Does Hume Commit a Fallacy?

One respondent to my previous post, “The Gospels and Critical History,” in addition to the usual bluster and bombast, manages to offer a few interesting arguments. He had this to say about Hume’s miracle argument from section 1o of An Enquiry Concerning Human Understanding:

“As for Hume’s beautiful argument; it is demonstrably fallacious. Hume had an excuse because probability calculus hadn’t been fully developed in his day, but we now know that what Hume forgot to factor was the probability that if a miraculous event didn’t happen, then we should have the evidence that we do. For example, the report of the winning lottery pick is an extraordinarliy [sic] improbable event, but the improbability that we should hear that number reported if it weren’t really the winning lotto pick is even higher. So, in terms of the resurrection, what is the probability that we would have the evidence of the empty tomb, the post-mortem appearances, and the origin of the disciples [sic] belief if the resurrection actually didn’t happen? Well, if that improbability is high enough, it outweighs any initial improbability. Why think there is any initial improbability to begin with? If there aren’t any conclusive arguments for atheism (which there aren’t), then an agnostic wouldn’t believe that miracles have a high intrinsic improbability. As for Fogelin’s book, I think he fell very short of refuting Earman’s argument. For example, Fogelin doesn’t interact with at least three fundamental arguments Earman raises: the epistemic significance of multiple witnesses, for example, or Hume’s neglect of the voluminous literature from the deist controversy, or the notorious passage on the Indian prince.

The first of these in particular is of the utmost importance. John DePoe has shown how just 10 witnesses can have the effect of overcoming a prior improbability of a million to one, with a posterior confidence of .9999!”

When you assert that something is “demonstrably fallacious,” it would be helpful to include the demonstration, but I cannot find one here.

Since Hume’s argument is not expressed in the probability calculus, let’s set out a simple Bayesian framework to make things clearer. M is the claim that a given miracle has occurred (the bodily resurrection of Jesus in this instance), T is the assertion that a given body of testimonial evidence exists, and K is the conjoint assertion of all relevant background knowledge. Hence, the probability that M has occurred given T and K [p(M/T&K;)] is given by Bayes’ Theorem (note: I have trouble getting math to properly display in this medium, so please bear with me):

p(T/M&K;) x p(M/K)

p(M/T&K;) = ——————————————–
p(T/M&K;) x p(M/K) + p(T/~M&K;) x p(~M/K)

Now the respondent’s argument is that Hume failed to consider how improbable it must be that we would have all of the evidence for the resurrection—the empty tomb, the postmortem appearances, the disciples’ belief in the resurrection, etc.—if the resurrection did not occur. In other words, Hume allegedly failed to note how small must be the likelihood p(T/~M&K;). If it is extremely unlikely that we would have the testimony for the resurrection if the resurrection did not occur, then this degree of improbability could be great enough to overcome the initially very low initial probability of the miracle—p(M/K).

But Hume explicitly mentions several reasons why we might have the testimony for miracles even if the miracles had not occurred. We today, knowing much more about psychology, can provide many additional reasons. In part II of section X, Hume notes:

“…The passion of surprise and wonder, arising from miracles, being an agreeable emotion gives a sensible tendency towards the belief of those events, from which it is derived. And this goes so far, that even those who cannot enjoy this pleasure immediately, nor can believe those miraculous events of which they are informed, yet love to partake the satisfaction at second-hand or by rebound, and place a pride and delight in exciting the admiration of others.

With what greediness are the miraculous accounts of travelers received, their descriptions of sea and land monsters, their relations of wonderful adventures, strange men, and uncouth manners? But if the spirit of religion join itself to the love of wonder, there is an end of common sense; and human testimony, in these circumstances, loses all pretensions to authority. A religionist may be an enthusiast [i.e., a fanatic], and imagine he sees what has no reality; he may know his narrative to be false, and yet persevere in it, with the best intentions in the world for the sake of promoting so holy a cause; or even where this delusion has not place, vanity, excited by so strong a temptation, operates on him more powerfully than on the rest of mankind in any other circumstance, and self-interest with equal force.”

In general, Hume attributes the generation of false testimony for miracle claims to the “knavery and folly” of mankind. In particular he notes, what is simply undeniable, that humans love hearing and passing on tales of the marvelous, and that when the “spirit of religion” synergizes with that natural appetite for the wondrous, then all sorts of wild stories can take wing.

Today we have copious experimental evidence showing just how easily eyewitnesses are misled and how easily false memories are created. It has been repeatedly shown how predispositions bias perceptions, that is, how easily we will “see” what we expect or want to see instead of what is there. We can watch these things as they happen (I have). Experimenters can induce false memories on the spot, and once spurious memories are created, it can be very hard to disabuse people of them. Could testimony about the empty tomb and the postmortem appearances have arisen even if Jesus was not resurrected? Of course it could have, and it does not even take much imagination to see how it might have happened. Could the disciples have come to believe that Jesus was resurrected even if he was not? Of course they could have. And such things happen all the time.

People go on TV claiming to have been abducted by aliens. These reports are often specific about time, place, and circumstance and often include a great deal of detail. I have met people, to all appearances mentally stable, who claim to have seen demons, healing miracles, or Bigfoot (the first was almost certainly a case of hypnopompic hallucination; the second had very likely been misled by a simple magic trick; the third I don’t know). Of the eleven “special witnesses” of the golden plates from which Joseph Smith Jr. supposedly translated the Book of Mormon, eight testified that they had not only seen but handled the plates. Innumerable people have seen ghosts and many famous people, like Hitler, Amelia Earhart, and Elvis, were repeatedly and independently spotted by “eyewitnesses” after their deaths. Detailed, explicit testimony from sane, honest, and intelligent people for miracles, monsters, paranormal happenings, and prodigies of all sorts can be compiled ad nauseam (see the past 35 years of back issues of Skeptical Inquirer). Is there any reason, any reason at all beyond special pleading, for thinking that the followers of Jesus of Nazareth were immune to the sorts of influences that have led untold numbers of people to concoct such reports? I simply defy anyone to show that they were.

Well, why begin with the assumption that miracles are extremely improbable, i.e., why assign p(M/K) such a low order of probability? It is important to remember that in Hume’s day, as in ours, miracle claims are often adduced as part of an apologetic enterprise. Apologetics is generally intended not just an exercise in self-justification for believers, but an attempt to take the battle to unbelievers and to meet them on their own epistemic turf. In that case, if you are trying to show me that a miracle has occurred, you have to address my priors, not yours. If you only meet your own burden of proof, my response will be a shrug and yawn. How low can I reasonably put my priors for the occurrence of an event that I regard as physically impossible, like resurrecting a dead body? Well, pretty much as low as I like. If I want to put it at one in a million, I can put it at one in a million. Show that I can’t. Prove that this would be unreasonable. If you can’t (and you can’t), then that is the burden of proof you have to meet: one in a million.

OK, well can’t the testimony of multiple witnesses overcome even very low initial probabilities, even one in a million? Not necessarily. Depending on the circumstances, 10 alleged witnesses or 500 might not be enough. Indeed, there are circumstances where many witnesses make for poorer, less credible testimony than a single witness. The 19th Century classic by Charles Mackay Extraordinary Popular Delusions and the Madness of Crowds showed how easily members of groups can reinforce each other’s delusions and credulity. Bandwagon effects most definitely occur in groups and here also psychological experiments have demonstrated how easily and effectively individual perceptions are warped by the perceptions of groups. Mob psychology is a poor basis for miracle claims.

Again, you can watch as these phenomena occur. About twenty years ago a woman in Conyers, Georgia claimed to experience Marian apparitions on the thirteenth of every month. When the thirteenth fell on a Sunday, huge crowds would gather to hear her report of the banal “revelations.” A skeptical friend attended one of these and, as she watched, members of the crowd, playing on each other’s excitement, were testifying that the sun was spinning and dancing in the sky, as was reported at the Fatima Marian apparitions. In the meantime, she had a telescope with a solar filter trained on the sun, demonstrating to anyone who would look that the sun was not dancing or spinning about the sky.

To assure the credibility of multiple alleged witnesses, their independence is a vital condition. We have to be sure that different witnesses did not influence each other and did not come under a common influence, otherwise what looks like many witnesses might really be just one. But even multiple instances of independent testimony might be worthless. Suppose that dozens of reports of independent sightings of the Kardashians start to flow in from shoppers at upscale malls and boutiques. Good evidence that your city is suffering a Kardashian invasion? Not necessarily. Suppose that you know that the Society of Kardashian Impersonators is currently holding a convention in town. In that case, you will rightly dismiss even dozens of independent Kardashian sightings. (BTW, I heard someone say that if the world does end in 2012, at least we will be rid of those goddamned Kardashians)

Further, if there are many independent testimonies, how do we deal with the inevitable differences between them? How different may such testimonies be and still be counted as good evidence? If three witnesses independently say that they saw Smith commit the crime, but Smith’s attorney demonstrates substantial discrepancies in their testimony (One says that Smith had an accomplice; the other two said he acted alone. One says that Smith held a knife; the other two say a gun. And so forth.), shouldn’t this plant a reasonable doubt in the minds of the jurors?
The upshot is that the conditions under which multiple alleged witnesses constitute good evidence are really quite complex and need to be spelled out in detail. Still, Hume himself recognized the value of multiple independent witnesses who give consistent testimony. He imagines an paradigm case:

“…suppose, all authors, in all languages, agree, that, from the first of January 1600, there was a total darkness over the whole earth for eight days: suppose that the tradition of this extraordinary event is still strong and lively among the people: that all travelers, who return from foreign countries, bring us accounts of the same tradition, without the least variation or contradiction: it is evident that our present philosophers, instead of doubting the fact, ought to receive it as certain…”

Even philosophers, says Hume, should receive consistent reports from so many independent witnesses as true, indeed certain.

Now suppose that we were to suggest to Hume that maybe the Gospel accounts of the resurrection of Jesus approximate this ideal case. I imagine that at first he would raise a quizzical eyebrow, but then relax into a placid smile and mildly remark, “Why, sir, I perceive that you do but jest.”

About Keith Parsons
  • http://www.blogger.com/profile/02649435667161300831 Peter

    I have a question. Can we ever meaningfully discuss the appropriateness of a given prior for a supposedly one-off event such as this?

  • http://www.blogger.com/profile/04029133398946303654 David B Marshall

    I think Dr. Parsons is wrong on both counts: (1) the prior probability of the resurrection is, I think, pretty high, and (2) the evidence given in the NT for that event is remarkably strong. I don't see how these two points could be adequately explained in less than a book, though: I will not try to do it here.

    I am, though, intrigued by these comments:

    "How low can I reasonably put my priors for the occurrence of an event that I regard as physically impossible, like resurrecting a dead body? Well, pretty much as low as I like. If I want to put it at one in a million, I can put it at one in a million. Show that I can’t. Prove that this would be unreasonable. If you can’t (and you can’t), then that is the burden of proof you have to meet: one in a million."

    Does this mean you are that confident that your honesty and clarity of thought are superior to those of intelligent believers who have thoroughly examined the evidence for miracles, or who have experienced them themselves, critically examined those experiences, and come to the conclusion they were real? Or who have examined the evidence for God in general, and concluded that it is solid? You think there is a less than one in a million chance that they have observed accurately or thought more clearly, than that your own view of the universe could be wrong?

    I wonder if one could justify such self-confidence on any objective grounds? Beginning, perhaps, with a theory of evolution that would bless one man with such vast cognitive superiority over his fellows, in a single generation?

    I hope I don't sound too sarcastic; I am serious about the question.

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    How likely is it that converts to Christianity would scoff at the very idea of their god choosing to raise corpses if their god had raised a corpse?

    In 1 Corinthians , Paul has to deal with Christian converts who certainly believed Jesus was alive, but were scoffing at the idea of a corpse being raised – 'With what sort of body do they come?'

    How likely is it that Christian converts would scoff at the idea of corpses rising if a corpse had not risen?

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    One in a million?

    The New Testament also has Moses and Elijah return to Earth.

    Shouldn't we now cube that 1 in a million?

    How likely is it that Moses would return to the Earth and no Jew would mention this for 30 years?

    How likely is it that Muhammad would return to the Earth and no Muslim would mention this for 30 years?

    How likely is it that Joseph Smith would return to the Earth and no Mormon would mention this for 30 years?

    The whole idea of the disciples seeing Moses return from the grave and not being overwhelmed by the experience is preposterous.

    Even I would be transformed, and I'm not even Jewish.

    How can grown people believe this stuff?

  • http://www.blogger.com/profile/18095903892283146064 Richard Wein

    Keith,

    –In that case, if you are trying to show me that a miracle has occurred, you have to address my priors, not yours. If you only meet your own burden of proof, my response will be a shrug and yawn.–

    I have a problem with this. Are you just talking about what it would take in practice to persuade you (regardless of reasonableness) or are you talking about what it's reasonable to believe? It seems to me you're doing a mixture of the two. You're addressing the question of what it's reasonable to believe, given your priors. But you're refusing to address the question of whether it's reasonable to have those priors. It seems to me, therefore, that you're failing to argue that your rejection of miracle claims is reasonable all things considered. Also, are you really only discussing what it's reasonable for you to believe? Don't you mean also to question the acceptance of miracle claims by others?

    After all, when we pitch an argument at a theist, we won't be impressed if he rejects it on the grounds that his priors for his religious beliefs are 99.9999%, and therefore it's reasonable for him to be almost immune to contrary evidence. We will probably suggest that those priors are not reasonable.

    I'm not unaware of the difficulties of epistemology, and of saying what it means for a belief (or priors) to be reasonable. I take a more-or-less reliabilist, naturalized approach to epistemology. That means I'm in the business of making a judgement about the reliability of the processes that went into the formation of the belief (or the prior) all the way back. So I ask, if someone was exposed to the best possible knowledge and education from birth, and all his cognitive processes were operating optimally, what would he probably believe (or what would his priors probably be)? My judgement is that a person exposed to enough science, having practised enough scientific thinking, and applying scientific thinking consistently, will tend to have low priors for supernatural claims. I can give some rough arguments to support low priors for supernatural claims, based on considerations like parsimony. But they're not deductive arguments from uncontroversial premises. They require a large dose of good epistemic judgement to get the right (as I see it) answer. Epistemic judgement is not just a matter of making and accepting arguments (including probability calculations). Much of it goes on at a subconscious level. And I would say that the subconscious epistemic processes of a supernaturalist are not of the sort to make reliable judgements on this subject (even if there are no deductive errors in his arguments).

    I think it's meaningful and useful to say that we are justified (in some reasonable sense) in assigning low priors to supernatural claims.

  • http://www.blogger.com/profile/18095903892283146064 Richard Wein

    P.S. Keith, I can see that you want to restrict your claims to ones that you can make a strong argument for. But I think that leads you to make only the weak and relatively uninteresting claim that rejecting miracles is consistent with your priors. On the other hand, if you make the stronger claim that it's right to have low priors for miracles (and therefore right to reject miracles all things considered) your argument will be more difficult and less convincing. It's a dilemma!

    Also, I made a mistake in relating my "all the way back" to the lifetime of an individual. I should have related it to the history of the human race. Knowledge (and particularly scientific knowledge) has been accumulated by the human race as a whole. And the effect of science in reducing supernatural beliefs can be seen more clearly at the level of the human race than at the level of individuals.

  • http://www.blogger.com/profile/02647353730607650698 Hiero5ant

    Hume had an excuse because probability calculus hadn't been fully developed in his day…

    Geez louise, what is the deal with the apologetic fetish for pseudomathematics and the anti-apologists' depressing willingness to play along?

    "If it didn't rain last night, then why is the driveway wet?"

    Do we seriously need a formalized treatment in terms of Bayes' theorem to have a rational discussion of other reasons why things might get wet?

  • http://www.blogger.com/profile/02647353730607650698 Hiero5ant

    Now the respondent’s argument is that Hume failed to consider how improbable it must be that we would have all of the evidence for the resurrection—the empty tomb, the postmortem appearances, the disciples’ belief in the resurrection, etc.—if the resurrection did not occur.

    In fact we have no such evidence at all, and this needs to be pointed out loudly and often.

    In the next paragraph you indeed note that what we are dealing with is "testimony about" these alleged events, but you don't emphasize it nearly enough, and so, the apologist looks like he's got the atheist on the ropes — he has all this "evidence" on his side, and the skeptic is on the defensive, frantic to come up with some way, any way, to handwave it out of court.

    But not only are we not dealing with any "facts" of the empty tomb, appearances etc., we are not even dealing with testimony about them! We are dealing with anonymous, hearsay reports (sometimes hearsay reports of hearsay reports!) of "facts".

    Any response to apologetic flim-flam that allows talk about empty tomb and resurrection appearances as "facts in evidence" to go unchallenged is doing a disservice to scholarship and argument.

  • http://www.blogger.com/profile/08733557675273087950 Patrick

    In my view the prior probability of the occurrence of a miracle depends on the probability of God’s existence. As far as I can see no one has so far been able to show that the probability of God’s existence is low.

  • http://www.blogger.com/profile/02647353730607650698 Hiero5ant

    In my view the prior probability of the occurrence of a miracle depends on the probability of God’s existence.

    The Jews, including the disciples, believed in the same miracle-working God the apologists believe in. But none of them at the time of crucifixion expected a miraculous resurrection.

    So it would seem belief in an Abrahamic god is neither here nor there. Just because you believe in a miracle working God doesn't mean you believe he performed any and every miracle anyone ever said he did!

    What you mean to talk about is, prior belief in a god who would do this specific miracle. But this belief only arises from a theology which accreted centuries after the alleged "fact". To say you believe in the sort of being who would do this sort of thing is a textbook example of begging the question, since you've simply swept the improbability under the rug prior which essentially restates your conclusion in its full description.

  • http://www.blogger.com/profile/02647353730607650698 Hiero5ant

    /"rug OF A prior"

  • http://www.blogger.com/profile/08733557675273087950 Patrick

    Hiero5ant: “We are dealing with anonymous, hearsay reports (sometimes hearsay reports of hearsay reports!) of "facts".”

    In 1 Corinthians 9,1 and 15,5-8 the apostle Paul speaks about his encounter with the risen Jesus; it is clearly a first hand testimony. One might ask if Paul had any reason not to tell the truth. Not only was his testimony the cause of much hardship (see 1 Corinthians 4,9-13, 15,30-32, 2 Corinthians 11,16-33), but in addition he had to fear that in the end he would turn out to be a false witness about God (1 Corinthians 15,15). According to Philippians 3,3-10, before his conversion Paul was a well-respected member of the Jewish community, so he didn’t have to become a Christian to win fame. From 1 Corinthians 9,3-18, 2 Corinthians 2,17 and 1 Thessalonians 2,9 one can see that Paul was not looking for financial advantage. Therefore, such a motive for his activities can also be ruled out.

    In the New Testament we can find references to experiences of other miracles than the Resurrection that amount to first hand testimonies of these events. They can be found in Romans 15,18-19, 1 Corinthians 12,9-10, 2 Corinthians 12,12 or Galatians 3,5. These passages wouldn’t make sense if no miracles or miracle-like events had happened. In addition they imply that the addressees of the respective letters had experienced such events, so there were quite a number of witnesses.

    Hiero5ant: “The Jews, including the disciples, believed in the same miracle-working God the apologists believe in. But none of them at the time of crucifixion expected a miraculous resurrection.”

    In my view if a miracle wasn’t expected the respective account of it is even more credible.

    Keith Parsons: “In general, Hume attributes the generation of false testimony for miracle claims to the “knavery and folly” of mankind. In particular he notes, what is simply undeniable, that humans love hearing and passing on tales of the marvelous, and that when the “spirit of religion” synergizes with that natural appetite for the wondrous, then all sorts of wild stories can take wing.”

    The following quote from page 103 of the book “Jesus and the Constraints of History” (Philadelphia 1982), written by A. E. Harvey, may show that at least in Antiquity the Biblical miracle accounts were quite unique and consequently such accounts were not common outside the Judeo-Christian culture (source: http://christianthinktank.com/mqfx.html):

    “It is in this light that we must judge the accounts we possess of other miracle-workers in Jesus' period and culture. We have already observed that the list of such occurrences is very much shorter than is often supposed. If we take the period of four hundred years stretching from two hundred years before to two hundred years after the birth of Christ, the number of miracles recorded which are remotely comparable with those of Jesus is astonishingly small. On the pagan side, there is little to report apart from the records of cures at healing shrines, which were certainly quite frequent, but are a rather different phenomenon from cures performed by an individual healer. Indeed it is significant that later Christian fathers, when seeking miracle workers with whom to compare or contrast Jesus, had to have recourse to remote and by now almost legendary figures of the past such as Pythagoras or Empedocles."

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    Paul also claimed to have gone to the 3rd Heaven.

    Presumably that was also first-hand testimony….

    Paul's encounter with the risen Jesus convinced him that 'the last Adam became a life-giving spirit.'

    Even Acts is adamant that Christians would see things that other people present could not see.

    Just look at the examples of Stephen and Paul in Acts, for obvious examples of Christians seeing and hearing things that other people present could not see or hear.

    As for miracles, Paul in 1 Corinthians pours scorn on Jews for expecting Christianity to be served up to them as a religion that told them about miracles.

    We can easily compare miracles done by Jesus to other figures.

    For the simple reason that the Christian frauds who wrote the New Testament plundered the Old Testament for plots and stories, in much the same way that Muhammad and Joseph Smith plundered the Old Testament looking for stories they could recycle.

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    PATRICK
    In the New Testament we can find references to experiences of other miracles than the Resurrection that amount to first hand testimonies of these events.
    They can be found in Romans 15,18-19…

    CARR
    Here is Romans 15:18-19

    I will not venture to speak of anything except what Christ has accomplished through me in leading the Gentiles to obey God by what I have said and done— by the power of signs and wonders, through the power of the Spirit of God.

    This is so vague that only a Christian could possibly regard it as evidence.

  • http://www.blogger.com/profile/01786844757672182664 K-Dog

    It is unfortunate that this wasn't more obvious to you, but it is Hume's IN PRINCIPLE argument against the identification of miracles that is demonstrably fallacious! His IN FACT argument revolves around four claims that do try to pull off what you said (congrats for that)…As far as your attempted parity of the resurrection with appeal to crazy things like aliens, bigfoot and the like, the burden of proof is on you to show that the evidence for the resurrection is on epistemic par with these other 'weird' events. Lastly, your appeal to recent findings in cognitive psychology trades on the a word play between 'some' and 'all.' Just because 'some' people may display various psychological features that help us understand why they believe strange things, it doesn't mean that 'all' of them do. So, once again, if you actually think the evidence used in the case for the resurrection can be explained by appealing to mob mentality, suggestibility, false memories, or what have you, then you have to actually explain why this is probable with respect to the historical specifics of the case udner consideration, it is not enough to merely make an appeal to possibility.

  • http://www.blogger.com/profile/16641266062186767500 Keith Parsons

    What is truly unfortunate is that we keep being promised a "demonstration" and keep not getting it.

  • http://www.blogger.com/profile/01786844757672182664 K-Dog

    When we talk about the probability of some event or hypothesis A, that probability is always
    relative to a body of background information B. So we speak of the probability of A on B, or of
    A with respect to B.

    So in order to figure out the probability of the resurrection, let B stand for our background
    knowledge of the world apart from any evidence for the resurrection. Let E stand for the specific
    evidence for Jesus’ resurrection: the empty tomb, the post-mortem appearances, and so on.
    Finally, let R stand for Jesus’ resurrection. Now what we want to figure out is the probability of
    Jesus’ resurrection given our background knowledge of the world and the specific evidence in
    this case.
    B = Background knowledge
    E = Specific evidence (empty tomb, postmortem
    appearances, etc.)
    R = Resurrection of Jesus
    Pr (R/B & E) = ?
    Pr (R/B&E;)=

    Pr (R/B) × Pr (E/B&R;)
    _________________________________ Pr (R/B) × Pr (E/B&R;) + Pr (not-R/B) × Pr (E/B& not-R)

    Pr (R/B) is called the intrinsic probability of the resurrection. It tells how probable the
    resurrection is given our general knowledge of the world. Pr (E/B&R;) is called the explanatory power of the resurrection hypothesis. It tells how probable the resurrection makes the evidence of the empty tomb and so forth. These two factors form the numerator of this ratio. Basically, Pr (not-R/B) × Pr (E/B& not-R) represent the intrinsic probability and explanatory power of all the naturalistic alternatives to Jesus’ resurrection. The probability of the resurrection could still be very high even though the Pr(R/B) alone is terribly low. Hume just ignores the crucial factors of the probability of the naturalistic alternatives to the resurrection [Pr(not-R/B) × Pr(E/B& not-R)]. If these are sufficiently low, they outbalance any intrinsic improbability of the resurrection hypothesis. Bayes has the form of x/x-y which means that as the explanatory power of the resurrection tends toward 1, and as the explanatory power of the naturalistic explanations tend toward zero, then any initial intrinsic improbability can be overcome.(Taken from William Lane Craig’s debate with Bart Ehrman).


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