ESP and the Other Guy’s Zombie Army

 

simpsons-you-and-what-armyHow much evidence would it take to get you to believe in ESP? Most of us who are skeptical would say it would take a lot of evidence to convince us – that the reason we’re unconvinced is that we haven’t seen such evidence. And yet, were we presented with such evidence, chances are good that we’d still disbelieve it. That’s irrational, right?

Well, not necessarily.

Our lived experience supplies us with initial impressions of how plausible various claims might be, plausibilities that can be estimated as prior probabilities. If we suppose our brains reason correctly in a Bayesian way, then finding a claim extremely implausible amounts to assigning it a very low prior probability. Not exactly zero, since assigning a prior probability of exactly zero is equivalent to asserting no amount of evidence, however good, could change the reasoner’s mind, and that’s not what implausible (as opposed to impossible) means. But close enough to zero to be treated as such for most purposes – except, of course, one would hope, when we’re asked to re-evaluate evidence of the claim itself.

Classical statistics makes fruitful use of cleverly dividing hypotheses up into the null hypothesis and one alternative hypothesis. However, the human imagination is capable of entertaining multiple alternative hypotheses at once, with an intuitive sense, based on experience, of how plausible each is even before new data is presented to it. Nor, Bayesians claim, is the human imagination irrational for doing so. Indeed, the faculty of drawing prior probabilities from experience and correctly updating them in light of new evidence is the essence of Bayesian rationality.

Different experiences lead to differing prior estimates, and because of this, it should not be surprising that different people require differing amounts of evidence to be convinced of a claim. When a claim is supported by evidence that already comports with our experience, we are naturally – and rationally – more inclined to lend it credence based on that evidence. When a claim seems extraordinary to us in some way, we trot out the line “extraordinary claims require extraordinary evidence,” and demand more. The seeming paradox – and evidence of our gross irrationality to the one trying to convince us – is that we may persist in our disbelief even in the face of that extraordinary evidence. Life teaches us the sad lesson that different people’s beliefs do not necessarily converge when presented with the same evidence, but may in fact diverge further! Irrational! Identity-protective cognition! Motivated reasoning! Human perversity!

Well, not so fast. As physicist and Bayesian scholar ET Jaynes points out, it is possible for this divergence to be entirely consistent with correct Bayesian reasoning on differing priors. As he notes, when we’re presented with evidence, we’re usually not experiencing the evidence directly, but hearing a report of it, and one hypothesis likely lurking in the back of our minds somewhere is that the evidence presented to us contains reporting errors. Has the evidence reported been filtered through some other guy’s cognitive biases, or perhaps through publication bias or some other form (however unintentional) of cherry-picking? Might we suspect that the extraordinary evidence is only extraordinary because of experimental error? Might we even sometimes suspect deliberate deception?

Not only may we, but the more extraordinarily the evidence that supports an extraordinary claim seems, the more we might suspect chicanery. These are our alternative hypotheses for explaining the data presented to us, and even where trust is high, and we’re willing to believe reporting error is unlikely, if the extraordinary claim we’re asked to believe on this evidence strikes us as even more unlikely than reporting error, all the evidence does is convince us of reporting error rather than the claim!

Jaynes calls such reporting errors “deception,” on the grounds that it does not matter whether the deception is completely inadvertent. But for many of us, deception implies intent, so I prefer calling it “reporting error” instead. In “Queer uses for probability theory”, perhaps one of the most entertaining chapters ever of an applied math book (the mathematically curious can follow along starting p 149 of this PDF), he discusses the famous Soal experiment in ESP and why “this kind of experiment can never convince [Jaynes] of the reality” of a person’s telepathic powers

… not because I assert [the probability of telepathic powers] = 0 dogmatically at the start, but because the verifiable facts can be accounted for by many alternative hypotheses, every one of which I consider inherently more plausible than [the hypothesis of telepathic powers], and none of which is ruled out by the information available to me.

Indeed the very evidence which the ESP’ers throw at us to convince us, has the opposite effect on our state of belief; issuing reports of sensational data defeats its own purpose. For if the prior probability of deception [reporting error] is greater than that of ESP, then the more improbable the data are on the null hypothesis of no deception and no ESP, the more strongly we are led to believe, not in ESP, but in deception. For this reason, the advocates of ESP (or any other marvel) will never succeed in persuading scientists that their phenomenon is real, until they learn how to eliminate the possibility of deception [reporting error] in the mind of the reader. As (5.15) shows, the reader’s total prior probability for deception by all mechanisms must be pushed down below that of ESP.

In claiming extraordinary evidence to support an extraordinary hypothesis, the claimant may inadvertently resurrect “dead hypotheses” members of his audience already regard as so implausible as to have likelihoods near zero – but still not, in their minds, as close to zero as the extraordinary hypothesis his evidence is claimed to support. You might call these zombie hypotheses, for their propensity to spring back to life in seemingly endless numbers and feast on people’s brains.

As Jaynes notes, an attack of zombie hypotheses can happen even in high-trust environments, and even when the extraordinary claim is true and the evidence supporting it is valid. Indeed, such things have happened to him in his work as a physicist. Such zombie attacks, he notes, have

… made us aware of an important general phenomenon, which has nothing to do with ESP; a person may tell the truth and not be believed, even though the disbelievers are reasoning in a rational, consistent way.

If such zombie attacks can occur even in high-trust environments among people (like scientists) who share a great deal of common background experience, how much more likely are they to occur in politics, where trust is lower and people routinely suspect “deception” not only in the form of innocent reporting error, but also in the sense of intentional, deliberate deception?

It is no accident that political debate so often devolves into resurrecting the other guy’s zombie hypotheses, then concluding from the sheer number of zombies that seem to exist in his mind, that he must be crazy, flagrantly and deliberately rationalizing, or both, for continuing to attack our own truthful reasoning with so many mythical creatures. That he may also be reasoning correctly, given his experience, and his zombie army might be evidence of this, is almost too horrible to think about.

“You and what army?” we’re often tempted to think of an opponent. His zombie army – the army of all the hypotheses our opponent may quite reasonably, based on his prior experience, find more plausible, according to the evidence we present him, than our claim — that’s who. For evidence cannot be interpreted except in light of prior beliefs. And because two people’s prior beliefs can differ

… probability theory appears to allow, in principle, that a single piece of new information D [D for “data”] could have every conceivable effect on their relative states of belief.

So unfortunately for us, even when everyone involved is reasoning perfectly, data never absolutely supports or refutes any claim, but only supports or refutes it relative to all the other (“prior”) information we have. When experience leads us to sufficiently differing prior beliefs, the same data that supports a claim for one of us may refute it for another – maddeningly, without either of us being in logical error!

We see that divergence of opinions is readily explained by probability theory as logic, and that it is to be expected when persons have widely different prior information.

Although we hope (and aren’t always disappointed) that the more data we share with one another, the more our beliefs will converge, it’s also logically possible for holding ever more data in common to drive two people’s opinions ever farther apart without either being in logical error. Now, logically possible isn’t the same as likely, and many of us, I’d guess, would find this possibility rather implausible. There is something too morally lazy – or simply too horrifying – about believing this logical possibility actually happens often enough to account for any significant portion of the disagreement in the world.

I know we have reasonable people on Ricochet on both sides of the ESP debate. I would be surprised if we had many on the side of “zombie hypotheses are often a good explanation for political disagreement” debate. Most of us, I think, have higher hopes for democracy than that, and would like to believe that “open discussion of public issues would tend to bring about a general consensus on them” whenever people are willing to be reasonable (thus preserving the inference that if consensus is absent, it’s because someone somewhere is being unreasonable). But – and perhaps it’s just because Halloween just past – I’ve been seeing a lot of zombies lately. What about you?

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  1. JLocked Inactive
    JLocked
    @CrazyHorse

    I’m creeped out by how smart you are. I guess it’s actually jealousy. But it’s Halloween so I’ll tell myself creeped out.

    • #1
  2. Arahant Member
    Arahant
    @Arahant

    I have direct evidence. So there. :P

    • #2
  3. JLocked Inactive
    JLocked
    @CrazyHorse

    Arahant:I have direct evidence. So there.

    What am I thinking now? Need more volume? Let me turn it up.

    • #3
  4. Percival Thatcher
    Percival
    @Percival

    A man breaking his journey between one place and another at a third place of no name, character, population or significance, sees a unicorn cross his path and disappear. That in itself is startling, but there are precedents for mystical encounters of various kinds, or to be less extreme, a choice of persuasions to put it down to fancy; until–“My God,” says a second man, “I must be dreaming, I thought I saw a unicorn.” At which point, a dimension is added that makes the experience as alarming as it will ever be. A third witness, you understand, adds no further dimension but only spreads it thinner, and a fourth thinner still, and the more witnesses there are the thinner it gets and the more reasonable it becomes until it is as thin as reality, the name we give to the common experience… “Look, look!” recites the crowd. “A horse with an arrow in its forehead! It must have been mistaken for a deer.”

    ― Tom Stoppard, Rosencrantz and Guildenstern Are Dead

    Good post, Midge.

    • #4
  5. Barfly Member
    Barfly
    @Barfly

    Roger Penrose thinks the mechanism of consciousness is hidden inside whatever underlies quantum mechanics, on the seeming basis of nothing at all. Should I entertain his conjecture?

    • #5
  6. Sabrdance Member
    Sabrdance
    @Sabrdance

    I was having this conversation with a colleague the other day -not about ESP, about zombie hypotheses.

    They are all I see at this point.  It frustrates me.  Everyone has their pet hypothesis, and everything proves it.  Politicians, scientists, academics.  Everyone around me, as far as I can see, is the homo unius libri.  And the really angering part -they all claim to be updating their priors because of the 2016 election, but they all just update their priors from “100% correct” to “100% correct, and I have even more evidence to prove it.”

    I have achieved the state of zen, where I simply believe everyone is gaslighting me until proven otherwise.

    Possibly by divine revelation only.

    • #6
  7. Chuck Enfield Inactive
    Chuck Enfield
    @ChuckEnfield

    Great post Midge.  I anticpate thinking about it a lot over the next few days.

    I find this hypothesis midly depressing.  It seems to leave us with no hope for resolving our fundamental differences.  You might think that should be severely depressing, but I held out very little hope before.  Of course this realization could spare us all a lot of frustration.  If we’re forced to conclude that every dispute will be resolved by either war or compromise, the latter looks far more attractive than it otherwise might.

    • #7
  8. Kay of MT Inactive
    Kay of MT
    @KayofMT

    Arahant:I have direct evidence. So there. ?

    In my experience, nobody believes in ESP until they have experienced it for themselves. And in a lot of cases they will dismiss it as a delusion. As has Arahant, I’ve also had many ESP experiences.

    • #8
  9. harrisventures Coolidge
    harrisventures
    @harrisventures

    Sabrdance: Possibly by divine revelation only.

    You may be on to something there…

    • #9
  10. Muleskinner Member
    Muleskinner
    @Muleskinner

    Midget Faded Rattlesnake: When experience leads us to sufficiently differing prior beliefs, the same data that supports a claim for one of us may refute it for another – maddeningly, without either of us being in logical error!

    Nice! Another way of putting this is using the Duhem-Quine thesis to add an additional set of priors about how we get the information. Duhem said that it is impossible to test a hypothesis in isolation, because any scientific test requires a set of assumptions about the testing equipment, etc., so that the “failure” of an experiment to falsify a scientific theory could be blamed on faulty equipment, etc.

    I once argued that economists were down playing strength of econometric tests, because over time, they were becoming stronger advocates of neoclassical theory, which says (among may other things) that returns to all sectors of the economy must be equal over time. While at the same time econometric studies consistently indicated that some sectors did indeed show persistent lower returns, even after accounting for risk. That is their posterior probabilities that the theory is true were increasing as econometric results indicated that the theory was false. My arguments that I was not claiming economists were irrational or unscientific were ignored–maddening indeed.

    • #10
  11. Midget Faded Rattlesnake Contributor
    Midget Faded Rattlesnake
    @Midge

    Sabrdance:I was having this conversation with a colleague the other day -not about ESP, about zombie hypotheses.

    They are all I see at this point. It frustrates me. Everyone has their pet hypothesis, and everything proves it.

    That’s more like a vampire or Rasputin hypothesis, no? People assign what I called their zombie hypotheses plausibilities near zero, only less near zero than a hypothesis they regard as an extraordinary claim. Hence evidence for the extraordinary claim resurrects the zombies instead (and they’re legion).

    A pet hypothesis whose plausibility seems to withstand any assault from incongruous evidence is not a hypothesis that’s resurrected, but one that seemingly cannot be killed – which I admit is also like a zombie in its own way, but not a hypothesis with low prior probability that got resurrected by the evidence; rather one with high probability that evidence cannot seem to kill.

    Still, I know what you mean. While vampires are “undead”, I think I like the visual image of Rasputin here – he just wouldn’t die. The difficulty in killing off pet hypotheses came up on another recent thread on the master persuader hypothesis:

    Midget Faded Rattlesnake: That Trump’s failure to win the presidency [would be] evidence against the master persuader hypothesis is more convincing if you already have doubts about that hypothesis. If your strength of belief in the hypothesis is already high, it is less convincing. If “zombie hypotheses” are “dead hypotheses” that get resurrected by the evidence, then maybe a good nickname for hypotheses that are hard to kill with evidence is “Rasputin hypotheses”?

    • #11
  12. Chuck Walla Member
    Chuck Walla
    @ChuckWalla

    I can’t improve on what you wrote, Midge, but a tangent comes to mind.  I can’t resist mentioning it.

    I seem to recall that in an earlier chapter, Jaynes  lists desiderata for plausible reasoning, known as Cox’s postulates.  These desiderata seem entirely plausible to me (There are two versions of the postulates, and I find the one without assuming the existence of real numbers the most compelling, but they end with the same conclusions).  These postulates provide a firm logical basis (even a mathematical proof of fulfilling the desiderata) for using probability theory, including Bayes’s theorem in the way that Bayesians use it, for extended logic.  By “extended,” we mean that this logic includes Aristotelian logic as a special case.

    That is, your subject is not merely Bayesian logic, it is all of plausible reasoning with imperfect information, i.e., almost everything we deal with in real life.

    That’s what Jaynes meant by including “The Logic of Science” in his subtitle, I think.  Am I right, or this too far afield?

    One thing I love about Jaynes’s book is that it is possible to gain so so much without diving into the math.

    • #12
  13. Midget Faded Rattlesnake Contributor
    Midget Faded Rattlesnake
    @Midge

    Barfly:Roger Penrose thinks the mechanism of consciousness is hidden inside whatever underlies quantum mechanics, on the seeming basis of nothing at all. Should I entertain his conjecture?

    Alas, I’m not the physics expert guys like anonymous, @zinmt, @mikeh, @markwilson, or @timh are. It’s possible you could entertain it with canapes and champagne – that would probably entertain me.

    • #13
  14. Midget Faded Rattlesnake Contributor
    Midget Faded Rattlesnake
    @Midge

    Chuck Walla: I seem to recall that in an earlier chapter, Jaynes lists desiderata for plausible reasoning, known as Cox’s postulates. These desiderata seem entirely plausible to me (There are two versions of the postulates, and I find the one without assuming the existence of real numbers the most compelling, but they end with the same conclusions). These postulates provide a firm logical basis (even a mathematical proof of fulfilling the desiderata) for using probability theory, including Bayes’s theorem in the way that Bayesians use it, for extended logic. By “extended,” we mean that this logic includes Aristotelian logic as a special case.

    Cox’s postulates seem eminently plausible to me, too. And yes, the way Jaynes frames it, Aristotelian logic is a special case of the extended logic including probability theory.

    • #14
  15. Titus Techera Contributor
    Titus Techera
    @TitusTechera

    If logic ends up making people’s daily dose of insanity seem logical, it’s worthless.

    I’m not sure if I can hunt Bayesians down one by one, or there’s some other way to do it, but they’re now on my list.

    The being of the human being is not really that rational or that consistent & it is an attack on humanity to try to prove otherwise. ‘Prior experience’ is a falsehood perpetrated on humanity. Experience is never independent of our interpretations except in our questing work of interpretation. The only thing that you can acquire independent of that interpretation of life, which tends to story-telling, is an understanding of man’s situation & predicament. What it is to be the part of the whole that inquires into the whole while supposing that knowledge of parts is independent of knowledge of the whole.

    The being of the human beings is tied up the opacity of body & name. There is no way around the shocking contradiction between knowledge, as in the arts & sciences, & self-understanding, the attempt to learn about the being of the human being. It’s not even clear what human being is beyond that attempt.

    • #15
  16. Arahant Member
    Arahant
    @Arahant

    Titus Techera: Experience is never independent of our interpretations except in our questing work of interpretation.

    Wait, what? I got the first part. That actually made a lot of sense, which probably means that you misstated it, but that’s a different issue. But your exception seems to say that experience is independent of interpretation when questing for interpretation. Do I have that right?

    • #16
  17. EJHill Podcaster
    EJHill
    @EJHill

    I have ESPN.

    • #17
  18. Arahant Member
    Arahant
    @Arahant

    Sorry to see, Midge, that you got demoted to the Main Feed. Better luck next time.

    • #18
  19. Matt Upton Inactive
    Matt Upton
    @MattUpton

    So we battle not only with prior assumptions, but also will dismiss new reports if they too closely resembles other reports we have already dismissed? Sound like an intellectual callous.

    I don’t know if this the would drastically change how a person would persuade to their beliefs. It would be impossible to know beforehand what argument might trigger a person’s call-to-arms for the zombie army (unless you have ESP).

    (Note to self: develop screenplay for mind-reading zombies).

    • #19
  20. michael johnson Inactive
    michael johnson
    @michaeljohnson

    Muleskinner: I once argued that economists were down playing strength of econometric tests, because over time, they were becoming stronger advocates of neoclassical theory, which says (among may other things) that returns to all sectors of the economy must be equal over time

    I always took shelter in the now obviously false belief that all academics where leftist trash.

    • #20
  21. Valiuth Inactive
    Valiuth
    @Valiuth

    Okay as an ESP skeptic who nevertheless enjoys a good scientific argument I accept your challenge my diminutive reptilian friend.  The first step to working out the reality of ESP is to define it. Is ESP the ability to move things with your mind? Read people’s thoughts? See the future? To be honest I am somewhat unclear about what it means. So we must define what it is. If it is all of these things then I think we need to focus in on one definition as the object of study and verification. Once we have the definition then we need to construct an experiment that will be able to demonstrate the hypothesis. So if some one claims to have the ability to move objects with their mind we can easily test this assertion in a controlled setting. If the objects move with consistency then we can further investigate the phenomenon to eliminate the possibility of other variables being responsible for the objects movement, and to gauge the extent of the power. I would be inclined to take seriously any such study if their methods where transparent and independently replicated.

    In my opinion claiming something like ESP is much like claiming one can do a back flip. If you can you can, then we can work to see if your ability is due to some unknown force or has a more mundane explanation.

    • #21
  22. Midget Faded Rattlesnake Contributor
    Midget Faded Rattlesnake
    @Midge

    Titus Techera:If logic ends up making people’s daily dose of insanity seem logical, it’s worthless.

    I’m not sure if I can hunt Bayesians down one by one, or there’s some other way to do it, but they’re now on my list.

    I might suggest hunting down all mathematicians if you’re concerned about people who allow daily doses of insanity to be considered logical ;-P

    The being of the human being is not really that rational or that consistent & it is an attack on humanity to try to prove otherwise.

    What Bayesian inference would suggest is that even if human beings were reasoning rationally and consistently, we would run into these problems. There are definitely Bayesians who believe that Bayesian reasoning (which they consider correct reasoning, because of course they do) is not intuitive for human beings. Others, like Jaynes, are more insistent that humans may be better Bayesian reasoners than researchers think.  But either way, pointing out that even a consistently reasoning being is likely to disbelieve extraordinary evidence for extraordinary claims not asserting that humans must be that being, just that our opponents may not be as thick or as hostile as we suspect they might be when they continue, maddeningly, to be unpersuaded.

    Experience is never independent of our interpretations

    I’m pretty sure Bayesians agree.

    except in our questing work of interpretation.

    I’m less clear on what these are, though.

    • #22
  23. Midget Faded Rattlesnake Contributor
    Midget Faded Rattlesnake
    @Midge

    Valiuth: Okay as an ESP skeptic who nevertheless enjoys a good scientific argument I accept your challenge my diminutive reptilian friend.

    I am likewise an ESP skeptic. Interestingly, now and then I’ve had experiences that seemed “paranormal” in some sense or other, but not in a way that would lead me to believe they were what they seemed.

    What I do know is that I know people who are no less reasonable than I who do find ESP in some form plausible, for one reason or another.

    anonymous‘s Fourmilab hosts some information on various ESP experiments.

    • #23
  24. Arahant Member
    Arahant
    @Arahant

    Valiuth: Is ESP the ability to move things with your mind?

    That would be psychokinesis, a related phenomenon, but not usually considered ESP.

    Read people’s thoughts?

    Telepathy could be considered a form of extra-sensory perception, as could remote viewing and psychometry (in the ESP sense, not as in testing people).

    See the future?

    This might be labeled under a number of names, depending on how it is done. The general term is prophecy, but there are a lot of flavors of it.

    • #24
  25. Arahant Member
    Arahant
    @Arahant

    ESP, of course, stands for Extra-Sensory Perception. It is sometimes referred to as the Sixth Sense. The most basic definition would be data that is not gathered through the traditional physical senses. This might come through visions, such as in remote viewing abilities, or through just suddenly knowing something. It could also come through communication with spirits. The psychometry I mentioned means the ability to read objects, such as being handed a ring and being able to tell about the history of the ring and the men who had owned it. Telepathy, or mind reading, can also be another method. Another way can be to gain the information through dreams, which is usually some combination of one or more of the others with some form of prophecy.

    Some people combine all of the above abilities.

    • #25
  26. Titus Techera Contributor
    Titus Techera
    @TitusTechera

    Arahant:

    Titus Techera: Experience is never independent of our interpretations except in our questing work of interpretation.

    Wait, what? I got the first part. That actually made a lot of sense, which probably means that you misstated it, but that’s a different issue. But your exception seems to say that experience is independent of interpretation when questing for interpretation. Do I have that right?

    Yes, exactly.

    I reason thusly. The work that is the quest for interpretation of experience is the work of an art or science. The most comprehensive name we give to that work is self-knowledge.
    Now, the work is in a sense separate from the result or end-product of the work. With the art of carpenting or the medical art, I can tell you what the end-product is. I am not sure, however, that all arts or sciences have such an end-product. Self-knowledge seems to be a work not an end-product.

    All knowledge is the work or the result of an art or science. All knowledge is knowledge of something rather than of itself. The carpenter, by his art or science, knows how to make wooden chairs, tables, &c. Carpenting is a domain of knowledge.
    Self-knowledge takes as its domain, obviously, human experience or the human things. It therefore conceives of it as a domain, something excepted from the usual conflation that makes a man both a human being & a carpenter.

     

    • #26
  27. Titus Techera Contributor
    Titus Techera
    @TitusTechera

    I am aware of the problem with the strange art of conversation, or dialectic, that does the work of self-knowledge. It implies metaphysics & psychology are connected in a fundamental way. Strange as that is, it seems to be true to the fact that human being is a problem for human beings, or a quest or investigation.

    • #27
  28. Arahant Member
    Arahant
    @Arahant

    Bartender, I’ll have whatever that guy has been drinking.

    • #28
  29. Titus Techera Contributor
    Titus Techera
    @TitusTechera

    Midget Faded Rattlesnake:

    Titus Techera:If logic ends up making people’s daily dose of insanity seem logical, it’s worthless.

    I’m not sure if I can hunt Bayesians down one by one, or there’s some other way to do it, but they’re now on my list.

    I might suggest hunting down all mathematicians if you’re concerned about people who allow daily doses of insanity to be considered logical

    I’m considering it, but I’ve still some hope that at least mathematicians still have some respect for the radical conflict of theory & practice.

    The being of the human being is not really that rational or that consistent & it is an attack on humanity to try to prove otherwise.

    What Bayesian inference would suggest is that even if human beings were reasoning rationally and consistently, we would run into these problems.

    That is a contradiction in terms. It is not radically different from saying mathematicians by their science would disagree about their science…

    Others, like Jaynes, are more insistent that humans may be better Bayesian reasoners than researchers think.

    That’s just dressing up common sense as rationality, which is insulting.

    […]pointing out that even a consistently reasoning being is likely to disbelieve extraordinary evidence for extraordinary claims […]our opponents may not be as thick or as hostile as we suspect they might be when they continue, maddeningly, to be unpersuaded.

    There is a contradiction between human being & human beings. That’s all there is…

    • #29
  30. Midget Faded Rattlesnake Contributor
    Midget Faded Rattlesnake
    @Midge

    Titus Techera:

    What Bayesian inference would suggest is that even if human beings were reasoning rationally and consistently, we would run into these problems.

    That is a contradiction in terms. It is not radically different from saying mathematicians by their science would disagree about their science…

    Because mathematicians in pure math have the luxury of working in what Jaynes calls pure Aristotelian terms – what Maxwell called “the actual science of logic” in this quote –

    The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man’s mind.

    these mathematicians have the luxury of not having to disagree on the weight of the evidence. One counterexample is enough to bring an entire edifice down, and valid proofs never fail. Weight of evidence (this is almost always true, or almost never true) doesn’t figure in to that type of explicit reasoning.

    Those doing applied math, where evidence matters, do disagree about it.

    • #30
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