Saturday, July 10, 2010

My Bayesian paper on Hume on Miracles

A  redated post. 

My first published paper, "Miracles and the Case for Theism" replied to Mackie's treatment of miracles in The Miracle of Theism. I discovered a formal error in Mackie's analysis, which violates the Mackie Revelance Principle. The paper came out in February 1989 International Journal for Philosophy of Religion. And, of course, a follow-up treatment of miracles is on Internet Infidels. Someone who wants to defend Mackie's or Hume's position might want to start by rebutting me in those papers.


Perezoso said...

Interesting discussion, sir. The material in the following paragraph, however, seems rather questionable:

""""But this argument conflates the claim that the future will resemble the past in some respect with the claim that nature is strictly uniform in the sense that it is deterministic and closed. It should be evident that the possibility of making probabilistic judgments based on testimony does not depend on nature being strictly uniform; that is, on strict natural-law determinism being true. If it did, then the acceptance of indeterminism in the area of quantum mechanics would have destroyed the scientific enterprise which, after all, relies heavily on testimony for its operation. We do need to believe that what has happened in the past is some indication of what is likely to happen in the future. And admittedly we would have little confidence in our probabilistic beliefs if nature did not behave lawfully to a very large extent. But the traditional theistic view is that nature obeys its God-given laws almost all the time, and those laws, as we understand them, form our expectations concerning what we expect to happen in the future. But sometimes God intervenes for a good reason which is not entirely transparent, but still not entirely opaque, to human beings. There are resemblances between the way in which nature behaves in the past and the way it will behave in the future (God the creator of nature sees to that). But beliefs about the likely plans and purposes of God must play a role in the credence functions, not only of believers, but of those who think God's existence epistemically possible. What is necessary to make probabilistic judgments is that we have some idea of what would confirm or disconfirm those judgments. It is not necessary to assume nature to be a closed, deterministic system."""

First, introducing God back into the discussion here may be unwarranted: Hume's point was that the dogma did not hold (at least in terms of proving the core doctrine of Judeo-Christianity), precisely because of the supernatural events, which run counter to the uniformity of experience. The text may not be therefore completely meaningless or worthless, but as evidence it is not authoritative.

The determinism/indeterminism discussion is another problem. It may not be necessary to assume that nature is a closed, deterministic system, but ordinary science suggests that is more than likely the case (notwithstanding a few possible subatomic glitches, which the uncertainty principle shows are negligible at extremely minute levels). Bricmont has addressed this issue in depth in his comments on misapplications of quantum mechanics and "chaos theory", and makes a convincing case for determinism (and even Darwinian mechanism), at least in terms of natural phenomena. I'm a networking guy, and merely armchair physicist, but the Copenhagen interpretation itself does not help the theist (and I believe locality holds, and thus object to the weirder readings of QM).

Indeed indeterminism (tho unlikely) might be read as showing a certain instability to nature, and disorder--at least in terms of challenging Newtonian mechanics (Hume sounds rather Newtonian at times as well, regardless of his doubts of causality--the doubts more about physics and inductive knowledge as contingent, and not necessary in an axiomatic, mathematical sense. Experience does show the regularity of nature. It's logically possible a billiard ball could fly upwards and hang in the air for a few minutes, but for all intensive purposes, unfeasible, and not worth considering. Popper himself did not quite get that, though Hume may have overstated the case for subjectivism on occasion (as Bricmont asserts as well)).

So, I don't think you've refuted Hume here (more to follow).

Victor Reppert said...

I think you have misunderstood my argument. First, if you have an argument that we can't do inductive inferences (and hence science) unless you presuppose that nature is a closed, deterministic system, then you rule out as pseudoscientific any suggestion, like the Copenhagen interpretation of QM, that nature isn't a deterministic system. Even if you buy in on some sort of "hidden variable" theory and think that in the final analysis determinism is true, I don't think you want this as an implication of your philosophy of science.

Bringing God into the discussion is possible here because the weight of my paper has been that you cannot logically go from past frequencies to antecedent probabilities. My view is that antecedent probabilities are subjective, that they can take into account whatever we happen to believe, including any beliefs we might have about God and what God is likely to do, and that we can only proceed by conditionalizing our beliefs on experience in order to get to anything like consensus.

Further, it is what is at issue whether presumably supernatural events go against uniform experience is precisely what's at issue. C. S. Lewis is right on this point:

CSL: Now of course we must agree with Hume that, if there is absolutely "uniform experience" against miracles, if, in other words, they have never happened, why then they never have. Unfortunately, we know the experience against them to be uniform only if we know that all the reports of them are false. And we can know all the reports of them to be false only if we know already that miracles have never occurred. In fact, we are arguing in a circle.

You have to face the fact that Hume simply did not have the kind of probability theory at his disposal to support the kind of argument he was making. When you give him a theory (Bayesianism) it turns out he ends up with a far weaker position than he was aiming for. Even atheist philosopher of science John Earman realizes this.

Perezoso said...

Do ancient, inconsistent anecdotal reports even count as evidence? Ich denke nicht. Even granting that all anecdotal reports of miracles for the last 2000 years may be used as evidence (and a hypothesis of "humans can rise back from the dead"), Bayes Theorem probably returns a likelihood of something like less than .001. Indeed, that's how it was originally used: to show that miracles were highly unlikely (the theist might say "that's shows they are miraculous!": thus showing he never wanted Bayes theorem to apply anyway).

Victor Reppert said...

So how would you reconstruct the founding events of Christianity. It looks easy to do, until you start trying to put together a story that is consistent with itself and the facts.

Victor Reppert said...

The problem is that there are a number of events which are attested by a lot of people which strong suggest that you had a bunch of people willing to change their lives in a huge way on the basis of having seen, or thought they had seen, miracles. You have devout Jews changing the Sabbath, claiming that God has come in the flesh in Jesus, claiming that Jesus was resurrected, forming a religious group which is in trouble with the authorities from the beginning, etc., all of which suggests to me that they really think that the Grand Miracle has occurred.

You have Peter, for example, getting the the face of the Jewish leaders and saying that the Jesus whom they crucified has been resurrected.

It's sometimes hard to get skeptics to see the problem with the origins of Christianity from a naturalistic standpoint. But there is a problem, and even if you don't think supernaturalism is the answer, the problem is still there.

J said...

Well, VR this Perezoso chap sounds

It's to be noted, however, that Hume's point on the presumption of the "uniformity of nature" was not meant to be taken as a rebuttal--but a presumption.

We presume the uniformity of nature--Newtonian reality, if you will. We presume that chupacabras don't exist. Only when there's clear and convincing evidence otherwise (like, a chupacabra running down the lane--not just hearsay reports, wacky blogs, etc) do we disregard the presumption.

Mark said...

So how would you reconstruct the founding events of Christianity. It looks easy to do, until you start trying to put together a story that is consistent with itself and the facts.

Maybe so. Does that make Christianity particularly likely? It seems to me that there have been so many miracle claims throughout history that, under the assumption that they're all naturalistic in origin, we would expect to find a few here or there that we couldn't readily explain away. It's like asking a million people to guess the number you're thinking of and then concluding the few who actually got it right must be psychic.

Doctor Logic said...


I think the Bayesian approach is the correct one, and while I agree that one cannot rule out all miracles from the get go, Hume is essentially correct.

1. There's a large volume of experience we have of the natural world. However, this volume is finite. In theory, we can acquire more evidence about a miracle in order to make the miracle believable. Although, I guess, the miracle becomes less miraculous in the process! (You seem to concede this point when you talk about extremely reliable witnesses, truth drugs, and so on. Let's throw in cameras, instrumentation, etc.)

That is, God could provide us with evidence if he wanted to. We can leverage naturalistic instrumentation in finding apparent deviations from natural law.

2. You then try to paint God into the background information by saying that maybe it is fairly likely that God would send his son and resurrect him. Let's suppose this was likely. How likely is it that you or I are divine sons of God? Well, presumably, it's pretty unlikely, as you think God only does this once. If it's a unique birthright, then the odds of any given person being the son of God is comparable to the odds of someone being resurrected. So, no help there.

If you start talking about what God would likely do (versus, say, gremlins), you'll run into the problem of evil.

3. You talk about the uncertainty in classification in the baseball player example. This is a fair point. However, it seems that the difficulty can be resolved by collecting more statistics. If Wallace hits .100 after a billion random sample points against pro pitchers, and is 2 for 2 against unremarkable pro pitcher Harris, can we rationally conclude that Wallace will continue to hit .500 against Harris? Clearly, not.

4. Improbable events in the past are likely to recede in credibility, even if true.

5. What if the apostles were the types of dudes willing to die for their beliefs before they met Jesus (or before they came to believe he was resurrected)? Because that's the way it looks. These guys followed Jesus on his traveling dog and pony show knowing full well that they risked getting crucified. They were religious fanatics from the get go.

6. Finally, the story of Jesus and his disciples comes to us by way of.... his disciples. And ONLY his disciples. It's not an independent source. The "witnesses" to the resurrection were not independent, either. It's not as if individuals in 10 different countries all had independent encounters, and wrote about them independently. You had a bunch of religious fanatics, in hiding, sharing visions, playing off each other's reactions, competing to be the most holy. They then wrote a book claiming there were 500 independent witnesses. At best, you have one witness in the entire account.

Doctor Logic said...

Duh! I meant "2 and 2".

Tim said...


Interesting paper. Minor point: I think you meant Philip Henry Gosse, in Omphalos (1857), not his son, Sir Edmund Gosse.

Bilbo said...

I confess that I didn't finish all of Vic's paper, so it might have discussed the following.

I think the readiness of Christians to believe that Jesus rose from the dead involves more than just the strength of the testimonial evidence that he did so. It also involves the testimony to his deeply moral, compassionate, commanding personality; his profound moral teaching; and what he claims about himself, including his claim that he came to give his life as a ransom for many, that he would rise from the dead, and that he had a unique father-son relationship to God. Yet when he said he was gentle and lowly in heart, we find this to be thoroughly credible. Certainly the Jesus of the Gospels is unique among men. If someone were going to experence so unique an event as rising from the dead, this would be the guy. That needs to be factored into our antecedent probabilities.

Tim said...


That's an interesting point, and it has perhaps even wider ramifications than those you describe. For example, the Gospels are each written with a somewhat different aim (Matthew to present Jesus as the Jewish Messiah, etc.); John's Gospel is notably different from the Synoptics. Yet the portrait of Jesus that emerges from them is a consistent portrait of the same personality. Quite apart from the sublimity of that personality, this consideration is an argument that they are all portraits drawn from life.

This argument is developed in several places in the older apologetic literature.

Walter said...

I think the readiness of Christians to believe that Jesus rose from the dead involves more than just the strength of the testimonial evidence that he did so

I think some of the readiness to believe comes from the promise of eternal life. We are terrified of the prospect that all that we are may cease to be at death. Immortality is seductive! Let us also not forget that conservative Christianity offers us the choice of the 'carrot' of eternal bliss or the 'stick' of an eternal suffering in hell. Belief in the Resurrection is not completely based on intellectual reasons; emotional factors play a large role as well.

Bilbo said...

Tim, Good point.

Walter, also a good point. But it's not just Christianity that offers us eternal life. It's Jesus who offers it. And though I wouldn't trust Christianity, I do trust the Jesus portrayed in the Gospels.
And if I'm wrong, what exactly have I lost? A life of trying to live the way I think Jesus would want me to live. That's not so bad.

Dustin Crummett said...

Belief in the Resurrection is not completely based on intellectual reasons; emotional factors play a large role as well.

This is also true of disbelief in the resurrection, though.

Walter said...

This is also true of disbelief in the resurrection, though.

I won't disagree. We cannot completely divorce ourselves from our desires. Desires which may cause us to skew the evidence in favor of a particular conclusion.