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Contradictions from WikiPedia:

In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical inversions of each other. Illustrating a general tendency in applied logic, Aristotle’s law of noncontradiction states that “One cannot say of something that it is and that it is not in the same respect and at the same time.”

By extension, outside of classical logic, one can speak of contradictions between actions when one presumes that their motives contradict each other.

In classical logic, particularly in propositional and first-order logic, a proposition is a contradiction if and only if . Since for contradictory it is true that for all ? (because ), one may prove any proposition from a set of axioms which contains contradictions. This is called the "principle of explosion" or "ex falso quodlibet" ("from falsity, whatever you like").

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