31 thoughts on “Minimal Facts Approach – Fact #3”

1. I was directed to this blog by your husband and chose to comment on this particular topic. Specifically on the final Habermas quote:

   “Skeptics must provide more than alternative theories to the Resurrection: they must provide first-century evidence for those theories.” – Dr. Gary Hambermas.

   D. Hume had already approached this problem by showing, quite conclusively, that the probability of someone lying was always greater than the probability of an actual miracle having occured– notwithstanding anecdotal evidence for the latter. It is simply too improbable given our experience of the natural world as best explained through science that an actual violation of nature will have occurred– and even if it did, we would always be better off being skeptical of any such claims.

2. Welcome, Arturo.

   I am familiar with David Hume’s, “On Miracles.” I realize the need for skepticism in general. It seems to me that if a person is not a general skeptic then 1)we could never really be sure of anything and/or 2) we would believe anything. However, in this case, including all four facts (which I haven’t finished posting yet) and considering my limited knowledge of the world, why would it be better for me to be skeptical in this particular case? If I chose not to explain these events through a resurrection, I would still need to offer an explanation. Then I would have to weigh that explanation against available evidence.

   What do you think?

   MJ

3. Thank you for your response MJ.

   The reason why I think it would be better to be skeptical in this particular case is because the claim in the case is contrary to our expectations (and experience of how nature works) Lets put it another way: say someone who lived in the tropics had never seen water converted into ice– would he be justified in being skeptical of the idea that water and ice are the same thing? Of course he would, since his experience does not justify believing that water and ice are actually the same substance. Lets expand on this and say that the the person in the tropics (call him X) had written reports from reliable sources (I am granting this for now) that said that water and ice are actually the same thing. However X knows that people lie or mistake some things for other…and he has experienced this directly…so he is always safer assuming that the account is false than asssuming that something seemingly contrary to all logic and nature is true: mainly that water and ice are the same substance. I await your response.

4. Arturo,

   You might want to have a look at John Earman’s book Hume’s Abject Failure: The Argument Against Miracles. Many contemporary philosophers have come to realize what Hume’s contemporaries Adams and Campbell saw clearly: Hume’s argument does not work, and if it did, it would prove too much and undermine scientific reasoning as well.

   Earman discusses the case of the Indian Prince in some detail, giving the history of the story in More and Locke and analyzing the treatment in various editions of Hume’s Enquiry. All subsequent discussions of Hume’s argument will have to grapple with Earman’s treatment.

5. Tim,

   I ask you, in proper philosophical spirit, to post the main argument of the book here so that we can see whether or not it truly does what you claim it does. At any rate it is easier (and faster) than reading an entire book only to return to a dead conversaion.

6. Arturo,

   I appreciate your desire to save yourself time by not reading Earman’s book for yourself, but I do not have the time to summarize 70 pages of argument and analysis on a blog thread. I can, however, give you the principal conclusion: to the extent that there is an argument in Part I of Hume’s famous essay on miracles, an argument purporting to show that testimony can never render a miracle credible, that argument is fatally flawed. A Bayesian analysis of the epistemic situation shows that a sufficient amount of concurrent, probabilistically independent testimony is capable of overcoming any finite presumption against an event.

   As Earman points out, the mathematical analysis of independent testimony was worked out essentially correctly by Charles Babbage in chapter X of his Ninth Bridgewater Treatise. Earman reprints this (along with other historically important documents) in the second half of his book. There are also useful references to more recent literature in Earman’s bibliographies.

   None of this proves that the New Testament evidence for the resurrection is, in fact, sufficient to warrant belief. It is not intended to do so. Earman’s point is simply that the a priori dismissal of testimony to a miracle is methodologically bankrupt. If we want to know what really happened in Palestine in the first century, we must roll up our sleeves and get to work looking at the sort of evidence MJ is discussing here.

7. Hey Arturo.

   I am looking at four historically probable events (as historically probable as anything we can know in history) and then offering an explanation for these events. After I post fact #4, I will then look at alternative theories to the resurrection hypothesis, such as legend, hallucination, and swoon theories, to see how these account for the evidence.

   Arturo, I am focusing down on the resurrection, itself, because without the resurrection of Jesus, there is no Christian faith. One of the apostles in the Biblical texts, Paul, says that if Christ was not raised, our “preaching is useless and so is your faith.” So I have chosen to investigate the most important event of the Bible to the Christian faith and see if it stands up to the scrutiny of historical criticism.

   I believe this to be a reasonable investigation because I can look at the facts surrounding an alleged miracle without addressing its supernatural agency.

   MJ

8. I was able to find this interesting article from The Philosophical Quarterly giving a Bayesian analysis of Hume’s argument against miracles.

   http://www.jstor.org/view/00318094/di983070/98p0140f/0

   Basically the entire matter rests on one thing (given that miracles are improbable): how reliable are the witnesses? I think not very reliable, you seem to think otherwise. Under Bayesian analysis even given 99% reliability and given that the chance of a miracle occuring is 1/10^6 there is still a 1/1000 chance that an account of a miracle is wrong.

9. Arturo,

   Because of the width of the window for Blogger comments, the URL you give above is truncated; even copying and pasting does not enable one to see the article to which you’re referring. From your description, I think it may be Jordan Howard Sobel’s “On the Evidence of Testimony for Miracles: A Bayesian Interpretation of David Hume’s Analysis,” Phil Quarterly 37 (1987): 166-86.

   Sobel’s discussion is now almost entirely superseded by Earman’s book, but it is worth noting that in order to secure Hume’s strong claim Sobel has to resort to saying that the probability of a miracle is infinitesimal (174ff), a position he reiterates in Logic and Theism (2004). Sobel offers no argument for this claim, but by his lights this is not a problem since, as a subjective Bayesian, he can set the prior probabilities anywhere he likes. This is not, however, a stance calculated to persuade anyone who has not already decided not to allow testimony to have bearing on the miraculous.

   You write:

   Basically the entire matter rests on one thing (given that miracles are improbable): how reliable are the witnesses? I think not very reliable, you seem to think otherwise. Under Bayesian analysis even given 99% reliability and given that the chance of a miracle occuring is 1/10^6 there is still a 1/1000 chance that an account of a miracle is wrong.

   What you say here doesn’t give enough information for me to reproduce your calculation. (How many witnesses? Are they independent? What exactly is meant by “reliability”?) And the entire matter does not, contrary to your assertion, rest on the reliability of the witnesses; even witnesses who are more likely to say something false than to tell the truth may, under certain circumstances, render an improbable event highly probable by their concurrent testimony, provided that there are enough of them. (This is a tricky one; it isn’t obvious at first because those circumstances have to be spelled out pretty carefully.) In any event, we need not be reduced to unargued intuitions regarding the credibility of the witnesses; there are historical data to take into account that amount to a substantial case for their credibility with respect to their eyewitness reports.

   But assuming that you have information in mind that would render your calculation correct, waiving the question of where you got your prior probability, and assuming that all available evidence is folded into your calculation, a posterior probability of .999 is certainly high enough to underwrite confidence in the truth of the claim. So I’m not sure what your point is in making it. Are you suggesting that anything short of absolute certainty is an inadequate reason for belief in God?

10. Tim,

    I did not write down the url since I thought it would be copied here correctly, but I am sure that it is not the Sobel paper (or the Holder or Owens papers for that mattr) If I find it I will repost the link here. There was also an error in stating that ” [there is] a 1/1000 chance that an account of a miracle is wrong. “what it should read is “there is only a 1/1000 chance that an account of a miracle is right” I have no doubt that given enough witnesses it is possible to make a miracle account seem likely– but lets just take as our base every recorded event of human history and divide the number of recorded miracles in human history and see exactly how many people would have to have witnessed a miracle for it to be likely. I think that you will quickly see that the number will astronomical. If you think it is fruitful, why don’t we make our own Bayesian calculation– just to see what happens.

11. Arturo,

    Thanks for clearing up the typo. I still do not see, however, how the calculation you have in mind is supposed to go.

    You write:

    I have no doubt that given enough witnesses it is possible to make a miracle account seem likely–

    This seems to be a shift, if not exactly of position, then certainly of emphasis from your opening contribution to this thread. Are you perhaps backing away from the claim that “the probability of someone lying [is] always greater than the probability of an actual miracle having occured– notwithstanding anecdotal evidence for the latter”?

    In any event, I find your proposal for trying to calculate the number of witnesses necessary to render a miracle probable very obscure. I’m always interested to hear new arguments against belief in miracles, though, so if you can fill it out with sufficient premises to indicate that an astronomically large number of witnesses would be required, then I suspect we can get somewhere by looking at those premises.

12. Tim,

    No I am not backing away from the claim…since as you will see the number of witnesses would have had to have been so large that there will not a single account of a miracle that can falsify my claim. Lets say for instance that the span of recorded human history in the world is 10’000 years and that an “event” happens ever minute for every person alive at a given time t (since events are not uniformly distributed over entire populations). So we have the following: 10’000 * 365 * 24 * 60 * number of people alive over the span of 10’000 years. We then count up the number of “miracles” which I will grant for now can be a number like ten thousand or so and divide this number by our previous calculation. That is the likelihood of a miracle having happened (without of course considering reliable eye witness testimony) Given that the number of people alive over 10’000 years is astronomically large the number of people who would have had to witness a miracle for the account to be believable will be quite large as well: a somewhat conservative estimate may be in the order of 1’000’000 or so.

13. Arturo,

    I’m completely baffled by this argument, which doesn’t seem to me to have anything like a Bayesian structure. In particular, it looks to me like your “conservative estimate” is simply pulled out of thin air.

    You write:

    We then count up the number of “miracles” which I will grant for now can be a number like ten thousand or so and divide this number by our previous calculation. That is the likelihood of a miracle having happened (without of course considering reliable eye witness testimony)

    I don’t understand this at all. You’re granting that miracles occur — indeed, lots of them — as an assumption of your argument. But in that case, the probability (I take it you are not using “likelihood” in its technical sense but just as a synonym for “probability”) that a miracle has occurred is 1; that is already part of the given information.

    If you are trying to indicate that miracles are rare events, every sensible Christian apologist will grant it. But by itself this will not take you where you wish to go. It is rare, in roughly the same sense, for someone to win a lottery with a prize of more than $10 million; but it does not require a million witnesses to the drawing of the winning number to render credible the claim that a particular individual has won.

14. Tim,

    (1) That is why I wrote “miracle” not miracle. (The details are important, especially when you are dealing with somewhat sensitive topics)

    (2) “It is rare, in roughly the same sense, for someone to win a lottery with a prize of more than $10 million; but it does not require a million witnesses to the drawing of the winning number to render credible the claim that a particular individual has won.”

    This tells me that you don’t really understand Bayesian probability: after all, althought the probability of any one number being chosen in a lottery drawing is vanishingly small the probability that a number will be chosen is close to 1. The same is not true for miracles.

    (3) My conservative estimate was in fact very conservative. Given my definition of event we have that the probability out of hand that any event is a miracle is

    1/(365*24*60* # of people who have been alive over 10’000 years)

    [Note that I canceled the original 10’000 because I have granted that there may have been 10’000 miracles over 10’000 years.] Now what remains to convert this to a Bayesian calculation is to determine how reliable our witnesses are and then to check how many witnesses we would need to make a miracle even .5 likely. Given that the numbers against are very large I think that 1/1’000’000 against is conservative, but you are welcome to disagree.

15. I’ve decided that it is no use dancing around the issue: I will simply do a calculation here.

    P[M]= a priori probability of a miracle occuring to a given person = 10’000 (# of miracles to have occurred) / (10’000 * 365 *24 *60 * 50’000’000’000)

    P[M|T]= probability of a miracle having occurred given testimony T= .5 (Considering that there are many “miracle” accounts which were later found to be supersitition)

    P[T|M]= Probability that testimony is provided given that a miracle has occurred= 1 (Lets assume that every miracle-like occurence was reported)

    P[T|~M]= probability that testimony is provided given that a miracle has not occurred=.5 (Given that half of all miracle accounts are attributed to false miracles)

    We have:

    P[M|T]= P[T|M] * P[M] / P[T|M] * P[M] + P[T|~M] * P[~M]

    So P[M|T] = [1 * (2.628 * 10^-20)]/[1 * (2.628 * 10^-20)] + {.5 *[(2.628 * 10^20)-10’000]/2.628*10^20}]

    Which comes out to:

    (1) Considering that the denominator reduces to something like: 2.628 * 10^-20 +.5

    And that this in fractional form

    We have something like

    2 * (2.628 * 10^-20) as our final probability:

    Which comes out to 1/[2.628 * 10^20)/2] which is a vanishingly small number. Multiple witnesses may increase the probability but I just don’t see where you are going to get these witnesses from, even given such conservative numbers regarding their reliability and the total number of miracles that I am estimating have occurred.

16. Arturo,

    In a previous note you quoted me regarding the rareness of miracles given the assumptions you had laid out at that point in the discussion:

    “It is rare, in roughly the same sense, for someone to win a lottery with a prize of more than $10 million; but it does not require a million witnesses to the drawing of the winning number to render credible the claim that a particular individual has won.”

    Then you wrote:

    This tells me that you don’t really understand Bayesian probability: after all, althought the probability of any one number being chosen in a lottery drawing is vanishingly small the probability that a number will be chosen is close to 1. The same is not true for miracles.

    I don’t see why it would tell you anything of the sort, though I am wryly amused at the bravado. Perhaps the problem is that you cut off the context of the quotation, which began:

    If you are trying to indicate that miracles are rare events, every sensible Christian apologist will grant it. But by itself this will not take you where you wish to go.

    My point, in short, was that rareness by itself will not render it incredible that an event has, in fact, occurred. The way you initially presented your argument, you seemed to be granting that miracles do, in fact, occur, then trying to argue (counter to this) that on this assumption, it is very improbable that a miracle has occurred. It was you, not I, who used the phrase “the likelihood of a miracle having happened.”

    Your subsequent post is much more explicit, and although I do not think your assumptions give us any real grip on the problem your explicitness enables me to understand, with certain qualifications detailed below, where you’re coming from.

    You write:

    P[M]= a priori probability of a miracle occuring to a given person = 10’000 (# of miracles to have occurred) / (10’000 * 365 *24 *60 * 50’000’000’000)

    This differs from what you wrote before, insofar as now you are specifying that P(M) is the probability of a miracle’s occurring to a given person, granting that miracles (10,000 of them) do, in fact, occur. Apparently you’re thinking of them as randomly sprinkled through the population of the earth across the past 10,000 years.

    Here at the outset you do seem to be running into the problem posed by the lottery analogy, since it’s guaranteed by the conditions you have set up that 10,000 of these events are out there and members of the population have an equal, if minute, chance to be among the lucky winners. It doesn’t help much to say, as you do, that the term “miracle” is in shudder quotes. After all, you put the term “event” in quotation marks too. If you don’t mean it literally, please tell us what you do mean.

    All of that being said, this calculation does not seem to me to be a compelling way to estimate the prior probability of a miracle’s having occurred in a particular instance since too many of the numbers seem to be arbitrarily selected. But determining priors is a big job on anyone’s account. Let’s move on.

    You go on:

    P[M|T]= probability of a miracle having occurred given testimony T= .5 (Considering that there are many “miracle” accounts which were later found to be supersitition)

    This seems completely unmotivated; the consideration you give should be reflected in the probability you give for P(T|~M). It is also inconsistent with the calculation you go on to give. More on this below.

    You go on:

    P[T|M]= Probability that testimony is provided given that a miracle has occurred= 1 (Lets assume that every miracle-like occurence was reported)

    This is probably somewhat too generous of you, but it’s the sort of simplifying assumption that it makes sense to make in a preliminary analysis of the problem.

    Next you say:

    P[T|~M]= probability that testimony is provided given that a miracle has not occurred=.5 (Given that half of all miracle accounts are attributed to false miracles)

    This looks like a mistake, both because your assignment seems unreasonable and because your rationale for the particular value appears to be confused. You seem to be connecting this to your having set P(M|T) = .5. But there is absolutely no general relationship between P(M|T) and P(T|~M) and certainly no reason to set them to the same number. As for my charge of unreasonableness, witnesses vary greatly in credibility, but setting the Bayes factor at 2 across the board is taking both simplification and skepticism a good deal farther than is reasonable. I’ll come back to this at the end.

    Now you try to put these together:

    We have:

    P[M|T]= P[T|M] * P[M] / P[T|M] * P[M] + P[T|~M] * P[~M]

    Good so far.

    So P[M|T] = [1 * (2.628 * 10^-20)]/[1 * (2.628 * 10^-20)] + {.5 *[(2.628 * 10^20)-10’000]/2.628*10^20}]

    Here trouble strikes: you’ve contradicted yourself, since this number isn’t anywhere in the vicinity of .5, which you gave above as the value for P(M|T). But I think that was a mistake anyway, so let it go. There is also a stray curly bracket in the denominator, but I think that is just a typo; I see what you mean. After a few more manipulations, you arrive at this conclusion:

    Which comes out to 1/[2.628 * 10^20)/2] which is a vanishingly small number. Multiple witnesses may increase the probability but I just don’t see where you are going to get these witnesses from, even given such conservative numbers regarding their reliability and the total number of miracles that I am estimating have occurred.

    There is a parenthesis missing in your expression, but if I understand you right it comes out to about 7.61 * 10^-21. This is just about the right order of magnitude, but it doesn’t seem to be quite right. Let k = (2.628 * 10^-20). The probability in question is, to an excellent approximation, k/(k + .5), which is about 5.256 * 10^-20.

    I’ve indicated above why I think the numbers going into this calculation are muddled in several ways. But out of interest, let’s see how many independent witnesses would be required to make M credible given your own assumptions. The odds against M, given your numbers, are (near as makes no difference) 2.628 * 10^20 to 1. The Bayes factors for the witnesses are P(T|M)/P(T|~M) = 2. Under independence, 70 witnesses with that level of credibility would render the probability of M greater than .8, since 2^70 is approximately 11.8 * 10^20. And every witness above that number would double the odds in favor of M.

    This is hardly an astronomical number, which is what you suggested would be required in one of your earlier posts above. Paul states flatly in I Corinthians 15 that the risen Christ appeared to over 500 people at once of whom the greater part were still at that time living.

    Notice also that your calculation is quite sensitive to the value one assigns to P(T|~M). Reduce this to .1, and only 22 witnesses are needed to push the posterior probability of M to over .97. But people do not bear witness in a vacuum, and one must take the circumstances into account, particularly when they face death if they are proclaiming something that is false. In the case of the Christians in first century Palestine who claimed to be eyewitnesses of the resurrection and who had excellent evidence that they could be put to death if they continued to proclaim the fact of the resurrection, P(T|~M) is more plausibly something like .000001 – and that, in my opinion, is being generous. But for those witnesses, given your value for P(T|M), that changes the Bayes factor to from 2 to 10^6. Just four such witnesses, under independence, overwhelm even your prior odds against M, putting the posterior probability well over .999.

17. Arturo,

    My apologies: upon squinting at your denominator in your final formula, I discovered that the stray bracket is square, not curly. This doesn’t affect the rest of my analysis.

18. “My point, in short, was that rareness by itself will not render it incredible that an event has, in fact, occurred. The way you initially presented your argument, you seemed to be granting that miracles do, in fact, occur, then trying to argue (counter to this) that on this assumption…”

    I think this is the source of the confusion, ignoring minor details: brackets…etc What we are discussing/evaluating is the credibility of MIRACLE TESTIMONY nor MIRACLES PER SE.

    “In the case of the Christians in first century Palestine who claimed to be eyewitnesses of the resurrection and who had excellent evidence that they could be put to death if they continued to proclaim the fact of the resurrection”

    This line of argument is laughable. People dying for a delusion does not make the delusion any more true. That you would alter the factor in such a fashion speaks of your overwhelming inability to consider the realities of human nature. People are deceived and people in turn deceive. This is nothing new.

    I think we may have reached the point where we are better of agreeing to disagree. Respectfully yours,

    Arturo

19. Arturo,

    I think nothing remains now of your original claim. Your calculation has been dismantled and found wanting, and you have been reduced to insisting without argument that the falsehood of the testimony is more likely than the truth of the event. Nothing prevents you from standing firm on this ground if you choose. This is, however, trivial; it is not a persuasive line of argument but rather a restatement of your commitments, and it does not get to the root of the question of the evidential value of testimony to the miraculous.

    Of course people are deceived and in turn deceive — they deceive when they believe it to be to their advantage, or at any rate not gravely to their disadvantage, and they are deceived when they are imposed upon by others or when the fact to which they are testifying is one about which they may easily be fooled. That is why the fact that the apostles were facing death over their stubborn insistence on a point of empirical fact is so important; it is the best evidence we could ask for that they believed what they claimed, namely, to have been eyewitnesses.

    Have you ever seen “The Princess Bride”? There is a wonderful scene where Westley, Inigo and Fezzik are trying to break into the castle. The gatekeeper stands in front of the closed gate.

    Westley: Give us the gate key.
    Gatekeeper: I have no gate key.
    Inigo: Fezzik, tear his arms off.
    Gatekeeper, suddenly producing a large key from under his cloak: Oh, you mean this gate key!

    The knowledge that one is about to undergo something exceedingly unpleasant for maintaining a lie has a wonderful effect on the would-be liar. This is really no more than Hume himself pointed out in the Enquiry Concerning Human Understanding:

    We cannot make use of a more convincing argument, than to prove that the actions ascribed to any person are directly contrary to the course of nature, and that no human motives, in such circumstances, could ever induce him to such a conduct.

    I submit to you that in this case it is you, not the Christians, who are ignoring what is known to be true of human nature.

20. Tim,

    That you feel confident in the reality of miracles has nothing at all to do with the truth of the matter. If by “dismantling” my calculations you mean your incredible ability to find missing parentheses and periods then yes I submit that my calculations have been dismantled. If by dismantling you mean that we are all to accept your preposterous claims as to the reliability of testimony then yes my calculations have been dismantled. Let me make this clear for you in child’s terms: The calculation is meant to show that a single account of a miracle must be corroborated by 50 or so independent accounts in order to be somewhat believable. Let me make the point explicit for you: an ACCOUNT is believable if corroborated by 50 independent accounts given that miracles DO occur. My calculations shows only the improbability of any given event being a miracle given that miracles DO occur. You cannot work backwards from the testimony. You should be clear about what you are saying: please do separate ACCOUNTS from REALITY. It is almost too painful to see you grasp for straws even when I have granted you a couple of straws for which to reach. If you want to debate the ACTUALITY or REALITY of miracles I will be glad to, but you should of course, obey certain philosophical rules: mainly that it is up to you to establish (1) That a miracle is possible (2) That a certain miracle account refers to an actual miracle and (3) That your description of this actual miracle makes any sense. Here you cannot invoke Bayes. Here you are at a loss to describe with reason that which your faith attempts to establish as dogma.

21. Arturo,

    You claimed to have an argument. I asked to see it, and after blustering about my not really understanding Bayesian probability you finally produced a calculation. The premises of that calculation were not well related to the question of the confirmation of belief in a miracle; apparently you did not intend the 10,000 special events used to give you P(M) to be miracles in the literal sense, though you haven’t told us even yet what you did mean by the term. So from the outset, this is a hopeless way to try to set P(M). Beyond that, your numerical assignments were inconsistent with each other, with your stated value for P(M|T) being approximately 19 orders of magnitude greater than your computed value of P(M|T). Your choice of a value for P(T|~M) was not the outcome of any compelling line of argument and showed no awareness of the factors affecting this conditional probability in the case of the people who claimed to be eyewitnesses of the risen Christ. Your computation of P(M|T) from your own numbers plugged into Bayes’s Theorem was incorrect. And even given your own numbers (aside from the inconsistent direct assignment P(M|T) = .5), the number of independent witnesses required to raise the probability of M to a believable level was not, as you had earlier claimed, “astronomical.”

    I think that pretty well qualifies as having your calculation dismantled, quite apart from stray brackets. Don’t you?

    At this point, it is unseemly for you to try to act condescending and put things “in child’s terms” or to tell us that we are “grasping at straws” as if you knew more about the mathematics of probable reasoning than the poor benighted Christians. It looks like an attempt to distract our attention from the fact that you have failed to present a cogent argument for the claim you made at the outset:

    D. Hume had already approached this problem by showing, quite conclusively, that the probability of someone lying was always greater than the probability of an actual miracle having occured

    If you have an argument for this claim, feel free to make it. We’re ready and willing to hear it. If you have an argument for the claim that the Christians who claimed to be eyewitnesses to the risen Christ would have been even remotely likely to say what they did — in the face of the consequences they knew awaited them — if the claim were false, then by all means make it. Address the Fezzik example. Tell us why P(T|~M), for those people, for that claim, in that setting, should not be very close to zero and in any event many orders of magnitude lower than P(T|M).

    Your last post does not contribute anything toward this end. In response to (1), of course miracles are possible, as Hume himself would have been the first to argue; for there is no logical contradiction in the assertion that God exists and has acted in such a way as to bring about events that would not have happened without His direct intervention. In response to (2), you might be plainer — are you suggesting that the resurrection of a dead man could plausibly be a natural event? or that the Romans didn’t know how to kill a man? As for your (3), we await an account of your criteria for a description’s making “any sense,” hoping that they will not be question begging.

    Arturo, if your arguments are poor, your premises irrelevant and inconsistent with each other, your conclusions non sequitur — as they were in your calculation — you must not expect the Christians to let these facts pass unremarked. You seem to suffer from the common misapprehension that all Christians have substituted faith for reason. On the contrary, some of us might fairly be described as Christian Rationalists. Let reason be kept to, and let us follow the evidence wherever it leads. This is an injunction we take with all seriousness: παντα δε δοκιμαζετε το καλον κατεχετε.

22. Tim,

    Very well. It seems to me that hastiness got in the way of making a point clear and I also assumed something that in the philosophical literature (at least after Frege) is taken for granted, mainly that things in quotes are different from things without quotes. I was, however, inconsistent in my usage of quotes as well as in my use of Bayes’ theorem. I will thus attempt to begin anew making explicitly clear to what my arguments refer to.

    You have quoted me as saying that:

    “D. Hume had already approached this problem by showing, quite conclusively, that the probability of someone lying was always greater than the probability of an actual miracle having occured.”

    I note for emphasis that there is a difference between an actual miracle and the report of a miracle. Now, reasonable people will agree that there is a difference between a text being reliable (in that we have other texts referring to that text) and what a text says being reliable. Bayes’ theorem in the way that I used it established that (1) Given that miracles occurred it follows that (2) We should be skeptical of miracle accounts not corroborated by a certain number of independent witnesses. I put the word miracles in parenthesis because I intended to mean “texts about miracles” and so what Bayes’ theorem established in that sense is that (1) Given a certain number of “texts about miracles” it follows that (2) we should be skeptical of texts about miracles not corroborated by a certain number of independent witnesses. How does this translate? It means that when we read a text that says that Poseidon did X given the improbability of this being an actual text we should ask for a certain number (4-70) of texts to corroborate this text. A reasonable person will see that the validity of the text itself has nothing at all to do with whether or not Poseidon did X. So Bayes’ theorem can never establish the actual probability of miracles having occurred or even how many eye-witnesses we need to render a miracle credible. It can, at best, tell us what the probability is of a certain piece of paper being a forgery (given that miracle accounts are somewhat rare [compared to hypothetical accounts of ordinary events]). So we are left with the question of whether we should believe that actual miracles are possible? I think that all of this depends on whether or not it is possible that god exists: meaning that the theist must prove that it is not necessary that god not exist (i.e. that none of his properties entail a self contradiction). If it is possible that god exists as defined then it is possible that a miracle would occur, and yet how to determine whether something is a genuine miracle? If someone goes on CNN and prays and the Atlantic parts should be say that it was the prayer that caused the Atlantic to part or his red shirt or his being in a studio in NY? Since miracles are by definition not explainable, we should be at a loss to determine what caused them.

23. Arturo,

    Briefly, on putting words in quotation marks: there are two conventions at work here. One, which is the convention of common parlance, is to put words in quotation marks when one does not intend them in their customary sense. These are called shudder quotes or scare quotes. (They are very common in the postmodernist literature, where it is fashionable to try to look deeply ironic by putting as many terms as possible in shudder quotes.) The other convention is the philosophical one of distinguishing use from mention by putting words one is mentioning in quotation marks; outside of philosophical writing, the same effect is sometimes achieved by italicizing the words or phrases in question, as I have above. Since your putting the word “miracle” in quotation marks could not reasonably be interpreted in line with the use/mention convention, I assumed that you were using shudder quotes and hence that you did not mean the word literally. That was the source of the confusion.

    I agree, of course, that there is a distinction between a miracle and a report of a miracle. I am not sure, however, what you mean by this sentence:

    Now, reasonable people will agree that there is a difference between a text being reliable (in that we have other texts referring to that text) and what a text says being reliable.

    Can you explain this in a little more detail? Do you mean the distinction between a text’s saying something similar to what other texts say – perhaps in the way one partisan newspaper will carry stories similar to those in another partisan newspaper of the same sort – and the text’s saying something true?

    You write:

    Bayes’ theorem in the way that I used it established that (1) Given that miracles occurred it follows that (2) We should be skeptical of miracle accounts not corroborated by a certain number of independent witnesses.

    I think this is nearly right. I would only add that the requirement of complete probabilistic independence is a simplifying assumption, however, and it is not strictly required for combined evidence – in this case corroborating testimony – to render a miracle report believable. However, in the limiting case where there is complete collusion, the subsequent testimonies add nothing to the first.

    But I find it more difficult to follow you when you go on:

    It means that when we read a text that says that Poseidon did X given the improbability of this being an actual text we should ask for a certain number (4-70) of texts to corroborate this text.

    What do you mean by “the improbability of this being an actual text”? I think we may simply be using the phrase “actual text” in different senses. Clearly, if I read in Herodotus that Poseidon did something, the text I am reading is an actual text. (There it is, in my hand or on my computer screen.) I suspect you are trying to say something different. Like you, I think it antecedently very improbable that any supernatural being answering to the description of Poseidon exists at all, and it would take a great deal of evidence to persuade me to the contrary. Like you, I am not inclined simply to take Herodotus’s word at face value. So I am inclined to try to paraphrase what you’re saying like this:

    “Just because some text ascribes act X to Poseidon, it does not follow that the claim ‘Poseidon did X’ is believable. If we have strong reason to doubt that Poseidon did X, we will want corroborating evidence of this fact. Given that the act is alleged to have taken place long ago, the corroborating evidence (if it can be found at all) will come in the form of texts reporting what others who were on the scene at the time said.”

    If I’m interpreting you correctly, I follow this; otherwise, you’ll have to help me out. But the next sentence stumps me:

    A reasonable person will see that the validity of the text itself has nothing at all to do with whether or not Poseidon did X.

    What do you mean by the validity of the text? Clearly you do not mean something about the logical relation between the premises and the conclusion of an argument.

    One of the reasons I’m sure I do not understand what you mean here is that in your next sentence you seem to be drawing a conclusion from this one:

    So Bayes’ theorem can never establish the actual probability of miracles having occurred or even how many eye-witnesses we need to render a miracle credible.

    Here I think we must disagree. By itself, of course, Bayes’s Theorem is just a mathematical equation, a consequence of Kolmogorov’s axioms for probability. It cannot, by itself, tell us anything interesting about any contingent matter. But with appropriate information available – a probability distribution, say, across a sigma-algebra including the relevant propositions – we can certainly use Bayes’s Theorem to determine the probability that a miracle has occurred; and with a subset of that information we can determine how many independent eye-witnesses of a given credibility are required to render the posterior probability of M higher than some pre-established value k in the interval (0,1). The difficult thing, not only in discussions of miracles but also in the probabilistic modeling of scientific reasoning, is getting a fix on the relevant information.

    Moving on to the question of possibility, you ask:

    So we are left with the question of whether we should believe that actual miracles are possible? I think that all of this depends on whether or not it is possible that god exists: meaning that the theist must prove that it is not necessary that god not exist (i.e. that none of his properties entail a self contradiction).

    I grant that the existence of God is a prerequisite for God’s working a miracle; and if we wish to reserve the term “miracle” to an event brought about by God’s power, then it is critically important for the defender of miracles to maintain that it is logically possible that God exists. But I disagree that the theist bears the responsibility to prove that it is not necessary that God not exist. Here the burdent of proof is on the atheist to show the incoherence in the concept of God. If the atheist thinks there is a contradiction, let him bring it forward for inspection. Given the dismal track record of such attempts, it doesn’t look promising. Kai Nielsen has been trying for decades to show that the concept of God is incoherent, but I do not know any professional philosophers who think his argument is cogent.

    You ask:

    … and yet how to determine whether something is a genuine miracle?

    I think a lot would depend on the context and the availability of other plausible explanations for the event. There is no general rule here; we must work on a case-by-case basis. But I can certainly describe circumstances in which I could be persuaded that I had witnessed a miracle and not just the operation of some hitherto-undiscovered law of nature.

24. Tim,

    I am, for the most part, not a fan of postmodernist literature.— I work within the analytic tradition and so what I say should be taken in that particular context. (This is not a reproach, it is simply a clarification)

    Now, reasonable people will agree that there is a difference between a text being reliable (in that we have other texts referring to that text) and what a text says being reliable.

    What I am getting at, and what was not clear, is that showing that some testimony or text remains unchanged is different from showing that what the testimony refers to or what the text refers to is true or false. If we have multiple sources corroborating the existence and format of a certain text we can conclude that the text is reliable but not that its content is true.

    It means that when we read a text that says that Poseidon did X given the improbability of this being an actual text we should ask for a certain number (4-70) of texts to corroborate this text.

    What I am saying is that making the daring and unjustified assumption that every single event in history has been recorded then we have reason to be skeptical both of whether or not a text has remained relatively unchanged from its initial state. Thus when I read my version of Herodotus I must first ask myself: is this text genuine? If I have 4-70 texts more or less corroborating that this text is genuine I can now proceed to ask whether or not what the text actually says is true or false. This point is trivial.

    So Bayes’ theorem can never establish the actual probability of miracles having occurred or even how many eye-witnesses we need to render a miracle credible.

    I am not making a mathematical point with this. It is clear to me that Bayes’ theorem is a well established mathematical result, hence, the fact that it is called a theorem and that it is derivable quite easily from the definition of conditional probability. I am making a philosophical point about the difference between information and events: it should be clear to us that mathematics works with information. The only real information that we have is a set of miracle accounts floating around in an ocean of other historical accounts. We can thus find the probability of any given account being a miracle account, and even how many witnesses we need to make probable the fact that what we are reading is a miracle account, but we cannot, I contend get an equally well grounded value for the probability of an actual miracle—we have no means by which to determine (i) if these miracles are even possible and (ii) how often they possibly happen. The first cannot be established unless we clearly define what we mean by a miraculous event, and in the case where the miracle is well defined (i.e. we know how it works) it does not seem like it is a miracle any longer. In order to determine the second, which is critical in establishing how probable a miracle is we must use the frequency of miracle accounts relative to the entire set of historical accounts— but then the theorem no longer differentiates between computing (i) whether or not we should believe that a given account is a miracle account and (ii) whether or not we should believe that the account is true. This may not be clear but I will expand.

    So we are left with the question of whether we should believe that actual miracles are possible? I think that all of this depends on whether or not it is possible that god exists: meaning that the theist must prove that it is not necessary that god not exist (i.e. that none of his properties entail a self contradiction).

    What you are asking, that the atheist prove the incoherency of the concept of god makes no sense. We must ask ourselves whether the atheist bears the responsibility of proving the incoherency of Zeus, Thor, unicorns, fairies, the spaghetti monster…etc. The answer is quite clearly no. Positive claims must be shown possible, later falsifiable and finally established through evidence. If the theist claims that god exists he must show it possible much as one who believes in the easter bunny must show that it is possible that the easter bunny exist.

25. Arturo,

    Thanks for the clarifications. I work entirely in the analytic tradition, so I’m glad to hear that you’re not a fan of postmodernism. My only point was that your initial use of quotation marks around the word “miracle” could not plausibly be interpreted as marking a distinction between use and mention.

    If I now understand you correctly, I think that “reliable” is not a good word to express what you mean. “T is a reliable text” means that most or all of what is claimed in T is true, and that is clearly not what you mean. But the distinction you are trying to express is, I think, a good one. It is one thing to say with confidence that we have (more or less) the original wording of a text and quite another to say that what the text claims is true.

    But when you go on to press this into an argument that Bayesian reasoning cannot render a reported miracle credible, your reasoning is unclear to me. Let R stand for “Jesus of Nazareth rose from the dead” and T1(R), …, Tn(R) be the testimonies of witnesses 1, …, n that R. If the credibilities of the witnesses (defined as P(Ti(R)|M)/P(Ti(R)|~M), for i = 1, …, n) are each greater than some number k > 1 and if the witnesses are independent, then the Humean claim that the combined testimony of the witnesses cannot overcome a finite presumption against R is simply false.

    Perhaps your point is that, for each i, and for our background evidence E, P(Ti(R)|E) < 1. The argument that the various Ti(R) provide strong evidence for R then requires two distinct steps. The first is to show that P(Ti(R)|E) is reasonably high for each i; the second is to show that, for each i, P(Ti(R)|R&E) >> P(Ti(R)|~R&E). I grant that these are distinct steps in the argument. But why should the fact that there are two steps mean that the various Ti(R) cannot provide strong evidence in favor of R?

    Your final paragraph seems to conflate the notions of possibility and plausibility. The atheist should simply grant ab initio that all of these things are possible, that is, not logically contradictory, and then await the evidence from easter bunny fans, et al. that these things are more than bare logical possibilities. But it is no more fair for the atheist to demand of the theist a proof of the possibility that God exists than for the theist to demand of the atheist a proof that the notion of a universe without God is not logically incoherent. Claims of logical impossibility need to be butressed with arguments. The burden of proof lies there.

26. Tim,

    I hope you will not mind too much if I change the venue a little bit. I talked to one of my professor about our conversation and he gave me what I think is a pretty neat and intuitive argument.

    (1) Miracles are only possible (i.e. the possibility of a miracle event occuring is non zero) if it is the case that a supernatural entity exists.

    (2) Without the assumption that a supernatural entity or entities exists P(M)=0 and no amount of evidence will suffice to make P(M|T)>0. I note also that if it is not given beforehand that a supernatural entity exists then every “miracle” can be interpreted to be nothing more than the expression of heretoforth undiscovered law of nature. (Given that without the supernatural everything is natural)

    (3) With the assumption I will grant for now (ignoring the subtleties that I raised before for now) that a sufficient number of witnesses makes a miracle possible.

    (4) However, if we assume that a supernatural entity exists for the purpose of establishing a non-zero possibility for miracles occuring we cannot, lest we engage in circularity, then use miracles to justify a belief in the supernatural.

    (5) The opposite also holds: i.e. assuming that god does not exist we cannot use the impossibility of miracles as an argument AGAINST god.

    Now a note on the burden of proof. I will grant that god is possible so long as I know what you mean by god: i.e. if you define god in such a way that it is completely clear that there is no lurking logical contradiction. I am not claiming that it is impossible that god exist, I am simply saying that pending a definition I cannot judge whether it is logically possible that he exist. I can’t grant you possibility an initio if I am not clear what you are talking about. Agree?

27. Arturo,

    I certainly don’t mind your consulting your professor, if that is what you mean. My students consult me constantly on all sorts of issues, and I think that’s a good thing.

    On getting a clear concept before conceding logical possibility – this is an absolutely reasonable request. I am using “God” in the classical sense: an eternal, personal being, creator of all other things, of unlimited power (within the bounds of logical possibility), knowledge, and goodness.

    I am not sure that I follow the argument you relay from your professor. It looks as though it might run something like this:

    “Either one assumes that God exists or one assumes that God does not exist. If one assumes that God exists, then one cannot use miracles to argue for the existence of God since they are presupposed; if one assumes that God does not exist, then one cannot use the impossibility of miracles to argue against the existence of God since their impossibility is presupposed. Either way, one cannot appeal to miracles. Therefore, an appeal to miracles is of no use in arguments for or against the existence of God.”

    If this is the argument, then I have to disagree with the first premise. We are not compelled either to assume the existence of God or to assume the nonexistence of God in order to reason from the public evidence regarding God’s existence; indeed, we had better not be, for this would entail a particularly deep and troubling form of epistemic relativism. The language of assumptions is misplaced here. And the same holds for the confirmation of scientific theories by empirical data. We need not assume either the truth or the falsehood of, say, general relativity in order to see it confirmed by the measured advance in the perihelion of Mercury.

    Let M be the statement that a particular miraculous event has occurred, let G be the claim that God exists, and let T be some piece of testimony in favor of M. It is quite correct to say that, by the theorem on total probability,

    P(M) = P(G) P(M|G) + P(~G) P(M|~G)

    Now if P(M|~G) = 0 (a simplifying assumption but one I think will make this discussion easier for the moment), then P(G) >= P(M). So of course, if someone starts out with P(G) = 0, then P(M) = P(M|T) = 0. But it is certainly possible to object that P(G) should not be set to 0 without thereby assuming that P(G) = 1. So the claim

    Without the assumption that a supernatural entity or entities exists P(M)=0 and no amount of evidence will suffice to make P(M|T)>0

    is false as it stands.

    The way that this paragraph continues seems to confirm that we are being confronted here with this false dilemma:

    I note also that if it is not given beforehand that a supernatural entity exists then every “miracle” can be interpreted to be nothing more than the expression of heretoforth undiscovered law of nature. (Given that without the supernatural everything is natural)

    (I’m assuming that the quotation marks here are shudder quotes.) If by “given beforehand” you mean that it is assumed that P(G) = 1, then this is at best ambiguous and at worst false. The problem is that “can be interpreted” is a very, very flexible phrase. Marine fossils on mountaintops can be interpreted as clever hoaxes planted by industrious aliens, but that doesn’t mean they are best or even reasonably interpreted that way. The phrase “Given that without the supernatural everything is natural” seems, once again, to fall into the trap of assuming that either we are given G or we are given ~G, i.e., that P(G) = 1 or P(G) = 0.

    This is not to say, of course, that there are no undiscovered laws of nature or that there is no risk of misinterpreting a natural phenomenon as a supernatural one. But if a dead man who claims to be the Son of God dies and rises again, “undiscovered natural law” is not the way to bet.

    When you write

    With the assumption I will grant for now (ignoring the subtleties that I raised before for now) that a sufficient number of witnesses makes a miracle possible.

    do you mean “… makes a miracle probable”? If so, I understand and agree. But I do not see how witnesses are either required or helpful in arguing that a miracle is possible.

    You write:

    However, if we assume that a supernatural entity exists for the purpose of establishing a non-zero possibility for miracles occuring we cannot, lest we engage in circularity, then use miracles to justify a belief in the supernatural.

    Here is that word “assume” again! I don’t know of any author in the history of philosophy who has assumed that God exists for the purpose of establishing a non-zero probability (I assume this is what you mean by “possibility”) for the occurrence of a miracle. So I am unaware of anyone who has ever engaged in this sort of circularity. Certainly it is possible to appeal to M in support of G, just as it is possible to appeal to empirical data that are predicted more strongly by a theory than by its negation as support for a theory.

28. Tim,

    “We need not assume either the truth or the falsehood of, say, general relativity in order to see it confirmed by the measured advance in the perihelion of Mercury.”

    I think that you are missing the point here. I define a miracle as a supernatural intervention on the natural world. Given this the following holds: (With M=miracle, N=natural, xCy= x caused by y)

    M(x) <--> ¬N(x)

    And given that Vx. ¬N(x) -> xCy & ¬Ny

    We have that M(x) <--> xCy & ¬Ny

    So if it is the case that ¬Ex. xCy & ¬Ny

    It is also the case that ¬Ex. M(x)

    All of this is quite inuitive: if miracles need a supernatural cause and we are given that there is no supernatural cause then it follows that miracles do not exist. I will further add that: Vx. M(x) v N(x). In the case where we assume that ¬Ex. xCy & ¬Ny then we have that ¬Ex. M(x) and in the case where we assume that Ex. xCy & ¬Ny then we have that Ex. M(x). Here is where your objection needs to be addressed: why can´t we just suspend judgment, that is, not assume anything? Well for one, that is because our definition of “miracle” depends on such an assumption (here used formally). It is still possible for the perihelion of Mercury to advance even if it is the case that relativity is false (it suffices to consider that this advancing does not eliminate the possibility of other counterexamples to relativity), whereas it is not the case that a miracle is possible if there is a not a supernatural agent causing the miracle. That is, the existence of a miracle, defined as a supernatural intervention in the natural world, fully assures us that it is true that a supernatural agent does exist. Your analogy then, fails to fully capture what is at hand. (Unless you have a different defintion for miracle)

    “P(M) = P(G) P(M|G) + P(~G) P(M|~G)”

    I think you get your interpretation of this wrong. Specifically given ¬Ex.Gx then of course P(Ex.Mx | ¬Ex.Gx)=0, and we would have given that if ¬Ex.Gx then Vx.¬Gx that P(G)=0. P(M)=0=P(G) and assuming that either Ex.Gx or ¬Ex.Gx then the other case would be that given Ex.Gx then P(Ex.Mx I Ex.Gx)=1 and that P(G)=1 so P(M)=1=P(G).

    Here is where we can nuance the argument: We can say that if it is possible that god exists then it is possible that miracles exist, and thus escape the bivalent calculations that I have made up to this point. The Bayesian calculation would then be able to establish that given a non zero probability of god existing there is a non zero probability of miracles existing and that given a non zero probability of god not existing there is a non zero probability of miracles not existing. The only support that miracles could provide support for god in that sense would be if P(M | T) was proportional to P(G | M). So that the more probable it was that a miracle had occurred given testimony the more probable it was that god existed given the miracle. The question then becomes whether given an initial non zero probability that Ex. Gx we can then establish any P(M | T) to any greater degree than P(G). This is analogous to: given a x% chance that general relativity is correct can any one event not contradicting general relativity establish the chances that general relativity is correct to greater than x%? The original probability of general relativity being correct is set (in an ideal world) according to the entire corpus of evidence available, and so it certainly does not seem to me that any one event in that corpus could every hope to establish the probability of g.r. to a greater degree than the entire corpus itself. Similarly with god: the probability that god exists is set according to the entire corpus of evidence (which here includes miracles and supernatural interventions) so it certainly does not seem like any one miracle could set the probability of god existing any higher than the set of miracles taken together. P(M | T) then can never establish Ex.Gx to a greater degree than P(G) was assumed to be in the first place.

    P(M | T) is =< to P(G) which is proportional to P(M)

29. Arturo,

    I think I see better what you’re saying, but it still seems profoundly mistaken. First, let me try to restate your argument:

    “One cannot appeal to miracles to defend the existence of God. For by definition miracles are events caused by God, and anyone who disagrees with the claim that God exists will disagree with the claim that these are miracles.”

    If this is a misunderstanding, try again. But if this is what’s being said, then the problem is that this argument is using too blunt a set of categories. There can be evidence that a particular event – secularly described – is a miracle. A secular description of the event does not build in the assumption that it is brought about by any supernatural agency. One might, of course, try to argue that the event thus described was merely an unusual natural event or to suspend judgment. In some cases this sort of response is exactly right. One might also insist that the evidence being given is inadequate to underwrite serious belief that the event (secularly described) took place at all. And in some cases this response is the most appropriate. But there is no reason a priori to assume that all events will be subsumed under one or the other of these alternatives.

    I think I follow your use of V and E for quantifiers, but I don’t see why you think my interpretation of “P(M) = P(G) P(M|G) + P(~G) P(M|~G)” is wrong. You seem to be moving from the fact that ‘(G v ~G)’ is a theorem to the conclusion that we must start out with the assumption that either P(G) = 1 or P(G) = 0. Why?

    You write:

    The question then becomes whether given an initial non zero probability that Ex. Gx we can then establish any P(M | T) to any greater degree than P(G). This is analogous to: given a x% chance that general relativity is correct can any one event not contradicting general relativity establish the chances that general relativity is correct to greater than x%? The original probability of general relativity being correct is set (in an ideal world) according to the entire corpus of evidence available, and so it certainly does not seem to me that any one event in that corpus could every hope to establish the probability of g.r. to a greater degree than the entire corpus itself.

    This is mistaken. It is not in general possible to set the “original” or prior probability relative to the entire corpus of evidence available, since the evidential relations are often too complex for direct assessment and we are apt to run into sheer clashes of intuition. The whole issue of finding priors in anything but the simplest cases is quite vexed, but the ideal procedure is to assess the probability of the hypothesis in question on the most general unproblematic information available and then conditionalize successively on the more specific pieces of information.

    And in fact, we want it to be this way in both science and other areas in order to be able to have a conversation about the evidence. Even if we can’t agree on a prior probability for G, we can try to disassemble the available relevant evidence into probabilistically independent components T1, …, Tn for which we can assess at least approximately the values of the respective Bayes factors [P(T1|G)/P(T1|~G)], …, [P(Tn|G)/P(Tn|~G)]. If the product of these factors is many orders of magnitude greater than 1, then the available relevant evidence provides a strong confirmation of G in just the sense that P(G|T1 & … & Tn) >> P(G), where P(G) is the prior.

    If, for the reasons you appeal to, we couldn’t do that then we would be left – in all fields, for all hypotheses – with an irreducible clash of intuitions as to what value to assign to P(G|K), where K is the total corpus of our evidence. And that is obviously false.

30. Arturo,

    Here is a compact way of putting the point I am trying to make. By your own assumptions, P(G|M) = 1, but P(G|~M) < 1. Since 0 < P(M) < 1, it follows that P(G|M) > P(G). If, therefore, for some piece of evidence E, P(M|E) > P(M) and ±M screens E from G, it follows that P(G|E) > P(G), which is to say, E confirms G. Now let E be some bit of testimonial or observational evidence in favor of M. In the case at hand, ±M screens E from G. We already know from your assumptions that P(G|M & E) = P(G|M) = 1, and since the testimony, if false, provides no evidence for or against G, P(G|~M & E) = P(G|~M). So the only way to deny that such evidence can confirm G is to deny that it can confirm M – to deny that there can be any E such that P(M|E) > P(M). But this last denial is insupportable: it is obvious that there are all sorts of possible E such that P(M|E) > P(M).

    Therefore there is nothing circular or otherwise epistemically illicit about appealing to such evidence in an argument for the existence of God. And that is what Deanna and MJ are doing on this site.

31. Nice work, ladies. I really enjoyed the PowerPoint. I’ve started putting one together myself. We are close to having the same presentation.

    I wanted to add an additional fact — The disciple’s despair after the death of Jesus. I think it’s both pivotal and well-accepted, given both normal human emotion and the fact that the death of the messiah was out-of-content with the expectations of Jesus’ followers.

    I also added some slides regarding the general categories of alternative explanations.

    Finally, I also added something of a disclaimer of the target audience. As we see in this blog discussion, these arguments don’t go far for people who refuse to think outside the constraints of naturalism. Unless your audience accepts theism or at least deism, you can expect a response something like: “well, I don’t know and I don’t think you do either”. When people say there is not a shred of evidence for the resurrection, they are really saying there is no naturalistic explanation of how dead people can do stuff. Any evidence that leads to a super-natural conclusion is immediately removed from the table.

    Your presentation is beautiful and mine is ugly. Would you consider giving me permission to lift some of your artwork and text? I would give you full credit on an opening slide, and also promise not to do anything evil like claim copyright on your material. I would not hold saying “no” against you, especially if there are permissions implications from your side.

    Either way, great work. To me this is like “scrubbing bubbles”. The scholars have done the work, so we don’t have to. By repeating claims accepted by the left, right, and center, we put ourselves in a position of reiterating data, rather than imposing belief.

Comments are closed.