Negation
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.
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Famous quotes containing the word negation:
“We make a mistake forsaking England and moving out into the periphery of life. After all, Taormina, Ceylon, Africa, America—as far as we go, they are only the negation of what we ourselves stand for and are: and we’re rather like Jonahs running away from the place we belong.”
—D.H. (David Herbert)
“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 (1874–1964)
“An “unemployed” existence is a worse negation of life than death itself.”
—José Ortega Y Gasset (1883–1955)