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)

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.

  • http://www.facebook.com/calumiller Calum Miller

    (Not related to this post, but I couldn’t seem to get the comment section working on the correct one: are you going to be speaking anywhere else in the UK when you come over? I may not be able to get there on 28th but would like to hear you speak.)

    • http://secularoutpost.infidels.org/ Jeffery Jay Lowder

      No, sorry.

  • busterggi

    Does Metacrock believe in all the deities credited with doing miracles because that would be several hundred at least going back thousands of years and all have the same ‘good’ evidence ? Because all are anecdotes, usually urban legend types from friends-of-a-friend, given by believers with personal agendas.
    Or are the only ‘real’ miracles the ones attributed to his deity?

    • Metacrock

      “Does Metacrock believe in all the deities credited with doing miracles
      because that would be several hundred at least going back thousands of
      years and all have the same ‘good’ evidence ?”

      >>>>why do they always assume that one thing can’t be better than another? It’s not necessary to accept all deities. In fact I do actually accept the idea that there’s one and the same reality behind all religions. they are made to appear different by the filter through which our experiences of the divine must pass in order to talk about them, that is to say cultural constructs.

      Neither do I just accept miracles becuase someone talks about them. The assertion that there’s never been any and thus no good evidence is false. there have good scientific evidences. They usually dismissed on the premise that “we didn’t accept this before so it’s ok to dismiss this one.”

      “Because all are
      anecdotes, usually urban legend types from friends-of-a-friend, given by
      believers with personal agendas.”

      >>>>weather or not that may be the case that doesn’t’ preclude good ones.

      “Or are the only ‘real’ miracles the ones attributed to his deity?”

      >>>>we don’t have to know all the real ones if we know one or two. I do know one or two. I don’t know all of them. As I say the true reality behind all religions is the only God there can be; the ground of being.

      Yes I’m a christian for further elaboration please read Doxa, my original website.

      (1) my theology and credo:

      http://www.doxa.ws/Theology/My_theo.html

      (2) Salvation and other faiths:

      http://www.doxa.ws/Theology/salvation_others2.html

  • Metacrock

    I appreciate Jeff’s willingness to make serious answers my article. I agree with a lot of what he says. I will answer it in full on my blog perhaps some time during the coming week if prior committemnts don’t force me to put off to next week. Here I just want make a couple of observations:

    (1) My rendition of the way naturalists think is the result of observing them argue for 16 years (that means thousands of posts). I’ve written over 100,0000 posts on message boards. most of them were answer to atheist posts. I think Jeff is responding t the way he wants to think not way in fact most atheists and naturalists wind up expressing their ideas.

    (2) I think his understanding of the history is incomplete. It’s not just a matter of saying “it’s in doubt,” or “it’s not in duobt.” that’s cover up the fact that it has been in doubt for most of its existence. The popularity it shares now is not due to mathematicians resurrecting it but naturalists and atheists resurrecting it as a tool in arguing about the existence of God. That’s the observation of pre Bayesian Sharon Berstch McGrayne, The Theory that will not die.She wasn’t just talking about prior to world war two. Even after it’s great track record in the war the theorem went back to the back burner among mathematicians until the 90s. Even though it was used by Army Math in the Bombing of Hanoi. Now I’m sure there are mathematicians would would say i’ts resurgence is due to it’s track record, and that may be, but the fact is (according to McGryne) that’s not the main thrust of it’s current popularity.

    Yes Jeff might have a point that it’s lack of polarity with mathematicians in the past may not be a real proof that it’s a problem.

    (3) My overall point is not that Bayes is no good and we should stop using it. It’s proved to be a valid way to proceed with probability and works when it’s used in the right area. But it’s not a major formula that automatically renders everything to which is is applied “probabalized.” Not everything can be transmitted into terms of probability.

    (4) the lynch pen of the argument is to use the theorem and get a probability one must have a prior probability and the accrual of that will determine the whole outcome. We can’t get a prior for God. The whole process turns upon having actuate prior and getting new information that. It’s just like gunner finding his range. That’s probably where Bayes got the idea. His original working method was a lot like a runner finding his range, he turned his back to a table and threw wads of paper over his shoulder until he had a sense of where they would go then he could estimate the odds of hitting the mark. But we can’t get new information about God by conventional means. God is no given in sense data. All the things that people use to try and find a prior for God are all ideologically driven answers in the first place.

    Ok more latter.

    • http://secularoutpost.infidels.org/ Jeffery Jay Lowder

      (1) My rendition of the way naturalists think is the result of
      observing them argue for 16 years (that means thousands of posts). I’ve
      written over 100,0000 posts on message boards. most of them were answer
      to atheist posts. I think Jeff is responding t the way he wants to
      think not way in fact most atheists and naturalists wind up expressing
      their ideas.

      As an autobiographical claim, I don’t doubt that Metacrock’s report of his experiences with atheists on message boards is accurate. But what Metacrock overlooks is that he has not been interacting with the best arguments for naturalism because he has not been interacting with naturalistic philosophers of religion.

      It’s as if Metacrock were an NBA player who declared, “All basketball players from California use strategy X,” but upon closer examination one learns that Metacrock’s experience with California basketball players were limited to high school athletes and that California NBA teams do not use X and instead use Y, a strategy which is not subject to the same vulnerabilities as X.

      Or to use a theological example: theists (rightly, IMO) complain when some atheists caricature cosmological arguments as relying upon the claim that “everything that exists must have a cause.” Theists correctly point out that no theistic philosopher uses an argument based upon such a premise. Metacrock’s defense here seems to be equivalent to an atheist critic of cosmological arguments saying, “Well, I’ve spent 1000s of hours on message boards and theists always use this version of the cosmological argument.” Assume the atheist’s claim is accurate. Even so, the fact is that the atheist is attacking a straw man and ignoring the best versions of the cosmological argument.

      (2) I think his understanding of the history is incomplete. It’s not just a matter of saying “it’s in doubt,” or “it’s not in duobt.” that’s
      cover up the fact that it has been in doubt for most of its existence. …

      Yes Jeff might have a point that it’s lack of polarity with
      mathematicians in the past may not be a real proof that it’s a problem.

      I deliberately said very little about Metacrock’s historical claims about BT for the simple reason that they are logically irrelevant. Assume that Metacrock is correct that, for most of its history, BT was in doubt. Even if that is so, that doesn’t change the fact that BT is now universally or (almost universally) accepted as having been proven, following directly from the Kolmogrov axioms of the probability calculus plus the definition of conditional probability. Metacrock’s historical angle, while interesting, is logically irrelevant to the truth of BT.

      (3) My overall point is not that Bayes is no good and we should stop using it. It’s proved to be a valid way to proceed with probability and works when it’s used in the right area. But it’s not a major formula
      that automatically renders everything to which is is applied “probabalized.” Not everything can be transmitted into terms of probability.

      (4) the lynch pen of the argument is to use the theorem and get a
      probability one must have a prior probability and the accrual of that
      will determine the whole outcome. We can’t get a prior for God. …

      See part 2 of my reply.

      • Metacrock

        “As an autobiographical claim, I don’t doubt that Metacrock’s report of
        his experiences with atheists on message boards is accurate. But what
        Metacrock overlooks is that he has not been interacting with the best
        arguments for naturalism because he has not been interacting with
        naturalistic philosophers of religion.”

        Sure I have. At Perkins (SMU–Graduate school). maybe on a couple of message boards too (academics do trickle in now and then). (Does Dr. Still count as such a philosopher?) I admit message board “debate” (I sue the term loosely) is not representative of the best very often.

        This is a nice long summary I will answer it in a more appropriate venue. maybe the cadre blog or my own. I’m not trying to start a journal war but I think I should answer interest when it’s shown. Taking the time to write so much about my ideas deserves a response.

        btw somewhere I had the idea that Still was an academic philosopher. Now I see looking him up he’s a soft ware guy. That’s ok but I did think he was a philosopher. I actually liked him we were sort of friends many years ago when I first stumbled onto the sec web..

  • Metacrock

    busterggi: “Does
    Metacrock believe in all the deities credited with doing miracles
    because that would be several hundred at least going back thousands of
    years and all have the same ‘good’ evidence ? Because all are
    anecdotes, usually urban legend types from friends-of-a-friend, given by
    believers with personal agendas.
    Or are the only ‘real’ miracles the ones attributed to his deity? ”

    That’s the divide and conquer strategy. It’s illogical to assume that there can’t be one right path becuase there are many paths. the fact of many paths does not prevent one right path. But in fact I have a complex theory about the nature of religious tradition, it invovled God working all cultures. The same reality stands behind all religious traditions. While I believe Jesus is the model and embodiment of the divine, that doesn’t mean that God isn’t doing things through other traditions.

    • busterggi

      “The same reality stands behind all religious traditions. ”

      Then why couldn’t god get his name right between them? If I introduce myself to someone I tell them my name, not another one picked at random.

      “that doesn’t mean that God isn’t doing things through other traditions.”

      Then why does god keep using alias and telling each little group of worshippers to exterminate all the competition?

      Sorry but your answers make no sense.

  • Pingback: Is It a Crock to Use Bayes’ Theorem to Measure Evidence about God? Part 2

  • staircaseghost

    1) looks at linked webpage 2) sees headline “new atheist ideology discredited” accompanied by photograph of Nazi rallies 3) wonders why anyone is treating this guy seriously


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