Psy-Kosh,

Curiously, I have just the opposite orientation -- I like the fact that probability theory can be derived as an extension of logic totally independently of decision theory. Cox's Theorem also does a good job on the "punishing stupid behavior" front. If someone demonstrate a system that disagrees with Bayesian probability theory, when you find a Bayesian solution you can go back to the desiderata and say which one is being violated. But on the math front, I got nothing -- there's no getting around the fact that functional equations are tougher than linear algebra.