Having commented on the meta-level of the debate, I now want to respond to the debate at a lower level. I want to point out the Vincent’s accusations that
is patently false, since besides my meta-level methodological “quibbles”, I have tried my best, for example, to respond to Vincent’s probabilistic arguments, despite my lack of historical training or knowledge about NT studies. I think the difference is that unlike you, I am way more cautious about proclaiming what a “impartial historian would do”, because I approach this subject as a humble layman.
Nevertheless, in this post I will pick up on a line of argument from our last exchange:
What I seriously think is that the whole business of assigning prior probabilities to events seems dubious and non-rigorous, such that I am happy with assigning 50-50 prior probabilities to most historical claims that are not immediately outlandish (such as a giant blue dragon appearing next to Jesus’ cross). I will elaborate on this claim in more detail here.
Can we psycho-analyze Pilate?
Let’s take, for example, the claim that Pilate would be reluctant to condemn a man accused of advocating insurrection. You base this on an psycho-analysis of Pilate based on his historical record:
Pilate’s alleged reluctance to condemn Jesus to death. This, I argued, is psychologically unlikely, given what we know of Pilate’s character. Here, Story1 is that Pilate was indeed reluctant to condemn Jesus, while Story 2 is that he sentenced Jesus to death without compunction. In my post, I described several incidents in the life of Pilate which illustrated his cruelty. Clearly, killing Jesus would not have been out of character for him. Given this background information about Pilate’s character, we might reasonably conclude that the ratio P(Story2)/P(Story1) is pretty high – say, 10 to 1.
And here is an example of an incident of Pilate’s brutality that you cite:
The Jewish historian Josephus chronicles Pilate’s brutal acts: he tells us (Antiquities 18.3.2) that on one occasion, when Pilate wanted to build an aqueduct to provide fresh water to Jerusalem, he decided to finance the undertaking by stealing the money from the treasury of the Jewish temple. When the Jewish authorities and the people of Jerusalem protested in outrage, Pilate responded brutally: on his command, his soldiers mingled with the crowds, in disguise, and then they suddenly attacked the people, not with swords but with clubs. Many Jews were slaughtered on that day, and many others were trampled to death.
But the above incident could also be interpreted as Pilate simply suppressing a potential rebellion stirred by the Jewish authorities. It is a different situation from responding to an odd, wacky religious leader which seems to be hated by the Jewish authorities for some reason but only had tens of unarmed, mostly poor and powerless followers. It is possible that Pilate would have reacted with the same brutality to Jesus. But it is also possible that he viewed Jesus differently, perhaps buoyed by his personal charisma. Or he just felt differently that day. We don’t know.
We also don’t know how much an account of Josephus (or several of the others you mentioned) is representative of Pilate on a day-to-day basis. It could be that Pilate was a level-headed, fair ruler who just had a bad day and responded brutally, and what gets recorded are the bad things. Of course, I could be wrong. My point is that there is a lot of uncertainty here in assigning the prior probability of Pilate condemning Jesus (versus him not condemning Jesus), P (S_1)/P(S_2) = 0.1. It could be 0.01. It could be 0.2. Or it could be 0.5, if perhaps Pilate was feeling good that day and wanted to toy with the Jewish authorities instead of simply acceding to their request to execute someone they hated.
The Impact of Uncertainty in Priors
This uncertainty in assigning P(S_1) has a great impact on your calculation of the Bayesian odds:
\frac{P(S_1|E)}{P(S_2|E)} = \frac{P(E|S_1)}{P(E|S_2)} \frac{P(S_1)}{P(S_2)}.
In your post, you claim that even if \frac{P(E|S_1)}{P(E|S_2)} = 5 (which we’ll grant as exactly right for the sake of argument), because you assign \frac{P(S_1)}{P(S_2)} = A = 0.1, then multiplying the factors together, we get \frac{P(S_1|E)}{P(S_2|E)} = 0.5. (Note that I have defined the new variable A for the sake of brevity in notation.)
Thus it is twice more likely that S_2 happened compared to S_1. Sounds reasonable!
But this factor of 2 has a huge uncertainty due to the uncertainty of A. If say, we take A = 0.2, then \frac{P(S_1|E)}{P(S_2|E)} = 1. Thus it is now equally likely that S_1 compared to S_2! And taking A = 0.2 is not utterly crazy - we are just saying that Pilate is 83% likely to condemn Jesus, instead of 91% likely.
In fact, if we set conservative limits for A, such as
0.01 < A < 0.5
Then we get
0.05 < \frac{P(S_1|E)}{P(S_2|E)} < 2.5.
In other words, as long as we are taking into account our uncertainties in psycho-analyzing Pilate’s state of mind on that day, affected by environmental and societal factors that we don’t fully have access to, our Bayesian calculations have a huge uncertainty on them - from telling us that it is utterly ridiculous to believe that Pilate could ever be reluctant to condemn Jesus, to telling us that it is 2.5 times more likely than not that he was reluctant to condemn Jesus.
Now if we were to be even more honest and start examining \frac{P(E|S_1)}{P(E|S_2)} which we assigned to be equal to 5 (based on the estimation of 20% probability of the Gospel writers fabricating or mis-remembering the account of the trial), the uncertainty in the calculation goes up even higher. Arguably, one could assign any reasonable value from 0.1 to 10. There is no rigorous argument for assigning it to be 20%. Thus, our bound becomes even looser:
0.0001 < \frac{P(S_1|E)}{P(S_2|E)} < 5
(Note: edited a miscalculation, but conclusion does not change)
As a physicist, a result like the above would raise eyebrows on the soundness of this whole business of trying to micro-analyze the Gospels and assign priors based on limited historical data. Even if I had access to a person whom I knew fairly well, I would not be able to assign A to them with an uncertainty of less than 20-30%. Why do we think we can do so for historical people we know comparatively very little about? At best, our assignment of A or other priors is a reflection of our subjective, personal belief of how probable some reported incident is, affected by our background beliefs and prior commitments. In this case, there’s a wild diversity in such beliefs.
A Note on the McGrews
Note that the McGrews also perform Bayesian analysis in making their case for the Resurrection, but they calculate the probability of general facts, not very specific facts that apply to variable historical situations like Pilate’s state of mind when being dealt with the Jesus case. In addition, the McGrews argue using extremely large or extremely small probabilities, such that a 20-30% uncertainty on their priors would not significantly affect their case. Still, the shakiness of assigning priors based on historical judgment and not more rigorous scientific reasons makes me not take their claim that the Resurrection happened with 0.9999 probability (from their essay in the Blackwell Companion to Natural Theology as literally true.
Edit: Licona and Bayesian Analysis
Thumbing through my copy of Licona’s The Resurrection of Jesus, I noticed that on pages 116-118, Licona basically makes the same argument as I did above, pointing out that historians (he cites David Bartholomew, C. B. McCullagh and even WLC) regard Bayesian analysis of history as subjective due to the inscrutability of priors. He also has a footnote that makes the same exception for the case of the McGrews, who argue that their case can overcome even very small priors.