David Chapman criticizes "pop Bayesianism" as just common-sense rationality dressed up as intimidating math[1]:

Bayesianism boils down to “don’t be so sure of your beliefs; be less sure when you see contradictory evidence.” Now that is just common sense. Why does anyone need to be told this? And how does [Bayes'] formula help? [...] The leaders of the movement presumably do understand probability. But I’m wondering whether they simply use Bayes’ formula to intimidate lesser minds into accepting “don’t be so sure of your beliefs.” (In which case, Bayesianism is not about Bayes’ Rule, after all.) I don’t think I’d approve of that. “Don’t be so sure” is a valuable lesson, but I’d rather teach it in a way people can understand, rather than by invoking a Holy Mystery.

What does Bayes's formula have to teach us about how to do epistemology, beyond obvious things like "never be absolutely certain; update your credences when you see new evidence"?

I list below some of the specific things that I learned from Bayesianism. Some of these are examples of mistakes I'd made that Bayesianism corrected. Others are things that I just hadn't thought about explicitly before encountering Bayesianism, but which now seem important to me.

I'm interested in hearing what other people here would put on their own lists of things Bayesianism taught them. (Different people would make different lists, depending on how they had already thought about epistemology when they first encountered "pop Bayesianism".)

I'm interested especially in those lessons that you think followed more-or-less directly from taking Bayesianism seriously as a normative epistemology (plus maybe the idea of making decisions based on expected utility). The LW memeplex contains many other valuable lessons (e.g., avoid the mind-projection fallacy, be mindful of inferential gaps, the MW interpretation of QM has a lot going for it, decision theory should take into account "logical causation", etc.). However, these seem further afield or more speculative than what I think of as "bare-bones Bayesianism".

So, without further ado, here are some things that Bayesianism taught me.

What items would you put on your list?

ETA: ChrisHallquist's post Bayesianism for Humans lists other "directly applicable corollaries to Bayesianism".

[1] See also Yvain's reaction to David Chapman's criticisms.

[2] ETA: My wording here is potentially misleading. See this comment thread.