Absurdum

Absurdum is Latin for "to the absurd." In logic and rhetoric, it forms the basis of the technique known as reductio ad absurdum or ad absurdum, a proof by contradiction. The method begins by assuming a proposition's negation and then derives a consequence that is clearly absurd, contradictory, or impossible. By showing that the assumption leads to an inconsistency, the original proposition is affirmed, or at least the negation is rejected. The approach is widely used in mathematics, philosophy, and formal argument.

Historically, reductio ad absurdum is central to Greek mathematics and philosophy and remains a standard device in Western thought. It is used when a direct constructive proof is difficult or unknown. In mathematics, proofs by contradiction have supported many foundational results, such as Euclid’s proof that there are infinitely many primes and the proof that sqrt(2) is irrational.

Variants include reductio ad impossibile and "proof by contradiction." In everyday language, "ad absurdum" may appear in phrases describing logical or rhetorical reaching "to an absurd conclusion." The term "absurdum" is primarily used in formal contexts; outside mathematics and logic, modern usage favors plain language.