Reductio ad absurdum

Argument that leads to a logical absurdity

In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity"), apagogical argument, or proof by contradiction, is the form of argument that attempts to establish a claim by showing that following the logic of a contrary proposition or argument would lead to absurdity or contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof. This argument form traces back to Ancient Greek philosophy and has been used throughout history in both formal mathematical and philosophical reasoning, as well as in debate.

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