Theology, philosophy, math, science, and random other things

Bayesian evaluation for the likelihood of Christ's resurrection (Part 48)

The following are the accounts of the healing miracles of the Roman emperor Vespasian.

Vespasian himself healed two persons, one having a withered hand, the other being blind, who had come to him because of a vision seen in dreams; he cured the one by stepping on his hand and the other by spitting upon his eyes.
 - Cassius Dio, Roman History, 65.8 

Vespasian as yet lacked prestige and a certain divinity, so to speak, since he was an unexpected and still new-made emperor; but these also were given him. A man of the people who was blind, and another who was lame, came to him together as he sat on the tribunal, begging for the help for their disorders which Serapis had promised in a dream; for the god declared that Vespasian would restore the eyes, if he would spit upon them, and give strength to the leg, if he would deign to touch it with his heel. Though he had hardly any faith that this could possibly succeed, and therefore shrank even from making the attempt, he was at last prevailed upon by his friends and tried both things in public before a large crowd; and with success. At this same time, by the direction of certain soothsayers, some vases of antique workmanship were dug up in a consecrated spot at Tegea in Arcadia and on them was an image very like Vespasian.
 - Suetonius, The Lives of the Twelve Caesars: Divine Vespasian, 7.2 

During the months while Vespasian was waiting at Alexandria for the regular season of the summer winds and a settled sea, many marvels continued to mark the favour of heaven and a certain partiality of the gods toward him. One of the common people of Alexandria, well known for his loss of sight, threw himself before Vespasian's knees, praying him with groans to cure his blindness, being so directed by the god Serapis, whom this most superstitious of nations worships before all others; and he besought the emperor to deign to moisten his cheeks and eyes with his spittle. Another, whose hand was useless, prompted by the same god, begged Caesar to step and trample on it. Vespasian at first ridiculed these appeals and treated them with scorn; then, when the men persisted, he began at one moment to fear the discredit of failure, at another to be inspired with hopes of success by the appeals of the suppliants and the flattery of his courtiers: finally, he directed the physicians to give their opinion as to whether such blindness and infirmity could be overcome by human aid. Their reply treated the two cases differently: they said that in the first the power of sight had not been completely eaten away and it would return if the obstacles were removed; in the other, the joints had slipped and become displaced, but they could be restored if a healing pressure were applied to them. Such perhaps was the wish of the gods, and it might be that the emperor had been chosen for this divine service; in any case, if a cure were obtained, the glory would be Caesar's, but in the event of failure, ridicule would fall only on the poor suppliants. So Vespasian, believing that his good fortune was capable of anything and that nothing was any longer incredible, with a smiling countenance, and amid intense excitement on the part of the bystanders, did as he was asked to do. The hand was instantly restored to use, and the day again shone for the blind man. Both facts are told by eye-witnesses even now when falsehood brings no reward.
 - Tacitus, Histories, 4.81

So, what are we to make of these accounts?

We apply the methodology that we've been using all this time. How much evidence is there for these miracles? And is it enough to overcome the small prior?

As before, we first look at the people providing the testimony. Who claimed that this actually happened? We have three accounts by three well-known historians, but they're merely reporting what they heard from others in their research. Now, we didn't count Matthew, Mark, Luke and John as witnesses for merely writing about Christ's resurrection. We only counted those who actually gave personal testimonies. So we can no more count the three historians above as witnesses. Who were their sources? Who were the actual, original individuals that personally witnessed and reported Vespasian's miracles?

None of the accounts give specific names for such individuals. We have some vague characters, such as "people of Alexandria" or "[Vespasian's'] friends" - but there are no named characters, except perhaps emperor Vespasian himself. However, this group of people seem to be well specified: they're better than the "some people" level of evidence that we've seen so much of thus far. The witnesses are the crowd of people who gathered in Alexandria and saw Vespasian heal these two people. Tacitus mentions eye-witnesses, and presumably he could have gotten to these specific individuals if he had to. So, overall, I would say that this testimony is on par with the 500 disciples witnessing Christ's resurrection. The Bayes' factor for such a testimony is in excess of 1e8, according to our previous calculations. It would be greater still if you counted Vespasian himself.

So, that's a pretty big Bayes' factor, right? So this event actually happened?

But now we run into the problem of precisely defining what "this event" was. Did Vespasian "heal" two people in front of a large crowd? The prior odds for such an event is decently large - certainly much larger than someone coming back from the dead. Let's say, for the sake of argument, that it's around 1e-6. This is easily overpowered by the Bayes' factor of the testimonies above, which exceeds 1e8. We can be decently confident that such an event happened.

But was the healing supernatural? Now we're talking about an entirely different kind of event, with different prior odds. A supernatural healing of this type would be almost as unlikely as a resurrection. Since a resurrection had prior odds of 1e-11, let's be generous and assign this a prior odds of 1e-8. But... isn't the Bayes' factor still large enough to overcome that?

No, not at all. For the Bayes' factor itself now changes. For one, we can no longer count on Vespasian's testimony at all. Apart from the massive conflict of interest (which we'll address later), Vespasian himself doesn't believe that he can actually heal these people in the beginning. Tacitus explicitly reports that everything was perfectly achievable through mundane means, and that Vespasian only attempted the healings when he was informed of this possibility.

Therefore, Vespasian himself is certainly not testifying to anything like a supernatural healing here. Neither, for that matter, is the crowd itself, if things went according to what's in Tacitus's account. In fact Tacitus goes to some lengths to provide naturalistic explanations for the "healing" - to such a degree that his account should actually be counted as evidence against a supernatural healing. He calls these people "most superstitious", and nearly explicitly says that anyone in the crowd who actually believed in a supernatural healing would have been deceived. And there is nothing in either of the other two accounts to contradict his.

Tacitus's account is the earliest, most detailed, and most explicit in mentioning witnesses. The other two are mostly just summaries of his. And yet, in this best account, the idea of a supernatural healing is almost explicitly refuted. So what happens to the evidence? Where is the testimony?

There is essentially none left. At best it's reduced to that familiar, unspecific "some people say..." level. This is nowhere enough to overcome a prior odds of 1e-8, and therefore we can be very confident that a supernatural healing did not take place here.

In summary: on the question of whether there was a public spectacle where Vespasian "healed" two people, a prior odds of something like 1e-6 is overcome by a Bayes' factor exceeding 1e8 - therefore we can reasonably hold that this actually took place. But on the question of whether this "healing" was supernatural, a prior odds of 1e-8 is essentially unmoved against a "some people say..." level of evidence. We are therefore very certain that the "healing" was not supernatural.

And all this is without taking into account the enormous potential for deception, conspiracy, political shenanigans, or a publicity stunt. Vespasian was a newly crowned Roman Emperor, after all. Taking that into account would lower the final probabilities even further, for both the supernatural and the mundane versions of the event. In the end, I think our methodology brings us to the point where there's something like even odds for some kind of public spectacle taking place, but the nature of the event was almost certainly not a supernatural healing.

Do you agree with that assessment? Does it seem reasonable to you? Good - then you are compelled to correspondingly increase your faith in the methodology we used, and therefore increase your degree of belief in Christ's resurrection.

But wait! Can a similar type of reasoning be used against Christ's resurrection? Could it be argued that "something" probably happened with a man we now call Jesus, but that it was not anything supernatural?

No, it cannot. The reasons that existed for Vespasian that allowed for such an argument simply does not exist for Christ's resurrection.

For one, a resurrection is nearly impossible to fake. One can fake being healed of blindness, or of a defective limb, without much effort. You can do it right now - you just need a little bit of acting skills. Just a bit of placebo effect or the excited anticipation of the crowd can be enough to get someone to walk around for a few steps, or convince a man with poor vision that he sees better. That is all that is required to generate the above accounts of Vespasian's miracles. But can you imagine making such an argument for a resurrection? "Are you sure that it wasn't just the placebo effect that cured his death? Or sometimes, if everyone in the crowd anticipates it, a corpse can be encouraged enough to get up and walk."

We believe that nothing supernatural took place in Vespasian's case, partly because what he achieved in healing is not all that remarkable. There are many possible naturalistic explanations. But in Christ's case, you need a naturalistic explanation for a man who was confirmed dead multiple times, who then came back walking, talking, eating, teaching, converting skeptics, and giving missions. Good luck getting all that with common naturalistic explanations like "placebo effect" or "crowd anticipation".

But secondly, and far more importantly, the evidence itself points towards a naturalistic explanation for Vespasian, and a supernatural event for Jesus. We are, as ever, evaluating and following the evidence. The evidence itself - in the form of Tacitus's account - spells out that Vespasian's miracles likely had naturalistic causes. In Jesus's case, it's again the evidence itself - in the form of the text of the New Testament - that consistently and repeatedly tells us that Jesus's resurrection was a supernatural event.

In order to draw an equivalence, and say that "something happened, but nothing supernatural" in both cases, you would need the same kind of evidence. You would need something like the Gospel of John explicitly stating that Jesus's disciples stole the body, and spelling out exactly how they did it and why there was nothing supernatural required. If the Gospel of John actually said such things, then you could draw an equivalence between the "miracles" of Vespasian and the resurrection of Jesus.

But, of course, the Gospel of John does not in fact say that. It is no good making up evidence you don't have - we are to only follow the evidence we do actually have. So, merely mentioning that "something happened, but probably nothing supernatural" is worthless. It's wishful thinking about evidence you don't have. Speculations - merely mentioning possibilities - do absolutely nothing against a Bayesian argument. It is evidence, not speculations, that move probabilities.

So in considering all of the above, you see that the methodology is perfectly consistent in concluding that nothing supernatural happened in Vespasian's stories, while also concluding that Jesus rose from the dead.

We will examine more cases next week.

You may next want to read:
Finding pi in a square grid: or, why you can have square brownies for pi day
I am a sinner.
Another post, from the table of contents

Show/hide comments(2 Comments)

2 comments on “Bayesian evaluation for the likelihood of Christ's resurrection (Part 48)”

  1. Is your post sarcastic? If anything, your argument debunks the gospel fairy tales. There is a similar story of Jesus healing a blind man with his magic mucus superpowers in Mark 8:23-25. Why should I believe this absurd story, written by some anonymous, biased member of your cult, who doesn't claim to be an eyewitness, writing in the third-person using the 'omniscient narrator' technique of fiction, while disregarding a similar account about Emperor Vespasian that's written about by 3 known, named Roman historians? You don't have a resurrection to explain, you have a *STORY* about a resurrection, by anonymous, biased cult members writing well after the supposed events, where our earliest complete manuscripts containing the story are dated to the 4th century, and are filled with proven fiction, forgery and fraud. What is the *MOST LIKELY EXPLANATION* for a *STORY* about a virgin-born demigod whose rotting corpse magically returned from the dead? (Such as Romulus, Hercules, Asclepius, Dionysus and Jesus.) 1) liars lied, or 2) these are real events that actually occurred? Clearly, the most likely explanation is that this is a false claim about a fictional event. If you claim otherwise, where's your evidence? 'Magic book says so' is not evidence that the book is magic, or that what it says is true. You're just using the circular reasoning fallacy. You don't believe the Quran or Book of Mormon when they make absurd supernatural claims, do you? They have just as much 'evidence' for their claims as you do for yours...absolutely nothing. Absurd supernatural claims are not 'evidence', they are the claims you need to back up with evidence. And you have none.

  2. Hi, welcome to my site!

    Unfortunately, you've jumped into a middle of a long series of posts here, without a lot of the prerequisite reading that came beforehand. I've actually consolidated the whole series into a single post, whose link I provide below:

    You may also want to learn more about the mathematical framework that I'm using, which will help you further understand my thoughts. Again, I provide the links below:

    I welcome any good criticisms of my work - so perhaps understanding what I'm saying here will help you towards that goal. I hope the above links are helpful in that regard!

Leave a Reply