Friday, December 03, 2010

Reply to Mark Frank on abusing probability theory

Mark Frank: You are quite right about abusing Bayes' theorem. Bayes also says we have to take into account the a priori probability of a natural or supernatural explanation. You have only considered the likelihood side of the equation. This is the famous gremlins in the attic paradox. Given gremlins in the attic it is very likely that they caused a noise. But that doesn't mean that Gremlins in the attic are a likely explanation of a noise in the attic.

Quite correct. However, we don't have any good way of measuring what the "prior" side of Bayes' theorem ought to be, and I presume that it can differ amongst reasonable people. That was the whole point of the anti-frequentism argument that I gave a few posts ago. I don't think there's a good way to go back into one's belief system and discount everything that is the product of a non-truth-conducive belief-producing mechanism, a la the Outsider Test. This is partly because it is not transparent to any of us why we think as we do. 

8 comments:

Brenda said...

I am absolutely certain that Bayesean probability theory will never apply to the odds of rolling a seven on a six sided die.

Victor Reppert said...

But that's a logical impossibility. Miracles or clairvoyance aren't logically impossible.

Brenda said...

Claims for miracles or clairvoyance are equivalent to claiming it is possible for one to roll a seven on a six sided die.

I am sure that somewhere there are gambler tales of miraculous dice that did physically impossible things. That's what it is to be a miracle.

Are you saying that god can't do things that are logically impossible? Heretic!

Victor Reppert said...

Heretic? Good heavens. That definition goes at least back to Thomas Aquinas. It's more Catholic than the Pope, and Protestants buy it also.

Mark Frank said...

However, we don't have any good way of measuring what the "prior" side of Bayes' theorem ought to be, and I presume that it can differ amongst reasonable people.

Of course it is hard and may not be possible to prove one set of beliefs to be correct - but that doesn't mean you can totally ignore the prior beliefs (or the gremlins always become the logical conclusion) or that you cannot have a rational discussion about the strength of prior belief.

Think of this way. If modern professional magician were to turn wine into water in front of your nose (and an invited audience)would you seriously think he had performed a miracle or would you assume there was a trick which you just hadn't worked out? I assume your answer is the second.

Now compare this to the account of Jesus doing the same trick. Your observational evidence for Jesus having turned wine into water is far weaker. But you believe the miracle is the correct explanation because of your prior beliefs.

Victor Reppert said...

A part of it has to do with how it fits into a broader account of Jesus' purpose on earth. Lewis's Miracles: A Preliminary Study is a must read here; not the famous third chapter that is the locus classicus for the AFR, but his Miracles of the Old Creation/Miracles of the New Creation discussion in the latter part of the book.

I don't think it's just arbitrary, or just canonical authority, that leads me to believe in water into wine but not clay pigeons turning into live pigeons.

Anonymous said...

Are you saying that god can't do things that are logically impossible? Heretic!

I just wanted to say that if you really believe that saying "God can't do the logically impossible" is heresy, you're hilariously ignorant and should probably hush up. You don't want to be "that atheist", the one that makes all the other atheists cringe whenever they talk. ;)

shiningwhiffle said...

"Claims for miracles or clairvoyance are equivalent to claiming it is possible for one to roll a seven on a six sided die."

Incorrect.

"That's what it is to be a miracle."

Nope.

There is, for I know, a vanishingly small probability that the items in my bedroom will spontaneously rearrange themselves to form the words of John 3:16.

Yet if this happened, which would seem the more reasonable response? "What a freak of quantum probabilities!" or "You know, I think Somebody's trying to tell me something..."