In my Contingency of Composition paper, I deny the commonly held claim that composition as identity (CAI) entails universalism about composition. (The entailment is defended by Sider, Merricks, et al.) My basic thought was: CAI says just that a complex object is identical to its parts – that tells us only that when you’ve got a complex object, it is identical to its parts, and this is silent about whether or not for any collection of objects there is such a complex object that they are identical to. If many-one identity makes sense then, prima facie, it makes sense to claim that for some collections of objects there’s a one that they are identical to, and some collections of objects such that there’s no one object that they are identical to. All CAI tells us is that it’s all and only the first collections that compose. To assume that every collection composes is just to assume that for any collection of objects, there’s a one to which they are identical. Why would I accept that if I doubted universalism?
In denying the entailment, I need to respond to an argument that both Sider and Merricks give for it. They argue as follows: Suppose (for reductio) the Xs don’t compose. They could do. Go to the world where they do (w). In w, there’s a one, A, that’s identical to the Xs. Given the necessity of identity, A is actually identical to the Xs. So the Xs actually compose A. Contradiction. Formally:
2) ◊(Xs=A) -> □(Xs=A)
In my paper I attempted to resist this argument with some pretty tricky moves – and while I still think they’re right, I think I haven’t exactly convinced the world! (See the earlier discussion on this blog) But I think I can actually make the point more simply than I did then.
The argument aims to prove that the Xs are actually identical to A. Thus, there is a one that the Xs are identical to: A. So since to compose is to be identical to a one, the Xs compose. But wait! All the argument shows is that it’s actually true that the Xs are A. Where do we get the claim that there’s a one that the Xs are identical to? This follows, obviously, if A is actually a one. But where does that claim come from? All we know is that A is possibly a one. Ex hypothesi A is a one in the world in which the Xs compose. But we can only conclude that A is actually a one – and hence that there’s a one that the Xs are actually identical to – if we have the assumption that anything that is possibly a one is necessarily a one. But what right do we have to make that assumption? If we’re leaving open the possibility that there’s a many that’s not a one but could be (and at this stage we must, lest we beg the question), we should also leave open the possibility that there’s a many that is a one but might not be. Since the many is the one, this is a one that might not be a one: a one that is a many, but that might have been a mere many – a many that is identical to no one. If the Xs don’t actually compose this is the status we should think A has in the world in which they do compose. So sure A is actually identical to the Xs: but A is actually just a name for the plurality, a plurality that don’t actually compose. A is only a one in the worlds in which that many do compose. And we’ve been given no reason to think we’re forced into thinking that our world is one of those.