Having defined what a miracle is (see here) and having established the relationship between evidence and probability (here), Hume is now ready to finally unveil his novel argument against miracles. To the point, for Hume “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 endeavours to establish …” (Hume, Of Miracles, Para. 13). In plain English, what Hume is saying here is that even when we have direct evidence of a miracle, such as eyewitness testimony, our inquiry is not over. We still have to weigh the evidence. Specifically, we must consider not only the probability that the evidence is reliable or true but also the probability that it is defective or false, or in the immortal words of David Hume himself:

“When any one 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. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle.” (Hume, Of Miracles, Para. 13, emphasis added)

Hume thus proposes a simple two-part probabilistic test for evaluating reports of miracles. The first part works as follows: if someone, for example, tells you X — that they saw a UFO or were abducted by aliens — you need to consider two separate probabilities: A and B, where A is the probability that X, the remarkable or unusual event in question, took place — i.e., how likely is it, given your own experience and common sense, that the UFO sighting or alien abduction really occurred? — and where B is the probability that the report is either mistaken or fraudulent or otherwise defective — or in Hume’s words, the probability “that its falsehood would be more miraculous, than the fact, which it endeavours to establish” (ibid.).

Next, after assigning probability values to both of these logical possibilities (A and B), the second and last part of Hume’s test is to compare both probabilities. According to Hume’s probabilistic logic, you should prefer the possibility whose probability value is greater. (Or, put another way, only if the probability of B is somehow smaller than that of A should you believe in X.)

This post concludes my review of Part 1 of Hume’s essay “Of Miracles” (paragraphs 1 to 13). Starting next week, I will present a “Bayesian” critique of Hume’s solution to the problem of miracles and then turn my attention to Part 2 of his essay (paragraphs 14 to 41). In the meantime, I would like you to think about the following question: is there any way a report of a miracle or other remarkable event could ever pass Hume’s probabilistic test?