Négation

Négation is the operation or relation that denies or contradicts a statement, assertion, or predicate. In philosophy, logic, linguistics, and everyday language, negation signals that the content of a proposition is false or opposite to what is asserted. In many systems, negation yields a proposition whose truth value is the opposite of the original.

In linguistics, negation is a grammatical category realized by a negation marker, often a particle, prefix, or auxiliary verb plus a negative word. It has scope, typically covering the predicate and its complements, and interacts with polarity and focus. Languages use diverse forms, such as French ne… pas, English not, Italian non, or Spanish no. Some languages exhibit negative concord, where multiple negative elements combine to express negation, while others require a single negation marker.

In logic and mathematics, negation is a unary operator on propositions, denoting not P. The truth of ¬P is the opposite of P. Negation obeys laws such as double negation (¬¬P ≡ P) and De Morgan’s laws for conjunctions and disjunctions. It also interacts with quantifiers: not all books are read becomes there exists a book not read.

The study of negation also covers related phenomena such as litotes (expressing something by negating its opposite), negative polarity items, and the cross-linguistic variation in how negation is formed and scoped. Different languages show a range of strategies, from clausal negation to explicit negative affixes or auxiliary constructions, reflecting broad typological diversity in expressing denial.