I think the simple solution is to not talk about logical tautologies and contradictions when expressing the Kolmogorov axioms for a theory of subjective Bayesianism. Instead talk about what we actually know a priori, not about tautologies which we merely could know a priori (if we were logically omniscient).
Yes, absolutely. When I apply probability theory it should represent my state of knowledge, not state of knowledge of some logically omniscient being. For me it seems such an obvious thing that I struggle to understand why it’s still not a standard approach.
So are there some hidden paradoxes of such approach that I just do not see yet? Or maybe some issues with formalization of the axioms?
Yes, absolutely. When I apply probability theory it should represent my state of knowledge, not state of knowledge of some logically omniscient being. For me it seems such an obvious thing that I struggle to understand why it’s still not a standard approach.
So are there some hidden paradoxes of such approach that I just do not see yet? Or maybe some issues with formalization of the axioms?
Yeah, I think it’s that one