Rational discourse is impossible without the Law of Non-Contradiction (somewhat ironically, it's sometimes called the Law of Contradiction). This concept asserts that A cannot equal non-A, where A represents any proposition (propositions are statements that are either true or false). This is typically classified as part of Aristotelian logic, since Aristotle stated, "One cannot say of something that it is and that it is not in the same respect and at the same time."

For example, if it is true that 2 + 2 = 4, it is not true that 2 + 2 = 22. You can write down a "2" and add one more "2" on the paper to make a "22" but this is not adding 2 + 2 in the same respect as adding 2 + 2 in proper numeric fashion.

The Law of Non-Contradiction is the enemy of relativism and the ally of absolute truth. Opposing it is self-defeating. If you say, "The Law of Non-Contradiction is invalid," you are asserting that your view is true and that therefore your view is not false. Of course, you are using the Law of Non-Contradiction in your attempt to disavow it. If your statement was correct, it would be equally valid to say that your view is false and the Law is indeed accurate, so you have gained nothing.