Evolving Thoughts

Evolution and accident

A common attack upon evolutionary biology, from ranking clerics in the Catholic church to the meanest creationist blogger, is that it implies that life arose and came to result in us by accident. We are asked to believe, they say, that three billion years led to us as a series of accidents. No matter how often evolutionary biologists and informed respondents try to point out that the sense of “accident” in biology is based on the lack of correlation between the future needs of organisms, the trope is repeated ad nauseum.

Why?

The reason is deep in the history of western thought. In reaction to the teleological views of the early Greek philosophers to Aristotle, the atomists held that the nature of things, including living things, arose from the properties of their parts (the atoms) in combination. This was deeply offensive to the teleological tradition, which held that the purposes of things made them what they were, and in particular the hylomorphism of Aristotle, in which form, and purpose, imposed themselves upon the substance, or as a recent metaphysician has called it, “gunk”, that made them.

Epicurus was perhaps the most offensively ateleological of the philosophers attacked by this tradition. He had, as reported by Lucretius in On the nature of things, proposed that once you knew the atoms from which things were made, and their properties, you had nothing remaining to explain. But Epicurus held that in the beginning of things developing, the universe was composed of atoms falling through the void in parallel, until a “swerve”, by uncaused accident, caused them to combine and form the earth and all living things.

Sound familiar? It should. It’s the modern “the universe cannot be accidental and life has to have meaning” canard that creationists proffer with such predictable regularity. It is supposed that evolution requires all the diversity of the world to have happened due to an accident.

Now evolution is indeed based on a number of kinds of randomness. But not the kind of randomness that means things “just happened”. The modern theological objections to evolution are just the latest in a series of attacks upon Epicurean philosophy. First the Greek and Roman philosophers and theologians, people like Cicero, attacked it for impiety. Then the Jewish and Christian theologians attacked it for atheism, and the Islamic philosophers inherited this from them. When Darwin published, he, too, was attacked for being an Epicurean.

Thing is, in a charitable and updated form, Epicurus was right about the natures of living things – science shows us (not just evolutionary biology, but all of science) that the natures of living things really are composed of their parts and the combinations of those parts. Once you have given a molecular, physical, explanation of what organisms do, there is nothing left over to explain. And the principle of natural selection shows us that any apparent teleology in biology is indeed due to physical, mechanical, processes.

So, what is left over that theology can be brought to bear on? Nothing.

The randomness of biology is not mere accident. There’s a causal explanation for all of it, at least in principle. Sure, evolution proceeds by contingent events in one sense. There’s no general reason why a certain mutation had to happen, or a given population lost this or that gene, but this is because either we do not know the conditions or because there is a stochastic scatter in physical processes (which does not rely on evolutionary biology, but upon the nature of things – the world is largely scattered as a matter of fact, in physics and sociology as well as in biology). No law tells us that a gamma particle had to hit a gene while a sperm or an egg was being formed, but if one does, then we know there will be a determinate outcome, a mutation, and selection and drift will happen to it.

It is my view that physical things are determinate – which means that if event A happens, result B will follow (although B may be a statistical distribution). Molecular properties tell us why metabolism, replication and mutation happen. If we have enough data, we can even predict what that will be in fine detail. Epicurus was right and Aristotle was wrong.

So the canard is in large part due to a failure of theology to catch up with the physical world. And they had better catch up soon, or they lose all semblance of intellectual respectability. Of course there is also the moral claim that if everything is an accident, there is no meaning to life, but we can let them have the view that life has meaning from some nonphysical source for now (though I don’t believe it for a moment). It’s time they dropped this once and for all.

A final note: “accident” is itself a questionable concept. We talk about a motor vehicle accident, but we explain the event in terms of the vehicle, the conditions or the driver quite determinately when we investigate the causes of it. In Aristotle’s metaphysics, and accident was something that could be otherwise without changing the nature of the thing. In that sense, there are no accidents in a physical explanation, because (i) there is nothing that is essential to being, say, a dog (which is the contrast class for “accidens”), and (ii) all causes are determinate in some manner in science. A mutation, that will later confer immunity to a disease or to injury, is an accident only in that it might have been otherwise, not because it has no cause or was not a necessary result of the conditions that did obtain.

Time to get with the 21st century in your metaphysics…

Comments

  1. #1 Roy
    March 10, 2007

    “… a failure of theology to catch up with the physical world.”

    Theology and reason are not poles apart, they are in orthogonal. One is wishful thinking, the other is science.

    The only way to ‘correct’ theology is to discard its parts. A fully correct theology would be an empty set.

  2. #2 John Pieret
    March 10, 2007

    There is a nuance I think is involved with many if not most creationists. The distinction they see isn’t between accident and purpose but between accident and intent. This article is particularly clear about it. To the author, “nature” is the same as “chance” and is to be contrasted with and is the opposite of “intelligence.”

    Mere purpose (in the generalized god-as-sustainer-of-nature concept of theistic evolution) is not sufficient. Life, particularly human life (and, ultimately, each individual human), must be the intended result of God’s deliberate action.

  3. #3 David Harmon
    March 10, 2007

    “It is my view that physical things are determinate”

    Sorry, that may work as a “usual rule”, but chaos theory knocks big holes in “complete” determinism, and quantum mechanics props the holes open. “… For want of a battle, the war was lost, and all for the want of a horseshoe nail.” Even statistical distributions can get swept up by attractors and/or basins.

    As far as I’m concerned, the most interesting thing about evolution is the fact that it can create telelogical pressures de novo, with contingency snatching straws from the infinite bundle of possibility, and weaving them into complex patterns. The beginning of an adaptation might be accidental, but it rapidly gets caught up in a feedback loop with its own effects, and “what succeeds, proceeds”. Evolution is even capable of generating computational structures to interpret and respond “sensibly” to changes in the environment. (It remains to be seen whether the most spectacular example can also respond sensibly to the results of their own collective behavior. ;-) )

  4. #4 mark
    March 10, 2007

    If the term “accident” is objectionable, how about “luck?”
    I come across numerous stochastic models in hydrology. If they can work so well to explain matters hydrological, why should biological systems be very different?

  5. #5 Reed A. Cartwright
    March 10, 2007

    John, can you link to this from PT?

  6. #6 John Wilkins
    March 10, 2007

    David, chaotic equations are fully deterministic. As to quantum, I retain the vain hope that it will be shown to be deterministic at the sub-Planck level, as suggested by a recent paper I read that I now can’t find. In any case, quantum is true for all deterministic systems, so we can leave quantum aside in most cases.

    I fully concur that biology snatches the necessary from a broad set of possible cases permitted by physics,but given the boundary conditions in each case, each case is necessary, given the laws of physics and chemistry.

  7. #7 Jonathan Vos Post
    March 10, 2007

    John Wilkins,

    There seems to be some debate about your claim:
    ” chaotic equations are fully deterministic” depending on whether the model is discrete or continuous.

    For example:

    http://arxiv.org/pdf/q-bio.PE/0702048
    Title: The Time Invariance Principle, Ecological (Non)Chaos, and A Fundamental Pitfall of Discrete Modeling
    Authors: Bo Deng
    Subj-class: Populations and Evolution
    Note: replaced with revised version Thu, 8 Mar 2007 19:53:28 GMT (18kb)
    Abstract:
    This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.

    or — is there a good reason to reject this paper?

  8. #8 Iorwerth Thomas
    March 11, 2007

    David,

    Even though standard interpretations of QM are indeterministic, it doesn’t mean that they’re random, in the sense that the term is used in John’s post. The evolution of the probability distribution between outcomes of a measurement is deterministic; it’s just that whichever one is selected on measurement is indeterminate.

    I suspect that the Creationists mean something stronger by ‘chance’ than this. (They must do; since some theologians have no problems with QM, or evolution, for that matter. Maybe it’s just that they talk to more scientists, though…) But I could be wrong in how I’m reading this.

    Even if QM is indeterministic, it should be worth noting that that might not necessarily drive one towards an indeterministic metaphysic; that’d depend on how much scientific realism that one wants to apply to the theory, and the degree to which one thinks that determinism is justified on other grounds. [Insert pithy Duheim quote here.]

    John,

    Are you thinking of Gerard t’Hooft’s theory, or someone else’s?

  9. #9 John Wilkins
    March 11, 2007

    Yes, t’Hooft, although I don’t understand it well if at all. I have always thought that the idea that underlying reality is indeterministic is just wrong – causality occurs, and it has to happen at all levels of reality, in my view. But whether or not quantum physics is indeterministic, it doesn’t matter at the biological level (Penrose notwithstanding) because of the averaging effect. This is just a prejudice of mine.

    And in any case it doesn’t matter in this context, because if physics is indeterminist, so is everything else, so this is not a special problem in biology.

  10. #10 Jorg
    March 11, 2007

    I tend to think of QM as deterministic; probabilistic, certainly, but the appearance of acausality goes away under some models. The paper is by ‘t Hooft and is available here: http://www.arxiv.org/abs/quant-ph/0604008 .
    (Hmmm…linking to this, I also see a more recent paper by him, entitled

  11. #11 Torbjörn Larsson
    March 12, 2007

    It is my view that physical things are determinate – which means that if event A happens, result B will follow (although B may be a statistical distribution).

    Well put. And I find an amusing parallel to the disappearance of “apparent teleology” in the disappearance of our local universe ‘apparent’ indeterminism in the birds-eye view of the many-worlds interpretation. (Which perspective btw perhaps resolves or at least informs John’s dilemma between causality and observed, supposedly genuine, stochasticity. The problem with t’Hooft ideas is to get around the prohibition against hidden variables, a problem I don’t think he has shown yet he has solved.)

    The problem with Aristotle’s views seems to be that they are based in folk psychology, far from physical models of causality such as deterministic process causality or emergent light-cone causality.

    Even statistical distributions can get swept up by attractors and/or basins.

    Chaos follows from classic determinism but the main characteristic is fundamental loss of total predictivity. Even finegraining will not help because of exponential divergences and state space folds.

    Contra-intuitively, as I understand it quantum deterministic systems doesn’t show quite this behavior, because their evolution is linear.

  12. #12 Torbjörn Larsson
    March 12, 2007

    The paper Jonathan linked to was interesting and a nice reference.

    As I understand it it finds that most simple discrete population models, such as the logistic map, are too coarse models. By using time invariance as criteria (TIP) they reject almost all such maps as unphysical.

    They can also conclude that “1 and 2 dimensional TIP-conforming maps cannot be chaotic”, which means that realistic models of single- and two-species population dynamics cannot be chaotic. This apparently resolves a difference between theory and observations on such systems – “ecological chaos is not to be expected in the wild”. (“Although laboratory chaos is possible with stringent setups, such systems are never simple. In fact, the dimension required is 3 or higher”.)

    I especially like that one method they propose to derive TIP-conformity for population maps is by using mass balance on available resources. When I last read about ecological models, IIRC they didn’t get very far with these ideas by themselves, which intrigued me at the time. Here they seem to be an indelible part of the picture.

  13. #13 mtraven
    March 12, 2007

    What about the effort to sneak teleology in by the back door via Anthropic Cosmology?

    Even if purpose is not part of the fundamental physics of the universe, the fact that it (and consciousness) emerged is interesting, and screams for better explanations. Natural selection can go a long way towards this but doesn’t completely satisfy as a theory.

    I’m curious as to how you think theology can catch up to science without disappearing altogether. Actually my own dream is to invent a theology that is completely consistent with naturalism, but I have only the vaguest idea what that would be…see here for some speculations.

  14. #14 shiva
    March 13, 2007

    John,

    Atomism in India went thru a few iterations. The earliest began when the grammarian Yaska around 700 BCE who identified words and their sub-units as carriers of meaning. The the Nyaya-Vaisesikas and the later Jains had an elaborate scheme in which atoms had many different classes (about 24) and combined in dyads and triads to give rise to the elements and their combination. The Buddhist view was qualitative and was probably a means to anchor the proposition that desire itself and its consequences are but the result of more fundamental interactions between substances. Atomism was discarded in later centuries and some say (highly debatable) that since it found no resonance in the ‘sacred’ texts it had no relevance. The 1500s work on logic, Gangesa’s Tattvacintamani (see here for more on a recent book http://tinyurl.com/2ebq8r) does without atomism.

  15. #15 Torbjörn Larsson
    March 13, 2007

    Even if purpose is not part of the fundamental physics of the universe, the fact that it (and consciousness) emerged is interesting, and screams for better explanations.

    Only if you make the usual mistake of confusing a priori probability with a posteriori outcome.

    The weak anthropic principle explains as much as the strong, while being just weaker on assumptions. OTOH the quest for a completely constrained theory isn’t over.

    Natural selection can go a long way towards this but doesn’t completely satisfy as a theory.

    I’m sure it will be news for practicing biologists that their basic science of evolution is wrong.

  16. #16 mtraven
    March 13, 2007

    I didn’t even suggest that “the basic science of evolution is wrong”, only that it might be incomplete. No scientific theory can claim to explain everything. I’m speculating that the constraints of the anthropic principle also impose constraints on natural selection that effectively introduce teleology. And I’m hoping for some intelligent conversation about this idea, rather than having people jump down my throat because they imagine I’m attacking their science somehow.

  17. #17 G
    March 14, 2007

    It seems to me that there is a lot of misunderstanding of Aristotle’s teleology lurking in this post: I won’t even try to correct all the confusions in a comment, but I can at least start by pointing the interested reader to Ernst Mayr’s The Growth of Biological Thought, where Mayr clearly and cogently separates cosmic teleology from various sorts of lesser teleology (and what he labels “teleonomy”) – and admits in a footnote that the common Medieval theological understanding of Aristotelian teleology may be based on a deep misunderstanding of any- and everything Aristotle actually had to say on the subject. (I would give page citations for this, but I seem to have loaned out my copy of the text in question.)

    My own take on this is that Aristotle’s teleology is mostly CORRECT with respect to organisms, except in the following sense: Aristotle argued that the telos of any thing – that which constituted its “thingness” – was a sort of homeostasis. Brilliant modern Aristotle scholar and translator Joe Sachs explains the fundamental Aristotelian concept of “thingness” (i.e. a thing’s identity with itself through time) as an ongoing process; any given thing is always (as Sachs translates the complex Aristotelian concept of entelecheia) being-at-work-staying-itself. In this, Aristotle was indeed wrong, but not ridiculously wrong. Homeostasis certainly is fundamental to the ongoing processes of a living organism, but mere metabolism is not the ultimate telos of an organism. Rather, an organism’s telos is making more of itself – or, more accurately, passing on the information represented in its genome to future generations (which allows for phenomena such as kin selection and so on in a way that over-simply calling self-replication the telos of every organism does not).

    Thus I believe that a careful reading of Aristotle (not corrupted Medieval theological misreadings of Aristotle, but Aristotle himself) leads to a teleology that is not nearly so flawed as this post indicates. While he may have gotten the precise telos wrong, the general notion that individual living organisms are teleological was actually a profound insight and not an error. In fact, Aristotle’s greatest problem was that he generalized from his observations of biology to physics – where his teleology is frankly awful. When applied to non-living nature, a fairly insightful understanding of how living things operate becomes an egregiously mistaken picture of physics.

    To put my point more in the terms discussed in this post: Every time any science defender has ever pointed out that creationists are misrepresenting evolution when they call it “random” – because selection by definition is not random, of course – the science defender is in effect taking an anti-Epicurean position. In fact, if one reads Aristotle carefully with an understanding of modern biology in mind, natural selection is where telos comes from.

    From the first self-replicating molecules which differed slightly from one another because of slight errors in replication, the differences between individual replicators which MADE A POSITIVE OR NEGATIVE DIFFERENCE with respect to the frequency or reliability of replication were represented in greater or fewer numbers in successive generations of replicators. That is, the operation of selection is exactly identical to the refining of replicators for successful replication – which, over time, changes a lineage of replicators so that they better fulfill the telos of replication (in a given set of prevailing local conditions). Replicators, error which produces differences between replicators, and differences between replicators that result in differential replication success/efficiency/frequency are the necessary fundamental features of any system in which evolution by natural selection can, does, and indeed MUST take place. What results in such a system? Replicators in which the various features and parts (and their operations) are increasingly organized around and directed towards successful replication. According to Aristole (in De Anima), telos simply is the principle or cause of the organization of the parts of a thing and their arrangement/operation. So, reproduction is the telos of any given individual organism.

    Note: In saying that organisms are teleological in the sense described above, I am not making the claim that evolution more generally is teleological. Teleological evolution (a la Tielhard de Chardin) is wrong-headed on the face of it, and is not supported by the evidence. But life is teleological – i.e. goal-oriented – insofar as individual organisms are organized and directed towards their own reproduction (or at least the reproduction of their own genomes). My overall point in this comment is that this use of the term “teleology” is consistent with Aristotle’s actual usage, but shorn of the the unsupported broader associations attached to it by Aristotle himself (his teleological physics) and Christian scholars (where all teleology is equated with or associated with cosmic teleology, the unfolding of the Divine Plan – which has fuck-all to do with anything Aristotle ever actually said).

  18. #18 John Wilkins
    March 14, 2007

    Aristotle himself tended to speak of final causes only in connection with living things, but I can guarantee Mayr will not be the best source for understanding Aristotle, as he paints him as the source of all error, which is simply wrong. You’d be better off reading Jim Lennox or Pierre Pellegrin.

    You are over interpreting Aristotle – homeostasis and feedback was invented much later, later even than Kant, who had the same problems himself. Equally, the scholastics are misinterpreted themselves. The macrocosmists did not generally argue from Aristotle, but from Porphyry, Plotinus, and ultimately Plato. The Aristotelian tradition was much less open to this kind of grandiose theorising and mysticism.

    But nevertheless, teleology is problematic for the reasons Kant and Hume pointed out – it puts the cause after the effect. Sure, we can charitably interpret Aristotle to be talking about homeostatic processes, but that is not what he thought. As Bacon noted, final causes are barren virgins (except when talking about human action). Not until we developed the notion of a feedback loop (initially in natural selection) did we have any explanation of final causes, and at the same time an elimination of them.

    Mayr appropriated the terms proposed by Pittenrigh : teleonomic, and teleomatic. In that frame, Aristotelian teleology is neither of these allowable views.

  19. #19 G
    March 15, 2007

    Your response seems to focus on trivial matters (some of which I discuss below) rather than actually responding to the main content of my post – the argument that telos is a result of the process of natural selection (NOT something that drives evolution, a mistaken but all-too frequently embraced idea). In short, the perspective I’m advancing is this: Because the sorting process of natural selection results in organisms whose parts and processes are increasingly organized for and directed towards self-replication (or, more precisely, genome-replication), it is accurate (and potentially useful) to describe that self-replication as the telos of each organism.

    I contend that this is wholly consistent with Aristotle’s use of the term telos throughout his corpus. The word telos can only roughly be translated as “end,” and somewhat more poorly translated as “purpose” or “goal” (poorly because these terms introduce elements of conscious intent that are not consistent with the broad range of things Aristotle refers to as teloi). The word telos is horribly mis-translated by the phrase “final cause,” however, because that carries the implication of the effect preceding the cause that is in no way consistent with Aristotle’s usage (and is rightly criticized by the philosophers you cite). Aristotle’s use of the word telos was primarily functional, which is not quite the same as causal, and was future-oriented only in the same sense that all functional concepts are.

    Clearly you are familiar either with the passage I referred to (The Growth of Biological Thought, pp. 48-51) or the earlier version from a paper, since you mention Mayr’s borrowing of the terms teleonomic and teleomatic from Pittenrigh. And this, I think, is where we part ways. Only the common “final cause” misunderstanding of Aristotle’s conception of telos makes Aristotelian teleology inconsistent with teleonomic and teleomatic processes – meaning that Pittenrigh introduced (and Mayr repeated) what are ultimately some spurious distinctions. A full argument for that point would require more than a blog comment, but I can sketch it briefly.

    What I’ve described above would fall under the Mayr/Pittenrigh categories of ‘teleonomic activities’ and ‘adapted systems.’ But both teleonomic activities and adapted systems were put forward to parse out and distinguish among supposedly confused/conflated concepts falling under the broad heading of teleology, so it makes sense to at least consider what the telos at stake here is. In other words, what is the nature of the telos around which each of these supposedly different classes of phenomena is ordered? If you go back to the definitions Mayr offers for these categories and consider what I’ve said here, I think you’ll find that the self-replicative telos I describe above fits both categories just fine – making the distinction unnecessary.

    This is not a complete argument, of course. Specifically, I haven’t done much to support my contention that telos as I’ve used it here is consistent with Aristotle’s usage, and that the common “final cause” understanding is flawed. But I thought it worthwhile to at least sketch out the perspective I’m coming from, since you seem to have assumed in the above response that I’m just confused or that I’m talking out of my ass.

    In any event, your mention of Mayr’s tendency to blame Aristotle for holding back biological progress is a bit of a red herring. Mayr’s primary problem with Aristotle was not his teleology, but his essentialism: The elements of the doctrine of forms that Aristotle retained from Plato were an obstacle to understanding biology because that view did not see organisms as individuals, but as types or kinds. (Baraminology is really on the cutting edge of 3rd century BCE science!) If one looks at individuals as mere variations on or less-than-perfect exemplars of some prior ideal form, one cannot easily bridge the gap to seeing organisms as populations of varying individuals – which is crucial to understanding evolution by natural selection.

    On the homeostasis point, I think you’re over-interpreting what I said. I don’t claim that Aristotle invented or understood the idea of homeostasis in organisms as we do. But Aristotle’s notion that the property which makes something a discrete, sustained entity (the “thingness” of a thing, if you will) is an ongoing active process of self-maintenance is more than a little analogous to the concept of homeostasis in organisms. For Arisotle, being means being-at-work; and being a particular kind of thing means being-at-work-staying-the-kind-of-thing-that-it-is. Aristotle even seems to have derived this concept from his study of and reflection on living things, making the similarity between the homeostasis and entelechia more clear and plausible. For more on this point (the meaning of entelechia part, not the homeostasis bit), see this excellent discussion by Joe Sachs in the Internet Encyclopedia of Philosophy.

    Incidentally, I’ve not only read Jim Lennox on Aristotle’s biology, I’ve argued with him about some of these same ideas. While we didn’t reach agreement on all points – philosophers rarely do – he didn’t think I was completely off-track in my understanding of Aristotle’s conception of telos.

  20. #20 truth machine
    March 15, 2007

    If we have enough data, we can even predict what that will be in fine detail.

    Only if “can” means “in theory”, and only if the theory includes us having access to considerably more computational power than than is buildable “in theory” from the entire content of the universe (and quantum computing doesn’t help, as Scott Aaronson explains in “NP-complete Problems and Physical Reality”). In other words, no we can’t.

    Also, I have to disagree with “Once you have given a molecular, physical, explanation of what organisms do, there is nothing left over to explain”. A complete molecular trace of my physical state throughout my entire life, together with a complete physical understanding of all those chemical reactions, won’t explain “what I do” — such an explanation is too low-level. It won’t explain, for instance, my behavior when asked various questions or upon encountering various traffic situations, even though all the knowledge I employ in my responses is physically encoded somehow in my brain. The claim that “there is nothing left over to explain” fails to take into account the contextual nature of explanation, that there are multiple explanations, at various levels, for the same phenomenon. To explain what Gary Kasparov does when presented with some chess position requires a knowledge of chess, not of his molecular composition.

  21. #21 truth machine
    March 15, 2007

    I have always thought that the idea that underlying reality is indeterministic is just wrong – causality occurs, and it has to happen at all levels of reality, in my view.

    Unless indeterminism is logically impossible, there’s no basis for “just wrong”. Consider Everett’s multiple worlds model — even if the complete panoply of worlds, taken as a whole, is fully determined, our individual futures are grossly underdetermined. And what causes the number of worlds to multiply? The claim that causality “has to happen at all levels of reality” entails an infinite regress; what “has to happen” is that the child’s “but why …” game must bottom out with a question that has no answer. But that doesn’t necessarily leave us with no explanation of why there are raw, uncaused facts; consider modal realism.

  22. #22 Torbjörn Larsson
    March 16, 2007

    only that it might be incomplete.

    Stating that “we don’t know” is a satisfactorily answer.

    But the point is that evolution has been a satisfactorily theory explaining common descent with modification.

    I’m speculating that the constraints of the anthropic principle also impose constraints on natural selection that effectively introduce teleology.

    That would be the strong version of the anthropic principle. That is a problematic theory exactly because it suggests teleology which natural theories doesn’t use. It is reversing the universal observed order of cause and effect, which invalidates such basic properties like Lorentz covariance. Its seeming appeal is based in simply mistaking a posteriori outcomes for a priori probabilities.

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