Philosophy Lexicon of Arguments

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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II 73
Double Negation/possible worlds/Proposition/indirect speech/Cresswell: Solution: if propositions are nothing but sets of possible worlds - then not-not-a means the same as a - (because of the complement formation of the set). - indirect speech: problem: if propositions should be something else than sets of possible worlds: then it may be that the speaker has said nothing at all - then the double negation is something else. ((s) "He has not said anything to this" does not mean that he rejects a.
II 73
Problem: but then the truth value differs against the logic. - Solution/Cresswell: Hyperintensionality: hyperintensional propositions express (despite the same intension of a and not-not-a) different propositions. - ((s) Intension unequal Proposition) - Solution/Cresswell: Structural ambiguity: "saying" is sometimes applied to whole sentence, sometimes to parts. - VsHyperintensionality: before, the meaning of "not" was clear, it is now unclear. - ((s) Hyperintensionality/(s): should be a solution, not the problem.)
II 74f
Double Negation/Cresswell: another problem: we can add to maximum inconsistent sets of propositions further inconsistent propositions - the sets are then equal with respect to the consistent propositions and differ only in the inconsistent ones. - N.B.: if there are only possible worlds (no impossible world), a and ~~a are equal. Impossible world: if they are admitted, there is a difference between position and double negation - that is because "~" is then no real negation.

Cr I
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988

M. J. Cresswell
Structured Meanings Cambridge Mass. 1984

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Ed. Martin Schulz, access date 2017-05-28