law of contradiction

In logic, the law of noncontradiction (also called the law of contradiction) states, in the words of Aristotle, that "one cannot say of something that it is and that it is not in the same respect and at the same time". In the symbolism of propositional logic, this is expressed as:According to Allan Bloom, "the earliest-known explicit statement of the principle of contradiction — the premise of philosophy and the foundation of rational discourse" — is given in Plato's Politeia (The Republic) where the character Socrates states, "It's plain that the same thing won't be willing at the same time to do or suffer opposites with respect to the same part and in relation to the same thing" (436B).
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one of three principles required by logical thinking set down by Aristotle.  A thing cannot be both itself and not itself.