Bayesianism Well, this is a very odd thing to say. Bayesianism is an empiricist approach, one based on observations. Empiricism is the polar opposite of rationalism. I think you need to discriminate between Bayesian math and Bayesian metaphysics. Bayesian math is /correct/. It’s not something you can disagree with. It doesn’t have a metaphysics, because it doesn’t make claims about the real world. Bayesian metaphysics is when mathematicians put on a philosopher’s hat and argue about how it applies to the real world. I haven’t bothered to see what they claim, because I don’t care, because the math works, and because I’m an empiricist, and in practice, decisions made using Bayesian analysis don’t change depending on your metaphysical claims about it. Bayesian math is an explicitly empiricist approach. Bayesian metaphysics are what rationalists make up to try to fit it into their worldview. This often happens because Bayesians are usually mathematicians, and before statistics, all mathematicians were strict rationalists. Bayesianism doesn’t try to rescue eternalism’s promise of certainty. I think you’re misinterpreting “convergence theorems”, which argue that Bayesian posteriors approach 1 or 0 in the limit. But that word “in the limit” implies “never”. A limit is a thing you never reach, and never can in this Universe, since it has only finite energy, hence a finite maximum number of computations can be done within it. Bayesianism actually proves you can /never/ have certainty, because that would require either beginning with at least one prior of zero or 1 (which then merely assumes the thing you’re trying to prove certain), or acquiring an infinite amount of information (which is impossible; see Finite Universe). It is one of several approaches which shows the correct way to integrate math and epistemology: “Mathematical certainty” applies to formal systems. Statistical epistemology, of which Bayesianism is just one kind and one part, isolates the propositions that can be expressed in a formal system, keeping track of the assumptions made in doing so. It then proves propositions about that formalization. When you finish an analysis, you have a provable statement about a formal system, but you can never prove that the formalization characterizes the real world. Frequentist statistics does the same thing; it just comes up with different types of propositions involving things like confidence intervals. Again, frequentist /statistics/ should be separated from frequentist /metaphysics/; the math is a formal system, and doesn’t care what you think it means about the real world. The prominent online LessWrong community is both Bayesian and rationalist. That, however, is a historical accident owing to the rationalism of its founder, Eliezer Yudkowsky.