I don’t think I have a lot of way-outside-the-mainstream philosophical beliefs; in fact I think I have considerably fewer of them than I’d like. Probably the most extreme of my positions is that I believe in modal parts.

The idea behind the doctrine of modal parts is that for any object o and class of worlds W such that o exists in every member of W, o has a part o’ that exists in every world in W and in no world outside of it. (The obvious analogy is to temporal parts. This analogy will get pressed a lot as we continue.) This isn’t quite a strong enough position, because this makes it sound as if actualism implies modal parts, and modal parts is meant to be a much more outrageous position. The trick, as with getting temporal parts and presentism to sing in harmony, is to restate the doctrine using operators, or something like them. Here’s what I take the position to be.

For any class of worlds W, let p_W be a proposition that is true at all and only the worlds in W. The doctrine is that for any object o and class of worlds W such that Necessarily, if p_W then o exists, o has a part o’ such that Necessarily, o’ exists iff p_W.

If modal realism is true, this is equivalent to the earlier statement of the doctrine of modal parts. However, even if modal realism is not true, this doctrine makes a striking claim about the existence of objects that are ‘world-bound’ relative to whatever our actualist takes worlds to be.

Given that I hold such a view, one might wonder what my arguments for it are. I was wondering just that this morning, and it seemed the arguments for it probably aren’t as bad as orthodoxy would have you think, but probably aren’t as good as I’d like.

The motivation for believing in modal parts is a generalised suspicion of extended simples. But suspicion is not an argument.

One real argument would be the problem of contingent intrinsics. In Plurality that’s Lewis’s main argument for (something like) the doctrine of modal parts. Stephen Yablo has argued that this argument won’t extend to objects that don’t vary in intrinsic property between worlds in W. In general I’ve never been strongly moved by arguments for parthood from intrinsicness, so I don’t want to rest too much weight on this.

Other arguments come from analogy with arguments for temporal parts. Since Ted Sider has collected so many of those in Four-Dimensionalism, I should just try stealing the best. (Ah, the advantages of theft over honest toil.)

One nice use for modal parts, I think probably the best use, is in resolving some of the paradoxes about coincidence and constitution. I think the modal partser has by far the best story to tell here. On the one hand, she can say that the statue and the lump are distinct fusions of modal parts, and hence respect the argument from Leibniz’s Law that they are not identical. On the other, she can say that there’s a good sense in which there is only one object here, because they both exist in virtue of having a common modal part. I’ve never seen another story about the paradoxes that gets nearly as close to capturing ordinary intuitions as the modal parts story.

Ted’s main argument for temporal parts, the argument from vagueness, also extends across. (The following sketch is incomplete at every step. I’ll try one day to write it up properly and see how the arguments carry across.) Assume that the doctrine of modal parts is not generally true. Still, it seems that for some o, W there will be an o’ such that Necessarily, o’ exists iff p_W. Any principle about when such an o’ exists (other than the no parts claim that o’ exists iff o’=o and W is the class of worlds at which o exists) will be vague. But that will imply that it is vague how many things there are, which is intolerable. So we should be ‘universalists’ about modal parts – for any o and W in which o exists, o has a part o’ in W only.

One class of arguments for temporal parts, however, does not carry across: the arguments from time travel. I assume that genuine travel between worlds is a conceptual impossibility, even for a modal realist. So we can’t argue that the possibility of modal travel requires modal parts, and modal travel is possible, so modal parts exist, because premise 2 is false. This is a disanalogy with the argument for temporal parts, and perhaps a fatal one.

I suspect the vagueness argument will turn out to have holes in it when the details are spelled out. I worry that the nihilist position may turn out to be quite plausible. And I worry that there will be no way to argue from the vagueness of an intermediate view to any vagueness in how many things there are. So the arguments from constitution may have to do all the work. I think they probably can, but it’s not the strongest foundation for a metaphysical theory.