Thursday, October 26, 2006

only existent boys&girls get presents

Priest presents a symantics in which non-existent objects can satisfy predicates in the same manner as existent objects. Thus Homer can worship Zeus even if Zeus doesn't exist, because there's nothing wrong with the two satisfying the intentional predicate Whz. However, Priest adds that most normal predicates are existence entailing, that is, only existent objects can satisfy the predicate. In footnote 6 on page 59 he states: "Consider the predicates 'x is transparent' and 'x is opaque'. These are both existence entailing. Hence, if x does not exist, 'x is transparent' and 'x is opaque' are both false"
This is an intuitive notion. After all, how can non-existent things have these properties? If we were able to actually assert things like "vampires are blood-drinkers" than we'd all have reason to fear vampires.
This view also poses a few problems. Statements like "Zeus is strong", "Zeus is bigger than Homer" etc. all come out false. Essentially, Homer is worshipping an entity that has no properties. This doesn't seem quite right either. For instance, is it correct to say that Thor has no hammer?
The easy answer would be yes. Zeus and Thor don't exist, so they are not strong and neither has a hammer. They are non-entities, but they remain distinct and retain meaning because they satisfy different intentional predicates. Thus, it is false to say that Thor has a hammer, but it is true to say in the scope of an intentional operator "We imagine Thor to have a hammer", or in the scope of an intentional predicate "I like the hammer that belongs to Thor" (3 place predicate). Thus Thor and Zeus are non-entities, but they do have distinct identities. Like the comic on the blog says: "Mind you, I don't mean just plain nothing. Not nothing nothing. But nothing as something.".
While this would work, it would be symantically annoying to spell out. We couldn't speak of nonexistent entities as having properties, we could only speak of them as being concieved as having certain properties. I suggest a simplification to the symatics. Instead of a predicate being existence entailing, let it be existence restrictive. This would mean, for these predicates, they must be satisfied by either all existing objects, or all non-existent objects. So if Kxy = x kicked y then it would be fine to say something like "Zeus kicked Hades" since neither Zeus nor Hades exists. However, you can't say "Zeus kicked Priest" since Priest exists, and Zeus does not. This would allow a more intuitive expression of sentences involving fiction and mythology and such. "Harry Potter found the philosopher's stone" would not need to be (as it shouldn't need to be) converted into an intentional context to be understood.


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