To me Shrodinger's cat illustrates that reality can be self contradictory and hence irrational. Einstein said that "reality is merely an illusion albeit a very persistant one." Only there could Shrodinger's reality exist. I think Einstein looked at his discoveries and came to his conclusion. How much sense does the origin of the universe and so much else make?
I don't see reality as contradictory but just more complex than it lets on. Then again, it's not the case that every conceivable event actually happens and that adds to the complexity as only some things are possible.