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.

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About Jeffery Jay Lowder

Jeffery Jay Lowder is President Emeritus of Internet Infidels, Inc., which he co-founded in 1995. He is also co-editor of the book, The Empty Tomb: Jesus Beyond the Grave.

  • Bradley Bowen

    Does Fisher give any reason or argument for her claim that BT is irrelevant to history?

    I took a glance at the article, and did not see a reason given.

  • Hiero5ant

    This comment has been removed by the author.

  • Hiero5ant

    It is "relevant" only in the most rarefied sense imaginable, just as propositional/polyadic logic is "relevant" to history or science etc.

    Both are purely formal, normative, ideal reconstructions of how reasoning ought to operate. But when was the last time you read a biology paper that used formal, deductive logic? Or thought to yourself that one could be improved by presenting its hypothesis in Standard Form?

    Rather, these formalisms seem to function as crutches propping up otherwise weak arguments. There is nothing in this silly fad of using pseudo-mathematical rigor other than ornamenting one's views with "the jargon of authenticity", burying them in arcane squiggles to give an unearned appearance of Scientific Certitude. This goes for Plantinga, Carrier, and the McGrews: there is nothing in their arguments using Bayes-squiggles that could not be stated equally as well — if not better — in plain english.

  • Jeffery Jay Lowder

    Bradley — If you follow the link to Fisher's article and then scroll down to the comments, you'll find where I and one other person have exchanged replies with Fisher and R Joseph Hoffmann about the relevance of BT to history.

    Hiero5ant wrote:

    Rather, these formalisms seem to function as crutches propping up otherwise weak arguments.

    This is a sweeping generalization that requires supporting evidence. I do not find such evidence in your post.

  • Hiero5ant

    This comment has been removed by the author.

  • Hiero5ant

    "Evolution only has an indirect concern for truth, because the focus of natural selection is adaptive behavior, not true belief. But since there is only one way to have true beliefs and many, many ways to have false-but-adaptive belief/behavior pairs, it is unlikely that unguided evolution would have given us true beliefs. Therefore, believing in unguided evolution is self-defeating."

    See? I've just presented Plantinga's argument in three sentences, in a form that any 12 year old should be able to understand. (And refute, if they understand anything about how actual biology works.)

    You can't convince me that the presentation in terms of bayes-squiggles is anything other than the old obscurantist trick straight out of the 60s and 70s YEC playbook: snow them under with sciency-sounding "it's just so improbable" language so that the non-mathematically inclined pew potatoes will nod their heads and think "well, he must be onto something… after all, he proved it — WITH NUMBERS AND EVERYTHING!!"

    I think the proper burden of proof here is to produce one good argument from philosophy or history that requires the formal use of Bayes, and cannot be stated at least as well in plain English.

  • Bradley Bowen

    Jeff – I see your comments below the Fisher article. And I have joined that discussion with my own comments.

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