Understanding the Spirit vs. the Letter of Probability

My apologies for there being so little activity on Civitas Humana for a long while now. I have been insanely busy and stressed lately (both professionally and personally), and I have only recently been able to catch up with blogging.

I’ll begin pumping some fresh blood into Civ by discussing Bayes’ theorem, the resurrection of Jesus, and why I think that, even with a non-zero prior (which is still very, very low) for the resurrection event, Paul’s letters and the Gospels are far too weak of consequent evidence to offset more probable (naturalistic or mundane) explanations for the same data.

Over a decade ago (March 2006) secular New Testament scholar Bart D. Ehrman debated Christian philosopher and theologian William Lane Craig about the evidence for the resurrection of Jesus (the transcript of the debate can be read here). Overall, the debate left me with the impression that Ehrman made a better case for naturalistic or non-paranormal explanations being more probable than a veridical resurrection event, with regards to the origin of the resurrection belief among Jesus’ disciples and the first generation of Christians. But there was one area where I think Craig scored a technical, though relatively minor point against Ehrman (as will be discussed below), and this was with regards to how Ehrman was defining a miracle event and conflating prior probability with posterior probability.

Lowder’s Summary of Craig’s First Rebuttal

Jeff Lowder on the Secular Outpost has made a useful summary of Craig’s critique of how Ehrman was defining a miracle event, and the arguments Ehrman had presented (in earlier publications) for why historians cannot argue that a miracle is the most probable explanation for a past event. This summary can be read in Lowder’s post “William Lane Craig’s Critique of Bart Ehrman on the Probability of Miracles.” Since the ensuing discussion involves Bayesian reasoning, you can read my essay “History, Probability, and Miracles” for a basic overview of how Bayesian logic works, if you are unfamiliar with the theorem.

Lowder begins by listing two published statements by Ehrman, which were quoted by Craig during the debate (bolding is my own):

(1) “Because historians can only establish what probably happened, and a miracle of this nature is highly improbable, the historian cannot say it probably occurred.”
(The Historical Jesus, part 2, page 50)
(2) “Since historians can establish only what probably happened in the past, they cannot show that miracles happened, since this would involve a contradiction — that the most improbable event is the most probable.”
(The New Testament: A Historical Introduction, page 229)
In his response to these statements of Ehrman, Craig critiques his line of reasoning by arguing that Ehrman is conflating prior probability with posterior probability. The odds that a given individual may resurrect from the dead could, indeed, be very, very low. But if there is very, very good evidence that such a resurrection event has occurred, it may offset the low prior, and even outweigh alternative explanations, to degree such that Pr (R/B & E) > 0.5 (perhaps even by a wide margin, e.g., +0.9).
Here is what Craig states in his own words (bolding is my own):
“In other words, in calculating the probability of Jesus’ resurrection, the only factor he [Ehrman] considers is the intrinsic probability of the resurrection alone [Pr(R/B)]. He just ignores all of the other factors. And that’s just mathematically fallacious. The probability of the resurrection could still be very high even though the Pr(R/B) alone is terribly low.”
Lowder likewise offers his own interpretation of Ehrman’s two quotations, and here is what he states regarding the first:
“I am inclined to interpret (1) as the following claim: (1′) Pr(R/B) is so low that it is impossible, even in theory, for there to be sufficient evidence to confer a high final epistemic probability on R, i.e., Pr(R/B & E) > 0.5.”

I would argue that to describe a miracle as an event that cannot be probable, even in theory, one would need to assign its prior probability a value of zero. And this is the same conclusion that Lowder reaches, when he states (bolding is my own):

The only way to reconcile (1′) with BT would be to assign Pr(R/B) a value of zero. If Pr(R/B) = 0, then it follows from BT that Pr(R/B&E;)=0. So, on the basis of (1) alone, as Craig has quoted Ehrman, I think it is premature to assume that Ehrman ‘just ignores all of the other factors.’ Maybe he does do that, but the quotation provided in (1) doesn’t show that. What I can say is that either Ehrman ignores all of the other factors or Ehrman assumes that historians must assign Pr(R/B) a value of zero. If the latter, then I think that is false.”

With regards to Ehrman’s second quotation, Lowder briefly states:

“Turning to (2), I don’t have much to say, other than I think Craig is 100% correct when he says that Ehrman ‘Confuses Pr (R/B & E) with Pr (R/B).’”

My Thoughts on Ehrman’s Quotes

At the end of this essay, I will make some suggestions for improving Ehrman’s arguments (which in spirit I think are correct, even if they may be formally invalid at parts). That said, I agree with Lowder’s conclusions on both accounts, for at least three reasons:

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Jeff Lowder, “The VICTIMs of Christian Apologetics”

I’ve been taking a break from blogging lately, in order to focus on my dissertation work, but a recent counter-apologetics video was posted that is worth mention. I have been co-authoring a critical review of apologists Norman Geisler and Frank Turek’s I Don’t Have Enough Faith to Be an Atheist, with Jeff Lowder, founder of the Internet Infidels and blogger at the Secular Outpost.

Both Geisler and Turek repeat the slogan “the atheist must borrow X from theism” (e.g., logic, morality, agency, mathematics, etc.) in a dozen of variations, all making assertions about metaphysical issues that allegedly cannot be explained under the hypothesis of naturalism, and require the existence of God. Of course, actual naturalist philosophers, such as Jack Ritche in Understanding Naturalism, have also thought about such things, and written philosophical resources extensively discussing issues of physicalism, logic, and value. But what is nice is that Lowder provides a detailed, point-by-point refutation against arguments of this sort in a two and half hour video, based on slides he used to prepare for a public debate with Turek.

A lot of the things that Lowder discusses have overlap with my metaphysics series–“Thinking about the ‘Metaphysics’ in Metaphysical Naturalism”–here on Civitas Humana, where I have discussed issues of cosmology, agency, and value from a secular and naturalistic point of view. Lowder’s video supplements this material quite nicely, so check it out (and take notes)!

-Matthew Ferguson