Books on Amazon
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.
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.)
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.
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988
M. J. Cresswell
Structured Meanings Cambridge Mass. 1984