William Lane Craig’s Critique of Bart Ehrman on the Probability of Miracles

As the saying goes, I have to “call ’em as I see ’em.”

I just read, for the first time, the transcript of William Lane Craig’s debate with Bart Ehrman. I read, with great interest, Craig’s first rebuttal, where he makes extensive use of Bayes’s Theorem (BT) to critique two of Ehrman’s statements. Those two statements were:

(1) Because historians can only establish what probably happened, and a miracle of this nature is highly improbable, the historian cannot say it probably occurred.
(The Historical Jesus, part 2, page 50)
(2) Since historians can establish only what probably happened in the past, they cannot show that miracles happened, since this would involve a contradiction — that the most improbable event is the most probable.
(The New Testament: A Historical Introduction, page 229)

Before commenting on Craig’s critique, let me review some basic notation. Let B be our background information; E be the evidence to be explained; and R be the resurrection hypothesis.

Let us now turn to Craig’s critique. 
Regarding (1), while I join Craig in rejecting (1), I disagree with his reason for doing so. Here is what Craig said in the debate.
In other words, in calculating the probability of Jesus’ resurrection, the only factor he [Ehrman] considers is the intrinsic probability of the resurrection alone [Pr(R/B)]. He just ignores all of the other factors. And that’s just mathematically fallacious. The probability of the resurrection could still be very high even though the Pr(R/B) alone is terribly low. 
With the caveat that I have not read Ehrman’s books and so I am assuming that Craig has not quoted Ehrman out of context, I am inclined to interpret (1) as the following claim.
(1′) Pr(R/B) is so low that it is impossible, even in theory, for there to be sufficient evidence to confer a high final epistemic probability on R, i.e., Pr(R/B & E) > 0.5. 
The only way to reconcile (1′) with BT would be to assign Pr(R/B) a value of zero. If Pr(R/B) = 0, then it follows from BT that Pr(R/B&E;)=0. So, on the basis of (1) alone, as Craig has quoted Ehrman, I think it is premature to assume that Ehrman “just ignores all of the other factors.” Maybe he does do that, but the quotation provided in (1) doesn’t show that. What I can say is that either Ehrman ignores all of the other factors or Ehrman assumes that historians must assign Pr(R/B) a value of zero. If the latter, then I think that is false. I don’t know why historians qua historians would be required to assign Pr(R/B) a value of zero. Assuming that Pr(R/B) is an epistemic probability, the value of Pr(R/B) is subjective. It is going to vary from person to person and from time to time. Theists, including theistic historians, are obviously going to assign Pr(R/B) a value greater than zero. It’s not obvious to me why they would be incorrect to do so, given the content of their background information.
Turning to (2),  I don’t have much to say, other than I think Craig is 100% correct when he says that Ehrman “Confuses Pr (R/B & E) with Pr (R/B).”
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