Merricks on universalism and composition as identity

My earlier request for comments on my revised version of my Phil Studies paper 'The Contingency of Composition' recevied a grand total of no results, so I'm going to post the argument I particularly wanted reactions on and see if that provokes any response. If it doesn't, I will take this as tacit consent from the entire philosophical community that I am right!

In the paper I claim that composition as identity is compatible with restricted composition. What I would like comments on is my response to Merricks' argument to the contrary. Merricks has us assume, for reductio, that composition as identity is true and that mereological universalism is false. From the latter assumption, there are some things, the Xs, that don't compose. But, says Merricks, they could compose. So there is a world, w, in which there is something that is composed of the Xs, call it A. Composition as identity, if true, is necessarily true, so A is identical to the Xs in w. Hence, from the necessity of identity, A is identical to the Xs in the actual world (@). And so, from composition as identity, the Xs actually compose in @, contrary to the initial assumption.

Now, I'm not sold on the necessity of identity at the best of times, but I think it's particularly problematic here. There are two ways in which we might try and use the Barcan/Kripke argument for the necessity of identity to show that if A is identical to the Xs in w then it is identical to the Xs in @. Firstly, we might argue as follows:

A is necessarily self-identical in w. So in w, A has the property being necessarily identical to A. So, since A is identical to the Xs in w, the Xs has the property being necessarily identical to A. Hence, in the actual world, the Xs has the property being identical to A. Hence, A is identical to the Xs in the actual world, and hence the Xs compose A in the actual world, contrary to the hypothesis that there is nothing that the Xs actually compose.

This argument doesn’t work, however. A familiar complication with the Barcan/Kripke argument is that we must bear in mind is that we are dealing with contingent existents. If A is not a necessary existent then it is not self-identical in every world; all we can say is that it is self-identical in every world in which it exists: that is, that is has the property necessarily, being identical to A, if A exists. So all we can say about the Xs in w is that it has this property; and so all we can conclude is that in the actual world the Xs has the property being identical to A, if A exists. But, of course, proving that the Xs has this property in the actual world doesn’t tell us anything about whether or not the Xs actually compose. All we can conclude is that they actually compose if A actually exists – but, of course, whether or not A exists is precisely what is up for debate.

The argument only has a hope at succeeding if we start not from the necessary self-identity of A but from the necessary self-identity of the Xs. In that case the contingent existence of the Xs is not a problem. We can argue as follows. In w, the Xs is necessarily self-identical, by which we mean that the Xs is self-identical in every world in which the Xs exist. Hence, the Xs has the property necessarily, being identical to the Xs, if the Xs exist. Hence, given Leibniz’s law, A has the property necessarily, being identical to the Xs, if the Xs exist in w, and therefore has the property being identical to the Xs, if the Xs exist in the actual world. Since we know, ex hypothesi, that the Xs exist in the actual world, we can conclude that A is actually identical to the Xs, from which it follows, given composition as identity, that the Xs actually compose A, contrary to the hypothesis that they don’t actually compose anything.

But while there is no problem in this version of the argument due to the contingent existence of the entities involved, there is a further problem that faces this version and not the earlier version. The problem is that, while I am happy to grant the assumption that A is necessarily self-identical in w, I am not happy to grant the assumption that the Xs are necessarily self-identical in w.

My claim is that it only makes sense to ascribe a property like being self-identical to a plurality of things if there is some thing that the plurality is identical to; i.e. if there is a one that the many are identical to. (We can say that each of the Xs is necessarily self-identical, but that won't help: we need the strong claim that the many are self-identical, and that only seems to make sense if there is a one that the many are identical to.) One can only infer that the Xs have the property of being self-identical at a world if we know that the Xs are identical to some thing at that world – i.e. if we know that they compose at that world (since, we are assuming for the sake of argument, what it is for a collection to compose is for them to be identical to some thing). So one cannot simply assume that the Xs are necessarily self-identical; to make this claim we would need to have a reason for thinking that they are necessarily identical to some thing or other. But that is simply the claim that they necessarily compose, which just begs the question. My contention – the claim Merricks is attempting to argue against – is precisely that the Xs compose in w but not the actual world: that there is some thing in w that they are identical to but that there is no thing in the actual world that they are identical to. In that case I deny that the Xs has the property being necessarily self-identical in w. All that we can say is that in w the Xs has the property being identical to the Xs, if identical to anything as a matter of necessity; but all that will prove is that A actually has the property of being identical to the Xs if identical to anything. And as before, that won’t tell us anything at all about whether A is composed of the Xs in the actual world, since whether or not A is identical to anything at the actual world depends on whether or not A actually exists, which is what is up for dispute.

So I don’t think there is any version of the Barcan/Kripke argument that can prove that A is actually identical to the Xs because A is identical to the Xs in w. We cannot start from the premise that the Xs is necessarily self-identical in w: that begs the question, because it assumes that there is necessarily a one that the Xs is identical to, which is just to assume that they necessarily compose. There is only something which is identical to the Xs if the Xs compose; so, since I take it to be contingent that the Xs compose, I also take it to be contingent that there is some thing that is identical to them, and hence I reject the first premise of the argument that they are necessarily identical to A. If Merricks appeals (on the assumption of composition as identity) to the necessity of the self-identity of the Xs in order to show that the Xs must actually compose then he assumes, I argue, that the Xs necessarily compose; and that is simply to beg the question against me. We can start from the assumption that A is necessarily self-identical – that is unproblematic provided we are careful to mean by this only that A is self-identical in every world in which it exists: but while the resulting argument has true premises, the conclusion is far from what Merricks wants – we cannot conclude that A is actually identical to the Xs, only that A is actually identical to the Xs if it (A) exists. Since the existence of A at the actual world is precisely the issue of disagreement between Merricks and myself, this argument obviously isn’t going to persuade me.