[jfoutz]

Math is independent. If physics works different, it may not support humans, so there's no one around to think those thoughts, but if you accept the axioms of math everything else follows.

Granted, in some bizzaro physics 2+2 may actually equal 3, (along these lines http://lesswrong.com/lw/jr/how_to_convince_me_that_2_2_3/) but you should still be able to construct a successor function and mechanically evaluate 2+2 = 4 according to our rules, even though the answers would seem weird.

We may indeed be assuming stuff we don't know we're assuming. Still the other people would see, oh they're assuming X which is wrong. but the other people take X to be true, it all works out.