Law of contradiction:
Also called the law (or principle) of non-contradiction. One of the traditional three laws of thought (the other two being the laws of identity and of excluded middle).
Variously formulated as saying that no proposition can be both true and not true; or that nothing can be – without qualification – the case and not the case at the same time; or that nothing can -without qualification – both have and lack a given property at the same time.
The law cannot be logically proved without begging the question, though arguments of a different kind (among those called transcendental arguments) have been offered in its defence since Aristotle (384-322 BC) in his Metaphysics (book 4, chapter 4).
However, recently a notion of dialetheism has been defended which allows breaches of the law in certain cases.
Also see: paraconsistency
G Priest, ‘Contradiction, Belief and Rationality’, Proceedings of the Aristotelian Society (1985-86)