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satt 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?
Bayes's theorem follows almost immediately from the ordinary definition of conditional probability, which I think is itself so reassuringly intuitive that no one who accepts the use of probabilities would worry about it (except perhaps in the corner case where the denominator's zero).