law of contradiction (logic)
What is the law of contradictions (inconsistency)? Meaning and usage - Cotobank
Nippon Encyclopedia (Nipponica) "Contradiction Rulings
law of contradiction
It is the law of contradiction that states that for any proposition, it cannot be both true and false at the same time. Using symbols, it can be formulated as A∧~A (A and not A) does not hold for any proposition A. Or it may be stated that no proposition can be true and false at the same time.
Like the law of excluded middle, the law of contradiction is a fundamental law of logic known since ancient times, but it was only after the establishment of modern logic that it came to be treated strictly within logic. In other words, modern propositional logic is formulated in such a way that the law of contradiction is derived as a theorem. However, when denial is understood constructively, it has become clear that the law of contradiction, like the law of excluded middle, does not necessarily hold.
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