Rebel1 wrote: @Victor Reppert: You completely missed the point, once again. YOU DON'T HAVE THE RIGHT TO USE THE WORD "BAYESIAN". It's a term that has a clear meaning in Mathematics, and it is clearly not the one you imagine. Is that clear enough, now that I've used ALL CAPS??? Bayes' Theorem REQUIRES quantifiable prior probabilities to have any meaning, especially when those probabilities are likely to be low. And miracles are not miracles if they are not highly improbable.
The very point made by many of your critics remain. If miracles exist, then they will be resistant to any sort of probabilistic analysis. You cannot steal the language of Mathematics to give your personal, unvalidated beliefs the credibility attached to that field. You are not even a philosopher, because I expect from philosophers a little rigour in their use of language.
What you are, is a hack, no better than Deepak Chopra when he uses the word Quantum to give his pablum a "sciency" air.
So stop using the word "Bayesian", and we might be able to have a conversation. Use the word, and all you'll get from people who actually know what the word means is ridicule.
VR: You might want to read John Earman's (University of Pittsburgh philosopher of science and an atheist, and Keith's former teacher) book "Hume's Abject Failure" before you accuse me of not knowing what the word Bayesian means. (He references one of my papers in his book). Or you might try convincing my philosophy of science teacher at the University of Illinois, Patrick Maher (author of books like Betting On Theories), who worked with me on Bayesian theory while I was getting my doctorate, and explain to him that I don't know anything about Bayesianism. If Jordan Howard Sobel were still alive, you might want to ask him also, since he read two of my papers, and found them reasonable efforts, even though he differed with my conclusions and is the leading defender of the Bayesianized version of Hume's argument against miracles. Or, you can ask Keith. NONE of these people believe in miracles, but all of them thought I made some reasonable points in my two papers, one which appears on Internet Infidels, and the other of which came out in International Journal for Philosophy of Religion in 1989.
You might also want to read up on the Personalist school of Bayesian prior probabilities, a school that has many adherents. You might want to read Colin Howson and Peter Urbach's Scientific Inference: A Bayesian Approach, before you dismiss personalism as hogwash.
You might also try examining my arguments in my Infidels paper on miracles against frequentism before you make charges like this.
You also might want to think twice about the fact that you completely misrepresented my position before you blast me into the outer darkness for a complete misunderstanding of Bayesianism. In short, you might want to do your homework.
The fact that Bayesian inference is used with certain conventions within your scientific enterprise doesn't mean that you can dismiss the work of many other people who use that same methodology in different contexts, with different ground rules. To me, Bayesian personalism isn't a way of claiming a kind of mathematical precision for beliefs about, say, the resurrection which I know to be impossible. It is an attempt on my part to think from the standpoint of a model which allows a plurality of antecedent probabilities to start with, but nevetheless leaves people open to the consideration of evidence for and against religious beliefs. It's the best model I know of to do this job.
I could be thoroughly misguided, but I think I can appeal to the authority of some people who know a lot more about Bayesianism than I do to show that I do know what Bayesianism is.