I've been trying to list out for myself the various arguments people give for going with Bayesian (or at least probabilistic) epistemology. Here's what I have so far:

1. Intuitive representation for degrees of belief: It seems pretty obvious that beliefs come in degrees. Representing degrees of belief as numbers between 0 and 1 that follow probability theory (including Bayes' Theorem) seems intuitively straightforward.
2. Cox's Theorem: Given some very plausible desiderata for rational thinking with degrees of belief, probability theory (including updating using Bayes' Theorem) follows.
3. von Neumann - Morgenstern (VNM) Representation Theorem: Any agent following certain very plausible desiderata for rational decision making can be represented as a Bayesian utility maximizer for some (perhaps extremely complicated) utility function.
4. Dutch Book arguments: Any agent violating Bayesian decision making can be "Dutch booked" with a set of deals that will result in a guaranteed loss for the agent.
5. Philosophy of science: Many philosophers of science think that science is (ideally) just Bayesian reasoning, in that it is trying to infer the probability that a theory is correct given the evidence. Alternative approaches to philosophy of science (e.g., Popperian falsificationism) have serious problems.
6. The Bayesian Brain hypothesis: Many cognitive scientists think that biological brains instantiate Bayesian reasoning as one of if not the primary thinking algorithm.
7. Evidence from superforecasting: Phil Tetlock and colleagues found that the best forecasters use (mostly intuitive versions of) Bayesian reasoning, among other techniques.
8. Paradoxes: Probabilistic reasoning helps resolve a bunch of philosophical paradoxes related to epistemology (e.g., Lottery Paradox, Preface Paradox, Raven Paradox).
   
   I'm pretty sure I'm missing some arguments though. What did I leave out?
   
   (Of course, there are also counterarguments to these given by opponents of Bayesianism, and there is also a long list of arguments people use *against* Bayesianism. But that's for next steps. At the moment I'm just trying to list out arguments people give *for* Bayesianism / Probabilism.)