If you model a human brain as a stochastic reasoning device, you can posit uncertainty as to whether the mechanism of the brain has, at some point in time, reached some logical conclusion and stored it for easy access. A device that must expend time/space to enumerate the deductive closure of its current knowledge base would at no finite time be deductively closed in a rich enough system. All this can be formalized within probability, although it requires some uncertainty either about the reasoning device---whether that's inherent stochasticity or uncertainty about its initial configuration, say.

If you model a human brain as a stochastic reasoning device, you can posit uncertainty as to whether the mechanism of the brain has, at some point in time, reached some logical conclusion and stored it for easy access. A device that must expend time/space to enumerate the deductive closure of its current knowledge base would at no finite time be deductively closed in a rich enough system. All this can be formalized within probability, although it requires some uncertainty about the reasoning device---whether that's inherent stochasticity or uncertainty about its initial configuration, say.