Because of how probability works, you shouldn’t believe someone who tells you she has witnessed a miracle.
Should you believe someone who tells you she has witnessed a miracle? This is a question David Hume—-the philosopher known as “the Great infidel” during his time–answers with a resounding “No”.
We usually think of miracles as events like walking on water or turning water into wine. As these examples suggest, Hume is concerned with religious miracles and not just any highly improbable event. Hume defines miracles as a violation of a law of nature or what we think of as laws of physics.
But this is not quite right either. Hume defines laws of natures as a kind of regularity in our experiences without exceptions. This means “the sun will rise tomorrow” is a law of nature because it has always happened in the past without exception. It would be a stretch to say this is a law of physics.
Alan Hájek (2008) defends Hume’s argument against a common type of criticism and criticizes it in his own way.1
Part of Hume’s argument depends on his so-called balancing principle: “The testimony should be believed if, and only if, the falsehood of the testimony is less probable than the event attested to” (Hájek, 94).
To see how this works, consider Hume’s example of hearing from someone who claims he saw a dead person come back to life. By the balancing principle, we should compare the probability of this person’s testimony being false and the probability of a dead person coming back to life. Whatever we think the probabilities are, Hume thinks we should assign greater probability to the person’s testimony being false. It is more likely the person is deceived or delusional. This means we should not believe that a dead person has come back to life.
Hume’s argument goes that we should never believe someone who claims to have witnessed a miracle because by the balancing principle the probabilities will never work out so that we should believe the testimony.
The main objection to the balancing principle is that if we accept the balancing principle then we should reject people who report to us historical events or improbable events like winning the lottery.
For example, if my local newspaper reports that Alice has won the lottery then by the balancing principle I should compare the probabilities of the newspaper’s report being false and Alice winning the lottery. Alice’s chances of winning the lottery are extremely small compared to the probability of the newspaper’s report being wrong. This means that we should not believe the newspaper’s report because the probability of the newspaper falsely reporting the winner of the lottery is larger than the probability of Alice winning the lottery.
We can imagine similar examples of testimony of highly improbable events and come out with the conclusion that if we use the balancing principle we cannot believe such testimony. But this is absurd. We believe what historians tell us and we believe newspapers when they tell us who won the lottery. It can’t be the case that we were always wrong to believe so. Thus, we should reject the balancing principle which got us into this mess.
Hájek thinks we have failed to notice something in these sorts of examples. What we have missed is that the probability of the event attested to actually changes after we receive a report. We are right to think that, for example, Alice’s chances of winning the lottery are miniscule. But after we read the newspaper’s report that Alice won the lottery, we should update that probability to be much bigger. Why so? Because we think the newspaper is reliable, we should assign high probability to the newspaper’s report being If the probability of the newspaper’s report being false is $10^{-3}$, then the probability of the newspaper’s report being true or the probability that Alice won the lottery is $1 - 10^{-3}$. Clearly, $10^{-3} < 1 - 10^{-3}$. true. This means that the probability of the newspaper’s report being false is now smaller than the probability of Alice winning the lottery (post-report) so we should believe the newspaper.
Another important part of Hume’s argument that Hájek points out is the notion of analogical probability or this new sense of probability that Hume has. The reason Hume needs this other sense of probability is that miracles are not simply improbable as we might understand winning the lottery is.
Miracles are improbable in the sense that they are infrequent, but they are also further improbable in the sense that they are disanalogous to anything from our past experiences. My winning the lottery is highly improbable, but it is not disanalogous to anything from my past experiences. I might have experienced winning with a similar sort of drawing or I’ve almost surely seen someone else winning a lottery. In other words, my winning the lottery is an event that resembles events from my past experience.
I do wonder though if watching zombie movies or reading the bible counts. But with events like a dead person coming back to life, these events don’t resemble any events from my past experience. This means miracles are improbable in the analogical probability sense as opposed to simply improbable events like winning the lottery.
Hume’s notion of analogical probability helps to determine the probabilities to use with the balancing principle. Only miracles are highly improbable unlike events like winning the lottery. This also helps Hume avoid the main objection to the balancing principle we covered above.
But Hájek points out that something goes terribly wrong if we use Hume’s notion of analogical probability. Just as we would reject testimony of miracles, we would also have to reject testimony of certain scientific findings.
Consider that certain astronomical and quantum mechanical phenomena do not resemble anything from our past experiences. This means that they are not only simply improbable but also improbable in the sense of analogical probability. Then, testimony of these scientific phenomena is treated the same way as testimony of miracles are: rejection.
Hájek thinks this is an absurd conclusion so we should reject Hume’s use of analogical probability. This doesn’t mean Hume’s argument for rejecting the testimony of miracles fails but just that we shouldn’t take Hume on his word.
Hájek, Alan. “Are Miracles Chimerical?” In Oxford Studies in Philosophy of Religion. Vol. 1. Edited by Kvanvig, Jonathan L. Oxford; New York: Oxford Univ. Press, 2008. ↩