The problem is not in one of the conditions separately but in their conjunction: see my follow-up comment. You could argue that learning an exact model of Carol doesn’t really imply condition 2 since, although the model does imply everything Carol is ever going to say, Alice is not capable of extracting this information from the model. But then it becomes a philosophical question of what does it mean to “believe” something. I think there is value in the “behaviorist” interpretation that “believing X” means “behaving optimally given X”. In this sense, Alice can separately believe the two facts described by conditions 1 and 2, but cannot believe their conjunction.
I still don’t get it but probably not worth digging further. My current confusion is that even under the behaviorist interpretation, it seems like just believing condition 2 implies knowing all the things Carol would ever say (or Alice has a mistaken belief). Probably this is a confusion that would go away with enough formalization / math, but it doesn’t seem worth doing that.
The problem is not in one of the conditions separately but in their conjunction: see my follow-up comment. You could argue that learning an exact model of Carol doesn’t really imply condition 2 since, although the model does imply everything Carol is ever going to say, Alice is not capable of extracting this information from the model. But then it becomes a philosophical question of what does it mean to “believe” something. I think there is value in the “behaviorist” interpretation that “believing X” means “behaving optimally given X”. In this sense, Alice can separately believe the two facts described by conditions 1 and 2, but cannot believe their conjunction.
I still don’t get it but probably not worth digging further. My current confusion is that even under the behaviorist interpretation, it seems like just believing condition 2 implies knowing all the things Carol would ever say (or Alice has a mistaken belief). Probably this is a confusion that would go away with enough formalization / math, but it doesn’t seem worth doing that.