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Eliezer_Yudkowsky comments on You only need faith in two things - Less Wrong
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To amplify on Qiaochu's answer, the part where you promote the Solomonoff prior is Bayesian deduction, a matter of logic - Bayes's Theorem follows from the axioms of probability theory. It doesn't proceed by saying "induction worked, and my priors say that if induction worked it should go on working" - that part is actually implicit in the Solomonoff prior itself, and the rest is pure Bayesian deduction.
Doesn't this add "the axioms of probability theory" ie "logic works" ie "the universe runs on math" to our list of articles of faith?
Edit: After further reading, it seems like this is entailed by the "Large ordinal" thing. I googled well orderedness, encountered the wikipedia article, and promptly shat a brick.
What sequence of maths do I need to study to get from Calculus I to set theory and what the hell well orderedness means?