In a forthcoming paper in Analysis (not yet available online) my colleague Elizabeth Barnes discusses some worries about ontic vagueness for sparse theories of properties (both theories of Universals and trope theories). One worry about sparse Universals is that issues of vague instantiation seem as relevant to them as to plentiful Universals. Another is that 'Aristotelians' about Universals (people who think Universals only exist instantiated) have some work to do if they are not to be committed to the vague existence of certain sparse Universals.
Rather than discussing the details of Elizabeth's interesting discussion, I just wanted to note an intuitive response I had to it. I often find myself tempted to believe in Universals and not to be Arisotelian about them, so I can regard Elizabeth's worries about vague existence as one more reason not to go Aristotelian. But the non-Aristotelian still faces the worry about vague instantiation. Instinctively, though, I am less worried by this that by the threat of vague existence.
But why? Vague instantiation is ontic vagueness - real vagueness out there in the world, not generated by our language - just as much as vague existence is. An initial thought is just this: I can understand (sort of) how two things, a Universal and a particular, could be vaguely related to each other, but not how one thing could exist vaguely.
A first attempt to say why is that if there is something of which it is true that it exists vaguely, then that thing exists. And we're not going to be comfortable with saying both that it exists and that it's a vague matter whether it exists or not. If vague instantiation is the worst thing we have to deal with, no similar problem arises - there is no comparable motivation to say both that some particular instantiates some Universal and that it is vague whether it instantiates it or not.
The obvious response is that the defender of vague existence is not committed to saying there is something which exists vaguely, merely that it is vague whether (to borrow Elizabeth's example) an Einsteinium Universal exists. As Katherine Hawley puts it in this paper, a 'modest' commitment to vague existence is a commitment to this claim:
it is indeterminate whether anything is F (for some F), this is not as a result of semantic indecision, and yet nothing is such that it is indeterminate whether it is F.
But I'm still uneasy. As good Quineans, anything that we quantify over is something that we should be happy to say exists. Therefore, you might think, no Einsteinium Universal can be among the range of our quantifiers, since we are not happy to say that an Einsteinium Universal exists (that would be in tension with the claim that it is indeterminate whether an Einsteinium Universal exists). But if no Einsteinium Universal is among the range of our quantifiers, we can truly say that nothing is an Einsteinium Universal. And that looks very much like a claim that no Einsteinium Universal exists, which is again in tension with the claim that it is indeterminate whether an Einsteinium Universal exists.
Maybe there is room to try and block this argument by claiming that it's indeterminate whether an Einsteinium Universal is among the range of our quantifiers. After all, our quantifiers range over everything that exists, and it's indeterminate whether an Einsteinium Universal exists.
But if our quantifying over something goes along with it's being the case that we should be happy to say that that thing exists, this proposal ought to give the result that it is indeterminate whether or not we should be happy to say that an Einsteinium Universal exists. Yet the defender of ontic vagueness will actually be unhappy about saying this, and will presumably think she is right to take that attitude, since saying this would amount to taking a stand where the world itself does not.
Putting the point another way, if it's a vague matter whether we're quantifying over an Einsteinium Universal, it's a vague matter whether we're committed to one or not. But the defender of ontic vagueness would surely deny that she is committed to the existence of an Einsteinium Universal (I am assuming that the view is meant to be neutral as to whether an Einsteinium Universal exists or not - i.e. not committed either way). And this sits uncomfortably with the thought that it's a vague matter whether she is or isn't so committed.
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Not that I have much truck for either Quineanism or vague existence, but I think there's a way out of this difficulty. You're worried about whether the Quinean can say that 'it's a vague matter whether we're committed to one or not'. But clearly the Quinean *can* say that it's a vague matter whether we *should* be committed to one or not, and that's all they need. As I understand the Quineans, they think that what exists isn't what our current theory commits us to, but what our best theory commits us to. So Quineans who admit that we don't have the best theory yet can say that we aren't committed to some vaguely existing objects, because what's vague is whether the best theory commits us to them, not whether current theory so commits us.
Further related point: perhaps Quineans can say that vague existence stems from vagueness in 'best theory'. So maybe ontic vagueness can still be linguistic rather than worldly.
If their existence is vague, surely the best theory is one which says their existence is vague, and therefore one which isn't committed to them?
On the further point - my idea was just to explore worldly vagueness (for now!).
Ok, and if the best theory says their existence is vague then it quantifies over them, and so is (vaguely?) committed to them after all. And that was your point.
So I suppose my first point does rely on my further point: Quineans can accept ontic vagueness iff they deny that it's worldly.
"if the best theory says their existence is vague then it quantifies over them, and so is (vaguely?) committed to them after all. And that was your point."
That's not quite how I was seeing it - my point was that if the best theory says their existence is vague then it isn't committed to them, but since the theory is committed to them iff they are among the range of the theory's quantifiers, this means they are not among the range of the theory's quantifiers. So the best theory can truly say that nothing is one of them. But that's weird, given that the theory was supposed to be saying that it's vague whether or not they exist ...
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