Last year historian Richard Carrier published On the Historicity of Jesus: Why We Might Have Reason for Doubt. While I haven’t read it (and therefore don’t plan on critiquing it now), it is on my reading list. As a grad student who messes around with Bayes’ Rule, it’s interesting to see its applications. But I’m especially skeptical of Carrier’s book because, while Bayes’ Rule is right, we can use it to make some very wrong assumptions. And we can create some very contradictory states of the world.

Again, while I haven’t read Carrier’s book, I can probably safely assume his equation looks something like this:

Although I could be wrong wrong, and if I am please correct me. I’m assuming he’s using this equation because it posits a dichotomy; either Jesus existed or he did not (that’s the bottom part of equation). Basically, applied to the historicity of Jesus, this equation determines the probability of Jesus existing given no historical evidence for his existence. We can work this out quite easily, but we don’t have to because I’m certain we’d find the answer is essentially zero. This is probably the kind of reasoning Carrier uses in his book.

And to stress yet a third time, this is not a critique of his book because I haven’t read it. But rather, this post is to serve as a warning to you mathematicians out there who want to use these equations as proof. It can be very misleading if you’re not careful.

To put this into another context let’s look at the bible. There are indeed many instances of the bible getting something right, be it moral, ethical, historical, or even scientific (Jeremiah 33:22, for example, or incalculable sand and stars). We can determine the likelihood that god exists given these predictions or estimations. If we ignore what the bible got wrong, we can very easily prove the bible is very likely to be inspired by god. Essentially we can prove we live in a world where Jesus exists with Bayes’ Rule if we’re willing to go down that rabbit hole.

I hope you can see the contradiction. Bayes’ Rule can simultaneously be used to prove that Jesus didn’t exist and that Jesus did exist at the same time! But the good news is that once we do that we’re left right where we started; either Jesus existed or he didn’t. Both can’t be true at the same time, no matter what Bayes’ Rule proves. So the moral is: Be very careful with Bayes’ Rule.

Eventually I’ll get around to Carrier’s book. Maybe he did some more advanced math, making this article even less applicable to him. And if that’s the case, I’m sure I’ll enjoy reading and checking his work.