The vagueness argument against restricted compositionality

Lewis and Sider have argued that if restricted compositionality is true—some but not all pluralities of two or more objects compose a whole—then there will be cases where it's vague how many objects there are. For instance, imagine two universes, A and B, each with the same finite set of n particles with the same intrinsic properties. But in A, the particles are neatly arranged into galaxies, trees, tables, buildings, etc. And in B there is just a blooming buzzing confusion. If restricted compositionality holds, then, assuming there are no immaterial objects, universe B has exactly n or at most n+1 objects—it's just too messy to have any cases of composition, except perhaps for the universe as a whole (that's why it might be n+1 rather than n). But A is much like our universe, and so we would expect lots of cases of composition, and hence the number of objects will be a lot more than n+1, say n+m for some large m. However, we can now imagine a continuous sequence of universes ranging from A to B, differing continuously in how the particles are arranged. As we move that continuous sequence, the number of objects will have to change from no more than n+m to n+1. But it is incredible that the object count should sharply change due to a very tiny shift in particle positions. Instead, the object count will at times be vague. But how many objects there are is a matter of which sentences using universal quantification, conjunction, negation and identity are true. But quantification, conjunction, negation and identity are not vague. So we have vagueness where we cannot have vagueness.

There may be some technical problems with the argument as I formulated it, given the assumption of no immaterial objects. Maybe we can't do without immaterial entities like God or numbers. One could reformulate the argument to restrict the counting to material entities, but "material" might actually be a vague term. Perhaps the best thing to do is to assume that these universes have no immaterial contingent entities, and then just count contingent entities. Contingency shouldn't be a vague matter, after all. The Aristotelian may balk at this. For it may well be that a necessary condition for a bunch of material entities to compose a whole that they have a form, and forms are immaterial but contingent. Maybe, though, "form" is not vague, and so we can just count the contingent non-forms.

But talking of forms suggests a more serious difficulty. If there are Aristotelian forms, then how many material objects there are may well not supervene on how material objects are spatiotemporally arranged and what intrinsic properties they have. For objects to come to compose a whole, there must come into existence a form. There is nothing absurd about there being sharp laws of nature specifying under which precise conditions a form comes into existence. There is no need for the laws of nature to be continuous (and the possibility of fundamental discreteness is empirically still open). Or perhaps God decides on a case-by-case basis whether to create a form. Then there is no vagueness as to how many material objects there are: the number of material objects equals the number of forms of material objects that in fact inform some matter (the souls of the resurrected are forms of material objects but temporarily fail to inform any matter). Of course in transitional cases we won't have much confidence whether some objects compose a whole, but that's just because we are unable to see forms except through their normal effects.