Thanks for that link. I did not know that this is a term used to describe this viewpoint. I would expect frequentist statisticians to also agree with “beliefs = probabilities”, and when they do so it would feel odd to be able to say they are being (or acting) Bayesian when doing so. They could agree with much of the viewpoint in that Wikipedia page.
Maybe the way I can reconcile this is to think of “Bayesian epistemology” and “Bayesian statistics” as two concepts inspired by the same source but with different breadths. Rather than only using Bayesian as a word to highlight the specific parts of a belief system that can’t be described by general probability, in epistemology we can use Bayesian as a broader term.
Good write-up. Something that has been nagging at me since reading is that I’m not sure this is specifically Bayesian. It’s not incompatible with Bayesian viewpoints, yet not exclusive to them either. When I try to describe this type of thinking to people I use the term “probabilistic”. In the Venn diagram of viewpoints, the “Bayesian” circle would fit entirely within the “probabilistic” circle. A non-Bayesian, such as someone with a frequentist interpretation of statistics, would still fit all of the reasoning given. This mindset would feel more Bayesian if anything depended on informed priors, or used a Bayesian updating formula, or directly cited Bayes theorem. Maybe what we need is a word for someone who believes in probabilistic rather than certain outcomes.