Fine on essence

I've put online a draft of a paper I'm writing for Phil Compass on the grounds of necessity. Comments on anything in it are welcome, but I'm going to post here some of the stuff I say about Kit Fine's reduction of modality to essence, since I'd especially welcome thoughts on that. So here's Fine:

"Necessity has its source in those objects which are the subject of the
underlying essentialist claim. . . We should view metaphysical necessity
as a special case of essence. . . . The metaphysically necessary truths
[are] . . .the propositions which are true in virtue of the nature of all
objects whatever."

Here are three thoughts (none intended as anything like insurmountable objections, just things to think about):

1) Prima facie, the view seems to require us to accept the existence of things like properties and relations, and thus appears to be incompatible with nominalism. For what entity can we plausibly say has a nature such as to guarantee the
truth of ‘If there are some things, there is a set of those things’ if not the
relation being a member of? No collection of actual individuals guarantees the
truth of that, because the claim says something about what happens no matter
what individuals are around.

2) If it’s necessary that there couldn’t be certain (kinds of) individuals
(universals, say, or God) then we must admit that some of the things that exist
have natures that exclude the existence of other things. You might find this
harder to accept than the claim that some things have natures that guarantee
the existence of other things. (Cf. the familiar objection to admitting
truthmakers for negative existentials: intuitively, they are true because some
things don’t exist, not because some thing does. Similarly, impossible
existents are impossible, intuitively, because there’s something about them
that’s impossible, not because, e.g., there’s something else whose essence is
such as to make them impossible.)

3) It’s easy to see how the essence of an entity e can account for the necessity of
a conditional the antecedent of which says that e exists. So my essence
grounds the truth of, hence accounts for the necessity of, ‘If Ross exists, he is
a human’. From this, it’s easy to see how unconditional necessities can be
grounded if the thing whose essence accounts for its truth has existence as part
of its essence. So were I an essential existent, my essence would account for
the necessity of the antecedent of the above conditional as well, and hence
account for the necessity of the consequent. But we might want to allow for
cases where an unconditional necessity is ‘multiply realized’ in the following
way. Suppose 2+2=4 is actually true in virtue of the essence of the numbers 2
and 4. So we account for the necessity of ‘If the numbers exist, 2+2=4’. But
it’s not just conditionally necessary that 2+2=4, ‘2+2=4’ is itself necessary.
But on this view, that’s not because the numbers exist necessarily: on this
view, while our actual world is Platonist, and mathematical truths are true
because of the numbers, structuralism is possibly true and ‘2+2=4’ is true in
virtue of the essence of certain structures, and maybe in some worlds there are
brute mathematical laws, and ‘2+2=4’ is true in virtue of these laws. So there
are multiple possible grounds for the arithmetical truth, and the truth is
necessary because it’s necessary that there is some ground or other. But what
actual things have essences such as to ground this last necessary truth? The
worry is that Fine can only account for conditional necessities or
unconditional necessities which are unconditionally necessary because there is
some essential existent that accounts for their truth in any possible circumstance.

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