Atheists still relying on Hume for support

An atheist visitor has attempted to use Hume's argument against miracles to deny the reality of Jesus' resurrection. And he's doing this even though he also rejects Hume's statements on cause and effect and asserts that the universe has existed from eternity or that it caused itself to come into being. He hasn't explained that to me yet. Don't get me started on that one.

Regardless, Hume’s “in principle” argument is today, generally recognised by philosophers to be, in the words of the atheist philosopher of science John Earman, an “abject failure.”

Hume’s maxim is as follows: No testimony . . . is sufficient to establish a miracle, unless this testimony is of such a kind that . . . its falsehood would be more miraculous, than the fact which it endeavours to establish.”

Hume’s argument actually falls into two more or less independent claims. On the one hand, there is his claim that miracles are by definition utterly improbable; on the other hand there is his claim that no evidence for a purported miracle can serve to overcome its intrinsic improbability. As it turns out, both of these claims are now known to be mistaken.

I’ll take his second claim first - No amount of evidence can serve to establish a miracle.

Probability theorists have asked just how much evidence it takes in order to establish the occurrence of highly improbable events. For a good example of this discussion see S. L. Zabell, “The Probabilistic Analysis of Testimony,” Journal of Statistical Planning and Inference 20 (1988): 327-54.

It is now realised that if one simply weighs the probability of the event against the reliability of the witness to the event, then we WOULD BE LED into denying the occurrence of events which, though highly improbable, we reasonable know to have happened. For example, if on the morning news you hear reported that the pick in last night’s lottery was 2198563, this is a report of an extraordinarily improbable event, perhaps one out of several million, and even if the morning news’ accuracy is known to be 99.99 %, the improbability of the event reported will swamp the probability of the witness’s reliability, so that we should never believe such reports. In order to believe the report, Hume would require us to have enough evidence in favour of the morning new’s reliability to counter-balance the improbability of the winning pick, which is absurd. This means that Hume’s argument could lead us into situations where we would be forced to deny the testimony of the most reliable witnesses because of general considerations. And that goes not only for miraculous events, but, for non-miraculous events as well, as Hume himself admitted with respect to the man in the tropics confronted with travellers’ tales of ice.

Probability theorists saw that what also needs to be considered is “What is the probability that the given testimony would have been given if in fact the event never happened?” One can immediately see the ramifications for the case at hand; How probable is it that the disciples would claim a resurrection took place when no such thing occurred?

Thus, to return to our example, the probability that the morning news would announce the pick as 2198563 if some other number had been chosen is incredibly small, given that the newscasters had no preference for the announced number. On the other hand, the announcement is much more probable if 2198563 were the actual number chosen. This comparative likelihood easily counterbalances the high prior improbability of the event reported.

The realisation on the part of probability theorists that other factors need to be included in the correct calculation of the probability of some event comes to expression in “Bayes’ Theorem.” In the case of miracles, where
M = some miraculous event
E = the specific evidence for that event and
B = our background knowledge apart from the specific evidence, the so-called “odds form” of the Bayes’ Theorem would look like this:
Pr(M/E&B) / Pr(not-M/E&B)
= Pr(M/B) / Pr(not-M/B)
x Pr(E/M&B) / Pr(E/not-M&B)

Given this ratio we can also compute the actual probability of M. If we represent the ratio as A/B then we can compute the probability of M given the total evidence by A/(A+B). So if the ratio is 2/3, then the probability of M given the total evidence is 2(2+3) = 2/5 = .4 or 40%.

Regarding the resurrection of Jesus, which would be a miracle, we’re asking here which best explains the specific evidence that we have, M (a miracle) or not M (no miracle).

The evidence that we have is:
. Jesus death by Crucifixion
. The empty tomb
. The conversion of the sceptic and Church persecutor Paul
. The conversion of the sceptic James
. The dramatic change in character of the disciples
. The explosive beginning of and current presence of the Christian Church

These are facts of history that demand an explanation. M or not M.

Unfortunately, Hume never discusses the second ratio representing the explanatory power of the miracle’s occurring or not occurring. He focuses almost exclusively on Pr(M/B), the intrinsic probability of a miracle, claiming that it is so inevitably low that no amount of evidence can establish a miracle. But that is plainly wrong, since no matter what non-zero value one assigns to the first ratio, the miracle may be very probable on the total evidence if the second ratio is sufficiently large.

A further factor which is neglected by Hume is the remarkable impact of multiple, independent testimony to some event. I’ve given you 23 independent extra Biblical testimonies to the events described above. If two witnesses are each 99% reliable, then the odds of their both independently testifying falsely to some event are only .01 x .01 = .0001, or one out of 10,000; the odds of three such witness’s being wrong is .01 x .01 x .01 = .000001, or one out of 1,000,000; and the odds of six such witness’s being mistaken is .01 x .01 x .01 x .01 x .01 x .01 = .000000000001, or one out of 1,000,000,000,000. In fact, the cumulative power of independent witnesses is such that individually they could be UNRELIABLE (as surely an atheist would claim them to be) more than 50% of the time and yet their testimony combined to make and event of apparently enormous improbability quite probable in light of their testimony. With respect to Jesus’ resurrection, it is difficult to know how independent some of the witness are - though in the case of people like Peter, James, and Paul, independence is well established.

So much for Hume’s in principle argument!

Again, Hume says, “No testimony . . . is sufficient to establish a miracle, unless this testimony is of such a kind that . . . its falsehood would be more miraculous, than the fact which it endeavours to establish.”

Hume’s way of putting his maxim is rhetorically loaded, however, equivocating on the term “miraculous.” since it is not at all miraculous that human testimony be false. Any miracle, no matter how small, would seem to be more miraculous than the testimony’s being false. Indeed, it would seem purely stupid to suggest that the disciple’s being mistaken would be a greater miracle than Christ’s resurrection! But Hume’s maxim is not really using “miraculous” in the sense of “naturally impossible.” To see this point, suppose, for the sake of argument, that it is more intrinsically probable that Jesus would rise from the dead than that the disciples were either liars or were lied to. In such a case their testimony may, indeed, be sufficient to establish the fact of Jesus’ resurrection, even though Jesus’ resurrection is, technically speaking, much, more miraculous than their testimony’s being false. Of course, Hume argues that a miraculous event will always be more improbable than the falsehood of the testimony in support of it.

But that only goes to underline the point that the real issue here is the probability of the events, NOT their miraculousness. The miraculousness of an event is merely the means by which Hume endeavours to show its improbability. It’s the improbability of miracle claims that Hume is after.

There is a line beloved in the “free thought” subculture that “extraordinary events require extraordinary evidence.” What we now see is that this seemingly commonsensical slogan is, in fact, false as usually understood. In order to establish the occurrence of a highly improbable event, one need not have lots of evidence. The only plausible sense in which the slogan is true is that in order to establish the occurrence of an event which has a very low intrinsic probability, then the evidence would also have to have a very low intrinsic probability, that is, Pr(E/B) would have to be very low. So, to return to our example of the pick in last night’s lottery, it is highly improbable, given our background knowledge of the world, that the morning news would announce just that specific number out of all the numbers that could have been announced. In that Pickwickian sense the evidence for the winning pick is, indeed, extraordinary. But obviously, that isn’t the sense that sceptics have in mind when they say that it take extraordinary evidence to establish the occurrence of an extraordinary event. For that condition is easily met in the Pickwickian sense.

The sceptic can’t reasonably mean that the miraculous events require miraculous evidence, for that would force us to reject any miracle claim, even if wholly natural evidence rendered the miracle more probable than not. What the sceptic seems to be saying by his slogan is that in order to believe rationally in a miraculous event, you must have an enormous amount of evidence. But why think that is the case? “Because a miracle is so improbable,” the sceptic will say. But Bayes’ Theorem shows that rationally believing in a highly improbable event doesn’t require an enormous amount of evidence. What is crucial is that the evidence be far more probable given that the event did occur than given that it did not. Again, how probable is it that the testimony has been given even though the event did not occur? The bottom line is that it doesn’t always take a huge amount of evidence to establish a miracle.

In order to show that no evidence can in principle establish the historicity of a miracle, Hume needs to show that the intrinsic probability of any miracle claim is so low that it can never be overcome. This takes us back to the first part of Hume’s argument, that miracles are by definition utterly improbable. Hume claimed that the uniform experience of mankind supports the laws of nature rather than miracles. Now such an assertion appears at face value to be question-begging.

To say that uniform experience is against miracles is implicitly to assume already that all miracle reports are false. That is to say, as we come to some alleged miracle claim, we do so knowing that all past miracle claims apart from this one have been spurious. Hume seems to be saying Pr(M/B) in terms of frequency. Miracles are utterly improbable because they diverge from mankind’s uniform experience. But the frequency model of probability simply will not work in this context. For trying to construe the probabilities in Bayes’ Theorem as objective frequencies would disqualify many of the theoretical hypotheses of the advanced science. For example, scientists are investing long hours and millions of dollars hoping for an observation of an event of proton decay, though such an event has never been observed. On Hume’s model of probability such research is a waste of time and money, since the event will have a probability of zero. In the case of Pr(M/B) the guidance for assigning probability cannot take the simple minded form of using the frequency of M-type events in past experience; that frequency may be flatly zero (as in proton decay), but it would be unwise to therefore see Pr(M/B)=0.

How we assess the intrinsic probability of M will depend on how M is characterised. Take the resurrection of Jesus, for example. The hypothesis “Jesus rose from the dead” is ambiguous, comprising two radically different hypotheses. One is that “Jesus rose naturally from the dead”; the other is that “Jesus rose supernaturally from the dead,” or that “God raised Jesus from the dead.” The former is agreed on all counts to be outrageously improbable. But the evidence for the laws of nature which renders improbable the hypothesis that Jesus rose naturally from the grave is simply irrelevant to the probability of the hypothesis that God raised Jesus from the dead. Since our interest is in whether Jesus rose supernaturally from the dead, we can assess this hypothesis on its own.

Bottom line, it is evident that there is no “in principle” argument here against miracles. Rather what will be at stake, as the example of Jesus’ resurrection illustrates, is an “in fact” argument that handles a putative miracle claim in its historical context, given the evidence for God’s existence. So the Humean sceptic has failed to show that any possible miracle claim has an insuperable low intrinsic probability. Couple this result with our earlier conclusion that even incredibly low intrinsic probabilities can be outweighed by other factors in Baye’s Theorem and it is evident why contemporary thinkers have come to see Hume’s argument as a failure.

Hume had an excuse for his abject failure because the probability calculus hadn’t yet been developed in his day. But today you no long have any excuse for using such a fallacious reasoning in denying the resurrection of Jesus the Christ.