[cubefox]

> The math doesn't need a 'true' or 'false' distribution; that just falls out of the use of a model ('false') to approximate reality ('true').

Looks like a contradiction. If you identify reality with a probability distribution (rather than just plain facts), then that requires a "true" objective probability distribution.

> If I'm indifferent to sports teams (very broad distribution) and you're a rabid fan of A (sharp, narrow distribution), then it might take you a long time to express a point in a way I'll understand – but conversely I might be able to express "team B is good actually" in a way that just does not compute for you.

That sounds far too vague for me.