Is Bayes’s Theorem Irrelevant to History?
On his blog, R. Joseph Hoffmann published an essay by Stephanie Louise Fisher which, among other things, argues that Bayes’s theorem (hereafter, BT) is irrelevant to historical scholarship. In her words, BT is “completely inappropriate for, and unrelated to historical occurrence and therefore irrelevant for application to historical texts.”
Whenever a historian argues that such-and-such an event probably did or did not happen, the historian is implicitly appealing to probability. For example, suppose that B is our relevant background knowledge and we have some historical text T which says that event E occurred. T’s report that E occurred does not entail that E occurred. T could report E and E could have occurred, but it also possible that T could report E and E did not occur. At best, then, T’s report is simply evidence that E occurred.
In mathematical notation, Pr(x | y) is the probability of x conditional upon y. So when we say T’s report is simply evidence that E occurred, we ordinarily mean that Pr(E | T & B) > Pr(E | B), i.e., E is more probable conditional upon T and B than on B alone. In other words, we are implicitly relying upon the concept of conditional probability. Furthermore, as is well known, BT can be derived from the axioms of the probability calculus and the definition of conditional probability. So BT is relevant to history in this sense.
In order to prevent some potential misunderstandings, I want to clarify two points.
1. I am not a mythicist; in fact, I have defended the historicity of Jesus elsewhere. I mention this solely because the context for Fisher’s essay is a response to Richard Carrier, who apparently is now a mythicist. My interest in the applicability of BT to historical claims is purely logical, not based upon some agenda to promote mythicism.
2. There are many interpretations or theories of probability; BT is compatible with all of them. Perhaps (?) one reason Fisher objects so strongly to the use of BT in history is the mistaken assumption that BT presupposes the frequency interpretation of probability, i.e., BT requires empirical data about the relative frequency of certain types of events. That assumption is false, however. BT is also compatible with the epistemic interpretation of probability, which is better suited for the assessment of historicity.