Cyan2 comments on Trust in Math - Less Wrong
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Brandon Reinhardt,
I'd recommend Jaynes's magnum opus for Bayesian philosophy, keeping in mind that Jaynes isn't infallible in spite of the fact that he writes as if he is.
For practical Bayesian statistics, a good undergraduate intro course is in Bayesian Statistics: An Introduction. Material for upper level undergrad to low level grad can be found in Bayesian Data Analysis, 2nd ed.
Note that I haven't read Howson and Urbach, so I don't know what overlap there might be.
If you know some calculus, I recommend: Box and Tiao: Bayesian Inference in Statistical Analysis.