Extraordinary Claims Require Extraordinary Evidence (ECREE), Part 2: Is ECREE False? A Reply to William Lane Craig

In my last post, I offered a Bayesian interpretation of the principle, “extraordinary claims require extraordinary evidence” (ECREE). William Lane Craig, however, disagrees with ECREE. In a response to philosopher Stephen Law, Craig wrote this.

This sounds so commonsensical, doesn’t it? But in fact it is demonstrably false. Probability theorists studying what sort of evidence it would take to establish a highly improbable event came to realize that if you just weigh the improbability of the event against the reliability of the testimony, we’d have to be sceptical of many commonly accepted claims. Rather what’s crucial is the probability that we should have the evidence we do if the extraordinary event had not occurred.3 This can easily offset any improbability of the event itself. In the case of the resurrection of Jesus, for example, this means that we must also ask, “What is the probability of the facts of the empty tomb, the post-mortem appearances, and the origin of the disciples’ belief in Jesus’ resurrection, if the resurrection had not occurred?” It is highly, highly, highly, improbable that we should have that evidence if the resurrection had not occurred.
————
[3] See the very nice account by S. L. Zabell, “The Probabilistic Analysis of Testimony,” Journal of Statistical Planning and Inference 20 (1988): 327-54.

I agree with Craig that it would be incorrect to “just weigh the improbability of the event against the reliability of the testimony.” I also agree with Craig that “the probability that we should have the evidence we do if the extraordinary event had not occurred … can easily offset any improbability of the event itself.” I disagree with Craig, however, regarding his interpretation that ECREE requires that we ignore that probability. This can be seen using Bayes’s Theorem (BT).

Let B represent our background information; E represent our evidence to be explained; H be an explanatory hypothesis, and ~H be the falsity of H. Here is one form of BT:

As I argued in my last post, an “extraordinary claim” is an explanatory hypothesis which is extremely improbable, conditional upon background information alone, i.e., Pr(H | B) <<<  0.5. And "extraordinary evidence" can be interpreted as the requirement that a hypothesis's explanatory power is proportionally high enough to offset its prior improbability (the “extraordinary claim”). Here I offer an even more precise definition.

It follows from BT that H will have a high epistemic probability on the evidence B and E:

just in case it has a greater overall balance of prior probability and explanatory power than its denial:


Thus, we can somewhat abstractly define “extraordinary evidence” as evidence that makes the following inequality true:

With that inequality in mind, let’s return to Craig’s objection to ECREE. Here again is the relevant portion of his objection:

Probability theorists studying what sort of evidence it would take to establish a highly improbable event came to realize that if you just weigh the improbability of the event against the reliability of the testimony, we’d have to be sceptical of many commonly accepted claims. Rather what’s crucial is the probability that we should have the evidence we do if the extraordinary event had not occurred.

It seems, then, that Craig’s objection to ECREE is based upon an interpretation of ECREE which requires that we only consider the “extraordinary claim,” i.e., Pr(H | B). If that interpretation is correct, then I will join Craig in rejecting ECREE. But is it correct?

In mathematical notation, “the probability that we should have the evidence we do if the extraordinary event had not occurred” is Pr(E | B & ~H). But now consider again the inequality used to define extraordinary evidence.

The expression, Pr(E | B & ~H), is literally right there, in the numerator on the right-hand side. It appears, then, that Craig’s objection is based upon a misinterpretation of ECREE. For the same reason, Craig’s reason that ECREE would cause us “to be sceptical of many commonly accepted claims” is therefore misplaced.

I could be wrong, but I suspect there are two factors which contributed to this misinterpretation. First, many skeptics have used ECREE in connection with (or as support for) Hume’s argument against miracles. While I’m inclined to agree with John Earman that Hume’s argument is highly overrated–i.e., it may be the case that BT does not provide Hume with the support many skeptics think it provides–this is not of obvious relevance to ECREE. ECREE, like BT, is not dependent on Hume.

The other factor which may have contributed to the misinterpretation is the definition of “extraordinary claim;” Craig may disagree with the criteria skeptics have used to determine whether a claim is extraordinary. I think it is helpful to use probabilistic notation to clarify the issue. Again, I proposed that an “extraordinary claim” is an explanatory hypothesis which is extremely improbable, conditional upon background information alone, i.e., Pr(H | B) <<<  0.5. Let's assume, for the sake of argument, that definition is wrong. Instead, define an "extraordinary claim" as any explanatory hypothesis H which has a prior probability below some number x, i..e., Pr(H | B) < x, where x can be any real number between 0 and 1. Here's the point. X can be any real number between 0 and 1. It doesn’t matter which value one chooses, since BT can accommodate all probability values. In terms of calculating the final probability of H, Pr(H | E & B), we use the same formula–BT–regardless of whether H is an extraordinary claim. From a mathematical perspective, it makes no difference whatsoever whether we label a claim “extraordinary” or “ordinary.” We can use BT to assess the epistemic probabilities of both types of claims.

About Jeffery Jay Lowder

Jeffery Jay Lowder is President Emeritus of Internet Infidels, Inc., which he co-founded in 1995. He is also co-editor of the book, The Empty Tomb: Jesus Beyond the Grave.

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

    Indeed.

    What is the probability of Paul reporting he had travelled to the third Heaven, if there were no third Heaven to go to?

    And what is the probability of the disciples looking into the sky after Jesus had ascended into the clouds , if Jesus had not flown into the sky?

    Miracles are very likely on Craig's world view but it is virtually impossible for religious people to be frauds….

  • http://www.blogger.com/profile/11030669424412573308 Chris

    I think Lisa above is a spammer/spambot. Spammers seem to either be using individuals with blogger accounts to spam websites now, or bots are getting more sophisticated. Hell, it sometimes takes me two times to post a comment correctly. What's next, I fail the Turing Test?

  • http://www.blogger.com/profile/12762450398018434571 J. Quinton

    My problem with WLC's argument is that the empty tomb, etc. are not facts. The only facts that we have is that we have communities of Christians and we have four gospels. Craig's "facts" are actually interpretations of the fact of Christianity/Gospels. It could be that the empty tomb was just a story created by Mark.

    He actually has the rather mundane story of an empty tomb, resurrection appearances, etc. as his evidence that his hypothesis "resurrection of Jesus" is attempting to explain. This evidence would be better explained by some other more mundane hypothesis instead of a bodily resurrection. Of course that doesn't work in his favor so he has to gloss over it.

  • http://www.blogger.com/profile/10289884295542007401 Jeffery Jay Lowder

    Yes, its possible that the empty tomb was just a story created by Mark. But what is probable? I may be an oddity among skeptics, since I'm inclined to agree that there probably was an empty tomb. I agree with you, however, that the Resurrection is not the best explanation. Using Bayes's Theorem, I don't think the available historical evidence establishes a high final epistemic probability for the Resurrection. See my book, The Empty Tomb: Jesus Beyond the Grave, for details.

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

    Jeff, did you take 200 pounds from my wallet, which I have just found empty?

    You are probably going to deny ever taking my money.

    What you probably are not going to do is wait 30 years, and then produce a story explaining that a group of you went to have a look at my wallet, which was freely accessible , and found that the money had mysteriously vanished, and never write one word against the charge that your group had stolen it.

    If there really had been an empty tomb, then there would have been charges of grave-robbing, but Mark is written in a way that implies that the idea of such charges had never entered the author's head.

    Only after Mark had written his story, did charges of stealing the body happen, which is why Matthew has to write what he did, and why John has to explain that only a woman would be foolish enough to think that the body had been taken.

    And, of course, not one single Christian in the first century ever put his name on a document saying he had seen an empty tomb…..

  • http://www.blogger.com/profile/15692946822896192833 Paul Vasquez

    I like Richard Carrier's argument regarding this point that none of the genuine Pauline epistles mention the resurrection or empty tomb. It's only after Paul's cult began to spread that the gospel of Mark appears with an empty tomb story, and the resurrection lines at the end were added later.

  • http://www.blogger.com/profile/07559081710058635050 Pulse

    Steven Carr said:

    If there really had been an empty tomb, then there would have been charges of grave-robbing, but Mark is written in a way that implies that the idea of such charges had never entered the author's head.

    Grave robbery is not the only mundane explanation for an empty tomb. Perhaps the disciples had searched the wrong tomb. Perhaps the tomb was only a temporary resting spot since it was nearby, and the body had been moved to a separate final resting place. Perhaps the body never made it to the tomb in the first place.

  • http://www.blogger.com/profile/13113358989259865484 Robin Lionheart

    Pulse,

    I'm reminded of the marvelous “No, that was a sword in a field” scene in The Messenger.

  • http://www.blogger.com/profile/14612283941807324298 Marcus Morgan

    The resurrection is a matter of testimony, and its probability is the probable accuracy of that testimony. The resurrection is a commonly accepted claim, and I am skeptical of it and many other claims. It it improbable that people will tell lies? No. So start from there when it comes to testimony.


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