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|Negation||EMD 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 - good example because no meaningless names.
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 third: then a problem in the meta language: between predicate negation and sentence negation - Standard solution for single negation in object language/meta language (+) - Problem: 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) not true that El Dorado is not-in-Venezuela (dashes) - this difference of predicate modification is not made clear in the modal logic.
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.
Sentence negation: here the functor leads from the predicate to predicate, e.g. from the universal predicate "lx (Socrates is bald)" (assuming he was bald) - to zero predicate "not[lx (Socrates is bald)])".
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 -> Definition fulfillment for sentences with "necessaary": Wiggins pro existence as necessary property -> existential generalization.
Essays on Identity and Substance Oxford 2016
G. Evans/J. McDowell
Truth and Meaning Oxford 1977
The Varieties of Reference (Clarendon Paperbacks) Oxford 1989