Does Craig Demonstrate a Fallacy in Hume?

A recent responder to my postings on Hume’s argument against miracles claims that Hume’s argument in Section X of An Inquiry Concerning Human Understanding is “demonstrably fallacious.” After a bit of coaxing, he has produced the following alleged demonstration, taken from William Lane Craig’s debate with Bart Ehrman:

”When we talk about the probability of some event or hypothesis A, that probability is always
relative to a body of background information B. So we speak of the probability of A on B, or of
A with respect to B.

So in order to figure out the probability of the resurrection, let B stand for our background
knowledge of the world apart from any evidence for the resurrection. Let E stand for the specific
evidence for Jesus’ resurrection: the empty tomb, the post-mortem appearances, and so on.
Finally, let R stand for Jesus’ resurrection. Now what we want to figure out is the probability of
Jesus’ resurrection given our background knowledge of the world and the specific evidence in
this case.
B = Background knowledge
E = Specific evidence (empty tomb, postmortem
appearances, etc.)
R = Resurrection of Jesus
Pr (R/B & E) = ?

Pr (R/B&E;)=

Pr (R/B) × Pr (E/B&R;)
_________________________________
Pr (R/B) × Pr (E/B&R;) + Pr (not-R/B) × Pr (E/B& not-R)

Pr (R/B) is called the intrinsic probability of the resurrection. It tells how probable the
resurrection is given our general knowledge of the world. Pr (E/B&R;) is called the explanatory power of the resurrection hypothesis. It tells how probable the resurrection makes the evidence of the empty tomb and so forth. These two factors form the numerator of this ratio. Basically, Pr (not-R/B) × Pr (E/B& not-R) represent the intrinsic probability and explanatory power of all the naturalistic alternatives to Jesus’ resurrection. The probability of the resurrection could still be very high even though the Pr(R/B) alone is terribly low. Hume just ignores the crucial factors of the probability of the naturalistic alternatives to the resurrection [Pr(not-R/B) × Pr(E/B& not-R)]. If these are sufficiently low, they outbalance any intrinsic improbability of the resurrection hypothesis. Bayes has the form of x/x-y which means that as the explanatory power of the resurrection tends toward 1, and as the explanatory power of the naturalistic explanations tend toward zero, then any initial intrinsic improbability can be overcome.” (Quoted from the correspondent “K-Dog”).

Does Craig demonstrate that Hume’s argument is fallacious? A couple of things to note: First, Hume does not employ Bayes’ Theorem in the presentation of his argument; it is expressed informally, and the Bayesian framework is imposed by later interpreters. Second, Hume does not directly address the resurrection of Jesus of Nazareth in “Of Miracles,” though his instance of an imagined report of the resurrection of Elizabeth I may be a coy allusion. Hume’s argument is about miracle claims in general and not a specific critique of the resurrection apologetic of the sort promoted by Craig.

Craig’s argument is that the likelihood of the evidence for the resurrection given the naturalistic alternatives to resurrection (i.e., given that the resurrection did not occur and given background information) might be so low as to counterbalance an extremely low probability of the resurrection given only background. In other words, p(E/~R & B) might be so very low, that even a very low p(R/B) might be overcome and the resultant p(R/E & B) might wind up very high (given, as seems reasonable, that p(E/ B & R) is not too low). Craig’s charge is that Hume simply ignores this possibility. This, presumably, is the demonstration of the claimed fallacy.
Does Hume ignore such a possibility? Even if Hume does, do we have to? That is, might we not adopt a neo-Humean argument against miracles that does consider what he failed to note?

Again, Hume is not specifically addressing claims about the resurrection, so to twit him for not taking into consideration specific evidence for the resurrection is obviously unfair. Well, then, does Hume consider, in general terms, the possibility that testimonial evidence for a miracle might exist even if the miracle did not occur? If we express it in formal terms, does Hume consider what values p(E/~M & B) might take, where E is the evidence for a miracle claim, M is that claim, and B is background? Well, he surely seems to. To take one succinct passage:

“When anyone tells me that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened (p. 149; from the edition by Antony Flew, Open Court, 1988).”

I think that a natural way to interpret this passage is that Hume is recommending that we consider that the testimony for a miracle might well exist even if the miracle did not occur, i.e., that p(E/~M & B) might not be low, because the testifier was either a deceiver or a victim of deception. How might we get miracle reports even when the reported miracles did not occur? The reporter might deceive or be deceived, and if we consider either probability not to be too low, then we will consider p(E/ ~M & B) not to be too low in that case.

In general, as I noted in an earlier post, Hume considers that the “knavery and folly” of humans is such that miracle reports are often likely even where no miracle has occurred. Further, if this is Hume’s claim, it is obviously right, as, indeed, everyone who is not totally credulous will admit. No rational person believes more than a small fraction of the myriad miracle reports that infest historical records and tales. Even some evangelical scholars now doubt some biblical miracle reports (one, Michael Licona, was recently fired for doing so). Clearly, then, miracle reports do frequently arise when no miracle has occurred.

Suppose, though, for the sake of argument, that Hume did not devote enough attention to the possibility that the evidence for a miracle might be very low given that the miracle did not occur. Do we modern-day neo-Humeans have to make that same mistake? No. We can simply revise Hume’s argument to take p(E/~M & B) into due consideration. And we do. Specifically, we can and do address the likelihood that there would be the given testimonial evidence for the resurrection of Jesus even if Jesus did not rise. We can and do judge p(E/~R & B) to not be terribly low—certainly not nearly low enough to counterbalance the very low background probability, p(R/B), that we rationally assign.

So, the above claim that Hume’s miracle argument commits a demonstrable fallacy amounts to nothing. The argument demonstrates only the perennial tendency of Hume’s critics to attribute to him a weaker argument than the one he makes.

About Keith Parsons
  • http://www.blogger.com/profile/12132821431322748921 LadyAtheist

    Craig has proven many times that he doesn't believe in more than two possible answers to a question, therefore when he suggests a third alternative I think something fishy is going on!

  • http://www.blogger.com/profile/10817974804323066290 shreddakj

    Now that I'm officially studying informal logic and statistics (after 4 years of studying Jazz and Science) I find these things much easier to comprehend. Excellent post Keith (as always!)

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    Matthew 6:14
    King Herod heard about this, for Jesus’ name had become well known. Some were saying, “John the Baptist has been raised from the dead, and that is why miraculous powers are at work in him.”

    How likely is that that 1st century Jews would claim that a recently unjustly killed preacher had been raised from the dead if no miracle had occurred?

    According to Craig, the probability of the Bible being truthful is extremely low, because, according to Craig, it is a fallacy to think that Jews would testify about a preacher being raised from the dead, if it had not happened.

  • http://www.blogger.com/profile/02108175024624509183 Domics

    Carr,
    And why the Jews could believe in John's rising from the dead but did not believe in the Jesus' rising?

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    Ask Paul why Christian converts were scoffing at the very idea of their god choosing to raise a corpse.

    Paul does answer part of your question, although it goes without saying that he never mentions John the Baptist.

    Why did Jews not believe in Jesus?

    Romans 10
    How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them?

    They did not believe in Jesus because they had never heard of him.

    Jews only heard about Jesus from people sent to preach the Gospel about Jesus.

    Obviously, Jews didn't get to hear about Jesus from general gossip among Jews. They only got to hear about Jesus from people sent to preach about him.

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    Domics has also missed the force of Craig's argument.

    Hume totally missed (according to Craig) the very low likelihood of Jews testifying that John the Baptist had been raised , if no miracle had occurred.

    So, according to Craig, such testimony as recorded in the Bible is very unlikely to have happened.

    So the Bible must be in error at that point.

  • http://www.blogger.com/profile/08733557675273087950 Patrick

    There is a difference between rumours of miracles and testimonies of miracles.

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    As always Christians pop up to explain why their religion is to be treated with different rules to everything else.

    A Christian miracle has 'testimony', while other miracles have 'rumours'

    How do rumours of something happening start unless at least 1 person had testified that something had happened?

  • http://www.blogger.com/profile/08733557675273087950 Patrick

    Hume’s argument is fallacious because it confuses the probability that someone lies or is deceived in general with the probability that someone lies or is deceived with respect to certain events or phenomena. Let’s assume that for an average person the probability that he lies or is deceived is 1:50. This means that out of 50 statements he makes one is not true, either because he is lying or because he is wrong. In that case any testimony to an event whose occurrence has a probability lower that 1:50 could never be regarded as true.

    Steven Carr: “How do rumours of something happening start unless at least 1 person had testified that something had happened?”

    The idea that John the Baptist had been raised from the dead was indeed based on testimonies. It was the testimonies that there was a man working amazing miracles. That this man was John the Baptist having been raised from the dead was an interpretation of these experiences. No one claimed to have seen John the Baptist being raised from the dead.

    Keith Parsons: “In general, as I noted in an earlier post, Hume considers that the “knavery and folly” of humans is such that miracle reports are often likely even where no miracle has occurred. Further, if this is Hume’s claim, it is obviously right, as, indeed, everyone who is not totally credulous will admit. No rational person believes more than a small fraction of the myriad miracle reports that infest historical records and tales. Even some evangelical scholars now doubt some biblical miracle reports (one, Michael Licona, was recently fired for doing so). Clearly, then, miracle reports do frequently arise when no miracle has occurred.”

    It is important to make a distinction between different kinds of miracle accounts. There are miracle accounts based on testimony, those based on rumour or those that are stylistic devices and consequently not to be taken literally. Relevant here are only those accounts that fall into the first category.

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    PATRICK
    That this man was John the Baptist having been raised from the dead was an interpretation of these experiences.

    CARR
    No , that is your intepretation of the Bible.

    PATRICK
    No one claimed to have seen John the Baptist being raised from the dead.

    CARR
    Another argument from silence. How can an argument from silence be valid?

    Craig would point out that his god would be expected to raise religiously significant people like the baptist.

    And, of course, once a bandwagon of rumours started, there would always be people jumping on the bandwagon and testifying to having personally seen Elvis, sorry, John the Baptist, or do I mean Jesus?

    Hard to keep track of all these people claimed to have cheated death.

    By the way, did any Christian in the first century put his name on a document claiming he personally saw a flesh and blood Jesus?

    Paul claimed to have gone to the third Heaven. Lunatics don't count as credible witnesses, unless you believe Paul was sane when he reported his trip to Heaven.

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    Of course, there are cases where people have testified first-hand to sorcery, even when they knew they would be killed for admitting to being a witch.

    Why would they Die for a lie?

    What principle does Patrick use to discredit Christian testimony of child-witches?

    Especially when children admit to being witches…

  • http://www.blogger.com/profile/02108175024624509183 Domics

    Carr,
    what a strange comparison …
    the witch is threatened and he risks his life; the witness of a resurrection risks instead of being ridiculed and not believed (even killed if considered blasphemous). This happened at that time and today.

    Regarding Romans 10, please read the whole piece to understand what Paul says. Paul with Romans is directing to Jews and Gentile people living in Greek and Roman world. He is not talking about Jews of the Palestine living at the time of Jesus. Paul itself says to have meet in Jerusalem first hand Jewish testimony…

  • http://www.blogger.com/profile/08733557675273087950 Patrick

    Steven Carr: “And, of course, once a bandwagon of rumours started, there would always be people jumping on the bandwagon and testifying to having personally seen Elvis, sorry, John the Baptist, or do I mean Jesus?”

    Those people who regarded Jesus as John the Baptist having been raised from the dead obviously didn’t know the latter very well, as they would otherwise have seen that Jesus didn’t look like him. As for Jesus, however, his disciples knew him very well, so it is very unlikely that they would have mistaken another man for Jesus.

    Steven Carr: “Paul claimed to have gone to the third Heaven. Lunatics don't count as credible witnesses, unless you believe Paul was sane when he reported his trip to Heaven.”

    If one assumes that there can be visions caused by God one doesn’t have to arrive at the conclusion that Paul was insane.

  • http://www.blogger.com/profile/11983601793874190779 Steven Carr

    DOMICS
    Regarding Romans 10, please read the whole piece to understand what Paul says. Paul with Romans is directing to Jews and Gentile people living in Greek and Roman world. He is not talking about Jews of the Palestine living at the time of Jesus. Paul itself says to have meet in Jerusalem first hand Jewish testimony…

    CARR
    This is all just made up.

    There is not one word in Romans 10 which claims Paul is not talking about all Jews, no matter where they are.

    You can imagine the Roman trials of witnesses for the resurrection.

    ROMAN INTERROGATOR
    Confess you are one of those Christians.

    TORTURE VICTIM
    No, you have the wrong person. I have never seen Jesus.

    ROMAN
    Liar! Confess you are a Christian.

    (I now skip the next 10 minutes. Think of the violence in the Passion of the Christ.)

    TORTURE VICTIM
    Yes, yes I saw Jesus rise from the grave. I can tell you the names of my friends who saw him. Please just kill me.

  • http://www.blogger.com/profile/02108175024624509183 Domics

    Carr,
    there are two possibilities: when Paul wrote the letter to the Romans has forgotten that he had personally met Jews who heard Jesus or, I repeat, someone has to read better Romans 10.

    In the Roman trial the witness in order to save himself had to say that nothing was true. Jesus was condemned because he refused to deny explicitly the allegations.

  • http://www.blogger.com/profile/05770427187548083625 Havok

    Patrick: As for Jesus, however, his disciples knew him very well, so it is very unlikely that they would have mistaken another man for Jesus.
    Is that why the gospels record his disciples and followers not recognising him?

  • http://www.blogger.com/profile/01786844757672182664 K-Dog

    Please correct me if I am wrong, but what Craig says in his written work (and in the debate with Bart Ehrman) is that Hume's in principle argument against the identification of miracles is demostrably fallacious and he goes on to show this in terms of Bayesian calculus. Craig explicitly says that Hume had an excuse because the probability calculus hadn't been developed in his day, but that neo-Humenas like yourself who still press Hume's in prinicple objection (as you did in your debate with Craig)no longer can rationally do so. Moreover, Craig only brings up the specific evidence for the resurrection because in the debate, and in his written work, he is defending a case for the resurrection, and he uses it as an illustration of the 'abstract' Bayesian formula to bring it down to earth so to speak. So, he is not unfairly criticizing Hume for not offering any specific considerations against the evidence for the resurrection (Indeed, the facts Craig uses in his case weren't even considered historical facts in Hume's day because the historical criteria used to establish them today weren't even developed yet), nor is he anachronistically accussing Hume of misusing Baye's theorem. But even if he was, who cares. What matter is whether Hume's IN PRINCIPLE argument against the identification of miracles is demostrably fallacious and you concede that it is. You then go on to accuse Hume's critics, and I suppose you are mostly talking about Craig given the title of your post here, of unfairly criticising Hume of a weaker argument then he in fact made because people may have been deceived, they may be lying, etc. But that is to conflate HUme's in fact objections against the identification of miracles with his in principle objection. Craig, and other critics who you unchartiably accuse of straw manning Hume, all admit that Hume's 4 in fact objections have some force, but that isn't what is at issue. What is at issue is Hume's in principle objection and that as you admit is demostrably fallacious. I find this to be a significant development and I am puzzled by your concluding comment that this amounts to nothing. Really?! I doubt you really mean that. In any case, it would be interesting to see if Hume'e in fact objections, general in character, can be used to undercut, or even rebut, the historical case for the resurrection when we look at the specifics. Perhaps you will be bold enough to try and show that they do.

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