stevens: experience as discriminating reaction": N,
    "BIS 40-60 read as 'not aware'": dict(Y, evidential_verb=False),
    "The metre, fixed by the speed of light (counterexample)": dict(N, conventional=True),
    "An operational definition of the luminous ground": dict(N, no_possible_check=True),
    "Kavitha's rewritten protocol": Y,
}
for name, c in cases.items():
    print(f"{name}\n  => {audit(c)}")

Running it gives this output. The judgements fed into it are mine, recorded so that you can disagree with each one.

Ward thermometer and fever (negative control)
  => operational definition
PCI with a stated benchmark (Casarotto 2016)
  => operational definition
Clarion brochure: 'the objective measure of awareness'
  => operationalist capture
Stevens: experience as discriminating reaction
  => operationalist capture
BIS 40-60 read as 'not aware'
  => proxy drift: fix evidential_verb
The metre, fixed by the speed of light (counterexample)
  => convention (closed by agreement; no gap needed)
An operational definition of the luminous ground
  => outside the method (no dissociation case could ever be checked)
Kavitha's rewritten protocol
  => operational definition

The positive case is PCI as reported by Casarotto and colleagues. The measure is named apart from consciousness, the benchmark population is stated in detail, and the nine vegetative-state patients above threshold are treated as a question rather than an answer. The negative case is the invented Clarion brochure, which fails every check. The negative control is the ward thermometer, which should pass and does. If the audit had flagged the thermometer, that would have been a sign the audit was too strict to be useful.

The counterexample is the metre. Its definition, according to the International Bureau of Weights and Measures, is fixed by "taking the fixed numerical value of the speed of light in vacuum" to be a stated number. The metre is whatever that operation gives, and nothing more. By the open-gap rule alone, that would be capture. It is not, because a unit is a convention. Nobody thinks there is a further fact about the metre that the definition could miss. The audit therefore needs an explicit exit for conventions, and it would be wrong without one. Consciousness is not a convention, which is the whole reason the rule applies to it.

A minimal worked case: the fever chart

Start with the smallest case I can think of. A nurse on a general ward writes "fever: temperature of 38°C or higher by mouth" at the top of a chart. Is that an operational definition, or has the thermometer decided what fever is?

Run the five checks. The measurement (a mouth reading) is named separately from the state (raised body temperature). The population is implied by the ward. A dissociation sentence is easy: a patient who has just drunk iced water could read normal with a raised core temperature. The check is to wait fifteen minutes and measure again, or to use a different site. The verb on the chart is a working rule, not an identity claim, because no nurse thinks fever is a reading on a stick. Verdict: operational definition. The gap is open, and everyone on the ward knows how to look into it.

A realistic worked case: rewriting the Friday protocol

Now Kavitha's case. Here is the core of the committee's draft, and the version she sends back on Thursday night. The changes are small. Each one moves the protocol from capture to an operational definition, without making it harder to use.

Three changes do most of the work. "Awareness criterion" becomes "trigger for review", which turns a definition into a rule for action. "Indicates the absence of awareness" becomes "is one piece of evidence about the likelihood of awareness", which restores the gap. And a new line names the dissociation cases the team must rule out before the trigger counts: sedative and paralysing drugs, a recent seizure and the possibility of covert awareness that only a command-following test could show. That last line is where the audit's third and fourth checks become clinical practice.

The committee pushes back on one point. A consultant asks whether "one piece of evidence" will confuse families who want a clear answer. Kavitha's reply is that the clear answer the draft offered was clear only because it was unexamined. A family that hears "the machine says he is not there" has been given a philosophy of mind in the voice of a fact. A family that hears "the machine gives us one piece of evidence, and here is what we are doing to check it" has been told the truth.

When the index becomes the target

One more risk sits behind every proxy that enters practice. The anthropologist Marilyn Strathern put Goodhart's law in its best-known form in 1997: "When a measure becomes a target, it ceases to be a good measure", in a paper on university audit. Suppose Clarion releases an update tuned to agree more closely with the nurses' bedside scale, because that is what hospitals complain about. Agreement with the bedside scale goes up. But the bedside scale is too narrow, in the way Owen's patient showed. So the update may make the Index better at what bedside staff already see, and worse at the cases nobody can see.

Exam marks and what students learn

Teachers know this pattern well. Exam marks are a decent proxy for learning, until a school is judged by its marks. Then lessons drift towards the exam, marks rise, and the link between marks and learning weakens. Nobody has lied. The proxy has been pulled towards the target it was built to track, and away from everything the exam never asked.

The open-gap rule cannot prevent this, though it can make it visible. A protocol that names its dissociation cases will notice when the Index stops disagreeing with the bedside, because covert awareness is one of the named cases, and silence on it becomes a warning sign rather than a comfort.

[AUTHOR NOTE: a short first-person account, only if true, of a software or data project in your own work where a metric quietly became the definition of the thing it was meant to track, and how it was noticed. Do not add any detail that did not happen.]

Where the audit stops working

The audit has a clear failure boundary, and I want to draw it before anyone else does. It checks whether a dissociation sentence can be stated and checked. It does not check whether the sentence is true, whether the proxy is accurate or whether the check is good enough. A proxy can pass all five checks and still be a poor measure. Passing means only that the gap is open, so the proxy can be shown wrong.

The audit also falls silent in two places. At the luminous ground it returns "outside the method", which is correct and unhelpful. And for populations where no check exists at all, such as AI systems for which there is no accepted independent sign of experience, the fourth check fails for every proxy. In those cases the audit cannot tell an honest proxy from captured language, except by the verbs. That is a real limit. It is also, I think, an accurate picture of where the science is.

What would change my mind

I hold the open-gap rule with moderate confidence, and I can name the results that would lower it.

If an identity theory of consciousness earned the kind of support that the kinetic theory of heat earned, I would relax the rule for that theory's measure. The support would need to include convergence between several independent methods, predictions of new dissociation cases that were then found, and agreement across rival research groups. At that point a definition by the measure would be the end of iteration, not a shortcut through it. I would still keep the dissociation sentence for the instrument, as thermometry does.

If clinicians who used identity language about a proxy made better decisions, by outcomes that families and patients value, than clinicians who used evidential language, I would have to rethink the practical half of the paper. I expect the opposite, because evidential language keeps people looking for covert cases. But that is an empirical bet, and it could be tested by comparing units that use different protocol wordings.

If raters given the same protocols disagreed widely on the audit's verdicts, the audit would be too vague to use. The third check, on dissociation, is the most likely source of disagreement. A small study with twenty protocols and five raters would settle this quickly.

There is also a philosophical result that would hurt. If someone showed that the luminous ground does make a testable difference at a lower layer, the "outside the method" exit would be wrong for RTM. I would welcome that. It would turn RTM's top layer from a commitment into a hypothesis, and the rule would then require a dissociation sentence for it like any other.

A final result would change how I teach the rule, if not the rule itself. If people who learned the dissociation sentence went on to treat every proxy as worthless, I would have built a tool for cynicism. The rule is meant to keep measures in use while keeping them honest. I would check this by asking clinicians, before and after a short session on the rule, how much weight they give a low Index alongside other findings.

What I still don't know

I don't know how to write a good dissociation sentence for an AI system. For humans, the check is usually report from the same person later, or a command-following test. For a language model, a "report" is generated text, and the same system that produces the proxy also produces the check. That may make the fourth check impossible to pass for any current AI proxy, which would mean every claim of the form "this model is aware because its score is high" is drift at best.

I also don't know whether the rule should treat infants and animals differently from AI. In infants, development gives a kind of slow check, because the infant grows into a reporting person. In many animals there is behavioural continuity with us. Neither check is available for AI. I suspect that difference matters, and that it should appear in the population line of the audit, but I have not worked it out.

Claim ledger

These are the paper's main claims as I would enter them in the programme's Claim Ledger. Confidence uses three bands: established (strong evidence and no serious challenge I know of), likely (the evidence or argument favours it, with live dispute) and speculative (my hypothesis, argued here but not tested).

There are two dated predictions. First, by 31 December 2029, at least one peer-reviewed study will report patients scoring below the published PCI threshold who nonetheless show command-following on functional imaging or EEG. I will judge it by a literature search, and if I find none I will record the prediction as failed rather than unresolved. Second, by 31 December 2028, I expect that a commercially marketed brain monitor or AI-based assessment tool will be publicly described by its maker as measuring "awareness" or "consciousness" outright, without an evidential verb. I will judge this from public product material, and I will record the first example I find with its date.

Glossary

Anuvyavasāya अनुव्यवसाय

In Nyāya, a later cognition that takes an earlier cognition as its object; often translated apperception.

Asambhava असम्भव

The fault of a definition that applies to nothing it should define.

Ativyāpti अतिव्याप्ति

The fault of a definition that is too wide, covering things outside what it defines.

Avyāpti अव्याप्ति

The fault of a definition that is too narrow, missing part of what it defines.

Bispectral index (BIS)

A processed EEG number from 0 to 100 used during anaesthesia.

Cit चित्

Awareness itself. RTM layer 5, the luminous ground.

Dissociation sentence

A statement of a case where a measure, working as designed, and the mental state it tracks would come apart.

Epistemic iteration

Hasok Chang's term for improving measurement standards step by step, each correcting the last.

Heterophenomenology

Daniel Dennett's method of treating reports as data about what a subject believes.

Lakṣaṇa लक्षण

A definition or defining mark, in Nyāya-Vaiśeṣika logic.

Open-gap rule

This paper's rule: an operational definition is legitimate only while a dissociation case can be stated and checked.

Operational definition

A definition given by the procedure used to measure or detect something.

Operationalism

The stronger view that a concept means nothing more than its operations.

Perturbational complexity index (PCI)

A measure of how hard the brain's response to a magnetic pulse is to compress.

Prakāśa प्रकाश

Light; in Kashmiri Śaiva thought, the awareness by which anything appears. RTM layer 2 borrows the name.

Pratyabhijñā प्रत्यभिज्ञा

Recognition. RTM layer 4 borrows the name for self-recognition.

Spanda स्पन्द

Pulse. RTM layer 1 borrows the name for responsiveness.

Svaprakāśa स्वप्रकाश

Self-luminous; awareness that is aware of itself without a second act.

Vimarśa विमर्श

Reflective grasp. RTM layer 3 borrows the name for reflexivity.

The sentence Kavitha adds on Thursday night

Kavitha signs the protocol on Friday morning, in its rewritten form. The committee accepts every change except one, and that one is a phrase about families that they will revisit in three months. The Index stays on the bed rail. Nobody removes a monitor. What changes is the job the monitor is allowed to do.

On Friday afternoon she sits with Meera in the relatives' room. Meera asks again whether her father is in there, and points again at the grey box. Kavitha gives her the answer the new protocol makes possible. The number is low, and that is one piece of evidence. It does not settle the question. On Monday the team will run a test that asks Mr Kulkarni, through the scanner, to think about moving his hand. If he can follow the instruction, the number will have been wrong about him. If he cannot, they will know more, and still not everything.

The test on Monday is not a final answer either. A command-following test can miss awareness in a patient who is aware but cannot sustain attention, or whose hearing is impaired, or who is simply exhausted on the day. Kavitha knows that, and the protocol now says so. Every check in the chain is a proxy, and the honest course is to name what each one could miss and to run more than one.

Kavitha also changes how the Index appears on the screen. The vendor's display shows a single large number in a coloured box. Her team asks for the number to sit beside a short line naming what it is evidence of, and a second line listing the conditions under which it is known to mislead. The vendor's first response is that clinicians will not read the extra text. Kavitha's answer is that they read it once, on the day they learn the system, and that once is enough to change the meaning of every number afterwards. The negotiation takes three weeks. The final screen is cluttered. Nobody thinks it looks better.

Small changes like this are where the open-gap rule does its work. It rarely forbids a measure. It changes the sentence the measure is allowed to complete, and that sentence travels from the brochure into the protocol, from the protocol onto the screen, and from the screen into the conversation with a frightened daughter.

Meera is quiet for a while. Then she says it is the first time anyone has told her what the machine cannot do. That sentence, more than any result, is what the open-gap rule is for. A family facing the worst week of their lives deserves measurements. They also deserve to know which questions the measurements have not answered.

The dissociation sentence now sits at the top of the new protocol. It reads: "The Index could be low while a patient is aware if sedating or paralysing drugs are present, if a seizure has occurred, or if awareness is covert and shows only on a command-following test." It lacks elegance, and it is the most honest line in the document, and it is the line that keeps the number from deciding what awareness is.

Sources

Cite this work

@misc{mahapatra_U0012,
  author       = {Mahapatra, Rajesh Ranjan},
  title        = {Operational definitions without operationalist metaphysics:
                  when a number on a monitor starts deciding what awareness is},
  howpublished = {Mind Frontier, paper U0012},
  url          = {https://rajeshrmahapatra.com/papers/mind-frontier/U0012-operational-definitions-without-operationalist-metaphysics.html},
  note         = {DOI: to be assigned}
}