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Negation in natural languages is very different from, and much more complicated than, negation in logic or mathematics. In many languages, for instance, it is not true that two negations correspond to a positive value according to the well-known formula —i—|P = P . Even in Latin, where non nullus ('not nobody') means—according to Classical texts— 'somebody,' it is possible to find two negative terms preserving a negative value: iura te non nociturum esse homini...nemini (Plautus) 'swear that you will not harm anybody'; cf. Cockney and Black English I don't see nothin' nowhere (for a not perfect correspondence between logical and linguistic negation see also Sect. 2 below).
Consider first the declarative negation which refers to a real state of affairs as in example (1). This declara- tive negation has to be distinguished from the pro- hibitive (e.g., 'Do not lean out') which does not refer to a real state of affairs and, on the contrary, is used in order to prevent the realization of a state of affairs (see Sect. 7).
The linguistic operation of negation (NEG) consists in denying the truth value of the negated sentence, or of a part of the sentence, by applying a NEGoperator (TTNEG) to a sentence like:
John likes to work gives John does not like to work, (la) i.e., [it is not true that [John likes to work]];
John does not like beer at lunch (Ib) i.e., [John does like beer, [JINEGADVSATELLITEat lunch]].
Negative sentences are most frequently used to cor- rect states of affairs assumed by the speaker to be
either shared knowledge or to represent the com- monest ones to be expected in the context. The post hasn't been delivered this morning' is a felicitous mess- age only under the assumption, shared by speaker and hearer, that the post has to be delivered every day. This is the reason why negative sentences are not normally used to introduce new propositions or new referents. The sentence 'A train didn't arrive yester- day,' extrapolated from a situational context which makes a sense possible, is deemed to be rather odd; not so its affirmative counterpart 'A train arrived yes- terday.' Another example is *When didn't a/the train arrive?—it does not make sense to ask when an event didn't happen.
The content resulting from a negated sentence can be either negative or positive: / know -*Ido not know; I ignore -* / do not ignore.
There are no known languages which do not possess a means for negating the truth value of a positive sentence. NEG is a linguistic universal: for cognitive and pragmatic reasons every language must have the possibility of asserting that the state of affairs ex- pressed by a sentence is not true.
1. The 'Scope' of NEC: Sentence versus Phrase Negation
By adducing examples (la) and (Ib), the notion of 'scope' has already been introduced implicitly. The widest 'scope' of NEG(i.e., its sphere or domain of operation) is the sentence (S), but NEG may apply also to sentence subunities, that is, to syntagms (noun phrases, prepositional phrases) or even lexemes:
Negation P. Ramat
Negation
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