In particular, it suggests strategically throwing away information to deal with self-referential tomfoolery—but continuing to use probabilities to represent the reduced information remaining.
[Emphasis added.] There didn’t seemed to be any examples of that in this post. This:
P[q|P[q|X]=p]=p.
seemed like moving self-referential/higher level probability down to the level we care about. (It’s also one of the few things that seems reasonable to accept as an axiom.)
Throwing away information to deal with self-reference is a natural strategy in general; the ideas in this post specifically suggest that we use probabilities to represent the information which remains.
[Emphasis added.] There didn’t seemed to be any examples of that in this post. This:
seemed like moving self-referential/higher level probability down to the level we care about. (It’s also one of the few things that seems reasonable to accept as an axiom.)
Throwing away information to deal with self-reference is a natural strategy in general; the ideas in this post specifically suggest that we use probabilities to represent the information which remains.