Is It a Crock to Use Bayes’ Theorem to Measure Evidence about God? Part 1

Over at the Christian Cadre, “Metacrock” has written a post entitled, “Bayes Theorum [sic] and Probability of God: No Dice!” Metacrock makes a number of points regarding the use of Bayes’ Theorem (BT) with evidence about God’s existence. I want to comment on many of those points.

It is understandable that naturalistic thinkers are uneasy with the concept of miracles.

I think I understand the point that Metacrock is trying to get across, but I disagree with this sentence as written. Metaphysical naturalists are not literally “uneasy” with the concept of miracles any more than they are “uneasy” with, say, the concept that the evil lord Sauron is a threat to Middle Earth. The point is that calling both things concepts means just that: they are concepts. Nothing more, nothing less. Being a “concept” is neutral about whether the concept is about something real (as theists believe God is) or something fictional (which everyone knows Sauron is).

I think the point that Metacrock is trying to make is that, if we define “miracle” as an event which requires a supernatural explanation, then by definition a miracle is logically incompatible with metaphysical naturalism, which denies the existence of all supernatural beings, including God. So naturalists can’t remain naturalists and believe a miracle has occurred. The options seem to be: (1) give up naturalism, (2) deny the event took place at all, or (3) agree the event did take place, but deny it has a supernatural explanation.

So should we all be watchful not to believe too quickly because its easy to get caught up in private reasons and ignore reason itself. Thus has more than one intelligent person been taken by both scams and honest mistakes. By the the same token it is equally a danger that one will remain too long in the skeptical place and become overly committed to doubting everything. From that position the circular reasoning of the naturalist seems so reasonable. There’s never been any proof of miracles before so we can’t accept that there is any now. But that’s only because we keep making the same assumption and thus have always dismissed the evidence that was valid.

I agree with everything Metacrock writes here, with two important exceptions. First, that metaphysical naturalists do, in fact, reason in the way he describes. Second, that metaphysical naturalists rely upon “circular reasoning” to avoid the conclusion that a miracle has occurred. It is true, of course, that some individual metaphysical naturalists have made fallacious inferences about miracles. The same could be said about some individual theists. But so what? Metacrock presents absolutely no evidence to justify the assumption that such individuals are representative of the position they represent. Metacrock is attacking a straw man of his own creation.

At this point most atheists will interject the ECREE issue (or ECREP—extraordinary claims require extraordinary evidence, or “proof”). That would justify the notion of remaining skeptical about miracle evidence even when its [sic] good.

With all due respect to Metacrock, this statement suggests he does not understand ECREE. As I have explained elsewhere, the best interpretation of ECREE is the Bayesian interpretation. According to BT, the final probability of a hypothesis is determined by two other values: the prior probability of a hypothesis and the hypothesis’s explanatory power. Now explanatory power is, by definition, a measure of how well a hypothesis “predicts” (i.e., make probable) the data.

Metacrock’s statement, “That would justify the notion of remaining skeptical about miracle evidence even when its [sic] good,” is ambiguous. “Good evidence for a miracle” could mean one of two things. First, it could mean the miracle hypothesis has high explanatory power with respect to the relevant data. Second, it could mean that, compared to rival explanations, the miracle hypothesis has the greatest overall balance of prior probability and explanatory power (and so the miracle hypothesis is probably true).

Depending on the miracle claim, metaphysical naturalists may agree with the first interpretation. It may indeed be the case that a particular hypothesis about miracles may have strong explanatory power but such low prior probability that the resulting final probability is low. (In other words, the miracle probably never happened.)

But, as pointed out earlier, as long as a person remains a metaphysical naturalist, the second interpretation is not an option. This seems to be what Metacrock has in mind. But notice that to write as if there is “good” evidence for one or more miracles is to beg the question. In fact, he writes in an unnecessarily partisan manner, as if it were only “atheists” who assign a low prior probability to miracles. That is, of course, false. Many theists can and do assign low prior probabilities to all sorts of miracles, such as miracles which are seen as “competing” with the claims of their own faith tradition or religious community. (For example, orthodox Christians don’t hesitate to assign a low prior probability to the Mormon claim that the angel Moroni revealed the Book of Mormon to Joseph Smith on golden tablets.) Even no less an authority than Christian philosopher Stephen T. Davis has written about the “shocking” nature of the Resurrection.

Moving on:

There are many refutations of this phrase, which was popularized by Karl [sic] Sagan. One of the major problems with this idea is that atheists rarely get around to defining “extraordinary” either in terms of the claim [sic]

Irrelevant. The fact that many atheists do not define “extraordinary” does not in any way “refute” ECREE.

(why would belief in God be extraordinary? 90% of humanity believe in some form of God) [1]

Again, with all due respect to Metacrock, this statement shows that Metacrock doesn’t understand ECREE. We don’t determine whether a belief is extraordinary by measuring the percentage of people who hold that belief. Rather, ECREE is epistemic in nature; it has to do with what we would expect to be the case based upon our background knowledge.

The slogan ECREE is usually said to be based upon the Bayes [sic] completeness theorem.

No, this isn’t true. ECREE is often said to be best interpreted by BT, not “Bayes [sic] completeness theorem.”

Sagan popularized the slogan ECREE but the mathematical formula that it is often linked to (but not identical to) was invented by the man whose name it bears, working in the seventeen forties but then he abandoned it, perhaps because mathematicians didn’t like it. It was picked up by the great scientist and atheist Laplace and improved upon.[2] This method affords new atheism the claim of a “scientific/mathematical” procedure that disproves God by demonstrating that God is totally improbable. It is also used to supposedly disprove supernatural effects as well as they are rendered totally improbable.[3]

It is often assumed that the theorem was developed to back up Hume’s argument against miracles. Bayes was trying to argue against Hume and to find a

mathematical way to prove that there must be a first cause to the universe.[4] Mathematicians have disapproved of the theorem for most of its existence. It has been rejected on the grounds that it’s based upon guesswork. It was regarded as a parlor trick until World War II then it was regarded as a useful parlor trick. This explains why it was strangely absent from my younger days and early education as a student of the existence of God. I used to pour through philosophy anthologies with God articles in them and never came across it. It was just part of the discussion on the existence of God until about the year 2000 suddenly it’s all over the net. It’s resurgence is primarily due to it’s use by skeptics in trying to argue that God is improbable. It was not taught in math from the end fo [sic] the war to the early 90s.[5]

There are several problems with this account, but I will mention just the two most important.

First, this history of BT is misleading insofar as it suggests that BT is in doubt. It isn’t. BT follows from the Kolmogorov axioms of the probability calculus. To be sure, there are disagreements over the proper interpretation of probability (such as frequency vs. epistemic), but those issues do nothing to undermine the truth of BT.

Second, if someone read nothing about BT except the paragraphs quoted above, they would get the impression that BT is used solely by atheists and skeptics. That is nonsense! BT is used around the world every day on a variety of statistical problems that have nothing whatsoever to do with God, miracles, or the philosophy of religion. Furthermore, even within the philosophy of religion, it’s not just atheists who employ BT.

To cite the most obvious counter-example, has Metacrock never heard of Richard Swinburne or read any of his numerous books which use BT to defend Christian theism? (See here, here, here, here, here, here, and here.) Or seen Tim and Lydia McGrew’s impressive use of BT to argue for the Resurrection in The Blackwell Companion to Natural Theology? (See here.)

Metacrock is simply “barking up the wrong tree” on this one. I cannot think of any way to salvage his point.

(to be continued)