Tuesday, May 24, 2005

Bayes Haze

Joe Carter at "the evangelical outpost" has a series of posts on Pascalian Bayesianism (for lack of a better label). As I've noted before, I think the only real sense one can make of Pascal's Wager is if one understands (1) that the textual context of the Wager is what seems to be notes for a dialogue; (2) that the point of the Wager is not to prove that God exists but to show that faith in His existence is not unreasonable.

When I get to the application of Bayesianism, though, and I see a phrase like "two times as likely if God exists," I think, "Two times as likely if God exists on what suppositions"? Without suppositions, nothing goes through. But if you have the suppositions, it is generally not necessary to bother with the Theorem; just use the suppositions themselves. Further, I'm not subjectivist about probabilities (I agree with Newman that there are no degrees of belief, just different kinds), so I'd need some prior rules for quantifying the probabilities. Since I am in the end a positivist about probability theory -- I think its only value is representing and classifying previously determined quantities and deducing their further relations in areas where we have reason to think this fruitful -- I would need (a) actually measurable quantities; and (b) reason to think that using Bayes's Theorem on these quantities would be fruitful (e.g., a general theory, or the successful use of the Theorem in analogous cases). I have no doubt that Bayes's Theorem is analogous to at least some kinds of probable inferences (in the old sense of 'probable'), but analogy is not an excuse for conflation. I have similar problems with Plantinga's argument against naturalism. I can make no sense of these sorts of arguments.

Those interested in the history of Bayes's Theorem can find Bayes's original essay (PDF) online.

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