Mótsögn

Mótsögn is a term in Icelandic that refers to a logical contradiction. It describes a statement or a set of statements that cannot all be true at the same time. The word is formed from mót- (opposition) and sögn (statement or claim). In formal logic, a simple mótsögn occurs when a proposition p and its negation ¬p are both asserted, as in “Það er sól” and “Það er ekki sól.”

More generally, a group of premises is mótsögn if it entails both a statement and its negation, i.e., the set is inconsistent. In philosophy, mathematics, and logic, detecting mótsögn is essential for assessing the soundness of arguments and theories. A theory that contains a mótsögn is considered unreliable, since from inconsistent premises many conclusions may follow; the usual remedy is to revise or discard the offending premises to restore consistency.

In everyday language, mótsögn is also used to describe ordinary contradictions or conflicts between claims within a discourse. Distinctions are sometimes drawn between a formal contradiction in a deductive system and a merely argumentative disagreement in ordinary conversation.

See also: contradiction, consistency, logical validity.