Reductio ad absurdum

In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.^[1][2][3][4]

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. Formally, the proof technique is captured by an axiom for "Reductio ad Absurdum", normally given the abbreviation RAA, which is expressible in propositional logic. This axiom is the introduction rule for negation (see negation introduction) and it is sometimes named to make this connection clear. It is a consequence of the related mathematical proof technique called proof by contradiction.