This got me thinking: How does one really justify the law of non-contradiction without just appealing to intuition?
If you accept logic, but specifically deny the law of non contradiction, the problem that arises is called the Principle of Explosion. From a contradiction, anything follows.
So, just imagine the worst most slanderous thing someone could say about you. If logic is generally true, but the law of noncontradiction is not, and there's some statement A that is both true and not true, then someone could use A and not A to prove that slanderous terrible thing about you.
But you know that terrible thing isn't true, so you know that the law of noncontradiction must also be true.
