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A Mathematics of History?

Before diving into the contents of Richard Carrier’s On the Historicity of Jesus (OHJ) I need to say a bit about the method he uses to organize his conclusions. Prior to this book Carrier wrote a book called Proving History. It was entirely concerned with what methodology he would be using to answer the question of Jesus’s historicity. It included a primer on historical inquiry in general, a critique of the methods biblical scholars use to “extract” historical information about Jesus from the gospels, and a defense of using Bayes’ Theorem in historical inquiry.

The Critique
Biblical scholars for some time have used various criteria which they claim allows them to separate the fictional elements of the gospels, added by the church, from the historical elements. Or, at least they claim it increases the likelihood that some element is historical. For example the criterion of embarrassment says if an element of the story would be embarrassing to the church it is not likely they would have invented it.

The criteria have come under strong criticism within the field. The logic of them often is not sound and scholars apply them in situations where they aren’t applicable, or apply them inconsistently. Indeed the history of their use is not very encouraging as each scholar who sets out to paint a picture of “the true historical Jesus” comes back with a different picture. Carrier cites a lot of this critical scholarship and adds his own critique. I’ll just give one example and summarize the analysis given by Carrier (which I agree with).

One of the supposed bedrock truths scholars have extracted from the gospels is that Jesus was baptized by John the Baptist. The criterion of embarrassment is invoked. Here is Jesus being portrayed as in some sense subordinate to John. In addition John’s baptism was for the remission of sin and wasn’t Jesus supposed to be without sin? Thus, the reasoning goes, this must have been something everyone knew about and it just couldn’t be avoided. Mark was written first and Matthew and Luke copied much of their material from him (often word for word, or nearly so). Matthew and Luke have tinkered with this story to make it less embarrassing.

It is a reasonable argument but there are several problems. The later gospel authors seem to have no compunction about altering stories to fit their agendas. They omit elements when it suits them. Why would Mark be any different? If he was embarrassed by this story why did he include it in the first place? In fact Mark shows no signs of embarrassment at all in telling this story. Let’s not forget that Mark was written roughly 35 years after Jesus would have lived. So are we to imagine the story of Jesus being baptized by John circulated for three and a half decades and no one noticed it was embarrassing? No one had already tinkered with the story before it reached Mark (and thus he would have already been reporting the apologetic in his gospel)? Suddenly, after Mark wrote his gospel, everyone finally noticed it was embarrassing and scrambled to explain it!

When you think it through it is a rather silly scenario. In fact, the actual sequence of events suggests quite the opposite of what the biblical scholars have concluded. Mark being completely unembarrassed by the story followed by signs of embarrassment after Mark wrote suggests that no one had heard the story before because Mark invented it! Either that or it simply wasn’t embarrassing to those that came before, but if that is case the criterion of embarrassment doesn’t apply!

I’ve gone one far longer than I intended so I’ll just leave it at that. I’ll just say I think Carrier, and the critics from within the field, have successfully called into question the validity of criteria based methods.

Bayes’ Theorem
The challenge facing anyone examining a complex historical scenario is this. Each individual artifact or document could have had several causes and in most cases you cannot rule out all but one of them. So how do you evaluate your overall thesis if each piece of evidence only partially supports it? Also, it will often be the case that some pieces of evidence are more likely on one theory but other pieces suggest another (while not ruling out the first one). Clearly what is needed is some way to state how much weight each piece of evidence carries, and by how much it favors one theory over another. Finally, there needs to be some way to combine those individual judgments in a fair and rigorous fashion.

That’s where Bayes’ Theorem comes in. Bayes’ Theorem is an equation in probability theory specifically geared towards comparing one hypothesis with another (or, rather, one hypothesis with its negation). If we can state our evaluations of the evidence in terms of probabilities (or ratios of probabilities) then we can use Bayes’ Theorem to combine them, giving us a number at the end that states how likely it is the theory we are considering is the cause of the evidence we have. Obviously that number is entirely dependent on how sound our evaluations were but at least it gives us a principled way to combine them while at the same time allowing others to see how we’ve weighted the evidence.

Carrier defends the use of Bayes’ Theorem in Proving History and responds to most of the common objections people advance. I’m not going to spend a lot of time on that material. I think it is an interesting subject and I may discuss it during the course of this series but for now I think it is enough to say that using Bayes’ Theorem seems reasonable enough. In OHJ Carrier simply tallies how strongly he thinks a piece of evidence favors one theory or the other, e.g. 5/4 in favor of mythicism, or 1/1 if it doesn’t favor either, etc. To combine them one simply multiplies the individual factors together to get a final ratio that tells you which theory is indicated by the evidence and how strongly.

So what do those ratios represent? I like to think of it in terms of the scientific method we all learned in school. The idealized scientific method is often presented as hypothesize, enumerate predictions, gather data, reach conclusions. The ratios represent the ‘enumerate predictions’ part of this picture. What we are doing is taking a hypothesis as a given, i.e. assuming it is true, and then asking ‘of all the possible worlds that could result with this hypothesis being true, what percentage of them will contain the piece of evidence we are evaluating?’ Then we do the same for the hypothesis we are comparing it to (or the combination of all hypotheses that aren’t the first one). Dividing the first by the second gets us our ratio. So if our ratio is 2/1 in favor of historicity, for example, we are saying a historical Jesus will produce the evidence twice as often as a mythical one will.

It should be noted that there is a certain level of generality involved here. If examining a document for instance, we aren’t asking how often that specific document with exactly the words it contains will arise. We are asking instead about general features of the document. Carrier mounts a defense of this approach in Proving History and I think it is generally sound, however I would point out it introduces another place where subjectivity can enter the picture. Which features are important and which features can be abstracted away?

There is one more feature of Bayes’ Theorem that must be mentioned. When you use it you must estimate the prior probability of the hypothesis you are testing. That is, before you even begin looking at evidence how likely is your hypothesis, based on your more general knowledge of the world? Carrier uses a scale, developed by Rank and Raglan, of traits often found in hero tales, on which Jesus scores very high. Though historical people sometimes have several of the traits, that arise in legends about them, no historical individuals score nearly as high as Jesus and the high scoring mythical beings. From this Carrier justifies starting with a prior probability that Jesus was historical of 33% (i.e. 1 in 3, or 2/1 against).

I’m not going to examine the issue of prior probability very closely at the moment. Nor will I be relying on his 33% estimate. The more important question is which hypothesis does the evidence favor, and by how much? If the evidence favors one hypothesis much more strongly than the other, then it won’t really matter much what prior you started with; it will be overwhelmed by the evidence. If the evidence is fairly close, then determination of the prior will become more important and can be pursued then.

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