Law of noncontradiction

From Wikipedia, the free encyclopedia

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:

$\neg (P \wedge \neg P).\!$

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 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.

1 The Law of Non-Contradiction is Indemonstrable
2 Quotes
3 See also
4 External links

[edit] The Law of Non-Contradiction is Indemonstrable

The law of non-contradiction is indemonstrable (neither verifiable nor falsifiable) in that anyone who attempts to disprove it must use the law itself, and thus beg the question. In this way it can be said to be undeniable, that is, literally impossible to deny. The law is impossible to prove for the same reason, since one has to use the law to prove the law, and this is a circular argument. (see Stanford Encyclopedia of Philosophy in External Links)

[edit] Quotes

“Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.” (Avicenna, Medieval Philosopher)