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How would you write a better "Probability theory, the logic of science"?

Brainstorming a bit:

accounting for the corrections and rederivations of Cox' theorem

more elementary and intermediate exercises

regrouping and expanding the sections on methods "from problem formulation to prior": uniform, Laplace, group invariance, maxent and its evolutions (MLM and minxent), Solomonoff

regroup and reduce all the "orthodox statistics is shit" sections

a chapter about anthropics

a chapter about Bayesian network and causality, that flows into...

an introduction to machine learning

My perspective on anthropics is somewhat different than many, but I think that in a probability theory textbook, anthropics should only be treated as a special case of assigning probabilities to events generated by causal systems. Which requires some familiarity with causal graphs. It might be worth thinking about organizing material like that into a second book, which can have causality in an early chapter.

I would include Savage's theorem, which is really pretty interesting. A bit more theorem-proving in general, really.

Solomonoff induction is a bit compl... (read more)