Comment on Reflection in Probabilistic Logic

Tue, 26 Mar 2013 13:18:56 GMT

Ok, for [a < P('G') < b] I see why you'd use a schema (because it's an object level axiom, not a meta-language axiom).

But this still seems possibly problematic. We know that adding axioms like [-1 < P('G') < 1] --> [P('-1 < P('G') < 1') = 1], would break the system. But I don't see a reason to suppose that the other reflection axioms don't break the system. It might or it might not, but I'm not sure; was there a proof along the lines of "this system is inconsistent if and only if the initial system is" or something?

Discuss