I was privileged to be able to sit in on some of a private virtual Q&A with Christian philosopher Daniel Bonevac regarding his peer-reviewed paper “The Argument from Miracles,” Oxford Studies in Philosophy of Religion 3 (2011), pp. 16-40. Many significant philosophers (atheist and Christian) were in attendance. Alas I missed most of it, and couldn’t participate beyond listening, owing to being on the road the whole time on family business. I hadn’t heard of his work before this, but was able to read his paper ahead of the event and submit questions in advance for the moderator to ask on my behalf (they got to one).

This whole affair interests me because Bonevac’s approach is enthusiastically Bayesian, and he sounds like one of those rarest of persons in my experience: a sincere Christian apologist. He genuinely believes what he says and actually does want to be corrected if wrong. Sure, he may be delusionally immune to being corrected, as is the way of all faith-based minds, but that’s a different problem than what we usually have to suffer through (which is smarmy disingenuous game-playing and rhetoric sprinkled with various shades of lying). This showed not only in the live talk, but it shows in his paper as well.

It’s hard to pin down exactly what I mean. But to take a stab: he lacks arrogance; his treatment of Bayesian argumentation is actually correct, not gamed or distorted to suit an agenda; and his false statements of fact appear genuinely ignorant and not deliberately crafted. And in result, half of what he says should change in field-wide conclusions is—shock!—actually correct. The rest is just old 1980s apologetics, fed him by his in-group, piped in as premises. So, very unusually for me, I have here a paper that is merely wrong, owing to a variety of technical errors Bonevac either isn’t aware of, or avoids admitting to himself via some stock slogans he’s conjured or bought into—much as we see flat-earthers and other sincere conspiracy theorists resort to when confronted with their own errors. And I’m starting to notice this more and more: after a lot of experience with both kinds of people—the grifters and liars on one side, and the genuinely delusional on the other—you can kind of tell.

Bonevac’s Thesis

Bonevac’s paper is worded “the argument from miracles” because his main aim is to try and revive what is really a dead approach in formal philosophy: that one can seriously argue from miracles to rationally justify a belief in God (outside of apologetics, philosophy has moved on). But I switched the word out in my own title because really what his paper does is (desperately) attempt across all of its pages to argue for miracles. And that’s the argument I will address here today: has Bonevac advanced a sound argument for miracles?

Because, in his paper, that one can then build from there an argument for God is almost an afterthought. It’s not really completed there; for example, Bonevac just assumes ‘if we prove Jesus rose from the dead (and maybe a bunch of other stuff amazing), we’ve proved God exists’, when formally, once you buy the premise, you still have to rule a lot else out first. Jesus could have been a graduate of a secret academy of wizards, and all the miracles sorcery, sans the existence of any gods—or someone in his entourage was, fooling even Jesus. Or he (or they) could have been using advanced tech in an orbiting spaceship to fool everyone. Or he might have been (unbeknownst to himself) a Mutant. The supernatural (apparent or real) does not require gods—as fantasy fiction endlessly demonstrates (there are no gods in the Harry Potter universe, for example, or in Forbidden Planet: two oddly specific examples I choose here for a reason; and everything depicted of Jesus is possible in both). To get from “miracles” to “Christianity” you need to adopt a rather elaborate conspiracy theory.

But it would be a mighty achievement even just to have proved the premise: that miracles really do happen, and Jesus’s resurrection was one of them. Of course authors arguing this never do this properly—Bonevac has conducted no study (much less a sound one) of global miracle claims across history and religions, to test his own methodological principles (can he establish any reports as true—and then distinguish true from false reports using only the testimony part?), and he’s never conducted any scientific examination of any accessible miracle so as to prove the phenomenon exists generally before trying to claim it existed historically (the real way this sort of thing is done).

But I do think in most cases that’s because these guys don’t know that’s how science works. There is a reason science moved from supernatural agency explanations to natural ones: that’s how the evidence always pans out. If you want to prove a general rule to the contrary, you’ve got to do at least the same work. If we got to hang out a few years at Hogwarts or with John Constantine, we’d get different results, and now would be teaching very different things about the cosmos in our universities. But that just isn’t the way it went. And that begs explanation. But since things haven’t gone the way Christians wanted, they all want to find some way to skip the queue and just prove themselves right without doing any of the real work (because doing the real work…never works).

The result is papers like this. Bonevac tries to get there by arguing two things, one of which is correct: (1) that philosophers have been misreading Hume’s argument on miracles, and have been adopting entirely incorrect assumptions (such as how to even define a miracle), and that a sound Bayesian approach could in fact establish the reality of miracles even from human testimony, in the right conditions; and (2) we have multiple independent witness testimony to the resurrection (and some other miracles) of Jesus, thus meeting ‘the right conditions’. You can probably guess which of those two arguments is correct, and which not. The first is a sound contribution to philosophy (alone making this paper of value to the field). The second is just a bunch of naive ball-dropping in the domain of historical and literary method.

The Correct Bit

Bonevac makes many dubious side-statements, mostly but not only in footnotes—like when he blames modern doubt of the supernatural on people like Sigmund Freud, rather than (far more plausibly) people like Harry Houdini, Joe Nickell, and James Randi. But I don’t want to become distracted by tangents. Just don’t blindly trust everything he says. Here I’ll focus on only the two parts of his argument I already mentioned: the bit he gets right; and the bit he gets wrong.

The bit he gets right concerns the semantics, ontology, and epistemology actually underlying the question of miracles—and his identifying a modern misreading of Hume. To that point first. “Hume does not argue that miracles are impossible,” Bonevac correctly notes, but “that it would never be rational to accept a miracle report, that is, a bit of testimony that a miracle had occurred,” because it’s always more likely, for example, that “the Apostles and the five hundred” brethren (whom Paul refers to as witnesses to the risen Jesus in 1 Corinthians 15) “were mistaken or lying than that anyone was actually raised from the dead” (p. 18). Bonevac agrees that “Hume shows that it would never be rational to accept a single miracle report in isolation, where the miracle in question involves a violation of natural law” (p. 19), which Hume only defined as regularities anyway, not inevitabilities.

But Hume did not address every condition. He was only speaking of his distrust in people: their honesty and accuracy is never miraculous, and yet only miraculously reliable testimony would warrant believing in a miraculous event. Extraordinary claims require extraordinary evidence. Bonevac concurs (unlike William Lane Craig). Hume didn’t address cases where you are seeing the miracle yourself (he might have had skeptical thoughts about that, too, but they’d be more complex), or when you have physical evidence corroborating the witnesses, for example (likewise). But we can reduce all those to the same essential problem: the evidence, whatever it is (your own eyewitness, physical evidence, or someone else’s report) must be more miraculous (meaning: more improbable unless true) than the event being related, before we can believe the event occurred. This is entirely correct. And Bonevac is right to chastise skeptics who say otherwise (and he quotes some to prove they do; I took on this same error myself once).

So all Bonevac really has to resolve is a single question: “Under what conditions is it rational to believe that events of the relevant kind have actually occurred?” (p. 25) Hume was incorrect, Bonevac avers, to believe testimony can never achieve the required conditions. And Bonevac is right, largely because Hume was not yet aware of Bayes’ Theorem (Thomas Bayes was busy inventing it at exactly the same time), but his essay On Miracles was getting very close to it. It just needs a slight tweak to get it there (and that is the actual thesis of John Earman’s book Hume’s Abject Failure: The Argument against Miracles—theists who don’t read that think he refuted Hume when in fact Earman fixes Hume).

It really has nothing to do with ontological assumptions (“miracles are impossible”); it has to do with epistemic realities. How probable is it? And how do we know that? Here Bonevac makes another correct move: he defines miracle not as a violation of the laws of nature, but as the effect of a supernatural agent. Because many such effects will not or need not violate natural laws (e.g. causally arranging natural coincidences to fulfill prophecy), and violations of natural laws need not be miracles (purely random deviations from natural laws are logically possible, yet no one would consider them miracles). Bonevac’s focus on the role of agency and its type is crucial to any sound Bayesian analysis of miracles, because the first step in Bayesian reasoning is correctly defining the hypotheses: first so you can correctly evaluate the prior probability—because only once you have fully described what actually it is you are claiming exists can you do that—and second so you can correctly deduce its expected effects to an estimable probability, and thus arrive at credible likelihoods. This bypasses the whole question of whether miracles “violate natural laws.” That’s besides the point. What you are really asking is whether a supernatural agent is acting in earthly affairs. Nothing else pertains.

Unfortunately, Bonevac never defines the supernatural (a flaw of the paper as a whole; for how I think one ought to do this, see my article Defining the Supernatural). Moreover, I think he probably should not have used that specific term, because in widest use it designates things that, actually, might be logically impossible (see The God Impossible). It would suffice to say, rather, “superhuman agent,” as in, the event could not likely have happened but for the intervention of a purposeful agent who also is more powerful than any otherwise-known agent. Then you don’t have to worry about defending “the supernatural.” God could be an alien superbeing, acting entirely in accord with natural laws. You can’t tell merely by his effects. Certainly to first century observers, a resurrection by a ghost’s magic looks identical to a resurrection by Klaatu’s medibay. So if you want to get from “there is a superhuman being” to “it is not a natural being” you have a lot more work cut out for you (see The Argument from Specified Complexity against Supernaturalism). And Bonevac’s argument for miracles only really trades on the first possibility (of a superhuman agent), not the second (of a supernatural agent). That he conflates them is an error, but it does not affect his argument; you can read the entire thing as only addressing superhuman agency, because really that’s all it actually does.

This brings us back to Hume’s point that the real issue is not whether miracles in this sense are ontologically possible, but whether they are epistemically credible. And that gets us back to the point Hume was making: that by the same means (our own observations and reliances on testimony) we also know that the known causes of error in miracle reports are more frequent, and thus more probable, than the phenomenon being reported. To Hume this seemed insurmountable. But Bonevac applies the arguments from multiple testimony and cumulative casing. The latter means, basically, a power evinced many different ways becomes more probable even when then used in a new but similar way—once you document Harry Potter successfully casting ten different spells, that he could cast a resurrection spell ceases to be as improbable as once was. But that reduces to the same general principle of multiple testimony: whether temporally or spatially, as witnesses accumulate to the existence of a superhuman agent, the probability that that agent exists (and what they can do) goes up.

That this compounding of testimony is extraordinarily powerful (and thus can actually achieve the required status of extraordinary evidence) was securely proved by Aviezer Tucker in “The Generation of Knowledge from Multiple Testimonies,” Social Epistemology 30.3 (2015). And indeed, were one able to interrogate Hume, he’d have to agree, because this is exactly how he says all knowledge—even of the regularities he calls laws of nature—is acquired. At some point, enough witnesses to fire-breathing dragons invading Europe constitutes adding “fire-breathing dragons” to the regularities of the world. Just like water becoming a white powder, or even turning to stone, when cold (an example Hume himself gave). That would be no weirder than fire-breathing dragons to someone who’d never seen it. But obviously sufficient testimony can establish it. So all one need figure out is—how much testimony, and of what kind, suffices to bring any claim into the orbit of “this is the sort of thing that happens in the world”?

Hence, Bonevac argues, “one encounter with a bush that burns but is not consumed might not support rational belief in supernatural agency, but a series of events beginning with that one might” (p. 20). Hang around with Harry Potter or John Constantine enough, and you will update your priors as to what really is a feature of the world. So, Bonevac argues, had we been witness to Moses’s prediction and then realization of all ten plagues upon Egypt in fast succession, we would be more than rationally justified in believing a superhuman agent existed. Though contrary to Bonevac’s undefended leaps of reasoning, we could not at that point say the agent was Yahweh and not, simply, Moses. Maybe Moses is a space alien or a mutant or a faerie or a wizard, and he is merely claiming Yahweh responsible, for humility’s sake or for its rhetorical or political advantages, or because he has to for the spells to work or to protect the innocent—or goals less admirable. Or maybe another superhuman agent tricked Moses into thinking that, an agent decidedly less significant than a god. Getting from “Moses really did that” to “Yahweh exists” requires more evidence than Bonevac discusses. But he is right that his method, used correctly, would get us to at least “a superhuman agency exists.”

The real problem for Bonevac is getting from “there is a book that says all this” to “people actually saw Moses do all that.” Which is where Bonevac’s thesis falls over (to that point we will turn next). Like most apologetics, it fails at the premises, not the logic. In the latter he’s right. “All the argument requires is that miracles be such that the best explanations for them invoke supernatural agency” (p. 21). But the trick is in the “such that.” For example, an analogy he makes is, “Suppose John reports that Mark hit a baseball 500 feet. Knowing that such an event is very unlikely, I refuse to believe it. And unfortunately there are no other witnesses I can ask. But I can see whether anyone has reported Mark doing something similar in the past, and wait to see whether there are reports of his doing it in the future” (p. 33). That would be one “such that,” but it fails to correspond to any case Bonevac wants to examine: he never met anyone who saw Jesus do anything, he can’t wait and see if Jesus will do more stuff to corroborate it, and he can’t consult any eyewitness report of him doing it before—only hearsay.

Bonevac’s analogy is also off by one move. Penn & Teller would explain to him there’s another step needed: you have to rule out other well-known causes. They can eat bullets fired from a gun; there are countless eyewitness reports of their having done it before; and Bonevac can go to Las Vegas and watch them do it practically any coming month. But does this mean they are actually catching bullets shot from guns, much less are therefore superhuman agents? Penn & Teller conclude all their shows by warning people the answer is no, so “don’t fall for anyone claiming they can really do this stuff.” If David Koresh told his followers they had to say he hit baseballs 500 feet all the time, and their salvation depended on their saying it, they’d say it. Many would even convince themselves to believe it. Can we therefore trust them? It would not matter a very great deal how many there were. Donald Trump has convinced millions of witnesses to believe they saw or heard things they didn’t. Hundreds claim to have seen the non-existent miracle at Fatima. That doesn’t raise the probability of a superhuman agent one tick.

To get the evidence to be improbable unless true, you need more than just “lots of people said it.” Think of how you would verify Penn & Teller were really catching bullets, and not just tricking you into believing it; and thus what you would need to do in order to verify someone was actually hitting balls 500 feet, and not just conning people into thinking they did, or manipulating them psychologically into believing they did. And there’s the rub. For indeed even elaborately implausible conspiracies to trick people are more frequent—and thus more probable—than superhuman agency. We know all the components of a conspiracy exist, even the required motives, no matter how rare; we know no such things about superhuman agents. So they start out lower in probability than even the absurdest of real things. And this is not a consequence of any assumption as to its impossibility; it is a consequence of the fact that such agents simply don’t show up when we look for them. We could have lived in the worlds of Potter or Constantine. We just don’t.

Finally, Bonevac does pause to extend his (and correct Hume’s) method to direct experience, remarking on whether “it would always be more rational to doubt the testimony of one’s [own] senses—to suspect illusion, hallucination, madness, confusion, dreaming, or some similar epistemic dysfunction—than to accept supernatural agency or the evidence that points to it” (p. 36). One would need to rule those other explanations out, as you know they do occur with some frequency, and indeed a higher frequency than miracles. And ruling them out means finding evidence that would be improbable on those hypotheses. And, contra Hume, that can in principle be done. But we can’t do that even in Paul’s case, much less the case of any other Apostles or witnesses, or even the Gospels. This is what Bonevac gets wrong.

In those cases it’s more probable the stories we find were invented precisely to persuade. That’s an issue I’ll get to. But Bonevac’s method is still correct in its logic: it cannot be that “no amount of evidence” would convince us we weren’t (say) hallucinating; obviously at some point we’d accumulate enough evidence that that hypothesis does more poorly to explain. At some point hanging out with Harry Potter or John Constantine you’d admit the probability of such a consistent and sustained hallucination is just too low to credit and you’d instead just revise your understanding of the contents of reality. Yes, you could yet be wrong, but the point is, that would be improbable on the information you have—and you can only warrant beliefs on the information you have. This is why all Cartesian Demon explanations of experience are never credible. Even the worst schizophrenics constantly come into conflict with reality, and must invent ever more elaborate excuses for that, rather than accepting those conflicts as proper Bayesian evidence of their condition rather than the truth of their delusions. And here even experiments you can perform, like seeing what happens on anti-psychotics, can seal the deal, confirming which evidence was a fiction all along, and which real.

The point is, Bonevac is right as to the methodology: there can always be enough evidence, even on testimony alone, to warrant believing anything coherent, no matter how fantastical by your current perspective; the question is only: “Is there?” And so far, the answer has simply been, “No.”

The Problem of the Priors

It didn’t have to be that way. If God existed and did stuff like this, we could be seeing it all the time. But he isn’t. So we don’t. This has consequences. Bonevac correctly realized we have to represent those consequences in the prior probability of whatever we are claiming. “Let’s estimate the probability of resurrection” as a general superhuman phenomenon “given the available evidence” at “1 in 10 billion,” or 10⁻¹⁰, while mentioning in a note that Timothy and Lydia McGrew set it much lower, at 10⁻⁴³ (p. 27). Their estimate is more accurate because he only calculates a quasi-Laplacean expectation of a resurrection after 10 billion people dying and staying dead, but that would only be the expectation if you did not know why resurrection was unlikely—if we didn’t know any of the limiting physics or biology. In fact we do know why resurrection is unlikely, not merely that it is infrequent; and the physical and biological facts entailing that are attested by thousands of witnesses. Bonevac does not have thousands of witnesses to the resurrection of Jesus. This is Hume’s point.

In truth, we would not need thousands of witnesses, because the theoretical entity in question would explain why those witnesses reported what they did; its action would not contradict them. If there are exceptions to a rule, then the probability of an exception being present is the governing probability, not the probability of the rule. So we just need enough witnesses to render their combined testimony less probable (unless they are reporting accurately) than the existence of the agent. But that is not the probability Bonevac calculated. It’s closer to the probability the McGrews calculated. Though I think it could be as high as 10⁻¹² if we abandoned all Bonevac’s specific theoretical requirements and asked, instead, whether, say, mere common sorcery effected the results, and not hyperpowered megagods.

For example, one can’t say (as Bonevac might) that God, just as a theoretical posit, chooses to hide all miracles, and that’s why we never document any in any reliable fashion; because that would contradict Bonevac’s entire thesis. If God is hiding miracles, then it is improbable that he would allow enough witnesses to the resurrection to believe it—the theory would be contradicting itself as to the intentions of its own proposed agent. You have to pick a lane. Either God does things like Bonevac wants (allows sufficient evidence to establish a miracle), or he doesn’t (in which case it’s unlikely he did so for Jesus, and therefore we should conclude that was all a con or an error in judgment and not a real event).

Rather, one has to propose a more convoluted motive for God (which starts to tank the prior probability of God, as the hypothesis then begins looking More Like a Conspiracy Theory). But apart from that, the mechanism at least resolves logical contradiction with prior (scientific) testimony: the existence of a superhuman agent allows doing things like reanimating bodies, even using the laws of physics of biology, or bypassing them through magic. It’s just that they didn’t do that in all the other cases witnessed. Usually God lets the program run; his interventions are few, so we should expect that relative frequency. Provided you can come up with a coherent motive for God to make his interventions so few, and even then the improbability of that gerrymandered motive reduces the prior. But still, once we accept that, “The laws of physics and biology entail people stay dead unless we add to the system Klaatu’s medibay and a motivated operator of it” is an entirely coherent statement, yet permits resurrection without violating any laws of physics or biology. Add magic, and even violating those laws becomes possible. One just has to account for when any relevant magic or mechanism is present or not.

So Bonevac is still correct as to the method: the prior probability of superhuman agents is never zero; and it is therefore always, however low, within some achievable probability to believe on human testimony (by Condorcet’s Jury Theorem, it’s just a question of stacking enough witnesses with any better-than-even trustworthiness). I give my own example in Proving History: the three-hour darkness over the Earth at Jesus’s death (pp. 41-45, 54-60). Now, as it happens (and this is often a fatal problem with case’s like Bonevac’s), no one who should have seen that and would have reported it, did. Which is astronomically improbable (pun intended). So in fact, we know that’s a made-up myth (which compounds Bonevac’s problem, as now we know for a fact that his sources are mythmongers, and thus not reliable reporters of events; I’ll get to that). But what if that hadn’t happened? What if instead we had multiple contemporaneous records made of that event in Rome, China, and Mesopotamia? What if we could confirm it’s extraordinarily unlikely those were retroactively forged after “the story” reached them?

At some point we would simply have to admit the sun went out (or was globally occluded) for three hours on the day recorded. We don’t have to agree as to its causes (no superhuman agent, or supernatural effect, is even required). But we’d have to agree it happened. It is simply not true that “no amount of records” would or should convince us of that. Hume was wrong on that one point, and Bonevac correct: it is possible, under certain conditions, to have enough testimony to meet any required bar. And the conditions required are those of extraordinary improbability: that all the astronomers of three independent civilizations would coordinate their testimony in error or a lie is simply not believably probable. It’s more likely the sun really did go out (or was blocked by some celestial object of far greater size than the moon). So there is some prior probability of that that can be beat. We just need to work out what it is. (In this case it would be closer to Bonevac’s prior, as infrequency of experience is the only evident obstacle to it happening, unlike resurrection.)

What Bonevac rightly infers (and Tucker formally proves) is that when you have witnesses with very low probabilities of coordination all agreeing in matters in ways that are very improbable by chance accident, the effect in combined probability is extremely powerful. It can overwhelm even a 10⁻⁴³ against in short order, because the improbabilities multiply. The only point at which Bonevac goes wrong is that he has no such witnesses, meeting no such conditions. The risen Jesus did not visit China so as to be documented by witnesses there. He did not attend the Roman Senate so as to get written up by several Senators in attendance in accounts we now get to read. We don’t even have a single eyewitness account at all, apart from Paul’s—and what Paul attests to is not what Bonevac claims. This is the second bit, where Bonevac goes wrong. So I’ll get to that later.

The present point to note is that setting the prior probability for the extremely bizarre and convolutedly-defined agent Bonevac wants to exist actually hurts his case. It will be astronomically lower than even the McGrews’ estimate. He’d be better off not being so implausibly ambitious. If you set the bar solely at “there is some kind of superhuman agent,” with no ambitious assumptions as to its motives or powers or properties beyond that, its prior probability will be orders of magnitude greater—far more in range of proving, as with the blotting out of the sun. This would then of course mean proving anything additional to that (like all the weirdo things any Christian creed requires) will require its own particular evidence, and sufficient evidence at that—merely proving Christian sages can do magic would not alone suffice. And Bonevac has only set out to get to step one: that one Christian sage could do magic. He doesn’t even succeed at step one; but only because of a failure in his premises, not his method. We could have proved Jesus rose from the dead—if we had the evidence that would require. We just don’t.

The Problem of the Likelihoods

Bayes’ Theorem entails the prior odds times the likelihood ratio equals the final odds. So once we settle on the most provable hypothesis (merely that a superhuman agent exists, and nothing else) we then have the priors (which we’ve resolved must be somewhere between 10⁻¹⁰ and 10⁻⁴³), leaving only the likelihoods. Bonevac proposes the probability that someone would report a miracle they saw if it was real is at least 99% (no disagreement here), and the probability that they would report a miracle that didn’t happen (and they were thus lying or mistaken) is 1% generally but 10% in the given case, because fanatics might be more inclined than just anyone to invent a false story of magical powers, whether honestly or not, and for Jesus we have no neutral observers, only fanatics (even Paul was a fanatic when he recorded in writing what he saw, influencing the honesty or accuracy of his reporting). Bonevac thus gets a likelihood ratio of approximately 10/1, meaning a witness is ten times more likely to have reported such a thing if it were real than if it were not.

This is not plausible, however. Bonevac has stumbled over a confusion: he is conflating two different hypotheses. His ratio is reasonable if we limit e, the evidence to be explained, to merely their report as-is, and not to the truth of it. But his hypothesis h is not “that’s what they saw” but “a superhuman agent did that.” And these are not the same thing. Yes, if all we are asking is “that’s what they saw,” and we have their own eyewitness record of what they saw, the general likelihood could be 10 to 1 they are telling the truth about that. I think that’s a bit high. I don’t think honesty or accuracy in human beings is quite that prevalent—even in general, but especially in communities well-documented to be very prone to lying or delusion. This isn’t some disinterested detail we are talking about here, but deep-seated, emotionally-motivated faith-claims. Those are the least reliable claims on Earth. But this doesn’t even matter. Because we aren’t asking whether someone saw something; we are asking whether a superhuman agent was required to produce what they saw.

UFO claims were brought up by experts in the discussion with Bonevac; I missed most of that, but it serves as an apt parallel. I wrote about this recently, in UFOs Are Not That Remarkable. There, we can fully grant that people saw (or, at least, remember seeing) everything they claim, in every detail they claim—and still it is not credible that what they saw was a spaceship, rather than a known optical or instrumental illusion (or defect of memory). This is the difference between establishing witnesses really saw what they claim, and establishing that it was what they believed it to be. Bonevac screws up here, at the point of likelihoods, by conflating the one with the other. And the rest of his argument proceeds on that error. So, again, his method is correct; it’s his premises that are wrong. This difference matters, because of the enormous difference that exists between what our only eyewitness says he saw, and what all the other sources Bonevac falsely represents as eyewitness sources claim they saw.

This gets back into “the bit he got wrong” so I’ll set that aside for my next section. For now, what you need to understand is the Bayesian methodology. The likelihood ratio that should go here is that pertaining to supernatural agency, not to merely whether witnesses saw what they claim. The probability that the hundreds of witnesses at Fatima lied or were mistaken as to what they saw is astronomically low; in fact it’s fully in accord with scientific expectation (we have a well-developed cognitive science of how the brain constructs perceptual models under comparable conditions). But the probability that they lied or were mistaken as to what it actually was is perfectly high, indeed near 100%. If there were a real miracle, the reports should be quite different (not matching scientific explainability), and nonbelievers should have reported seeing it too; that only believers saw it, and only saw what science expects their brains to erroneously see (or in some cases fib about), is more likely if the event wasn’t a miracle. Having hundreds of witnesses then actually has the opposite effect Bonevac wants: the more witnesses agree in the details of this event, the more unlikely it is to have been a miracle. Because their testimony only corroborates in confirming a nonmiraculous event occurred.

So Bonevac needs to distinguish seeing a thing, with the probability that that thing was caused by a superhuman agent. And this requires actually spelling out the contents of e, the “evidence,” in the equation (in his equation he designates e with “T,” for Testimony, but it’s still just e, evidence: the existence of the testimony). Because there are enormous discrepancies in his source material. What the Gospels report is not what Paul reports, and what we need to explain are the reports. What the probability is that the Gospels would report as they do if what they are reporting is true, vs. false, is not going to come out Bonevac’s way, because the Gospels are not eyewitness reports, and contain not even the quotation (much less named citation) of any eyewitness report. When we get to an actual eyewitness report (there is only one, Paul’s), it sounds quite different, and thus is likely to have quite a different explanation. Bonevac’s error in not distinguishing these data is reflected in his final equation which only considers the contrary possibility the testifier is lying; he fails to account for a third, and very common, possibility, that the testifier is mistaken. He also conflates Paul and the Gospels (an error that’s Apologetics 101: see Resurrection: Faith or Fact? ). To that we now turn.

The Incorrect Bit

After settling the method, Bonevac moves to import his premises. He’s right that “it might be rational to accept the testimony of several witnesses that a law of nature had been violated” (many a new law of nature violates some past law of nature, and we accept testimony to this all the time: it’s called science). But then he says “the central miracles of the Judeo-Christian tradition are attested by multiple witnesses” (p. 25), indeed “even the most private miracles, such as the Transfiguration, are witnessed by several disciples” (p. 26). This isn’t true. And that’s where Bonevac goes wrong. We do not have any testimony from any disciple, much less to this. The only witness to anything at all that we do have is a singular person, who wasn’t a disciple: Paul. And we don’t have access to him. We only have access to an edited collection of things he said whose reliability of transmission is not even that secure (certainly not enough to meet the high bar required for proving a supernatural agency). This is all very bad evidence; not “extraordinary” evidence.

Hume imagined his argument applied a fortiori even to having the actual testimonies of witnesses. But he was aware of the difference between witness testimony and hearsay, even if he uses both kinds as examples. Bonevac fully conflates them. In actual fact, with regard to any actual facts that could be accounted evidence for the real (rather than imagined or pretended) resurrection of Jesus, we do indeed have (if we are loose with the meaning of “have”) only one eyewitness testimony (Paul’s), not several. The Gospels are not written by witnesses and their authors don’t even claim to have met any. That’s hearsay at best, fabrication at worst. Even Paul tells us very little—but importantly enough (as I’ll point out in a moment). Everything else we have is not just hearsay, but double hearsay, as we cannot establish any author even heard anything they wrote from a witness, rather than someone conveying a tradition passed down from them. In fact, it’s anonymous hearsay (if not outright fabrication: cf. Robyn Faith Walsh and the Gospels as Literature and Mark’s Use of Paul’s Epistles). Hearsay is not the same thing as testimony. And yet even testimony by itself is weak as evidence to anything.

In courts of law, direct testimony is not even admitted that can’t be cross-examined—as only if it can be is it deemed possible to believe beyond a reasonable doubt. The Gospels (and even Paul’s own testament) would never be allowed as that kind of evidence in court—and that’s merely to prove the mundane fact of a crime, not an extraordinary fact of a superhuman being’s activity in the world. That’s how weak this is as evidence. Hearsay is even worse. In law, hearsay without provenance is wholly disallowed. The Gospels are hearsay without provenance. No exception clears them as believable even to prove a mundane fact; they cannot therefore operate to prove an extraordinary one. The exceptions to the hearsay exclusion in U.S. law prove the point: in most cases, the hearsay is admitted only if a witness to the statement can be presented and cross examined. For example, the Present Sense Exception, whereby “a statement” is allowed “describing or explaining an event or condition, made while or immediately after the declarant perceived it” still requires an examinable witness to the declarant having said it. We don’t have this for Paul (there is no living person we can cross examine who heard him speak—at all, much less shortly after seeing Jesus). And so on down the line.

Even the Statements in Ancient Documents exception only holds for originals and legally authenticated duplications, not unprovenanced copies. We don’t have any original letter Paul wrote to anyone; and there has been no documented chain of custody to the copies we have. Moreover, the Ancient Documents rule only pertains to documents prepared in ignorance of the controversy they are being offered to adjudicate—and that does not apply here. Paul has every incentive to fib or dissemble or exaggerate over this very matter precisely to maintain his position of authority and influence over his congregations (or even just to convince himself of his own beliefs, as all delusional people do). This doesn’t fly in court if we aren’t allowed to question him—or his records weren’t validated by a provably trustworthy chain of custody, but even then nothing of what he recorded would count as admissible evidence under any of the other records exceptions.

Ironically, though, this means there is one respect in which Paul’s letters in extant form might be admissible as evidence in court (it would be a longshot but a lawyer could at least try a motion for it): as Statements Against Interest. One could argue that, even in a potentially doctored copy, anything in Paul’s Epistles that actually is evidence against the truth of his claims, and would not have been perceived by him (or anyone who would have had access to alter his text in any way not now detectable) to have been evidence for the truth of his claims, arguably might stand under an Ancient Documents exception, owing to the fact that the author and any potential editors would not have understood the need to invent or alter it to conform to any interest they had.

In Bayesian terms, the probability that such a statement would be there, given all we know about Paul’s and every custodian’s interests, unless it were an honest declaration of Paul’s, is extremely low. Low enough to meet the bar against admitting unreliable hearsay. No other statements of Paul’s could pass this bar, however. It’s all inadmissible hearsay. I doubt even this convoluted exception I just imagined would fly. But it’s the best we could ever grant Bonevac. Yet it gets the opposite conclusion to what he wants: the counter-biased elements of Paul’s testimony indicate a nonmiraculous event. Meanwhile the Gospels are right out. They don’t even preserve any statement of a declarant they were witness to, much less a statement against interest (see Proving History, index, “Criterion of Embarrassment”). Yes, Bonevac believes they do, but beliefs aren’t facts. There is no evidence that any sentence in any Gospel is a direct record of an eyewitness’s words as heard from them by the author. Even the Gospel of John, whose authors (plural) cite an eyewitness source, admit they did not know him or speak to him. They don’t even name him. But what they say is that they had something they think he wrote. That does not count as having transcribed something they heard him say in person (unlike, for example, an old newspaper quoting witness accounts of the causes of a local fire). By any rational standard, Ancient Documents fail to be admissible as evidence when they violate the double hearsay rule.

So if Bonevac couldn’t even get this evidence to be considered to prove even a mundane claim, he cannot regard it as so reliable as to prove an extraordinary one. But this error is not in his method. It’s in his premised facts. If we did have access to witnesses, we could get to his analysis. But we don’t. His claim that we have “multiple witnesses” is simply false. We only have one. And that one is so poorly recorded it wouldn’t even count as evidence of a crime, much less a god. In legal parlance, this testimony is so poor it inherently entails reasonable doubts. In Bayesian terms: this evidence is more likely to be fabricated, tampered with, deceitful, or erroneous than miraculous; not the other way around, as Bonevac’s method requires. We could have had the kind of witnessing he imagines. We just don’t. The kind of testimony he wants is generated by every field of science every day—including historical sciences. But it has never been generated for any purported miracle—ancient or modern.

What We Actually Have

“Paul assures us,” Bonevac says, “that Christ was raised to life; there is the solid testimony of a multitude of eyewitnesses to Christ’s resurrection” and therefore “Christian belief, Paul maintains, rests on firm empirical evidence” (p. 18). Now you know where Stephen Meyer got that apologetic tack. But none of this is true. Paul does not quote any testimony at all. So, zero witness testimonies there. We have only his, and what he testifies to is not a resurrected corpse (or indeed even a missing body), but a dream or vision. Those are not the same things. But even missing bodies usually go missing for other reasons than resurrections (by a frequency of thousands if not millions to one), so there’s no way to get any likelihood favoring resurrection from that, even if we had a witness testifying to it, and we don’t. And people seen alive again after their perceived deaths likewise tend to be for reasons other than resurrections. So that, too, wouldn’t even suffice as evidence for a resurrection, much less sufficient evidence to believe one.

What one needs for a claim so bizarre and contrary to all usual causes is a lot more specific and complicated. If we had a roman doctor’s certificate of death attesting he personally confirmed Jesus was dead (and describing what he did to conform that and it is a method we know to be reliable), and we had an original sworn affidavit from twelve separate witnesses who put their hands inside the risen Jesus’s open wounds and saw him fly off into space, then we’d be getting close at least to what Bonevac needs. At the very least, we’d have probability-increasing evidence in that case. We don’t even have that right now. But it still wouldn’t be enough. And in his heart of hearts, Bonevac knows this. Because the Mormons do have that. And last I heard Bonevac hasn’t converted. So even he knows that’s not enough.

As Hume would put it, it’s more likely the Mormon witnesses colluded to lie, or erred in their judgment, than that what they say they saw was real; particularly as having been given a vested interest they would all be especially prone to lying or motivated error. But even if each such document increased the probability of the extraordinary hypothesis by a factor of ten, as Bonevac avers, at a more credible prior of 10⁻⁴³, twelve genuine affidavits would only get you to 10⁻³¹, nowhere near credibility. He thus needs the prior to be far more favorable—and that’s why he tries to argue for 10⁻¹⁰. But even if we granted so implausibly high a prior for so implausibly absurd a claim, we don’t have these twelve affidavits. Only the Mormons do. One can challenge that by saying what they have is not “literally” twelve sworn affidavits but something somewhat less secure, but that only proves my point: what they do have is still a far sight better than what Bonevac has. So if you do not find that credible, a fortiori, you cannot find anything for the resurrection of Jesus credible.

The problem is worse than even that, of course. Because e in the Mormon-equivalent case does not consist solely of the affidavit-like testimonies. Remember, apologetics is not a truth-seeking enterprise, but a truth-hiding one, and thus operates always on leaving evidence out that, when put back in, reverses all its conclusions. In the Mormon case, e includes the peculiar fact that only interested parties ever saw the alleged evidence. But if the angel Moroni’s story (and tablets attesting it) were true, there should be a whole lot of other evidence, both physical and testimonial. It does not make sense that a God trying to sell something to humankind would not simply broadcast it to everyone (Captain Kirk’s point was correct: God Does Not Need a Starship). That means the mere fact that that didn’t happen casts doubt on anything really happening: the probability of “only a few insiders and the odd convert got the memo” on the hypothesis that “a cosmic superpower desperately wants to sell us all on something” is astronomically small, and thus the likelihood ratio actually tanks in the other direction, supporting the conclusion that the testimonies are false. The opposite of what Bonevac wants.

So the isolated likelihood that a witness would report a miracle may be as near to 100% as makes all odds. But on Bonevac’s specific hypothesis, the likelihood that only those witnesses would see and report it is as near to zero as breaks all odds. Whereas that they would collude to say it for reasons of personal or social benefit is respectably high. The likelihood ratio is therefore reversed. These testimonies are too peculiar to be believed. The same follows for the Gospels: their frequency of patent fabrication and recourse to the implausible is so high (see Chapter 10 of On the Historicity of Jesus and Chapter 6 of Jesus from Outer Space) that the likelihood anything else they say of that kind is true is low, not high, and the likelihood that they would say such things even though they weren’t true is instead thereby demonstrated to be high. So the likelihood ratio goes the other way.

And I should remind you that this extends well beyond “the miraculous” to include failures of credibility even regarding the mundane. As I wrote before:

For example, it’s well known that the Pharisees did not forbid healing on the Sabbath, yet they are depicted as arguing this with Jesus repeatedly, when the arguments put in the mouth of Jesus are actually the same Rabbinical arguments used by the actual Pharisees themselves (e.g., see Geza Vermes’ discussion in The Authentic Gospel of Jesus, pp. 46-47). Similarly, none of the Gospels presents a trial sequence that is at all plausible within the known laws and customs of the time (Proving History, p. 154). The clearing of the temple scene is not at all plausible given the known facts of the temple layout and its police force (OHJ, pp. 431-32). The Barabbas narrative invents non-existent Roman customs to create an ahistorical Jewish symbolism (OHJ, pp. 402-08). Matthew ridiculously has Jesus ride into town on an adult and a baby donkey simultaneously (OHJ, pp. 459-60). The disciples abandon their jobs and property and families, and pick up and follow and completely devote themselves to Jesus after he, a complete stranger and a pauper, just walks up to them and utters a few sentences. And so on (cf. OHJ, pp. 435-36). Verisimilitude is not actually so prominent a feature of the Gospels.

The Gospels too obviously are fabrications to even trust them as relaters of hearsay. But even if they were relating hearsay, that’s still useless as evidence. Because hearsay with respect to the incredible tends to be false, not true.

That didn’t have to be the case. As I said, if God wanted us to be rationally justified in believing Jesus rose from the dead, he would not require us to be so irrationally gullible as to be easily duped by whatever erroneous or collusive hearsay anyone might contrive; to the contrary, he would provide the evidence epistemically required for rational belief: the risen Jesus would appear to many more disinterested parties who could not share the same error or motive. Ancient Chinese record books corroborating ancient Roman record books beyond any plausible collusion or shared error would suffice to establish Jesus was superhuman and at least survived his reputed death. Getting specifically passed the bar of “he faked his death” would be harder, as now we’re positing he has superpowers, making faking his death even easier. But it’s only Bonevac who needs a resurrection to be real. If all we care about is proving Jesus was a superhuman agent, we don’t need that; whereas if for some reason God needed us to believe resurrection possible, there are far more convincing ways to establish that—just resurrect a deserving innocent every year, in conditions scientifically verifiable, proving that a feature of our divinely governed universe. That God does not do that (or anything else as trustworthy) counts as evidence against God wanting us to have any rational belief in it, not the other way around.

Formalized Gullibility

Bonevac’s bogus premises stem from Formalized Gullibility as a Modern Christian Methodology. When he says it’s “hard to give any naturalistic explanation of the Passover, of Elisha’s raising the son of the Shunammite woman from the dead (2 Kings 4:18–37), or, especially, of Jesus’s resurrection” (p. 23) he somehow completely blanks on the fact that this is, to the contrary, extremely easy to do: the authors of these books just made it up. That’s the number one most common “naturalistic explanation” for the existence of miracle claims. They are playing people for dupes by inventing these stories specifically to activate the persuasive power that folks like Bonevac are openly admitting they are entirely vulnerable to.

The priors bear this out. Add up all the miracle claims in all the books of all cultures and religions across history. How often are they made up? Almost always. And of the ones that aren’t, none testify to anything actually miraculous. And this is where we get the real problem with miracle claims, which is not a logical problem, but an evidential one:

Atheism predicts random good luck and bad luck will be observed, and therefore anything we can confirm happened that seems miraculous will be physically explicable (because, not really miraculous) and rare (because, random). Without a parade of excuses, theism predicts miracles will be commonplace and physically inexplicable (e.g. Christian healing wings in hospitals would exist where amputees have their limbs restored by prayer, or anything like that; yet we observe not a single thing like that). Likewise, atheism predicts the only miracle claims that will “survive scrutiny,” are claims that are never reliably investigated; and that every time a miracle claim gets proper scrutiny, it dissolves. And lo and behold, that is also what we see. Thus, again, what we observe is exactly what is expected on atheism, not at all what we expect on theism. So even the evidence of miracles refutes theism and confirms atheism.

The correct likelihood ratio is:

• How probable is it, if any miracles are real, that miracle stories always happen where we can’t vet them, whereas every time we can vet them, they prove never to have happened? Well, low.
• How probable is all that, if no miracles are real? Well, high.

The likelihoods therefore always tank belief in miracles. If God didn’t want this to happen, he’d have provided the requisite evidence, by reversing this order of observation. He didn’t. So we should conclude he didn’t want to. God cannot want us to rationally believe any miracle. Of course, this is also predicted by the theory that there is no God, so that a lot else backs that up should be heeded. But we’ll stick to Bonevac’s idea-space here.

Consider the only real-world analogy Bonevac builds out as if to illustrate his position:

Paul was in a far better epistemic state with respect to Christ’s Resurrection than we are, say, with respect to the attack on a canoeing President Carter by a crazed, swimming rabbit in 1980 [actually 1979–ed.]. That was surely an improbable event, a little further removed in time, witnessed by only a few government employees whose reliability may not compare very well with that of the disciples. Yet most of us—rationally—believe that it occurred.

Bonevac, “Argument from Miracles,” p. 30.

So, maybe Bonevac wasn’t aware, but we have photographs documenting that attack. That puts us in a far better position than Paul. It also isn’t unusual. Contrary to popular misbelief, rabbits are vicious. Carter also related conditions well-documented to turn prey berserk: the rabbit was chased into the water by a pack of hounds and misperceived his boat as dry land and set to attacking the animal it saw (a certain member of the species Homo sapiens) blocking its escape. One should also note that swamp rabbits are nearly two feet long and weigh five pounds. Having once been savaged myself by a comparably scaled cat (while rescuing it from harm; I endured its biting and clawing until it was in safety), I can vouch for this being more serious than silly. Indeed a relative of mine was mauled so grievously by her pet rabbit she had to have facial reconstructive surgery. One can easily find widespread records of such attacks and their effects. So this event was actually a Humean regularity of nature; not a disbelievable improbability.

But put that all aside. Notice what happens when we apply Bonevac’s own analogy correctly: what Paul actually testifies to, like rabbit attacks, isn’t even unusual, much less miraculous. Seeing gods in dreams and ecstatic states, and believing them to be real encounters, was normal back then (and still in many cultures, and subcultures, that have resisted modernization). This affords no evidence at all of superhuman agency—to the contrary, this disproves superhuman agency. That a real superhuman agent would only appear by means known to be routinely bogus is simply improbable; whereas, had such an agent appeared in a manner that could not be ascribed to means known to be routinely bogus, that would be evidence supporting superhuman agency. Which is why, an average lifetime later, the Gospels fabricated exactly that kind of story, which is also evidence against their truth. No such tales were known to Paul. He only heard of revelations. A lifetime later, this has exploded into space travel and dinner parties. Miracles only show up when we can’t vet them; never when we can. That’s how we know there are no real miracles.

My Questions

So now that you know all that, you can understand the questions I had planned to ask. My first question was the only one asked, alas, and he gave a two minute reply that didn’t really address the point, but just tried to make the evidence go away by routine apologetics:

Question 1: The Acts of John claims seven named people and their families, so a dozen or more people, witnessed Saint John command an army of bedbugs do his bidding and march to and from his bed. Does that mean we have seven or a dozen witnesses of that and therefore Bayes’ Theorem entails we should believe that happened? Bonevac answered that late stories should be ignored as untrustworthy. But we don’t actually know this is any later than our Gospels, and Bonevac never established any Bayesian reason (or any reason at all) to believe there was any meaningful difference between 50 years and 150 years. Mark begins his Gospel tales over forty years later; average life expectancy for an adult back then was 48; and we have no evidence any witness was alive when Mark published, much less where he published (or even could read Mark; few Palestinians were literate, and fewer knew Greek); nor, even if there were, do we get to hear from anyone who was (so we can’t say what they said about it). What we have instead is solid proof Christians were willing to invent witnesses (even give them names!) and no one ever challenged them on it. That remains a problem Bonevac never accounts for in his math.

Question 2: Hearsay is a condition of evidence that is not even accepted in a court of law, much less as overthrowing all modern scientific knowledge. Yet Bonevac’s entire argument rests on an error of conflating Paul with the Gospels, which were written what was then an average lifetime after the events they relate, in a foreign land and a foreign language, by authors unknown, whose honesty is completely beyond our vouching. We don’t have hundreds or twelve or six or even two witnesses. We have only one: Paul. He makes claims about other witnesses, but we don’t hear from them, and he never says they saw anything different than he did. Whereas the Gospels aren’t witnesses at all, and their authors never even claim to have met one. “So,” I asked, “how do you get multiple witnesses out of hearsay? Please give us a Bayesian defense of trusting that.” We never got to hear him attempt to. It is, of course, impossible. A million independent testimonies to the same urban legend does not increase the probability of it being true even a tick. So it can’t do any more for Jesus.

Question 3: In Galatians 1 and Romans 16 Paul says—and using the same language in 1 Corinthians 15 he further implies—that the risen Jesus was only seen in dreams or visions; not “flesh and blood,” he says (Gal. 1:16; cf. Gal. 1:11 and 1 Cor. 15:50), but “a revelation” (Gal. 1:12; cf. Rom. 16:25-26), literally “in me”; he even reports continuing mental conversations with Jesus in 2 Corinthians 12. As William Harris shows in Dreams and Experience in Classical Antiquity, ancient authors did not always distinguish seeing or meeting gods in dreams from waking visions, they often used the same vocabulary for both, so Paul could even mean for all we know just meeting Jesus in dreams; while at best, he means altered states of consciousness. We know today that that is not evidence of a resurrection. That they believed it was does not increase the probability that it was. So, I asked, “How do you make a Bayesian argument that ‘I dreamt I saw Jesus’ or ‘I saw Jesus in a revelation’ counts as evidence of actually seeing Jesus?” We never got to hear him attempt this. Of course, it can’t be done.

Question 4: In 1 Corinthians 15 Paul says no appearance of Jesus was communal except one: only one event does he say happened “all at once” to many brethren; but he doesn’t say what exactly they saw. For all we know it could simply have been a light in the sky that they took to be Jesus (or were told was Jesus by trusted apostles), just as a comet that people saw was publicly claimed (such as by Ovid and the whole Augustan state) to be the risen Julius Caesar flying to heaven. Thousands of witnesses thus attested to seeing the risen Julius Caesar. Does that increase the probability that he actually survived his death? And if not, how can we say it does for an even vaguer report in Paul about Jesus Christ? We never got to hear Bonevac’s answer. But you can’t claim to have testimony you don’t in fact have—and we don’t have any testimony to what those brethren saw (see Then He Appeared to Over Five Hundred Brethren at Once!). This simply destroys Bonevac’s argument, and by his own method.

Paul only attests to known natural phenomena (dreams or ecstatic states that often convince people like him that they saw the gods), which is evidence against, not for, the activity of a supernatural agent. Bonevac needs to get the Gospels to be in Paul, but they simply aren’t. Those stories are not told by witnesses, are not credited to any known witnesses, and were not vetted or vouched for by any known witnesses. And they were told a lifetime later. And they contradict what Paul claims he saw and implies anyone saw. They therefore far more probably exist because they are convenient propagandistic fabrications than that they are recording anything anyone ever said they saw. And as making up stories like that, and for that reason, and on that time scale, was common, the likelihood of it as explanation is high. Whereas the supernatural agents Bonevac is stumping for entail much more and better evidence should exist than this, so that likelihood is small. The likelihood ratios thus go the other way than he avers: the Gospels being dubious, incredible, motivated, late, unsourced, unvouched for, and contradicting of our only witness is far more likely if their claims are false than if they are true.

And Bonevac’s Methods

So, Bonevac starts with a sound method (the right kind of testimonial evidence will have a positive likelihood ratio, and then all you need is enough of those to overcome any prior odds). But then screws up the inputs, with a series of false descriptions of the evidence and conflation fallacies, and leaving contrary evidence out of account.

Bonevac does this again when he says, “The more typical miracles of healing involve events whose prior probability is far higher, since spontaneous remission, psychosomatic illness, and so on are well documented” (p. 31), but those are for that very reason not miracles. Naturally occurring events (e.g. psychosomatic conditions and cures) evince no supernatural agency. Those stories in the Gospels are also not believable, for other reasons; but they mimic known phenomena, I suspect, because they are celebrating and authorizing in myth the regular tent-show spectacles of Christian missionaries (which even Paul repeatedly alludes to). But regardless, even a thousand witnesses to the occurrence of such events, competently cross-examined in a court of law and placed into a certified court transcript, offers zero evidence for superhuman agency. To the contrary, if that’s all agents can pull off, this is evidence against their being superhuman. The “superhuman” hypothesis predicts real superhuman feats, like restoring lost limbs or organs or eradicating demonstrably somatic diseases from whole regions with a word, such that not witnessing any from them is improbable on that hypothesis, because it is contrary to expectation whereas “they can only do parlor tricks” is exactly what is otherwise expected.

Another example of Bonevac dropping his own methods is when he claims “differences” between the Gospels indicate they had independent sources. Of course “independent” still does not mean “witnesses.” Hearsay is routinely independent yet still traces to no witness; that’s why urban legends have dozens of variant iterations. But Bonevac’s more general error here is that whenever he invents an apologetic to conjure out of thin air a fact that doesn’t exist (like that the Gospels or even Paul count as “multiple independent witnesses”), or to make some inconvenient fact go away (like all the evidence ancient Christians were liars, and particularly about miracles; remember the Acts of John?), suddenly he drops his Bayesian methodology. This is another example.

You might suspect why. If Bonevac stuck to it, he’d have to admit that, all else equal, the Bayesian likelihood that differences between stories arise by creative impulse is the same as that they arose from independent sources (the effect is observed 100% of the time in each case), and thus he cannot conclude “differences” mean “sources.” Since it’s just as likely they don’t mean sources, you need some actual evidence that sources were involved—something other than that there are differences. And yet Bayesian methodology requires updating your priors. The more examples you find of creative license being the cause of differences in a similarly-constructed body of literature, like the Gospels, and with no evidence arising at all that sources are the cause, the prior probability that the next “difference” you point to was caused by creative license and not sources goes up. In fact, starting at “we don’t know” (50/50), if every instance you can determine the answer to turns out to be creative license, and zero instances you can determine the answer to turn out to be sources (and this is where we are with the Gospels), it simply becomes improbable that “differences mean sources,” quite the opposite conclusion Bonevac wants to reach.

The same error results in Bonevac getting the opposite conclusion than he would if he stuck to his Bayesian method when it comes to his argument from “series” of miracles. He starts by arguing that if we saw someone perform lots of wonders, this would increase the probability that they are a superhuman agent, and that they genuinely did perform yet another wonder in line with those. This is true in the ideal case; as I said: hang around Harry Potter or John Constantine enough… But then Bonevac immediately applies this finding to storybooks. Record scratch. Those aren’t the same things. If you think it would be hard for natural causes to explain all the things you see around Potter and Constantine, you would not think so of a storybook. That a storybook would contain made-up stories is typical, not remarkable, much less difficult to explain. So the analogy does not hold.

In fact, the conditions are exactly reversed. If you read a book full of implausible claims, this reduces its trustworthiness, not increases it, precisely because it is so easy and so typical for books full of the implausible to be full of shit (see Craig vs. Law on the Argument from Contamination and For the Existence of Jesus, Is the Principle of Contamination Invalid?). Bonevac is thus here promoting methodological gullibility: all a liar need do to convince him of anything is tell more lies. Because by Bonevac’s method, the more lies he tells, the more likely he’s telling the truth instead! (I detected the same folly in Pascal’s Wager, and the analysis there applies here.) Likewise, all Bonevac needs to believe a schizophrenic’s every claim is that they make a lot of claims; instead of realizing that someone who makes a lot of unbelievable claims probably is less likely to be reporting real events, rather than more so. So Bonevac’s “series” argument is defunct; it just circularly assumes what is to be proved. Bonevac isn’t applying his Bayesian reasoning correctly here, precisely when doing so would get the wrong result. He only sticks to it when it gets what he wants. He drops it the moment it would turn on him.

In the same fashion, Bonevac claims a historical chain of witnesses establishes our canonical Gospels were reliably transmitted and vouched for, simply because Tertullian claimed this centuries later. This rests entirely on the dubious testimony of Tertullian, someone known to be unreliable, and on a point for which he offers no supporting evidence whatever. It’s just something he believes, or that people claimed to him. It’s not a fact vouched for in any reliable way. It’s also not true. Tertullian only said this of the Epistles of Paul; and that we know is false: the current Epistles deemed authentic are hashed up edits of multiple letters mashed together, and thus clearly not untampered with in their transmission; while the other half of them are proven forgeries (see On the Historicity of Jesus, pp. 280 n. 50 and 511 n. 4). It’s clear Bonevac has tossed Bayesian reasoning to the wind here and just fallen back into the ruts of dubious apologetical argumentation. Anything anyone ever claimed is now simply “true,” all evidence and probability be damned. Whereas any actual Bayesian analysis of what Tertullian said would not get us to a probability that it was true (see my Second Reply to Sheffield on this point; and my followup).

The same thing happens when other apologists try to bypass common sense by making things up like “the Apostles would not die for a lie.” Literally nothing in that statement is true (see Did the Apostles Die for a Lie?). Or “no author could get away with false claims while witnesses were still around.” All history proves otherwise (see, for example, No, Mr. Christian, A.N. Sherwin-White Didn’t Say That. And Even What He Did Say Was Wrong. and The Rain Miracle of Marcus Aurelius: A Case Study in Christian Lies). And so on. Here Bayesian logic is simply being ditched altogether, facts are being invented, and conclusions built on those fabrications. That’s apologetics; not rational belief.

Correcting Bonevac’s Inputs

So after all that, we can now correct Bonevac’s faulty inputs.

I already explained why his assigned prior probability is implausibly too high; a resurrection is far less likely than 10⁻¹⁰; it’s certainly much closer to what the McGrews’ suggest, which is 10⁻⁴³. An improbability of 10⁻¹⁰ would only define the reference class of events we can show to be physically possible but that just haven’t happened in human history yet. In other words, by Bonevac’s own formulation, 10⁻¹⁰ describes simply anything no human has ever seen happen in their lifetimes, not anything superhuman. To be superhuman entails far more than that no one has seen it; it entails something that cannot happen without the presence of an agent whose mere existence would rewrite all known science. That’s far less likely. Again, it needn’t have been that way; there could have been by now tons of evidence for such agents. But there isn’t. And that has to be explained—with evidence (and Bonevac has none; conjectures, remember, are not evidence)—or else it has to be accounted for by a far lower prior probability than holds for just things no one has seen happen yet.

But worse than that is Bonevac’s failure to develop credible likelihoods. First he invents evidence that doesn’t exist: Paul and the Gospels become “multiple eyewitness testimony,” when in reality they contain only one witness’s testimony—and it’s vague, poorly transmitted, and contradicts what Bonevac wants. Then he assigns entirely the wrong likelihood ratio to what actually does exist, because he develops his ratio in respect to the wrong hypothesis: he gets a 10/1 likelihood of truthful testimony in what Paul says he saw; but what Paul saw is not evidence of a superhuman agent, and Bonevac is supposed to be testing the hypothesis of a supernatural agent, not whether some ancient religious fanatics imagined they met their god in a dream or some other altered cognitive state.

Hence Bonevac’s own method requires we get a different likelihood ratio than he does. His ratio of 10/1 would entail that 9 in 10 eyewitness miracle reports are true. Because then we’d have “reporting witnesses” who are wrong, by his measure, only 10% of the time (as he says there is only a 10% chance there’d be witnesses giving a false report). Which we know is false. Most miracle reports by far, even by eyewitnesses, are false—even if the witnesses sincerely believe what they are saying, and even if they really saw what they said. Remember, hundreds of people at Fatima believed they were seeing a supernatural agency; none were correct about that. So Bonevac’s likelihood ratio should be closer to 10/9 at best, rather than 10/1. His 10/1 is reasonable (even if a bit optimistic about human beings) with respect to what the only eyewitness report we have reports having seen; but we aren’t asking if Paul saw what he claims (I also think the probability he lied about it is more than 10%; but let that go for the sake of argument, and pretend we have abundant evidence that Paul was uncommonly honest). Rather, we are asking if what Paul saw was a resurrected Jesus. That’s different.

And I don’t even think this should be 10/9. The probability Paul would report what he says if it wasn’t Jesus is indeed quite high (because, in context, he was exactly the sort of man who would believe dreams and revelations were real), whereas the probability Paul would report what he does if it was Jesus is actually quite low—because a real resurrected Jesus would not just show up in dreams and revelations. Paul should be reporting what the Gospels do: that he met Jesus, fondled his wounds, had dinners with him, and visited with him for weeks, before watching him fly off into outer space.

Moreover, as I keep pointing out, apologetics always operates by leaving evidence out of e that, when put back in, reverses the conclusion—like what I just said above: we are there putting back in what Bonevac left out, which is the actual thing Paul claims to have seen, and what he didn’t claim anyone saw. Another thing Bonevac is leaving out is all the other evidence there should be. As I’ve often said:

A walking corpse—indeed a flying corpse (Luke 24:51 and Acts 1:9–11) or a teleporting corpse (Luke 24:31–37 and John 20:19–26)—could have visited Pilate, Herod, the Sanhedrin, the masses of Jerusalem, the Roman legions, even the emperor and senate of Rome. He could even have flown to America (as the Mormons actually believe he did), and even China, preaching in all the temples and courts of Asia. In fact, being God, he could have appeared to everyone on earth. He could visit me right now. Or you! And yet, instead, besides his already fanatical followers, just one odd fellow ever saw him.

If Jesus was a god and really wanted to save the world, he would have appeared and delivered his Gospel personally to the whole world. He would not appear only to one small group of believers and one lone outsider, in one tiny place, just one time, two thousand years ago, and then give up.

This is our actual e. And this e is exactly what we expect if what the witnesses saw was not Jesus, but just figments of their troubled imaginations. Whereas if Jesus really did rise from the dead—indeed for the very purpose Christians claim (beginning with Paul, as even Bonevac quotes)—then the probability that this is what we’d see is near zero; the probability is instead very high that we’d have seen a very different result, exactly as I suggest in the analogy of the blotting out of the sun: had that happened, the evidence we had would be quite different; that that is not what happened is therefore improbable, not probable, on the miracle hypothesis. This is a mathematical necessity: if h entails it’s probable you’d see x, then it is logically necessarily the case that it will be improbable for you to see instead ~x. These are in fact converse probabilities: P(~x|h) = 1 – P(x|h), so if it’s 80% likely we’d see something like x, it can be only 20% probable we wouldn’t (see Proving History, index, “Argument from Silence,” and pp. 230, 255-56, and 302 n. 13). Background knowledge, b (which Bonevac designates with K), can change this (Ibid.), but not in any way pertinent here.

This means the likelihood ratio, for the only eyewitness report we have, is the opposite of Bonevac’s—actually closer to 1/10 or worse, not his 10/1. The evidence we actually have thus reduces the prior, not ups it! The analogy to the UFO cases I recently discussed is again apt: the testimony we have is actually in line with known illusions, which is too coincidental, and therefore actually many times more likely if what they saw wasn’t a spaceship than if it was. And that’s how we know it wasn’t.

Conclusion

Bonevac is correct to conclude that “what is right in Hume’s argument is fully compatible with rationally believing that God revealed Himself to Moses, sent him to Pharaoh, sent the plagues on Egypt, brought the Israelites out of Egypt, rescued them from Pharaoh’s army, and led them (circuitously!) to the promised land” (p. 39), so long as the only people you are talking about are actual eyewitnesses to all that—but that isn’t what we are talking about. We are talking about a fable claiming that. And that is simply not the same thing. There is no rational way to get from a propagandistic myth composed by an unknown author in an unknown time, in an era ubiquitously prone to such fabrications, and without any access to the testimony of anyone who would have known better, to “what that myth says really happened.” And so you certainly can’t get from there to “therefore a superhuman agent exists.” A story claiming witnesses exist is not “multiple independent witnesses.” It’s not even a single witness—as that story wasn’t written or vouched for by anyone who was there. Such fables throughout history have typically been bogus. So you need evidence to confirm this as an exception. And there is none.

The same goes for “rationally believing that Elijah trounced the priests of Ba’al” (p. 40) or that Jesus died but then walked out of a tomb alive and threw dinner parties for a month before flying into space. Sure, if we were there, maybe (though Penn & Teller would rightly advise you not to be too gullible here; as even then we’d need to collect evidence we weren’t being conned). But that’s not what we have. We don’t even have certified statements from any witness. We have one witness’s rhetorical act of persuasion that was subject to a compromised transmission. That’s it. And nothing he attests to, or attests anyone else witnessed, is at all miraculous. So that one witness’s testimony contains no evidence of superhuman agents at all. Bonevac has no evidence for his method to work on. Which really should lead him to the opposite conclusion: the most probable explanation for this failure is that superhuman agents don’t exist.

Bonevac is trapped in a delusion, a delusion born of motivated reasoning. As he himself admits, when he says his “Christian faith rests, at least in part, on reports of miracles found in the Scriptures” (p. 35) and even though “we may not go so far as Paul, who says that ‘If the dead are never raised to life, let us eat and drink, for tomorrow we die’ (1 Corinthians 15:32),” nevertheless “if we have no evidence for [those] miracles, we have no evidence of God’s interaction with Israel, with the world, or with us” (p. 35). Usually this would be easy to grant (no one is bothered by finding out Hercules didn’t perform his twelve labors or that Glycon wasn’t a real snake who could predict the future), unless you are desperately in horror of granting it. Bonevac needs his myth to be true; therefore he needs the results of a Bayesian analysis of Paul and the Gospels to get that result; but he’s too honest to misdescribe a sound Bayesian analysis, so he has to slip into it bogus premises instead: he calculates the wrong prior; he calculates the wrong likelihoods; he invents evidence that doesn’t exist; and he ignores crucial evidence that does.

Nevertheless, I can say for Daniel Bonevac that, unlike some other apologists, this doesn’t make him a crank; it just makes him wrong.