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|Possible World Semantics||II 41
Property/Denotation/possible world/poss.w./Possible World Semantics/Field: E.g. "Russell is bald" is true in every world w where Russell exists (denoted by "Russell" in the actual world) and where Russell is bald (i.e. has the property for which "bald" stands in the actual world). - N.B.: "stand for": we must now understand it like this: a predicate does not stand for a set (its extension), but for a property that exists in the actual world. - Problem: relation between predicates and properties. - Problem: Properties determine extensions of the predicates, but are not determined by them - solution: within the possible world semantics: causal theory of the reference. - Problem: we are not coming into contact with all extensions of "bald" solution: property instead of extension - or the extension is determined by a property. - Then what is associated with the predicate is not its extension, but a property. - The relation can be causal or non-causal.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980