That still doesn't change the fact that the two statements he is believing are semantically identical, he is believing A and not A at the same time. Jeff, regarding your first sentence, I am accusing you of sophistry . No, I don't mean that. It also does have nothing to do with any of those things you named off, the example could be restated with different variables. I think you might be overlooking the problem, that A is (semantically speaking)believing Pv~P at the same time. Sure, its not a wholly pragmatic problem, or a mind-blowing question, but there is still a puzzle involved.