Correction: (max 500 charact.)
The complaint will not be published.
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).
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Double negation , >
Possible worlds .
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.)
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Indirect speech .
II 73
Problem: but then the truth value differs against the logic.
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Truth values .
Solution/Cresswell: Hyperintensionality: hyperintensional propositions express (despite the same intension of a and not-not-a) different propositions.
((s) Then intension is unequal proposition).
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Hyperintensionality .
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.
II 74f
Double Negation/Cresswell: another problem: we can add to maximum consistent sets of propositions further inconsistent propositions. - The sets are then equal with respect to the consistent propositions and differ only in the inconsistent ones.
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maximum consistent .
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.
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Impossible world .