I was using “crazy” to mean something like “too different from what we are familiar with”, but I take your point. It’s not clear we should want to preserve Aumann.
To be clear, rejecting Aumann’s account of common knowledge would make his proof unsound (albeit still valid), but it would not solve the general “disagreement paradox”, the counterintuitive conclusion that rational disagreements seem to be impossible: There are several other arguments which lead this conclusion, and which do not rely on any notion of common knowledge.
I was using “crazy” to mean something like “too different from what we are familiar with”, but I take your point. It’s not clear we should want to preserve Aumann.
Interesting, thanks for pointing this out!
Okay, this makes sense. (I also added a link to a paper at the end, which may have overlapped with your reply.)