How does this lead to something that will convince a random third party, outside of Alice and Bob, in a way that can be uniquely identified as 'Bayesian math'?
How random is the third party? What epistemic frameworks do they find acceptable? (sorry if I am not getting what you are asking).
A theological argument (no matter how good) is unlikely to convince an atheist of anything.
In a perfect world if we agree that bayesian epistemology makes sense and I accept your priors and your model then I should be willing to accept your conclusions. But because of bounded rationality and other factors like https://slatestarcodex.com/2019/06/03/repost-epistemic-learn... then I might still refuse to do so if your conclusions are ludicrous or repugnant to me :)
> How random is the third party? What epistemic frameworks do they find acceptable?
Any of the 8 billion people, who are not Alice and Bob, passing by... who, largely, don't even care about the concept of 'epistemic frameworks' in the first place.
Writing an explanation that only is convincing if the reader already believes in 'Bayesian Math' in the first place seems redundant, hence me pointing it out.
Is this a good faith question? Or is it intended as a "gotcha"? I'm fine to spend a few minutes if you find this sort of thing fun.
I think I could, given the universe of people P, a set of belief frameworks E and a mapping B(belief) from P -> set(E). I would then try to say that my prior about B is that there's no E shared by all P.
Put another way, I think it's very likely there's nothing you can say that will convince everyone.
This would be an overly simplified model of reality because merely stating a valid argument in framework E held by some P is not sufficient to "convince" them. Also "epistemological frameworks" don't really exist, they're just a shorthand we can use to describe clusters of beliefs that often go together. Lots of other things about the argument matter, like how complex it is (reduces trust) or who is presenting it. Also, a given argument might be "valid" in multiple belief systems at once. Maybe we could add in the idea that a particular statement of an argument (call it A) which means different things in E1 and E2 is really two different arguments A1 and A2. How far you want to go with modelling is a matter of taste.
Do we disagree? Where? Maybe we can find a mutually acceptable model if you are interested.
If your overall point is that often people write complete garbage in the shape of a formal argument and then act like they've "proven" something - I 100% agree with you. We can't "mathematically prove" non-trivial things about reality but we can construct models and use tools to reason about them. I do believe that the activity of stating your model and then using tools can be helpful.
Pretty quickly we can tell if we disagree about the whole framing of something (the overall model) or our priors are just very different.
The explicitness of priors is a big feature and when they're wildly different we can discuss / present evidence for those.
We can also see how much our priors matter in terms of outcome, i.e, what are the "load bearing beliefs" that lead us to make a certain prediction.