Logicians pride themselves that they can offer with their "law of contradiction" a perfect test of truth. They call it the fundamental law on which reasoning rests. Put into a few words it declares, "A proposition cannot be both true and false." The extraordinary thing about this law is that its own truth cannot be proved by logicians themselves. They can offer an indirect or roundabout proof by assuming the contrary, and affirming that a proposition may be both true and false. The significance of such a statement, however, is as even the tentative denial of the law implies, that at the same time it may also be true. But this is a contradiction. Therefore, the law must be true. Unfortunately for the logicians, such a proof is hardly valid because it is applying the very law which is called into question. So they are forced to content themselves by regarding the law as a self-evident one.
-- Notebooks Category 7: The Intellect > Chapter 4 : Abstract Thought > # 38
