Friday, June 29, 2012

The Mind Projection Fallacy


There is an argument that I have noted a couple of times when scientific colleagues with religious beliefs have tried to explain to me how they reconcile these seemingly contradictory things. Reality, they say, is divided into two classes of phenomena: the natural and the supernatural. Natural phenomena, they say, are the things that fall into the scope of science, while the supernatural lies outside of science’s grasp, and can not be addressed by rational investigation. This is completely muddle-headed, and seems to me to be based on an example of something called the mind projection fallacy.

A similar argument also crops up occasionally when advocates of alternative medicine try to rationalize the complete failure of their favorite pseudoscientific therapy to provide any evidence of efficacy in rigorous trials.

The very word ‘supernatural,’ at its heart, though, is one of those utterly self-defeating terms, like ‘free will’ and ‘alternative medicine,’ completely devoid of meaning and philosophically bankrupt. What is this free will that people keep going on about? Is it the freedom to break the laws of physics? No, and since every particle in your brain obeys the laws of physics, you are not free to make non-mechanistic decisions, so can we please shut up about free will? (Granted, I am using a restricted meaning of the term ‘free will.’)

And what is alternative medicine? Medicine is the use of interventions that are known to work in order to lessen the effects of disease. If it doesn’t work, or is not known to work, then its not medicine, full stop. There is no alternative. Lets please shut about alternative medicine.

What is the supernatural? Nature is by definition everything that exists and happens. What is outside nature is therefore necessarily an empty set.

The etymology of the word ‘supernatural’ is the result of an error of thinking. This error is the mind projection fallacy: falsely assuming that the properties of one’s model of reality necessarily exhibit correspondence with the actual properties of reality. The following dictionary definition of ‘supernatural’ was quoted to me in a recent discussion of the term (reportedly from Webster’s):

Supernatural. [adjective:] 1. of, pertaining to, or being ‘above or beyond what is natural or explainable by natural law’. 2. of, pertaining to, or attributed to God or a deity. 3. of a superlative degree; preternatural. 4. pertaining to or attributed to ghosts, goblins, or other unearthly beings; eerie; occult.

Number 1, is where we have to focus. Numbers 2 and 4 are, in origin at least, based on erroneous application of number 1, while number 3 is just weird. ‘Of a superlative degree’? That’s not supernatural, by any reasonable standard. ‘Preturnatural’? This word has two meanings (according to Dictionary.com): one is ‘supernatural’ (wow, that’s helpful) and the other is ‘exceptional or abnormal.’ Finding a hundred euros on the pavement would be both exceptional and abnormal, but again, not supernatural unless we are willing to debase the meanings of words to the level of uselessness.

So what about the primary meaning of supernatural, ‘above or beyond what is natural or explainable by natural law.’ The first part poses a problem, since there is no supplied procedure for determining what is natural, other than the obvious definition: ‘whatever is not supernatural.’ Now I’m aware that all word definitions are ultimately circular, but this is a case where the radius of curvature is clearly far to small to represent any useful addition to the language. The second part stipulates ‘explainable by natural law,’ which succumbs to exactly the same objection, but I strongly suspect that many people have failed to see this exactly because they have committed the mind projection fallacy – in this case, conflation of natural law with our description of it. Natural law is the set of principles, whatever they may be, that determine how real phenomena evolve. If a phenomenon is real, then it would be explainable by natural law. If a phenomenon is not real, then what is the point in debating whether or not it is supernatural? I feel, however, that too many people think that natural law is some set of equations, like E = mc2, written down in text books – but this is merely our model of natural law. I see no other convincing way to account for the appearance of this phrase in the quoted dictionary definition, than to assume that natural law is being commonly confused with known science in this way, since there seems to be no other good reason to postulate that a phenomenon is not governed by natural law (I know, the exact word was ‘explainable,’ but I think it is hard to rescue the situation by invoking this subtle difference).

By this common understanding of ‘supernatural,’ the photoelectric effect would have been supernatural in and prior to 1904, but natural before the end of 1905. A strange state of affairs, you might think.

Of course, word meanings don’t have to stick exactly to their original literal meanings, and anybody is free to apply the word ‘supernatural’ to any putative phenomenon they wish: gods, ghosts, whatever (as long as they are clear in what they are doing), but I argue firstly, that this is a misnomer, as nothing can be literally beyond nature (supernatural) and secondly, that use of this misguided word leads to horrendous confusions, such as those allowing highly educated and otherwise rational people to claim that religious phenomena (or homeopathy or chi) are by definition supernatural, and therefore by definition beyond the scrutiny of science.

The mind projection fallacy also raises its head in science, all too often, such as in quantum physics, and, in my opinion, in thermodynamics. It has also had very substantial consequences in the development and application of probability theory. Since scientific method generally strives to avoid fallacious reasoning, I feel that it is important to get well acquainted with this particular mental glitch, and to recognize some of the fields in which it still extends a corrupting influence.

Looking at thermodynamics, the famous second law, stating that the entropy of a closed system tends to increase, is often explained by the experts as resulting from our inability to distinguish between individual molecules (or other particles). My conviction, however, is that the mechanical evolution of an ensemble of such particles is unchanged if we are granted a means to identify them after they have evolved. The real reason for the second law seems to be that the proportion of possible initial microstates that result in non-increased entropy is very tiny (and such states appear, therefore with vanishing probability), but polluted with the standard language of the discipline, one can find it hard to grasp this. Why is this standard language an example of the mind projection fallacy? Because there is something unknown to us (the identities of the particles), and the fact of it being unknown is attributed as the cause of the physical evolution of the system, and therefore a physical property of the system. It is not, though, it is a property of our knowledge of the system.

With regard to quantum mechanics, I am open minded on the matter of whether or not nature evolves deterministically or non-deterministically. As I try to be a good scientist, I wait for the evidence to favour one hypothesis strongly over the other before casting my judgement. As much as we know about quantum mechanics already, that evidence is not yet in. I am, however, highly uncomfortable and skeptical about the possibility of something operating without a causal mechanism, yet exhibiting clear tendencies. It seems I am not alone in this, as several other well regarded thinkers have apparently shared this view, notably among them, the exceptional theoretical physicists Albert Einstein, Louis de Broglie, David Bohm, John Bell, and Edwin Jaynes. Imagine my delight, therefore, when I discovered the following passage by Jaynes in a book of conference proceedings1, articulating magnificently (and far better than I ever could) many of my own long-felt misgivings about the language of quantum mechanics:

The current literature on quantum theory is saturated with the Mind Projection Fallacy. Many of us were first told, as undergraduates, about Bose and Fermi statistics by an argument like this: “You and I cannot distinguish between the particles; therefore the particles behave differently than if we could.” Or the mysteries of the uncertainty principle were explained to us thus: “The momentum of the particle is unknown; therefore it has a high kinetic energy.” A standard of logic that would be considered a psychiatric disorder in other fields, is the accepted norm in quantum theory. But this is really a form of arrogance, as if one were claiming to control Nature by psychokinesis.

Whether or not the position and momentum of a particle (as related in the most familiar version of the Heisenberg principle) are truly ‘undetermined’ or merely unknowable to us, I am unsure, but there is a commonly encountered assumption that these two possibilities must be the same, and this results from the mind projection fallacy. It is indeed a mighty challenge to reconcile quantum phenomena with a fully deterministic mechanics. Some have succeeded, but it remains a challenge to pin down whether or not this is nature’s way. Many, however, follow Bohr and assert that there can be no underlying mechanism behind quantum phenomena. Let me quote Jaynes again (this time from ‘Probability theory: the logic of science’):

the ‘central dogma’ [of quantum theory]… draws the conclusion that belief in causes, and searching for them, is philosophically naïve, If everybody accepted this and abided by it, no further advances in understanding of physical law would ever be made… it seems to us that this attitude places a premium on stupidity.


The field in which the mind projection fallacy has had its most significant practical consequences is perhaps probability theory, which is a colossal shame, as probability is the king of theories: the meta-theory that decides how all other theories are obtained.

If you scan through the articles I have posted here on probability, you’ll observe that most if not all make use of Bayes’ theorem. It is an incredibly important and useful part of statistical reasoning, and represents the core of how human knowledge advances. It is also derived simply, as a trivial rearrangement of two of the most basic principles of probability theory: the product and sum rules. Yet, for a significant portion of the 20th century, when statistical theory was undergoing explosive development, Bayes’ theorem was rejected by the majority of authorities and practitioners in the field. How on Earth could this have come about? The mind projection fallacy, of course.

Because the theory models real phenomena in terms of probabilities, it was assumed that these probabilities must be real properties of the phenomena. Yet Bayes’ theorem converts a prior probability into a posterior probability by the addition of mere information. And since merely changing the amount of information cannot affect the physical properties of a system, then Bayes’ theorem must simply be wrong. QED.

The property that probability was thought to correspond to was frequency. For example, a coin has a 50% probability to land heads up because the relative frequency with which it does so is one half. For this reason, the orthodox school of statistical thought has become known as frequentist statistics.

One of the most extraordinary scientists of the 20th century, Ronald Fisher, for example, was one of the people who dominated the development of statistical theory during his lifetime. In his highly influential book, ‘The design of experiments,’2 he gave three reasons for rejecting Bayes’ theorem, foremost of which is:

… advocates of inverse probability [Bayes’ theorem] seem forced to regard probability not as an objective quantity measured by observable frequencies….

Clearly, he meant that the impossibility to reconcile Bayes’ theorem with the view of probability as a physical property of real objects (the frequencies with which different events occur) made it impossible to accept the theorem. (His other two reasons are just as bad.) It was Fisher’s deeply held objection to the logical foundations of probability theory that led him to do some of the most important work developing and popularizing the frequentist significance tests, which, as I have argued in detail here and here, are a poor method for assessing data. 

Another influential textbook, by Harald Cramér3, asserts that ‘any random variable has a unique probability distribution.’ Again, assuming that the probability is something objective and immutable, a physical property. The randomness is assumed to be necessarily a property of the system under study, rather than a statement of our lack of information – our inability to predict it before hand. To instantly recognize the ridiculousness of both Fisher’s and Cramér’s views, consider that I have just tossed a coin, which has landed, and I am asking you to assess the probability that the face of the coin pointing up is the one depicting the head: your only rational answer is 0.5, and it is the correct answer, for you. For me though, the correct answer is 1, because I am looking at the coin, and I can see the head facing up. Same physical system, different probabilities, dependent on the available information.

On the subject of probabilities as physical properties of the systems we study, I can again quote Jaynes, who has summarized the situation beautifully:

It is therefore illogical to speak of verifying [the Bernoulli urn rule, a law for determining probabilities] by performing experiments with the urn; that would be like trying to verify a boy’s love for his dog by performing experiments on the dog.

We can easily identify other instances of the mind projection fallacy in probability reasoning, some of which I have already discussed in earlier posts. For example, the error of thinking discussed in Logical v’s Causal Dependence, consisting of the belief that the expression P(A|B) can only be different from P(A) if B exerts a causal effect on A (an error that has made it into a number of influential textbooks on statistical mechanics) seems to arise from the conviction that a probability is an objective property of the system under study. If B changes the probability for A, then according to this belief, B changes the physical properties of A, and must therefore be, at least partially, the cause of A.

Another instance is to be found in The Raven Paradox, and consists of the belief that whether or not a particular piece of evidence supports a hypothesis is an objective property of the hypothesis, or the real system to which the hypothesis relates. In that post, we examined the supposition that observation of a sequence of exclusively black ravens supports the hypothesis that all ravens are black. We discovered an instance where such observations actually support the opposite hypothesis, illustrating that the relationship between the hypothesis and the data is entirely dependent on the model we chose. To think otherwise was shown to lead to disturbing and indefensible conclusions about ravens. 





[1] 'Maximum Entropy and Bayesian Methods,' edited by J. Skilling, Kluwer Publishing, 1989

[2] 'The Design of Experiements,' R.A. Fisher, Oliver and Boyd, 1935

[3] 'Mathematical Methods of Statistics,' H. Cramér, Princeton University Press, 1946


10 comments:

  1. Hi,

    I'm a new reader to the blog (referred to here by Richard Carrier's blog) and basically wanted to say thank you for all your great posts, especially on Bayes' Theorem. I still have to chew on them, but you write well and your choice of topics is excellent - I'm especially impressed with your treatment of Occam's Razor, which I still need to digest but is certainly the best I've seen.

    Regarding the name of the blog - are you aware of the work by Ariel Caticha? He seems to have an "ME" method that sounds plausible and generalizes maximum entropy. I'd be glad if you could make posts on those issues.

    I chose to comment on this post since I disagree with parts of it.

    First, I advocate an understanding of the "supernatual" as what deviates from uniform, simple, laws of nature, in particular in ways that relate to the level of the person or above. You can think of "laws of nature" in the above definition as "ways things usually behave", and deviations from that are those unusual occurrences where things (supposedly) behave differently. People usually sink through water; Jesus walks on water. That kind of thing.

    I can attest that this is essentially the usual Orthodox Jewish understanding of miracles - things behave in a general way (by the rules of general divine providence), but there are times and places where miracles occur and this "general way" is violated. See http://en.wikipedia.org/wiki/Divine_providence_in_Judaism

    I find this view both makes more sense than the dictionary definitions, and allows one to see quite well why miracles are so abhorrent to modern, scientific, thought.

    Secondly, on the issue of thermodynamics - indistinguishability is the root of the solution of Gibbs' paradox, not of the second law. Your explanation is the standard explanation of the second law. Jaynes' (or Caticha's, etc. - the Bayesian) explanation is that it's a matter of knowledge, which I actually see as the mind projection fallacy and I find hard to swallow. The sun's temperature and life cycle isn't a matter of our knowledge or of ensembles of hypothetical suns.

    At the quantum level, thermodynamics appears as a short-time approximation whenever we divide the world into system and environment, given certain kinds of "environment"; in these cases I believe the root cause of the 2nd law is similar to that raised in your argument, although the concern seems to shift to the structure of Hilbert space in general almost regardless of macroscopic considerations (a good exposition in in Mahler's "Quantum Thermodynamics", although I don't buy his entire approach).

    Thirdly, on quantum mechanics - Unfortunately, QM is a theory about what we'll observe in experiments, not about what the world is. So we have to come up with a "metaphysical" overlay - a world view that will give us the results of QM in experiments. The most straightforward ones (Contextual and Many Worlds) describe a world where events are fundamentally uncaused, while the interpretation that tries to maintain causality (Hidden Variables) not only posits stuff we cannot see, that strongly violates locality, and that seems suspiciously to allow anything to be explained with yet more hidden variables (much like epicycles), but also is technically not an option as it cannot be generalized to the Standard Model (and, likely, Quantum Gravity).

    I have no problem with causes existing in nature all the way through; I do think it's unlikely given our current state of knowledge, however, and that one should not stick to that as a dogma - when the evidence says there are no causes, accept that and move on (until and unless you prove otherwise!).

    On the probability section I have no critique :) I'm still trying to learn all that stuff.

    Thanks again for this excellent blog, and cheers,

    Yair Rezek

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    1. Many thanks for your comments, and the tip about Ariel Caticha, I see he has an interesting looking e-book on entropic inference.

      Disagreements are highly welcomed! I'll take your points in order:

      1) On supernatural: certainly the dictionary definition makes little sense, but why bother trying to fix it? Why not just drop the word altogether? Most ways of understanding the term make no relevant distinction between types of phenomena, and those that do (non-standard, in my opinion) will be misunderstood when used for a general audience. I confess that your own interpretation of the word makes little sense to me either.

      You say that miracles occasionally happen. I'm curious to know if you have an example backed by decent evidence.

      2) On thermodynamics: we agree perfectly that the evolution of the sun is not a matter of our knowledge – it is the standard textbook story, though, invoking the Boltzman interpretation of entropy, that tries to explain such matters in terms of our knowledge. This is what I complain about.

      3) On quantum mechanics: I expect what we see in experiments to be intimately connected with what the world is.

      Jaynes' main points about QM, with which I absolutely agree, were (A) to say that there are no causes is weird and anti-scientific. (B) to say (as many textbooks do) that particles evolve according to how much we know about them places humanity outside normal physics (supernatural?), and (C) the dogmatic insistence / widespread acceptance that there are no causes has inhibited progress in physics. This is not to say there are no good physicists questioning this assumption.

      I'd say that the hidden variable theories do have an advantage, in that they provide a mechanism to get causation at the macroscopic level, which seems to me quite valuable.

      Thanks again.

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    2. You're most welcome, I'm glad to have the opportunity to talk with you. My replies in order,

      1. I do not believe miracles, or magic, ever happened. (Or to be more exact, under a Many World interpretation, the fraction of world-histories of the world we inhabit that include miracles or magic is infinitesimally small.) To be able to coherently say so, however, requires me to have a coherent conception of what "miracle" (or "magic") is. As you explain well, the usual conception is quite hopeless. I suggest this can be corrected by adopting a part of the traditional Jewish Orthodox view on the matter, amended in light of our clearer contemporary views on what "laws of nature" or (to use Hume's language) "regularities in nature" are. The advantage of doing so is that it clarifies what the naturalistic worldview is in a positive manner, namely that the world behaves in a uniform and indifferent manner, not caring (at the lowest, fundamental level) what people think, whether the bullet is made of silver, or the person is "righteous", or so on.

      2. We seem to be in agreement, and just have a different experience with our textbooks :)

      3A. To say that there are no causes is certainly weird. That isn't much of an argument. It is also, philosophically, to be expected at the most fundamental level under the Humean/regulatory understanding of what laws of nature are. So I don't think that the lack of causes are a problem; it appears to me more as a symptom of getting to really fundamental descriptions of reality.

      Simply saying that there are no causes is also unscientific. However, when you construct a scientific theory about how things happens, and this theory happens to include causeless/indeterministic events, this does not render the theory unscientific. It is refusing to accept this theory because of the metaphysical "principle" that things must be caused that is unscientific.

      3B. In principle, I agree - no view that places humans at a special place in the cosmos is worth considering. However, I would note that the "relational" interpretations of QM actually say everything is relational to everything else, so humans aren't special - we're just looking at things from our point of view, but we can just-as-well calculate things from the teapot's point of view. I'm still very doubtful of such information-based, relativistic, interpretations, since I find it difficult to comprehend how things can be "relative" without an underlying objective thing that can have information, point of view, and so on.

      3C. That is simply too soon to tell. I suspect this isn't the case, in that the "next big thing" will only be more causeless - but I may be wrong.

      Finally - from a Baysian perspective, in what way is the presence of a causal mechanism an advantage? Why should we find such a theory more plausible than one without a mechanism? As I said, fundamentally causality is a matter of certain types of regular patterns in existence. Why should we give greater weight to the existence of causal over non-causal patterns?

      Thanks again for the discussion and blog,

      Yair

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  2. We appear to agree on much.

    Refusing to work with a theory because it excludes the possibility of causes is indeed daft (at least without a compelling logical argument). Neither Jaynes, nor me, nor any other scientist I can think of off the top of my head has done that. In my article, I'm careful to say that I am open minded. What I complain of is a similar sin - demanding that there are no causes, without a solid basis.

    From a Bayesian perspective, I find a theory with microscopic causes plausible, because we observe (the very strong appearance of) causes at the macroscopic level. 'Standard' QM (eg Copenhagen interpretation) can not provide these macroscopic causes, because 'wavefunction collapse' seems to place humanity outside the loop, which, as you rightly say, is not woth considering. Its a simple matter of going with the hypothesis that fits the data.

    I don't know how to perform this Bayesian calculation, however, because formally, I can't say what constitutes a cause. Perhaps there is a way around it without invoking the concept of 'cause'.

    Cheers,
    Tom

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  3. << I find a theory with microscopic causes plausible, because we observe (the very strong appearance of) causes at the macroscopic level. >>

    :shrug: No matter what, QM forces us to conclude that something basic breaks down in classical mechanics when you delve deeply enough. I have no problem with that something being causality; I much prefer that to locality.

    << Its a simple matter of going with the hypothesis that fits the data. >>

    But all interpretations do. Granted, the "standard" Copenhagen doesn't - but there are Copenhagen-like (Contextual) interpretations that do. That's why I'm rather at a loss here - there is an overabundance of interpretations, and I'm far from certain which is the most reasonable (although I'm attracted to the Many Worlds).

    << I don't know how to perform this Bayesian calculation, however, because formally, I can't say what constitutes a cause. Perhaps there is a way around it without invoking the concept of 'cause'. >>

    There a number of arguments - like the Copernican principle above - that I find convincing even though I can't phrase them formally in Bayesian terms. That's one of the reasons I'm still somewhat hesitant about Bayesianism - I think it's a great step forwards, but not the end of the story.

    As for 'cause', I would suggest to treat it as a regularity in phenomena so that the occurrence of a "cause" of type A increases the probability of a later "effect" of type B; at the limit, it necessitates it (bringing its probability to 1). This is the Humean perspective, and while more elaborate formulations are often invoked (especially ones considering imaginary, counter-factual, scenarios), I think they ultimately reduce to it.

    I fail to see why patterns must always be near the classical limit, or why events that cannot be attributed to a 'cause' should be barred from manifesting. A flexible probabilistic framework, with room for uncaused and unlikely events, is far more general and thus appears to me more a-priori likely. And lo and behold, that's precisely what most interpretations of QM say reality is like.

    Cheers,
    Yair

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    1. ...so that the occurrence of a "cause" of type A increases the probability of a later "effect" of type B...

      But this is not a suitable criterion for establishing causation. What you are describing is not causation, but logical dependence. See my Logical v's Causal Dependence to understand the difference, and see simple examples of how this way reasoning fails in my Booze, sexual discrimination, and the best pills to prevent being murdered.

      What Hume did was to write down guidelines for strongly suspecting causation. I think even he knew that each of them could be defeated with counter examples. I'm not aware, though, of anybody ever having done a better job.

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    2. The Humean-like account I stated treats "probabilities" as Frequencies. It is concerned with identifying patterns in the temporal sequences of events as they actually happen, not with rationally inferring future events given partial information. The objections you raise are therefore inapplicable.

      As I understand him, Hume suggested a deflationary re-conception of causality, under which there is no such thing as "cause" but merely a stream of events that we divide into "cause" and "effect". His guidelines are about what to identify as causes, not about discovering causes - since "causes", as such, don't exist.

      Yair

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    3. Probabilities are not frequencies, as demonstrated by the simple thought experiment above, and things that alter probabilities are not necessarily causes, as detailed in the two linked articles. I feel that my objections are not inapplicable.

      I struggle to understand your point, though, because you say causes do not exist, yet in the same sentence, you talk about ways to identify them.

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    4. Probability theory is an axiomatic system. Any axiomatic system can be applied to various models. Cox's Theorem assures us that probability theory can be used to represent rational degrees of belief. Great. It does not preclude the same theory from applying to other subjects. In particular, probabilities are well-suited to describe frequencies. If it bothers you, however, just replace the word "probability" in the definition above with "frequency".

      As you do that, it is important to remember you're switching models. As Fisher pointed out, the Frequency interpretation is only rigorously valid within infinite ensembles of repeated experiments. So if you learn that the second ball is Red, for example, this does not change the frequency that the first ball pulled was Red - in repeated experiments. It hence has no causal effect on the first ball's color. It should change your rational expectation of whether the first drawn ball was red, however - so it should change your Bayesian probability for that. There is no contradiction here, the two meanings of "probability" refer to different things.

      Now to Hume. Hume's position boils down to the idea that what exists are events in space-time, and we can describe and find patterns in their spread. When we find a pattern of perfect regularity - events of type A always followed by ones of type B - we call this a "causal" pattern. But this does not mean that a "cause" exists. Assuming causes, or causal powers, actually exist (apart from and in addition to events in spacetime) is superfluous and does no work. It does not change the patterns of events in spacetime, which is really what we're basing our causal reasoning on. So it should be rejected. Thus, there is no "cause" in some metaphysical sense, only "cause" in the descriptive sense, in the sense that there are certain patterns in the distribution of events in spacetime, patterns we can call "causal" and use to divide things into "cause" and "effect".

      Yair

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  4. Proof of how slowly my brain works: I just remembered that those criteria for identifying causation I referred to in the comment above (September 15th) were not due to Hume, but to John Stuart Mill. Apologies for the inaccuracy, I shall stand in the corner for the rest of the evening.

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