When did I claim that rationality was mathematics?
Right here:
you are attempting to disagree with a mathematical fact.
it needs a mathematical proof.
Here you go.
Maybe not "rationality" exactly but Aumann's work, whatever it is you call what we're doing here. Rational decision-making.
So yes, Aumann's theorem can be proven using a certain system of formalization, taking a certain set of definitions and assumptions. What I'm saying is not that I disagree with the derivation I gave, but that I don't fully agree with its premises.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.