Negation

Negation, in its most basic sense, changes the truth value of a statement to its opposite. It is an operation needed chiefly in logic, mathematics, and grammar. __TOC__ == Logic and mathematics == In logic, logical negation is a unary operator logical operator that reverses the truth value of its operand. The negation of the statement ''p'' is written in various ways: * ''p'' (which is ''p'' with a bar over it) * ~''p'' * ¬''p'' * NOT ''p'' * !''p'' It is read as "It is not the case that ''p''", or simply "not ''p''". ~''p'' is true iff ''p'' is false. For instance, if ''p'' denotes the statement "today is Saturday", then its negation ~''p'' is the statement "today is not Saturday". In classical logic, double negation means affirmation; i.e., the statements ''p'' and ~(~''p'') are logical equivalence. In intuitionistic logic, however, ~~''p'' is a weaker statement than ''p''. Nevertheless, ~~~''p'' and ~''p'' are logically equivalent. Logical negation can be defined in terms of other logical operations. For example, ~''p'' can be defined as ''p'' → ''F'', where → is material implication and ''F'' is absolute falsehood. Conversely, one can define ''F'' as ''p'' & ~''p'' for any proposition ''p'', where & is logical conjunction. The idea here is that any contradiction is false. While these ideas work in both classical and intuitionistic logic, they don't work in Brazilian logic, where contradictions are not necessarily false. But in classical logic, we get a further identity: ''p'' → ''q'' can be defined as ~''p'' ∨ ''q'', where ∨ is logical disjunction. Algebraically, logical negation corresponds to the ''complement'' in a Boolean algebra (for classical logic) or a Heyting algebra (for intuitionistic logic). == Grammar == In grammar, negation is the process that turns an affirmative statement (''I Am the Walrus'') into its opposite denial (''I am not the walrus''). Nouns as well as verbs can be grammatically negated, by the use of a negative adjective (''There is no walrus''), a negative pronoun (''Nobody is the walrus''), or a negative adverb (''I never was the walrus''). In English language, negation for most verbs other than ''Copula'' and ''have'', or verb phrases in which ''be'', ''have'' or ''do'' already occur, requires the recasting of the sentence using the dummy auxiliary verb ''do'', which adds little to the meaning of the negative phrase, but serves as a place to attach the negative particles ''not'', or its contracted form ''-n't'', to: * ''I have a walrus.'' * ''I haven't a walrus.'' (rare, but it is still possible to negate ''have'' without the auxiliary ''do''.) * ''I don't have a walrus.'' (the most common way in contemporary English.) In Middle English, the particle ''not'' could be attached to any verb: * ''I see not the walrus.'' In Modern English, these forms fell out of use, and the use of an auxiliary such as ''do'' or ''be'' is obligatory in most cases: * ''I do not see the walrus.'' * ''I am not seeing the walrus.'' * ''I have not seen the walrus.'' Curiously, the verb ''do'' requires a second instance of itself in order to be marked for negation: * ''The walrus doesn't do tricks'' : not * ''The walrus doesn't tricks.'' In English, as in most other Germanic languages, the use of double negatives as grammatical intensifiers was formerly in frequent use: * ''We don't have no walruses here.'' Prescription and description consider this use of double negatives to be a solecism, and condemn it. It makes the rhetorical figure of litotes ambiguous. It remains common in colloquial English. Other languages have simpler forms of negation; in Latin, simple negation is a matter of adding the negative particles ''non'' or ''ne'' to the verb. In French language, the most basic form of verb negation involves adding the circumflexion ''ne ... pas'' to the main verb or its auxiliary; ''je veux un morse'' ("I want a walrus"); ''je ne veux pas un morse'' ("I do not want a walrus.") Philologically, from the Latin non: no, not indeed, a categoric negative root concept found in languages, even if in different forms. "Not that I know of", expressive of categoric negative assertion, egotistic, defensive, cognitive. Also a negative prefix to concepts, especially as expressed in L. nihil, Eng. emphatic no, definitively not. L. nemo is person oriented, and opposite to L. nihil and means no man, nobody. ne hemo (old form) = no man (homo). Nihil, no+thing, nothing is thing oriented, opposite to nemo. L. nullus means no, not, none (of all those or anything involved). ne ullus = not any one, where unulus is the diminutive of unus, one. Both person and thing oriented, where emphasis is on insignificance. None has ever been so - emphatic, person oriented expression, emphasis being here also denoted by ever (L. aevum, Gr. aion}which here really means: No (one + ever) has been. Logic Grammar th:นิเสธ

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Words begining with Negation:

Negation
Negationism
Negationism
Negation_(comics)
Negation_normal_form