In logic and mathematics, negation, also called logical complement, is a unary logical connective. It is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified with the truth function that takes truth to falsity and vice versa. In intuitionistic logic, according to the Brouwer–Heyting–Kolmogorov interpretation, the negation of a proposition p is the proposition whose proofs are the refutations of p. In Kripke semantics where the semantic values of formulae are sets of possible worlds, negation is set-theoretic complementation.
Famous quotes containing the word negation:
“Michelangelo said to Pope Julius II, Self negation is noble, self-culture is beneficent, self-possession is manly, but to the truly great and inspiring soul they are poor and tame compared to self-abuse. Mr. Brown, here, in one of his latest and most graceful poems refers to it in an eloquent line which is destined to live to the end of timeNone know it but to love it, None name it but to praise.”
—Mark Twain [Samuel Langhorne Clemens] (18351910)
“I am firmly opposed to the government entering into any business the major purpose of which is competition with our citizens ... for the Federal Government deliberately to go out to build up and expand ... a power and manufacturing business is to break down the initiative and enterprise of the American people; it is the destruction of equality of opportunity amongst our people, it is the negation of the ideals upon which our civilization has been based.”
—Herbert Hoover (18741964)
“An unemployed existence is a worse negation of life than death itself.”
—José Ortega Y Gasset (18831955)