While we disagree on some of the details, both Robbie and I agree one can admit that there are complex objects without, in some sense, being ontologically committed to complex objects: there need be no complex objects in fundamental ontology.
What complex objects exist derivatively then? Well, if they’re not really extra elements of our ontology we might think we should just go ahead and say that the claims of universalism come out true: that for any collection of objects, there is (derivatively) a sum of those objects. That, I think, is Armstrong’s view: complex objects are an ontological free lunch, so we might as well be universalists.
But we’re certainly not forced into saying that. Just as we are concerned with reconciling a nihilistic ontology with the truth of everyday judgements concerning the existence of tables and persons, etc, we might also be concerned with not going too far – that is, preserving the everyday judgements concerning the non-existence of the sum of Hitler’s left ear, an atom in the sun, and the number 2. So we might tell a story whereby our fundamental, atomistic, ontology accounts for the truth of some theory of restricted composition.
Indeed, it seems that we can avoid one of the main objections to restricted composition: namely, the Sider-Lewis objection from vagueness. If composition is restricted, they say, it must be either brute or vague. If it’s brute, that’s metaphysically arbitrary in an objectionable way. But if it’s vague then this must be ontic vagueness, since there’s no vagueness in the language of quantificational theory, and that’s no good because ontic vagueness is A Bad Thing.
There’s plenty to say about that argument as applied against run-of-the-mill restricted composition theorists, of course, (Is brutality really all that bad? Is ontic vagueness?), but even if you think the argument is good there, it seems to have no weight at all against the kind of restricted composition you would get on the Robbie/Ross route.
Suppose we go organicist. A complex object only (derivatively) exists if the simples that account for its existence jointly and exhaustively participate in some life. There will be cases where it is vague whether we have a complex object. Is this objectionable? It seems not – even on the assumption that there cannot be ontic vagueness. Because what there really is is (we may suppose) perfectly precise. It’s just vague whether some collections of the fundamental existents account for the existence of a complex object. In my terminology, it will be vague whether they make true any existence claims concerning complex objects. Ontic vagueness only looks worrying, if it ever does, if it infects fundamental ontology: the derivative can be as indeterminate as you like. (C.f. Elizabeth’s ‘Ontic vagueness without supervenience’.)
(Maybe this gives us an argument for priority monism: the view (defended by Jonathan Schaffer) that the one big whole is what’s fundamental, and the parts derivative on it. Quantum mechanics tells us (my esteemed colleagues tell me!) that the very smallest things are indeterminate. Maybe that gives us reason to deny that they’re fundamental and instead accept that the quantum particles are derivative on the fundamental whole.)
If that’s right, it seems to apply to other cases as well. I’m thinking in particular of dialetheism. Many people find objectionable the idea that both a proposition and its negation can be true. I share the suspicion if the proposition concerns how fundamental ontology is; but it doesn’t seem objectionable to me if fundamental reality is consistent, but the consistent way fundamental reality is results in an inconsistent derivative reality.
Think of the particular cases of true contradictions dialetheists are fond of. The Liar sentence – L – springs to mind. L is both true and false! But who cares? Sentences are not, we might think, part of fundamental ontology. What’s fundamental is, on my view, just the truthmakers. So what would be objectionable is if, say, the truthmaker for L both existed and didn’t exist, for then fundamental reality would be inconsistent. But the dialetheist is not committed to anything like this. We could easily tell a story whereby fundamental reality (for me, the truthmakers) is consistent and makes true both L and its negation. And this just doesn’t seem objectionable to me. Why should I care about some sentence being both true and false? Why should I care, even, if some thing both does and doesn’t exist – provided the sense in which it exists is mere derivative existence? All that seems bad to me is if there is inconsistency at the fundamental level; if our best theory tells us that this consistent fundamental reality accounts for true inconsistencies, so be it.
 See Ned Markosian’s ‘Brutal Composition’, Daniel Nolan’s ‘Vagueness, Multiplicity and Parts’ and my ‘The Contingency of Composition’.