|Negation, philosophy, logic: negation of a sentence. In logic, this is done by prefixing the negation symbol. Colloquially expressed by the word "not", which can be at different positions in the sentence. If the negation refers only to one sentence part, this must be made clear by the position, e.g. a predicate can be denied without negating the whole sentence. In logic, therefore, inner and outer negation is distinguished by the use of different symbols.|
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double negation: "not-(not-q)" is weaker than "q" - it is the same as "may" ("might") - not the same as "would".
Philosophical Explanations Oxford 1981
The Nature of Rationality 1994