A recent responder to my postings on Hume’s argument against miracles claims that Hume’s argument in Section X of An Inquiry Concerning Human Understanding is “demonstrably fallacious.” After a bit of coaxing, he has produced the following alleged demonstration, taken from William Lane Craig’s debate with Bart Ehrman:

”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.” (Quoted from the correspondent “K-Dog”).

Does Craig demonstrate that Hume’s argument is fallacious? A couple of things to note: First, Hume does not employ Bayes’ Theorem in the presentation of his argument; it is expressed informally, and the Bayesian framework is imposed by later interpreters. Second, Hume does not directly address the resurrection of Jesus of Nazareth in “Of Miracles,” though his instance of an imagined report of the resurrection of Elizabeth I may be a coy allusion. Hume’s argument is about miracle claims in general and not a specific critique of the resurrection apologetic of the sort promoted by Craig.

Craig’s argument is that the likelihood of the evidence for the resurrection given the naturalistic alternatives to resurrection (i.e., given that the resurrection did not occur and given background information) might be so low as to counterbalance an extremely low probability of the resurrection given only background. In other words, p(E/~R & B) might be so very low, that even a very low p(R/B) might be overcome and the resultant p(R/E & B) might wind up very high (given, as seems reasonable, that p(E/ B & R) is not too low). Craig’s charge is that Hume simply ignores this possibility. This, presumably, is the demonstration of the claimed fallacy.
Does Hume ignore such a possibility? Even if Hume does, do we have to? That is, might we not adopt a neo-Humean argument against miracles that does consider what he failed to note?

Again, Hume is not specifically addressing claims about the resurrection, so to twit him for not taking into consideration specific evidence for the resurrection is obviously unfair. Well, then, does Hume consider, in general terms, the possibility that testimonial evidence for a miracle might exist even if the miracle did not occur? If we express it in formal terms, does Hume consider what values p(E/~M & B) might take, where E is the evidence for a miracle claim, M is that claim, and B is background? Well, he surely seems to. To take one succinct passage:

“When anyone tells me that he saw a dead man restored to life, I immediately consider with myself, 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 (p. 149; from the edition by Antony Flew, Open Court, 1988).”

I think that a natural way to interpret this passage is that Hume is recommending that we consider that the testimony for a miracle might well exist even if the miracle did not occur, i.e., that p(E/~M & B) might not be low, because the testifier was either a deceiver or a victim of deception. How might we get miracle reports even when the reported miracles did not occur? The reporter might deceive or be deceived, and if we consider either probability not to be too low, then we will consider p(E/ ~M & B) not to be too low in that case.

In general, as I noted in an earlier post, Hume considers that the “knavery and folly” of humans is such that miracle reports are often likely even where no miracle has occurred. Further, if this is Hume’s claim, it is obviously right, as, indeed, everyone who is not totally credulous will admit. No rational person believes more than a small fraction of the myriad miracle reports that infest historical records and tales. Even some evangelical scholars now doubt some biblical miracle reports (one, Michael Licona, was recently fired for doing so). Clearly, then, miracle reports do frequently arise when no miracle has occurred.

Suppose, though, for the sake of argument, that Hume did not devote enough attention to the possibility that the evidence for a miracle might be very low given that the miracle did not occur. Do we modern-day neo-Humeans have to make that same mistake? No. We can simply revise Hume’s argument to take p(E/~M & B) into due consideration. And we do. Specifically, we can and do address the likelihood that there would be the given testimonial evidence for the resurrection of Jesus even if Jesus did not rise. We can and do judge p(E/~R & B) to not be terribly low—certainly not nearly low enough to counterbalance the very low background probability, p(R/B), that we rationally assign.

So, the above claim that Hume’s miracle argument commits a demonstrable fallacy amounts to nothing. The argument demonstrates only the perennial tendency of Hume’s critics to attribute to him a weaker argument than the one he makes.