Wednesday, December 20, 2006

Bart Ehrman on History and Miracles

I'm just about finished listening to an audio CD lecture series entitled "The Historical Jesus" by Bart Ehrman. It's an interesting series by a scholar who, I gather, represents more-or-less a mainstream position in biblical scholarship. In other words, Ehrman is neither an out-and-out debunker of orthodox Christianity nor an out-and-out advocate and apologist. Rather, he styles himself as a professional "historian" and limits himself to what he thinks can be established with reasonable historical certainty. The result is that Ehrman accepts much of the New Testament account of the life of Jesus, but also rejects significant parts of the account.

As for the miracles attributed to Jesus, Ehrman neither affirms nor denies them. Rather, he invokes a kind of "historian's privilege", arguing that as a historian he cannot, in principle, affirm that a miracle, any miracle, has occurred in the past. Here's where I was most disappointed with Ehrman, because his a priori justification of this agnostic stance rests on what stikes me as a transparently fallacious argument. Here, in a nutshell, is his case:
  1. It is the job of the professional historian to determine what probably happened in the past.
  2. Miracles are, by definition, improbable.
  3. Therefore, the professional historian cannot as such affirm that a miracle has occurred.
The problem with this argument is the Ehrman conflates prior probabilities with posterior probabilities. The sense in which miracles are definitionally "improbable" according to premise 2 has to do with their having a low prior probability. In other words, miracles are not the sort of things that, given our usual background assumptions about the world, could be predicted in advance. Instead, we would expect under normal conditions that miracles would not happen. But the sense in which it is the job of the historian to determine what "probably" happened according to premise 1 has to do with posterior probabilities, that is, with the probability of a given reconstruction of events in the light of all of the available historical evidence. Since the relevant sense of "probability" shifts from premise 1 to premise 2, Ehrman's argument commits the fallacy of equivocation, and is therefore invalid.

Let me put my point more precisely with the help of Bayes' Theorem, which is provably true given the standard axioms of probability theory and widely used in philosophy of science as a model for evaluating the degree of support given to a hypothesis by new evidence.
  • Let B=a set of background assumptions
  • Let M=the hypothesis that a given miracle has occurred (say, the resurrection of Jesus)
  • Let E=the totality of historical data in addition to B that bear on M
  • Let PrB(X)=the prior epistemic probability that X is true in the light of B
  • Let PrB(X|Y)=the posterior epistemic probability in the light of B that X is true given that Y is true.
In these terms, Bayes' Theorem states that

PrB(M|E) = [PrB(E|M) × PrB(M)] / PrB(E)

With Ehrman, let's suppose that the prior probability of a miracle is very small, i.e., PrB(M) is close to, but not equal to zero.It is possible in principle that we could have good enough evidence to raise the posterior probability of the miracle to greater than 0.5? Sure. All we need, in this scenario, is for the value of

PrB(E|M) / PrB(E)

to be sufficiently high. PrB(E|M) represents the predictiveness of the miracle hypothesis. What are the odds that we would have the evidence we do if the miracle hypothesis were true? In general, it is not hard to get this probability as close to 1 as we please by choosing a suitably elaborated miracle hypothesis. The more crucial factor is PrB(E). This represents the surprisingness of the evidence. To get a high value for PrB(M|E) we need PrB(E) to be as low as possible. Thus, the more surprising the evidence, the better. Using another result or probability theory, we can say that

PrB(E) = [PrB(E|M) × PrB(M)] + [PrB(E|~M) × PrB(~M)],

where ~M stands for the complement of M, i.e., all of the ways in which M could fail to be true. Presumably, PrB(~M) is going to be fairly high (close to 1), whereas PrB(M) is going to be fairly low (close to 0). Now the value of PrB(E|M) must be less than or equal to one, and since that times a very low number is a very low number, the left hand part of the sum will generally be very low. What matters, then, if we are to have a low value for PrB(E), is that PrB(E|~M) be very small, sufficiently small to more than overcome the large value for PrB(~M). In other words, the predictiveness of the miracle hypothesis must be much higher than the predictiveness of any hypothesis not involving a miracle.

In sum then, Ehrman is wrong. A historian can in principle be warranted in believing that a miracle has occurred.


At 12/20/2006 7:25 PM, Blogger brinticus said...

I agree w/ you that "A historian can in principle be warranted in believing that a miracle has occurred", but in practice it would get him/her labled "liberal". Now people who reguarly buy and read commentaries on the Bible self confess as "conservative" (so I hear); thus, this large buying block would then avoid buying his work! Better to be agnostic on hot topics than transparent but never read.

At 12/20/2006 10:05 PM, Blogger Shane said...

To see a brief (and quite funny) video interview with Ehrman (by a comedian impersonating a fundamentalist journalist) concerning the scripture and history, check out this link and click on The Colbert Report video interview. It had me laughing. You can find similar interviews on Colbert's site with Richard Dawkins, Francis Collins, Peter Singer, and others (just search by name). It's a fun blending of academic and comedic cultures you don't see all that often. :-)

Keep up the great work, Alan.

Merry Christmas!


At 12/21/2006 12:12 PM, Blogger Alan Rhoda said...


I agree that Ehrman's agnosticism contributes to his marketability. My point was that his agnosticism is in some respects a reflection of a deeper and unjustified dogmatism, in particular his claim that historians cannot in principle be warranted in positing that a miracle has occurred.

Merry Christmas to you.

At 12/21/2006 12:16 PM, Blogger Alan Rhoda said...


That was pretty funny. Thanks for the link.

Merry Christmas to you and your as well.


At 12/22/2006 1:59 AM, Blogger Ocham said...

Suppose a historical figure claimed to have squared the circle, or to have disproved Godel, and that it is the historians job to determine whether the character was a charlatan or crank or whatever. The historian (who is not a mathematician) then needs to establish the likelihood of the proof being false. The only way of doing this is to consult the literature on mathematical proofs of this sort. The literature will show that all of the people who have claimed to have squared the circle, or disproved Godel, were demonstrably charlatans or cranks. So the historian will conclude that the character was, probably, a crank.

Is it the job of the professional historian to be a mathematician? Surely not. Their job to look at all sorts of evidence from expert sources, and make the corresponding judgment. In the case of miracles, the historian would look at all sorts of evidence from the appropriate sources, such as physics. (And also psychology – let's not forget Hume's point that men in all ages have been liars and rogues). I appreciate this is not Ehrman's argument, as you have summarised it.

At 12/22/2006 3:03 PM, Blogger Alan Rhoda said...


If one starts out by assigning a miracle hypothesis a zero prior probability (as I presume we would assign to the claim that someone has squared a circle), then it follows from Bayes' Theorem that no amount of evidence could ever raise its posterior probability. But if the hypothesis has a non-zero prior, however small, then it is possible in principle for evidence to raise its posterior probability as close to one as one might like.

The upshot is that the only way to maintain that a miracle hypothesis cannot "in principle" be evidentially warranted is to assume a dogmatic stance at the outset against the very possibility of a miracle or against the very possibility of evidence for a miracle. My beef with Ehrman is that he hasn't justified either sort of dogmatic stance.

At 12/23/2006 12:50 AM, Blogger Ocham said...

I think I already accepted that point. I was thinking about, and am still thinking about, what what the 'professional historian''s profession actually is. Clearly it is not the same as a mathematician's, but on the other hand mathematics would have to come into it, in the example cited. Remember the epistemic possibility that Cantor's proof is wrong, is non-zero. Perhaps all the mathematicians in the world who looked at it, really did make a mistake.

After I posted that, I thought about why paleontologists or astronomers (the big bang kind) aren't historians, since their job is to look at the distant past. Ehrman's point seems correct: there are certain jobs that aren't part of the historian's job, but it's hard to put your finger on it. I agree that the reason he gives is wrong, but he is nonetheless right. It's not the professional historian's job to take a view on miracles. (Except insofar as his job is to take a view on the reliability of witnesses, of course).

Happy Christmas to you and your readers!

At 12/28/2006 6:42 AM, Blogger danversgunners said...

Dear Alan,

The difficulty I see with your argument is how one could ever arrive at a number for the prior probability of a miracle. We don't know that the number is zero, true, but neither do we know how small it is. In fact, we don't know much about it all. Whatever value we set for this number will be more or less arbitrary. And any results we derive from the number will be arbitrary.

So while it is true that, in principle, evidence could be found such that the posterior probability of a miracle is close to one for any prior probability, it is also true that an even smaller prior probability can be found that makes that posterior probability close to zero. I can always trump your evidence with a smaller prior probability, and we have no way of determining which is the actual prior probability.

A similar thing happens with arguments about life on other planets. Some scientists (Carl Sagan, for example) will invent a probability that life might evolve on an Earth-like planet. Then he estimates the number of Earth-like planets in the universe and, lo and behold, he arrives at the conclusion that it is highly likely that life exists elsewhere in the universe. But the "garbage in, garbage out" principle applies. His prior probability of life evolving is a pure invention and entirely arbitrary; results derived from it will also be arbitrary. I think the same thing happens with a prior probability of a miracle.

David tye

At 1/02/2007 3:39 PM, Blogger Alan Rhoda said...

Hi David,

Good point. I agree that there are problems with assigning values to the priors. In the end, I doubt that there is any purely objective or neutral way to do this. Different people tend to assess priors differently in accordance with their own background assumptions and often in accordance with what they want to be true rather than in accordance with the "facts" (whatever those are, exactly).

Thus, with respect to the prior probability of a miracle, a person who starts with a disposition toward materialism is likely to evaluate the prior as being quite a bit lower than someone with a disposition toward theism. I don't think this licenses us to conclude that either side (or both) are being irrational. What it does mean is that how strong the evidence must be to justify a belief is the miraculous is going to be, to some extent, audience-relative.

My objection to Ehrman is to his dogmatism. He purports to be offering a necessary and objective constraint on historical research. But he hasn't shown that the constraint is necessary, and I am suspicious that his pretensions to objectivity mask an unacknowledged

At 1/08/2007 9:49 PM, Blogger Edward T. Babinski said...

Hume's point that I believe Bart Ehrman was seeking to employ in some fashion, and as found in Hume's essay On Miracles, is that in considering the evidence for an extremely implausible event (which is what the word 'miracle' implies, namely something amazing or to be wondered at, something which is scarcely believable), we must always consider which is more implausible, the miraculous event itself, or the possibility that the evidence for it is flawed in some way, however small.

Secondly, added to the above consideration one must add the possibility that the evidence being flawed is greatly increased when the person producing the evidence has some interest in what it is evidence for. If the motive for writing the Gospels were in any way correlated (think of official histories) with the need to prove them correct, we might deservedly be suspicious. [above is from the blog, BEYOND NECESSITY:

But let me expand on the second point. Crticial considerations concerning stores told by believers whose interests are invested in their beliefs being "true" rather than "false."

Riesenfeld and Gerhardsson applied rabbinic methods of
tradition-transmission to the early Christian situation. But that is not the only possible analogy in the history of middle-eastern religion. Early Muslims were concerned to hand down the hadith, or oral traditions of the Prophet Muhammad. How did they accomplish this? R. D. Smith has this to say:

...regarding the character of the transmitters of the traditions,
especially during that vulnerable century when they were transmitted only by word of mouth and memory, two ancient Moslem authorities agree that "a holy man is nowhere more inclined to lie than in the matter of traditions."

There are many venerated Moslems who actually are known to have succumbed to this temptation, some of them explicitly admitting that they did so. It is important to note, moreover, that in spite of the fact that these men were known as forgers, they were nevertheless revered as holy men because their lies were considered to be completely unobjectionable. It was a quasi-universal conviction that it was licit in the interest of encouraging virtue and submisssion to the law, to concoct and put into circulation sayings of the Prophet. [34]

Jan Vansina, in his Oral Tradition as History, comments:

Historical truth is also a notion that is culture specific.... When G. Gossen reports that the Chamuleros (Maya Chiapas) believe that any coherent account about an event which has been retold several times is true the historian does not feel satisfied.... In many cultures truth is what is being faithfully repeated as content and has been certified as true by the ancestors. But sometimes truth does not include the notion
that x and y really happened.... One cannot just assume that truth means faithful transmission of the content of a message. The historian must be on his guard; he cannot assume anything on this score, but must elucidate it for the culture he studies. [35]

Thus, by ancient middle-eastern standards, it is not at all certain that faithful "ministers of the word" would never dare let a "phoney" saying slip in. This might be the very thing they should do!

Gershom Scholem's study of the seventeenth century messianic pretender Sabbatai Sevi provides a productive parallel here. Sevi was able to arouse apocalyptic fervor among Jews all over the Mediterranean during the 1660s.
The movement suffered a serious setback when the messiah apostasized to Islam! But still it did not die away. The history of Sabbatai Sevi is more readily accessible to the modern historian than are the gospel events. Sabbatai Sevi lived much closer to our own era and much documentary evidence of various kinds survives him. Here, too, according to the apologists, legends should have waited at least a couple of generations
till they reared their heads. But Gershom Scholem speaks of "the sudden and almost explosive surge of miracle stories" concerning Sabbatai Sevi within weeks or even days of his public appearances! Listen to his description:

The... realm of imaginative legend... soon dominated the mental climate in Palestine [during Sevi's residence there]. The sway of imagination was
strongly in evidence in the letters sent to Egypt and elsewhere and which, by the autumn of 1665 [the same year] had assumed the character of regular
messianic propaganda in which fiction far outweighed the facts: [e.g.] the prophet was "encompassed with a Fiery Cloud" and "the voice of an angel
was heard from the cloud." [6]

Letters from December of the same year related that Sabbatai "command a Fire to be made in a publick place, in the presence of many beholders...
and entered into the fire twice or thrice, without any hurt to his
garments or to a hair on his head." Other letters tell of his raising the dead. He is said to have left his prison through locked and barred doors which opened by themselves after his chains miraculously broke. He kills a group of highwaymen merely with the word of his mouth. Interestingly, the miracle stories often conformed to the patterns of contemporary saints' legends.[7] The spread of such tales recalls the statements by the synoptic evangelists that many of their miracle stories came from popular
reportage (cf. Luke 1:65-66; 2:18, 38, 47; 4:14, 37; 5:15, 26; 6:17-18; 7:17, 22; 8:34-39, 47; 9:6-7, 9; 9:43; 12:1; 13:17; 18:43; 19:7, 37, 48).

A similar phenomenon occured with Jehudah the Said (died 1217). In his own lifetime, legends made him a great purveyor of religious magic, though actually Jehudah was a staunch opponent of such things! [8] More recently, African prophet and martyr Simon Kimbangu became another "living legend" despite his own wishes. One group of his followers, the "Ngunzists," spread his fame as the "God of the blacks," even while Kimbangu himself disavowed the role. Legends of Kimbangu's childhood, miracles and prophetic visions began within his own generation.

[9] Faith-healer William Marrion Branham was held in exaggerated esteem by legions of his followers, many of whom believed him to be Jesus Christ returned or even a new incarnation of God. He, however, did not teach such notions. In fact, once on a visit
to such a group of devotees in Latin America he explicitly denied any such wild claims made for him, but his followers reasoned that he was just testing their faith! Many believed in Branham's virgin birth despite his published recollections of his alcoholic mother.[10]

A final example is
more recent still. Researcher Ed Sanders encountered a number of legends about Charlie Manson during the writing of his book The Family. On one particular bus trip in Death Valley, "several miracles were alleged to have been performed by Charles Manson." One story relates that "Charlie
levitated the bus over a creek crag." [11]

So it seems that an interval of thirty or forty years could indeed
accomodate the intrusion of legendary materials into the gospel tradition. (Whether or not this actually occured is a different question.)


Friedrich Heiler, in his sympathetic biography, The Gospel of Sadhu Sundar Singh (Oxford University Press, 1927), did not dispute the recollections
of miracles by the famed Sikh convert to Christianity, Sadhu Sundar Singh, nor did he dispute the sincerity of his faith, but cautiously added some
"Critical Considerations":

"In contradistinction to the... religious explanation of the miracle of Sundar's conversion, modern religious science suggests one that is natural and psychological. The psychological process which those who have studied conversion experiences have discovered is easily discernable in the Sadhu's experience: the utmost tension of effort, followed by a state of
despair and complete cessation from struggle, culminating in a sudden inflow of assurance. The 'local color' on the fantasy side of the experience is easily explained by the influence of the story of Paul's conversion, which is obviously very similar. Although the Sadhu does not
remember having heard of Paul's vision of Christ on the road to Damascus, this still seems probable, as the New Testament was read daily in the mission school. It seems quite likely that Sundar Singh's inward struggles and their solution were inevitably colored by the Pauline experience.
Finally, we have to remember that such experiences of conversion are not all that rare in India. A leading figure in the Indian Methodist Church, Theophilus Subrahmanyam, was also led to Christ, and to work for Him among
the outcasts, by a wonderful vision. The famous Mahratta evangelist and poet, Narayan Vaman Tilak, had a vision of Christ in August 1917, a few months before his death... The Indian mind is much more prone to visionary
experience than the European [Emphasis added. - ED.]... To point out that this conversion resembles the conversion of St. Paul, to say that the whole experience conforms to a certain type and that similar experiences
often occur among Indian Christians, does not offer any clear and complete explanation; it only makes it somewhat easier to understand."[85]

Sundar also told many miraculous stories (besides his conversion account) which included Sundar's meeting with a "365-year-old Maharishi of Kailash," Sundar's fasting for "forty days," being thrown into and plucked out of a Tibetan well, and stories of miraculous rescues and martyrdoms of others. Even his sympathetic biographer, Heiler, pointed out that "The critical historian... draws special attention to the curious sameness of the miracle motif [in Sundar's stories]. There are really only two types of miracles which appear in slightly varied form again and again in his
stories. In the larger number of incidents supernatural figures appear and disappear with startling suddenness. The martyr-stories too, which the Sadhu tells, are almost all of the same type; in the midst of terrible
suffering the martyrs are filled with supernatural joy which convinces the spectators of the truth of their Faith... We cannot, however, help noticing one curious fact: the converts and martyrs of whom Sundar Singh speaks reveal exactly the same kind of experience as the Sadhu; they think, feel, and talk just as he does...Finally, various parallels from the New Testament, and from the legendary literature of Christianity and Buddhism, show that many of the leading ideas in the Sadhu's miracle-stories are in
no way either new or original... In addition, in all these tales of the miraculous the whole mentality of the Indian and especially of the Indian ascetic, must be taken into account. One of the most able students of the history of Indian literature says decidedly: 'Indians have never made any distinction between Saga, legend, and history.' This applies particularly to ascetics, who for days at a time are quite alone among the magnificent mountains of the Himalayas, and who give themselves up exclusively to the
contemplation of Nature, to inward concentration, and supernatural ecstasy [exactly as Sundar did, who spent much time travelling alone in his beloved Himalayas, and who admitted that he slipped into and out of "spiritual ecstasy" (or, as the Hindus call it, "samadhi;" or as we would call it today, "altered states of consciousness") spontaneously and
frequently, which included seeing visions and hearing voices - ED.]. In their experience the inner vision becomes developed to such an extent that the usual difference between subjective and objective truth disappears entirely. [Even Sundar's supporters and personal friends admitted that he had difficulty at times in distinguishing between vision and empirical reality.[86] - ED.] All this suggests that some of the Sadhu's stories of
the miraculous need not be considered as historical facts, but as legends; doubtless they have some solid foundation, but, in the form in which they are told, they have been worked up by a creative miracle-fantasy. Even
scholars who admit the possibility of the miraculous cannot refuse to
consider such a suggestion...Those who are familiar with the problems of biblical and hagiographical miracle find, to their astonishment, in the anecdotes which the Sadhu tells over and over again, certain clear principles, which show how legends are formed: repetition of the same
motif, doublets, and variants. It is a striking and significant fact that we can thus confirm these principles of the growth of legends in people belonging to our own day, for the Sadhu's stories deal exclusively with experiences of his own and of his contemporaries. So we see that legends do not necessarily arise after the death of a saint, and within the inner circle of his disciples, but during his own lifetime, and perhaps even in
his own mind."[87]

Based on writings by
Robert M. Price
Edward T. Babinski

The case of Bahuallah, the founder of the Ba'hai religion is also
interesting. He too denied performing miracles when he was alive, but a generation after his death/martyrdom, stories arose that made him into a
miracle worker.

At 1/13/2007 3:09 PM, Blogger Alan Rhoda said...


Interesting stuff, but it's all irrelevant to the point I'm making vis-a-vis Ehrman's position. I'll concede to you (and Hume) that the rationality of belief in miracle reports ordinarily requires very strong evidence and that such evidence is often not available or not available in sufficient quantities. My point is that none of this licenses Ehrman's dogmatic exclusion of the miraculous from historical consideration.

At 1/16/2007 11:50 PM, Blogger Vlastimil Vohánka said...

Dear Alan,

I am a Czech grad student in philosophy who wants to write a dissertation concerning contemporary analytical philosophy of religion, mainly the evidence for the resurrection of Jesus Christ. I am interested especially in R. Swinburne and W. L. Craig. Your post about Ehrman is very useful, so I will try to ask you for an advice.

Currently, I have, say, a problem with an argument against miraculous events in Jordan Howard Sobel’s Logic and Theism (2004, Cambridge UP).

There is, in Sobel, pp. 332f., a proof of a Bayesian proposition which Sobel calls Hume’s Theorem. It concerns conditions of the establisment of an event by a testimony and, in adapted notation, reads as follows: [(P(tM) > 0) and (P(M/tM) > 0.5] only if [P(M) > P(tM and not-M)]. P: probability; M: an event occurs; tM: a testimony for M occurs. I think the Theorem is a real theorem (i.e., is validly deduced) in the Bayesian probability calculus and the used premises of this calculus seem to be true.

Now, if M is a miraculous event, P(M) is, according to Sobel, ALWAYS extremely small: nearly 0. Why? It seems Sobel gets the value of P(M) as the rate of miraculous events of certain kind on the one hand and of all events of this kind on the other. E.g., sum of human-water-walking-events / sum of human-water-walking-events + sum of human-disability-of-water-walking-events; or sum of the resurrected people / sum of those people who died.

The following (adapted) citation illustrates and explains this way of determining P(M) in cases when we want to determine P(M/tM), i.e., the probability of some event M given a testimony for M. I. Hacking, An Introduction to Probability and Inductive Logic, 2001, Cambridge UP, p. 72f.: „You have been called to jury in a town where there are two taxi companies, Green Cabs Ltd. and Blue Cabs Inc. Green Cabs dominate the market, with 85% of the taxis on the road. On a misty winter night a taxi sideswiped another car and drove off. A witness says it was a blue cab. The witness is tested under conditions like those on the night of the accident, and 80% of the time she correctly reports the color of the cab that is seen. That is, regardless of whether she is shown a blue or a green cab in misty evening light, she gets the color right 80% of the time. You conclude, on the basis of this information:
(a) The probability that the sideswiper was blue is 0.8.
(b) It is more likely that the sideswiper was blue, but the probability is less than 0.8.
(c) It is just like probable that the sideswiper was green as that it was blue.
(d) It is more likely that not that the sideswiper was green.
This question was invented by Amos Tversky and Daniel Kahneman. They have done very extensive psychological testing on this question, and found that many people think that (a) or (b) is correct. Yet (d) is, in the natural probability model, the right answer! Here is how Bayes‘ Rule [a valid theorem in the Bayesian probability calculus] answers the question. Let G = A taxi selected at random is green. P(G) = 0.85. Let B = A taxi selected at random is blue. P(B) = 0.15. Let tB = The witness states that the taxi is blue. P(tB/B) = 0.8. P(tB/G) = 0.2, because the witness gives a wrong answer 20% of the time, so the probability that she says “blue” when the cab was green is 20%. We require P(B/tB) and P(G/tB). According to the Bayes’ Rule: P(B/tB) = [P(B)*P(tB/B)]/[(P(B)*P(tB/B)) + (P(G)*P(tB/G))]. Thus, P(B/tB) = (0.15*0.8)/[(0.15*0.8) + (0.85*0.2)] = 0.41. And P(G/tB) =
1 – 0.41 = 0.59. So, it is more likely that the sideswiper was green.
Why do so few people feel, intuitively, that (d) is the right answer? Tversky and Kahneman argue that people tend to ignore the base rate or background information. We focus on the fact that the witness is right 80% of the time. We ignore the fact that most of the cabs in the town are green. Suppose that we made a great many experiments with the witness, randomly selecting cabs and showing them to her on a misty night. If 100 cabs were picked at random, then we’d expect something like this: The witness sees about 85 green cabs. She correctly identifies 80% of these as green: about 68. She incorrectly identifies 20% of these as blue: avout 17. She sees 15 blue cabs. She correctly identifies 80% of these as blue: about 12. She incorrectly identifies 20% as green: about 3. So the witness identifies about 29 cabs as blue, but only 12 of these are blue! In fact, the more we think of the problem as one about frequencies, the clearer the Bayesian account becomes.“ Another typical example (next to taxicabs), showing the importance of base rates, is the case of a medical test. The example is constructed in such a way that: the test has very high veracity, the test reports that your are seriously ill, however it is more probable than not that you are not seriously ill because the illness is extremely rare (the base rate for the illness is extremely low).

Now back to Sobel’s argument. Remember that M is a miraculous event. P(tM), the probability of the occurence of a testimony for M, is greater than 0 and not nearly 0. As was said above, P(M) is nearly 0, which implies that P(not-M) is nearly 1. Now recall Hume‘s Theorem: [(P(tM) > 0) and (P(M/tM) > 0.5] only if [P(M) > P(tM and not-M)]. Thus, [(P(tM) > 0) and (P(M/tM) > 0.5] only if [P(tM and not-M) is nearly 0 or 0]. However, the last consequent is not true. So, the second conjunct of the antecedent is not true (the first one is true). We see that P(tM and not-M) is greater than P(M), and, according to Hume’s Theorem, a miraculous event M is not established by testimony: P(M/tM) is not greater than 0.5. (Cf. Sobel, pp. 336-37.) Hume’s Theorem, P(M) nearly 0, and P(tM) greater than 0 and not nearly 0, taken together, renders the miraculous event as not being established by testimony.

I think there are some possible objections to the argument:
(a) P(M), if taken as a measure of rational belief that M, can be much higher, maybe it equals 1, because belief that M has some special (properly basic)warrant (like in Plantinga’s Warranted Christian Belief, 2000). Which can be true even if the statement that the belief has the warrant is controversial and, in a sense, non-evident.
(b) P(M) can be made much higher in a way different from (a), somehow. E.g., by making use of the remaining total relevant evidence (one should not state Hume’s Theorem as [(P(tM) > 0) and (P(M/tM) > 0.5] only if [P(M) > P(tM and not-M)], but rather as [(P(tM/T) > 0) and (P(M/tM and T) > 0.5] only if [P(M/T) > P(tM and not-M/T)], where T is the remaining total relevant evidence; then it could be seen that the consequent in this version can be true) or by pointing to some relevant differences between determining the value of P(M) in the case of taxicabs (or medical tests) and in the case of alleged miraculous events (e.g., that in the former case, P(M), which actually means the probability that the testifier encounters the event, is determined by some stochastic process, but in the latter case by some another process, maybe specially directed by God).
I think that your way is (b) and that you are unsatisfied with (a). But, still, I wonder what (b) would be (in detail). I’ll be grateful for the tips on (your or someone’s else) literature (papers, books) concerning the mentioned problem, too.

Thank you very much,
Best regard,
Vlastimil Vohánka,

It is interesting how Sobel treats the following objection to his Bayesian argument. Sobel, p. 324f. (adapted quotation): „Suppose that a trustworthy reporter has said that the number drawn from some lottery was 79. If one were to take into account the great antecedent improbability of this number’s being drawn, as Hume would have one do, then, notwithstanding the reporter’s veracity, one would not believe him. But this objection is wrong; for sound Bayesian reasoning that takes into account the improbability of the draw says that in common circumstances, nothwistanding the antecedent improbability, we should believe the report according to how we consider the reporter to be.
Suppose possible draws are from numbers 1 through 1000 and that for each number n in this range the probability, P(n), that it will be drawn, is 0.001. Suppose it is certain that the reporter has said of a particular number, perhaps 79, that it was drawn. Let the veracity of the reporter in this case be such that, for each n in this range, P(tn/n) = 0.9, and by implication P(not-tn/n) = 0.1. Suppose additionaly that, whatever number had been in fact drawn, it is as likely that the reporter would have erred in favor of one other number, as that he would have erred in favor of another number. I am assuming that, for any two distinct numbers n and n‘ in the lottery’s range, P(tn‘/n) = 0.1/999: The 0.1-probability of not reporting a number drawn correctly is, I am supposing, distributed completely and evenly among the 999 possible misreports of it.
According to the Bayes’ Rule: P(79/t79) = [P(79)*P(t79/79)]/[(P(79)*P(t79/79)) + (P(not-79)*P(t79/not-79))].”
Sobel shows plausibly that (P(not-79)*P(t79/not-79)) = sum of P(n)*P(t79/n), for every n greater than 0 and lower than or equal to 1000 and not equal to 79. Thus, since (1) for each n greater than 0 and lower than or equal to 1000, including 79, P(n) = 0.001 and (2) for each of the 999 numbers in the range other than 79, P(t79/n) = 0.1/999, (P(not-79)*P(t79/not-79)) = 999*(0.001*(0.1/999)) = 0.001*0.1.
So, P(79/t79) = (0.001*0.9)/[(0.001*0.9) + (0.001*0.1)] = 0.9.

And, according to the genereal rule of cunjunction, P(not-79 and t79) = P(not-79)*P(t79/not-79) = (0.999*(0.1/999)) = 0,0001. Whereas P(79) = 0.001. Which is, in turn, in accord with Hume’s Theorem.

One only still wonders what, exactly, is supposed to be the relevant difference between lottery-cases and miraculous cases, and whether, to paraphrase Sobel’s words, there is a sound Bayesian reasoning that says that even in (some) miraculous circumstances, nothwistanding the antecedent improbability, we should believe the report according to how we consider the reporter to be.

At 1/17/2007 10:13 AM, Blogger Alan Rhoda said...


You raise some very interesting questions. Give me a day or two to respond.


At 2/18/2007 10:59 AM, Blogger Retha said...

Edward T Babinsky said: “that the evidence being flawed is greatly increased when the person producing the evidence has some interest in what it is evidence for. If the motive for writing the Gospels were in any way correlated with the need to prove them correct, we might deservedly be suspicious.... Criticial considerations concerning stores told by believers whose interests are invested in their beliefs being "true" rather than "false." ”


I agree a person’s interest in the topic at hand must be taken into account.
The gospel writers had incentive for writing in a certain direction because of the circumstances: The early tellers of the gospel story were persecuted and killed for telling it. (Before the resurrection miracle they speak of, the disciples themselves in fact admit in their own accounts that they were cowering in a locked-up room.) They thus had a vested interest to deny the whole story and say they were just friends of an ordinary man, Jesus.
They also had another vested interest in denying that this Jesus was God. They were from the strongly monotheistic Jewish culture. They would therefore (from a human point of view) have fared better at getting followers if claiming to follow a prophet, than claiming this was God in the flesh.

What could be their interest in claiming that Jesus was a miracle-doer, God incarnate, who rose from the dead? It could not be human respect – they got scoffing, inprisonment, stonings and lashings for it.
They could not have hoped to get in the good books of a Supreme Being either. If they did not believe in Christ’s miracles, the biggest being the resurrection, they would have had no reason to regard what they did and said as something God would approve of.

Historians claim that all of the disciples, except John, died martyr’s deaths. To quote Paul Little: “Men will die for what they believe to be true, though it may actually be false. They do not, however, die for what they know is a lie.......... They constantly referred to the resurrection as the basis for their teaching, preaching, living and- significantly– dying.”

So, the gospel writers had good, sensible reasons (live and dead!) to write in one direction- and still chose to write the opposite. That has to filter into the equation of how likely the miracle accounts are to be true.

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