II 295
Inner/outer negation/Brian Medlin: E.g. paradox of movement.
Problem: to choose between the last moment of rest and the first movement (two Dedekind cuts)
1. "not moving rrr or rr (followed or led or both: of rest)
2. "it is not the case that x was moving: not rbr
3. x was moving: only bb or bbb
This is a good example because it has no meaningless names.
II 299
Inner/outer negation/Wiggins: the problem: (distinguishing between final rest/first movement) appears in a simple language elsewhere, even if one has avoided "is in motion".
Instead formula with "satisfies": "at which point did it stopped being true that "not (x moved)" even though x itself still does not move?"
No solution: intuitionistic, sentence of the excluded middle: then there is a problem in the meta language: between predicate negation and sentence negation.
>
Excluded middle.
Standard solution for single negation in object language/meta language (+) - Problem: it does not explain why it is attractive to make the difference:
a) it can be true that it is not the case, that El Dorado is located in Venezuela - and
b) it is not true that El Dorado is not-in-Venezuela (dashes).
This difference of predicate modification is not made clear in the modal logic.
>
Modal logic.
II 300
Solution: uniform functor of predicates on predicates, long and short range, both forms derivable apart.
Semantically different interpretations, to build syntactically distinguishable structures.
Predicate negation: here the functor "no" leads from the predicate to its complement.
II 301
Sentence negation: here the functor leads from the predicate to predicate, e.g. from the universal predicate
"λx (Socrates is bald)"
(assuming he was bald) to zero predicate
"not[λx (Socrates is bald)])".
II 301
Necessary/Wiggins: analog to inner/outer negation: Tradition: to blurr difference after the first method: E.g. "necessarily Socrates is a human" and "Socrates is necessarily a human".
Wiggins pro second method >
satisfaction
for sentences with "necessary": Wiggins per existence as necessary property >
existential generalization.
