Bayesian arguments: Swinburne, Collins, and the McGrews

In a previous thread, Caleb O wrote:

I think I am one of those atheists who is slightly impressed with Bayesian arguments for the existence of God (Swinburne, Collins). At least they appear to be more successful than deductive arguments. What are these “ridiculously ill-supported assumptions” you speak of?

Now before I address the specific question, I should back up and say that Bayesian arguments–and probabilistic arguments in general–aren’t fundamentally different from traditional deductive arguments for the existence of God. Probabilistic arguments are really a kind of deductive argument, but one where you’re reasoning about probabilities. Alternatively, deductive can be seen as a special kind of probabilistic argument where all the probabilities are either 1 or 0.

Either way you see it, Bayesian arguments and deductive arguments are alike in that they’re only as good as their premises. My suspicion of Bayesian arguments isn’t that there’s anything inherently wrong with them. Rather, the issue is this: People are rarely impressed with deductive arguments simply because they’re deductive. Deductive arguments with utterly ridiculous premises tend to get laughed at.

Bayesian arguments, though, are unusual enough that to some extent you can impress people with them just because they’re Bayesian. This means when you hear about an awesome Bayesian argument, you have to wonder if there’s any reason why whoever is promoting it, aside from the fact that it’s Bayesian. It gives Christian apologists an incentive to dress up ridiculous arguments in Bayesian terms.

So I’m just going to go through and point out some of the most glaring issues with the most prominent attempts to give a Bayesian case for the existence of God. The original defender of the Bayesian approach to arguing for the existence of God is Richard Swinburne. With Swinburne, he basically admits that the evidence in favor of God isn’t all that great, and for the balance of probability to favor God, Swinburne feels the need to totally dismiss the problem of evil. And unfortunately, he takes the unconvincing and frankly offensive approach of trying to suggest compensating goods that might have come out of particular evils (including, notoriously, saying that the Holocaust gave the Jews an opportunity to display courage).

Robin Collins has risen to prominence recently for his Bayesian formulation of the fine-tuning argument. As with Swinburne, the handling of the problem of evil is sloppy, though in a different way: Collins focuses on a comparison of theism to what he calls the “naturalistic single universe” hypothesis (NSU), and rests his case on claiming that even if the problem of evil is some evidence for NSU over theism, fine-tuning is even stronger evidence in the other direction. He ignores the problem (pointed out by Hume) that even if we accept the argument from design, the problem of evil would still favor the hypothesis of an amoral or indifferent designer over traditional theism.

Collins also dismisses a number of versions of the multiverse hypothesis as “speculation,” though he never explains what he means by this or why the God hypothesis counts as more than mere speculation.

Tim and Lydia McGrew have also gained a bit of notoriety for taking a Bayesian approach to defending the resurrection of Jesus. Yet here are the assumptions they make (with scarcely any argument):

Our argument will proceed on the assumption that we have a substantially accurate text of the four Gospels, Acts, and several of the undisputed Pauline epistles (most significantly Galatians and 1 Corinthians); that the Gospels were written, if not by the authors whose names they now bear, at least by disciples of Jesus or people who knew those disciples – people who knew at first hand the details of his life and teaching or people who spoke with those eyewitnesses – and that the narratives, at least where not explicitly asserting the occurrence of a miracle, deserve as much credence as similarly attested documents would be accorded if they reported strictly secular matters.5 Where the texts do assert something miraculous – for example, Jesus’ postresurrection appearances – we take it, given the basic assumption of authenticity, that the narrative represents what someone relatively close to the situation claimed.

It doesn’t seem to even occur to them that they might need to invest actual effort arguing these claims . This is some Josh McDowell-level shit. And actually, it screws up their entire Bayesian set-up. The proper way to set up the question from a Bayesian point of view isn’t to assume the Gospels are mostly true and then ask the probability of it all happening in a non-miraculous manner. Rather, the question they should be asking what the probability is that people would tell stories like the ones in the gospels even if no miracles happened. And given all the crazy stories people tell, that second probability is pretty high.

What’s striking about all this is the problems with these arguments are problems you find in apologists who no one takes seriously, including Josh McDowell. The Bayesian framework doesn’t do anything to correct for the problems, it just creates a distraction from them.

  • josh

    Do apologists ever offer a Frequentist analysis of biblical claims? I see ‘Bayesian’ and ‘Christianity’ and I immediately prepare myself for non-experts abusing a technical term in hopes of impressing the ignorant. Bayesian to these people just means ‘I gussied up a lame probability argument because I couldn’t make a compelling case in more familiar language.’ It’s a patina of sophistication over the same old dross.

    What they like about Bayesian terminology is the emphasis on ‘prior probability’. They think they can just set that arbitrarily high and then draw the conclusion they like.

    “What’s the prior probability that God wrote the Bible?”
    “Like, a billion! It says so in the Bible!”
    “Cool! And the probability that Jesus was resurrected, given that God wrote the Bible must be one. So the posterior probability, after we conduct our Bible reading experiment and see that it says Jesus was resurrected, is almost perfect certainty that Jesus WAS resurrected!”
    “Wow! What a tour-de-force for mathematics and apologetics.”

    • charleshogg

      What are your favorite examples of this?

      • Sarah

        You won’t get a reply, because the people who mostly do this are Atheist apologists. (See LessWrong for example)

        • charleshogg

          I figured I wouldn’t get a reply, but more because the thread was long-dead by the time I found my way here.

  • Reginald Selkirk

    “Bayesian” is to apologists what “quantum” is to Deepak Chopra. They have no obligation to use the word accurately, it is just another veggie to throw in their word salad.

  • http://www.richardcarrier.info/ Richard Carrier

    Amen, Chris. Your post is succinct and spot on.

  • piero

    Excellent post and excellent comments. I’ll shamelessly steal Reginald’s ““Bayesian” is to apologists what “quantum” is to Deepak Chopra.”. I know Reginald won’t mind, because I did a Bayesian analysis and he most probably won’t find out when I’m stealing it.

  • kraut

    “that the Gospels were written, if not by the authors whose names they now bear, at least by disciples of Jesus or people who knew those disciples – people who knew at first hand

    Like those UFO abductees – they all had those probes inserted, they are all first hand witnesses, no doubt. And the X-files are a documentary.

  • snafu

    The proper way to set up the question from a Bayesian point of view isn’t to assume the Gospels are mostly true and then ask the probability of it all happening in a non-miraculous manner. Rather, the question they should be asking what the probability is that people would tell stories like the ones in the gospels even if no miracles happened.

    The sound of nails meeting hammer heads is deafening.

    ====

    Another example from Swinburne’s key text:

    As you say, in TEoG he actually goes as far as saying the evidence for God isn’t that great, and as Chris says above, his PoE theodicies are subject to the usual criticisms. But he claims what swings it right at the end of the last chapter is his consideration of personal testimony. And that depends crucially on what he calls his “Principles of credulity/testimony” – roughly, that we should believe any religious hokum we hear absent any reason to disbelieve it.

    This is, of course, pretty much the same move that the McGrews make. It’s *anti-Bayesian*, because we have ample evidence that false religious claims are made all the time, particularly so from ancient sources. If you’re a good Bayesian, you’ll base your prior probabilities on real data that you actually have, not some metaphysical “principle” that (frankly) has been pulled out of your ***.

    I sometimes call this move “begging your priors” – because it’s the inductive equivalent of “begging the question” – ie building whatever conditions you feel like into the prior probability in order to get the inference you want.

  • http://aigbusted.blogspot.com Ryan

    Hi Chris,

    A while back I wrote a series of blog posts on the McGrews’ article:

    http://aigbusted.blogspot.com/2011/01/was-jesus-raised-index.html

    Though I didn’t write posts addressing all of there points, it should be fairly clear from what I’ve written that there “facts” and much of their reasoning about them is way off base.

    I think the most egregious error on the McGrews part is that they believe that if the resurrection did *not* take place, there would only be a 1 in 1000 chance of any individual disciple saying they saw the risen Jesus. And that’s obvious nonsense, to anyone who knows about grief hallucinations or group delusions. I’ll leave a couple of handy links for anyone interested in those:
    http://www.scientificamerican.com/article.cfm?id=ghost-stories-visits-from-the-deceased

    http://www.skeptically.org/skepticism/id11.html

  • http://www.russellturpin.com/ Russell

    Bostrom’s argument that we are a simulation created by our descendants is kind of fun.

  • http://oldtimeatheism.blogspot.com/ Andy.scicluna

    I’ve always found the level of dismissivness towards the multiverse hypothesis disturbing- particularly from people who expect us to believe in invisible entities like God and, to a lesser extent, angels.

  • robertlandbeck

    Whtvr Bysn rgmnts m xst, thr cntmprr sch s ths mntnd bv r thrs rstng w frm rlr hstr, ll ‘rgmnt’ s bt t b vr thrwn. Hstr nw hs t’s frst ltrl nd dmnstrbl prf fr fth!

    Th frst whll nw ntrprttn fr tw thsnd yrs f th mrl tchngs f Chrst s pblshd n th wb. Rdcll dffrnt frm nythng ls w knw f frm hstr, ths nw tchng s prdctd pn prcs, prdfnd nd prdctbl xprnc nd clld ‘th frst Rsrrctn’ n th sns tht th Rsrrctn f Jss ws ntndd t dmnstrt Gds’ wllngnss t rl Hmslf nd ntrvn drctl nt th ntrl wrld fr ths bdnt t Hs wll, pvng th w fr ccss, b fth, t th pwr f dvn trnscndnc.

    Ths ‘fth’ s th pth, th srch nd dscvr f ths drct ndvdl ntrvntn nt th ntrl wrld b mnptnt pwr t cnfrm dvn wll, Lw, cmmnd nd cvnnt, “crrctng hmn ntr b chng n ntrl lw, ltrng blg, cnscsnss nd hmn thcl prcptn bynd ll ntrl vltnr bndrs.” S lk t r n, nw rlgs tchng, tstbl b fth, mtng ll nlghtnmnt crtr f vdnc bsd cstn nd dfntv prf nw xsts. Nthng shrt f n ntllctl, mrl nd rlgs rvltn s gttng ndr w. T tst r nt t tst, tht s th qstn? Mr nf t http://www.nrgn.rg.k http://slgnrng.cm////th-fnl-frdms/

    I can tell when something was cut & pasted. – Hallq

    • robert landbeck

      What is particularly interesting is that your intellectually dishonest corruption of my post is exactly what I have also experienced from religious sites. One can only conclude that not only is atheism no more than the opposite side of the same coin of profound ignorance that religious tradition pretends to, but has no interest in any knowledge that doesn’t fit it own set of prejudices and preconceived notions. Too bad really!

      • http://www.facebook.com/chris.hallquist Chris Hallquist

        No, what I have no interest in is people spamming my blog.

        • robert landbeck

          I haven’t spammed your blog. Again, anything but confront new ideas on their own merit, that contradict your own. Unable to contemplate changing your mind in the light of new discovery. If science had that mind set, we’d still be in the dark ages. And you call that rational? Now you know why the world is so f**ked up.

          I did cut and paste part of original post, but only from from my own original material. My first comment remains legitimate. All intellectual ‘arguments’ Bayesian or otherwise are now redundant. History has its’ first fully demonstrable proof for faith. Don’t like it? Too bad. I’ve already fully tested and confirmed it. And it’s only a matter of time before the numbers confirming this new reality will establish what you have already discounted as an inescapable fact. Enjoy your future.

          • http://www.facebook.com/chris.hallquist Chris Hallquist

            Let me make this real simple for you: post another obvious cut & paste here again, and I’ll disemvowel it again.

  • Robert B.

    Wow! So, if the Bible is true, the Bible is probably true? Amazing!¿

    It’s really depressing to see “Bayesian” reasoning advanced in favor of superstition. It’s like “creation science” all over again.

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  • http://www.philochristos.blogspot.com Sam

    I think the most egregious error on the McGrews part is that they believe that if the resurrection did *not* take place, there would only be a 1 in 1000 chance of any individual disciple saying they saw the risen Jesus. And that’s obvious nonsense, to anyone who knows about grief hallucinations or group delusions.

    This doesn’t strike me as being an egregious error. Granted, grief hallucinations and group delusions are fairly common, but how common is it that one of these types of hallucinations or delusions result in people thinking the dead person was really alive or had risen from the dead? A person saying they saw a hallucination or a ghost is quite different than somebody saying they saw a flesh and blood tangible human being in front of them who had risen from the dead. The question isn’t “What are the chances that the disciples would’ve claimed to have seen Jesus’ ghost or to have had a dream, vision, or hallucination of Jesus, or had just felt his presence?” The question is, “What are the chances the disciples would’ve claimed to have seen a living breathing flesh and bones Jesus who had risen from the dead?”

    With that being said, I haven’t actually read the McGrew article, and I have no idea where the 1 in 1000 figure came from. Given the way you have worded their statistic, I would probably give it a much lower probability just because of how common hallucinations are and how rare it is (if it ever happens at all) that it leads to people claiming that the object of their hallucination was a physically resurrected person.

  • Mike

    I’m not so sure about dismissing the Bayesian Idea. Richard Carrier is an expert on historical investigations of the resurrection, and he is in favor of using Bayesian reasoning for historical claims.

  • Troy

    Chris,

    I don’t think this is a very fair representation of the McGrews’ argument. First, they do spend time arguing for the claims you mention — that’s what most of the next 8 or so pages of the text do. I don’t think they *establish* those claims there, but I also don’t think they would claim to. They’re merely trying to show that they’re defensible before moving on to the meat of their argument. They can’t completely discuss everything in one argument or in one paper. At any rate, Tim has argued for these claims elsewhere. I don’t know if he’s written any professional articles doing so, but you can find online recordings of various talks he’s given on the subject.

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  • Rick Taylor

    To me it seems the fundamental problem with using the Bayesian formula to compute probabilities of historic events is that Bayes formula was created assuming we are doing a controlled experiment and are specifying what constitutes support of the hypothesis in advance (that is exactly how it is used in statistics).

    Using it historically gives a spurious sense we’re being mathematically precise. For example, what is the probability that the resurrection of Jesus would have been documented by multiple contemporaneous observers who were not believers if in fact Jesus did not rise from the dead? Pretty low don’t you think? I’m sure if that had actually happened, it would have been factored in as strong evidence for the resurrection. So, since it didn’t happen, that fact should be factored in against the resurrection. And there’s the problem; we’re picking what counts as evidence and what doesn’t after the fact.

    That doesn’t discount the general idea that in order to support a miraculous occurrence, in some sense the occurrence of the evidence we have must be strong to support it; Hume argued as much without introducing spurious calculations. But the idea we can compute real objective probabilities is absurd.

    • charleshogg

      …But the idea we can compute real objective probabilities is absurd.

      I wholeheartedly agree. But the subjectivist Bayesian viewpoint avoids this criticism. On this view, probability theory describes how agents update their beliefs as new evidence accumulates.

      IIRC, the subjectivist Bayes perspective is explicitly espoused in the McGrew paper. It’s not so much a calculation as a blueprint for a calculation: they state some numbers they find reasonable, and you can plug in your own and see where you end up.


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