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)
“An “unemployed” existence is a worse negation of life than death itself.”
—José Ortega Y Gasset (1883–1955)
“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 time—”None know it but to love it, None name it but to praise.””
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)