During his debate with William Lane Craig, Bart Ehrman was discussing whether it is possible for a historian to affirm a miracle. Here is what he said:
Historians can only establish what probably happened in the past, and by definition a miracle is the least probable occurrence. And so, by the very nature of the canons of historical research, we can’t claim historically that a miracle probably happened. By definition, it probably didn’t. And history can only establish what probably did.
Craig was expecting this statement apparently and had alluded to it in his opening statement. In his first rebuttal he replied:
Dr. Ehrman maintains that we can never say that a miracle like the resurrection probably occurred because miracles by their very nature are inherently improbable. Now despite what he said, this argument is nothing new. It was already propounded in the 18th century by David Hume in his essay “Of Miracles.” Dr. Ehrman’s argument is just a warmed-over version of Hume’s reasoning.
The first thing I want to say is as far as I know this is not Hume's argument. Hume didn't argue that miracles were unknowable. Here is what Hume said:
No testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavors to establish... When anyone tells me that he saw a dead man restored to life, I immediately consider... whether it be more probable that this person should either deceive or be deceived, or that the fact which he relates should really have happened. I weigh the one miracle against the other... and always reject the greater miracle. If the falsehood of his testimony would be more miraculous than the event which he relates-then, and not until then, can he pretend to command my belief or opinion.[Hume, "of Miracles"]
According to Hume a miracle is known if its falsehood is more miraculous than the fact that it endeavors to establish. Miracles are knowable.
This statement is a great expression of how a miraculous claim would apply to Bayes' Theorem. Bayes' Theorem is a mathematical expression that can be used to help a person understand whether or not they ought to believe a certain proposition. It produces a number between 0 and 1 representing the probability that a given proposition ought to be believed based upon your own subjective assessments.
It is explained by my brother here, and applied to the resurrection by my brother here, here, and here. Two important terms in the expression are terms which represent the initial probability of a claim and also a term which represents how well alternative explanations fit the evidence.
What Hume is saying basically is that a miracle carries a strong presumption against it. Extremely strong. So to affirm a miracle it would have to be the case that alternative explanations would have to fit the data EXTREMELY poorly. Not just poorly, but EXTREMELY poorly. In other words, the "initial probability" term in Bayes' Theorem is extremely low. To affirm a miracle the term that represents how well the alternative explanations fit the data must also be extremely low. It would have to be about as low as the initial probability term.
So back to the debate between Craig and Ehrman, Craig rolled out Bayes' Theorem and made this point, and explained it all under the heading "Ehrman's Egregious Error". It was a bit of a stunt, and it probably played well to the audience. Bayes' Theorem looks like complicated math, so likely few knew what was being said. Ehrman wasn't prepared to respond to it because he probably didn't even really know what was being said. Craig made the point that if the term that represents how well the alternative explanations fit the data were low enough, then you could conclude that a miracle had occurred.
Technically I think Craig is right. In theory it is possible to know a miracle, and Bayes' Theorem shows this. But for practical purposes Ehrman is right. To say that we can't know a miracle by definition is going too far. But as far as the historian is concerned in the real world you can't know a miracle. You don't control the conditions by which you attain knowledge well enough to have confidence in a miraculous claim. The alternative explanation term in Bayes' Theorem may be low, but it is never low enough to conclude that a miracle occurred. The expression "extraordinary claims require extraordinary evidence" is another way of stating Bayes' Theorem, and as applied to a miracle you recognize that the evidence for claims of the miraculous are never good enough.
So this is where Craig's kettle logic once again manifests itself. Bayes' Thoerem does show that you can't go so far as to say that it is logically impossible to know a miracle. But Bayes' Theorem also makes it clear that extraordinary claims require extraordinary evidence. Craig doesn't like this conclusion because he knows it is devastating to his position.
So during the question and answer period Craig was confronted with this issue. He was asked to actually use Bayes' Theorem, which is the equation he used to rebut Ehrman, and apply it to the resurrection. Now, this is not a path Craig wants to travel on. He is going to want to avoid inserting real numbers because in conceding the usefulness of Bayes' Theorem he would be forced to admit that extraordinary claims require extraordinary evidence. But if Bayes' Theorem is valid in rebuttal to Ehrman, how can it not be valid for Craig? Here is how Craig goes about avoiding the issue:
Question for Dr. Craig: I am very interested in the probability equation you gave. To say it’s probable that Jesus was resurrected, you must put numbers into that equation and get a answer greater than 0.5. I am very interested in what the actual number was and the margin of error for it. And how were the numbers for it determined?
Answer from Dr. Craig: Thank you for that question! Richard Swinburne, who’s a professor at Oxford University, has written a book on incarnation and resurrection in which he actually uses the probability calculus that I have just given. He comes up with an estimate of 0.97 for the resurrection of Jesus in terms of its probability, and you can look at his book for that. I myself don’t use the probability calculus in arguing for resurrection of Jesus. The reason I brought it up is because of the response to the Humean sort of argument that Dr. Ehrman was offering, which I think is completely misconceived because he tries to say that the resurrection is improbable simply because of the improbability of the resurrection on the background information alone. In fact, I think that that probability is inscrutable, given that we’re dealing with a free agent. I don’t see how we can assess or assign specific numbers for those.
When Bayes' Theorem can be used to expose another person's error, then it's a great tool. But in the case where it would also expose Craig's error, suddenly these things are "inscrutable" and Bayes' Theorem isn't useful. But if it is impossible to know what numbers should be involved, then how can we know that Ehrman is wrong when he says miracles are unknowable? If these things are impossible to assess, then the term which Craig says could in theory be low enough to allow knowledge of a miracle can never be known to be low enough. Craig wants to have his cake and eat it too.