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[THINKING ABOUT SCIENCE M A S S IMO P IGL I U C CI Massimo Pigliucci is professor of philosophy at the City University of New York–Lehman College, a fellow of the American Association for the Advance ment of Science, and author of Nonsense on Stilts: How to Tell Sci- ence from Bunk. His essays can be found at www.rationallyspeaking.org.

On Miracles—Again

rguably, one of the most oft- repeated mantras in the skeptic A community is “Extraordinary claims require extraordinary evidence,” the modern rendition of David Hume’s idea that “a wise man proportions his be- lief to the evidence.” Hume wrote about adjusting belief according to the avail- able evidence in his famous essay “Of Miracles,” published in 1748 as part of his Enquiry Concerning Human Under- standing. I discussed this topic in this col- umn back in 2005 (SI’s March/April issue, 14–15), but because Hume’s dic- tum is a crucial component of modern skepticism, and also because the three hundredth anniversary of the famous philosopher’s birthday has just been cel- ebrated throughout Europe, it is perhaps worth taking another look at what the principle entails and why we still think it is worth our attention today. Hume’s analysis was based on his def- inition of miracle, a definition that actu- ally applies to many areas of inquiry in skepticism and can easily be extended to occurrences that, while not strictly mirac- ulous, are nonetheless extraordinary enough to fall under Hume’s analysis. For the Scottish philosopher, “a miracle is a violation of the laws of nature; and as a firm and unalterable experience has es- tablished these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from expe- rience can possibly be imagined.” David Hume

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This passage has occasioned much experience. But obviously we cannot What about the probabilities to be misunderstanding. (Two good refer- leave things there; otherwise we would attached to the testimony of an unusual ences for those interested in the philo- never accept the discovery of any new or miraculous event? Hume tells us that sophical controversy and modern inter- phenomenon on the simple basis that we “a general maxim worthy of our atten- pretations of Hume’s reasoning are hadn’t encountered it before. tion [is] that no testimony is sufficient Jordan Howard Sobel’s “On the Evi- At this point Hume differentiates to establish a miracle, unless the testi- dence of Testimony for Miracles” and truly extraordinary events from simply mony be of such a kind, that its false- David Owen’s “Hume versus Price on rare occurrences: “It is no miracle that a hood would be more miraculous than Miracles and Prior Probabilities,” both man, seemingly in good health, should the fact which it endeavors to establish.” of which appeared in the April 1987 die on a sudden: because such a kind of Again, we see echoes of Bayesianism, Philosophical Quarterly.) In particular, death, though more unusual than any even though scholars are fairly certain disagreement often focuses on the word other, has yet been frequently observed that Hume did not know of Reverend proof, which if interpreted in contem- to happen. But it is a miracle that a dead Bayes’s work (despite the fact that Bayes died in 1761 and his seminal essay was published posthumously in 1763, when Hume was alive and well). It isn’t impossible to have sufficient We are now talking about likelihoods: the probability that the testimony is evidence to believe in miracles correct assuming that the event actually occurred. According to Bayes’s theorem, (or paranormal phenomena)—it just the priors multiplied by the likelihood are proportional to the posteriors (the takes an extraordinary amount of it for probability that the event occurred given the evidence) like this: P(M|T) ~ that belief to become reasonable. P(T|M) * P(M). This means that the probability of a miracle oc curring given the testimony is proportional to the probability of the testimony given the miracle occurred times the prior prob- porary terms seems to imply absolute man should come to life; because that ability of the miracle. If one standard- certainty. But it is easy to show that has never been observed in any age or izes these quantities, one may substitute Hume was not endorsing certainty in country.” For readers inclined to see the equal sign for the proportionality. any matters, as is clear from the context things in a Bayesian framework—one of To simplify: uB ~ nE * pB (updated Be- of all of his writings, and that the word the most powerful modern approaches lief is proportional to the product of proof was used by philosophers of the in both probability theory and episte- new Evidence and prior Belief). time to indicate what we today would mology—this can be translated in the So Hume’s idea can be recast in these call the degree of probability or likeli- following fashion. The prior probability terms: if the priors are already high (as hood of a proposition. Indeed, Hume of, say, a sudden heart attack is non-neg- in the case of a man suddenly dying of a explicitly says that “in our reasoning ligible depending on the frequency with heart attack), the testimony need not be concerning matters of fact, there are all which such events take place in the gen- particularly overwhelming (moderate imaginable degrees of assurance, from eral population. In contrast, the prior likelihoods will do) for us to believe that the highest certainty to the lowest probability attached to a violation of the the event occurred (medium to high species of evidence.” laws of nature (or even to a paranormal posteriors). But if the priors are very low So, let’s consider the report of a mir- phenomenon) has to be very low simply (a miracle occurring), then it takes over- acle (or a UFO or a ghost). Hume be - because we have never reliably observed whelmingly strong evidence (very high gins by pitting two types of experience such an event, nor do we have any good likelihoods) to yield an even modest against each other: the fact that we al- reason to believe that it can occur (how- posterior. In other words, it isn’t impos- most never observe miracles (or UFOs ever, again, its probability cannot be ex- sible to have sufficient evidence to be- or ghosts) against a new report of just actly zero; otherwise we would be ab- lieve in miracles (or paranormal phe- one such experience. An initial analysis solutely certain of the impossibility of nomena)—it just takes an extraordinary gives us good reason to be skeptical of the event, and no amount of new infor- amount of it for that belief to become the extraordinary claim, because the un- mation could possibly change our be- reasonable. Exactly how extraordinary extraordinary explanation starts out with lief—the very definition of a closed- can now be calculated by means of a very large degree of support from our minded position). Bayes’s theorem.

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