In a previous thread, Caleb O wrote:

I think I am one of those atheists who is slightly impressed with Bayesian arguments for the existence of God (Swinburne, Collins). At least they appear to be more successful than deductive arguments. What are these “ridiculously ill-supported assumptions” you speak of?

Now before I address the specific question, I should back up and say that Bayesian arguments–and probabilistic arguments in general–aren’t fundamentally different from traditional deductive arguments for the existence of God. Probabilistic arguments are really a kind of deductive argument, but one where you’re reasoning about probabilities. Alternatively, deductive can be seen as a special kind of probabilistic argument where all the probabilities are either 1 or 0.

Either way you see it, Bayesian arguments and deductive arguments are alike in that they’re only as good as their premises. My suspicion of Bayesian arguments isn’t that there’s anything inherently wrong with them. Rather, the issue is this: People are rarely impressed with deductive arguments simply because they’re deductive. Deductive arguments with utterly ridiculous premises tend to get laughed at.

Bayesian arguments, though, are unusual enough that to some extent you can impress people with them just because they’re Bayesian. This means when you hear about an awesome Bayesian argument, you have to wonder if there’s any reason why whoever is promoting it, aside from the fact that it’s Bayesian. It gives Christian apologists an incentive to dress up ridiculous arguments in Bayesian terms.

So I’m just going to go through and point out some of the most glaring issues with the most prominent attempts to give a Bayesian case for the existence of God. The original defender of the Bayesian approach to arguing for the existence of God is Richard Swinburne. With Swinburne, he basically admits that the evidence in favor of God isn’t all that great, and for the balance of probability to favor God, Swinburne feels the need to totally dismiss the problem of evil. And unfortunately, he takes the unconvincing and frankly offensive approach of trying to suggest compensating goods that might have come out of particular evils (including, notoriously, saying that the Holocaust gave the Jews an opportunity to display courage).

Robin Collins has risen to prominence recently for his Bayesian formulation of the fine-tuning argument. As with Swinburne, the handling of the problem of evil is sloppy, though in a different way: Collins focuses on a comparison of theism to what he calls the “naturalistic single universe” hypothesis (NSU), and rests his case on claiming that even if the problem of evil is some evidence for NSU over theism, fine-tuning is even stronger evidence in the other direction. He ignores the problem (pointed out by Hume) that even if we accept the argument from design, the problem of evil would still favor the hypothesis of an amoral or indifferent designer over traditional theism.

Collins also dismisses a number of versions of the multiverse hypothesis as “speculation,” though he never explains what he means by this or why the God hypothesis counts as more than mere speculation.

Tim and Lydia McGrew have also gained a bit of notoriety for taking a Bayesian approach to defending the resurrection of Jesus. Yet here are the assumptions they make (with scarcely any argument):

Our argument will proceed on the assumption that we have a substantially accurate text of the four Gospels, Acts, and several of the undisputed Pauline epistles (most significantly Galatians and 1 Corinthians); that the Gospels were written, if not by the authors whose names they now bear, at least by disciples of Jesus or people who knew those disciples – people who knew at first hand the details of his life and teaching or people who spoke with those eyewitnesses – and that the narratives, at least where not explicitly asserting the occurrence of a miracle, deserve as much credence as similarly attested documents would be accorded if they reported strictly secular matters.5 Where the texts do assert something miraculous – for example, Jesus’ postresurrection appearances – we take it, given the basic assumption of authenticity, that the narrative represents what someone relatively close to the situation claimed.

It doesn’t seem to even occur to them that they might need to invest actual effort arguing these claims . This is some Josh McDowell-level shit. And actually, it screws up their entire Bayesian set-up. The proper way to set up the question from a Bayesian point of view isn’t to assume the Gospels are mostly true and then ask the probability of it all happening in a non-miraculous manner. Rather, the question they should be asking what the probability is that people would tell stories like the ones in the gospels even if no miracles happened. And given all the crazy stories people tell, that second probability is pretty high.

What’s striking about all this is the problems with these arguments are problems you find in apologists who no one takes seriously, including Josh McDowell. The Bayesian framework doesn’t do anything to correct for the problems, it just creates a distraction from them.

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