When I first read Bob Drury’s article, “Bayesian Reasoning in Religious Studies”, I remarked to him tongue-in-cheek that Bayesian reasoning proves the reports of Powerball jackpot winners to be inauthentic because the probability of anyone drawing the winning number combination is nearly zero—3.4223 × 10-9, to be precise. Drury’s essay shows how Dr. Rafael Lataster’s “Bayesian reasoning” is a misuse of mathematics in Biblical criticism. My concern here is how Lataster’s use of probability reflects a general misunderstanding of what probability really represents, especially as it appears in arguments between theists and antitheists.
No Probability without Possibility
Of course, we know people really have won Powerball jackpots, that two and three people (or groups of people) at a time have picked the same winning numbers. In fact, the more tickets are sold, the more likely it is that more than one ticket will have the winning combination. The probability of any two bullets fired in opposite directions meeting nose-to-nose is absurdly low, yet people have found Minié balls fused together just so on a few Civil War battlefields, especially at the “Devil’s Den” at Gettysburg. If something happened, the odds against it happening are irrelevant save as commentary.
In statistics, probability (P) is a value expressed as a decimal between 0 (impossible) and 1 (inevitable). Only values of 0 and 1 can be said to be certain; between those two points, uncertainty not only exists but reigns. Oh, you could pick arbitrary values—say, below .005 and above .995—and call the areas between those values and the endpoints ranges of virtual or moral certainty. But the fact remains: So long as the probability is neither 0 nor 1, a door has been left open to the unexpected. Just ask Hillary Clinton.
There’s no denying the prudence of using extremely low P-values to make everyday, commonsense decisions. It’s theoretically possible you might be struck by a meteor as you walk out to your office parking lot to get in your car, but do you need to live in fear of it? It’s fun to play the lottery, but I wouldn’t base my retirement plan on winning. The thing to remember, nevertheless, is that you can’t even begin to calculate how improbable a thing or event is until you concede that it is possible. There is neither probability nor improbability without possibility.
Chance Not a “God of the Gaps”
Numbers are preter-real; that is, they’re real only so far as they inhere in real, countable beings. Probabilities are pure abstractions meant to illustrate, not dictate, certain operations in the real world. As such, even the smallest of knowable probabilities presents no real barrier or hurdle to overcome. Atheists know this and are wont to argue that sufficient time conquers even the greatest of odds. Biologist Richard Dawkins has even suggested that, since atoms aren’t static, it isn’t impossible for their natural motions to account for a statue of the Blessed Virgin waving at someone (The Blind Watchmaker, 159).
But because probabilities are descriptive rather than prescriptive, chance “causes” nothing. Chance is merely the intersection of two or more independent lines of causality; it isn’t a chaotic force that makes inexplicable things happen. The mere introduction of a random element doesn’t of itself make possible the impossible. Chance, therefore, can’t properly function as an atheist “god of the gaps.” Writes physicist Anthony Rizzi:
… [C]hance is the absence of an explanation. Proposing chance as an explanation is the refusal to give an explanation. We’ve already seen that statistics are used [in science] when we don’t know or want to ignore some aspect of reality. In general, it’s the admission that we don’t know something. When I say “That happened by chance,” I am really saying I don’t know why that happened. (The Science Before Science, 256)
On the other hand, and more to the point, when discussing miracles and divine action, to insist that the probability of X happening is “infinitely small” is too often a restatement of the drearily obvious. If virgins gave birth as often as people win Powerball jackpots, we’d find nothing extraordinary about the Incarnation. There would be nothing remarkable about Herod Antipas being struck down by an angel if it were a regular occurrence in the Roman Empire. Christians already know such things aren’t predictable features of the universe. Their improbability is irrelevant to their factuality.
Herod Antipas and Flavius Josephus
Now, we must look at the prior probability in Lataster’s Bayesian reasoning: “The inherent probability of the theory [that Herod Antipas was struck down by an angel, cf. Acts 12:23] (without yet considering the available evidence, such as the reference in Acts), P(h|b), is infinitely small.”
Flavius Josephus’ Antiquities 19.8.2 has an account of Herod Antipas’ death that parallels Acts 12:20-24, except instead of mentioning an angel Josephus speaks of an owl which, according to Antiquities 18.6.7, was foretold to Herod would signal his impending death. However, as the first pains struck his belly, Herod rebuked the crowd: “I, whom you call a god, am commanded presently to depart this life; while Providence thus reproves the lying words you just now said to me; and I, who was by you called immortal, am immediately to be hurried away by death.” He died five days later.
So does Josephus’ account prove the angel a “fabrication”? Certainly, we believe God can work and has worked through His creatures, so nothing we know about angels makes it inherently improbable that God would use them as agents of His justice. On the other hand, it’s just as likely that St. Luke or his source used “an angel” much as we would use “the hand of God;” that is, as a metaphor for God’s direct action. And Josephus’ account indirectly imputes a divine vector to Herod’s final illness. At worst (from a skeptic’s view), it can only suggest an unnecessary correlation; we need not charge the evangelist with intent to deceive.
Ironically, the passage in Acts reads that Herod died “eaten by worms.” This was hardly unheard-of in the Mediterranean world. Even modern, medically advanced countries such as the U.S. record occasional deaths by parasitic infections, including worms. Jewish kashruth includes stringent meat-preparation regulations, but Josephus argues that Herod’s diet wasn’t consistently kosher. The symptoms he records present much like trichinosis, though Herod’s death was relatively fast. Whether it was set in motion by an angel or by treif meat, that Herod died of a natural cause is beyond dispute. Lataster is solving the wrong problem.
Probability and Fig-Leaf Agnosticism
The real question, then, is not whether Herod’s death was unnatural but whether it was set in motion by a supernatural agent. The number of “act of God” deaths outside of Scripture, however, is unknown and unguessable. Because statistics-gathering is a modern passion, the best we have for the time frame of Acts are estimates based on what few records we do have. Consequently, Lataster has no unimpeachable extra-biblical data from which he can draw his prior probability; he can only pull it out of a hat.
Lataster knows this, so he asserts his prior probability “without considering the available evidence.” This is a methodological no-no—the available evidence is the only ground from which a valid probability can be inferred. If only one person out of the estimated 100 billion humans who have ever died did so through supernatural agency, the probability may be 10-11, but we don’t know before considering the evidence that only one has died so. Lataster tries to overcome this ignorance by calling the probability inherent; that is, by saying it exists “as a permanent, essential, or characteristic attribute.” But an attribute of what?
Lataster’s prior is typical of what I call fig-leaf agnosticism. There are people who, for all practical purposes, are firm materialists yet publicly profess to be agnostics because “after all, I could be wrong, y’know.” A pure materialism would set the probability at zero—not nearly zero; not infinitely small. An honest agnosticism would assert that there is no reliable statistical basis for an estimate of probability. Lataster’s “infinitely small probability” is a pro forma concession to the (theoretical) possibility that angels exist while trying to keep his general conclusion—that reports of angelic agency are false—outside the reach of reasonable doubt.
But it also reveals his “Bayesian reasoning” to be so much question-begging dressed in misused math. His argument, stripped to its essentials, is that we already know (almost) all reports of death by divine command are false, so St. Luke’s report must be false as well. But we can’t know (almost) all reports to be false until we know each individual report (save one or two) to be false. Lataster is assuming as an implicit premise what he purports to demonstrate in his conclusion. And having admitted that at least one may be true, he cannot prevent others from being true without solid counterevidence. The argument fails.
Ultimately, because probability is uncertainty quantified, it’s too equivocal a basis for either theist or antitheist arguments: it can never firmly close the door on the opposition. Both sides ought to understand that improbable and impossible aren’t interchangeable concepts: the former tentatively, even carelessly admits while the latter definitely excludes. And for all their practicality, as mere numbers probabilities can neither dictate the future nor contradict the past. If the Associated Press reports that a man from the tiny village of Ismay, Montana won the Powerball jackpot, no manipulation of odds or census data will give us sufficient reason to call the report false.
We know Herod’s death was natural. Whether it was directly induced by God (acting through an angel) or by infected meat eaten a couple days before (in which case it still might qualify as temporal punishment), your mileage may vary according to your metaphysics. But if you’re bound and determined to disbelieve all accounts of divine intervention, you shouldn’t look to probability theory to provide a shield against them. If anything, probability theory proves only that our knowledge and its certainty have limits. It also shows, I believe, that God has a sense of humor.