E. T. Jaynes
I just read a very interesting book by E. T. Jaynes called Probability Theory: The Logic of Science. He doesn't rely on Kolmogorov measure-theoretic foundations, and instead attempts to construct probability theory from Aristotlean logic. He is, of course, a Bayesian - though quite different from what your standard frequentist professor would have you believe. And his tome written over some 30 year period (published posthumously), is a very heartfelt textbook - you can actually feel his soul in it (whatever that means for an experimental physicist). I'm not really going to go into it in any depth here about the concepts he puts forth. But I'll say this. Agree or disagree with it - it is definitely an interesting read.
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