Swinburne’s Bayesian Arguments

I recently looked through Nature’s List of Top 50 Science Blogs and ended up reading quite a lot of the Good Math, Bad Math Weblog of Mark Chu-Carroll, a computer scientist at a major industry research center who is enamoured of mathematics.

The Science Top 50 Weblogs seems to be heavy on biology and the U.S. Theme du Jour – maybe Theme du Siecle – which seems to be evolution versus creationism. Chu-Carroll came across an argument for the likelihood of the resurrection of the incarnation of God, proposed by Richard Swinburne, Emeritus Nolloth Professor of the Philosophy of the Christian Religion at the University of Oxford, and Fellow of the British Academy. Swinburne proposed his argument in a book, The Resurrection of God Incarnate, published by the Clarendon Press of Oxford University Press in 2003.

Now, I am no connoisseur of arguments about a god – any god – nor do I usually have much interest in such. However, Chu-Carroll’s comment awoke my interest, not only because of its less than deferential nature, but also because I recall Swinburne writing a book on Bayesian confirmation theory in the early 1970’s, which I tried to use – and failed – as a student trying to distinguish good arguments from bad arguments when the premisses were not certain (if the premisses are certain, deductive logic is good enough – I leave aside the question of which deductive logic……). And so it seemed to me that assigning Swinburne’s argument to a category of “bad math”, indeed, according to Chu-Carroll, “mind-numbingly stupid math”, was probably mistaken.

Chu-Carroll’s argument shows a misunderstanding of Bayesian confirmation, which I think is worth pointing out. His Article reads as follows:

An alert reader just forwarded me a link to this mind-bogglingly stupid article. This is one of the dumbest pseudo-mathematical arguments that I’ve ever seen – and that’s a mighty strong statement. This Oxford University Professor! argues that he can mathematically prove the resurrection of Jesus. Get a load of this:

This stunning conclusion was made based on a series of complex calculations grounded in the following logic:
(1) The probably of God’s existence is one in two. That is, God either exists or doesn’t.
(2) The probability that God became incarnate, that is embodied in human form, is also one in two.
(3) The evidence for God’s existence is an argument for the resurrection.
(4) The chance of Christ’s resurrection not being reported by the gospels has a probability of one in 10.
(5) Considering all these factors together, there is a one in 1,000 chance that the resurrection is not true.

Where to start with shredding this? Is it even worth the effort?

By a similar argument, I can say that probability of pink winged monkeys flying out of my butt is one in two: that is, either they will fly out of my butt, or they won’t. The probability that those monkeys will fly to the home of this Oxford professor and pelt it with their feces is one in two. If pink winged monkeys fly out of my butt, that’s an argument for the likelyhood of a fecal attack on his home by flying pink monkeys.

Do I really need to continue this? I don’t think so; I’d better go stock up on monkey food in my bathroom.

One problem with this argument is that Chu-Carroll misstates premisses in (1) and (2). A second is that his “similar argument” isn’t. Here are the reasons.

There is a notion in Bayesian confirmation of “prior probability”, which refers to my personal degree of belief in a proposition before I start to modify this belief in the light of evidence. I modify this belief according to the evidence by applying Bayes’s Theorem to obtain the “posterior probability”, that is, my modified degree of belief in the proposition upon taking account of the evidence. Thus, the premisses in (1) and (2) should read that my prior degree of belief in the propositions “God exists”, respectively “God became incarnate”, are 1/2. Why should this be?
Suppose one accepts Bayesian modes of argument, which not all do. There is a simple argument that my prior belief in any proposition in which I have no evidence or argument for or against should be 1/2, as follows. If A is such a proposition, then so is not-A, the contrary of A. Whatever prior I have reason to assign to A, the same reason leads me to assign the same prior to not-A. Since the probabilities of mutually exclusive, exhaustive alternatives should add up to 1 (on pain of a Dutch-book argument), it follows that I should assign a prior of 1/2 to both A and not-A. So the assignments of priors in both premisses in (1) and (2) are appropriate, when one has neither arguments for nor against the premisses, that is, when one is disinterestedly and rigorously agnostic as to the truth of the premisses.

Whatever Swinburne’s original argument, let us focus on this justification for the prior assignment. Chu-Carroll suggests that the prior assignment in premisses (1) and (2) is similar to a prior assignment of 1/2 that “pink winged monkeys [fly] out of [his] butt”. Now, I could well be rigorously agnostic about this, not knowing the man at all, but I very much doubt that either Chu-Carroll or his doctor can be. He has lots of evidence against (surely not for?) this proposition, so he cannot argue reasonably that his prior should be 1/2. His attempted ridicule fails; his argument is not similar.

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