Law of noncontradiction
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In logic, the law of noncontradiction 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 calculus, this is expressed as:
- <math> \neg (P \wedge \neg P).\, </math>
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).
According to Aristotle and Thomas Aquinas, this is a fundamental principle of human thought, which can only be proved by showing the opponents of the Principle to be themselves committed to it. Thus, Aristotle considers the case of someone who denies the Principle in the strong way – holding that every proposition is both true and false – and asks why such a person goes on the Megara road to get to Megara from Athens, since on such a person's view it is just as true that any other road would get him to Megara.
Bivalence and related laws examines how the law of non-contradiction is related to similar laws, such as the principle of bivalence, with which it should not be confused.
See also
fr:Loi de non-contradiction he:חוק אי הסתירה pt:Lei da não-contradição ru:Закон противоречия zh:无矛盾律