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 t

heir 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.”