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This suggests that questions like the following are ill-posed and not worth arguing over:https://twitter.com/3blue1brown/status/1074415844715782144 …
This doesn't mean that we can't advocate for Bayesianism. I think science should use more Bayesian methods (because it concerns our subjective beliefs about the world). It's just that there isn't One True Way, definitionally speaking.
IMO, the best way is to define probability as the expected value of the indicator (or a Boolean) function. The expected value just has satisfy some properties about linearity. Most fields have a very good idea of what expected value means in their domain (incl quantum mechanics).
Also just a reminder that although probability theory is usually developed by defining probability and deducing expectation, it can equally be developed by defining expectation and deducing probability.
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