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Contradiction

In 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. more...

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Illustrating a general tendency in applied logic, Aristotleâ€™s law of noncontradiction states that â€œOne cannot say of something that it is and that it is not in the same respect and at the same time.â€

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

Contradiction in formal logic

In formal logic, particularly in propositional and first-order logic, a proposition $\text{[math]}$ Ïˆ (because $\text{[math]}$

Proof by contradiction

For a proposition $\text{[math]}$

Contradictions and philosophy

Adherents of the epistemological theory of coherentism typically claim that as a necessary condition of the justification of a belief, that belief must form a part of a logically non-contradictory (consistent) system of beliefs. Some dialetheists, including Graham Priest, have argued that coherence may not require consistency.

Meta-contradiction

It often occurs in philosophy that the presence of the argument contradicts the claims of the argument; for example: Heraclitusâ€™s proposition that knowledge is impossible; or, arguably, Nietzscheâ€™s statement that one should not obey others.

Contradiction outside formal logic

In colloquial speech

Colloquial usage can label actions or statements (or both) as contradicting each other when due (or perceived as due) to presuppositions which are contradictory in the logical sense.