TM: One of the hazards of writing technical philosophy is the risk that someone who lacks the appropriate expertise will attempt to critique it. In the case of the article on the resurrection that Lydia and I wrote for The Blackwell Companion to Natural Theology, this has already happened. It is hard enough to correct misimpressions of this sort on a relatively neutral topic; when the subject rouses passions of the sort that, as Hume reminds us, religious disputes are apt to generate, then the difficulties are redoubled.
But one thing that we did not anticipate is that people who are completely clueless would undertake to explain the article to the rest of the world, in the process completely garbling the central claim and shedding absolutely no light on any of the surrounding issues. Since this particular exhibition of aggressive incompetence is now being uncritically rebroadcast by people who are unable or unwilling actually to read the article, it is worth making a few salient points:
1. Nowhere in the article do we give, estimate, or suggest "odds on the resurrection." Near the outset we explicitly disclaim any attempt to do so, writing:
Even as we focus on the resurrection of Jesus, our aim is limited. To show that the probability of R given all evidence relevant to it is high would require us to examine other evidence bearing on the existence of God, since such other evidence – both positive and negative – is indirectly relevant to the occurrence of the resurrection. Examining every piece of data relevant to R more directly – including, for example, the many issues in textual scholarship and archeology which we shall discuss only briefly – would require many volumes. Our intent, rather, is to examine a small set of salient public facts that strongly support R. The historical facts in question are, we believe, those most pertinent to the argument. Our aim is to show that this evidence, taken cumulatively, provides a strong argument of the sort Richard Swinburne calls “C-inductive” – that is, whether or not P(R) is greater than some specified value such as .5 or .9 given allevidence, this evidence itself heavily favors R over ~R.
The ratio of 10^44 to 1 is a likelihood ratio, not odds. People who do not understand the difference between these two ratios should not attempt to discuss the mathematical parts of the article.
2. We are very explicit about our assumptions. In the online version of the article, on p. 39, we make it plain that our calculation
is predicated on the assumption that in matters other than the explicit claims of miracles, the gospels and the book of Acts are generally reliable – that they may be trusted as much as any ordinary document of secular history with respect to the secularly describable facts they affirm. And where they do recount miraculous events, such as Jesus' post-resurrection appearances, we assume that they are authentic – that is, that they tell us what the disciples claimed. This calculation tells us little about the evidence for the resurrection if those assumptions are false. We have provided reasons to accept them, but of course there is much more to be said on the issue.
3. We are quite aware that the assumption of independence is critical, and we discuss this matter extensively on pp. 40-46. It is wearying to see commentators who have not bothered actually to read the article confidently proclaiming that we have overlooked the possibility of dependence.
Readers are of course free to disagree with our actual conclusions. It would be cheering, however, if they would first take the trouble to understand what those conclusions are.
40 comments:
"The ratio of 10^44 to 1 is a likelihood ratio, not odds."
Could someone supply the following for my poor humanities-major self?
1) A recognized technical distinction between "likelihood ratio" and "odds"
2) A demonstration that the criticism leveled depends ineliminably on considerations that apply exclusively to the latter and not the former?
Thanks in advance.
Hiero5ant,
1) Here:
Likelihood ratio:
P(E|H)/P(E|~H)
Posterior Odds:
P(H|E)/P(~H|E)
2) The criticism depends on the idea that the claim being made is a claim about P(H|E). Given the posterior odds, one can derive P(H|E). But from the likelihood ratio alone, one can't. QED.
I wonder if Loftus ever gets tired of getting called out on his nonsense?
Can someone explain in plain english what all this bayesian math is supposed to prove concerning the resurrection? Please dumb down your answer so that Dick and Jane can follow it.
Walter,
Not everything can be dumbed down for Dick and Jane. That's kind of the point of this post.
Could I interest you in a book on probability theory?
Tim aren't those two ratios technically identical if you assume equal priors for H and ~H? If so, your opponent could say they are granting some pretty generous priors for H.
More generally, it seems a bit strange to get so caught up in people confusing likelihoods versus posteriors as if considerations for one have no bearing on the other. It is more complicated than that, as the previous paragraph shows. I think a little charity grease could go a long way here, even if they don't know how to apply it.
Much of their criticism involves wrangling over the probabilities you assign to individual events, and the plausibility you grant to specific claims in the Bible. This is indeed likely the most crucial debate, in fact, that can't be decided by math: it's what determines what numbers to plug into the equations.
They also wrangle about how to generate probabilities of joint events in these high-dimensional event spaces (e.g., generating probability of ten people claiming X based on the probability of an individual claiming X). This seems an extremely important issue, and also relevant, not missing the point. However, ignoring your discussion of issues of statistical independence? That's bad. OTOH, I noticed this was discussed some in the comments at one of the links so it isn't as if everyone is ignoring such issues. These, however, seem secondary to the issues I mention in the previous paragraph.
I haven't read the article, incidentally, I'm just doing meta-commentary at this point. But it seems you could do a charitable reconstructoin of criticisms of your article, even if they got some of the details wrong.
However, I could well be wrong, as I said I haven't read the article I'm just shooting from the hip based on the commentaries I've read.
Walter: it's supposed to show that the evidence we have is much more likely to have obtained under the assumption that the resurrection happened, than under the assumption that it did not happen.
It seems a clever argument, though frankly I have seen so many damned clever probabilistic arguments that end up with some supernaturalistic lunacy at the end that I pretty much ignore them at this point (sorry Tim).
They take a long time to work through thoroughly, and it is at that point easy to find problems with them. But then you are ten hours in the hole.
So I now use others as a filter for such probabilistic arguments (last one I actually read was from Dembski many years ago). When someone I respect shows some respect for the technical aspects of one of these arguments, then I take a look (and the people I respect on such matters are way under the radar: obviously I'm not talking about John Loftus (or even atheists for that matter, there are plenty of skeptical Christians I know)).
But that's cuz I'm trying to finish up a post-doc and get on the job market. If I were an undergrad, or early in my grad school career, I'd be diving in more because these arguments are fun exercises at worst.
Alas now I'm just part of the noisy blog commentariat playing devil's advocate to everything. :)
I have a take on the role of probabilistic arguments that might be of help here. Look, when it comes to the resurrection of Jesus, a person's decision to accept or not accept the Resurrection is likely to be a combination of the evidence specific to the Resurrection, and a prior assessment of how likely the background beliefs that are behind belief in the resurrection are to be true. We know that people who are thinking about the Resurrection are bound to differ about whether the claim that Jesus rose from the dead is antecedently plausible. There's going to be people who find the fact that something would have to be explained as a divine miracle grounds for giving it as close to a probability of zero as you can get. There are some people who are already committed to some form of supernaturalism, and who are not going to be deterred by the fact that the explanation involves the miraculous. So, how can we carry on the discussion? One way of doing it is to ask merely whether the evidence in more like what we should expect if the Resurrection happened, or whether it's more like what we should expect if it didn't. In other words, is there anything in the reports coming out of the first-century church that is more like what you should expect if Jesus was raised than if Jesus was not raised. If the answer to that question is yes, then the evidence confirms the resurrection, but it might still be rejected by reasonable people on the grounds that a Resurrection would commit you to the existence of God, or other features of Christianity that you consider to be improbable. Fine, but you can at least say, in response to the evidence, that the evidence directly bearing on the resurrection of Jesus is easier to explain if the Resurrection occurred than if it didn't. In other words, we can isolate one particular piece of evidence from the total evidence we have that bears on the issue and ask whether this piece of evidence supports the Christian claim that Jesus was resurrected or not.
I understand that some people do Bayesian probability theory to get a correct final conclusion based upon agreed-upon methods for ascertaining probabilities. That's legitimate, but we also might like to isolate the impact of a piece of evidence on the overall plausibility of theism and Christianity. I find Bayes' theorem to be a helpful tool in doing that, even though I do not expect an agreed-upon conclusion concerning the Resurrection after we are done. To me, it's not a misuse of Bayes' theorem, just a different use.
I always wondered which was the clearer author - the McGrews or God.
Now I know.
It is possible for intellectually honest people to fail to grasp the meaning of a piece of scripture.
After all, it was only inspired by God, not a McGrew.
But no intellectually honest person should fail to grasp the meaning of a piece of McGrew writing. If they do, they are not intellectually honest.
What is the likelihood of the resurrected Jesus flying into the sky?
Is it more likely than the chance of Pegasus flying into the sky?
"What is the likelihood of the resurrected Jesus flying into the sky?
Is it more likely than the chance of Pegasus flying into the sky?"
Words fail one...
Tim,
Yes, what is the best book for the Dicks and Janes?
Yep, Steven Carr is back.
My three favorite entry-level probability/statistics books are this and this and this. Not philosophical, just nuts and bolts stuff. They are in order of decreasing sophistication. The third one is an especially easy read, and has a nice explanation of the relationship between probability theory and statistics. I don't think I really understood statistical thinking at an intuitive level until I read that book.
Incidentally, I find when picking up ideas in probability and statistics, it is really helpful (and easy) to run simulations in Matlab. Unfortunately I'm not sure of the best 'Intro to Prob and Stats' book that uses Matlab extensively. Something like this book. Note I have NOT read it, so cannot vouch for it, but based on browsing it at Amazon, it seems like a solid choice. It is hard to overstate the utility of running simulations to quickly correct and build one's intuitions. It isn't a substitute for working through the math, but a great complement.
I largely agree with Victor's analysis above of how Bayesian thinking can be helpful in a qualitative way.
I'd also be interested in a book recommendation from Dr. McGrew, seeing as he's formally trained in that area.
Anon,
I have a small, introductory bibliography on the subject here: http://homepages.wmich.edu/~mcgrew/bayes.htm
BDK said,
"...Much of their criticism involves wrangling over the probabilities you assign to individual events, and the plausibility you grant to specific claims in the Bible. This is indeed likely the most crucial debate, in fact, that can't be decided by math: it's what determines what numbers to plug into the equations."
This is the part I was objecting to on DC. Y'all may also take note that I haven't sent out an answer yet, as I was poring through the article in detail, along with gathering supplementary reference so that I would be able to make a cogent, educated and non-inflammatory response. The article deserves that much at least. I have other stuff going on in my life, and as I said on John's page, it may take me a couple of months to sort out the nuance without looking like an idiot in the end.
But again, I'm with BDK when he says "It seems a clever argument, though frankly I have seen so many damned clever probabilistic arguments that end up with some supernaturalistic lunacy at the end that I pretty much ignore them at this point (sorry Tim)."
...as it stands, I'm not really an important player in all this. I'm just a guy with an opinion, like everyone else in here.
GearHed it is smart to take your time with this stuff. People who formulate a response within an hour of seeing the article are typically going to embarass themselves. Pretty much definitional of the internet culture.
"It seems a clever argument, though frankly I have seen so many damned clever probabilistic arguments that end up with some supernaturalistic lunacy at the end that I pretty much ignore them at this point (sorry Tim)."
Yeah - there's just a low prior probability that probabilistic arguments will turn out to be good ones, and we should ignore them. Yeah, that's a great one. I'm with BDK too. I, like BDK read Dembski's work already and I didn't like it. This counts heavily against the McGrews.
Wait wait... I should've wrote:
"Yeah - there's just a low prior probability that probabilistic arguments [FOR GOD] will turn out to be good ones, and we should ignore them."
Only the ones for God or the supernatural are suspect. The other ones...those are okay.
Thanks, Anonymous. From your gentle parody I now realize I was being a total racist to assign a low prior probability of this Nigerian banker email being fraudulent just because I've seen so many of them turn out that way in the past. Each argument should be evaluated in a historical vacuum.
"high probability of being fraudulent", obviously; "low probability of being true". Mercy, for an edit post function...
The paper basically says that if you assume the New testament is an accurate reflection of the claims of the individuals involved, with no application of selective recording of information, based on timelines very favorable to such a notion, then it is more likely the clais are based on real events. Not surprising given the giant caveat, and not convincing.
One Brow: that seems about right, which is why I focused above on when I said:
"Much of their criticism involves wrangling over the probabilities you assign to individual events, and the plausibility you grant to specific claims in the Bible. This is indeed likely the most crucial debate, in fact, that can't be decided by math: it's what determines what numbers to plug into the equations."
The McGrews seem to technically avoid circularity by bracketing out the resurrection claim in question, while accepting everything else at "face value." Frankly, that seems a naive approach to a religious canon, especially one with the hermeneutic thickets associated with the New Testament. For instance, what of concerns about what early Christians actually thought about the resurrection (as discussed here and in the other posts)? It really isn't that clear at all. It seems there is no univocal answer.
Given all this controversy, taking the text at "face value" actually means assenting to a tendentious interpretation of this religious canon, one that tends to make X likely, and then finding he likelihood of claim X to be high.
Heiro: these probabilistic arguments are fun exercises, if you have the time. As I said, I largely use people I respect as my personal filter at this point rather than take the 10 hours to go through them myself. Nothing interesting has squeaked through the filter yet, in about 8 years. Doesn't mean something won't eventually, but my attitude is that if there really is a good argument out there, it will propagate and I'll hear about it eventually. No need to waste my time scouring the primary theological literature because one of them might end up being a good argument. If it is good, it will rise to the top of the pile.
But again, that's the perspective of someone that spent a lot of time on this stuff, and got sick of it. I remember as an undergrad (I was a math major) I wrote a long two-part article for the school paper using simple mathematical arguments against young earth creationism (e.g., calculating the required volume of the ark, other fish-in-barrel type arguments). That was back when Gish and Morris were all the rage.
Many years later, after going to churches and learning their arguments, talking to dozens of these folks, it was clear how different their orientation toward argumentation and evidence was. There are good reasons no other discipline has an 'apologetics' branch. It's a foreign country, and after visiting there for a while, it was good to get back home where things aren't decided ahead of time.
Enough people told me that Dembski was the bomb, that he was the real deal, that I spent many months working through his book the Design Inference. Another egg, simply obvious problems with it. Later when I pushed those people on what they liked, it was clear they hadn't read or understood his work, they were just parroting apologetic talking points. So now my filter is much stronger: it has to be people with expertise in the mathematics, people that I have prior reason to trust.
Since then I've wasted no time with this crap. But as I said, I will go back if anything rises to the top of the heap.
You have to choose what you will not learn before you die. Every choice about what you will spend time on, is a choice to stay ignorant about something else. E.g., I am ignorant of Rennaisance Poetry, I would love to know a lot about it, but given my priorities it just isn't something I'm going to learn about before I die. It is sad, it sucks, but ya' gotta make those decisions.
That's why I find people like Loftus puzzling (aside from the fact that he still has the mentality of an apologist). Or atheistic philosophers of religion that continue to spend all this time wrapped up in that world. Go into science, produce what you think is right. Merleau-Ponty said, 'I find refutations uninteresting. It is far better to produce what one reproaches others for not bringing forth.' For young skeptics, for people embarking on intellectual persuits, I strongly advise go into science, math, whatever. Don't go into philosophy to study religion, do you want to look back having produced nothing but refutations your whole life? Or do you want to make a positive contribution?
As far as anonymous commenters my new policy is to only respond when they aren't being trolls, and make an intelligent point that deserves my time.
Hiero: Thanks, Anonymous. From your gentle parody I now realize I was being a total racist to assign a low prior probability of this Nigerian banker email being fraudulent just because I've seen so many of them turn out that way in the past. Each argument should be evaluated in a historical vacuum.
Anon: I'm with you, Hiero. John Loftus turned out to be a real dope. So I just can't take skeptics seriously, bro. We should not evaluate arguments based on their own merits, man. My good friend from Nigeria and is in the banking industry, and he *seems* like one of the most honest people I've ever met, but he needs to overcome my probabilistically justified bias towards Nigerians. I film him secretly whenever he comes over, in case I have to use the restroom or something.
Anyway, I'm with BDK and Hiero. These arguments can all be lumped under the heading of "crap". If its got probability calculus, and Christians think it supports their faith, its probably just crap.
BDK writes: "No need to waste my time scouring the primary theological literature because one of them might end up being a good argument. If it is good, it will rise to the top of the pile."
Anon: This is a very rational method. It is just obvious that the most technical/rigorous arguments made by those with true mathematical expertise, are the ones that really penetrate the broader popular culture - being both the most easily understood and employed by the masses.
Rick Warren's next book is actually called _The Probability Driven Life_.
The most dense "crap" usually sinks, folks. Only scoop it out and investigate if it floats to the top of the bowl.
BDK: For instance, what of concerns about what early Christians actually thought about the resurrection (as discussed here and in the other posts)? It really isn't that clear at all. It seems there is no univocal answer.
Anon: Yup, same with the Big Bang. There's just no univocal answer on that one. Hawking even makes the singularity disappear by invoking imaginary time. And we all know how smart he is. I mean, all we have to do is look at any field and find some dissenters. We don't need to evaluate these arguments on our own and attempt to defend our own stance. It is a waste of time. I've heard there are even neuroscientists who think materialism is false. So that one is in question too.
Dear blog readers,
For all this BDK's posturing, I doubt he has better credentials in mathematics than William. It is great that he finally understood statistical thinking at an intuitive level, when he read an introductory level work, but I haven't seen mention of anything actually published in refutation of William, or anything published in mathematics at all. Cambridge University Press chose to publish William's work (aka "crap" according to this BDK) in their series, Studies in Probability, Induction and Decision Theory. This BDK, OTOH, writes mostly on blogs? Has published what on mathematics? BDK's work has been reviewed by who? Where? When? I am amazed at the lack of charity I see sometimes within the blogging community, but even more so the distortion of reality.
Sincerely,
Alan Baker
Who is William? Tim McGrew?
Vic,
I believe Anon is talking about William Dembski.
Alan: credential fetishism is not something I play. Talk to John Loftus if that is your game.
If you want to defend the explanatory filter as a rigorous principle of inference, be my guest. I'm happy to engage with arguments.
BDK (old): When someone I respect shows some respect for the technical aspects of one of these arguments, then I take a look...So now my filter is much stronger: it has to be people with expertise in the mathematics, people that I have prior reason to trust... Since then I've wasted no time with this crap.
BDK (new): credential fetishism is not something I play...I'm happy to engage with arguments.
LOL touché anon. Good one.
However, What that quote shows is that I fetishize competence, not credentials. I wont' ask for your CV. The closest I've ever come to such silliness is in my parodies of Loftus who once dismissed Tim as an "uncredentialed hack" instead of addressing his arguments.
My main point being missed is that everyone has a threshold (set by interest level, time commitments, initial plausibility, etc) below which they won't put the time in to study something. I was simply being up front that my threshold is extremely high for quantitative apologetics. I didn't say this means I should be trusted on Tim's argument specifically; quite the contrary. If you see my first post, I was explicit that I was only commenting on the blog post and links so might need to be set straight on some things. I don't know how I could have been more clear about that.
BDK: However, What that quote shows is that I fetishize competence, not credentials.
Anon: The two usually go hand in hand, as one usually must gain and prove competence in acquiring credentials. This is why we generally respect credentials.
Anon credentials and competence are correlated but not the same, so your initial confusion is understandable. Glad to help.
BDK - I think we can generally assume that a reasonable level of competence in mathematics has been acquired along the way to Dembski's credentials. It is also pretty safe to assume, based on credentials and publication history, that he is more competent in mathematics than you are (even with your "mathematical agument against Creationism", being published in the school paper).
Saw this response the other day to the McGrews' resurrection argument, see what you guys think http://failingtheinsidertest.blogspot.com/2011/05/my-rebuttal-to-mcgrews-rewritten.html
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