I've just finished reading a very interesting paper on metaphysical dependence (the kind of fact-fact relation that philosophers often use 'in virtue of' to express) by Gideon Rosen, which he presented at the last Arche modality workshop. I won't comment on the contents of the paper as it's a work in progress, but I did want to post some thoughts about a question I was inspired to think about by reading it.
The question is: can it happen that a single fact P obtains wholly in virtue of one fact Q and also wholly in virtue of a distinct fact R? I'm not particularly wedded to any answer to this question, but here are some prima facie reasons for answering 'yes'. The fact that my poppies are red obtains in virtue of the fact that they are scarlet. (Actually all my poppies are disappointingly pink this year - but let's pretend they're not.) And the fact that these poppies are red obtains in virtue of their surfaces being microphysically structured in such a way as to look red under normal conditions. A little more controversially, the fact that Jeff has decided to go somewhere sunny for his holiday obtains in virtue of the fact that he has decided to go to Spain for his holiday, and it also obtains in virtue of the fact that Jeff's brain is (or has been) in a state constitutive of his having decided to go somewhere sunny for his holiday.
But one could try to resist this by saying that in these cases the 'two facts' mentioned are really the same fact. On the face of it, that seems crazy: a poppy's being microphysically structured in such a way as to look red under normal conditions doesn't even entail that it is scarlet. So how can these two facts be the same? One response might be to argue that there is no real (worldly) fact corresponding to anything as general as the 'fact' of the poppy's being scarlet or that of its being microphysically structured in such a way as to look red under normal conditions; to argue, that is, that the only real facts are very detailed facts about the poppy's particular microphysical structure. We could then say that the two sentences cited when saying what it is in virtue of which the poppy is red are (regardless of what we happen to think about the matter - and regardless of how much we know about the worldly - i.e. particular - facts) just two ways of picking out the same particular fact or facts about the poppy.
An objection to this view is that it makes 'in virtue of' relations into relations of fact-identity (or perhaps at best fact-inclusion). For presumably the worldly fact(s) corresponding to my poppy's being red are the same as those corresponding to its being scarlet and its surface having a certain microphysical structure. But I can imagine this bullet being bitten; maybe IVO claims really are made true by relations of fact-identity or fact-inclusion. Maybe they are interesting, non-trivial and assymmetric only for epistemic reasons, having to do with the ways the facts are picked out. This line has its advantages if you are inclined to think that worldly metaphysical grounding is a weird sort of notion that we are well shot of.
A less radical way of taking this kind of approach, however, would be to argue that although the less particular facts are also 'real', they are not the sorts of things that facts can obtain 'in virtue of'; only the very particular facts can play the metaphysical grounding role. When we appear to cite a less particular fact as the metaphysical ground of some other fact, we are actually just gesturing towards the kind of real (particular) fact that is doing the work.
There are problem cases for either version of this sort of strategy, however. It seems that my mother is a parent in virtue of having given birth to me, and she is also a parent in virtue of having given birth to each of my brothers. But however particular you take them to be, these facts are surely not the same fact.
In response to this kind of point, perhaps we might deny that she is a parent wholly in virtue of having given birth to me. Although she could have been a parent wholly in virtue of having given birth to just one of us, and indeed was so at one point, maybe we just need to be careful not to confuse that claim with any claim about the actual metaphysical ground of the present tense fact that she is a parent.
One way to motivate that line could be to argue, in sympathy with the more radical of the two options considered above, that, as things currently stand, the sentence 'My mother is a parent' must pick out a bunch of particular worldly facts which involve (the microphysical parts of) me and all my brothers, and so could not obtain wholly in virtue of her having given birth to me. It must pick out this bunch of facts, we might think, because there's no unspecific wordly fact (her being a parent) that it could pick out, because unspecific facts aren't 'real', and to say it picks out specific facts about (the microphysical parts of) her and only one of her children seems to be privileging that child in an unprincipled way. (And we don't want to encourage sibling rivalry.)
However, we don't need to say anything as strong as this in order to appreciate that there is some intuitive motivation for the claim that my mother's being a parent does not obtain wholly in virtue of the fact that she has given birth to me (or to just one of my brothers). Or so it seems to me.