principle of non-contradiction

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The law of logic that it is not the case that (p & not-p). Contradiction is the final logical stopping point: if we can derive a contradiction from a set of premises, then at least one of them is false (see reductio ad absurdum). If we ask what is so bad about contradiction, one answer is that a contradiction cannot be true (classically, if one conjunct p is true, then the other not-p is false, and vice versa, so they cannot be true together; see also negation). Another answer is that from a contradiction anything whatsoever can be derived, which is true in classical logical systems. See dialetheia; strict implication, paradox of.

Subjects: Philosophy.

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