Today I gave a brief consideration that could be turned into an argument against the following thesis from Divers (which Divers was just presenting, not defending):
(1) x is essentially F iff for all metaphysically possible worlds w, if x exists in w then x is F in w.
Here is a case (this is from Kit Fine's "Essence and Modality"): the essential properties of an object, in the Aristotelian sense, stem from the nature or identity of that object. Intuitively, it is no part of the nature of Sparky that he is a member of a set. But if he exists at w, then he is a member of a set at w. So by (1), being a member of a set is an essential feature of Sparky. So (1) is false. (I hope it's obvious how to make this argument valid.)
If this is right, then the right-to-left direction of (1) fails, but (2) may still be plausible:
(2) If x is essentially F, then for all metaphysically possible worlds w, x is F in w.
Carl suggested that Ben rejects (1) because of the "existence restriction" in the right-hand side. I take it that Ben instead endorses (3) (?):
(3) x is essentially F iff for all metaphysically possible worlds w, x is F in w.
(I assume Ben holds that objects can have properties at worlds where they are absent? (Homework: State the assumption I am attributing to Ben in a way that does not imply the truth of that assumption.))
So if one accepted both Fine's argument and Ben's point, the (partial) account would be (4):
(4) If x is essentally F, then for all metaphysically possible worlds w, x is F in w.
Joe Salerno at Knowability argues here that there are contingent essential properties. So his view is that (5) is correct:
(5) x is essentially F iff if nothing were F, then x would not exist.
This account has several interesting features. One of them is that the right-hand-side counterfactual conditional is, on his view, not vacuously true if the antecedent is impossible. Any thoughts on which, if any of these accounts, is correct, or on what, if anything, can be added to (2) or (4) to yield a more complete account?