Richard Carrier is well known for his advocacy of the use of the Bayes’ theorem in historical Jesus studies. (Find the link to Bayes’ Theorem for Beginners here or go direct to the pdf article here.) Carrier has enumerated its advantages, and I highlight the ones that are my own personal favourites (all quotations are from the pdf article, Bayes’ Theorem for Beginners):
1. Helps to tell if your theory is probably true rather than merely possibly true
2. Inspires closer examination of your background knowledge and assumptions of likelihood
3. Forces examination of the likelihood of the evidence on competing theories
4. Eliminates the Fallacy of Diminishing Probabilities
5. Bayes’ Theorem has been proven to be formally valid
6. Bayesian reasoning with or without math exposes assumptions to criticism & consequent revision and therefore promotes progress
The reason 2, 3 and 6 stand out for me is because they are at the heart of my past criticisms of historical Jesus studies that typically begin with assumptions of historicity, and avoid (or fail to comprehend or even attack) alternative explanations that do not support those assumptions. One does not really need Bayes theorem to expose your assumptions to criticism, but the formality of this method does potentially encourage stronger awareness of where we may be failing to do this adequately.
My first reaction on hearing of Bayes’ theorem being applied to history was to think that it was probably just another pseudo-scientific attempt to make a non-science field of investigation sound scientifically certain. But Carrier seeks to calm such fears:
One common objection to using Bayes’ Theorem in history is that Bayes’ is a model of mathematical precision in a field that has nothing of the kind. This precision of the math can create the illusion of precision in the estimates and results. But as long as you do not make this mistake, it will not affect your results.
The correct procedure is to choose values for the terms in the equation that are at the limit of what you can reasonably believe them to be, to reflect a wide margin of error, thus ensuring a high confidence level (producing an argument a fortiori), regardless of any inexactness in your estimations.
That’s okay, I think.
But I like his reassurance that complex mathematics is not necessary even more:
1. You don’t have to use scary math to think like a Bayesian, unless the problem is highly complex, or you want clearer ideas of relative likelihood. For instance…
2. Easy Case of Rejection: If you estimate that the prior probability of h must be at least somewhat low (any degree of “h is unlikely, given just b”), and you estimate the evidence is no more likely on h than on ~h, then h is probably false (“h is unlikely even given e”).
EXAMPLE: Talking donkeys are unlikely, given everything we know about the world. That there would be a story about a talking donkey is just as likely if there were a real talking donkey than if someone just made up a story about a talking donkey. Therefore, e is no more likely on h (Balaam’s donkey actually spoke) than on ~h (Someone made up a story about Balaam’s donkey speaking), and h (Balaam’s donkey actually spoke) is already initially unlikely, whereas ~h (Someone made up a story about Balaam’s donkey speaking) is initially quite likely (since on b we know people make up stories all the time, but we don’t know of any talking donkeys). Therefore, we can be reasonably certain that Balaam’s donkey didn’t talk. Note how this conclusion is worldview- independent. It follows from plain facts everyone can agree on.
But I like Carrier’s assurance that using Bayes’ theorem correctly means being careful to avoid logical fallacies. (Why should Bayes’ theorem be necessary for this? But practical experience teaches us that every tool helps.)
The Fallacy of Confusing Evidence with Theories:
A single example will suffice: William Lane Craig frequently argues that historians need to explain the evidence of the empty tomb. But in a Bayesian equation, the evidence is not the discovery of an empty tomb, but the production of a story about the discovery of an empty tomb. That there was an actual empty tomb is only a theory (a hypothesis, i.e. h) to explain the production of the story (which is an element of e). But this theory must be compared with other possible explanations of why that story came to exist (= ~h, or = h2, h3, etc.), and these must be compared on a total examination of the evidence (all elements of e, in conjunction with b and the resulting prior probabilities).
Hence a common mistake is to confuse actual hypotheses about the evidence, with the actual evidence itself (which should be tangible physical facts, i.e. actual surviving artifacts, documents, etc., and straightforward generalizations therefrom).
Again, one does not need Bayes’ theorem to sift evidence from theories. But it would be interesting to see what probability results are arrived at when one does this as a theorem exercise.
Another nice-looking section in Carrier’s discussion is his discussion of several common criteria used in biblical studies, and how to think these through clearly by means of syllogisms.
EXAMPLE 3: The Criterion of Embarrassment : “Since Christian authors would not invent anything that would embarrass them, anything embarrassing in the tradition must be true.”
Major Premise 1: Christians would not invent anything that would embarrass them.
Minor Premise 1: The crucifixion of Jesus would embarrass Christians.
Conclusion 1: Therefore, Christians did not invent the crucifixion of Jesus.
Major Premise 2: A report is either invented or it is true.
Minor Premise 2 (= Conclusion 1): The crucifixion of Jesus was not invented.
Conclusion 2: Therefore, the crucifixion of Jesus is true.
Another way to test rules of inference is to try them out on contrary cases. For example:
Major Premise 1: Cybeleans would not invent anything that would embarrass them.
Minor Premise 1: The castration of Attis would embarrass Cybeleans.
Conclusion 1: Therefore, Cybeleans did not invent the castration of Attis.
Major Premise 2: A report is either invented or it is true.
Minor Premise 2 (= Conclusion 1): The castration of Attis was not invented.
Conclusion 2: Therefore, the castration of Attis is true.
RESULT: This is obviously not a credible conclusion. We have no good reason to believe there was ever an actual Attis who was castrated and it is commonly assumed the story was invented for some particular symbolic reason. The same, then, could be true of the crucifixion of Jesus. Tacitus reports that the castration of Attis was indeed embarrassing (it is grounds for his disgust at the religion), yet the castration of Attis is not a credible story, therefore the criterion of embarrassment is in some manner fallacious.
An example within the Christian tradition is the astonishing stupidity of the Disciples, especially in the earliest Gospel of Mark. Their depiction is in fact so unrealistic it isn’t credible (real people don’t act like that), which means Mark (or his sources) invented that detail despite its potential embarrassment. Hence the flaw in the criterion of embarrassment is in assuming that historical truth is the only factor that can overcome the potential embarrassment of some reported detail, when in fact moral or doctrinal or symbolic truth can also override such concerns.
This particular illustration tells me the debate is not between two sides with an equal interest in the facts. I’m reminded the first day I read a breaking news story claiming that a boatload of refugees had threatened to throw their children overboard unless they were allowed entry into Australia. My immediate response was that the story was bollocks, since I know parents do not behave like that. But there was enough prejudice nation-wide for the story to take hold — trusted political leaders and news sources repeated it as if it were a fact — and it eventually took a government inquiry to put the story to rest.
So maybe an advantage of working with Bayes theorem is that it assists both sides to be conscious of and factor in alternative possibilities and probabilities.
For example, Dennis MacDonald argues this attribute emulates the equally- unrealistic stupidity of the crew of Odysseus and thus stands as a marker of the same things that their stupidity represented. That may be true. But I also argue it furthers a literary theme found throughout Mark of the Reversal of Expectation. Thus everything that seems embarrassing in Mark might be an intentional fabrication meant to convey a lesson. Mark echoes the gospel theme that “the least shall be first” in his construction of all his stories: although Jesus tells Simon Peter he must take up the cross and follow him, Simon the Cyrenean does this instead; although the pillars James and John debate who will sit at Jesus’ right and left at the end, instead two nameless thieves sit at his right and left at the end; although the lofty male Disciples flee and abandon Jesus, the lowly female followers remain faithful, and as a result the least are the first to discover that Christ is risen; and while Mark begins his Gospel with the “good news” of the “voice crying out” of the lone man who boldly came forward as a “messenger who will prepare our way,” he ends his Gospel with several women, fleeing in fear and silence, and not delivering the good news, exactly the opposite of how his book began. So since details that seem embarrassing in Mark might serve his literary intentions, we can’t be certain they’re true.
This final example exposes the importance of testing criteria by comparing them with alternative theories of the evidence. You must ask yourself, what if I’m wrong? What other reasons might Christians have for inventing potentially embarrassing stories? And how do those reasons compare with the theory that they reported embarrassing stories because they were true? Bayes’ Theorem suits exactly such an analysis.
Each time I look at Bayes’ theorem and at what Carrier says about it, I do find something more of interest in it. Maybe it should be seen as something of a goad whose purpose is to keep both sides in a debate honest.
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