I can admit the possibility that probability doesn’t work, but not have to do anything about it. If probability doesn’t work and I can’t make rational decisions, I can expect to be equally screwed no matter what I do, so it cancels out of the equation.
The definable real numbers are a countable superset of the computable ones, I think. (I haven’t studied this formally or extensively.)
I can admit the possibility that probability doesn’t work, but not have to do anything about it. If probability doesn’t work and I can’t make rational decisions, I can expect to be equally screwed no matter what I do, so it cancels out of the equation.
The definable real numbers are a countable superset of the computable ones, I think. (I haven’t studied this formally or extensively.)