In a debate about faith and doubt in which I was doubting all existence and my friend argued in favor of existence, he challenged my rationalistic perspective by asking me this: Your reasoning depends upon the rules of logic, but there is a problem: how do you KNOW, conclusively, that the rules of logic are sound? Isn't that an act of faith? Can't you conceive of a universe in which logic *appears* to work, but in which logic is actually an illusion? How do you know that you don't live in that universe? Cogito ergo sum did not cover this one. I was stumped. Can you help me out?
If a logical principle such as "F, therefore F or G" is false in some universe, then that universe contains a contradiction, and contradictions are impossible. So no universe containing a violation of logic could exist.