# Reductio ad absurdum

From Encyclopedia of Mathematics

A logical derivation rule that allows one to conclude that if a list of statements and a statement imply both a statement and the statement , then implies . The rule of reductio ad absurdum can, e.g., be written in the form

Reductio ad absurdum is a sound rule in the majority of logico-mathematical calculi.

#### Comments

Informally, the name "reductio ad absurdum" is also used for the rule that if together with implies a contradiction, then implies . This is of course equivalent to the above (and therefore sound) in classical logic, but it is not a sound rule of inference in intuitionistic logic.

**How to Cite This Entry:**

Reductio ad absurdum.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Reductio_ad_absurdum&oldid=16889

This article was adapted from an original article by S.Yu. Maslov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article