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jimrandomh comments on Open Thread, August 2010 - Less Wrong
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In an argument with a philosopher, I used Bayesian updating as an argument. Guy's used to debating theists and was worried it wasn't bulletproof. Somewhat akin to how, say, the sum of angles of a triangle only equals 180 in Euclidian geometry.
My question: what are the fundamental assumptions of Bayes theorem in particular and probability theory in general? Are any of these assumptions immediate candidates for worry?
Jaynes' book PT:LoS has a good chapter on this, where he derives Bayes' theorem from simple assumptions (use of numbers to represent plausibility, consistency between paths that compute the same value, continuity, and agreement with common sense qualitative reasoning). The assumptions are sound.
Note that the validity of Bayes' theorem is a separate question from the validity of any particular set of prior probabilities, which is on much shakier ground.